{"id":101,"date":"2020-08-21T19:42:56","date_gmt":"2020-08-21T23:42:56","guid":{"rendered":"https:\/\/opentextbc.ca\/introalgebra\/chapter\/use-the-language-of-algebra\/"},"modified":"2021-03-24T10:51:35","modified_gmt":"2021-03-24T14:51:35","slug":"use-the-language-of-algebra","status":"publish","type":"chapter","link":"https:\/\/opentextbc.ca\/introalgebra\/chapter\/use-the-language-of-algebra\/","title":{"raw":"1.2 Use the Language of Algebra","rendered":"1.2 Use the Language of Algebra"},"content":{"raw":"[latexpage]\n<div class=\"textbox textbox--learning-objectives\"><header class=\"textbox__header\">\n<p class=\"textbox__title\">Learning Objectives<\/p>\n\n<\/header>\n<div class=\"textbox__content\">\n\nBy the end of this section, you will be able to:\n<ul>\n \t<li>Use variables and algebraic symbols<\/li>\n \t<li>Identify expressions and equations<\/li>\n \t<li>Simplify expressions with exponents<\/li>\n \t<li>Simplify expressions using the order of operations<\/li>\n<\/ul>\n<\/div>\n<\/div>\n<h1>Use Variables and Algebraic Symbols<\/h1>\n<p id=\"fs-id2425891\">Greg and Alex have the same birthday, but they were born in different years. This year Greg is \\(20\\) years old and Alex is \\(23\\), so Alex is \\(3\\) years older than Greg. When Greg was \\(12\\), Alex was \\(15\\). When Greg is \\(35\\), Alex will be \\(38\\). No matter what Greg\u2019s age is, Alex\u2019s age will always be \\(3\\) years more, right?<\/p>\nIn the language of algebra, we say that Greg\u2019s age and Alex\u2019s age are <span class=\"no-emphasis\" data-type=\"term\">variable<\/span> and the three is a <span class=\"no-emphasis\" data-type=\"term\">constant<\/span>. The ages change, or vary, so age is a variable. The \\(3\\) years between them always stays the same, so the age difference is the constant.\n<p id=\"fs-id1633275\">In algebra, letters of the alphabet are used to represent variables. Suppose we call Greg\u2019s age \\(g\\). Then we could use \\(g+3\\) to represent Alex\u2019s age. See the table below.<\/p>\n\n<table id=\"fs-id2953912\" class=\"aligncenter\" summary=\"This table has five rows and two columns. The first row is a header row and is labeled \u201cGreg\u2019s age\u201d, the second \u201cAlex\u2019s age\u201d. Under the \u201cGreg\u2019s age\u201d column are the values: twelve, twenty, and thirty-five. The last row has the letter G. Under the \u201cAlex\u2019s age\u201d column are the values: fifteen, twenty-three, and thirty-eight. The last row is the letter g plus three.\">\n<thead>\n<tr valign=\"top\">\n<th style=\"text-align: center;\" scope=\"col\" data-align=\"center\">Greg\u2019s age<\/th>\n<th style=\"text-align: center;\" scope=\"col\" data-align=\"center\">Alex\u2019s age<\/th>\n<\/tr>\n<\/thead>\n<tbody>\n<tr valign=\"top\">\n<td style=\"text-align: center;\" data-align=\"center\">\\(12\\)<\/td>\n<td style=\"text-align: center;\" data-align=\"center\">\\(15\\)<\/td>\n<\/tr>\n<tr valign=\"top\">\n<td style=\"text-align: center;\" data-align=\"center\">\\(20\\)<\/td>\n<td style=\"text-align: center;\" data-align=\"center\">\\(23\\)<\/td>\n<\/tr>\n<tr valign=\"top\">\n<td style=\"text-align: center;\" data-align=\"center\">\\(35\\)<\/td>\n<td style=\"text-align: center;\" data-align=\"center\">\\(38\\)<\/td>\n<\/tr>\n<tr valign=\"top\">\n<td style=\"text-align: center;\" data-align=\"center\">\\(g\\)<\/td>\n<td style=\"text-align: center;\" data-align=\"center\">\\(g+3\\)<\/td>\n<\/tr>\n<\/tbody>\n<\/table>\n<p id=\"fs-id2137950\">Letters are used to represent variables. Letters often used for variables are \\(x,y,a,b,\\text{and}\\phantom{\\rule{0.2em}{0ex}}c\\).<\/p>\n\n<div id=\"fs-id2399231\" data-type=\"note\">\n<div data-type=\"title\">\n<div class=\"textbox textbox--key-takeaways\"><header class=\"textbox__header\">\n<p class=\"textbox__title\">Variables and Constants<\/p>\n\n<\/header>\n<div class=\"textbox__content\">\n<p id=\"fs-id2203250\">A variable is a letter that represents a number or quantity whose value may change.<\/p>\n<p id=\"fs-id1604743\">A constant is a number whose value always stays the same.<\/p>\n\n<\/div>\n<\/div>\n<\/div>\n<\/div>\n<p id=\"fs-id1722327\">To write algebraically, we need some symbols as well as numbers and variables. There are several types of symbols we will be using. In <a href=\"\/introalgebra\/chapter\/whole-numbers\/\">1.1 Whole Numbers<\/a>, we introduced the symbols for the four basic arithmetic <span class=\"no-emphasis\" data-type=\"term\">operations<\/span>: addition, subtraction, multiplication, and division. We will summarize them here, along with words we use for the operations and the result.<\/p>\n\n<table id=\"fs-id1891703\" style=\"width: 100%;\" summary=\"This table has five rows and four columns. The first row is a header row. Each column is labeled accordingly: the first is labeled \u201cOperation\u201d, the second \u201cNotation\u201d, the third \u201cSay\u201d and the last \u201cThe result is...\u201d. Under the \u201cOperation\u201d column are the words: addition, multiplication, subtraction and division. Under the \u201cNotation\u201d column are algebraic expressions. The first row shows the letter a, the plus symbol, and the letter b. The next row shows four algebraic expressions. The first is the letter a, dot multiplication symbol, and the letter b. The second expression is the letter a in parentheses and the letter b in parentheses. The third expression is the letter a in parentheses and the letter b. The fourth expression is the letter a and the letter b in parentheses. The next row shows the letter a, the minus symbol, and the letter b. The last row shows four algebraic expressions. The first is the letter a, division symbol, and the letter b. The second expression is the letter a, the backslash symbol and the letter b. The third expression is the letter a above the fraction bar and the letter b below the fraction bar. The fourth expression is the letter b outside the division bracket and the letter a inside the division bracket.\" data-label=\"\">\n<thead>\n<tr valign=\"top\">\n<th scope=\"col\" data-align=\"left\">Operation<\/th>\n<th scope=\"col\" data-align=\"left\">Notation<\/th>\n<th scope=\"col\" data-align=\"left\">Say:<\/th>\n<th scope=\"col\" data-align=\"left\">The result is\u2026<\/th>\n<\/tr>\n<\/thead>\n<tbody>\n<tr valign=\"top\">\n<td data-align=\"left\">Addition<\/td>\n<td data-align=\"left\">\\(a+b\\)<\/td>\n<td data-align=\"left\">\\(a\\phantom{\\rule{0.2em}{0ex}}\\text{plus}\\phantom{\\rule{0.2em}{0ex}}b\\)<\/td>\n<td data-align=\"left\">the sum of \\(a\\) and \\(b\\)<\/td>\n<\/tr>\n<tr valign=\"top\">\n<td data-align=\"left\">Subtraction<\/td>\n<td data-align=\"left\">\\(a-b\\)<\/td>\n<td data-align=\"left\">\\(a\\phantom{\\rule{0.2em}{0ex}}\\text{minus}\\phantom{\\rule{0.2em}{0ex}}b\\)<\/td>\n<td data-align=\"left\">the difference of \\(a\\) and \\(b\\)<\/td>\n<\/tr>\n<tr valign=\"top\">\n<td data-align=\"left\">Multiplication<\/td>\n<td data-align=\"left\">\\(a\\cdot b,\\left(a\\right)\\left(b\\right),\\left(a\\right)b,a\\left(b\\right)\\)<\/td>\n<td data-align=\"left\">\\(a\\phantom{\\rule{0.2em}{0ex}}\\text{times}\\phantom{\\rule{0.2em}{0ex}}b\\)<\/td>\n<td data-align=\"left\">The product of \\(a\\) and \\(b\\)<\/td>\n<\/tr>\n<tr valign=\"top\">\n<td data-align=\"left\">Division<\/td>\n<td data-align=\"left\">\\(a\\div b,a\/b,\\phantom{\\rule{0.2em}{0ex}}\\frac{a}{b},b\\overline{)a}\\)<\/td>\n<td data-align=\"left\">\\(a\\) divided by \\(b\\)<\/td>\n<td data-align=\"left\">The quotient of \\(a\\) and \\(b\\)<\/td>\n<\/tr>\n<\/tbody>\n<\/table>\n<p id=\"fs-id1560745\">In algebra, the cross symbol, \u00d7, is not used to show multiplication because that symbol may cause confusion. Does \\(3xy\\) mean \\(3 \\phantom{\\rule{0.2em}{0ex}} \\times \\phantom{\\rule{0.2em}{0ex}}y\\) (three times \\(y\\)) or \\(3 \\cdot x \\cdot y\\) (three times \\(x\\phantom{\\rule{0.2em}{0ex}}\\text{times}\\phantom{\\rule{0.2em}{0ex}}y\\))? To make it clear, use \u2022 or parentheses for multiplication.<\/p>\n<p id=\"fs-id1885631\">We perform these operations on two numbers. When translating from symbolic form to words, or from words to symbolic form, pay attention to the words <em data-effect=\"italics\">of<\/em> or <em data-effect=\"italics\">and<\/em> to help you find the numbers.<\/p>\n\n<ul>\n \t<li>The <em data-effect=\"italics\">sum<\/em> <strong data-effect=\"bold\"><em data-effect=\"italics\">of<\/em><\/strong> \\(5\\) <strong data-effect=\"bold\"><em data-effect=\"italics\">and<\/em><\/strong> \\(3\\) means add \\(5\\) plus \\(3\\), which we write as \\(5+3\\).<\/li>\n \t<li>The <em data-effect=\"italics\">difference<\/em> <strong data-effect=\"bold\"><em data-effect=\"italics\">of<\/em><\/strong> \\(9\\) <strong data-effect=\"bold\"><em data-effect=\"italics\">and<\/em><\/strong> \\(2\\) means subtract \\(9\\) minus \\(2\\), which we write as \\(9-2\\).<\/li>\n \t<li>The <em data-effect=\"italics\">product<\/em> <strong data-effect=\"bold\"><em data-effect=\"italics\">of<\/em><\/strong> \\(4\\) <strong data-effect=\"bold\"><em data-effect=\"italics\">and<\/em><\/strong> \\(8\\) means multiply \\(4\\) times \\(8\\), which we can write as \\(4\\cdot 8\\).<\/li>\n \t<li>The <em data-effect=\"italics\">quotient<\/em> <strong data-effect=\"bold\"><em data-effect=\"italics\">of<\/em><\/strong> \\(20\\) <strong data-effect=\"bold\"><em data-effect=\"italics\">and<\/em><\/strong> \\(5\\) means divide \\(20\\) by \\(5\\), which we can write as \\(20 \\div 5\\).<\/li>\n<\/ul>\n<div class=\"textbox textbox--examples\"><header class=\"textbox__header\">\n<p class=\"textbox__title\">EXAMPLE 1<\/p>\n\n<\/header>\n<div class=\"textbox__content\">\n<div id=\"fs-id1804532\" data-type=\"problem\">\n<p id=\"fs-id2430630\">Translate from algebra to words:<\/p>\n\n<ol id=\"eip-id1168469763234\" class=\"circled\" type=\"a\">\n \t<li>\\(\\phantom{\\rule{0.2em}{0ex}}12+14\\phantom{\\rule{0.2em}{0ex}}\\)<\/li>\n \t<li>\\(\\phantom{\\rule{0.2em}{0ex}}\\left(30\\right)\\left(5\\right)\\phantom{\\rule{0.2em}{0ex}}\\)<\/li>\n \t<li>\\(\\phantom{\\rule{0.2em}{0ex}}64 \\div 8\\phantom{\\rule{0.2em}{0ex}}\\)<\/li>\n \t<li>\\(\\phantom{\\rule{0.2em}{0ex}}x-y\\)<\/li>\n<\/ol>\n<\/div>\n<div id=\"fs-id1604284\" data-type=\"solution\">\n<div data-type=\"title\"><\/div>\n<div style=\"text-align: left;\" data-type=\"title\"><strong>Solution<\/strong><\/div>\n<div data-type=\"title\"><\/div>\n<table id=\"eip-815\" class=\"unnumbered unstyled\" summary=\".\" data-label=\"\">\n<tbody>\n<tr>\n<td>a.<\/td>\n<\/tr>\n<tr>\n<td data-align=\"center\">\\(12+14\\)<\/td>\n<\/tr>\n<tr>\n<td data-align=\"center\">12 plus 14<\/td>\n<\/tr>\n<tr>\n<td data-align=\"center\">the sum of twelve and fourteen<\/td>\n<\/tr>\n<\/tbody>\n<\/table>\n<table id=\"eip-653\" class=\"unnumbered unstyled\" summary=\".\" data-label=\"\">\n<tbody>\n<tr>\n<td>b.<\/td>\n<\/tr>\n<tr>\n<td data-align=\"center\">\\(\\left(30\\right)\\left(5\\right)\\)<\/td>\n<\/tr>\n<tr>\n<td data-align=\"center\">30 times 5<\/td>\n<\/tr>\n<tr>\n<td data-align=\"center\">the product of thirty and five<\/td>\n<\/tr>\n<\/tbody>\n<\/table>\n<table id=\"eip-id1164753916055\" class=\"unnumbered unstyled\" summary=\".\" data-label=\"\">\n<tbody>\n<tr>\n<td>c.<\/td>\n<\/tr>\n<tr>\n<td data-align=\"center\">\\(64\\div 8\\)<\/td>\n<\/tr>\n<tr>\n<td data-align=\"center\">64 divided by 8<\/td>\n<\/tr>\n<tr>\n<td data-align=\"center\">the quotient of sixty-four and eight<\/td>\n<\/tr>\n<\/tbody>\n<\/table>\n<table id=\"eip-id1164753916109\" class=\"unnumbered unstyled\" summary=\".\" data-label=\"\">\n<tbody>\n<tr>\n<td>d.<\/td>\n<\/tr>\n<tr>\n<td data-align=\"center\">\\(x-y\\)<\/td>\n<\/tr>\n<tr>\n<td data-align=\"center\">\\(x\\) minus \\(y\\)<\/td>\n<\/tr>\n<tr>\n<td data-align=\"center\">the difference of \\(x\\) and \\(y\\)<\/td>\n<\/tr>\n<\/tbody>\n<\/table>\n<\/div>\n<\/div>\n<\/div>\n<div class=\"textbox textbox--exercises\"><header class=\"textbox__header\">\n<p class=\"textbox__title\">TRY IT 1.1<\/p>\n\n<\/header>\n<div class=\"textbox__content\">\n<div id=\"fs-id2205513\" data-type=\"problem\">\n<p id=\"fs-id1807700\">Translate from algebra to words.<\/p>\n\n<ol id=\"eip-id1168469668897\" class=\"circled\" type=\"a\">\n \t<li>\\(\\phantom{\\rule{0.2em}{0ex}}18+11\\phantom{\\rule{0.4em}{0ex}}\\)<\/li>\n \t<li>\\(\\phantom{\\rule{0.2em}{0ex}}\\left(27\\right)\\left(9\\right)\\phantom{\\rule{0.4em}{0ex}}\\)<\/li>\n \t<li>\\(\\phantom{\\rule{0.2em}{0ex}}84\\div 7\\)<\/li>\n \t<li>\\(p-q\\)<\/li>\n<\/ol>\n<\/div>\n<div id=\"fs-id1383680\" data-type=\"solution\"><details><summary>Show Answer<\/summary>\n<ol id=\"eip-id1168469837643\" class=\"circled\" type=\"a\">\n \t<li>18 plus 11; the sum of eighteen and eleven<\/li>\n \t<li>27 times 9; the product of twenty-seven and nine<\/li>\n \t<li>84 divided by 7; the quotient of eighty-four and seven<\/li>\n \t<li><em data-effect=\"italics\">p<\/em> minus <em data-effect=\"italics\">q<\/em>; the difference of <em data-effect=\"italics\">p<\/em> and <em data-effect=\"italics\">q<\/em><\/li>\n<\/ol>\n<\/details><\/div>\n<\/div>\n<\/div>\n<div class=\"textbox textbox--exercises\"><header class=\"textbox__header\">\n<p class=\"textbox__title\">TRY IT 1.2<\/p>\n\n<\/header>\n<div class=\"textbox__content\">\n<div id=\"fs-id2161871\" data-type=\"problem\">\n<p id=\"fs-id1171104039532\">Translate from algebra to words.<\/p>\n\n<ol id=\"eip-id1168468485516\" class=\"circled\" type=\"a\">\n \t<li>\\(\\phantom{\\rule{0.2em}{0ex}}47-19\\phantom{\\rule{0.4em}{0ex}}\\)<\/li>\n \t<li>\\(\\phantom{\\rule{0.2em}{0ex}}72\\div 9\\phantom{\\rule{0.4em}{0ex}}\\)<\/li>\n \t<li>\\(\\phantom{\\rule{0.2em}{0ex}}m+n\\phantom{\\rule{0.4em}{0ex}}\\)<\/li>\n \t<li>\\(\\phantom{\\rule{0.2em}{0ex}}\\left(13\\right)\\left(7\\right)\\)<\/li>\n<\/ol>\n<\/div>\n<div id=\"fs-id1887825\" data-type=\"solution\"><details><summary>Show Answer<\/summary>\n<ol id=\"eip-id1168465110670\" class=\"circled\" type=\"a\">\n \t<li>47 minus 19; the difference of forty-seven and nineteen<\/li>\n \t<li>72 divided by 9; the quotient of seventy-two and nine<\/li>\n \t<li><em data-effect=\"italics\">m<\/em> plus <em data-effect=\"italics\">n<\/em>; the sum of <em data-effect=\"italics\">m<\/em> and <em data-effect=\"italics\">n<\/em><\/li>\n \t<li>13 times 7; the product of thirteen and seven<\/li>\n<\/ol>\n<\/details><\/div>\n<\/div>\n<\/div>\nWhen two quantities have the same value, we say they are equal and connect them with an <em data-effect=\"italics\">equal sign<\/em>.\n<div id=\"fs-id1603053\" data-type=\"note\">\n<div data-type=\"title\">\n<div class=\"textbox textbox--key-takeaways\"><header class=\"textbox__header\">\n<p class=\"textbox__title\">Equality Symbol<\/p>\n\n<\/header>\n<div class=\"textbox__content\">\n<p id=\"fs-id1885124\">\\(a=b\\phantom{\\rule{0.2em}{0ex}}\\text{is read}\\phantom{\\rule{0.2em}{0ex}}a\\phantom{\\rule{0.2em}{0ex}}\\text{is equal to}\\phantom{\\rule{0.2em}{0ex}}b\\)<\/p>\n<p id=\"fs-id2775026\">The symbol \\(=\\) is called the <span class=\"no-emphasis\" data-type=\"term\">equal sign<\/span>.<\/p>\n\n<\/div>\n<\/div>\nAn <span class=\"no-emphasis\" data-type=\"term\">inequality<\/span> is used in algebra to compare two quantities that may have different values. The number line can help you understand inequalities. Remember that on the number line the numbers get larger as they go from left to right. So if we know that \\(b\\) is greater than \\(a\\), it means that \\(b\\) is to the right of \\(a\\) on the number line. We use the symbols &lt; and &gt; for inequalities.\n\n<\/div>\n<\/div>\n<div id=\"fs-id2650456\" data-type=\"note\">\n<div data-type=\"title\">\n<div class=\"textbox textbox--key-takeaways\"><header class=\"textbox__header\">\n<p class=\"textbox__title\">Inequality<\/p>\n\n<\/header>\n<div class=\"textbox__content\">\n<p id=\"fs-id3202723\">\\(a\\) &lt; \\(b\\) is read \\(a\\) is less than \\(b\\)<\/p>\n<p id=\"fs-id2700412\">\\(a\\) is to the left of \\(b\\) on the number line<\/p>\n<span id=\"fs-id1933083\" data-type=\"media\" data-alt=\"The figure shows a horizontal number line that begins with the letter a on the left then the letter b to its right.\"><img class=\"aligncenter\" src=\"https:\/\/opentextbc.ca\/accessibilitytoolkit\/wp-content\/uploads\/sites\/333\/2020\/08\/CNX_BMath_Figure_02_01_001-1.jpg\" alt=\"The figure shows a horizontal number line that begins with the letter a on the left then the letter b to its right.\" data-media-type=\"image\/jpeg\"><\/span>\n<p id=\"fs-id2495460\">\\(a\\) &gt; \\(b\\) is read \\(a\\) is greater than \\(b\\)<\/p>\n<p id=\"fs-id1379804\">\\(a\\) is to the right of \\(b\\) on the number line<\/p>\n<span id=\"fs-id1467098\" data-type=\"media\" data-alt=\"The figure shows a horizontal number line that begins with the letter b on the left then the letter a to its right.\"><img class=\"aligncenter\" src=\"https:\/\/opentextbc.ca\/accessibilitytoolkit\/wp-content\/uploads\/sites\/333\/2021\/03\/CNX_BMath_Figure_02_01_002-1.jpg\" alt=\"The figure shows a horizontal number line that begins with the letter b on the left then the letter a to its right.\" data-media-type=\"image\/jpeg\"><\/span>\n\n<\/div>\n<\/div>\n<p class=\"p1\">The expressions \\(a\\) &lt; \\(b\\phantom{\\rule{0.2em}{0ex}}\\text{and}\\phantom{\\rule{0.2em}{0ex}}a\\) &gt; \\(\\phantom{\\rule{0.2em}{0ex}}b\\) can be read from left-to-right or right-to-left, though in English we usually read from left-to-right. In general,<\/p>\n<img class=\"alignnone wp-image-59 size-full\" src=\"https:\/\/opentextbc.ca\/accessibilitytoolkit\/wp-content\/uploads\/sites\/333\/2021\/03\/Screenshot-2021-02-22-at-8.59.13-AM.png\" alt=\"&quot;7 is less than 11&quot; equivalent to &quot;11 is greater than 7&quot;\" width=\"2394\" height=\"222\">\n\n<\/div>\n<\/div>\n<p id=\"fs-id2903489\">When we write an inequality symbol with a line under it, such as \\(a\\le b\\), it means \\(a&lt;b\\) or \\(a=b\\). We read this \\(a\\) is less than or equal to \\(b\\). Also, if we put a slash through an equal sign, \\(\\ne\\) it means not equal.<\/p>\n<p id=\"fs-id1238987\">We summarize the symbols of equality and inequality in the table below.<\/p>\n\n<table class=\"grid\" style=\"width: 100%;\" summary=\"This table has seven rows and two columns. The first row is a header row and it labels each column. The first column is labeled \u201cAlgebraic Notation\u201d, the second \u201cSay\u201d. Under the \u201cAlgebraic Notation\u201d column are the algebraic expressions: a equals b; a is not equal to b; a is less than b; a is greater than b; a is less than or equal to b; a is greater than or equal to b. Under the \u201cSay\u201d column are the phrases: \u201ca is equal to b\u201d, \u201ca is not equal to b\u201d, \u201ca is less than b\u201d, \u201ca is greater than b\u201d, \u201ca is less than or equal to b\u201d, and \u201ca is greater than or equal to b\u201d.\">\n<thead>\n<tr valign=\"top\">\n<th style=\"width: 50%;\" scope=\"col\" data-align=\"center\">Algebraic Notation<\/th>\n<th style=\"width: 50%;\" scope=\"col\" data-align=\"center\">Say<\/th>\n<\/tr>\n<\/thead>\n<tbody>\n<tr valign=\"top\">\n<td style=\"width: 50%;\" data-align=\"left\">\\(a=b\\)<\/td>\n<td style=\"width: 50%;\" data-align=\"left\">\\(a\\) is equal to \\(b\\)<\/td>\n<\/tr>\n<tr valign=\"top\">\n<td style=\"width: 50%;\" data-align=\"left\">\\(a\\ne b\\)<\/td>\n<td style=\"width: 50%;\" data-align=\"left\">\\(a\\) is not equal to \\(b\\)<\/td>\n<\/tr>\n<tr valign=\"top\">\n<td style=\"width: 50%;\" data-align=\"left\">\\(a\\) &lt; \\(b\\)<\/td>\n<td style=\"width: 50%;\" data-align=\"left\">\\(a\\) is less than \\(b\\)<\/td>\n<\/tr>\n<tr valign=\"top\">\n<td style=\"width: 50%;\" data-align=\"left\">\\(a\\) &gt; \\(b\\)<\/td>\n<td style=\"width: 50%;\" data-align=\"left\">\\(a\\) is greater than \\(b\\)<\/td>\n<\/tr>\n<tr valign=\"top\">\n<td style=\"width: 50%;\" data-align=\"left\">\\(a\\le b\\)<\/td>\n<td style=\"width: 50%;\" data-align=\"left\">\\(a\\) is less than or equal to \\(b\\)<\/td>\n<\/tr>\n<tr valign=\"top\">\n<td style=\"width: 50%;\" data-align=\"left\">\\(a\\ge b\\)<\/td>\n<td style=\"width: 50%;\" data-align=\"left\">\\(a\\) is greater than or equal to \\(b\\)<\/td>\n<\/tr>\n<\/tbody>\n<\/table>\n<div data-type=\"note\">\n<div data-type=\"title\">\n<div class=\"textbox textbox--key-takeaways\"><header class=\"textbox__header\">\n<p class=\"textbox__title\">Symbols &lt; and &gt;<\/p>\n\n<\/header>\n<div class=\"textbox__content\">\n<p id=\"fs-id1508974\">The symbols &lt; and &gt; each have a smaller side and a larger side.<\/p>\n<p id=\"eip-id1168265897874\">smaller side &lt; larger side\nlarger side &gt; smaller side<\/p>\n\n<\/div>\n<\/div>\nThe smaller side of the symbol faces the smaller number and the larger faces the larger number.\n\n<\/div>\n<div class=\"textbox textbox--examples\"><header class=\"textbox__header\">\n<p class=\"textbox__title\">EXAMPLE 2<\/p>\n\n<\/header>\n<div class=\"textbox__content\">\n<div id=\"fs-id2199402\" data-type=\"problem\">\n\nTranslate from algebra to words:\n<ol id=\"eip-id1168466395280\" class=\"circled\" type=\"a\">\n \t<li>\\(\\phantom{\\rule{0.2em}{0ex}}20\\le 35\\)<\/li>\n \t<li>\\(\\phantom{\\rule{0.2em}{0ex}}11\\ne 15-3\\)<\/li>\n \t<li>\\(\\phantom{\\rule{0.2em}{0ex}}9\\) &gt; \\(\\phantom{\\rule{0.2em}{0ex}}10\\div 2\\)<\/li>\n \t<li>\\(\\phantom{\\rule{0.2em}{0ex}}x+2\\) &lt; \\(\\phantom{\\rule{0.2em}{0ex}}10\\)<\/li>\n<\/ol>\n<\/div>\n<div id=\"fs-id1210439\" data-type=\"solution\">\n<div data-type=\"title\"><\/div>\n<div data-type=\"title\"><strong>Solution<\/strong><\/div>\n<div data-type=\"title\"><\/div>\n<table id=\"eip-399\" class=\"unnumbered unstyled\" summary=\".\" data-label=\"\">\n<tbody>\n<tr>\n<td>a.<\/td>\n<\/tr>\n<tr>\n<td>\\(20\\le 35\\)<\/td>\n<\/tr>\n<tr>\n<td>20 is less than or equal to 35<\/td>\n<\/tr>\n<\/tbody>\n<\/table>\n<table id=\"eip-id1164752763787\" class=\"unnumbered unstyled\" summary=\".\" data-label=\"\">\n<tbody>\n<tr>\n<td>b.<\/td>\n<\/tr>\n<tr>\n<td>\\(11\\ne 15-3\\)<\/td>\n<\/tr>\n<tr>\n<td>11 is not equal to 15 minus 3<\/td>\n<\/tr>\n<\/tbody>\n<\/table>\n<table id=\"eip-id1164753846062\" class=\"unnumbered unstyled\" summary=\".\" data-label=\"\">\n<tbody>\n<tr>\n<td>c.<\/td>\n<\/tr>\n<tr>\n<td>\\(9\\) &gt; \\(10\\div 2\\)<\/td>\n<\/tr>\n<tr>\n<td>9 is greater than 10 divided by 2<\/td>\n<\/tr>\n<\/tbody>\n<\/table>\n<table id=\"eip-id1164752824586\" class=\"unnumbered unstyled\" summary=\".\" data-label=\"\">\n<tbody>\n<tr>\n<td>d.<\/td>\n<\/tr>\n<tr>\n<td>\\(x+2\\) &lt; \\(10\\)<\/td>\n<\/tr>\n<tr>\n<td>\\(x\\) plus 2 is less than 10<\/td>\n<\/tr>\n<\/tbody>\n<\/table>\n<\/div>\n<\/div>\n<\/div>\n<div class=\"textbox textbox--exercises\"><header class=\"textbox__header\">\n<p class=\"textbox__title\">TRY IT 2.1<\/p>\n\n<\/header>\n<div class=\"textbox__content\">\n<div id=\"fs-id1205270\" data-type=\"problem\">\n<p id=\"fs-id2903606\">Translate from algebra to words.<\/p>\n\n<ol id=\"eip-id1168466011782\" class=\"circled\" type=\"a\">\n \t<li>\\(\\phantom{\\rule{0.2em}{0ex}}\\text{14}\\le 27\\phantom{\\rule{0.2em}{0ex}}\\)<\/li>\n \t<li>\\(\\phantom{\\rule{0.2em}{0ex}}19-2\\ne 8\\phantom{\\rule{0.2em}{0ex}}\\)<\/li>\n \t<li>\\(\\phantom{\\rule{0.2em}{0ex}}12\\) &gt; \\(4\\phantom{\\rule{0.2em}{0ex}}\\div 2\\phantom{\\rule{0.2em}{0ex}}\\)<\/li>\n \t<li>\\(\\phantom{\\rule{0.2em}{0ex}}x-7\\) &lt; \\(\\phantom{\\rule{0.2em}{0ex}}1\\)<\/li>\n<\/ol>\n<\/div>\n<div id=\"fs-id2816995\" data-type=\"solution\"><details><summary>Show Answer<\/summary>\n<ol id=\"eip-id1168466395276\" class=\"circled\" type=\"a\">\n \t<li>fourteen is less than or equal to twenty-seven<\/li>\n \t<li>nineteen minus two is not equal to eight<\/li>\n \t<li>twelve is greater than four divided by two<\/li>\n \t<li><em data-effect=\"italics\">x<\/em> minus seven is less than one<\/li>\n<\/ol>\n<\/details><\/div>\n<\/div>\n<\/div>\n<\/div>\n<div id=\"fs-id1297928\" class=\"try\" data-type=\"note\">\n<div id=\"fs-id2310743\" data-type=\"exercise\">\n<div id=\"fs-id1205270\" data-type=\"problem\">\n<div class=\"textbox textbox--exercises\"><header class=\"textbox__header\">\n<p class=\"textbox__title\">TRY IT 2.2<\/p>\n\n<\/header>\n<div class=\"textbox__content\">\n<div id=\"fs-id1614444\" data-type=\"problem\">\n<p id=\"fs-id1171103156301\">Translate from algebra to words.<\/p>\n\n<ol id=\"eip-id1168469636286\" class=\"circled\" type=\"a\">\n \t<li>\\(\\phantom{\\rule{0.2em}{0ex}}19\\ge 15\\phantom{\\rule{0.2em}{0ex}}\\)<\/li>\n \t<li>\\(\\phantom{\\rule{0.2em}{0ex}}7=12-5\\phantom{\\rule{0.2em}{0ex}}\\)<\/li>\n \t<li>\\(\\phantom{\\rule{0.2em}{0ex}}15\\div 3\\) &lt; \\(8\\phantom{\\rule{0.2em}{0ex}}\\)<\/li>\n \t<li>\\(\\phantom{\\rule{0.2em}{0ex}}y-3\\) &gt; \\(6\\phantom{\\rule{0.2em}{0ex}}\\)<\/li>\n<\/ol>\n<\/div>\n<div id=\"fs-id1567145\" data-type=\"solution\"><details><summary>Show Answer<\/summary>\n<ol id=\"eip-id1168469636381\" class=\"circled\" type=\"a\">\n \t<li>nineteen is greater than or equal to fifteen<\/li>\n \t<li>seven is equal to twelve minus five<\/li>\n \t<li>fifteen divided by three is less than eight<\/li>\n \t<li><em data-effect=\"italics\">y<\/em> minus three is greater than six<\/li>\n<\/ol>\n<\/details><\/div>\n<\/div>\n<\/div>\n<\/div>\n<\/div>\n<\/div>\n<div id=\"fs-id1171104414920\" class=\"try\" data-type=\"note\">\n<div id=\"fs-id1573881\" data-type=\"exercise\">\n<div id=\"fs-id1614444\" data-type=\"problem\">\n<div class=\"textbox textbox--examples\"><header class=\"textbox__header\">\n<p class=\"textbox__title\">EXAMPLE 3<\/p>\n\n<\/header>\n<div class=\"textbox__content\">\n<div id=\"fs-id2471355\" data-type=\"problem\">\n<p id=\"fs-id1825021\">The information in <a class=\"autogenerated-content\" href=\"#CNX_BMath_Figure_02_01_003\">(Figure 1)<\/a> compares the fuel economy in miles-per-gallon (mpg) of several cars. Write the appropriate symbol \\(\\text{symbol},\\text{=},\\) &lt; \\(,\\text{or}\\) &gt;. in each expression to compare the fuel economy of the cars.<\/p>\n\n<div id=\"CNX_BMath_Figure_02_01_003\" class=\"bc-figure figure\">\n<div class=\"bc-figcaption figcaption\">(credit: modification of work by Bernard Goldbach, Wikimedia Commons)<\/div>\n\n[caption id=\"\" align=\"aligncenter\" width=\"632\"]<img src=\"https:\/\/opentextbc.ca\/accessibilitytoolkit\/wp-content\/uploads\/sites\/333\/2021\/03\/CNX_BMath_Figure_02_01_003-1.jpg\" alt=\"This table has two rows and six columns. The first column is a header column and it labels each row The first row is labeled \u201cCar\u201d and the second \u201cFuel economy (mpg)\u201d. To the right of the \u2018Car\u2019 row are the labels: \u201cPrius\u201d, \u201cMini Cooper\u201d, \u201cToyota Corolla\u201d, \u201cVersa\u201d, \u201cHonda Fit\u201d. Each of these columns contains an image of the labeled car model. To the right of the \u201cFuel economy (mpg)\u201d row are the algebraic equations: the letter p, the equals symbol, the number forty-eight; the letter m, the equals symbol, the number twenty-seven; the letter c, the equals symbol, the number twenty-eight; the letter v, the equals symbol, the number twenty-six; and the letter f, the equals symbol, the number twenty-seven.\" width=\"632\" height=\"117\" data-media-type=\"image\/jpeg\"> Figure 1[\/caption]\n\n<\/div>\n<ol id=\"eip-id1168467200954\" class=\"circled\" type=\"a\">\n \t<li>MPG of Prius_____ MPG of Mini Cooper<\/li>\n \t<li>MPG of Versa_____ MPG of Fit<\/li>\n \t<li>MPG of Mini Cooper_____ MPG of Fit<\/li>\n \t<li>MPG of Corolla_____ MPG of Versa<\/li>\n \t<li>MPG of Corolla_____ MPG of Prius<\/li>\n<\/ol>\n<\/div>\n<div id=\"fs-id1215439\" data-type=\"solution\">\n<div data-type=\"title\"><\/div>\n<div data-type=\"title\"><strong>Solution<\/strong><\/div>\n<div data-type=\"title\"><\/div>\n<table id=\"eip-254\" style=\"width: 100%;\" summary=\".\" data-label=\"\">\n<tbody>\n<tr>\n<td>a.<\/td>\n<td><\/td>\n<\/tr>\n<tr>\n<td><\/td>\n<td data-align=\"center\">MPG of Prius____MPG of Mini Cooper<\/td>\n<\/tr>\n<tr>\n<td>Find the values in the chart.<\/td>\n<td data-align=\"center\">48____27<\/td>\n<\/tr>\n<tr>\n<td>Compare.<\/td>\n<td data-align=\"center\">48 &gt; 27<\/td>\n<\/tr>\n<tr>\n<td><\/td>\n<td data-align=\"center\">MPG of Prius &gt; MPG of Mini Cooper<\/td>\n<\/tr>\n<\/tbody>\n<\/table>\n<table id=\"eip-id1164755344638\" style=\"width: 100%;\" summary=\".\" data-label=\"\">\n<tbody>\n<tr>\n<td>b.<\/td>\n<td><\/td>\n<\/tr>\n<tr>\n<td><\/td>\n<td data-align=\"center\">MPG of Versa____MPG of Fit<\/td>\n<\/tr>\n<tr>\n<td>Find the values in the chart.<\/td>\n<td data-align=\"center\">26____27<\/td>\n<\/tr>\n<tr>\n<td>Compare.<\/td>\n<td data-align=\"center\">26 &lt; 27<\/td>\n<\/tr>\n<tr>\n<td><\/td>\n<td data-align=\"center\">MPG of Versa &lt; MPG of Fit<\/td>\n<\/tr>\n<\/tbody>\n<\/table>\n<table id=\"eip-id1164755344710\" style=\"width: 100%;\" summary=\".\" data-label=\"\">\n<tbody>\n<tr>\n<td>c.<\/td>\n<td><\/td>\n<\/tr>\n<tr>\n<td><\/td>\n<td data-align=\"center\">MPG of Mini Cooper____MPG of Fit<\/td>\n<\/tr>\n<tr>\n<td>Find the values in the chart.<\/td>\n<td data-align=\"center\">27____27<\/td>\n<\/tr>\n<tr>\n<td>Compare.<\/td>\n<td data-align=\"center\">27 = 27<\/td>\n<\/tr>\n<tr>\n<td><\/td>\n<td data-align=\"center\">MPG of Mini Cooper = MPG of Fit<\/td>\n<\/tr>\n<\/tbody>\n<\/table>\n<table id=\"eip-id1164755231773\" style=\"width: 100%; height: 70px;\" summary=\".\" data-label=\"\">\n<tbody>\n<tr style=\"height: 14px;\">\n<td style=\"height: 14px;\">d.<\/td>\n<td style=\"height: 14px;\"><\/td>\n<\/tr>\n<tr style=\"height: 14px;\">\n<td style=\"height: 14px;\"><\/td>\n<td style=\"height: 14px;\" data-align=\"center\">MPG of Corolla____MPG of Versa<\/td>\n<\/tr>\n<tr style=\"height: 14px;\">\n<td style=\"height: 14px;\">Find the values in the chart.<\/td>\n<td style=\"height: 14px;\" data-align=\"center\">28____26<\/td>\n<\/tr>\n<tr style=\"height: 14px;\">\n<td style=\"height: 14px;\">Compare.<\/td>\n<td style=\"height: 14px;\" data-align=\"center\">28 &gt; 26<\/td>\n<\/tr>\n<tr style=\"height: 14px;\">\n<td style=\"height: 14px;\"><\/td>\n<td style=\"height: 14px;\" data-align=\"center\">MPG of Corolla &gt; MPG of Versa<\/td>\n<\/tr>\n<\/tbody>\n<\/table>\n<table id=\"eip-id1164755231845\" style=\"width: 100%;\" summary=\".\" data-label=\"\">\n<tbody>\n<tr>\n<td>e.<\/td>\n<td><\/td>\n<\/tr>\n<tr>\n<td><\/td>\n<td data-align=\"center\">MPG of Corolla____MPG of Prius<\/td>\n<\/tr>\n<tr>\n<td>Find the values in the chart.<\/td>\n<td data-align=\"center\">28____48<\/td>\n<\/tr>\n<tr>\n<td>Compare.<\/td>\n<td data-align=\"center\">28 &lt; 48<\/td>\n<\/tr>\n<tr>\n<td><\/td>\n<td data-align=\"center\">MPG of Corolla &lt; MPG of Prius<\/td>\n<\/tr>\n<\/tbody>\n<\/table>\n<\/div>\n<\/div>\n<\/div>\n<div class=\"textbox textbox--exercises\"><header class=\"textbox__header\">\n<p class=\"textbox__title\">TRY IT 3.1<\/p>\n\n<\/header>\n<div class=\"textbox__content\">\n<div id=\"fs-id1567666\" data-type=\"problem\">\n<p id=\"fs-id2173921\">Use <a class=\"autogenerated-content\" href=\"#CNX_BMath_Figure_02_01_003\">Figure 1<\/a> to fill in the appropriate \\(\\text{symbol},\\text{=},\\) &lt; \\(,\\text{or}\\) &gt;.<\/p>\n\n<ol id=\"eip-id1168468772318\" class=\"circled\" type=\"a\">\n \t<li>MPG of Prius_____MPG of Versa<\/li>\n \t<li>MPG of Mini Cooper_____ MPG of Corolla<\/li>\n<\/ol>\n<\/div>\n<div id=\"fs-id611660\" data-type=\"solution\"><details><summary>Show Answer<\/summary>\n<ol id=\"eip-id1168468400876\" class=\"circled\" type=\"a\">\n \t<li>&gt;<\/li>\n \t<li>&lt;<\/li>\n<\/ol>\n<\/details><\/div>\n<\/div>\n<\/div>\n<div class=\"textbox textbox--exercises\"><header class=\"textbox__header\">\n<p class=\"textbox__title\">TRY IT 3.2<\/p>\n\n<\/header>\n<div class=\"textbox__content\">\n<div id=\"fs-id1824239\" data-type=\"problem\">\n<p id=\"fs-id1171104004719\">Use <a class=\"autogenerated-content\" href=\"#CNX_BMath_Figure_02_01_003\">Figure 1<\/a> to fill in the appropriate \\(\\text{symbol},\\text{=},\\) &lt; \\(,\\text{or}\\) &gt;.<\/p>\n\n<ol id=\"eip-id1168467211692\" class=\"circled\" type=\"a\">\n \t<li>MPG of Fit_____ MPG of Prius<\/li>\n \t<li>MPG of Corolla _____ MPG of Fit<\/li>\n<\/ol>\n<\/div>\n<div id=\"fs-id2270408\" data-type=\"solution\"><details><summary>Show Answer<\/summary>\n<ol id=\"eip-id1168468505851\" class=\"circled\" type=\"a\">\n \t<li>&lt;<\/li>\n \t<li>&lt;<\/li>\n<\/ol>\n<\/details><\/div>\n<\/div>\n<\/div>\nGrouping symbols in algebra are much like the commas, colons, and other punctuation marks in written language. They indicate which expressions are to be kept together and separate from other expressions. The table below lists three of the most commonly used grouping symbols in algebra.\n\n<\/div>\n<\/div>\n<\/div>\n<table id=\"fs-id2856176\" class=\"grid\" style=\"width: 100%;\" summary=\"This table has four rows and two columns. The first row spans both columns and is a header reading \u201cCommon Grouping Symbols\u201d. The second row is labeled \u201cparentheses\u201d in the first column and the shows the open parentheses symbol followed by the close parentheses symbol. The third row is labeled \u201cBrackets\u201d in the first column and the shows the open square bracket symbol followed by the close square bracket symbol. The third row is labeled \u201cbraces\u201d in the first column and the shows the open curly brace symbol followed by the close curly brace symbol.\"><caption>Common Grouping Symbols<\/caption>\n<tbody>\n<tr valign=\"top\">\n<td style=\"text-align: left;\" data-align=\"left\">parentheses<\/td>\n<td style=\"text-align: left;\" data-align=\"center\">\\(\\left(\\phantom{\\rule{0.5em}{0ex}}\\right)\\)<\/td>\n<\/tr>\n<tr valign=\"top\">\n<td style=\"text-align: left;\" data-align=\"left\">brackets<\/td>\n<td style=\"text-align: left;\" data-align=\"center\">\\(\\left[\\phantom{\\rule{0.5em}{0ex}}\\right]\\)<\/td>\n<\/tr>\n<tr valign=\"top\">\n<td style=\"text-align: left;\" data-align=\"left\">braces<\/td>\n<td style=\"text-align: left;\" data-align=\"center\">\\(\\left\\{\\phantom{\\rule{0.5em}{0ex}}\\right\\}\\)<\/td>\n<\/tr>\n<\/tbody>\n<\/table>\nHere are some examples of expressions that include grouping symbols. We will simplify expressions like these later in this section.\n<div id=\"fs-id2221712\" class=\"unnumbered\" data-type=\"equation\" data-label=\"\">\\(8\\left(14-8\\right)\\phantom{\\rule{4em}{0ex}}21-3\\left[2+4\\left(9-8\\right)\\right]\\phantom{\\rule{4em}{0ex}}24\\div \\left\\{13-2\\left[1\\left(6-5\\right)+4\\right]\\right\\}\\)<\/div>\n<h1>Identify Expressions and Equations<\/h1>\n<p id=\"fs-id2139102\">What is the difference in English between a phrase and a sentence? A phrase expresses a single thought that is incomplete by itself, but a sentence makes a complete statement. \u201cRunning very fast\u201d is a phrase, but \u201cThe football player was running very fast\u201d is a sentence. A sentence has a subject and a verb.<\/p>\n<p id=\"fs-id1171104014483\">In algebra, we have <em data-effect=\"italics\">expressions<\/em> and <em data-effect=\"italics\">equations<\/em>. An <span class=\"no-emphasis\" data-type=\"term\">expression<\/span> is like a phrase. Here are some examples of expressions and how they relate to word phrases:<\/p>\n\n<table id=\"fs-id2472125\" style=\"width: 100%;\" summary=\"This table has five rows and three columns. The first row is a header row and it labels each column. The first column is labeled \u201cExpression\u201d, the second \u201cWords\u201d and the third \u201cPhrase\u201d. In the second row, under the \u201cExpression\u201d column is three plus five. Under the \u201cWords\u201d column is the phrase \u201cthree plus five\u201d. Under the \u201cPhrase\u201d column is the phrase \u201cthe sum of three and five\u201d. In the third row, under the \u201cExpression\u201d column is n minus one. Under the \u201cWords\u201d column is the phrase \u201cn minus one.\u201d Under the \u201cPhrase\u201d column is the phrase \u201cthe difference of n and one.\u201d In the fourth row, under the \u201cExpression\u201d column is six times seven. Under the \u201cWords\u201d column is the phrase \u201csix times seven.\u201d Under the \u201cPhrase\u201d column is the phrase \u201cthe product of six and seven.\u201d In the fifth row, under the \u201cExpression\u201d column is x divided by y. Under the \u201cWords\u201d column is the phrase \u201cx divided by y.\u201d Under the \u201cPhrase\u201d column is the phrase \u201cthe quotient of x and y.\u201d\" data-label=\"\">\n<thead>\n<tr valign=\"top\">\n<th style=\"text-align: left;\" scope=\"col\" data-align=\"left\">Expression<\/th>\n<th style=\"text-align: left;\" scope=\"col\" data-align=\"left\">Words<\/th>\n<th style=\"text-align: left;\" scope=\"col\" data-align=\"left\">Phrase<\/th>\n<\/tr>\n<\/thead>\n<tbody>\n<tr valign=\"top\">\n<td style=\"text-align: left;\" data-align=\"left\">\\(3+5\\)<\/td>\n<td style=\"text-align: left;\" data-align=\"left\">\\(3\\phantom{\\rule{0.2em}{0ex}}\\text{plus}\\phantom{\\rule{0.2em}{0ex}}5\\)<\/td>\n<td style=\"text-align: left;\" data-align=\"left\">the sum of three and five<\/td>\n<\/tr>\n<tr valign=\"top\">\n<td style=\"text-align: left;\" data-align=\"left\">\\(n-1\\)<\/td>\n<td style=\"text-align: left;\" data-align=\"left\">\\(n\\) minus one<\/td>\n<td style=\"text-align: left;\" data-align=\"left\">the difference of \\(n\\) and one<\/td>\n<\/tr>\n<tr valign=\"top\">\n<td style=\"text-align: left;\" data-align=\"left\">\\(6\\cdot 7\\)<\/td>\n<td style=\"text-align: left;\" data-align=\"left\">\\(6\\phantom{\\rule{0.2em}{0ex}}\\text{times}\\phantom{\\rule{0.2em}{0ex}}7\\)<\/td>\n<td style=\"text-align: left;\" data-align=\"left\">the product of six and seven<\/td>\n<\/tr>\n<tr valign=\"top\">\n<td style=\"text-align: left;\" data-align=\"left\">\\(\\frac{x}{y}\\)<\/td>\n<td style=\"text-align: left;\" data-align=\"left\">\\(x\\) divided by \\(y\\)<\/td>\n<td style=\"text-align: left;\" data-align=\"left\">the quotient of \\(x\\) and \\(y\\)<\/td>\n<\/tr>\n<\/tbody>\n<\/table>\nNotice that the phrases do not form a complete sentence because the phrase does not have a verb. An <span class=\"no-emphasis\" data-type=\"term\">equation<\/span> is two expressions linked with an equal sign. When you read the words the symbols represent in an equation, you have a complete sentence in English. The equal sign gives the verb. Here are some examples of equations:\n<table id=\"fs-id2658369\" style=\"width: 100%;\" summary=\"This table has six rows and two columns. The first row is a header row labeling each column. The first column is labeled \u201cEquation\u201d and the second \u201cSentence\u201d. In the second row, under the \u201cEquation\u201d column is three plus five equals eight. Under the \u201cSentence\u201d column is the sentence \u201cThe sum of three and five is equal to eight\u201d. In the third row, under the \u201cEquation\u201d column is n minus one equals fourteen. Under the \u201cSentence\u201d column is the Sentence \u201cThe difference of n and one equals fourteen.\u201d In the fourth row, under the \u201cEquation\u201d column is six times seven equals forty-two. Under the \u201cSentence\u201d column is the sentence \u201cThe product of six and seven is equal to forty-two.\u201d In the fifth row, under the \u201cEquation\u201d column is x equals fifty-three. Under the \u201cSentence\u201d column is the sentence \u201cx is equal to fifty-three.\u201d In the sixth row, under the \u201cEquation\u201d column is y plus nine equals two times y minus 3. Under the \u201cSentence\u201d column is the sentence \u201cy plus nine is equal to two y minus three.\u201d\" data-label=\"\">\n<thead>\n<tr valign=\"top\">\n<th style=\"text-align: left;\" scope=\"col\" data-align=\"left\">Equation<\/th>\n<th style=\"text-align: left;\" scope=\"col\" data-align=\"left\">Sentence<\/th>\n<\/tr>\n<\/thead>\n<tbody>\n<tr valign=\"top\">\n<td style=\"text-align: left;\" data-align=\"left\">\\(3+5=8\\)<\/td>\n<td style=\"text-align: left;\" data-align=\"left\">The sum of three and five is equal to eight.<\/td>\n<\/tr>\n<tr valign=\"top\">\n<td style=\"text-align: left;\" data-align=\"left\">\\(n-1=14\\)<\/td>\n<td style=\"text-align: left;\" data-align=\"left\">\\(n\\) minus one equals fourteen.<\/td>\n<\/tr>\n<tr valign=\"top\">\n<td style=\"text-align: left;\" data-align=\"left\">\\(6\\cdot 7=42\\)<\/td>\n<td style=\"text-align: left;\" data-align=\"left\">The product of six and seven is equal to forty-two.<\/td>\n<\/tr>\n<tr valign=\"top\">\n<td style=\"text-align: left;\" data-align=\"left\">\\(x=53\\)<\/td>\n<td style=\"text-align: left;\" data-align=\"left\">\\(x\\) is equal to fifty-three.<\/td>\n<\/tr>\n<tr valign=\"top\">\n<td style=\"text-align: left;\" data-align=\"left\">\\(y+9=2y-3\\)<\/td>\n<td style=\"text-align: left;\" data-align=\"left\">\\(y\\) plus nine is equal to two \\(y\\) minus three.<\/td>\n<\/tr>\n<\/tbody>\n<\/table>\n<div id=\"fs-id1365219\" data-type=\"note\">\n<div data-type=\"title\">\n<div class=\"textbox textbox--key-takeaways\"><header class=\"textbox__header\">\n<p class=\"textbox__title\">Expressions and Equations<\/p>\n\n<\/header>\n<div class=\"textbox__content\">\n\nAn expression is a number, a variable, or a combination of numbers and variables and operation symbols.\n<p id=\"fs-id2451266\">An equation is made up of two expressions connected by an equal sign.<\/p>\n\n<\/div>\n<\/div>\n<\/div>\n<div class=\"textbox textbox--examples\"><header class=\"textbox__header\">\n<p class=\"textbox__title\">EXAMPLE 4<\/p>\n\n<\/header>\n<div class=\"textbox__content\">\n<div data-type=\"problem\">\n<p id=\"fs-id1544580\">Determine if each is an expression or an equation:<\/p>\n\n<ol id=\"eip-id1168469631637\" class=\"circled\" type=\"a\">\n \t<li>\\(\\phantom{\\rule{0.2em}{0ex}}16-6=10\\)<\/li>\n \t<li>\\(\\phantom{\\rule{0.2em}{0ex}}4\\cdot 2+1\\)<\/li>\n \t<li>\\(\\phantom{\\rule{0.2em}{0ex}}x\\div 25\\)<\/li>\n \t<li>\\(\\phantom{\\rule{0.2em}{0ex}}y+8=40\\)<\/li>\n<\/ol>\n<\/div>\n<div id=\"fs-id1584678\" data-type=\"solution\">\n<div data-type=\"title\"><\/div>\n<div data-type=\"title\"><strong>Solution<\/strong><\/div>\n<div data-type=\"title\"><\/div>\n<table id=\"eip-id1166346957031\" class=\"unnumbered unstyled\" summary=\".\" data-label=\"\">\n<tbody>\n<tr>\n<td>a. \\(\\phantom{\\rule{0.2em}{0ex}}16-6=10\\)<\/td>\n<td>This is an equation\u2014two expressions are connected with an equal sign.<\/td>\n<\/tr>\n<tr>\n<td>b. \\(\\phantom{\\rule{0.2em}{0ex}}4\\cdot 2+1\\)<\/td>\n<td>This is an expression\u2014no equal sign.<\/td>\n<\/tr>\n<tr>\n<td>c. \\(\\phantom{\\rule{0.2em}{0ex}}x\\div 25\\)<\/td>\n<td>This is an expression\u2014no equal sign.<\/td>\n<\/tr>\n<tr>\n<td>d. \\(\\phantom{\\rule{0.2em}{0ex}}y+8=40\\)<\/td>\n<td>This is an equation\u2014two expressions are connected with an equal sign.<\/td>\n<\/tr>\n<\/tbody>\n<\/table>\n<\/div>\n<\/div>\n<\/div>\n<div class=\"textbox textbox--exercises\"><header class=\"textbox__header\">\n<p class=\"textbox__title\">TRY IT 4.1<\/p>\n\n<\/header>\n<div class=\"textbox__content\">\n<div id=\"fs-id2650086\" data-type=\"problem\">\n<p id=\"fs-id1619065\">Determine if each is an expression or an equation:<\/p>\n\n<ol id=\"eip-id1168468600384\" class=\"circled\" type=\"a\">\n \t<li>\\(\\phantom{\\rule{0.2em}{0ex}}23+6=29\\phantom{\\rule{0.4em}{0ex}}\\)<\/li>\n \t<li>\\(\\phantom{\\rule{0.2em}{0ex}}7\\cdot 3-7\\)<\/li>\n<\/ol>\n<\/div>\n<div id=\"fs-id1346095\" data-type=\"solution\"><details><summary>Show Answer<\/summary>\n<ol id=\"eip-id1168468285584\" class=\"circled\" type=\"a\">\n \t<li>equation<\/li>\n \t<li>expression<\/li>\n<\/ol>\n<\/details><\/div>\n<\/div>\n<\/div>\n<div class=\"textbox textbox--exercises\"><header class=\"textbox__header\">\n<p class=\"textbox__title\">TRY IT 4.2<\/p>\n\n<\/header>\n<div class=\"textbox__content\">\n<div id=\"fs-id1789247\" data-type=\"problem\">\n<p id=\"fs-id1171103307873\">Determine if each is an expression or an equation:<\/p>\n\n<ol id=\"eip-id1168469631624\" class=\"circled\" type=\"a\">\n \t<li>\\(\\phantom{\\rule{0.2em}{0ex}}y\\div 14\\phantom{\\rule{0.4em}{0ex}}\\)<\/li>\n \t<li>\\(\\phantom{\\rule{0.2em}{0ex}}x-6=21\\)<\/li>\n<\/ol>\n<\/div>\n<div id=\"fs-id1577444\" data-type=\"solution\"><details><summary>Show Answer<\/summary>\n<ol id=\"eip-id1168469631663\" class=\"circled\" type=\"a\">\n \t<li>expression<\/li>\n \t<li>equation<\/li>\n<\/ol>\n<\/details><\/div>\n<\/div>\n<\/div>\n<\/div>\n<h1>Simplify Expressions with Exponents<\/h1>\n<p id=\"fs-id1392631\">To simplify a numerical expression means to do all the math possible. For example, to simplify \\(4\\cdot2+1\\) we\u2019d first multiply \\(4\\cdot2\\) to get \\(8\\) and then add the \\(1\\) to get \\(9\\). A good habit to develop is to work down the page, writing each step of the process below the previous step. The example just described would look like this:<\/p>\n\n<div id=\"fs-id1308315\" class=\"unnumbered\" data-type=\"equation\" data-label=\"\">\\(4\\cdot2+1\\)<\/div>\n<div id=\"fs-id2495596\" class=\"unnumbered\" data-type=\"equation\" data-label=\"\">\\(8+1\\)<\/div>\n<div id=\"fs-id3016728\" class=\"unnumbered\" data-type=\"equation\" data-label=\"\">\\(9\\)<\/div>\n<p id=\"fs-id2144760\">Suppose we have the expression \\(2\\cdot2\\cdot2\\cdot2\\cdot2\\cdot2\\cdot2\\cdot2\\cdot2\\). We could write this more compactly using exponential notation. Exponential notation is used in algebra to represent a quantity multiplied by itself several times. We write \\(2\\cdot2\\cdot2\\) as \\({2}^{3}\\) and \\(2\\cdot2\\cdot2\\cdot2\\cdot2\\cdot2\\cdot2\\cdot2\\cdot2\\) as \\({2}^{9}\\). In expressions such as \\({2}^{3}\\), the \\(2\\) is called the base and the \\(3\\) is called the exponent. The exponent tells us how many factors of the base we have to multiply.<\/p>\n<span id=\"fs-id2149605\" data-type=\"media\" data-alt=\"The image shows the number two with the number three, in superscript, to the right of the two. The number two is labeled as \u201cbase\u201d and the number three is labeled as \u201cexponent\u201d.\"><img class=\"aligncenter\" src=\"https:\/\/opentextbc.ca\/accessibilitytoolkit\/wp-content\/uploads\/sites\/333\/2021\/03\/CNX_BMath_Figure_02_01_003_img-1.jpg\" alt=\"The image shows the number two with the number three, in superscript, to the right of the two. The number two is labeled as \u201cbase\u201d and the number three is labeled as \u201cexponent\u201d.\" data-media-type=\"image\/jpeg\"><\/span>\n<div id=\"fs-id2669230\" class=\"unnumbered\" data-type=\"equation\" data-label=\"\">\\(\\text{means multiply three factors of 2}\\)<\/div>\n<p id=\"fs-id2295676\">We say \\({2}^{3}\\) is in exponential notation and \\(2\\cdot2\\cdot2\\) is in expanded notation.<\/p>\n\n<div id=\"fs-id1243267\" data-type=\"note\">\n<div data-type=\"title\">\n<div class=\"textbox textbox--key-takeaways\"><header class=\"textbox__header\">\n<p class=\"textbox__title\">Exponential Notation<\/p>\n\n<\/header>\n<div class=\"textbox__content\">\n<p id=\"fs-id2283832\">For any expression \\({a}^{n},a\\) is a factor multiplied by itself \\(n\\) times if \\(n\\) is a positive integer.<\/p>\n\n<div id=\"fs-id1882026\" class=\"unnumbered\" data-type=\"equation\" data-label=\"\">\\({a}^{n}\\text{means multiply}\\phantom{\\rule{0.2em}{0ex}}n\\phantom{\\rule{0.2em}{0ex}}\\text{factors of}\\phantom{\\rule{0.2em}{0ex}}a\\)<\/div>\n<span id=\"fs-id2284773\" data-type=\"media\" data-alt=\"At the top of the image is the letter a with the letter n, in superscript, to the right of the a. The letter a is labeled as \u201cbase\u201d and the letter n is labeled as \u201cexponent\u201d. Below this is the letter a with the letter n, in superscript, to the right of the a set equal to n factors of a.\"><img class=\"aligncenter\" src=\"https:\/\/opentextbc.ca\/accessibilitytoolkit\/wp-content\/uploads\/sites\/333\/2021\/03\/CNX_BMath_Figure_02_01_010_img-1.jpg\" alt=\"At the top of the image is the letter a with the letter n, in superscript, to the right of the a. The letter a is labeled as \u201cbase\u201d and the letter n is labeled as \u201cexponent\u201d. Below this is the letter a with the letter n, in superscript, to the right of the a set equal to n factors of a.\" data-media-type=\"image\/jpeg\"><\/span>\n<p id=\"fs-id2786021\">The expression \\({a}^{n}\\) is read \\(a\\) to the \\({n}^{th}\\) power.<\/p>\n\n<\/div>\n<\/div>\nFor powers of \\(n=2\\) and \\(n=3\\), we have special names.\n\n<\/div>\n<\/div>\n<div id=\"fs-id1547556\" class=\"unnumbered\" data-type=\"equation\" data-label=\"\">\\(\\begin{array}{l}{a}^{2}\\phantom{\\rule{0.2em}{0ex}}\\text{is read as}\\phantom{\\rule{0.2em}{0ex}}\\text{\"}a\\phantom{\\rule{0.2em}{0ex}}\\text{squared\"}\\\\ {a}^{3}\\phantom{\\rule{0.2em}{0ex}}\\text{is read as}\\phantom{\\rule{0.2em}{0ex}}\\text{\"}a\\phantom{\\rule{0.2em}{0ex}}\\text{cubed\"}\\end{array}\\)<\/div>\n<p id=\"fs-id1387277\">The table below lists some examples of expressions written in exponential notation.<\/p>\n\n<table id=\"fs-id1830286\" style=\"width: 100%;\" summary=\"This table has five rows and two columns. The first row is a header row and it labels each column. The first column is labeled \u201cExponential Notation\u201d and the second \u201cIn Words\u201d. The second row shows the number seven followed by the superscript two in the first column and the phrase \u201cseven to the second power, or seven squared\u201d in the second column. The next row shows the number five followed by the superscript three in the first column and the phrase \u201cfive to the third power, or five cubed\u201d in the second column. The next row shows the number nine followed by the superscript four in the first column and the phrase \u201cnine to the fourth power\u201d in the second column. The last row shows the number twelve followed by the superscript five in the first column and the phrase \u201ctwelve to the fifth power\u201d in the second column.\">\n<thead>\n<tr valign=\"top\">\n<th style=\"text-align: left;\" scope=\"col\" data-align=\"left\">Exponential Notation<\/th>\n<th style=\"text-align: left;\" scope=\"col\" data-align=\"center\">In Words<\/th>\n<\/tr>\n<\/thead>\n<tbody>\n<tr valign=\"top\">\n<td style=\"text-align: left;\" data-align=\"left\">\\({7}^{2}\\)<\/td>\n<td style=\"text-align: left;\" data-align=\"left\">\\(7\\) to the second power, or \\(7\\) squared<\/td>\n<\/tr>\n<tr valign=\"top\">\n<td style=\"text-align: left;\" data-align=\"left\">\\({5}^{3}\\)<\/td>\n<td style=\"text-align: left;\" data-align=\"left\">\\(5\\) to the third power, or \\(5\\) cubed<\/td>\n<\/tr>\n<tr valign=\"top\">\n<td style=\"text-align: left;\" data-align=\"left\">\\({9}^{4}\\)<\/td>\n<td style=\"text-align: left;\" data-align=\"left\">\\(9\\) to the fourth power<\/td>\n<\/tr>\n<tr valign=\"top\">\n<td style=\"text-align: left;\" data-align=\"left\">\\({12}^{5}\\)<\/td>\n<td style=\"text-align: left;\" data-align=\"left\">\\(12\\) to the fifth power<\/td>\n<\/tr>\n<\/tbody>\n<\/table>\n<div data-type=\"example\">\n<div class=\"textbox textbox--examples\"><header class=\"textbox__header\">\n<p class=\"textbox__title\">EXAMPLE 5<\/p>\n\n<\/header>\n<div class=\"textbox__content\">\n<div id=\"fs-id2692026\" data-type=\"problem\">\n<p id=\"fs-id1969755\">Write each expression in exponential form:<\/p>\n\n<ol id=\"eip-id1168469525719\" class=\"circled\" type=\"a\">\n \t<li>\\(\\phantom{\\rule{0.2em}{0ex}}16\\cdot16\\cdot16\\cdot16\\cdot16\\cdot16\\cdot16\\)<\/li>\n \t<li>\\(\\phantom{\\rule{0.2em}{0ex}}9\\cdot9\\cdot9\\cdot9\\cdot9\\)<\/li>\n \t<li>\\(\\phantom{\\rule{0.2em}{0ex}}x\\cdot x\\cdot x\\cdot x\\)<\/li>\n \t<li>\\(\\phantom{\\rule{0.2em}{0ex}}a\\cdot a\\cdot a\\cdot a\\cdot a\\cdot a\\cdot a\\cdot a\\)<\/li>\n<\/ol>\n<\/div>\n<div id=\"fs-id4124564\" data-type=\"solution\">\n<div data-type=\"title\"><\/div>\n<div data-type=\"title\"><strong>Solution<\/strong><\/div>\n<div data-type=\"title\"><\/div>\n<table id=\"eip-id1168469627334\" style=\"width: 100%;\" summary=\".\" data-label=\"\">\n<tbody>\n<tr>\n<td>a. The base 16 is a factor 7 times.<\/td>\n<td>\\({16}^{7}\\)<\/td>\n<\/tr>\n<tr>\n<td>b. The base 9 is a factor 5 times.<\/td>\n<td>\\({9}^{5}\\)<\/td>\n<\/tr>\n<tr>\n<td>c. The base \\(x\\) is a factor 4 times.<\/td>\n<td>\\({x}^{4}\\)<\/td>\n<\/tr>\n<tr>\n<td>d. The base \\(a\\) is a factor 8 times.<\/td>\n<td>\\({a}^{8}\\)<\/td>\n<\/tr>\n<\/tbody>\n<\/table>\n<\/div>\n<\/div>\n<\/div>\n<div class=\"textbox textbox--exercises\"><header class=\"textbox__header\">\n<p class=\"textbox__title\">TRY IT 5.1<\/p>\n\n<\/header>\n<div class=\"textbox__content\">\n<div id=\"fs-id2214154\" data-type=\"problem\">\n<p id=\"fs-id1859717\">Write each expression in exponential form:<\/p>\n<p id=\"fs-id1611515\">\\(41\\cdot41\\cdot41\\cdot41\\cdot41\\)<\/p>\n\n<\/div>\n<div id=\"fs-id2276750\" data-type=\"solution\"><details><summary>Show Answer<\/summary>\n<p id=\"fs-id1377278\">41<sup>5<\/sup><\/p>\n\n<\/details><\/div>\n<\/div>\n<\/div>\n<div class=\"textbox textbox--exercises\"><header class=\"textbox__header\">\n<p class=\"textbox__title\">TRY IT 5.2<\/p>\n\n<\/header>\n<div class=\"textbox__content\">\n<div id=\"fs-id1345426\" data-type=\"problem\">\n<p id=\"fs-id1171104403843\">Write each expression in exponential form:<\/p>\n<p id=\"fs-id2216220\">\\(7\\cdot7\\cdot7\\cdot7\\cdot7\\cdot7\\cdot7\\cdot7\\cdot7\\)<\/p>\n\n<\/div>\n<div id=\"fs-id2782287\" data-type=\"solution\"><details><summary>Show Answer<\/summary>\n<p id=\"fs-id1390717\">7<sup>9<\/sup><\/p>\n\n<\/details><\/div>\n<\/div>\n<\/div>\n<\/div>\n<div id=\"fs-id1171103024968\" class=\"try\" data-type=\"note\">\n<div id=\"fs-id2669743\" data-type=\"exercise\">\n<div id=\"fs-id1345426\" data-type=\"problem\">\n<div class=\"textbox textbox--examples\"><header class=\"textbox__header\">\n<p class=\"textbox__title\">EXAMPLE 6<\/p>\n\n<\/header>\n<div class=\"textbox__content\">\n<div id=\"fs-id1842666\" data-type=\"problem\">\n<p id=\"fs-id2270606\">Write each exponential expression in expanded form:<\/p>\n\n<ol id=\"eip-id1168469513220\" class=\"circled\" type=\"a\">\n \t<li>\\(\\phantom{\\rule{0.2em}{0ex}}{8}^{6}\\phantom{\\rule{0.2em}{0ex}}\\)<\/li>\n \t<li>\\(\\phantom{\\rule{0.2em}{0ex}}{x}^{5}\\)<\/li>\n<\/ol>\n<\/div>\n<div id=\"fs-id2150233\" data-type=\"solution\">\n<div data-type=\"title\"><\/div>\n<div data-type=\"title\"><strong>Solution<\/strong><\/div>\n<div data-type=\"title\"><\/div>\n<p id=\"fs-id3177573\">a. The base is \\(8\\) and the exponent is \\(6\\), so \\({8}^{6}\\) means \\(8\\cdot 8\\cdot 8\\cdot 8\\cdot 8\\cdot 8\\)<\/p>\n<p id=\"fs-id2845374\">b. The base is \\(x\\) and the exponent is \\(5\\), so \\({x}^{5}\\) means \\(x\\cdot x\\cdot x\\cdot x\\cdot x\\)<\/p>\n\n<\/div>\n<\/div>\n<\/div>\n<div class=\"textbox textbox--exercises\"><header class=\"textbox__header\">\n<p class=\"textbox__title\">TRY IT 6.1<\/p>\n\n<\/header>\n<div class=\"textbox__content\">\n<div id=\"fs-id2150329\" data-type=\"problem\">\n<p id=\"fs-id1337149\">Write each exponential expression in expanded form:<\/p>\n\n<ol id=\"eip-id1168466675879\" class=\"circled\" type=\"a\">\n \t<li>\\(\\phantom{\\rule{0.2em}{0ex}}{4}^{8}\\)<\/li>\n \t<li>\\(\\phantom{\\rule{0.2em}{0ex}}{a}^{7}\\)<\/li>\n<\/ol>\n<\/div>\n<div id=\"fs-id1245764\" data-type=\"solution\"><details><summary>Show Answer<\/summary>\n<ol id=\"eip-id1168466512417\" class=\"circled\" type=\"a\">\n \t<li>\\(4 \\cdot 4 \\cdot 4 \\cdot 4 \\cdot 4 \\cdot 4 \\cdot 4 \\cdot 4\\)<\/li>\n \t<li>\\(a \\cdot a \\cdot a \\cdot a \\cdot a \\cdot a \\cdot a\\)<\/li>\n<\/ol>\n<\/details><\/div>\n<\/div>\n<\/div>\n<div class=\"textbox textbox--exercises\"><header class=\"textbox__header\">\n<p class=\"textbox__title\">TRY IT 6.2<\/p>\n\n<\/header>\n<div class=\"textbox__content\">\n<div id=\"fs-id1215612\" data-type=\"problem\">\n<p id=\"fs-id1171103315685\">Write each exponential expression in expanded form:<\/p>\n\n<ol id=\"eip-id1168467437310\" class=\"circled\" type=\"a\">\n \t<li>\\({\\phantom{\\rule{0.2em}{0ex}}8}^{8}\\phantom{\\rule{0.4em}{0ex}}\\)<\/li>\n \t<li>\\(\\phantom{\\rule{0.2em}{0ex}}{b}^{6}\\)<\/li>\n<\/ol>\n<\/div>\n<div id=\"fs-id1302295\" data-type=\"solution\"><details><summary>Show Answer<\/summary>\n<ol id=\"eip-id1168468532157\" class=\"circled\" type=\"a\">\n \t<li>\\(8 \\cdot 8 \\cdot 8 \\cdot 8 \\cdot 8 \\cdot 8 \\cdot 8 \\cdot 8\\)<\/li>\n \t<li>\\(b \\cdot b \\cdot b \\cdot b \\cdot b \\cdot b\\)<\/li>\n<\/ol>\n<\/details><\/div>\n<\/div>\n<\/div>\n<\/div>\n<\/div>\n<\/div>\n<p id=\"fs-id2661619\">To simplify an exponential expression without using a calculator, we write it in expanded form and then multiply the factors.<\/p>\n\n<div class=\"textbox textbox--examples\"><header class=\"textbox__header\">\n<p class=\"textbox__title\">EXAMPLE 7<\/p>\n\n<\/header>\n<div class=\"textbox__content\">\n<div data-type=\"problem\">\n<p id=\"fs-id1603288\">Simplify: \\({3}^{4}\\).<\/p>\n\n<\/div>\n<div id=\"fs-id1762208\" data-type=\"solution\">\n<div data-type=\"title\"><\/div>\n<div data-type=\"title\"><strong>Solution<\/strong><\/div>\n<div data-type=\"title\"><\/div>\n<table id=\"eip-id1164752752096\" style=\"width: 100%;\" summary=\".\" data-label=\"\">\n<tbody>\n<tr>\n<td><\/td>\n<td data-align=\"center\">\\({3}^{4}\\)<\/td>\n<\/tr>\n<tr>\n<td>Expand the expression.<\/td>\n<td data-align=\"center\">\\(3\\cdot 3\\cdot 3\\cdot 3\\)<\/td>\n<\/tr>\n<tr>\n<td>Multiply left to right.<\/td>\n<td data-align=\"center\">\\(9\\cdot 3\\cdot 3\\)<\/td>\n<\/tr>\n<tr>\n<td><\/td>\n<td data-align=\"center\">\\(27\\cdot 3\\)<\/td>\n<\/tr>\n<tr>\n<td>Multiply.<\/td>\n<td data-align=\"center\">\\(81\\)<\/td>\n<\/tr>\n<\/tbody>\n<\/table>\n<\/div>\n<\/div>\n<\/div>\n<div class=\"textbox textbox--exercises\"><header class=\"textbox__header\">\n<p class=\"textbox__title\">TRY IT 7.1<\/p>\n\n<\/header>\n<div class=\"textbox__content\">\n<div id=\"fs-id1578312\" data-type=\"problem\">\n<p id=\"fs-id2784369\">Simplify:<\/p>\n\n<ol id=\"eip-id1168466339424\" class=\"circled\" type=\"a\">\n \t<li>\\(\\phantom{\\rule{0.2em}{0ex}}{5}^{3}\\phantom{\\rule{0.4em}{0ex}}\\)<\/li>\n \t<li>\\(\\phantom{\\rule{0.2em}{0ex}}{1}^{7}\\)<\/li>\n<\/ol>\n<\/div>\n<div id=\"fs-id3294286\" data-type=\"solution\"><details><summary>Show Answer<\/summary>\n<ol id=\"eip-id1168466339465\" class=\"circled\" type=\"a\">\n \t<li>125<\/li>\n \t<li>1<\/li>\n<\/ol>\n<\/details><\/div>\n<\/div>\n<\/div>\n<div class=\"textbox textbox--exercises\"><header class=\"textbox__header\">\n<p class=\"textbox__title\">TRY IT 7.2<\/p>\n\n<\/header>\n<div class=\"textbox__content\">\n<div id=\"fs-id1917006\" data-type=\"problem\">\n<p id=\"fs-id1171103315179\">Simplify:<\/p>\n\n<ol id=\"eip-id1168467189297\" class=\"circled\" type=\"a\">\n \t<li>\\(\\phantom{\\rule{0.2em}{0ex}}{7}^{2}\\phantom{\\rule{0.4em}{0ex}}\\)<\/li>\n \t<li>\\(\\phantom{\\rule{0.2em}{0ex}}{0}^{5}\\)<\/li>\n<\/ol>\n<\/div>\n<div id=\"fs-id1152934\" data-type=\"solution\"><details><summary>Show Answer<\/summary>\n<ol id=\"eip-id1168467343038\" class=\"circled\" type=\"a\">\n \t<li>49<\/li>\n \t<li>0<\/li>\n<\/ol>\n<\/details><\/div>\n<\/div>\n<\/div>\n<h1>Simplify Expressions Using the Order of Operations<\/h1>\n<p id=\"fs-id1357642\">We\u2019ve introduced most of the symbols and notation used in algebra, but now we need to clarify the <span class=\"no-emphasis\" data-type=\"term\">order of operations<\/span>. Otherwise, expressions may have different meanings, and they may result in different values.<\/p>\n<p id=\"fs-id1171101101203\">For example, consider the expression:<\/p>\n\n<div id=\"fs-id1171101101206\" class=\"unnumbered\" data-type=\"equation\" data-label=\"\">\\(4+3\\cdot 7\\)<\/div>\n<div id=\"fs-id1171103305974\" class=\"unnumbered\" data-type=\"equation\" data-label=\"\">\\(\\begin{array}{cccc}\\hfill \\text{Some students say it simplifies to 49.}\\hfill &amp; \\phantom{\\rule{2em}{0ex}}&amp; &amp; \\hfill \\text{Some students say it simplifies to 25.}\\hfill \\\\ \\begin{array}{ccc}&amp; &amp; \\hfill 4+3\\cdot 7\\hfill \\\\ \\text{Since}\\phantom{\\rule{0.2em}{0ex}}4+3\\phantom{\\rule{0.2em}{0ex}}\\text{gives 7.}\\hfill &amp; \\phantom{\\rule{2em}{0ex}}&amp; \\hfill 7\\cdot 7\\hfill \\\\ \\text{And}\\phantom{\\rule{0.2em}{0ex}}7\\cdot 7\\phantom{\\rule{0.2em}{0ex}}\\text{is 49.}\\hfill &amp; \\phantom{\\rule{2em}{0ex}}&amp; \\hfill 49\\hfill \\end{array}&amp; &amp; &amp; \\begin{array}{ccc}&amp; &amp; \\hfill 4+3\\cdot 7\\hfill \\\\ \\phantom{\\rule{0.2em}{0ex}}\\text{Since}\\phantom{\\rule{0.2em}{0ex}}3\\cdot 7\\phantom{\\rule{0.2em}{0ex}}\\text{is 21.}\\hfill &amp; &amp; \\hfill 4+21\\hfill \\\\ \\phantom{\\rule{0.2em}{0ex}}\\text{And}\\phantom{\\rule{0.2em}{0ex}}21+4\\phantom{\\rule{0.2em}{0ex}}\\text{makes 25.}\\hfill &amp; &amp; \\hfill 25\\hfill \\end{array}\\hfill \\end{array}\\)<\/div>\n<p id=\"fs-id1530117\">Imagine the confusion that could result if every problem had several different correct answers. The same expression should give the same result. So mathematicians established some guidelines called the order of operations, which outlines the order in which parts of an expression must be simplified.<\/p>\n\n<div id=\"fs-id1715524\" data-type=\"note\">\n<div data-type=\"title\">\n<div class=\"textbox textbox--key-takeaways\"><header class=\"textbox__header\">\n<p class=\"textbox__title\">Order of Operations<\/p>\n\n<\/header>\n<div class=\"textbox__content\">\n<p id=\"fs-id2750738\">When simplifying mathematical expressions perform the operations in the following order:<\/p>\n<p id=\"fs-id1834652\">1. <strong data-effect=\"bold\">P<\/strong>arentheses and other Grouping Symbols<\/p>\n\n<ul id=\"fs-id1171104029952\" data-bullet-style=\"bullet\">\n \t<li>Simplify all expressions inside the parentheses or other grouping symbols, working on the innermost parentheses first.<\/li>\n<\/ul>\n<p id=\"fs-id1570796\">2. <strong data-effect=\"bold\">E<\/strong>xponents<\/p>\n\n<ul id=\"fs-id1171104407077\" data-bullet-style=\"bullet\">\n \t<li>Simplify all expressions with exponents.<\/li>\n<\/ul>\n<p id=\"fs-id1894922\">3. <strong data-effect=\"bold\">M<\/strong>ultiplication and <strong data-effect=\"bold\">D<\/strong>ivision<\/p>\n\n<ul id=\"fs-id1171103140103\" data-bullet-style=\"bullet\">\n \t<li>Perform all multiplication and division in order from left to right. These operations have equal priority.<\/li>\n<\/ul>\n<p id=\"fs-id3402451\">4. <strong data-effect=\"bold\">A<\/strong>ddition and <strong data-effect=\"bold\">S<\/strong>ubtraction<\/p>\n\n<ul id=\"fs-id1171104002792\" data-bullet-style=\"bullet\">\n \t<li>Perform all addition and subtraction in order from left to right. These operations have equal priority.<\/li>\n<\/ul>\nStudents often ask, \u201cHow will I remember the order?\u201d Here is a way to help you remember: Take the first letter of each key word and substitute the silly phrase.\n<p id=\"fs-id1269648\" style=\"text-align: center;\"><strong data-effect=\"bold\">P<\/strong>lease <strong data-effect=\"bold\">E<\/strong>xcuse <strong data-effect=\"bold\">M<\/strong>y <strong data-effect=\"bold\">D<\/strong>ear <strong data-effect=\"bold\">A<\/strong>unt <strong data-effect=\"bold\">S<\/strong>ally.<\/p>\n\n<table id=\"fs-id1786633\" class=\"grid\" style=\"width: 100%;\" summary=\"This table has five rows and two columns. The first row spans both columns and is a header reading \u201cOrder of Operations\u201d. In the second row the first column contains the word please with the p in bold and the second column contains the word parentheses with the p in bold. In the next row the first column contains the word excuse with the first e in bold and the second column contains the word exponents with the first e in bold. The next row contains the phrase \u201cmy dear\u201d in the first column with the m in my and the d in dear in bold and the second column contains the phrase \u201cmultiplication and division\u201d with the m in multiplication and the d in division in bold. The last row contains the phrase \u201cAunt Sally\u201d in the first column with the a in aunt and the s in Sally in bold and the second column contains the phrase \u201caddition and subtraction with the a in addition and the s in subtraction in bold.\" data-label=\"\">\n<tbody>\n<tr valign=\"top\">\n<td style=\"width: 50%;\" data-align=\"left\"><strong data-effect=\"bold\">P<\/strong>lease<\/td>\n<td style=\"width: 50%;\" data-align=\"left\"><strong data-effect=\"bold\">P<\/strong>arentheses<\/td>\n<\/tr>\n<tr valign=\"top\">\n<td style=\"width: 50%;\" data-align=\"left\"><strong data-effect=\"bold\">E<\/strong>xcuse<\/td>\n<td style=\"width: 50%;\" data-align=\"left\"><strong data-effect=\"bold\">E<\/strong>xponents<\/td>\n<\/tr>\n<tr valign=\"top\">\n<td style=\"width: 50%;\" data-align=\"left\"><strong data-effect=\"bold\">M<\/strong>y <strong data-effect=\"bold\">D<\/strong>ear<\/td>\n<td style=\"width: 50%;\" data-align=\"left\"><strong data-effect=\"bold\">M<\/strong>ultiplication and <strong data-effect=\"bold\">D<\/strong>ivision<\/td>\n<\/tr>\n<tr valign=\"top\">\n<td style=\"width: 50%;\" data-align=\"left\"><strong data-effect=\"bold\">A<\/strong>unt <strong data-effect=\"bold\">S<\/strong>ally<\/td>\n<td style=\"width: 50%;\" data-align=\"left\"><strong data-effect=\"bold\">A<\/strong>ddition and <strong data-effect=\"bold\">S<\/strong>ubtraction<\/td>\n<\/tr>\n<\/tbody>\n<\/table>\n<p id=\"fs-id1785127\">It\u2019s good that \u2018<strong data-effect=\"bold\">M<\/strong>y <strong data-effect=\"bold\">D<\/strong>ear\u2019 goes together, as this reminds us that <strong data-effect=\"bold\">m<\/strong>ultiplication and <strong data-effect=\"bold\">d<\/strong>ivision have equal priority. We do not always do multiplication before division or always do division before multiplication. We do them in order from left to right.<\/p>\n<p id=\"fs-id1389767\">Similarly, \u2018<strong data-effect=\"bold\">A<\/strong>unt <strong data-effect=\"bold\">S<\/strong>ally\u2019 goes together and so reminds us that <strong data-effect=\"bold\">a<\/strong>ddition and <strong data-effect=\"bold\">s<\/strong>ubtraction also have equal priority and we do them in order from left to right.<\/p>\n\n<\/div>\n<\/div>\n<\/div>\n<\/div>\n<div id=\"eip-313\" class=\"manipulative-math\" data-type=\"note\">\n<div class=\"textbox textbox--examples\"><header class=\"textbox__header\">\n<p class=\"textbox__title\">EXAMPLE 8<\/p>\n\n<\/header>\n<div class=\"textbox__content\">\n<div id=\"fs-id2588260\" data-type=\"problem\">\n<p id=\"fs-id1270576\">Simplify the expressions:<\/p>\n\n<ol id=\"eip-id1168467381591\" class=\"circled\" type=\"a\">\n \t<li>\\(\\phantom{\\rule{0.2em}{0ex}}4+3\\cdot 7\\phantom{\\rule{0.2em}{0ex}}\\)<\/li>\n \t<li>\\(\\phantom{\\rule{0.2em}{0ex}}\\left(4+3\\right)\\cdot 7\\)<\/li>\n<\/ol>\n<\/div>\n<div data-type=\"solution\">\n<div data-type=\"title\"><\/div>\n<div data-type=\"title\"><strong>Solution<\/strong><\/div>\n<div data-type=\"title\"><\/div>\n<table id=\"eip-id1164750479370\" class=\"unnumbered unstyled\" summary=\"The table shows the expression four plus three times seven. On the next line it states are there any parentheses in the expression? No. The line below that states are there any exponents in the expression? No. The next line states is there any multiplication or division in the expression? Yes. The next line states Multiply first and is followed by the expression of four plus three times seven. The expression is now four plus twenty-one. The last operation is addition. Add four and twenty-one to get twenty-five.\" data-label=\"\">\n<tbody>\n<tr>\n<td>a.<\/td>\n<td><\/td>\n<\/tr>\n<tr>\n<td><\/td>\n<td><span id=\"eip-id1164750479401\" data-type=\"media\" data-alt=\".\"><img src=\"https:\/\/opentextbc.ca\/accessibilitytoolkit\/wp-content\/uploads\/sites\/333\/2021\/03\/CNX_BMath_Figure_02_01_011_img-01-1.png\" alt=\".\" data-media-type=\"image\/png\"><\/span><\/td>\n<\/tr>\n<tr>\n<td>Are there any <strong>p<\/strong>arentheses? No.<\/td>\n<td><\/td>\n<\/tr>\n<tr>\n<td>Are there any <strong>e<\/strong>xponents? No.<\/td>\n<td><\/td>\n<\/tr>\n<tr>\n<td>Is there any <strong>m<\/strong>ultiplication or <strong>d<\/strong>ivision? Yes.<\/td>\n<td><\/td>\n<\/tr>\n<tr>\n<td>Multiply first.<\/td>\n<td><span id=\"eip-id1164754094653\" data-type=\"media\" data-alt=\".\"><img src=\"https:\/\/opentextbc.ca\/accessibilitytoolkit\/wp-content\/uploads\/sites\/333\/2021\/03\/CNX_BMath_Figure_02_01_011_img-02-1.png\" alt=\".\" data-media-type=\"image\/png\"><\/span><\/td>\n<\/tr>\n<tr>\n<td>Add.<\/td>\n<td><span id=\"eip-id1164754094670\" data-type=\"media\" data-alt=\".\"><img src=\"https:\/\/opentextbc.ca\/accessibilitytoolkit\/wp-content\/uploads\/sites\/333\/2021\/03\/CNX_BMath_Figure_02_01_011_img-03-1.png\" alt=\".\" data-media-type=\"image\/png\"><\/span><\/td>\n<\/tr>\n<tr>\n<td><\/td>\n<td><span id=\"eip-id1164754094685\" data-type=\"media\" data-alt=\".\"><img src=\"https:\/\/opentextbc.ca\/accessibilitytoolkit\/wp-content\/uploads\/sites\/333\/2021\/03\/CNX_BMath_Figure_02_01_011_img-04-1.png\" alt=\".\" data-media-type=\"image\/png\"><\/span><\/td>\n<\/tr>\n<\/tbody>\n<\/table>\n<table id=\"eip-id1164754514704\" class=\"unnumbered unstyled\" summary=\"The image shows the expression four plus three in parentheses times seven. Are there any parentheses? Yes, simplify inside the parentheses by adding four and three to get seven. The expression is now seven times seven. Is there any multiplication or division? Yes, multiply seven by seven to get forty-nine.\" data-label=\"\">\n<tbody>\n<tr>\n<td>b.<\/td>\n<td><\/td>\n<\/tr>\n<tr>\n<td><\/td>\n<td><span id=\"eip-id1164754514734\" data-type=\"media\" data-alt=\".\"><img src=\"https:\/\/opentextbc.ca\/accessibilitytoolkit\/wp-content\/uploads\/sites\/333\/2021\/03\/CNX_BMath_Figure_02_01_012_img-01-1.png\" alt=\".\" data-media-type=\"image\/png\"><\/span><\/td>\n<\/tr>\n<tr>\n<td>Are there any <strong>p<\/strong>arentheses? Yes.<\/td>\n<td><span id=\"eip-id1164754514754\" data-type=\"media\" data-alt=\".\"><img src=\"https:\/\/opentextbc.ca\/accessibilitytoolkit\/wp-content\/uploads\/sites\/333\/2021\/03\/CNX_BMath_Figure_02_01_012_img-02-1.png\" alt=\".\" data-media-type=\"image\/png\"><\/span><\/td>\n<\/tr>\n<tr>\n<td>Simplify inside the parentheses.<\/td>\n<td><span id=\"eip-id1164754514771\" data-type=\"media\" data-alt=\".\"><img src=\"https:\/\/opentextbc.ca\/accessibilitytoolkit\/wp-content\/uploads\/sites\/333\/2021\/03\/CNX_BMath_Figure_02_01_012_img-03-1.png\" alt=\".\" data-media-type=\"image\/png\"><\/span><\/td>\n<\/tr>\n<tr>\n<td>Are there any <strong>e<\/strong>xponents? No.<\/td>\n<td><\/td>\n<\/tr>\n<tr>\n<td>Is there any <strong>m<\/strong>ultiplication or <strong>d<\/strong>ivision? Yes.<\/td>\n<td><\/td>\n<\/tr>\n<tr>\n<td>Multiply.<\/td>\n<td><span id=\"eip-id1164754514814\" data-type=\"media\" data-alt=\".\"><img src=\"https:\/\/opentextbc.ca\/accessibilitytoolkit\/wp-content\/uploads\/sites\/333\/2021\/03\/CNX_BMath_Figure_02_01_012_img-04-1.png\" alt=\".\" data-media-type=\"image\/png\"><\/span><\/td>\n<\/tr>\n<\/tbody>\n<\/table>\n<\/div>\n<\/div>\n<\/div>\n<div class=\"textbox textbox--exercises\"><header class=\"textbox__header\">\n<p class=\"textbox__title\">TRY IT 8.1<\/p>\n\n<\/header>\n<div class=\"textbox__content\">\n<div id=\"fs-id1496028\" data-type=\"problem\">\n<p id=\"fs-id2132962\">Simplify the expressions:<\/p>\n\n<ol id=\"eip-id1168467165875\" class=\"circled\" type=\"a\">\n \t<li>\\(\\phantom{\\rule{0.2em}{0ex}}12-5\\cdot 2\\phantom{\\rule{0.4em}{0ex}}\\)<\/li>\n \t<li>\\(\\phantom{\\rule{0.2em}{0ex}}\\left(12-5\\right)\\cdot 2\\)<\/li>\n<\/ol>\n<\/div>\n<div id=\"fs-id1732185\" data-type=\"solution\"><details><summary>Show Answer<\/summary>\n<ol id=\"eip-id1168468411163\" class=\"circled\" type=\"a\">\n \t<li>2<\/li>\n \t<li>14<\/li>\n<\/ol>\n<\/details><\/div>\n<\/div>\n<\/div>\n<div class=\"textbox textbox--exercises\"><header class=\"textbox__header\">\n<p class=\"textbox__title\">TRY IT 8.2<\/p>\n\n<\/header>\n<div class=\"textbox__content\">\n<div id=\"fs-id1622271\" data-type=\"problem\">\n<p id=\"fs-id1171100608975\">Simplify the expressions:<\/p>\n\n<ol id=\"eip-id1168468535071\" class=\"circled\" type=\"a\">\n \t<li>\\(\\phantom{\\rule{0.2em}{0ex}}8+3\\cdot 9\\phantom{\\rule{0.4em}{0ex}}\\)<\/li>\n \t<li>\\(\\left(8+3\\right)\\cdot 9\\)<\/li>\n<\/ol>\n<\/div>\n<div id=\"fs-id2265132\" data-type=\"solution\"><details><summary>Show Answer<\/summary>\n<ol id=\"eip-id1168467599044\" class=\"circled\" type=\"a\">\n \t<li>35<\/li>\n \t<li>99<\/li>\n<\/ol>\n<\/details><\/div>\n<\/div>\n<\/div>\n<\/div>\n<div id=\"fs-id1171104389195\" class=\"try\" data-type=\"note\">\n<div id=\"fs-id2478161\" data-type=\"exercise\">\n<div id=\"fs-id1622271\" data-type=\"problem\">\n<div class=\"textbox textbox--examples\"><header class=\"textbox__header\">\n<p class=\"textbox__title\">EXAMPLE 9<\/p>\n\n<\/header>\n<div class=\"textbox__content\">\n<div id=\"fs-id3340653\" data-type=\"problem\">\n<p id=\"fs-id1714375\">Simplify:<\/p>\n\n<ol id=\"eip-id1168468508209\" class=\"circled\" type=\"a\">\n \t<li>\\(\\phantom{\\rule{0.2em}{0ex}}\\text{18}\\div \\text{9}\\cdot \\text{2}\\phantom{\\rule{0.2em}{0ex}}\\)<\/li>\n \t<li>\\(\\phantom{\\rule{0.2em}{0ex}}\\text{18}\\cdot \\text{9}\\div \\text{2}\\)<\/li>\n<\/ol>\n<\/div>\n<div id=\"fs-id1231784\" data-type=\"solution\">\n<div data-type=\"title\"><\/div>\n<div data-type=\"title\"><strong>Solution<\/strong><\/div>\n<div data-type=\"title\"><\/div>\n<table id=\"eip-id1164754213884\" class=\"unnumbered unstyled\" summary=\"The table shows the expression eighteen divided by nine times two. Are there any parentheses? No. Are there any exponents? No. Is there any multiplication or division? Yes, there is both multiplication and division. Perform multiplication and division from left to right so, divide first. Divide eighteen by nine to get two. The expression is now two times two. The last operation is multiplication. Multiply two by two to get four.\" data-label=\"\">\n<tbody>\n<tr>\n<td>a.<\/td>\n<td><\/td>\n<\/tr>\n<tr>\n<td><\/td>\n<td><span id=\"eip-id1164754213914\" data-type=\"media\" data-alt=\".\"><img src=\"https:\/\/opentextbc.ca\/accessibilitytoolkit\/wp-content\/uploads\/sites\/333\/2021\/03\/CNX_BMath_Figure_02_01_013_img-01-1.png\" alt=\".\" data-media-type=\"image\/png\"><\/span><\/td>\n<\/tr>\n<tr>\n<td>Are there any <strong>p<\/strong>arentheses? No.<\/td>\n<td><\/td>\n<\/tr>\n<tr>\n<td>Are there any <strong>e<\/strong>xponents? No.<\/td>\n<td><\/td>\n<\/tr>\n<tr>\n<td>Is there any <strong>m<\/strong>ultiplication or <strong>d<\/strong>ivision? Yes.<\/td>\n<td><\/td>\n<\/tr>\n<tr>\n<td>Multiply and divide from left to right. Divide.<\/td>\n<td><span id=\"eip-id1164752720013\" data-type=\"media\" data-alt=\".\"><img src=\"https:\/\/opentextbc.ca\/accessibilitytoolkit\/wp-content\/uploads\/sites\/333\/2021\/03\/CNX_BMath_Figure_02_01_013_img-02-1.png\" alt=\".\" data-media-type=\"image\/png\"><\/span><\/td>\n<\/tr>\n<tr>\n<td>Multiply.<\/td>\n<td><span id=\"eip-id1164752720030\" data-type=\"media\" data-alt=\".\"><img src=\"https:\/\/opentextbc.ca\/accessibilitytoolkit\/wp-content\/uploads\/sites\/333\/2021\/03\/CNX_BMath_Figure_02_01_013_img-03-1.png\" alt=\".\" data-media-type=\"image\/png\"><\/span><\/td>\n<\/tr>\n<\/tbody>\n<\/table>\n<table id=\"eip-id1164752720001\" class=\"unnumbered unstyled\" summary=\"The table shows the expression eighteen times nine divided by two. Are there any parentheses? No. Are there any exponents? No. Is there any multiplication or division? Yes, there is both multiplication and division. Perform multiplication and division from left to right so, multiply first. Multiply eighteen by nine to get one hundred sixty-two. The expression is now one hundred sixty-two divided by two. The last operation is division. divide one hundred sixty-two by two to get eighty-one.\" data-label=\"\">\n<tbody>\n<tr>\n<td>b.<\/td>\n<td><\/td>\n<\/tr>\n<tr>\n<td><\/td>\n<td><span id=\"eip-id1164752720032\" data-type=\"media\" data-alt=\".\"><img src=\"https:\/\/opentextbc.ca\/accessibilitytoolkit\/wp-content\/uploads\/sites\/333\/2021\/03\/CNX_BMath_Figure_02_01_014_img-01-1.png\" alt=\".\" data-media-type=\"image\/png\"><\/span><\/td>\n<\/tr>\n<tr>\n<td>Are there any <strong>p<\/strong>arentheses? No.<\/td>\n<td><\/td>\n<\/tr>\n<tr>\n<td>Are there any <strong>e<\/strong>xponents? No.<\/td>\n<td><\/td>\n<\/tr>\n<tr>\n<td>Is there any <strong>m<\/strong>ultiplication or <strong>d<\/strong>ivision? Yes.<\/td>\n<td><\/td>\n<\/tr>\n<tr>\n<td>Multiply and divide from left to right.<\/td>\n<td><\/td>\n<\/tr>\n<tr>\n<td>Multiply.<\/td>\n<td><span id=\"eip-id1164752720096\" data-type=\"media\" data-alt=\".\"><img src=\"https:\/\/opentextbc.ca\/accessibilitytoolkit\/wp-content\/uploads\/sites\/333\/2021\/03\/CNX_BMath_Figure_02_01_014_img-02-1.png\" alt=\".\" data-media-type=\"image\/png\"><\/span><\/td>\n<\/tr>\n<tr>\n<td>Divide.<\/td>\n<td><span id=\"eip-id1164752720113\" data-type=\"media\" data-alt=\".\"><img src=\"https:\/\/opentextbc.ca\/accessibilitytoolkit\/wp-content\/uploads\/sites\/333\/2021\/03\/CNX_BMath_Figure_02_01_014_img-03-1.png\" alt=\".\" data-media-type=\"image\/png\"><\/span><\/td>\n<\/tr>\n<\/tbody>\n<\/table>\n<\/div>\n<\/div>\n<\/div>\n<div class=\"textbox textbox--exercises\"><header class=\"textbox__header\">\n<p class=\"textbox__title\">TRY IT 9.1<\/p>\n\n<\/header>\n<div class=\"textbox__content\">\n<div id=\"fs-id2626286\" data-type=\"problem\">\n<p id=\"fs-id1632084\">Simplify:<\/p>\n<p id=\"fs-id2626288\">\\(42\\div 7\\cdot 3\\)<\/p>\n\n<\/div>\n<div id=\"fs-id2755325\" data-type=\"solution\"><details><summary>Show Answer<\/summary>\n<p id=\"fs-id2755327\">18<\/p>\n\n<\/details><\/div>\n<\/div>\n<\/div>\n<div class=\"textbox textbox--exercises\"><header class=\"textbox__header\">\n<p class=\"textbox__title\">TRY IT 9.2<\/p>\n\n<\/header>\n<div class=\"textbox__content\">\n<div id=\"fs-id2877181\" data-type=\"problem\">\n<p id=\"fs-id1171097539626\">Simplify:<\/p>\n<p id=\"fs-id2877183\">\\(12\\cdot 3\\div 4\\)<\/p>\n\n<\/div>\n<div id=\"fs-id2877202\" data-type=\"solution\"><details><summary>Show Answer<\/summary>\n<p id=\"fs-id2877204\">9<\/p>\n\n<\/details><\/div>\n<\/div>\n<\/div>\n<\/div>\n<\/div>\n<\/div>\n<div class=\"textbox textbox--examples\"><header class=\"textbox__header\">\n<p class=\"textbox__title\">EXAMPLE 10<\/p>\n\n<\/header>\n<div class=\"textbox__content\">\n<div id=\"fs-id2877215\" data-type=\"problem\">\n<p id=\"fs-id2308683\">Simplify: \\(18\\div 6+4\\left(5-2\\right)\\).<\/p>\n\n<\/div>\n<div id=\"fs-id4127406\" data-type=\"solution\">\n<div data-type=\"title\"><\/div>\n<div data-type=\"title\"><strong>Solution<\/strong><\/div>\n<div data-type=\"title\"><\/div>\n<table id=\"eip-id1164754213917\" class=\"unnumbered unstyled\" summary=\"The image shows the expression eighteen divided by six plus four, in parentheses, five minus two. Are there any parentheses? Yes, perform the subtraction inside the parentheses. Five minus two becomes three inside the parentheses. The expression is now eighteen divided by six plus four, in parentheses, three. Are there any exponents? No. Is there any multiplication or division? Yes, there is both multiplication and division. Divide first because multiplication and division are performed left to right. Divide eighteen by six to get three. The expression is now three plus four, in parentheses, three. Now multiply four by the three in parentheses to get twelve. The expression becomes three plus twelve. Add three and twelve to get fifteen.\" data-label=\"\">\n<tbody>\n<tr>\n<td><\/td>\n<td><span id=\"eip-id1164754213936\" data-type=\"media\" data-alt=\".\"><img src=\"https:\/\/opentextbc.ca\/accessibilitytoolkit\/wp-content\/uploads\/sites\/333\/2021\/03\/CNX_BMath_Figure_02_01_015_img-01-1.png\" alt=\".\" data-media-type=\"image\/png\"><\/span><\/td>\n<\/tr>\n<tr>\n<td>Parentheses? Yes, subtract first.<\/td>\n<td><span id=\"eip-id1164752719997\" data-type=\"media\" data-alt=\".\"><img src=\"https:\/\/opentextbc.ca\/accessibilitytoolkit\/wp-content\/uploads\/sites\/333\/2021\/03\/CNX_BMath_Figure_02_01_015_img-02-1.png\" alt=\".\" data-media-type=\"image\/png\"><\/span><\/td>\n<\/tr>\n<tr>\n<td>Exponents? No.<\/td>\n<td><\/td>\n<\/tr>\n<tr>\n<td>Multiplication or division? Yes.<\/td>\n<td><\/td>\n<\/tr>\n<tr>\n<td>Divide first because we multiply and divide left to right.<\/td>\n<td><span id=\"fs-id1166567548482\" data-type=\"media\" data-alt=\".\"><img src=\"https:\/\/opentextbc.ca\/accessibilitytoolkit\/wp-content\/uploads\/sites\/333\/2021\/03\/CNX_BMath_Figure_02_01_015_img-03-1.png\" alt=\".\" data-media-type=\"image\/png\"><\/span><\/td>\n<\/tr>\n<tr>\n<td>Any other multiplication or division? Yes.<\/td>\n<td><\/td>\n<\/tr>\n<tr>\n<td>Multiply.<\/td>\n<td><span id=\"eip-id1164752720057\" data-type=\"media\" data-alt=\".\"><img src=\"https:\/\/opentextbc.ca\/accessibilitytoolkit\/wp-content\/uploads\/sites\/333\/2021\/03\/CNX_BMath_Figure_02_01_015_img-04-1.png\" alt=\".\" data-media-type=\"image\/png\"><\/span><\/td>\n<\/tr>\n<tr>\n<td>Any other multiplication or division? No.<\/td>\n<td><\/td>\n<\/tr>\n<tr>\n<td>Any addition or subtraction? Yes.<\/td>\n<td><span id=\"eip-id1164752720083\" data-type=\"media\" data-alt=\".\"><img src=\"https:\/\/opentextbc.ca\/accessibilitytoolkit\/wp-content\/uploads\/sites\/333\/2021\/03\/CNX_BMath_Figure_02_01_015_img-05-1.png\" alt=\".\" data-media-type=\"image\/png\"><\/span><\/td>\n<\/tr>\n<\/tbody>\n<\/table>\n<\/div>\n<\/div>\n<\/div>\n<div class=\"textbox textbox--exercises\"><header class=\"textbox__header\">\n<p class=\"textbox__title\">TRY IT 10.1<\/p>\n\n<\/header>\n<div class=\"textbox__content\">\n<div id=\"fs-id2876989\" data-type=\"problem\">\n<p id=\"fs-id2876984\">Simplify:<\/p>\n<p id=\"fs-id2876991\">\\(30\\div 5+10\\left(3-2\\right)\\)<\/p>\n\n<\/div>\n<div id=\"fs-id2626124\" data-type=\"solution\"><details><summary>Show Answer<\/summary>\n<p id=\"fs-id2626126\">16<\/p>\n\n<\/details><\/div>\n<\/div>\n<\/div>\n<div class=\"textbox textbox--exercises\"><header class=\"textbox__header\">\n<p class=\"textbox__title\">TRY IT 10.2<\/p>\n\n<\/header>\n<div class=\"textbox__content\">\n<div id=\"fs-id2626133\" data-type=\"problem\">\n<p id=\"fs-id1171103163957\">Simplify:<\/p>\n<p id=\"fs-id2626135\">\\(70\\div 10+4\\left(6-2\\right)\\)<\/p>\n\n<\/div>\n<div id=\"fs-id2562999\" data-type=\"solution\"><details><summary>Show Answer<\/summary>\n<p id=\"fs-id2563001\">23<\/p>\n\n<\/details><\/div>\n<\/div>\n<\/div>\n<p id=\"fs-id2563008\">When there are multiple grouping symbols, we simplify the innermost parentheses first and work outward.<\/p>\n\n<div class=\"textbox textbox--examples\"><header class=\"textbox__header\">\n<p class=\"textbox__title\">EXAMPLE 11<\/p>\n\n<\/header>\n<div class=\"textbox__content\">\n<div id=\"fs-id2563015\" data-type=\"problem\">\n<p id=\"fs-id2563017\">\\(\\text{Simplify:}\\phantom{\\rule{0.2em}{0ex}}5+{2}^{3}+3\\left[6-3\\left(4-2\\right)\\right]\\).<\/p>\n\n<\/div>\n<div id=\"fs-id2308936\" data-type=\"solution\">\n<div data-type=\"title\"><\/div>\n<div data-type=\"title\"><strong>Solution<\/strong><\/div>\n<div data-type=\"title\"><\/div>\n<table id=\"eip-id1164754129434\" class=\"unnumbered unstyled\" summary=\"The image shows the expression five plus two cubed plus three, open bracket, six minus three, open parentheses, four minus two close parentheses, close bracket. Are there any parentheses (or other grouping symbols)? Yes, there are parentheses within brackets. Start with the innermost grouping, the parentheses. Inside the parentheses subtract two from four to get two. The expression becomes five plus two cubed plus three, open bracket, six minus three, in parentheses, two, close bracket. Within the brackets is six minus three, in parentheses, two. Multiply three by two since multiplication comes before subtraction. The expression becomes five plus two cubed plus three, in brackets, six minus six. Finish simplifying inside the brackets by performing the subtraction. Six minus six leaves zero. The expression is now five plus two cubed plus three, in brackets, zero. Are there exponents? Yes, two cubed is eight and the expression becomes five plus eight plus three, in brackets, zero. Is there any multiplication or division? Yes, multiply three by zero to get zero. The expression is now five plus eight plus zero. The remaining operations are both addition. Perform the addition from left to right. five plus eight is thirteen. Thirteen plus zero is thirteen.\" data-label=\"\">\n<tbody>\n<tr>\n<td><\/td>\n<td><span id=\"eip-id1164754129452\" data-type=\"media\" data-alt=\".\"><img src=\"https:\/\/opentextbc.ca\/accessibilitytoolkit\/wp-content\/uploads\/sites\/333\/2021\/03\/CNX_BMath_Figure_02_01_016_img-01-1.png\" alt=\".\" data-media-type=\"image\/png\"><\/span><\/td>\n<\/tr>\n<tr>\n<td>Are there any parentheses (or other grouping symbol)? Yes.<\/td>\n<td><\/td>\n<\/tr>\n<tr>\n<td>Focus on the parentheses that are inside the brackets.<\/td>\n<td><span id=\"eip-id1164754129478\" data-type=\"media\" data-alt=\".\"><img src=\"https:\/\/opentextbc.ca\/accessibilitytoolkit\/wp-content\/uploads\/sites\/333\/2021\/03\/CNX_BMath_Figure_02_01_016_img-02-1.png\" alt=\".\" data-media-type=\"image\/png\"><\/span><\/td>\n<\/tr>\n<tr>\n<td>Subtract.<\/td>\n<td><span id=\"eip-id1164754129495\" data-type=\"media\" data-alt=\".\"><img src=\"https:\/\/opentextbc.ca\/accessibilitytoolkit\/wp-content\/uploads\/sites\/333\/2021\/03\/CNX_BMath_Figure_02_01_016_img-03-1.png\" alt=\".\" data-media-type=\"image\/png\"><\/span><\/td>\n<\/tr>\n<tr>\n<td>Continue inside the brackets and multiply.<\/td>\n<td><span id=\"eip-id1164754129512\" data-type=\"media\" data-alt=\".\"><img src=\"https:\/\/opentextbc.ca\/accessibilitytoolkit\/wp-content\/uploads\/sites\/333\/2021\/03\/CNX_BMath_Figure_02_01_016_img-04-1.png\" alt=\".\" data-media-type=\"image\/png\"><\/span><\/td>\n<\/tr>\n<tr>\n<td>Continue inside the brackets and subtract.<\/td>\n<td><span id=\"eip-id1164754129529\" data-type=\"media\" data-alt=\".\"><img src=\"https:\/\/opentextbc.ca\/accessibilitytoolkit\/wp-content\/uploads\/sites\/333\/2021\/03\/CNX_BMath_Figure_02_01_016_img-05-1.png\" alt=\".\" data-media-type=\"image\/png\"><\/span><\/td>\n<\/tr>\n<tr>\n<td>The expression inside the brackets requires no further simplification.<\/td>\n<td><\/td>\n<\/tr>\n<tr>\n<td>Are there any exponents? Yes.<\/td>\n<td><\/td>\n<\/tr>\n<tr>\n<td>Simplify exponents.<\/td>\n<td><span id=\"eip-id1164752650667\" data-type=\"media\" data-alt=\".\"><img src=\"https:\/\/opentextbc.ca\/accessibilitytoolkit\/wp-content\/uploads\/sites\/333\/2021\/03\/CNX_BMath_Figure_02_01_016_img-06-1.png\" alt=\".\" data-media-type=\"image\/png\"><\/span><\/td>\n<\/tr>\n<tr>\n<td>Is there any multiplication or division? Yes.<\/td>\n<td><\/td>\n<\/tr>\n<tr>\n<td>Multiply.<\/td>\n<td><span id=\"eip-id1164752650693\" data-type=\"media\" data-alt=\".\"><img src=\"https:\/\/opentextbc.ca\/accessibilitytoolkit\/wp-content\/uploads\/sites\/333\/2021\/03\/CNX_BMath_Figure_02_01_016_img-07-1.png\" alt=\".\" data-media-type=\"image\/png\"><\/span><\/td>\n<\/tr>\n<tr>\n<td>Is there any addition or subtraction? Yes.<\/td>\n<td><\/td>\n<\/tr>\n<tr>\n<td>Add.<\/td>\n<td><span id=\"eip-id1164752650718\" data-type=\"media\" data-alt=\".\"><img src=\"https:\/\/opentextbc.ca\/accessibilitytoolkit\/wp-content\/uploads\/sites\/333\/2021\/03\/CNX_BMath_Figure_02_01_016_img-08-1.png\" alt=\".\" data-media-type=\"image\/png\"><\/span><\/td>\n<\/tr>\n<tr>\n<td>Add.<\/td>\n<td><span id=\"eip-id1164752650735\" data-type=\"media\" data-alt=\".\"><img src=\"https:\/\/opentextbc.ca\/accessibilitytoolkit\/wp-content\/uploads\/sites\/333\/2021\/03\/CNX_BMath_Figure_02_01_016_img-09-1.png\" alt=\".\" data-media-type=\"image\/png\"><\/span><\/td>\n<\/tr>\n<tr>\n<td><\/td>\n<td><span id=\"eip-id1164752650751\" data-type=\"media\" data-alt=\".\"><img src=\"https:\/\/opentextbc.ca\/accessibilitytoolkit\/wp-content\/uploads\/sites\/333\/2021\/03\/CNX_BMath_Figure_02_01_016_img-10-1.png\" alt=\".\" data-media-type=\"image\/png\"><\/span><\/td>\n<\/tr>\n<\/tbody>\n<\/table>\n<\/div>\n<\/div>\n<\/div>\n<div class=\"textbox textbox--exercises\"><header class=\"textbox__header\">\n<p class=\"textbox__title\">TRY IT 11.1<\/p>\n\n<\/header>\n<div class=\"textbox__content\">\n<div id=\"fs-id2308958\" data-type=\"problem\">\n<p id=\"fs-id2308953\">Simplify:<\/p>\n<p id=\"fs-id2308960\">\\(9+{5}^{3}-\\left[4\\left(9+3\\right)\\right]\\)<\/p>\n\n<\/div>\n<div id=\"fs-id1956245\" data-type=\"solution\"><details><summary>Show Answer<\/summary>\n<p id=\"fs-id1956247\">86<\/p>\n\n<\/details><\/div>\n<\/div>\n<\/div>\n<div class=\"textbox textbox--exercises\"><header class=\"textbox__header\">\n<p class=\"textbox__title\">TRY IT 11.2<\/p>\n\n<\/header>\n<div class=\"textbox__content\">\n<div id=\"fs-id1956255\" data-type=\"problem\">\n<p id=\"fs-id1171101067875\">Simplify:<\/p>\n<p id=\"fs-id1956257\">\\({7}^{2}-2\\left[4\\left(5+1\\right)\\right]\\)<\/p>\n\n<\/div>\n<div id=\"fs-id1956294\" data-type=\"solution\"><details><summary>Show Answer<\/summary>\n<p id=\"fs-id1956296\">1<\/p>\n\n<\/details><\/div>\n<\/div>\n<\/div>\n<div id=\"fs-id2308949\" class=\"try\" data-type=\"note\">\n<div id=\"fs-id2308956\" data-type=\"exercise\">\n<div id=\"fs-id1956245\" data-type=\"solution\">\n<div class=\"textbox textbox--examples\"><header class=\"textbox__header\">\n<p class=\"textbox__title\">EXAMPLE 12<\/p>\n\n<\/header>\n<div class=\"textbox__content\">\n<div id=\"fs-id1956307\" data-type=\"problem\">\n<p id=\"fs-id1956309\">Simplify: \\({2}^{3}+{3}^{4}\\div 3-{5}^{2}\\).<\/p>\n\n<\/div>\n<div id=\"fs-id1956342\" data-type=\"solution\">\n<div data-type=\"title\"><\/div>\n<div data-type=\"title\"><strong>Solution<\/strong><\/div>\n<div data-type=\"title\"><\/div>\n<table id=\"eip-id1164754324162\" class=\"unnumbered unstyled\" summary=\"The image shows the expression two cubed plus three to the fourth divided by three minus five squared. Are there any parentheses? No. Are there any exponents? Yes, several. Simplify each exponent. Two cubed is eight, three to the fourth is eighty-one, and five squared is twenty-five. The expression becomes eight plus eighty-one divided by three minus twenty-five. Is there any multiplication or division? Yes, just division. Divide eighty-one by three to get twenty-seven. The expression is now eight plus twenty-seven minus five. There is both addition and subtraction left. Perform these from left to right. Eight plus twenty-seven is thirty-five. Now the expression is thirty-five minus twenty five which leaves ten.\" data-label=\"\">\n<tbody>\n<tr>\n<td><\/td>\n<td><span id=\"eip-id1164754324181\" data-type=\"media\" data-alt=\".\"><img src=\"https:\/\/opentextbc.ca\/accessibilitytoolkit\/wp-content\/uploads\/sites\/333\/2021\/03\/CNX_BMath_Figure_02_01_017_img-01-1.png\" alt=\".\" data-media-type=\"image\/png\"><\/span><\/td>\n<\/tr>\n<tr>\n<td>If an expression has several exponents, they may be simplified in the same step.<\/td>\n<td><\/td>\n<\/tr>\n<tr>\n<td>Simplify exponents.<\/td>\n<td><span id=\"eip-id1164754324206\" data-type=\"media\" data-alt=\".\"><img src=\"https:\/\/opentextbc.ca\/accessibilitytoolkit\/wp-content\/uploads\/sites\/333\/2021\/03\/CNX_BMath_Figure_02_01_017_img-02-1.png\" alt=\".\" data-media-type=\"image\/png\"><\/span><\/td>\n<\/tr>\n<tr>\n<td>Divide.<\/td>\n<td><span id=\"eip-id1164754324223\" data-type=\"media\" data-alt=\".\"><img src=\"https:\/\/opentextbc.ca\/accessibilitytoolkit\/wp-content\/uploads\/sites\/333\/2021\/03\/CNX_BMath_Figure_02_01_017_img-03-1.png\" alt=\".\" data-media-type=\"image\/png\"><\/span><\/td>\n<\/tr>\n<tr>\n<td>Add.<\/td>\n<td><span id=\"eip-id1164754324240\" data-type=\"media\" data-alt=\".\"><img src=\"https:\/\/opentextbc.ca\/accessibilitytoolkit\/wp-content\/uploads\/sites\/333\/2021\/03\/CNX_BMath_Figure_02_01_017_img-04-1.png\" alt=\".\" data-media-type=\"image\/png\"><\/span><\/td>\n<\/tr>\n<tr>\n<td>Subtract.<\/td>\n<td><span id=\"eip-id1164754324256\" data-type=\"media\" data-alt=\".\"><img src=\"https:\/\/opentextbc.ca\/accessibilitytoolkit\/wp-content\/uploads\/sites\/333\/2021\/03\/CNX_BMath_Figure_02_01_017_img-05-1.png\" alt=\".\" data-media-type=\"image\/png\"><\/span><\/td>\n<\/tr>\n<tr>\n<td><\/td>\n<td><span id=\"eip-id1164754324272\" data-type=\"media\" data-alt=\".\"><img src=\"https:\/\/opentextbc.ca\/accessibilitytoolkit\/wp-content\/uploads\/sites\/333\/2021\/03\/CNX_BMath_Figure_02_01_017_img-06-1.png\" alt=\".\" data-media-type=\"image\/png\"><\/span><\/td>\n<\/tr>\n<\/tbody>\n<\/table>\n<\/div>\n<\/div>\n<\/div>\n<div class=\"textbox textbox--exercises\"><header class=\"textbox__header\">\n<p class=\"textbox__title\">TRY IT 12.1<\/p>\n\n<\/header>\n<div class=\"textbox__content\">\n<div id=\"fs-id1956364\" data-type=\"problem\">\n<p id=\"fs-id1956359\">Simplify:<\/p>\n\\({3}^{2}+{2}^{4}\\div 2+{4}^{3}\\)\n\n<\/div>\n<div id=\"fs-id1956396\" data-type=\"solution\"><details open=\"open\"><summary>Show Answer<\/summary>\n<p id=\"fs-id1956399\">81<\/p>\n\n<\/details><\/div>\n<\/div>\n<\/div>\n<div class=\"textbox textbox--exercises\"><header class=\"textbox__header\">\n<p class=\"textbox__title\">TRY IT 12.2<\/p>\n\n<\/header>\n<div class=\"textbox__content\">\n<div id=\"fs-id1956406\" data-type=\"problem\">\n<p id=\"fs-id1171104064837\">Simplify:<\/p>\n<p id=\"fs-id1956408\">\\({6}^{2}-{5}^{3}\\div 5+{8}^{2}\\)<\/p>\n\n<\/div>\n<div id=\"fs-id2327292\" data-type=\"solution\"><details open=\"open\"><summary>Show Answer<\/summary>\n<p id=\"fs-id2327294\">75<\/p>\n\n<\/details><\/div>\n<\/div>\n<\/div>\nACCESS ADDITIONAL ONLINE RESOURCES\n\n<\/div>\n<\/div>\n<\/div>\n<div id=\"fs-id2327301\" class=\"media-2\" data-type=\"note\">\n<ul id=\"fs-id2327307\" data-display=\"block\">\n \t<li><a href=\"http:\/\/openstaxcollege.org\/l\/24orderoperate\">Order of Operations<\/a><\/li>\n \t<li><a href=\"http:\/\/openstaxcollege.org\/l\/24orderbasic\">Order of Operations \u2013 The Basics<\/a><\/li>\n \t<li><a href=\"http:\/\/openstaxcollege.org\/l\/24Evalexpress\">Ex: Evaluate an Expression Using the Order of Operations<\/a><\/li>\n \t<li><a href=\"http:\/\/openstaxcollege.org\/l\/24evalexpress3\">Example 3: Evaluate an Expression Using The Order of Operations<\/a><\/li>\n<\/ul>\n<\/div>\n<h1>Key Concepts<\/h1>\n<table id=\"eip-id1168265095050\" class=\"grid\" summary=\"This table has five rows and four columns. The first row is a header row. Each column is labeled accordingly: the first is labeled \u201cOperation\u201d, the second \u201cNotation\u201d, the third \u201cSay\u201d and the last \u201cThe result is...\u201d. Under the \u201cOperation\u201d column are the words: addition, multiplication, subtraction and division. Under the \u201cNotation\u201d column are algebraic expressions. The first row shows the letter a, the plus symbol, and the letter b. The next row shows four algebraic expressions. The first is the letter a, dot multiplication symbol, and the letter b. The second expression is the letter a in parentheses and the letter b in parentheses. The third expression is the letter a in parentheses and the letter b. The fourth expression is the letter a and the letter b in parentheses. The next row shows the letter a, the minus symbol, and the letter b. The last row shows four algebraic expressions. The first is the letter a, division symbol, and the letter b. The second expression is the letter a, the backslash symbol and the letter b. The third expression is the letter a above the fraction bar and the letter b below the fraction bar. The fourth expression is the letter b outside the division bracket and the letter a inside the division bracket.\" data-label=\"\">\n<thead>\n<tr valign=\"top\">\n<th data-align=\"left\"><strong data-effect=\"bold\">Operation<\/strong><\/th>\n<th data-align=\"left\"><strong data-effect=\"bold\">Notation<\/strong><\/th>\n<th data-align=\"left\"><strong data-effect=\"bold\">Say:<\/strong><\/th>\n<th data-align=\"left\"><strong data-effect=\"bold\">The result is\u2026<\/strong><\/th>\n<\/tr>\n<\/thead>\n<tbody>\n<tr valign=\"top\">\n<td data-align=\"left\">Addition<\/td>\n<td data-align=\"left\">\\(a+b\\)<\/td>\n<td data-align=\"left\">\\(a\\phantom{\\rule{0.2em}{0ex}}\\text{plus}\\phantom{\\rule{0.2em}{0ex}}b\\)<\/td>\n<td data-align=\"left\">the sum of \\(a\\) and \\(b\\)<\/td>\n<\/tr>\n<tr valign=\"top\">\n<td data-align=\"left\">Multiplication<\/td>\n<td data-align=\"left\">\\(a\\cdot b,\\left(a\\right)\\left(b\\right),\\left(a\\right)b,a\\left(b\\right)\\)<\/td>\n<td data-align=\"left\">\\(a\\phantom{\\rule{0.2em}{0ex}}\\text{times}\\phantom{\\rule{0.2em}{0ex}}b\\)<\/td>\n<td data-align=\"left\">The product of \\(a\\) and \\(b\\)<\/td>\n<\/tr>\n<tr valign=\"top\">\n<td data-align=\"left\">Subtraction<\/td>\n<td data-align=\"left\">\\(a-b\\)<\/td>\n<td data-align=\"left\">\\(a\\phantom{\\rule{0.2em}{0ex}}\\text{minus}\\phantom{\\rule{0.2em}{0ex}}b\\)<\/td>\n<td data-align=\"left\">the difference of \\(a\\) and \\(b\\)<\/td>\n<\/tr>\n<tr valign=\"top\">\n<td data-align=\"left\">Division<\/td>\n<td data-align=\"left\">\\(a\\div b,a\/b,\\phantom{\\rule{0.2em}{0ex}}\\frac{a}{b},b\\overline{)a}\\)<\/td>\n<td data-align=\"left\">\\(a\\) divided by \\(b\\)<\/td>\n<td data-align=\"left\">The quotient of \\(a\\) and \\(b\\)<\/td>\n<\/tr>\n<\/tbody>\n<\/table>\n<ul id=\"eip-740\">\n \t<li><strong>Equality Symbol<\/strong>\n<ul id=\"eip-id1168262501679\">\n \t<li>\\(a=b\\) is read as \\(a\\) is equal to \\(b\\)<\/li>\n \t<li>The symbol \\(=\\) is called the equal sign.<\/li>\n<\/ul>\n<\/li>\n \t<li><strong>Inequality<\/strong>\n<ul id=\"eip-id1168263909662\">\n \t<li>\\(a\\) &lt; \\(b\\) is read \\(a\\) is less than \\(b\\)<\/li>\n \t<li>\\(a\\) is to the left of \\(b\\) on the number line\n<span id=\"eip-id1168264918525\" data-type=\"media\" data-alt=\"..\"><img src=\"https:\/\/opentextbc.ca\/accessibilitytoolkit\/wp-content\/uploads\/sites\/333\/2021\/03\/CNX_BMath_Figure_02_01_018_img-1.jpg\" alt=\"..\" data-media-type=\"image\/jpg\"><\/span><\/li>\n \t<li>\\(a\\) &gt; \\(b\\) is read \\(a\\) is greater than \\(b\\)<\/li>\n \t<li>\\(a\\) is to the right of \\(b\\) on the number line\n<span id=\"eip-id1168264785219\" data-type=\"media\" data-alt=\"..\"><img src=\"https:\/\/opentextbc.ca\/accessibilitytoolkit\/wp-content\/uploads\/sites\/333\/2021\/03\/CNX_BMath_Figure_02_01_019_img-1.jpg\" alt=\"..\" data-media-type=\"image\/jpg\"><\/span><\/li>\n<\/ul>\n<\/li>\n<\/ul>\n<table id=\"eip-455\" summary=\"This table has seven rows and two columns. The first row is a header row and it labels each column. The first column is labeled \u201cAlgebraic Notation\u201d, the second \u201cSay\u201d. Under the \u201cAlgebraic Notation\u201d column are the algebraic expressions: a equals b; a is not equal to b; a is less than b; a is greater than b; a is less than or equal to b; a is greater than or equal to b. Under the \u201cSay\u201d column are the phrases: \u201ca is equal to b\u201d, \u201ca is not equal to b\u201d, \u201ca is less than b\u201d, \u201ca is greater than b\u201d, \u201ca is less than or equal to b\u201d, and \u201ca is greater than or equal to b\u201d.\">\n<thead>\n<tr valign=\"top\">\n<th data-align=\"center\">Algebraic Notation<\/th>\n<th data-align=\"center\">Say<\/th>\n<\/tr>\n<\/thead>\n<tbody>\n<tr valign=\"top\">\n<td data-align=\"left\">\\(a=b\\)<\/td>\n<td data-align=\"left\">\\(a\\) is equal to \\(b\\)<\/td>\n<\/tr>\n<tr valign=\"top\">\n<td data-align=\"left\">\\(a\\ne b\\)<\/td>\n<td data-align=\"left\">\\(a\\) is not equal to \\(b\\)<\/td>\n<\/tr>\n<tr valign=\"top\">\n<td data-align=\"left\">\\(a\\) &lt; \\(b\\)<\/td>\n<td data-align=\"left\">\\(a\\) is less than \\(b\\)<\/td>\n<\/tr>\n<tr valign=\"top\">\n<td data-align=\"left\">\\(a\\) &gt; \\(b\\)<\/td>\n<td data-align=\"left\">\\(a\\) is greater than \\(b\\)<\/td>\n<\/tr>\n<tr valign=\"top\">\n<td data-align=\"left\">\\(a\\le b\\)<\/td>\n<td data-align=\"left\">\\(a\\) is less than or equal to \\(b\\)<\/td>\n<\/tr>\n<tr valign=\"top\">\n<td data-align=\"left\">\\(a\\ge b\\)<\/td>\n<td data-align=\"left\">\\(a\\) is greater than or equal to \\(b\\)<\/td>\n<\/tr>\n<\/tbody>\n<\/table>\n<ul id=\"eip-910\">\n \t<li><strong>Exponential Notation<\/strong>\n<ul id=\"eip-id1168266330675\">\n \t<li>For any expression \\({a}^{n}\\) is a factor multiplied by itself \\(n\\) times, if \\(n\\) is a positive integer.<\/li>\n \t<li>\\({a}^{n}\\) means multiply \\(n\\) factors of \\(a\\)\n<span id=\"eip-id1168266330736\" data-type=\"media\" data-alt=\"..\"><img class=\"aligncenter\" src=\"https:\/\/opentextbc.ca\/accessibilitytoolkit\/wp-content\/uploads\/sites\/333\/2021\/03\/CNX_BMath_Figure_02_01_020_img-1.jpg\" alt=\"..\" data-media-type=\"image\/jpg\"><\/span><\/li>\n \t<li>The expression of \\({a}^{n}\\) is read \\(a\\) to the \\(n\\text{th}\\) power.<\/li>\n<\/ul>\n<\/li>\n<\/ul>\n<p id=\"eip-908\"><strong>Order of Operations<\/strong> When simplifying mathematical expressions perform the operations in the following order:<\/p>\n\n<ul id=\"eip-id1168264820124\" data-bullet-style=\"bullet\">\n \t<li>Parentheses and other Grouping Symbols: Simplify all expressions inside the parentheses or other grouping symbols, working on the innermost parentheses first.<\/li>\n \t<li>Exponents: Simplify all expressions with exponents.<\/li>\n \t<li>Multiplication and Division: Perform all multiplication and division in order from left to right. These operations have equal priority.<\/li>\n \t<li>Addition and Subtraction: Perform all addition and subtraction in order from left to right. These operations have equal priority.<\/li>\n<\/ul>\n<h1>Glossary<\/h1>\n<div class=\"textbox shaded\">\n<dl id=\"fs-id2645686\">\n \t<dt>expressions<\/dt>\n \t<dd id=\"fs-id2645692\">An expression is a number, a variable, or a combination of numbers and variables and operation symbols.<\/dd>\n<\/dl>\n<dl id=\"fs-id2645696\">\n \t<dt>equation<\/dt>\n \t<dd id=\"fs-id2645701\">An equation is made up of two expressions connected by an equal sign.<\/dd>\n<\/dl>\n<\/div>\n<h1>Practice Makes Perfect<\/h1>\n<h2>Use Variables and Algebraic Symbols<\/h2>\nIn the following exercises, translate from algebraic notation to words.\n<table style=\"border-collapse: collapse; width: 100%; height: 135px;\" border=\"0\">\n<tbody>\n<tr style=\"height: 15px;\">\n<td style=\"width: 50%; height: 15px;\">1. \\(16-9\\)<\/td>\n<td style=\"width: 50%; height: 15px;\">2. \\(25-7\\)<\/td>\n<\/tr>\n<tr style=\"height: 15px;\">\n<td style=\"width: 50%; height: 15px;\">3. \\(5 \\cdot 6\\)<\/td>\n<td style=\"width: 50%; height: 15px;\">4. \\(3 \\cdot 9\\)<\/td>\n<\/tr>\n<tr style=\"height: 15px;\">\n<td style=\"width: 50%; height: 15px;\">5. \\(28 \\div 4\\)<\/td>\n<td style=\"width: 50%; height: 15px;\"><span style=\"text-align: initial; background-color: initial;\">6. \\(45 \\div 5\\)<\/span><\/td>\n<\/tr>\n<tr style=\"height: 15px;\">\n<td style=\"width: 50%; height: 15px;\">7. \\(x+8\\)<\/td>\n<td style=\"width: 50%; height: 15px;\">8. \\(x+11\\)<\/td>\n<\/tr>\n<tr style=\"height: 15px;\">\n<td style=\"width: 50%; height: 15px;\">9. \\(\\left(2\\right)\\left(7\\right)\\)<\/td>\n<td style=\"width: 50%; height: 15px;\">10. \\(\\left(4\\right)\\left(8\\right)\\)<\/td>\n<\/tr>\n<tr style=\"height: 15px;\">\n<td style=\"width: 50%; height: 15px;\">11. \\(14\\) &lt; \\(21\\)<\/td>\n<td style=\"width: 50%; height: 15px;\">12. \\(17\\) &lt; \\(35\\)<\/td>\n<\/tr>\n<tr style=\"height: 15px;\">\n<td style=\"width: 50%; height: 15px;\">13. \\(36\\ge 19\\)<\/td>\n<td style=\"width: 50%; height: 15px;\">14. \\(42\\ge 27\\)<\/td>\n<\/tr>\n<tr style=\"height: 15px;\">\n<td style=\"width: 50%; height: 15px;\">15. \\(3n=24\\)<\/td>\n<td style=\"width: 50%; height: 15px;\">16. \\(6n=36\\)<\/td>\n<\/tr>\n<tr style=\"height: 15px;\">\n<td style=\"width: 50%; height: 15px;\">17. \\(y-1\\) &gt; \\(6\\)<\/td>\n<td style=\"width: 50%; height: 15px;\">18. \\(y-4\\) &gt; \\(8\\)<\/td>\n<\/tr>\n<tr>\n<td style=\"width: 50%;\">19. \\(2\\le 18 \\div 6\\)<\/td>\n<td style=\"width: 50%;\">20. \\(3\\le 20 \\div 4\\)<\/td>\n<\/tr>\n<tr>\n<td style=\"width: 50%;\">21. \\(a\\ne 7\\cdot 4\\)<\/td>\n<td style=\"width: 50%;\">22. \\(a\\ne 1\\cdot 12\\)<\/td>\n<\/tr>\n<\/tbody>\n<\/table>\n<h2>Identify Expressions and Equations<\/h2>\n<p id=\"eip-578\">In the following exercises, determine if each is an expression or an equation.<\/p>\n\n<table style=\"border-collapse: collapse; width: 100%; height: 90px;\" border=\"0\">\n<tbody>\n<tr style=\"height: 15px;\">\n<td style=\"width: 50%; height: 15px;\">23. \\(9\\cdot 6=54\\)<\/td>\n<td style=\"width: 50%; height: 15px;\">24. \\(7\\cdot 9=63\\)<\/td>\n<\/tr>\n<tr style=\"height: 15px;\">\n<td style=\"width: 50%; height: 15px;\">25. \\(5\\cdot 4+3\\)<\/td>\n<td style=\"width: 50%; height: 15px;\">26. \\(6\\cdot 3+5\\)<\/td>\n<\/tr>\n<tr style=\"height: 15px;\">\n<td style=\"width: 50%; height: 15px;\">27. \\(x+7\\)<\/td>\n<td style=\"width: 50%; height: 15px;\">28. \\(x+9\\)<\/td>\n<\/tr>\n<tr style=\"height: 15px;\">\n<td style=\"width: 50%; height: 15px;\">29. \\(y-5=25\\)<\/td>\n<td style=\"width: 50%; height: 15px;\">30. \\(y-8=32\\)<\/td>\n<\/tr>\n<\/tbody>\n<\/table>\n<h2>Simplify Expressions with Exponents<\/h2>\n<p id=\"eip-595\">In the following exercises, write in exponential form.<\/p>\n\n<table style=\"border-collapse: collapse; width: 100%;\" border=\"0\">\n<tbody>\n<tr>\n<td style=\"width: 50%;\">31. \\(3\\cdot 3\\cdot 3\\cdot 3\\cdot 3\\cdot 3\\cdot 3\\)<\/td>\n<td style=\"width: 50%;\">32. \\(4\\cdot 4\\cdot 4\\cdot 4\\cdot 4\\cdot 4\\)<\/td>\n<\/tr>\n<tr>\n<td style=\"width: 50%;\">33. \\(x\\cdot x\\cdot x\\cdot x\\cdot x\\)<\/td>\n<td style=\"width: 50%;\">34. \\(y\\cdot y\\cdot y\\cdot y\\cdot y\\cdot y\\)<\/td>\n<\/tr>\n<\/tbody>\n<\/table>\n<p id=\"fs-id4333539\">In the following exercises, write in expanded form.<\/p>\n\n<table style=\"border-collapse: collapse; width: 100%;\" border=\"0\">\n<tbody>\n<tr>\n<td style=\"width: 50%;\">35. \\({5}^{3}\\)<\/td>\n<td style=\"width: 50%;\">36. \\({8}^{3}\\)<\/td>\n<\/tr>\n<tr>\n<td style=\"width: 50%;\">37. \\({2}^{8}\\)<\/td>\n<td style=\"width: 50%;\">38. \\({10}^{5}\\)<\/td>\n<\/tr>\n<\/tbody>\n<\/table>\n<h2>Simplify Expressions Using the Order of Operations<\/h2>\n<p id=\"eip-246\">In the following exercises, simplify.<\/p>\n\n<table style=\"border-collapse: collapse; width: 100%; height: 274px;\" border=\"0\">\n<tbody>\n<tr style=\"height: 109px;\">\n<td style=\"width: 50%; height: 109px;\">39.\n\na.\\(\\phantom{\\rule{0.2em}{0ex}}3+8\\cdot 5\\phantom{\\rule{0.2em}{0ex}}\\phantom{\\rule{0.4em}{0ex}}\\)\n\nb.\\(\\phantom{\\rule{0.2em}{0ex}}\\text{(3+8)}\\cdot \\text{5}\\)<\/td>\n<td style=\"width: 50%; height: 109px;\">40.\n\na.\\(\\phantom{\\rule{0.2em}{0ex}}2+6\\cdot 3\\phantom{\\rule{0.2em}{0ex}}\\phantom{\\rule{0.4em}{0ex}}\\)\n\nb.\\(\\phantom{\\rule{0.2em}{0ex}}\\text{(2+6)}\\cdot \\text{3}\\)<\/td>\n<\/tr>\n<tr style=\"height: 15px;\">\n<td style=\"width: 50%; height: 15px;\">41. \\({2}^{3}-12 \\div \\left(9-5\\right)\\)<\/td>\n<td style=\"width: 50%; height: 15px;\">42. \\({3}^{2}-18\\div \\left(11-5\\right)\\)<\/td>\n<\/tr>\n<tr style=\"height: 15px;\">\n<td style=\"width: 50%; height: 15px;\">43. \\(3\\cdot 8+5\\cdot 2\\)<\/td>\n<td style=\"width: 50%; height: 15px;\">44. \\(4\\cdot 7+3\\cdot 5\\)<\/td>\n<\/tr>\n<tr style=\"height: 15px;\">\n<td style=\"width: 50%; height: 15px;\">45. \\(2+8\\left(6+1\\right)\\)<\/td>\n<td style=\"width: 50%; height: 15px;\">46. \\(4+6\\left(3+6\\right)\\)<\/td>\n<\/tr>\n<tr style=\"height: 15px;\">\n<td style=\"width: 50%; height: 15px;\">47. \\(4\\cdot 12\/8\\)<\/td>\n<td style=\"width: 50%; height: 15px;\">48. \\(2\\cdot 36\/6\\)<\/td>\n<\/tr>\n<tr style=\"height: 15px;\">\n<td style=\"width: 50%; height: 15px;\">49. \\(6+10\/2+2\\)<\/td>\n<td style=\"width: 50%; height: 15px;\">50. \\(9+12\/3+4\\)<\/td>\n<\/tr>\n<tr style=\"height: 15px;\">\n<td style=\"width: 50%; height: 15px;\">51. \\(\\left(6+10\\right)\\div \\left(2+2\\right)\\)<\/td>\n<td style=\"width: 50%; height: 15px;\">52. \\(\\left(9+12\\right)\\div \\left(3+4\\right)\\)<\/td>\n<\/tr>\n<tr style=\"height: 15px;\">\n<td style=\"width: 50%; height: 15px;\">53. \\(20\\div 4+6\\cdot5\\)<\/td>\n<td style=\"width: 50%; height: 15px;\">54. \\(33\\div 3+8\\cdot2\\)<\/td>\n<\/tr>\n<tr style=\"height: 15px;\">\n<td style=\"width: 50%; height: 15px;\">55. \\(20\\div \\left(4+6\\right)\\cdot 5\\)<\/td>\n<td style=\"width: 50%; height: 15px;\">56. \\(33\\div \\left(3+8\\right)\\cdot 2\\)<\/td>\n<\/tr>\n<tr style=\"height: 15px;\">\n<td style=\"width: 50%; height: 15px;\">57. \\({4}^{2}+{5}^{2}\\)<\/td>\n<td style=\"width: 50%; height: 15px;\">58. \\({3}^{2}+{7}^{2}\\)<\/td>\n<\/tr>\n<tr style=\"height: 15px;\">\n<td style=\"width: 50%; height: 15px;\">59. \\({\\left(4+5\\right)}^{2}\\)<\/td>\n<td style=\"width: 50%; height: 15px;\">60. \\({\\left(3+7\\right)}^{2}\\)<\/td>\n<\/tr>\n<tr style=\"height: 15px;\">\n<td style=\"width: 50%; height: 15px;\">61. \\(3\\left(1+9\\cdot 6\\right)-{4}^{2}\\)<\/td>\n<td style=\"width: 50%; height: 15px;\">62. \\(5\\left(2+8\\cdot 4\\right)-{7}^{2}\\)<\/td>\n<\/tr>\n<tr>\n<td style=\"width: 50%;\">63. \\(2\\left[1+3\\left(10-2\\right)\\right]\\)<\/td>\n<td style=\"width: 50%;\"><span style=\"text-align: initial; background-color: initial;\">64. \\(5\\left[2+4\\left(3-2\\right)\\right]\\)<\/span><\/td>\n<\/tr>\n<\/tbody>\n<\/table>\n<h2>Everyday Math<\/h2>\n<table style=\"border-collapse: collapse; width: 100%;\" border=\"0\">\n<tbody>\n<tr>\n<td style=\"width: 50%;\">\n<p id=\"fs-id2757048\"><strong data-effect=\"bold\">65. Basketball<\/strong> In the 2014 NBA playoffs, the San Antonio Spurs beat the Miami Heat. The table below shows the heights of the starters on each team. Use this table to fill in the appropriate symbol ( = ,&lt;,\u00a0 &gt;).<\/p>\n\n<table id=\"fs-id2757058\" class=\"unnumbered\" summary=\"This table has six rows and five columns. The first row is a header row and it labels each column. The first column is labeled \u201cSpurs\u201d, the next \u201cHeight\u201d, the third column is blank to distinguish the next column labeled \u201cHeat\u201d and the last column is also labeled \u201cHeight\u201d. Under the \u201cSpurs\u201d column are names of players: Tim Duncan, Boris Diaw, Kawhi Leonard, Tony Parker, and Danny Green. Under the \u201cHeight\u201d column are the heights of the five spurs players: eighty-three inches, eighty inches, seventy-nine inches, seventy four inches and seventy-eight inches. Under the \u201cHeat\u201d column are names of players: Rashard Lewis, LeBron James, Chris Bosh, Dwayne Wade, and Ray Allen. Under the \u201cHeight\u201d column are the heights of the five Heat players: eighty-two inches, eighty inches, eighty-three inches, seventy-six inches and seventy-seven inches.\" data-label=\"\">\n<thead>\n<tr valign=\"top\">\n<th data-align=\"center\"><strong data-effect=\"bold\">Spurs<\/strong><\/th>\n<th data-align=\"center\"><strong data-effect=\"bold\">Height<\/strong><\/th>\n<th><\/th>\n<th data-align=\"center\"><strong data-effect=\"bold\">Heat<\/strong><\/th>\n<th data-align=\"center\"><strong data-effect=\"bold\">Height<\/strong><\/th>\n<\/tr>\n<\/thead>\n<tbody>\n<tr valign=\"top\">\n<td data-align=\"left\">Tim Duncan<\/td>\n<td data-align=\"center\">\\(83''\\)<\/td>\n<td rowspan=\"6\"><\/td>\n<td data-align=\"left\">Rashard Lewis<\/td>\n<td data-align=\"center\">\\(82''\\)<\/td>\n<\/tr>\n<tr valign=\"top\">\n<td data-align=\"left\">Boris Diaw<\/td>\n<td data-align=\"center\">\\(80''\\)<\/td>\n<td data-align=\"left\">LeBron James<\/td>\n<td data-align=\"center\">\\(80''\\)<\/td>\n<\/tr>\n<tr valign=\"top\">\n<td data-align=\"left\">Kawhi Leonard<\/td>\n<td data-align=\"center\">\\(79''\\)<\/td>\n<td data-align=\"left\">Chris Bosh<\/td>\n<td data-align=\"center\">\\(83''\\)<\/td>\n<\/tr>\n<tr valign=\"top\">\n<td data-align=\"left\">Tony Parker<\/td>\n<td data-align=\"center\">\\(74''\\)<\/td>\n<td data-align=\"left\">Dwyane Wade<\/td>\n<td data-align=\"center\">\\(76''\\)<\/td>\n<\/tr>\n<tr valign=\"top\">\n<td data-align=\"left\">Danny Green<\/td>\n<td data-align=\"center\">\\(78''\\)<\/td>\n<td data-align=\"left\">Ray Allen<\/td>\n<td data-align=\"center\">\\(77''\\)<\/td>\n<\/tr>\n<\/tbody>\n<\/table>\n<ol id=\"eip-id1168466360092\" class=\"circled\" type=\"a\">\n \t<li>Height of Tim Duncan____Height of Rashard Lewis<\/li>\n \t<li>Height of Boris Diaw____Height of LeBron James<\/li>\n \t<li>Height of Kawhi Leonard____Height of Chris Bosh<\/li>\n \t<li>Height of Tony Parker____Height of Dwyane Wade<\/li>\n \t<li>Height of Danny Green____Height of Ray Allen<\/li>\n<\/ol>\n<\/td>\n<td style=\"width: 50%;\">\n<p id=\"fs-id2935753\"><strong data-effect=\"bold\">66. Elevation<\/strong> In Colorado there are more than \\(50\\) mountains with an elevation of over \\(14,000\\phantom{\\rule{0.2em}{0ex}}\\text{feet.}\\) The table shows the ten tallest. Use this table to fill in the appropriate inequality symbol.<\/p>\n\n<table id=\"fs-id2935762\" class=\"unnumbered\" summary=\"This table has eleven rows and two columns. The first row is a header row and labels the first column \u201cMountain\u201d and the second column \u201cElevation\u201d. Under the \u201cMountain\u201d column are the mountain names: Mt. Elbert, Mt Massive, Mt. Harvard, Blanca Peak, La Plata Peak, Uncompahgre Peak, Crestone Peak, Mt. Lincoln, Grays Peak and Mt. Antero. Under the \u201cElevation\u201d column are the heights: 14,433 feet, 14,421 feet, 14,420 feet, 14,345 feet, 14,336 feet, 14,309 feet, 14,294 feet, 14,286 feet, 14,270 feet, and 14269 feet.\" data-label=\"\">\n<thead>\n<tr valign=\"top\">\n<th data-align=\"left\">Mountain<\/th>\n<th data-align=\"left\">Elevation<\/th>\n<\/tr>\n<\/thead>\n<tbody>\n<tr valign=\"top\">\n<td data-align=\"left\">Mt. Elbert<\/td>\n<td data-align=\"left\">\\(14,433'\\)<\/td>\n<\/tr>\n<tr valign=\"top\">\n<td data-align=\"left\">Mt. Massive<\/td>\n<td data-align=\"left\">\\(14,421'\\)<\/td>\n<\/tr>\n<tr valign=\"top\">\n<td data-align=\"left\">Mt. Harvard<\/td>\n<td data-align=\"left\">\\(14,420'\\)<\/td>\n<\/tr>\n<tr valign=\"top\">\n<td data-align=\"left\">Blanca Peak<\/td>\n<td data-align=\"left\">\\(14,345'\\)<\/td>\n<\/tr>\n<tr valign=\"top\">\n<td data-align=\"left\">La Plata Peak<\/td>\n<td data-align=\"left\">\\(14,336'\\)<\/td>\n<\/tr>\n<tr valign=\"top\">\n<td data-align=\"left\">Uncompahgre Peak<\/td>\n<td data-align=\"left\">\\(14,309'\\)<\/td>\n<\/tr>\n<tr valign=\"top\">\n<td data-align=\"left\">Crestone Peak<\/td>\n<td data-align=\"left\">\\(14,294'\\)<\/td>\n<\/tr>\n<tr valign=\"top\">\n<td data-align=\"left\">Mt. Lincoln<\/td>\n<td data-align=\"left\">\\(14,286'\\)<\/td>\n<\/tr>\n<tr valign=\"top\">\n<td data-align=\"left\">Grays Peak<\/td>\n<td data-align=\"left\">\\(14,270'\\)<\/td>\n<\/tr>\n<tr valign=\"top\">\n<td data-align=\"left\">Mt. Antero<\/td>\n<td data-align=\"left\">\\(14,269'\\)<\/td>\n<\/tr>\n<\/tbody>\n<\/table>\n<ol id=\"eip-id1168468729595\" class=\"circled\" type=\"a\">\n \t<li>Elevation of La Plata Peak____Elevation of Mt. Antero<\/li>\n \t<li>Elevation of Blanca Peak____Elevation of Mt. Elbert<\/li>\n \t<li>Elevation of Gray\u2019s Peak____Elevation of Mt. Lincoln<\/li>\n \t<li>Elevation of Mt. Massive____Elevation of Crestone Peak<\/li>\n \t<li>Elevation of Mt. Harvard____Elevation of Uncompahgre Peak<\/li>\n<\/ol>\n<\/td>\n<\/tr>\n<\/tbody>\n<\/table>\n<h2>Writing Exercises<\/h2>\n<table style=\"border-collapse: collapse; width: 100%;\" border=\"0\">\n<tbody>\n<tr>\n<td style=\"width: 50%;\">67.Explain the difference between an expression and an equation.<\/td>\n<td style=\"width: 50%;\">68. Why is it important to use the order of operations to simplify an expression?<\/td>\n<\/tr>\n<\/tbody>\n<\/table>\n<h1>Answers<\/h1>\n<table style=\"border-collapse: collapse; width: 100%;\" border=\"0\">\n<tbody>\n<tr>\n<td style=\"width: 33.3333%;\">1. 16 minus 9, the difference of sixteen and nine<\/td>\n<td style=\"width: 33.3333%;\">3. 5 times 6, the product of five and six<\/td>\n<td style=\"width: 33.3333%;\">5. 28 divided by 4, the quotient of twenty-eight and four<\/td>\n<\/tr>\n<tr>\n<td style=\"width: 33.3333%;\">7<em data-effect=\"italics\">. x<\/em> plus 8, the sum of <em data-effect=\"italics\">x<\/em> and eight<\/td>\n<td style=\"width: 33.3333%;\">9. 2 times 7, the product of two and seven<\/td>\n<td style=\"width: 33.3333%;\">11. fourteen is less than twenty-one<\/td>\n<\/tr>\n<tr>\n<td style=\"width: 33.3333%;\">13. thirty-six is greater than or equal to nineteen<\/td>\n<td style=\"width: 33.3333%;\">15. 3 times n equals 24, the product of three and n equals twenty-four<\/td>\n<td style=\"width: 33.3333%;\">17.<em data-effect=\"italics\"> y<\/em> minus 1 is greater than 6, the difference of <em data-effect=\"italics\">y<\/em> and one is greater than six<\/td>\n<\/tr>\n<tr>\n<td style=\"width: 33.3333%;\">19. 2 is less than or equal to 18 divided by 6; 2 is less than or equal to the quotient of eighteen and six<\/td>\n<td style=\"width: 33.3333%;\">21<em data-effect=\"italics\">. a<\/em> is not equal to 7 times 4, <em data-effect=\"italics\">a<\/em> is not equal to the product of seven and four<\/td>\n<td style=\"width: 33.3333%;\">23. equation<\/td>\n<\/tr>\n<tr>\n<td style=\"width: 33.3333%;\">25. expression<\/td>\n<td style=\"width: 33.3333%;\">27. expression<\/td>\n<td style=\"width: 33.3333%;\">29. equation<\/td>\n<\/tr>\n<tr>\n<td style=\"width: 33.3333%;\">31. 3<sup>7<\/sup><\/td>\n<td style=\"width: 33.3333%;\">33<em data-effect=\"italics\">. x<\/em><sup>5<\/sup><\/td>\n<td style=\"width: 33.3333%;\">35. 125<\/td>\n<\/tr>\n<tr>\n<td style=\"width: 33.3333%;\">37. 256<\/td>\n<td style=\"width: 33.3333%;\">39.\n\na. 43\n\nb. 55<\/td>\n<td style=\"width: 33.3333%;\">41. 5<\/td>\n<\/tr>\n<tr>\n<td style=\"width: 33.3333%;\">43. 34<\/td>\n<td style=\"width: 33.3333%;\">45. 58<\/td>\n<td style=\"width: 33.3333%;\">47. 6<\/td>\n<\/tr>\n<tr>\n<td style=\"width: 33.3333%;\">49. 13<\/td>\n<td style=\"width: 33.3333%;\">51. 4<\/td>\n<td style=\"width: 33.3333%;\">53. 35<\/td>\n<\/tr>\n<tr>\n<td style=\"width: 33.3333%;\">55. 10<\/td>\n<td style=\"width: 33.3333%;\">57. 41<\/td>\n<td style=\"width: 33.3333%;\">59. 81<\/td>\n<\/tr>\n<tr>\n<td style=\"width: 33.3333%;\">61. 149<\/td>\n<td style=\"width: 33.3333%;\">63. 50<\/td>\n<td style=\"width: 33.3333%;\">65. a. &gt; b. \\(=\\) c. &lt; d. &lt; e. &gt;<\/td>\n<\/tr>\n<tr>\n<td style=\"width: 33.3333%;\">67. Answer may vary.<\/td>\n<td style=\"width: 33.3333%;\"><\/td>\n<td style=\"width: 33.3333%;\"><\/td>\n<\/tr>\n<\/tbody>\n<\/table>\n<h1>Attributions<\/h1>\nThis chapter has been adapted from \u201cUse the Language of Algebra\u201d in <a href=\"https:\/\/openstax.org\/details\/books\/prealgebra-2e\"><em>Prealgebra<\/em><\/a> (OpenStax) by Lynn Marecek, MaryAnne Anthony-Smith, and Andrea Honeycutt Mathis, which is under a <a href=\"https:\/\/creativecommons.org\/licenses\/by\/4.0\/\">CC BY 4.0 Licence<\/a>. Adapted by Izabela Mazur. See the Copyright page for more information.","rendered":"<div class=\"textbox textbox--learning-objectives\">\n<header class=\"textbox__header\">\n<p class=\"textbox__title\">Learning Objectives<\/p>\n<\/header>\n<div class=\"textbox__content\">\n<p>By the end of this section, you will be able to:<\/p>\n<ul>\n<li>Use variables and algebraic symbols<\/li>\n<li>Identify expressions and equations<\/li>\n<li>Simplify expressions with exponents<\/li>\n<li>Simplify expressions using the order of operations<\/li>\n<\/ul>\n<\/div>\n<\/div>\n<h1>Use Variables and Algebraic Symbols<\/h1>\n<p id=\"fs-id2425891\">Greg and Alex have the same birthday, but they were born in different years. This year Greg is <img loading=\"lazy\" decoding=\"async\" src=\"https:\/\/opentextbc.ca\/introalgebra\/wp-content\/ql-cache\/quicklatex.com-930d01a5f622cee5952bab4752e56063_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"&#50;&#48;\" title=\"Rendered by QuickLaTeX.com\" height=\"12\" width=\"18\" style=\"vertical-align: 0px;\" \/> years old and Alex is <img loading=\"lazy\" decoding=\"async\" src=\"https:\/\/opentextbc.ca\/introalgebra\/wp-content\/ql-cache\/quicklatex.com-e554ca92166de4bd98acfbef8f678cd2_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"&#50;&#51;\" title=\"Rendered by QuickLaTeX.com\" height=\"12\" width=\"18\" style=\"vertical-align: 0px;\" \/>, so Alex is <img loading=\"lazy\" decoding=\"async\" src=\"https:\/\/opentextbc.ca\/introalgebra\/wp-content\/ql-cache\/quicklatex.com-4a1d3ea4963f568cabd97329456036b6_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"&#51;\" title=\"Rendered by QuickLaTeX.com\" height=\"12\" width=\"9\" style=\"vertical-align: 0px;\" \/> years older than Greg. When Greg was <img loading=\"lazy\" decoding=\"async\" src=\"https:\/\/opentextbc.ca\/introalgebra\/wp-content\/ql-cache\/quicklatex.com-40f7428479801bf4ef27a5149e9df526_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"&#49;&#50;\" title=\"Rendered by QuickLaTeX.com\" height=\"13\" width=\"16\" style=\"vertical-align: -1px;\" \/>, Alex was <img loading=\"lazy\" decoding=\"async\" src=\"https:\/\/opentextbc.ca\/introalgebra\/wp-content\/ql-cache\/quicklatex.com-b59223d2c162a0fdd163af8597f0845e_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"&#49;&#53;\" title=\"Rendered by QuickLaTeX.com\" height=\"14\" width=\"16\" style=\"vertical-align: -1px;\" \/>. When Greg is <img loading=\"lazy\" decoding=\"async\" src=\"https:\/\/opentextbc.ca\/introalgebra\/wp-content\/ql-cache\/quicklatex.com-6bff01d8c87d130da6950c561718ce13_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"&#51;&#53;\" title=\"Rendered by QuickLaTeX.com\" height=\"13\" width=\"17\" style=\"vertical-align: 0px;\" \/>, Alex will be <img loading=\"lazy\" decoding=\"async\" src=\"https:\/\/opentextbc.ca\/introalgebra\/wp-content\/ql-cache\/quicklatex.com-4d761d015714dab15099f98dec9a6f60_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"&#51;&#56;\" title=\"Rendered by QuickLaTeX.com\" height=\"12\" width=\"18\" style=\"vertical-align: 0px;\" \/>. No matter what Greg\u2019s age is, Alex\u2019s age will always be <img loading=\"lazy\" decoding=\"async\" src=\"https:\/\/opentextbc.ca\/introalgebra\/wp-content\/ql-cache\/quicklatex.com-4a1d3ea4963f568cabd97329456036b6_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"&#51;\" title=\"Rendered by QuickLaTeX.com\" height=\"12\" width=\"9\" style=\"vertical-align: 0px;\" \/> years more, right?<\/p>\n<p>In the language of algebra, we say that Greg\u2019s age and Alex\u2019s age are <span class=\"no-emphasis\" data-type=\"term\">variable<\/span> and the three is a <span class=\"no-emphasis\" data-type=\"term\">constant<\/span>. The ages change, or vary, so age is a variable. The <img loading=\"lazy\" decoding=\"async\" src=\"https:\/\/opentextbc.ca\/introalgebra\/wp-content\/ql-cache\/quicklatex.com-4a1d3ea4963f568cabd97329456036b6_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"&#51;\" title=\"Rendered by QuickLaTeX.com\" height=\"12\" width=\"9\" style=\"vertical-align: 0px;\" \/> years between them always stays the same, so the age difference is the constant.<\/p>\n<p id=\"fs-id1633275\">In algebra, letters of the alphabet are used to represent variables. Suppose we call Greg\u2019s age <img loading=\"lazy\" decoding=\"async\" src=\"https:\/\/opentextbc.ca\/introalgebra\/wp-content\/ql-cache\/quicklatex.com-d208fd391fa57c168dc0f151de829fee_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"&#103;\" title=\"Rendered by QuickLaTeX.com\" height=\"12\" width=\"9\" style=\"vertical-align: -4px;\" \/>. Then we could use <img loading=\"lazy\" decoding=\"async\" src=\"https:\/\/opentextbc.ca\/introalgebra\/wp-content\/ql-cache\/quicklatex.com-74d1178e56bae429838cf72d578bc9bc_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"&#103;&#43;&#51;\" title=\"Rendered by QuickLaTeX.com\" height=\"16\" width=\"40\" style=\"vertical-align: -4px;\" \/> to represent Alex\u2019s age. See the table below.<\/p>\n<table id=\"fs-id2953912\" class=\"aligncenter\" summary=\"This table has five rows and two columns. The first row is a header row and is labeled \u201cGreg\u2019s age\u201d, the second \u201cAlex\u2019s age\u201d. Under the \u201cGreg\u2019s age\u201d column are the values: twelve, twenty, and thirty-five. The last row has the letter G. Under the \u201cAlex\u2019s age\u201d column are the values: fifteen, twenty-three, and thirty-eight. The last row is the letter g plus three.\">\n<thead>\n<tr valign=\"top\">\n<th style=\"text-align: center;\" scope=\"col\" data-align=\"center\">Greg\u2019s age<\/th>\n<th style=\"text-align: center;\" scope=\"col\" data-align=\"center\">Alex\u2019s age<\/th>\n<\/tr>\n<\/thead>\n<tbody>\n<tr valign=\"top\">\n<td style=\"text-align: center;\" data-align=\"center\"><img loading=\"lazy\" decoding=\"async\" src=\"https:\/\/opentextbc.ca\/introalgebra\/wp-content\/ql-cache\/quicklatex.com-40f7428479801bf4ef27a5149e9df526_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"&#49;&#50;\" title=\"Rendered by QuickLaTeX.com\" height=\"13\" width=\"16\" style=\"vertical-align: -1px;\" \/><\/td>\n<td style=\"text-align: center;\" data-align=\"center\"><img loading=\"lazy\" decoding=\"async\" src=\"https:\/\/opentextbc.ca\/introalgebra\/wp-content\/ql-cache\/quicklatex.com-b59223d2c162a0fdd163af8597f0845e_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"&#49;&#53;\" title=\"Rendered by QuickLaTeX.com\" height=\"14\" width=\"16\" style=\"vertical-align: -1px;\" \/><\/td>\n<\/tr>\n<tr valign=\"top\">\n<td style=\"text-align: center;\" data-align=\"center\"><img loading=\"lazy\" decoding=\"async\" src=\"https:\/\/opentextbc.ca\/introalgebra\/wp-content\/ql-cache\/quicklatex.com-930d01a5f622cee5952bab4752e56063_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"&#50;&#48;\" title=\"Rendered by QuickLaTeX.com\" height=\"12\" width=\"18\" style=\"vertical-align: 0px;\" \/><\/td>\n<td style=\"text-align: center;\" data-align=\"center\"><img loading=\"lazy\" decoding=\"async\" src=\"https:\/\/opentextbc.ca\/introalgebra\/wp-content\/ql-cache\/quicklatex.com-e554ca92166de4bd98acfbef8f678cd2_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"&#50;&#51;\" title=\"Rendered by QuickLaTeX.com\" height=\"12\" width=\"18\" style=\"vertical-align: 0px;\" \/><\/td>\n<\/tr>\n<tr valign=\"top\">\n<td style=\"text-align: center;\" data-align=\"center\"><img loading=\"lazy\" decoding=\"async\" src=\"https:\/\/opentextbc.ca\/introalgebra\/wp-content\/ql-cache\/quicklatex.com-6bff01d8c87d130da6950c561718ce13_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"&#51;&#53;\" title=\"Rendered by QuickLaTeX.com\" height=\"13\" width=\"17\" style=\"vertical-align: 0px;\" \/><\/td>\n<td style=\"text-align: center;\" data-align=\"center\"><img loading=\"lazy\" decoding=\"async\" src=\"https:\/\/opentextbc.ca\/introalgebra\/wp-content\/ql-cache\/quicklatex.com-4d761d015714dab15099f98dec9a6f60_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"&#51;&#56;\" title=\"Rendered by QuickLaTeX.com\" height=\"12\" width=\"18\" style=\"vertical-align: 0px;\" \/><\/td>\n<\/tr>\n<tr valign=\"top\">\n<td style=\"text-align: center;\" data-align=\"center\"><img loading=\"lazy\" decoding=\"async\" src=\"https:\/\/opentextbc.ca\/introalgebra\/wp-content\/ql-cache\/quicklatex.com-d208fd391fa57c168dc0f151de829fee_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"&#103;\" title=\"Rendered by QuickLaTeX.com\" height=\"12\" width=\"9\" style=\"vertical-align: -4px;\" \/><\/td>\n<td style=\"text-align: center;\" data-align=\"center\"><img loading=\"lazy\" decoding=\"async\" src=\"https:\/\/opentextbc.ca\/introalgebra\/wp-content\/ql-cache\/quicklatex.com-74d1178e56bae429838cf72d578bc9bc_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"&#103;&#43;&#51;\" title=\"Rendered by QuickLaTeX.com\" height=\"16\" width=\"40\" style=\"vertical-align: -4px;\" \/><\/td>\n<\/tr>\n<\/tbody>\n<\/table>\n<p id=\"fs-id2137950\">Letters are used to represent variables. Letters often used for variables are <img loading=\"lazy\" decoding=\"async\" src=\"https:\/\/opentextbc.ca\/introalgebra\/wp-content\/ql-cache\/quicklatex.com-d0677cc1ef8b048f8fab638c1b7c9f0d_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"&#120;&#44;&#121;&#44;&#97;&#44;&#98;&#44;&#92;&#116;&#101;&#120;&#116;&#123;&#97;&#110;&#100;&#125;&#92;&#112;&#104;&#97;&#110;&#116;&#111;&#109;&#123;&#92;&#114;&#117;&#108;&#101;&#123;&#48;&#46;&#50;&#101;&#109;&#125;&#123;&#48;&#101;&#120;&#125;&#125;&#99;\" title=\"Rendered by QuickLaTeX.com\" height=\"16\" width=\"108\" style=\"vertical-align: -4px;\" \/>.<\/p>\n<div id=\"fs-id2399231\" data-type=\"note\">\n<div data-type=\"title\">\n<div class=\"textbox textbox--key-takeaways\">\n<header class=\"textbox__header\">\n<p class=\"textbox__title\">Variables and Constants<\/p>\n<\/header>\n<div class=\"textbox__content\">\n<p id=\"fs-id2203250\">A variable is a letter that represents a number or quantity whose value may change.<\/p>\n<p id=\"fs-id1604743\">A constant is a number whose value always stays the same.<\/p>\n<\/div>\n<\/div>\n<\/div>\n<\/div>\n<p id=\"fs-id1722327\">To write algebraically, we need some symbols as well as numbers and variables. There are several types of symbols we will be using. In <a href=\"\/introalgebra\/chapter\/whole-numbers\/\">1.1 Whole Numbers<\/a>, we introduced the symbols for the four basic arithmetic <span class=\"no-emphasis\" data-type=\"term\">operations<\/span>: addition, subtraction, multiplication, and division. We will summarize them here, along with words we use for the operations and the result.<\/p>\n<table id=\"fs-id1891703\" style=\"width: 100%;\" summary=\"This table has five rows and four columns. The first row is a header row. Each column is labeled accordingly: the first is labeled \u201cOperation\u201d, the second \u201cNotation\u201d, the third \u201cSay\u201d and the last \u201cThe result is...\u201d. Under the \u201cOperation\u201d column are the words: addition, multiplication, subtraction and division. Under the \u201cNotation\u201d column are algebraic expressions. The first row shows the letter a, the plus symbol, and the letter b. The next row shows four algebraic expressions. The first is the letter a, dot multiplication symbol, and the letter b. The second expression is the letter a in parentheses and the letter b in parentheses. The third expression is the letter a in parentheses and the letter b. The fourth expression is the letter a and the letter b in parentheses. The next row shows the letter a, the minus symbol, and the letter b. The last row shows four algebraic expressions. The first is the letter a, division symbol, and the letter b. The second expression is the letter a, the backslash symbol and the letter b. The third expression is the letter a above the fraction bar and the letter b below the fraction bar. The fourth expression is the letter b outside the division bracket and the letter a inside the division bracket.\" data-label=\"\">\n<thead>\n<tr valign=\"top\">\n<th scope=\"col\" data-align=\"left\">Operation<\/th>\n<th scope=\"col\" data-align=\"left\">Notation<\/th>\n<th scope=\"col\" data-align=\"left\">Say:<\/th>\n<th scope=\"col\" data-align=\"left\">The result is\u2026<\/th>\n<\/tr>\n<\/thead>\n<tbody>\n<tr valign=\"top\">\n<td data-align=\"left\">Addition<\/td>\n<td data-align=\"left\"><img loading=\"lazy\" decoding=\"async\" src=\"https:\/\/opentextbc.ca\/introalgebra\/wp-content\/ql-cache\/quicklatex.com-38830949a60ce6786a6fdf6309482002_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"&#97;&#43;&#98;\" title=\"Rendered by QuickLaTeX.com\" height=\"15\" width=\"39\" style=\"vertical-align: -2px;\" \/><\/td>\n<td data-align=\"left\"><img loading=\"lazy\" decoding=\"async\" src=\"https:\/\/opentextbc.ca\/introalgebra\/wp-content\/ql-cache\/quicklatex.com-04ba1b81da8ae280d26d1991b56eec6d_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"&#97;&#92;&#112;&#104;&#97;&#110;&#116;&#111;&#109;&#123;&#92;&#114;&#117;&#108;&#101;&#123;&#48;&#46;&#50;&#101;&#109;&#125;&#123;&#48;&#101;&#120;&#125;&#125;&#92;&#116;&#101;&#120;&#116;&#123;&#112;&#108;&#117;&#115;&#125;&#92;&#112;&#104;&#97;&#110;&#116;&#111;&#109;&#123;&#92;&#114;&#117;&#108;&#101;&#123;&#48;&#46;&#50;&#101;&#109;&#125;&#123;&#48;&#101;&#120;&#125;&#125;&#98;\" title=\"Rendered by QuickLaTeX.com\" height=\"16\" width=\"56\" style=\"vertical-align: -3px;\" \/><\/td>\n<td data-align=\"left\">the sum of <img loading=\"lazy\" decoding=\"async\" src=\"https:\/\/opentextbc.ca\/introalgebra\/wp-content\/ql-cache\/quicklatex.com-5c53d6ebabdbcfa4e107550ea60b1b19_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"&#97;\" title=\"Rendered by QuickLaTeX.com\" height=\"8\" width=\"9\" style=\"vertical-align: 0px;\" \/> and <img loading=\"lazy\" decoding=\"async\" src=\"https:\/\/opentextbc.ca\/introalgebra\/wp-content\/ql-cache\/quicklatex.com-f56d50c26583f9a035ff6b4e3c0ca5c0_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"&#98;\" title=\"Rendered by QuickLaTeX.com\" height=\"13\" width=\"8\" style=\"vertical-align: 0px;\" \/><\/td>\n<\/tr>\n<tr valign=\"top\">\n<td data-align=\"left\">Subtraction<\/td>\n<td data-align=\"left\"><img loading=\"lazy\" decoding=\"async\" src=\"https:\/\/opentextbc.ca\/introalgebra\/wp-content\/ql-cache\/quicklatex.com-b644d18119c5701b308f883bd50656d9_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"&#97;&#45;&#98;\" title=\"Rendered by QuickLaTeX.com\" height=\"13\" width=\"39\" style=\"vertical-align: 0px;\" \/><\/td>\n<td data-align=\"left\"><img loading=\"lazy\" decoding=\"async\" src=\"https:\/\/opentextbc.ca\/introalgebra\/wp-content\/ql-cache\/quicklatex.com-d626cdf4753df75818707f16d7b6dc4e_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"&#97;&#92;&#112;&#104;&#97;&#110;&#116;&#111;&#109;&#123;&#92;&#114;&#117;&#108;&#101;&#123;&#48;&#46;&#50;&#101;&#109;&#125;&#123;&#48;&#101;&#120;&#125;&#125;&#92;&#116;&#101;&#120;&#116;&#123;&#109;&#105;&#110;&#117;&#115;&#125;&#92;&#112;&#104;&#97;&#110;&#116;&#111;&#109;&#123;&#92;&#114;&#117;&#108;&#101;&#123;&#48;&#46;&#50;&#101;&#109;&#125;&#123;&#48;&#101;&#120;&#125;&#125;&#98;\" title=\"Rendered by QuickLaTeX.com\" height=\"13\" width=\"70\" style=\"vertical-align: 0px;\" \/><\/td>\n<td data-align=\"left\">the difference of <img loading=\"lazy\" decoding=\"async\" src=\"https:\/\/opentextbc.ca\/introalgebra\/wp-content\/ql-cache\/quicklatex.com-5c53d6ebabdbcfa4e107550ea60b1b19_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"&#97;\" title=\"Rendered by QuickLaTeX.com\" height=\"8\" width=\"9\" style=\"vertical-align: 0px;\" \/> and <img loading=\"lazy\" decoding=\"async\" src=\"https:\/\/opentextbc.ca\/introalgebra\/wp-content\/ql-cache\/quicklatex.com-f56d50c26583f9a035ff6b4e3c0ca5c0_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"&#98;\" title=\"Rendered by QuickLaTeX.com\" height=\"13\" width=\"8\" style=\"vertical-align: 0px;\" \/><\/td>\n<\/tr>\n<tr valign=\"top\">\n<td data-align=\"left\">Multiplication<\/td>\n<td data-align=\"left\"><img loading=\"lazy\" decoding=\"async\" src=\"https:\/\/opentextbc.ca\/introalgebra\/wp-content\/ql-cache\/quicklatex.com-7c63a9888ac8ae036ae37309dee0451c_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"&#97;&#92;&#99;&#100;&#111;&#116;&#32;&#98;&#44;&#92;&#108;&#101;&#102;&#116;&#40;&#97;&#92;&#114;&#105;&#103;&#104;&#116;&#41;&#92;&#108;&#101;&#102;&#116;&#40;&#98;&#92;&#114;&#105;&#103;&#104;&#116;&#41;&#44;&#92;&#108;&#101;&#102;&#116;&#40;&#97;&#92;&#114;&#105;&#103;&#104;&#116;&#41;&#98;&#44;&#97;&#92;&#108;&#101;&#102;&#116;&#40;&#98;&#92;&#114;&#105;&#103;&#104;&#116;&#41;\" title=\"Rendered by QuickLaTeX.com\" height=\"19\" width=\"171\" style=\"vertical-align: -5px;\" \/><\/td>\n<td data-align=\"left\"><img loading=\"lazy\" decoding=\"async\" src=\"https:\/\/opentextbc.ca\/introalgebra\/wp-content\/ql-cache\/quicklatex.com-6e4e96a7e0e7b4b2dc622423b51fc66b_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"&#97;&#92;&#112;&#104;&#97;&#110;&#116;&#111;&#109;&#123;&#92;&#114;&#117;&#108;&#101;&#123;&#48;&#46;&#50;&#101;&#109;&#125;&#123;&#48;&#101;&#120;&#125;&#125;&#92;&#116;&#101;&#120;&#116;&#123;&#116;&#105;&#109;&#101;&#115;&#125;&#92;&#112;&#104;&#97;&#110;&#116;&#111;&#109;&#123;&#92;&#114;&#117;&#108;&#101;&#123;&#48;&#46;&#50;&#101;&#109;&#125;&#123;&#48;&#101;&#120;&#125;&#125;&#98;\" title=\"Rendered by QuickLaTeX.com\" height=\"13\" width=\"66\" style=\"vertical-align: 0px;\" \/><\/td>\n<td data-align=\"left\">The product of <img loading=\"lazy\" decoding=\"async\" src=\"https:\/\/opentextbc.ca\/introalgebra\/wp-content\/ql-cache\/quicklatex.com-5c53d6ebabdbcfa4e107550ea60b1b19_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"&#97;\" title=\"Rendered by QuickLaTeX.com\" height=\"8\" width=\"9\" style=\"vertical-align: 0px;\" \/> and <img loading=\"lazy\" decoding=\"async\" src=\"https:\/\/opentextbc.ca\/introalgebra\/wp-content\/ql-cache\/quicklatex.com-f56d50c26583f9a035ff6b4e3c0ca5c0_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"&#98;\" title=\"Rendered by QuickLaTeX.com\" height=\"13\" width=\"8\" style=\"vertical-align: 0px;\" \/><\/td>\n<\/tr>\n<tr valign=\"top\">\n<td data-align=\"left\">Division<\/td>\n<td data-align=\"left\"><img loading=\"lazy\" decoding=\"async\" src=\"https:\/\/opentextbc.ca\/introalgebra\/wp-content\/ql-cache\/quicklatex.com-1dc71412a2af9fb0a0b48f86c64005ed_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"&#97;&#92;&#100;&#105;&#118;&#32;&#98;&#44;&#97;&#47;&#98;&#44;&#92;&#112;&#104;&#97;&#110;&#116;&#111;&#109;&#123;&#92;&#114;&#117;&#108;&#101;&#123;&#48;&#46;&#50;&#101;&#109;&#125;&#123;&#48;&#101;&#120;&#125;&#125;&#92;&#102;&#114;&#97;&#99;&#123;&#97;&#125;&#123;&#98;&#125;&#44;&#98;&#92;&#111;&#118;&#101;&#114;&#108;&#105;&#110;&#101;&#123;&#41;&#97;&#125;\" title=\"Rendered by QuickLaTeX.com\" height=\"22\" width=\"128\" style=\"vertical-align: -6px;\" \/><\/td>\n<td data-align=\"left\"><img loading=\"lazy\" decoding=\"async\" src=\"https:\/\/opentextbc.ca\/introalgebra\/wp-content\/ql-cache\/quicklatex.com-5c53d6ebabdbcfa4e107550ea60b1b19_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"&#97;\" title=\"Rendered by QuickLaTeX.com\" height=\"8\" width=\"9\" style=\"vertical-align: 0px;\" \/> divided by <img loading=\"lazy\" decoding=\"async\" src=\"https:\/\/opentextbc.ca\/introalgebra\/wp-content\/ql-cache\/quicklatex.com-f56d50c26583f9a035ff6b4e3c0ca5c0_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"&#98;\" title=\"Rendered by QuickLaTeX.com\" height=\"13\" width=\"8\" style=\"vertical-align: 0px;\" \/><\/td>\n<td data-align=\"left\">The quotient of <img loading=\"lazy\" decoding=\"async\" src=\"https:\/\/opentextbc.ca\/introalgebra\/wp-content\/ql-cache\/quicklatex.com-5c53d6ebabdbcfa4e107550ea60b1b19_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"&#97;\" title=\"Rendered by QuickLaTeX.com\" height=\"8\" width=\"9\" style=\"vertical-align: 0px;\" \/> and <img loading=\"lazy\" decoding=\"async\" src=\"https:\/\/opentextbc.ca\/introalgebra\/wp-content\/ql-cache\/quicklatex.com-f56d50c26583f9a035ff6b4e3c0ca5c0_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"&#98;\" title=\"Rendered by QuickLaTeX.com\" height=\"13\" width=\"8\" style=\"vertical-align: 0px;\" \/><\/td>\n<\/tr>\n<\/tbody>\n<\/table>\n<p id=\"fs-id1560745\">In algebra, the cross symbol, \u00d7, is not used to show multiplication because that symbol may cause confusion. Does <img loading=\"lazy\" decoding=\"async\" src=\"https:\/\/opentextbc.ca\/introalgebra\/wp-content\/ql-cache\/quicklatex.com-c6ca1b49e7bbd5453cebf69bacc11790_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"&#51;&#120;&#121;\" title=\"Rendered by QuickLaTeX.com\" height=\"16\" width=\"28\" style=\"vertical-align: -4px;\" \/> mean <img loading=\"lazy\" decoding=\"async\" src=\"https:\/\/opentextbc.ca\/introalgebra\/wp-content\/ql-cache\/quicklatex.com-b6506b30a670b89e6ab1a81aeb6a2d5c_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"&#51;&#32;&#92;&#112;&#104;&#97;&#110;&#116;&#111;&#109;&#123;&#92;&#114;&#117;&#108;&#101;&#123;&#48;&#46;&#50;&#101;&#109;&#125;&#123;&#48;&#101;&#120;&#125;&#125;&#32;&#92;&#116;&#105;&#109;&#101;&#115;&#32;&#92;&#112;&#104;&#97;&#110;&#116;&#111;&#109;&#123;&#92;&#114;&#117;&#108;&#101;&#123;&#48;&#46;&#50;&#101;&#109;&#125;&#123;&#48;&#101;&#120;&#125;&#125;&#121;\" title=\"Rendered by QuickLaTeX.com\" height=\"16\" width=\"47\" style=\"vertical-align: -4px;\" \/> (three times <img loading=\"lazy\" decoding=\"async\" src=\"https:\/\/opentextbc.ca\/introalgebra\/wp-content\/ql-cache\/quicklatex.com-0af556714940c351c933bba8cf840796_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"&#121;\" title=\"Rendered by QuickLaTeX.com\" height=\"12\" width=\"9\" style=\"vertical-align: -4px;\" \/>) or <img loading=\"lazy\" decoding=\"async\" src=\"https:\/\/opentextbc.ca\/introalgebra\/wp-content\/ql-cache\/quicklatex.com-eb218ff670db6e07da5d07f602fc22fd_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"&#51;&#32;&#92;&#99;&#100;&#111;&#116;&#32;&#120;&#32;&#92;&#99;&#100;&#111;&#116;&#32;&#121;\" title=\"Rendered by QuickLaTeX.com\" height=\"16\" width=\"54\" style=\"vertical-align: -4px;\" \/> (three times <img loading=\"lazy\" decoding=\"async\" src=\"https:\/\/opentextbc.ca\/introalgebra\/wp-content\/ql-cache\/quicklatex.com-75f96701922fe212597a2a9731e93400_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"&#120;&#92;&#112;&#104;&#97;&#110;&#116;&#111;&#109;&#123;&#92;&#114;&#117;&#108;&#101;&#123;&#48;&#46;&#50;&#101;&#109;&#125;&#123;&#48;&#101;&#120;&#125;&#125;&#92;&#116;&#101;&#120;&#116;&#123;&#116;&#105;&#109;&#101;&#115;&#125;&#92;&#112;&#104;&#97;&#110;&#116;&#111;&#109;&#123;&#92;&#114;&#117;&#108;&#101;&#123;&#48;&#46;&#50;&#101;&#109;&#125;&#123;&#48;&#101;&#120;&#125;&#125;&#121;\" title=\"Rendered by QuickLaTeX.com\" height=\"16\" width=\"68\" style=\"vertical-align: -4px;\" \/>)? To make it clear, use \u2022 or parentheses for multiplication.<\/p>\n<p id=\"fs-id1885631\">We perform these operations on two numbers. When translating from symbolic form to words, or from words to symbolic form, pay attention to the words <em data-effect=\"italics\">of<\/em> or <em data-effect=\"italics\">and<\/em> to help you find the numbers.<\/p>\n<ul>\n<li>The <em data-effect=\"italics\">sum<\/em> <strong data-effect=\"bold\"><em data-effect=\"italics\">of<\/em><\/strong> <img loading=\"lazy\" decoding=\"async\" src=\"https:\/\/opentextbc.ca\/introalgebra\/wp-content\/ql-cache\/quicklatex.com-8995e2084120c1c1f4b53f490d281bc4_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"&#53;\" title=\"Rendered by QuickLaTeX.com\" height=\"13\" width=\"8\" style=\"vertical-align: 0px;\" \/> <strong data-effect=\"bold\"><em data-effect=\"italics\">and<\/em><\/strong> <img loading=\"lazy\" decoding=\"async\" src=\"https:\/\/opentextbc.ca\/introalgebra\/wp-content\/ql-cache\/quicklatex.com-4a1d3ea4963f568cabd97329456036b6_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"&#51;\" title=\"Rendered by QuickLaTeX.com\" height=\"12\" width=\"9\" style=\"vertical-align: 0px;\" \/> means add <img loading=\"lazy\" decoding=\"async\" src=\"https:\/\/opentextbc.ca\/introalgebra\/wp-content\/ql-cache\/quicklatex.com-8995e2084120c1c1f4b53f490d281bc4_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"&#53;\" title=\"Rendered by QuickLaTeX.com\" height=\"13\" width=\"8\" style=\"vertical-align: 0px;\" \/> plus <img loading=\"lazy\" decoding=\"async\" src=\"https:\/\/opentextbc.ca\/introalgebra\/wp-content\/ql-cache\/quicklatex.com-4a1d3ea4963f568cabd97329456036b6_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"&#51;\" title=\"Rendered by QuickLaTeX.com\" height=\"12\" width=\"9\" style=\"vertical-align: 0px;\" \/>, which we write as <img loading=\"lazy\" decoding=\"async\" src=\"https:\/\/opentextbc.ca\/introalgebra\/wp-content\/ql-cache\/quicklatex.com-801284eae9d4b66b01d49ee1b141eddc_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"&#53;&#43;&#51;\" title=\"Rendered by QuickLaTeX.com\" height=\"15\" width=\"40\" style=\"vertical-align: -2px;\" \/>.<\/li>\n<li>The <em data-effect=\"italics\">difference<\/em> <strong data-effect=\"bold\"><em data-effect=\"italics\">of<\/em><\/strong> <img loading=\"lazy\" decoding=\"async\" src=\"https:\/\/opentextbc.ca\/introalgebra\/wp-content\/ql-cache\/quicklatex.com-e99b7c7ddd421682faf67e5b5f865882_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"&#57;\" title=\"Rendered by QuickLaTeX.com\" height=\"12\" width=\"9\" style=\"vertical-align: 0px;\" \/> <strong data-effect=\"bold\"><em data-effect=\"italics\">and<\/em><\/strong> <img loading=\"lazy\" decoding=\"async\" src=\"https:\/\/opentextbc.ca\/introalgebra\/wp-content\/ql-cache\/quicklatex.com-e584dd0bab4e6c8efc164939c28db757_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"&#50;\" title=\"Rendered by QuickLaTeX.com\" height=\"12\" width=\"8\" style=\"vertical-align: 0px;\" \/> means subtract <img loading=\"lazy\" decoding=\"async\" src=\"https:\/\/opentextbc.ca\/introalgebra\/wp-content\/ql-cache\/quicklatex.com-e99b7c7ddd421682faf67e5b5f865882_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"&#57;\" title=\"Rendered by QuickLaTeX.com\" height=\"12\" width=\"9\" style=\"vertical-align: 0px;\" \/> minus <img loading=\"lazy\" decoding=\"async\" src=\"https:\/\/opentextbc.ca\/introalgebra\/wp-content\/ql-cache\/quicklatex.com-e584dd0bab4e6c8efc164939c28db757_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"&#50;\" title=\"Rendered by QuickLaTeX.com\" height=\"12\" width=\"8\" style=\"vertical-align: 0px;\" \/>, which we write as <img loading=\"lazy\" decoding=\"async\" src=\"https:\/\/opentextbc.ca\/introalgebra\/wp-content\/ql-cache\/quicklatex.com-69648e1f94305e4b341ad945d086ccba_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"&#57;&#45;&#50;\" title=\"Rendered by QuickLaTeX.com\" height=\"12\" width=\"39\" style=\"vertical-align: 0px;\" \/>.<\/li>\n<li>The <em data-effect=\"italics\">product<\/em> <strong data-effect=\"bold\"><em data-effect=\"italics\">of<\/em><\/strong> <img loading=\"lazy\" decoding=\"async\" src=\"https:\/\/opentextbc.ca\/introalgebra\/wp-content\/ql-cache\/quicklatex.com-6111a899fd636b7a5238708f8679f6ec_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"&#52;\" title=\"Rendered by QuickLaTeX.com\" height=\"13\" width=\"9\" style=\"vertical-align: -1px;\" \/> <strong data-effect=\"bold\"><em data-effect=\"italics\">and<\/em><\/strong> <img loading=\"lazy\" decoding=\"async\" src=\"https:\/\/opentextbc.ca\/introalgebra\/wp-content\/ql-cache\/quicklatex.com-23212a120eb92d226d44696a0b80bead_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"&#56;\" title=\"Rendered by QuickLaTeX.com\" height=\"12\" width=\"9\" style=\"vertical-align: 0px;\" \/> means multiply <img loading=\"lazy\" decoding=\"async\" src=\"https:\/\/opentextbc.ca\/introalgebra\/wp-content\/ql-cache\/quicklatex.com-6111a899fd636b7a5238708f8679f6ec_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"&#52;\" title=\"Rendered by QuickLaTeX.com\" height=\"13\" width=\"9\" style=\"vertical-align: -1px;\" \/> times <img loading=\"lazy\" decoding=\"async\" src=\"https:\/\/opentextbc.ca\/introalgebra\/wp-content\/ql-cache\/quicklatex.com-23212a120eb92d226d44696a0b80bead_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"&#56;\" title=\"Rendered by QuickLaTeX.com\" height=\"12\" width=\"9\" style=\"vertical-align: 0px;\" \/>, which we can write as <img loading=\"lazy\" decoding=\"async\" src=\"https:\/\/opentextbc.ca\/introalgebra\/wp-content\/ql-cache\/quicklatex.com-426ede6b851d4de880585a7ce942963f_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"&#52;&#92;&#99;&#100;&#111;&#116;&#32;&#56;\" title=\"Rendered by QuickLaTeX.com\" height=\"12\" width=\"31\" style=\"vertical-align: 0px;\" \/>.<\/li>\n<li>The <em data-effect=\"italics\">quotient<\/em> <strong data-effect=\"bold\"><em data-effect=\"italics\">of<\/em><\/strong> <img loading=\"lazy\" decoding=\"async\" src=\"https:\/\/opentextbc.ca\/introalgebra\/wp-content\/ql-cache\/quicklatex.com-930d01a5f622cee5952bab4752e56063_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"&#50;&#48;\" title=\"Rendered by QuickLaTeX.com\" height=\"12\" width=\"18\" style=\"vertical-align: 0px;\" \/> <strong data-effect=\"bold\"><em data-effect=\"italics\">and<\/em><\/strong> <img loading=\"lazy\" decoding=\"async\" src=\"https:\/\/opentextbc.ca\/introalgebra\/wp-content\/ql-cache\/quicklatex.com-8995e2084120c1c1f4b53f490d281bc4_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"&#53;\" title=\"Rendered by QuickLaTeX.com\" height=\"13\" width=\"8\" style=\"vertical-align: 0px;\" \/> means divide <img loading=\"lazy\" decoding=\"async\" src=\"https:\/\/opentextbc.ca\/introalgebra\/wp-content\/ql-cache\/quicklatex.com-930d01a5f622cee5952bab4752e56063_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"&#50;&#48;\" title=\"Rendered by QuickLaTeX.com\" height=\"12\" width=\"18\" style=\"vertical-align: 0px;\" \/> by <img loading=\"lazy\" decoding=\"async\" src=\"https:\/\/opentextbc.ca\/introalgebra\/wp-content\/ql-cache\/quicklatex.com-8995e2084120c1c1f4b53f490d281bc4_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"&#53;\" title=\"Rendered by QuickLaTeX.com\" height=\"13\" width=\"8\" style=\"vertical-align: 0px;\" \/>, which we can write as <img loading=\"lazy\" decoding=\"async\" src=\"https:\/\/opentextbc.ca\/introalgebra\/wp-content\/ql-cache\/quicklatex.com-107c508bcb660d64a391a43c6dc3d9ea_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"&#50;&#48;&#32;&#92;&#100;&#105;&#118;&#32;&#53;\" title=\"Rendered by QuickLaTeX.com\" height=\"14\" width=\"47\" style=\"vertical-align: -1px;\" \/>.<\/li>\n<\/ul>\n<div class=\"textbox textbox--examples\">\n<header class=\"textbox__header\">\n<p class=\"textbox__title\">EXAMPLE 1<\/p>\n<\/header>\n<div class=\"textbox__content\">\n<div id=\"fs-id1804532\" data-type=\"problem\">\n<p id=\"fs-id2430630\">Translate from algebra to words:<\/p>\n<ol id=\"eip-id1168469763234\" class=\"circled\" type=\"a\">\n<li><img loading=\"lazy\" decoding=\"async\" src=\"https:\/\/opentextbc.ca\/introalgebra\/wp-content\/ql-cache\/quicklatex.com-1d9250461fb3c88f6c7b2044484a1094_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"&#92;&#112;&#104;&#97;&#110;&#116;&#111;&#109;&#123;&#92;&#114;&#117;&#108;&#101;&#123;&#48;&#46;&#50;&#101;&#109;&#125;&#123;&#48;&#101;&#120;&#125;&#125;&#49;&#50;&#43;&#49;&#52;&#92;&#112;&#104;&#97;&#110;&#116;&#111;&#109;&#123;&#92;&#114;&#117;&#108;&#101;&#123;&#48;&#46;&#50;&#101;&#109;&#125;&#123;&#48;&#101;&#120;&#125;&#125;\" title=\"Rendered by QuickLaTeX.com\" height=\"14\" width=\"56\" style=\"vertical-align: -2px;\" \/><\/li>\n<li><img loading=\"lazy\" decoding=\"async\" src=\"https:\/\/opentextbc.ca\/introalgebra\/wp-content\/ql-cache\/quicklatex.com-24234d5921936ae0ec1c50595f2e20ca_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"&#92;&#112;&#104;&#97;&#110;&#116;&#111;&#109;&#123;&#92;&#114;&#117;&#108;&#101;&#123;&#48;&#46;&#50;&#101;&#109;&#125;&#123;&#48;&#101;&#120;&#125;&#125;&#92;&#108;&#101;&#102;&#116;&#40;&#51;&#48;&#92;&#114;&#105;&#103;&#104;&#116;&#41;&#92;&#108;&#101;&#102;&#116;&#40;&#53;&#92;&#114;&#105;&#103;&#104;&#116;&#41;&#92;&#112;&#104;&#97;&#110;&#116;&#111;&#109;&#123;&#92;&#114;&#117;&#108;&#101;&#123;&#48;&#46;&#50;&#101;&#109;&#125;&#123;&#48;&#101;&#120;&#125;&#125;\" title=\"Rendered by QuickLaTeX.com\" height=\"18\" width=\"55\" style=\"vertical-align: -4px;\" \/><\/li>\n<li><img loading=\"lazy\" decoding=\"async\" src=\"https:\/\/opentextbc.ca\/introalgebra\/wp-content\/ql-cache\/quicklatex.com-5084d05b7ea76ea50c620eb68bbc548b_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"&#92;&#112;&#104;&#97;&#110;&#116;&#111;&#109;&#123;&#92;&#114;&#117;&#108;&#101;&#123;&#48;&#46;&#50;&#101;&#109;&#125;&#123;&#48;&#101;&#120;&#125;&#125;&#54;&#52;&#32;&#92;&#100;&#105;&#118;&#32;&#56;&#92;&#112;&#104;&#97;&#110;&#116;&#111;&#109;&#123;&#92;&#114;&#117;&#108;&#101;&#123;&#48;&#46;&#50;&#101;&#109;&#125;&#123;&#48;&#101;&#120;&#125;&#125;\" title=\"Rendered by QuickLaTeX.com\" height=\"13\" width=\"48\" style=\"vertical-align: -1px;\" \/><\/li>\n<li><img loading=\"lazy\" decoding=\"async\" src=\"https:\/\/opentextbc.ca\/introalgebra\/wp-content\/ql-cache\/quicklatex.com-fae9b271c0a817a7619245e931adb737_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"&#92;&#112;&#104;&#97;&#110;&#116;&#111;&#109;&#123;&#92;&#114;&#117;&#108;&#101;&#123;&#48;&#46;&#50;&#101;&#109;&#125;&#123;&#48;&#101;&#120;&#125;&#125;&#120;&#45;&#121;\" title=\"Rendered by QuickLaTeX.com\" height=\"12\" width=\"40\" style=\"vertical-align: -4px;\" \/><\/li>\n<\/ol>\n<\/div>\n<div id=\"fs-id1604284\" data-type=\"solution\">\n<div data-type=\"title\"><\/div>\n<div style=\"text-align: left;\" data-type=\"title\"><strong>Solution<\/strong><\/div>\n<div data-type=\"title\"><\/div>\n<table id=\"eip-815\" class=\"unnumbered unstyled\" summary=\".\" data-label=\"\">\n<tbody>\n<tr>\n<td>a.<\/td>\n<\/tr>\n<tr>\n<td data-align=\"center\"><img loading=\"lazy\" decoding=\"async\" src=\"https:\/\/opentextbc.ca\/introalgebra\/wp-content\/ql-cache\/quicklatex.com-e51cb7e53962479ee1c26793c678f35d_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"&#49;&#50;&#43;&#49;&#52;\" title=\"Rendered by QuickLaTeX.com\" height=\"14\" width=\"56\" style=\"vertical-align: -2px;\" \/><\/td>\n<\/tr>\n<tr>\n<td data-align=\"center\">12 plus 14<\/td>\n<\/tr>\n<tr>\n<td data-align=\"center\">the sum of twelve and fourteen<\/td>\n<\/tr>\n<\/tbody>\n<\/table>\n<table id=\"eip-653\" class=\"unnumbered unstyled\" summary=\".\" data-label=\"\">\n<tbody>\n<tr>\n<td>b.<\/td>\n<\/tr>\n<tr>\n<td data-align=\"center\"><img loading=\"lazy\" decoding=\"async\" src=\"https:\/\/opentextbc.ca\/introalgebra\/wp-content\/ql-cache\/quicklatex.com-c47f08a5e99fec7e08c38758cc5dfa38_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"&#92;&#108;&#101;&#102;&#116;&#40;&#51;&#48;&#92;&#114;&#105;&#103;&#104;&#116;&#41;&#92;&#108;&#101;&#102;&#116;&#40;&#53;&#92;&#114;&#105;&#103;&#104;&#116;&#41;\" title=\"Rendered by QuickLaTeX.com\" height=\"18\" width=\"55\" style=\"vertical-align: -4px;\" \/><\/td>\n<\/tr>\n<tr>\n<td data-align=\"center\">30 times 5<\/td>\n<\/tr>\n<tr>\n<td data-align=\"center\">the product of thirty and five<\/td>\n<\/tr>\n<\/tbody>\n<\/table>\n<table id=\"eip-id1164753916055\" class=\"unnumbered unstyled\" summary=\".\" data-label=\"\">\n<tbody>\n<tr>\n<td>c.<\/td>\n<\/tr>\n<tr>\n<td data-align=\"center\"><img loading=\"lazy\" decoding=\"async\" src=\"https:\/\/opentextbc.ca\/introalgebra\/wp-content\/ql-cache\/quicklatex.com-44e1208ef5bbea5fb7eb98cc6f454a48_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"&#54;&#52;&#92;&#100;&#105;&#118;&#32;&#56;\" title=\"Rendered by QuickLaTeX.com\" height=\"13\" width=\"48\" style=\"vertical-align: -1px;\" \/><\/td>\n<\/tr>\n<tr>\n<td data-align=\"center\">64 divided by 8<\/td>\n<\/tr>\n<tr>\n<td data-align=\"center\">the quotient of sixty-four and eight<\/td>\n<\/tr>\n<\/tbody>\n<\/table>\n<table id=\"eip-id1164753916109\" class=\"unnumbered unstyled\" summary=\".\" data-label=\"\">\n<tbody>\n<tr>\n<td>d.<\/td>\n<\/tr>\n<tr>\n<td data-align=\"center\"><img loading=\"lazy\" decoding=\"async\" src=\"https:\/\/opentextbc.ca\/introalgebra\/wp-content\/ql-cache\/quicklatex.com-331229c156db2bcd09ba326e0d1819e6_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"&#120;&#45;&#121;\" title=\"Rendered by QuickLaTeX.com\" height=\"12\" width=\"41\" style=\"vertical-align: -4px;\" \/><\/td>\n<\/tr>\n<tr>\n<td data-align=\"center\"><img loading=\"lazy\" decoding=\"async\" src=\"https:\/\/opentextbc.ca\/introalgebra\/wp-content\/ql-cache\/quicklatex.com-ede05c264bba0eda080918aaa09c4658_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"&#120;\" title=\"Rendered by QuickLaTeX.com\" height=\"8\" width=\"10\" style=\"vertical-align: 0px;\" \/> minus <img loading=\"lazy\" decoding=\"async\" src=\"https:\/\/opentextbc.ca\/introalgebra\/wp-content\/ql-cache\/quicklatex.com-0af556714940c351c933bba8cf840796_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"&#121;\" title=\"Rendered by QuickLaTeX.com\" height=\"12\" width=\"9\" style=\"vertical-align: -4px;\" \/><\/td>\n<\/tr>\n<tr>\n<td data-align=\"center\">the difference of <img loading=\"lazy\" decoding=\"async\" src=\"https:\/\/opentextbc.ca\/introalgebra\/wp-content\/ql-cache\/quicklatex.com-ede05c264bba0eda080918aaa09c4658_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"&#120;\" title=\"Rendered by QuickLaTeX.com\" height=\"8\" width=\"10\" style=\"vertical-align: 0px;\" \/> and <img loading=\"lazy\" decoding=\"async\" src=\"https:\/\/opentextbc.ca\/introalgebra\/wp-content\/ql-cache\/quicklatex.com-0af556714940c351c933bba8cf840796_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"&#121;\" title=\"Rendered by QuickLaTeX.com\" height=\"12\" width=\"9\" style=\"vertical-align: -4px;\" \/><\/td>\n<\/tr>\n<\/tbody>\n<\/table>\n<\/div>\n<\/div>\n<\/div>\n<div class=\"textbox textbox--exercises\">\n<header class=\"textbox__header\">\n<p class=\"textbox__title\">TRY IT 1.1<\/p>\n<\/header>\n<div class=\"textbox__content\">\n<div id=\"fs-id2205513\" data-type=\"problem\">\n<p id=\"fs-id1807700\">Translate from algebra to words.<\/p>\n<ol id=\"eip-id1168469668897\" class=\"circled\" type=\"a\">\n<li><img loading=\"lazy\" decoding=\"async\" src=\"https:\/\/opentextbc.ca\/introalgebra\/wp-content\/ql-cache\/quicklatex.com-346c70db82d26e05cc50f2a79369e95b_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"&#92;&#112;&#104;&#97;&#110;&#116;&#111;&#109;&#123;&#92;&#114;&#117;&#108;&#101;&#123;&#48;&#46;&#50;&#101;&#109;&#125;&#123;&#48;&#101;&#120;&#125;&#125;&#49;&#56;&#43;&#49;&#49;&#92;&#112;&#104;&#97;&#110;&#116;&#111;&#109;&#123;&#92;&#114;&#117;&#108;&#101;&#123;&#48;&#46;&#52;&#101;&#109;&#125;&#123;&#48;&#101;&#120;&#125;&#125;\" title=\"Rendered by QuickLaTeX.com\" height=\"14\" width=\"55\" style=\"vertical-align: -2px;\" \/><\/li>\n<li><img loading=\"lazy\" decoding=\"async\" src=\"https:\/\/opentextbc.ca\/introalgebra\/wp-content\/ql-cache\/quicklatex.com-e78f136718f3b99ffab2e091edfa4452_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"&#92;&#112;&#104;&#97;&#110;&#116;&#111;&#109;&#123;&#92;&#114;&#117;&#108;&#101;&#123;&#48;&#46;&#50;&#101;&#109;&#125;&#123;&#48;&#101;&#120;&#125;&#125;&#92;&#108;&#101;&#102;&#116;&#40;&#50;&#55;&#92;&#114;&#105;&#103;&#104;&#116;&#41;&#92;&#108;&#101;&#102;&#116;&#40;&#57;&#92;&#114;&#105;&#103;&#104;&#116;&#41;&#92;&#112;&#104;&#97;&#110;&#116;&#111;&#109;&#123;&#92;&#114;&#117;&#108;&#101;&#123;&#48;&#46;&#52;&#101;&#109;&#125;&#123;&#48;&#101;&#120;&#125;&#125;\" title=\"Rendered by QuickLaTeX.com\" height=\"18\" width=\"55\" style=\"vertical-align: -4px;\" \/><\/li>\n<li><img loading=\"lazy\" decoding=\"async\" src=\"https:\/\/opentextbc.ca\/introalgebra\/wp-content\/ql-cache\/quicklatex.com-c73aa0a31d5775003bd89f492c8669cb_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"&#92;&#112;&#104;&#97;&#110;&#116;&#111;&#109;&#123;&#92;&#114;&#117;&#108;&#101;&#123;&#48;&#46;&#50;&#101;&#109;&#125;&#123;&#48;&#101;&#120;&#125;&#125;&#56;&#52;&#92;&#100;&#105;&#118;&#32;&#55;\" title=\"Rendered by QuickLaTeX.com\" height=\"14\" width=\"48\" style=\"vertical-align: -1px;\" \/><\/li>\n<li><img loading=\"lazy\" decoding=\"async\" src=\"https:\/\/opentextbc.ca\/introalgebra\/wp-content\/ql-cache\/quicklatex.com-30d56d06ffc0da9a48515013fa7d6992_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"&#112;&#45;&#113;\" title=\"Rendered by QuickLaTeX.com\" height=\"12\" width=\"40\" style=\"vertical-align: -4px;\" \/><\/li>\n<\/ol>\n<\/div>\n<div id=\"fs-id1383680\" data-type=\"solution\">\n<details>\n<summary>Show Answer<\/summary>\n<ol id=\"eip-id1168469837643\" class=\"circled\" type=\"a\">\n<li>18 plus 11; the sum of eighteen and eleven<\/li>\n<li>27 times 9; the product of twenty-seven and nine<\/li>\n<li>84 divided by 7; the quotient of eighty-four and seven<\/li>\n<li><em data-effect=\"italics\">p<\/em> minus <em data-effect=\"italics\">q<\/em>; the difference of <em data-effect=\"italics\">p<\/em> and <em data-effect=\"italics\">q<\/em><\/li>\n<\/ol>\n<\/details>\n<\/div>\n<\/div>\n<\/div>\n<div class=\"textbox textbox--exercises\">\n<header class=\"textbox__header\">\n<p class=\"textbox__title\">TRY IT 1.2<\/p>\n<\/header>\n<div class=\"textbox__content\">\n<div id=\"fs-id2161871\" data-type=\"problem\">\n<p id=\"fs-id1171104039532\">Translate from algebra to words.<\/p>\n<ol id=\"eip-id1168468485516\" class=\"circled\" type=\"a\">\n<li><img loading=\"lazy\" decoding=\"async\" src=\"https:\/\/opentextbc.ca\/introalgebra\/wp-content\/ql-cache\/quicklatex.com-f098a0b51962e63f8f3f5e85fa21f5b5_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"&#92;&#112;&#104;&#97;&#110;&#116;&#111;&#109;&#123;&#92;&#114;&#117;&#108;&#101;&#123;&#48;&#46;&#50;&#101;&#109;&#125;&#123;&#48;&#101;&#120;&#125;&#125;&#52;&#55;&#45;&#49;&#57;&#92;&#112;&#104;&#97;&#110;&#116;&#111;&#109;&#123;&#92;&#114;&#117;&#108;&#101;&#123;&#48;&#46;&#52;&#101;&#109;&#125;&#123;&#48;&#101;&#120;&#125;&#125;\" title=\"Rendered by QuickLaTeX.com\" height=\"14\" width=\"57\" style=\"vertical-align: -1px;\" \/><\/li>\n<li><img loading=\"lazy\" decoding=\"async\" src=\"https:\/\/opentextbc.ca\/introalgebra\/wp-content\/ql-cache\/quicklatex.com-5e4595d4c791a9e61e6faced52148356_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"&#92;&#112;&#104;&#97;&#110;&#116;&#111;&#109;&#123;&#92;&#114;&#117;&#108;&#101;&#123;&#48;&#46;&#50;&#101;&#109;&#125;&#123;&#48;&#101;&#120;&#125;&#125;&#55;&#50;&#92;&#100;&#105;&#118;&#32;&#57;&#92;&#112;&#104;&#97;&#110;&#116;&#111;&#109;&#123;&#92;&#114;&#117;&#108;&#101;&#123;&#48;&#46;&#52;&#101;&#109;&#125;&#123;&#48;&#101;&#120;&#125;&#125;\" title=\"Rendered by QuickLaTeX.com\" height=\"14\" width=\"48\" style=\"vertical-align: -1px;\" \/><\/li>\n<li><img loading=\"lazy\" decoding=\"async\" src=\"https:\/\/opentextbc.ca\/introalgebra\/wp-content\/ql-cache\/quicklatex.com-5edc0ef5cee6994c8ef4abfc9f714c98_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"&#92;&#112;&#104;&#97;&#110;&#116;&#111;&#109;&#123;&#92;&#114;&#117;&#108;&#101;&#123;&#48;&#46;&#50;&#101;&#109;&#125;&#123;&#48;&#101;&#120;&#125;&#125;&#109;&#43;&#110;&#92;&#112;&#104;&#97;&#110;&#116;&#111;&#109;&#123;&#92;&#114;&#117;&#108;&#101;&#123;&#48;&#46;&#52;&#101;&#109;&#125;&#123;&#48;&#101;&#120;&#125;&#125;\" title=\"Rendered by QuickLaTeX.com\" height=\"13\" width=\"48\" style=\"vertical-align: -2px;\" \/><\/li>\n<li><img loading=\"lazy\" decoding=\"async\" src=\"https:\/\/opentextbc.ca\/introalgebra\/wp-content\/ql-cache\/quicklatex.com-4621044a8f1af1194b89e6cdfd391c72_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"&#92;&#112;&#104;&#97;&#110;&#116;&#111;&#109;&#123;&#92;&#114;&#117;&#108;&#101;&#123;&#48;&#46;&#50;&#101;&#109;&#125;&#123;&#48;&#101;&#120;&#125;&#125;&#92;&#108;&#101;&#102;&#116;&#40;&#49;&#51;&#92;&#114;&#105;&#103;&#104;&#116;&#41;&#92;&#108;&#101;&#102;&#116;&#40;&#55;&#92;&#114;&#105;&#103;&#104;&#116;&#41;\" title=\"Rendered by QuickLaTeX.com\" height=\"18\" width=\"55\" style=\"vertical-align: -4px;\" \/><\/li>\n<\/ol>\n<\/div>\n<div id=\"fs-id1887825\" data-type=\"solution\">\n<details>\n<summary>Show Answer<\/summary>\n<ol id=\"eip-id1168465110670\" class=\"circled\" type=\"a\">\n<li>47 minus 19; the difference of forty-seven and nineteen<\/li>\n<li>72 divided by 9; the quotient of seventy-two and nine<\/li>\n<li><em data-effect=\"italics\">m<\/em> plus <em data-effect=\"italics\">n<\/em>; the sum of <em data-effect=\"italics\">m<\/em> and <em data-effect=\"italics\">n<\/em><\/li>\n<li>13 times 7; the product of thirteen and seven<\/li>\n<\/ol>\n<\/details>\n<\/div>\n<\/div>\n<\/div>\n<p>When two quantities have the same value, we say they are equal and connect them with an <em data-effect=\"italics\">equal sign<\/em>.<\/p>\n<div id=\"fs-id1603053\" data-type=\"note\">\n<div data-type=\"title\">\n<div class=\"textbox textbox--key-takeaways\">\n<header class=\"textbox__header\">\n<p class=\"textbox__title\">Equality Symbol<\/p>\n<\/header>\n<div class=\"textbox__content\">\n<p id=\"fs-id1885124\"><img loading=\"lazy\" decoding=\"async\" src=\"https:\/\/opentextbc.ca\/introalgebra\/wp-content\/ql-cache\/quicklatex.com-728a2d777181b337d462fcbed6511948_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"&#97;&#61;&#98;&#92;&#112;&#104;&#97;&#110;&#116;&#111;&#109;&#123;&#92;&#114;&#117;&#108;&#101;&#123;&#48;&#46;&#50;&#101;&#109;&#125;&#123;&#48;&#101;&#120;&#125;&#125;&#92;&#116;&#101;&#120;&#116;&#123;&#105;&#115;&#32;&#114;&#101;&#97;&#100;&#125;&#92;&#112;&#104;&#97;&#110;&#116;&#111;&#109;&#123;&#92;&#114;&#117;&#108;&#101;&#123;&#48;&#46;&#50;&#101;&#109;&#125;&#123;&#48;&#101;&#120;&#125;&#125;&#97;&#92;&#112;&#104;&#97;&#110;&#116;&#111;&#109;&#123;&#92;&#114;&#117;&#108;&#101;&#123;&#48;&#46;&#50;&#101;&#109;&#125;&#123;&#48;&#101;&#120;&#125;&#125;&#92;&#116;&#101;&#120;&#116;&#123;&#105;&#115;&#32;&#101;&#113;&#117;&#97;&#108;&#32;&#116;&#111;&#125;&#92;&#112;&#104;&#97;&#110;&#116;&#111;&#109;&#123;&#92;&#114;&#117;&#108;&#101;&#123;&#48;&#46;&#50;&#101;&#109;&#125;&#123;&#48;&#101;&#120;&#125;&#125;&#98;\" title=\"Rendered by QuickLaTeX.com\" height=\"16\" width=\"204\" style=\"vertical-align: -3px;\" \/><\/p>\n<p id=\"fs-id2775026\">The symbol <img loading=\"lazy\" decoding=\"async\" src=\"https:\/\/opentextbc.ca\/introalgebra\/wp-content\/ql-cache\/quicklatex.com-b8690b7efd237bfe32a6e92e3b699b96_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"&#61;\" title=\"Rendered by QuickLaTeX.com\" height=\"4\" width=\"13\" style=\"vertical-align: 2px;\" \/> is called the <span class=\"no-emphasis\" data-type=\"term\">equal sign<\/span>.<\/p>\n<\/div>\n<\/div>\n<p>An <span class=\"no-emphasis\" data-type=\"term\">inequality<\/span> is used in algebra to compare two quantities that may have different values. The number line can help you understand inequalities. Remember that on the number line the numbers get larger as they go from left to right. So if we know that <img loading=\"lazy\" decoding=\"async\" src=\"https:\/\/opentextbc.ca\/introalgebra\/wp-content\/ql-cache\/quicklatex.com-f56d50c26583f9a035ff6b4e3c0ca5c0_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"&#98;\" title=\"Rendered by QuickLaTeX.com\" height=\"13\" width=\"8\" style=\"vertical-align: 0px;\" \/> is greater than <img loading=\"lazy\" decoding=\"async\" src=\"https:\/\/opentextbc.ca\/introalgebra\/wp-content\/ql-cache\/quicklatex.com-5c53d6ebabdbcfa4e107550ea60b1b19_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"&#97;\" title=\"Rendered by QuickLaTeX.com\" height=\"8\" width=\"9\" style=\"vertical-align: 0px;\" \/>, it means that <img loading=\"lazy\" decoding=\"async\" src=\"https:\/\/opentextbc.ca\/introalgebra\/wp-content\/ql-cache\/quicklatex.com-f56d50c26583f9a035ff6b4e3c0ca5c0_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"&#98;\" title=\"Rendered by QuickLaTeX.com\" height=\"13\" width=\"8\" style=\"vertical-align: 0px;\" \/> is to the right of <img loading=\"lazy\" decoding=\"async\" src=\"https:\/\/opentextbc.ca\/introalgebra\/wp-content\/ql-cache\/quicklatex.com-5c53d6ebabdbcfa4e107550ea60b1b19_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"&#97;\" title=\"Rendered by QuickLaTeX.com\" height=\"8\" width=\"9\" style=\"vertical-align: 0px;\" \/> on the number line. We use the symbols &lt; and &gt; for inequalities.<\/p>\n<\/div>\n<\/div>\n<div id=\"fs-id2650456\" data-type=\"note\">\n<div data-type=\"title\">\n<div class=\"textbox textbox--key-takeaways\">\n<header class=\"textbox__header\">\n<p class=\"textbox__title\">Inequality<\/p>\n<\/header>\n<div class=\"textbox__content\">\n<p id=\"fs-id3202723\"><img loading=\"lazy\" decoding=\"async\" src=\"https:\/\/opentextbc.ca\/introalgebra\/wp-content\/ql-cache\/quicklatex.com-5c53d6ebabdbcfa4e107550ea60b1b19_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"&#97;\" title=\"Rendered by QuickLaTeX.com\" height=\"8\" width=\"9\" style=\"vertical-align: 0px;\" \/> &lt; <img loading=\"lazy\" decoding=\"async\" src=\"https:\/\/opentextbc.ca\/introalgebra\/wp-content\/ql-cache\/quicklatex.com-f56d50c26583f9a035ff6b4e3c0ca5c0_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"&#98;\" title=\"Rendered by QuickLaTeX.com\" height=\"13\" width=\"8\" style=\"vertical-align: 0px;\" \/> is read <img loading=\"lazy\" decoding=\"async\" src=\"https:\/\/opentextbc.ca\/introalgebra\/wp-content\/ql-cache\/quicklatex.com-5c53d6ebabdbcfa4e107550ea60b1b19_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"&#97;\" title=\"Rendered by QuickLaTeX.com\" height=\"8\" width=\"9\" style=\"vertical-align: 0px;\" \/> is less than <img loading=\"lazy\" decoding=\"async\" src=\"https:\/\/opentextbc.ca\/introalgebra\/wp-content\/ql-cache\/quicklatex.com-f56d50c26583f9a035ff6b4e3c0ca5c0_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"&#98;\" title=\"Rendered by QuickLaTeX.com\" height=\"13\" width=\"8\" style=\"vertical-align: 0px;\" \/><\/p>\n<p id=\"fs-id2700412\"><img loading=\"lazy\" decoding=\"async\" src=\"https:\/\/opentextbc.ca\/introalgebra\/wp-content\/ql-cache\/quicklatex.com-5c53d6ebabdbcfa4e107550ea60b1b19_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"&#97;\" title=\"Rendered by QuickLaTeX.com\" height=\"8\" width=\"9\" style=\"vertical-align: 0px;\" \/> is to the left of <img loading=\"lazy\" decoding=\"async\" src=\"https:\/\/opentextbc.ca\/introalgebra\/wp-content\/ql-cache\/quicklatex.com-f56d50c26583f9a035ff6b4e3c0ca5c0_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"&#98;\" title=\"Rendered by QuickLaTeX.com\" height=\"13\" width=\"8\" style=\"vertical-align: 0px;\" \/> on the number line<\/p>\n<p><span id=\"fs-id1933083\" data-type=\"media\" data-alt=\"The figure shows a horizontal number line that begins with the letter a on the left then the letter b to its right.\"><img decoding=\"async\" class=\"aligncenter\" src=\"https:\/\/opentextbc.ca\/accessibilitytoolkit\/wp-content\/uploads\/sites\/333\/2020\/08\/CNX_BMath_Figure_02_01_001-1.jpg\" alt=\"The figure shows a horizontal number line that begins with the letter a on the left then the letter b to its right.\" data-media-type=\"image\/jpeg\" \/><\/span><\/p>\n<p id=\"fs-id2495460\"><img loading=\"lazy\" decoding=\"async\" src=\"https:\/\/opentextbc.ca\/introalgebra\/wp-content\/ql-cache\/quicklatex.com-5c53d6ebabdbcfa4e107550ea60b1b19_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"&#97;\" title=\"Rendered by QuickLaTeX.com\" height=\"8\" width=\"9\" style=\"vertical-align: 0px;\" \/> &gt; <img loading=\"lazy\" decoding=\"async\" src=\"https:\/\/opentextbc.ca\/introalgebra\/wp-content\/ql-cache\/quicklatex.com-f56d50c26583f9a035ff6b4e3c0ca5c0_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"&#98;\" title=\"Rendered by QuickLaTeX.com\" height=\"13\" width=\"8\" style=\"vertical-align: 0px;\" \/> is read <img loading=\"lazy\" decoding=\"async\" src=\"https:\/\/opentextbc.ca\/introalgebra\/wp-content\/ql-cache\/quicklatex.com-5c53d6ebabdbcfa4e107550ea60b1b19_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"&#97;\" title=\"Rendered by QuickLaTeX.com\" height=\"8\" width=\"9\" style=\"vertical-align: 0px;\" \/> is greater than <img loading=\"lazy\" decoding=\"async\" src=\"https:\/\/opentextbc.ca\/introalgebra\/wp-content\/ql-cache\/quicklatex.com-f56d50c26583f9a035ff6b4e3c0ca5c0_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"&#98;\" title=\"Rendered by QuickLaTeX.com\" height=\"13\" width=\"8\" style=\"vertical-align: 0px;\" \/><\/p>\n<p id=\"fs-id1379804\"><img loading=\"lazy\" decoding=\"async\" src=\"https:\/\/opentextbc.ca\/introalgebra\/wp-content\/ql-cache\/quicklatex.com-5c53d6ebabdbcfa4e107550ea60b1b19_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"&#97;\" title=\"Rendered by QuickLaTeX.com\" height=\"8\" width=\"9\" style=\"vertical-align: 0px;\" \/> is to the right of <img loading=\"lazy\" decoding=\"async\" src=\"https:\/\/opentextbc.ca\/introalgebra\/wp-content\/ql-cache\/quicklatex.com-f56d50c26583f9a035ff6b4e3c0ca5c0_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"&#98;\" title=\"Rendered by QuickLaTeX.com\" height=\"13\" width=\"8\" style=\"vertical-align: 0px;\" \/> on the number line<\/p>\n<p><span id=\"fs-id1467098\" data-type=\"media\" data-alt=\"The figure shows a horizontal number line that begins with the letter b on the left then the letter a to its right.\"><img decoding=\"async\" class=\"aligncenter\" src=\"https:\/\/opentextbc.ca\/accessibilitytoolkit\/wp-content\/uploads\/sites\/333\/2021\/03\/CNX_BMath_Figure_02_01_002-1.jpg\" alt=\"The figure shows a horizontal number line that begins with the letter b on the left then the letter a to its right.\" data-media-type=\"image\/jpeg\" \/><\/span><\/p>\n<\/div>\n<\/div>\n<p class=\"p1\">The expressions <img loading=\"lazy\" decoding=\"async\" src=\"https:\/\/opentextbc.ca\/introalgebra\/wp-content\/ql-cache\/quicklatex.com-5c53d6ebabdbcfa4e107550ea60b1b19_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"&#97;\" title=\"Rendered by QuickLaTeX.com\" height=\"8\" width=\"9\" style=\"vertical-align: 0px;\" \/> &lt; <img loading=\"lazy\" decoding=\"async\" src=\"https:\/\/opentextbc.ca\/introalgebra\/wp-content\/ql-cache\/quicklatex.com-71809cd3555d6e746725d2e12cbbcd52_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"&#98;&#92;&#112;&#104;&#97;&#110;&#116;&#111;&#109;&#123;&#92;&#114;&#117;&#108;&#101;&#123;&#48;&#46;&#50;&#101;&#109;&#125;&#123;&#48;&#101;&#120;&#125;&#125;&#92;&#116;&#101;&#120;&#116;&#123;&#97;&#110;&#100;&#125;&#92;&#112;&#104;&#97;&#110;&#116;&#111;&#109;&#123;&#92;&#114;&#117;&#108;&#101;&#123;&#48;&#46;&#50;&#101;&#109;&#125;&#123;&#48;&#101;&#120;&#125;&#125;&#97;\" title=\"Rendered by QuickLaTeX.com\" height=\"13\" width=\"52\" style=\"vertical-align: -1px;\" \/> &gt; <img loading=\"lazy\" decoding=\"async\" src=\"https:\/\/opentextbc.ca\/introalgebra\/wp-content\/ql-cache\/quicklatex.com-dfda230d82d07c923aeb595245f74958_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"&#92;&#112;&#104;&#97;&#110;&#116;&#111;&#109;&#123;&#92;&#114;&#117;&#108;&#101;&#123;&#48;&#46;&#50;&#101;&#109;&#125;&#123;&#48;&#101;&#120;&#125;&#125;&#98;\" title=\"Rendered by QuickLaTeX.com\" height=\"12\" width=\"8\" style=\"vertical-align: 0px;\" \/> can be read from left-to-right or right-to-left, though in English we usually read from left-to-right. In general,<\/p>\n<p><img loading=\"lazy\" decoding=\"async\" class=\"alignnone wp-image-59 size-full\" src=\"https:\/\/opentextbc.ca\/accessibilitytoolkit\/wp-content\/uploads\/sites\/333\/2021\/03\/Screenshot-2021-02-22-at-8.59.13-AM.png\" alt=\"&quot;7 is less than 11&quot; equivalent to &quot;11 is greater than 7&quot;\" width=\"2394\" height=\"222\" srcset=\"https:\/\/opentextbc.ca\/introalgebra\/wp-content\/uploads\/sites\/333\/2021\/03\/Screenshot-2021-02-22-at-8.59.13-AM.png 2394w, https:\/\/opentextbc.ca\/introalgebra\/wp-content\/uploads\/sites\/333\/2021\/03\/Screenshot-2021-02-22-at-8.59.13-AM-300x28.png 300w, https:\/\/opentextbc.ca\/introalgebra\/wp-content\/uploads\/sites\/333\/2021\/03\/Screenshot-2021-02-22-at-8.59.13-AM-1024x95.png 1024w, https:\/\/opentextbc.ca\/introalgebra\/wp-content\/uploads\/sites\/333\/2021\/03\/Screenshot-2021-02-22-at-8.59.13-AM-768x71.png 768w, https:\/\/opentextbc.ca\/introalgebra\/wp-content\/uploads\/sites\/333\/2021\/03\/Screenshot-2021-02-22-at-8.59.13-AM-1536x142.png 1536w, https:\/\/opentextbc.ca\/introalgebra\/wp-content\/uploads\/sites\/333\/2021\/03\/Screenshot-2021-02-22-at-8.59.13-AM-2048x190.png 2048w, https:\/\/opentextbc.ca\/introalgebra\/wp-content\/uploads\/sites\/333\/2021\/03\/Screenshot-2021-02-22-at-8.59.13-AM-65x6.png 65w, https:\/\/opentextbc.ca\/introalgebra\/wp-content\/uploads\/sites\/333\/2021\/03\/Screenshot-2021-02-22-at-8.59.13-AM-225x21.png 225w, https:\/\/opentextbc.ca\/introalgebra\/wp-content\/uploads\/sites\/333\/2021\/03\/Screenshot-2021-02-22-at-8.59.13-AM-350x32.png 350w\" sizes=\"auto, (max-width: 2394px) 100vw, 2394px\" \/><\/p>\n<\/div>\n<\/div>\n<p id=\"fs-id2903489\">When we write an inequality symbol with a line under it, such as <img loading=\"lazy\" decoding=\"async\" src=\"https:\/\/opentextbc.ca\/introalgebra\/wp-content\/ql-cache\/quicklatex.com-22bb7f496e0a4516393886afb53ffa7c_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"&#97;&#92;&#108;&#101;&#32;&#98;\" title=\"Rendered by QuickLaTeX.com\" height=\"16\" width=\"41\" style=\"vertical-align: -3px;\" \/>, it means <img loading=\"lazy\" decoding=\"async\" src=\"https:\/\/opentextbc.ca\/introalgebra\/wp-content\/ql-cache\/quicklatex.com-9b57677a3c7d31d00aea3cdd09443b09_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"&#97;&#60;&#98;\" title=\"Rendered by QuickLaTeX.com\" height=\"13\" width=\"41\" style=\"vertical-align: 0px;\" \/> or <img loading=\"lazy\" decoding=\"async\" src=\"https:\/\/opentextbc.ca\/introalgebra\/wp-content\/ql-cache\/quicklatex.com-e69295ccf8d8ca292abcc97f861e345f_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"&#97;&#61;&#98;\" title=\"Rendered by QuickLaTeX.com\" height=\"13\" width=\"41\" style=\"vertical-align: 0px;\" \/>. We read this <img loading=\"lazy\" decoding=\"async\" src=\"https:\/\/opentextbc.ca\/introalgebra\/wp-content\/ql-cache\/quicklatex.com-5c53d6ebabdbcfa4e107550ea60b1b19_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"&#97;\" title=\"Rendered by QuickLaTeX.com\" height=\"8\" width=\"9\" style=\"vertical-align: 0px;\" \/> is less than or equal to <img loading=\"lazy\" decoding=\"async\" src=\"https:\/\/opentextbc.ca\/introalgebra\/wp-content\/ql-cache\/quicklatex.com-f56d50c26583f9a035ff6b4e3c0ca5c0_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"&#98;\" title=\"Rendered by QuickLaTeX.com\" height=\"13\" width=\"8\" style=\"vertical-align: 0px;\" \/>. Also, if we put a slash through an equal sign, <img loading=\"lazy\" decoding=\"async\" src=\"https:\/\/opentextbc.ca\/introalgebra\/wp-content\/ql-cache\/quicklatex.com-ec2abdb669c9bb51bbc68474d39dd99f_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"&#92;&#110;&#101;\" title=\"Rendered by QuickLaTeX.com\" height=\"17\" width=\"13\" style=\"vertical-align: -4px;\" \/> it means not equal.<\/p>\n<p id=\"fs-id1238987\">We summarize the symbols of equality and inequality in the table below.<\/p>\n<table class=\"grid\" style=\"width: 100%;\" summary=\"This table has seven rows and two columns. The first row is a header row and it labels each column. The first column is labeled \u201cAlgebraic Notation\u201d, the second \u201cSay\u201d. Under the \u201cAlgebraic Notation\u201d column are the algebraic expressions: a equals b; a is not equal to b; a is less than b; a is greater than b; a is less than or equal to b; a is greater than or equal to b. Under the \u201cSay\u201d column are the phrases: \u201ca is equal to b\u201d, \u201ca is not equal to b\u201d, \u201ca is less than b\u201d, \u201ca is greater than b\u201d, \u201ca is less than or equal to b\u201d, and \u201ca is greater than or equal to b\u201d.\">\n<thead>\n<tr valign=\"top\">\n<th style=\"width: 50%;\" scope=\"col\" data-align=\"center\">Algebraic Notation<\/th>\n<th style=\"width: 50%;\" scope=\"col\" data-align=\"center\">Say<\/th>\n<\/tr>\n<\/thead>\n<tbody>\n<tr valign=\"top\">\n<td style=\"width: 50%;\" data-align=\"left\"><img loading=\"lazy\" decoding=\"async\" src=\"https:\/\/opentextbc.ca\/introalgebra\/wp-content\/ql-cache\/quicklatex.com-e69295ccf8d8ca292abcc97f861e345f_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"&#97;&#61;&#98;\" title=\"Rendered by QuickLaTeX.com\" height=\"13\" width=\"41\" style=\"vertical-align: 0px;\" \/><\/td>\n<td style=\"width: 50%;\" data-align=\"left\"><img loading=\"lazy\" decoding=\"async\" src=\"https:\/\/opentextbc.ca\/introalgebra\/wp-content\/ql-cache\/quicklatex.com-5c53d6ebabdbcfa4e107550ea60b1b19_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"&#97;\" title=\"Rendered by QuickLaTeX.com\" height=\"8\" width=\"9\" style=\"vertical-align: 0px;\" \/> is equal to <img loading=\"lazy\" decoding=\"async\" src=\"https:\/\/opentextbc.ca\/introalgebra\/wp-content\/ql-cache\/quicklatex.com-f56d50c26583f9a035ff6b4e3c0ca5c0_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"&#98;\" title=\"Rendered by QuickLaTeX.com\" height=\"13\" width=\"8\" style=\"vertical-align: 0px;\" \/><\/td>\n<\/tr>\n<tr valign=\"top\">\n<td style=\"width: 50%;\" data-align=\"left\"><img loading=\"lazy\" decoding=\"async\" src=\"https:\/\/opentextbc.ca\/introalgebra\/wp-content\/ql-cache\/quicklatex.com-8740efbef2c653ea7d353859ecc91afd_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"&#97;&#92;&#110;&#101;&#32;&#98;\" title=\"Rendered by QuickLaTeX.com\" height=\"17\" width=\"41\" style=\"vertical-align: -4px;\" \/><\/td>\n<td style=\"width: 50%;\" data-align=\"left\"><img loading=\"lazy\" decoding=\"async\" src=\"https:\/\/opentextbc.ca\/introalgebra\/wp-content\/ql-cache\/quicklatex.com-5c53d6ebabdbcfa4e107550ea60b1b19_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"&#97;\" title=\"Rendered by QuickLaTeX.com\" height=\"8\" width=\"9\" style=\"vertical-align: 0px;\" \/> is not equal to <img loading=\"lazy\" decoding=\"async\" src=\"https:\/\/opentextbc.ca\/introalgebra\/wp-content\/ql-cache\/quicklatex.com-f56d50c26583f9a035ff6b4e3c0ca5c0_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"&#98;\" title=\"Rendered by QuickLaTeX.com\" height=\"13\" width=\"8\" style=\"vertical-align: 0px;\" \/><\/td>\n<\/tr>\n<tr valign=\"top\">\n<td style=\"width: 50%;\" data-align=\"left\"><img loading=\"lazy\" decoding=\"async\" src=\"https:\/\/opentextbc.ca\/introalgebra\/wp-content\/ql-cache\/quicklatex.com-5c53d6ebabdbcfa4e107550ea60b1b19_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"&#97;\" title=\"Rendered by QuickLaTeX.com\" height=\"8\" width=\"9\" style=\"vertical-align: 0px;\" \/> &lt; <img loading=\"lazy\" decoding=\"async\" src=\"https:\/\/opentextbc.ca\/introalgebra\/wp-content\/ql-cache\/quicklatex.com-f56d50c26583f9a035ff6b4e3c0ca5c0_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"&#98;\" title=\"Rendered by QuickLaTeX.com\" height=\"13\" width=\"8\" style=\"vertical-align: 0px;\" \/><\/td>\n<td style=\"width: 50%;\" data-align=\"left\"><img loading=\"lazy\" decoding=\"async\" src=\"https:\/\/opentextbc.ca\/introalgebra\/wp-content\/ql-cache\/quicklatex.com-5c53d6ebabdbcfa4e107550ea60b1b19_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"&#97;\" title=\"Rendered by QuickLaTeX.com\" height=\"8\" width=\"9\" style=\"vertical-align: 0px;\" \/> is less than <img loading=\"lazy\" decoding=\"async\" src=\"https:\/\/opentextbc.ca\/introalgebra\/wp-content\/ql-cache\/quicklatex.com-f56d50c26583f9a035ff6b4e3c0ca5c0_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"&#98;\" title=\"Rendered by QuickLaTeX.com\" height=\"13\" width=\"8\" style=\"vertical-align: 0px;\" \/><\/td>\n<\/tr>\n<tr valign=\"top\">\n<td style=\"width: 50%;\" data-align=\"left\"><img loading=\"lazy\" decoding=\"async\" src=\"https:\/\/opentextbc.ca\/introalgebra\/wp-content\/ql-cache\/quicklatex.com-5c53d6ebabdbcfa4e107550ea60b1b19_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"&#97;\" title=\"Rendered by QuickLaTeX.com\" height=\"8\" width=\"9\" style=\"vertical-align: 0px;\" \/> &gt; <img loading=\"lazy\" decoding=\"async\" src=\"https:\/\/opentextbc.ca\/introalgebra\/wp-content\/ql-cache\/quicklatex.com-f56d50c26583f9a035ff6b4e3c0ca5c0_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"&#98;\" title=\"Rendered by QuickLaTeX.com\" height=\"13\" width=\"8\" style=\"vertical-align: 0px;\" \/><\/td>\n<td style=\"width: 50%;\" data-align=\"left\"><img loading=\"lazy\" decoding=\"async\" src=\"https:\/\/opentextbc.ca\/introalgebra\/wp-content\/ql-cache\/quicklatex.com-5c53d6ebabdbcfa4e107550ea60b1b19_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"&#97;\" title=\"Rendered by QuickLaTeX.com\" height=\"8\" width=\"9\" style=\"vertical-align: 0px;\" \/> is greater than <img loading=\"lazy\" decoding=\"async\" src=\"https:\/\/opentextbc.ca\/introalgebra\/wp-content\/ql-cache\/quicklatex.com-f56d50c26583f9a035ff6b4e3c0ca5c0_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"&#98;\" title=\"Rendered by QuickLaTeX.com\" height=\"13\" width=\"8\" style=\"vertical-align: 0px;\" \/><\/td>\n<\/tr>\n<tr valign=\"top\">\n<td style=\"width: 50%;\" data-align=\"left\"><img loading=\"lazy\" decoding=\"async\" src=\"https:\/\/opentextbc.ca\/introalgebra\/wp-content\/ql-cache\/quicklatex.com-22bb7f496e0a4516393886afb53ffa7c_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"&#97;&#92;&#108;&#101;&#32;&#98;\" title=\"Rendered by QuickLaTeX.com\" height=\"16\" width=\"41\" style=\"vertical-align: -3px;\" \/><\/td>\n<td style=\"width: 50%;\" data-align=\"left\"><img loading=\"lazy\" decoding=\"async\" src=\"https:\/\/opentextbc.ca\/introalgebra\/wp-content\/ql-cache\/quicklatex.com-5c53d6ebabdbcfa4e107550ea60b1b19_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"&#97;\" title=\"Rendered by QuickLaTeX.com\" height=\"8\" width=\"9\" style=\"vertical-align: 0px;\" \/> is less than or equal to <img loading=\"lazy\" decoding=\"async\" src=\"https:\/\/opentextbc.ca\/introalgebra\/wp-content\/ql-cache\/quicklatex.com-f56d50c26583f9a035ff6b4e3c0ca5c0_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"&#98;\" title=\"Rendered by QuickLaTeX.com\" height=\"13\" width=\"8\" style=\"vertical-align: 0px;\" \/><\/td>\n<\/tr>\n<tr valign=\"top\">\n<td style=\"width: 50%;\" data-align=\"left\"><img loading=\"lazy\" decoding=\"async\" src=\"https:\/\/opentextbc.ca\/introalgebra\/wp-content\/ql-cache\/quicklatex.com-4925aae9d8237338b0824392ba2d182a_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"&#97;&#92;&#103;&#101;&#32;&#98;\" title=\"Rendered by QuickLaTeX.com\" height=\"16\" width=\"41\" style=\"vertical-align: -3px;\" \/><\/td>\n<td style=\"width: 50%;\" data-align=\"left\"><img loading=\"lazy\" decoding=\"async\" src=\"https:\/\/opentextbc.ca\/introalgebra\/wp-content\/ql-cache\/quicklatex.com-5c53d6ebabdbcfa4e107550ea60b1b19_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"&#97;\" title=\"Rendered by QuickLaTeX.com\" height=\"8\" width=\"9\" style=\"vertical-align: 0px;\" \/> is greater than or equal to <img loading=\"lazy\" decoding=\"async\" src=\"https:\/\/opentextbc.ca\/introalgebra\/wp-content\/ql-cache\/quicklatex.com-f56d50c26583f9a035ff6b4e3c0ca5c0_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"&#98;\" title=\"Rendered by QuickLaTeX.com\" height=\"13\" width=\"8\" style=\"vertical-align: 0px;\" \/><\/td>\n<\/tr>\n<\/tbody>\n<\/table>\n<div data-type=\"note\">\n<div data-type=\"title\">\n<div class=\"textbox textbox--key-takeaways\">\n<header class=\"textbox__header\">\n<p class=\"textbox__title\">Symbols &lt; and &gt;<\/p>\n<\/header>\n<div class=\"textbox__content\">\n<p id=\"fs-id1508974\">The symbols &lt; and &gt; each have a smaller side and a larger side.<\/p>\n<p id=\"eip-id1168265897874\">smaller side &lt; larger side<br \/>\nlarger side &gt; smaller side<\/p>\n<\/div>\n<\/div>\n<p>The smaller side of the symbol faces the smaller number and the larger faces the larger number.<\/p>\n<\/div>\n<div class=\"textbox textbox--examples\">\n<header class=\"textbox__header\">\n<p class=\"textbox__title\">EXAMPLE 2<\/p>\n<\/header>\n<div class=\"textbox__content\">\n<div id=\"fs-id2199402\" data-type=\"problem\">\n<p>Translate from algebra to words:<\/p>\n<ol id=\"eip-id1168466395280\" class=\"circled\" type=\"a\">\n<li><img loading=\"lazy\" decoding=\"async\" src=\"https:\/\/opentextbc.ca\/introalgebra\/wp-content\/ql-cache\/quicklatex.com-ebd774688b40361e9ff79f6e7ef9c5b2_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"&#92;&#112;&#104;&#97;&#110;&#116;&#111;&#109;&#123;&#92;&#114;&#117;&#108;&#101;&#123;&#48;&#46;&#50;&#101;&#109;&#125;&#123;&#48;&#101;&#120;&#125;&#125;&#50;&#48;&#92;&#108;&#101;&#32;&#51;&#53;\" title=\"Rendered by QuickLaTeX.com\" height=\"16\" width=\"58\" style=\"vertical-align: -3px;\" \/><\/li>\n<li><img loading=\"lazy\" decoding=\"async\" src=\"https:\/\/opentextbc.ca\/introalgebra\/wp-content\/ql-cache\/quicklatex.com-d8a9060de600e6f43fe2ba15115302b3_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"&#92;&#112;&#104;&#97;&#110;&#116;&#111;&#109;&#123;&#92;&#114;&#117;&#108;&#101;&#123;&#48;&#46;&#50;&#101;&#109;&#125;&#123;&#48;&#101;&#120;&#125;&#125;&#49;&#49;&#92;&#110;&#101;&#32;&#49;&#53;&#45;&#51;\" title=\"Rendered by QuickLaTeX.com\" height=\"17\" width=\"88\" style=\"vertical-align: -4px;\" \/><\/li>\n<li><img loading=\"lazy\" decoding=\"async\" src=\"https:\/\/opentextbc.ca\/introalgebra\/wp-content\/ql-cache\/quicklatex.com-544374eaf662f0eb11f1dc78fcc76b4a_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"&#92;&#112;&#104;&#97;&#110;&#116;&#111;&#109;&#123;&#92;&#114;&#117;&#108;&#101;&#123;&#48;&#46;&#50;&#101;&#109;&#125;&#123;&#48;&#101;&#120;&#125;&#125;&#57;\" title=\"Rendered by QuickLaTeX.com\" height=\"12\" width=\"9\" style=\"vertical-align: 0px;\" \/> &gt; <img loading=\"lazy\" decoding=\"async\" src=\"https:\/\/opentextbc.ca\/introalgebra\/wp-content\/ql-cache\/quicklatex.com-38be36e50261abc7d256f42d96b6c48a_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"&#92;&#112;&#104;&#97;&#110;&#116;&#111;&#109;&#123;&#92;&#114;&#117;&#108;&#101;&#123;&#48;&#46;&#50;&#101;&#109;&#125;&#123;&#48;&#101;&#120;&#125;&#125;&#49;&#48;&#92;&#100;&#105;&#118;&#32;&#50;\" title=\"Rendered by QuickLaTeX.com\" height=\"13\" width=\"46\" style=\"vertical-align: -1px;\" \/><\/li>\n<li><img loading=\"lazy\" decoding=\"async\" src=\"https:\/\/opentextbc.ca\/introalgebra\/wp-content\/ql-cache\/quicklatex.com-6d1a5c6178bcaa2513caf22fa7edd7a7_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"&#92;&#112;&#104;&#97;&#110;&#116;&#111;&#109;&#123;&#92;&#114;&#117;&#108;&#101;&#123;&#48;&#46;&#50;&#101;&#109;&#125;&#123;&#48;&#101;&#120;&#125;&#125;&#120;&#43;&#50;\" title=\"Rendered by QuickLaTeX.com\" height=\"14\" width=\"39\" style=\"vertical-align: -2px;\" \/> &lt; <img loading=\"lazy\" decoding=\"async\" src=\"https:\/\/opentextbc.ca\/introalgebra\/wp-content\/ql-cache\/quicklatex.com-b4cd02c4519abf1b236ead3979bff0a7_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"&#92;&#112;&#104;&#97;&#110;&#116;&#111;&#109;&#123;&#92;&#114;&#117;&#108;&#101;&#123;&#48;&#46;&#50;&#101;&#109;&#125;&#123;&#48;&#101;&#120;&#125;&#125;&#49;&#48;\" title=\"Rendered by QuickLaTeX.com\" height=\"13\" width=\"17\" style=\"vertical-align: -1px;\" \/><\/li>\n<\/ol>\n<\/div>\n<div id=\"fs-id1210439\" data-type=\"solution\">\n<div data-type=\"title\"><\/div>\n<div data-type=\"title\"><strong>Solution<\/strong><\/div>\n<div data-type=\"title\"><\/div>\n<table id=\"eip-399\" class=\"unnumbered unstyled\" summary=\".\" data-label=\"\">\n<tbody>\n<tr>\n<td>a.<\/td>\n<\/tr>\n<tr>\n<td><img loading=\"lazy\" decoding=\"async\" src=\"https:\/\/opentextbc.ca\/introalgebra\/wp-content\/ql-cache\/quicklatex.com-99d2c6eb13d73ba115691df1ce8c8ff6_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"&#50;&#48;&#92;&#108;&#101;&#32;&#51;&#53;\" title=\"Rendered by QuickLaTeX.com\" height=\"16\" width=\"58\" style=\"vertical-align: -3px;\" \/><\/td>\n<\/tr>\n<tr>\n<td>20 is less than or equal to 35<\/td>\n<\/tr>\n<\/tbody>\n<\/table>\n<table id=\"eip-id1164752763787\" class=\"unnumbered unstyled\" summary=\".\" data-label=\"\">\n<tbody>\n<tr>\n<td>b.<\/td>\n<\/tr>\n<tr>\n<td><img loading=\"lazy\" decoding=\"async\" src=\"https:\/\/opentextbc.ca\/introalgebra\/wp-content\/ql-cache\/quicklatex.com-c16060c2dfd4974acad3bc0dc68940df_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"&#49;&#49;&#92;&#110;&#101;&#32;&#49;&#53;&#45;&#51;\" title=\"Rendered by QuickLaTeX.com\" height=\"17\" width=\"89\" style=\"vertical-align: -4px;\" \/><\/td>\n<\/tr>\n<tr>\n<td>11 is not equal to 15 minus 3<\/td>\n<\/tr>\n<\/tbody>\n<\/table>\n<table id=\"eip-id1164753846062\" class=\"unnumbered unstyled\" summary=\".\" data-label=\"\">\n<tbody>\n<tr>\n<td>c.<\/td>\n<\/tr>\n<tr>\n<td><img loading=\"lazy\" decoding=\"async\" src=\"https:\/\/opentextbc.ca\/introalgebra\/wp-content\/ql-cache\/quicklatex.com-e99b7c7ddd421682faf67e5b5f865882_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"&#57;\" title=\"Rendered by QuickLaTeX.com\" height=\"12\" width=\"9\" style=\"vertical-align: 0px;\" \/> &gt; <img loading=\"lazy\" decoding=\"async\" src=\"https:\/\/opentextbc.ca\/introalgebra\/wp-content\/ql-cache\/quicklatex.com-e4d638009e32fef081c6d28c5607d7cb_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"&#49;&#48;&#92;&#100;&#105;&#118;&#32;&#50;\" title=\"Rendered by QuickLaTeX.com\" height=\"13\" width=\"46\" style=\"vertical-align: -1px;\" \/><\/td>\n<\/tr>\n<tr>\n<td>9 is greater than 10 divided by 2<\/td>\n<\/tr>\n<\/tbody>\n<\/table>\n<table id=\"eip-id1164752824586\" class=\"unnumbered unstyled\" summary=\".\" data-label=\"\">\n<tbody>\n<tr>\n<td>d.<\/td>\n<\/tr>\n<tr>\n<td><img loading=\"lazy\" decoding=\"async\" src=\"https:\/\/opentextbc.ca\/introalgebra\/wp-content\/ql-cache\/quicklatex.com-d4baf3c092ee3bd5ae188f77cf55175b_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"&#120;&#43;&#50;\" title=\"Rendered by QuickLaTeX.com\" height=\"14\" width=\"40\" style=\"vertical-align: -2px;\" \/> &lt; <img loading=\"lazy\" decoding=\"async\" src=\"https:\/\/opentextbc.ca\/introalgebra\/wp-content\/ql-cache\/quicklatex.com-5450913cc453faf132dc56e5965ca797_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"&#49;&#48;\" title=\"Rendered by QuickLaTeX.com\" height=\"13\" width=\"17\" style=\"vertical-align: -1px;\" \/><\/td>\n<\/tr>\n<tr>\n<td><img loading=\"lazy\" decoding=\"async\" src=\"https:\/\/opentextbc.ca\/introalgebra\/wp-content\/ql-cache\/quicklatex.com-ede05c264bba0eda080918aaa09c4658_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"&#120;\" title=\"Rendered by QuickLaTeX.com\" height=\"8\" width=\"10\" style=\"vertical-align: 0px;\" \/> plus 2 is less than 10<\/td>\n<\/tr>\n<\/tbody>\n<\/table>\n<\/div>\n<\/div>\n<\/div>\n<div class=\"textbox textbox--exercises\">\n<header class=\"textbox__header\">\n<p class=\"textbox__title\">TRY IT 2.1<\/p>\n<\/header>\n<div class=\"textbox__content\">\n<div id=\"fs-id1205270\" data-type=\"problem\">\n<p id=\"fs-id2903606\">Translate from algebra to words.<\/p>\n<ol id=\"eip-id1168466011782\" class=\"circled\" type=\"a\">\n<li><img loading=\"lazy\" decoding=\"async\" src=\"https:\/\/opentextbc.ca\/introalgebra\/wp-content\/ql-cache\/quicklatex.com-2fa076bf0da0dc96e0542b1eed8c85e1_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"&#92;&#112;&#104;&#97;&#110;&#116;&#111;&#109;&#123;&#92;&#114;&#117;&#108;&#101;&#123;&#48;&#46;&#50;&#101;&#109;&#125;&#123;&#48;&#101;&#120;&#125;&#125;&#92;&#116;&#101;&#120;&#116;&#123;&#49;&#52;&#125;&#92;&#108;&#101;&#32;&#50;&#55;&#92;&#112;&#104;&#97;&#110;&#116;&#111;&#109;&#123;&#92;&#114;&#117;&#108;&#101;&#123;&#48;&#46;&#50;&#101;&#109;&#125;&#123;&#48;&#101;&#120;&#125;&#125;\" title=\"Rendered by QuickLaTeX.com\" height=\"16\" width=\"58\" style=\"vertical-align: -3px;\" \/><\/li>\n<li><img loading=\"lazy\" decoding=\"async\" src=\"https:\/\/opentextbc.ca\/introalgebra\/wp-content\/ql-cache\/quicklatex.com-a5470f6465269ee12065b9f627305f4f_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"&#92;&#112;&#104;&#97;&#110;&#116;&#111;&#109;&#123;&#92;&#114;&#117;&#108;&#101;&#123;&#48;&#46;&#50;&#101;&#109;&#125;&#123;&#48;&#101;&#120;&#125;&#125;&#49;&#57;&#45;&#50;&#92;&#110;&#101;&#32;&#56;&#92;&#112;&#104;&#97;&#110;&#116;&#111;&#109;&#123;&#92;&#114;&#117;&#108;&#101;&#123;&#48;&#46;&#50;&#101;&#109;&#125;&#123;&#48;&#101;&#120;&#125;&#125;\" title=\"Rendered by QuickLaTeX.com\" height=\"17\" width=\"79\" style=\"vertical-align: -4px;\" \/><\/li>\n<li><img loading=\"lazy\" decoding=\"async\" src=\"https:\/\/opentextbc.ca\/introalgebra\/wp-content\/ql-cache\/quicklatex.com-d39cdd5c825f65b60f378f7174861ce3_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"&#92;&#112;&#104;&#97;&#110;&#116;&#111;&#109;&#123;&#92;&#114;&#117;&#108;&#101;&#123;&#48;&#46;&#50;&#101;&#109;&#125;&#123;&#48;&#101;&#120;&#125;&#125;&#49;&#50;\" title=\"Rendered by QuickLaTeX.com\" height=\"13\" width=\"16\" style=\"vertical-align: -1px;\" \/> &gt; <img loading=\"lazy\" decoding=\"async\" src=\"https:\/\/opentextbc.ca\/introalgebra\/wp-content\/ql-cache\/quicklatex.com-c0bd1a58fd6c83b4797715e57262a904_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"&#52;&#92;&#112;&#104;&#97;&#110;&#116;&#111;&#109;&#123;&#92;&#114;&#117;&#108;&#101;&#123;&#48;&#46;&#50;&#101;&#109;&#125;&#123;&#48;&#101;&#120;&#125;&#125;&#92;&#100;&#105;&#118;&#32;&#50;&#92;&#112;&#104;&#97;&#110;&#116;&#111;&#109;&#123;&#92;&#114;&#117;&#108;&#101;&#123;&#48;&#46;&#50;&#101;&#109;&#125;&#123;&#48;&#101;&#120;&#125;&#125;\" title=\"Rendered by QuickLaTeX.com\" height=\"13\" width=\"42\" style=\"vertical-align: -1px;\" \/><\/li>\n<li><img loading=\"lazy\" decoding=\"async\" src=\"https:\/\/opentextbc.ca\/introalgebra\/wp-content\/ql-cache\/quicklatex.com-301957e1618f9ce9cc09980a939b99a4_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"&#92;&#112;&#104;&#97;&#110;&#116;&#111;&#109;&#123;&#92;&#114;&#117;&#108;&#101;&#123;&#48;&#46;&#50;&#101;&#109;&#125;&#123;&#48;&#101;&#120;&#125;&#125;&#120;&#45;&#55;\" title=\"Rendered by QuickLaTeX.com\" height=\"13\" width=\"40\" style=\"vertical-align: 0px;\" \/> &lt; <img loading=\"lazy\" decoding=\"async\" src=\"https:\/\/opentextbc.ca\/introalgebra\/wp-content\/ql-cache\/quicklatex.com-7842aa3b9094636b29b225c702b545d1_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"&#92;&#112;&#104;&#97;&#110;&#116;&#111;&#109;&#123;&#92;&#114;&#117;&#108;&#101;&#123;&#48;&#46;&#50;&#101;&#109;&#125;&#123;&#48;&#101;&#120;&#125;&#125;&#49;\" title=\"Rendered by QuickLaTeX.com\" height=\"13\" width=\"7\" style=\"vertical-align: -1px;\" \/><\/li>\n<\/ol>\n<\/div>\n<div id=\"fs-id2816995\" data-type=\"solution\">\n<details>\n<summary>Show Answer<\/summary>\n<ol id=\"eip-id1168466395276\" class=\"circled\" type=\"a\">\n<li>fourteen is less than or equal to twenty-seven<\/li>\n<li>nineteen minus two is not equal to eight<\/li>\n<li>twelve is greater than four divided by two<\/li>\n<li><em data-effect=\"italics\">x<\/em> minus seven is less than one<\/li>\n<\/ol>\n<\/details>\n<\/div>\n<\/div>\n<\/div>\n<\/div>\n<div id=\"fs-id1297928\" class=\"try\" data-type=\"note\">\n<div id=\"fs-id2310743\" data-type=\"exercise\">\n<div id=\"fs-id1205270\" data-type=\"problem\">\n<div class=\"textbox textbox--exercises\">\n<header class=\"textbox__header\">\n<p class=\"textbox__title\">TRY IT 2.2<\/p>\n<\/header>\n<div class=\"textbox__content\">\n<div id=\"fs-id1614444\" data-type=\"problem\">\n<p id=\"fs-id1171103156301\">Translate from algebra to words.<\/p>\n<ol id=\"eip-id1168469636286\" class=\"circled\" type=\"a\">\n<li><img loading=\"lazy\" decoding=\"async\" src=\"https:\/\/opentextbc.ca\/introalgebra\/wp-content\/ql-cache\/quicklatex.com-085089fcf28dc7fb62cb74ccd5e5754d_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"&#92;&#112;&#104;&#97;&#110;&#116;&#111;&#109;&#123;&#92;&#114;&#117;&#108;&#101;&#123;&#48;&#46;&#50;&#101;&#109;&#125;&#123;&#48;&#101;&#120;&#125;&#125;&#49;&#57;&#92;&#103;&#101;&#32;&#49;&#53;&#92;&#112;&#104;&#97;&#110;&#116;&#111;&#109;&#123;&#92;&#114;&#117;&#108;&#101;&#123;&#48;&#46;&#50;&#101;&#109;&#125;&#123;&#48;&#101;&#120;&#125;&#125;\" title=\"Rendered by QuickLaTeX.com\" height=\"16\" width=\"57\" style=\"vertical-align: -3px;\" \/><\/li>\n<li><img loading=\"lazy\" decoding=\"async\" src=\"https:\/\/opentextbc.ca\/introalgebra\/wp-content\/ql-cache\/quicklatex.com-1b074e620fe06150e16c98d86bcf501e_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"&#92;&#112;&#104;&#97;&#110;&#116;&#111;&#109;&#123;&#92;&#114;&#117;&#108;&#101;&#123;&#48;&#46;&#50;&#101;&#109;&#125;&#123;&#48;&#101;&#120;&#125;&#125;&#55;&#61;&#49;&#50;&#45;&#53;&#92;&#112;&#104;&#97;&#110;&#116;&#111;&#109;&#123;&#92;&#114;&#117;&#108;&#101;&#123;&#48;&#46;&#50;&#101;&#109;&#125;&#123;&#48;&#101;&#120;&#125;&#125;\" title=\"Rendered by QuickLaTeX.com\" height=\"14\" width=\"79\" style=\"vertical-align: -1px;\" \/><\/li>\n<li><img loading=\"lazy\" decoding=\"async\" src=\"https:\/\/opentextbc.ca\/introalgebra\/wp-content\/ql-cache\/quicklatex.com-9fa3f962379175aa2af299dda6fc03ab_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"&#92;&#112;&#104;&#97;&#110;&#116;&#111;&#109;&#123;&#92;&#114;&#117;&#108;&#101;&#123;&#48;&#46;&#50;&#101;&#109;&#125;&#123;&#48;&#101;&#120;&#125;&#125;&#49;&#53;&#92;&#100;&#105;&#118;&#32;&#51;\" title=\"Rendered by QuickLaTeX.com\" height=\"14\" width=\"47\" style=\"vertical-align: -1px;\" \/> &lt; <img loading=\"lazy\" decoding=\"async\" src=\"https:\/\/opentextbc.ca\/introalgebra\/wp-content\/ql-cache\/quicklatex.com-b520c35e6d0dfd050fd4330dfe8a0712_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"&#56;&#92;&#112;&#104;&#97;&#110;&#116;&#111;&#109;&#123;&#92;&#114;&#117;&#108;&#101;&#123;&#48;&#46;&#50;&#101;&#109;&#125;&#123;&#48;&#101;&#120;&#125;&#125;\" title=\"Rendered by QuickLaTeX.com\" height=\"12\" width=\"9\" style=\"vertical-align: 0px;\" \/><\/li>\n<li><img loading=\"lazy\" decoding=\"async\" src=\"https:\/\/opentextbc.ca\/introalgebra\/wp-content\/ql-cache\/quicklatex.com-a5efba58c5c94fb9c925bac2786d3d9d_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"&#92;&#112;&#104;&#97;&#110;&#116;&#111;&#109;&#123;&#92;&#114;&#117;&#108;&#101;&#123;&#48;&#46;&#50;&#101;&#109;&#125;&#123;&#48;&#101;&#120;&#125;&#125;&#121;&#45;&#51;\" title=\"Rendered by QuickLaTeX.com\" height=\"16\" width=\"40\" style=\"vertical-align: -4px;\" \/> &gt; <img loading=\"lazy\" decoding=\"async\" src=\"https:\/\/opentextbc.ca\/introalgebra\/wp-content\/ql-cache\/quicklatex.com-c64c990aa212df6c031bb873ad2f2ef8_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"&#54;&#92;&#112;&#104;&#97;&#110;&#116;&#111;&#109;&#123;&#92;&#114;&#117;&#108;&#101;&#123;&#48;&#46;&#50;&#101;&#109;&#125;&#123;&#48;&#101;&#120;&#125;&#125;\" title=\"Rendered by QuickLaTeX.com\" height=\"12\" width=\"9\" style=\"vertical-align: 0px;\" \/><\/li>\n<\/ol>\n<\/div>\n<div id=\"fs-id1567145\" data-type=\"solution\">\n<details>\n<summary>Show Answer<\/summary>\n<ol id=\"eip-id1168469636381\" class=\"circled\" type=\"a\">\n<li>nineteen is greater than or equal to fifteen<\/li>\n<li>seven is equal to twelve minus five<\/li>\n<li>fifteen divided by three is less than eight<\/li>\n<li><em data-effect=\"italics\">y<\/em> minus three is greater than six<\/li>\n<\/ol>\n<\/details>\n<\/div>\n<\/div>\n<\/div>\n<\/div>\n<\/div>\n<\/div>\n<div id=\"fs-id1171104414920\" class=\"try\" data-type=\"note\">\n<div id=\"fs-id1573881\" data-type=\"exercise\">\n<div id=\"fs-id1614444\" data-type=\"problem\">\n<div class=\"textbox textbox--examples\">\n<header class=\"textbox__header\">\n<p class=\"textbox__title\">EXAMPLE 3<\/p>\n<\/header>\n<div class=\"textbox__content\">\n<div id=\"fs-id2471355\" data-type=\"problem\">\n<p id=\"fs-id1825021\">The information in <a class=\"autogenerated-content\" href=\"#CNX_BMath_Figure_02_01_003\">(Figure 1)<\/a> compares the fuel economy in miles-per-gallon (mpg) of several cars. Write the appropriate symbol <img loading=\"lazy\" decoding=\"async\" src=\"https:\/\/opentextbc.ca\/introalgebra\/wp-content\/ql-cache\/quicklatex.com-fefddd3656bfbfe5250ca84d77b0a7a2_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"&#92;&#116;&#101;&#120;&#116;&#123;&#115;&#121;&#109;&#98;&#111;&#108;&#125;&#44;&#92;&#116;&#101;&#120;&#116;&#123;&#61;&#125;&#44;\" title=\"Rendered by QuickLaTeX.com\" height=\"16\" width=\"80\" style=\"vertical-align: -4px;\" \/> &lt; <img loading=\"lazy\" decoding=\"async\" src=\"https:\/\/opentextbc.ca\/introalgebra\/wp-content\/ql-cache\/quicklatex.com-3a2d99fc726cd1dd8743213eeaeac0e3_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"&#44;&#92;&#116;&#101;&#120;&#116;&#123;&#111;&#114;&#125;\" title=\"Rendered by QuickLaTeX.com\" height=\"12\" width=\"23\" style=\"vertical-align: -4px;\" \/> &gt;. in each expression to compare the fuel economy of the cars.<\/p>\n<div id=\"CNX_BMath_Figure_02_01_003\" class=\"bc-figure figure\">\n<div class=\"bc-figcaption figcaption\">(credit: modification of work by Bernard Goldbach, Wikimedia Commons)<\/div>\n<figure style=\"width: 632px\" class=\"wp-caption aligncenter\"><img loading=\"lazy\" decoding=\"async\" src=\"https:\/\/opentextbc.ca\/accessibilitytoolkit\/wp-content\/uploads\/sites\/333\/2021\/03\/CNX_BMath_Figure_02_01_003-1.jpg\" alt=\"This table has two rows and six columns. The first column is a header column and it labels each row The first row is labeled \u201cCar\u201d and the second \u201cFuel economy (mpg)\u201d. To the right of the \u2018Car\u2019 row are the labels: \u201cPrius\u201d, \u201cMini Cooper\u201d, \u201cToyota Corolla\u201d, \u201cVersa\u201d, \u201cHonda Fit\u201d. Each of these columns contains an image of the labeled car model. To the right of the \u201cFuel economy (mpg)\u201d row are the algebraic equations: the letter p, the equals symbol, the number forty-eight; the letter m, the equals symbol, the number twenty-seven; the letter c, the equals symbol, the number twenty-eight; the letter v, the equals symbol, the number twenty-six; and the letter f, the equals symbol, the number twenty-seven.\" width=\"632\" height=\"117\" data-media-type=\"image\/jpeg\" \/><figcaption class=\"wp-caption-text\">Figure 1<\/figcaption><\/figure>\n<\/div>\n<ol id=\"eip-id1168467200954\" class=\"circled\" type=\"a\">\n<li>MPG of Prius_____ MPG of Mini Cooper<\/li>\n<li>MPG of Versa_____ MPG of Fit<\/li>\n<li>MPG of Mini Cooper_____ MPG of Fit<\/li>\n<li>MPG of Corolla_____ MPG of Versa<\/li>\n<li>MPG of Corolla_____ MPG of Prius<\/li>\n<\/ol>\n<\/div>\n<div id=\"fs-id1215439\" data-type=\"solution\">\n<div data-type=\"title\"><\/div>\n<div data-type=\"title\"><strong>Solution<\/strong><\/div>\n<div data-type=\"title\"><\/div>\n<table id=\"eip-254\" style=\"width: 100%;\" summary=\".\" data-label=\"\">\n<tbody>\n<tr>\n<td>a.<\/td>\n<td><\/td>\n<\/tr>\n<tr>\n<td><\/td>\n<td data-align=\"center\">MPG of Prius____MPG of Mini Cooper<\/td>\n<\/tr>\n<tr>\n<td>Find the values in the chart.<\/td>\n<td data-align=\"center\">48____27<\/td>\n<\/tr>\n<tr>\n<td>Compare.<\/td>\n<td data-align=\"center\">48 &gt; 27<\/td>\n<\/tr>\n<tr>\n<td><\/td>\n<td data-align=\"center\">MPG of Prius &gt; MPG of Mini Cooper<\/td>\n<\/tr>\n<\/tbody>\n<\/table>\n<table id=\"eip-id1164755344638\" style=\"width: 100%;\" summary=\".\" data-label=\"\">\n<tbody>\n<tr>\n<td>b.<\/td>\n<td><\/td>\n<\/tr>\n<tr>\n<td><\/td>\n<td data-align=\"center\">MPG of Versa____MPG of Fit<\/td>\n<\/tr>\n<tr>\n<td>Find the values in the chart.<\/td>\n<td data-align=\"center\">26____27<\/td>\n<\/tr>\n<tr>\n<td>Compare.<\/td>\n<td data-align=\"center\">26 &lt; 27<\/td>\n<\/tr>\n<tr>\n<td><\/td>\n<td data-align=\"center\">MPG of Versa &lt; MPG of Fit<\/td>\n<\/tr>\n<\/tbody>\n<\/table>\n<table id=\"eip-id1164755344710\" style=\"width: 100%;\" summary=\".\" data-label=\"\">\n<tbody>\n<tr>\n<td>c.<\/td>\n<td><\/td>\n<\/tr>\n<tr>\n<td><\/td>\n<td data-align=\"center\">MPG of Mini Cooper____MPG of Fit<\/td>\n<\/tr>\n<tr>\n<td>Find the values in the chart.<\/td>\n<td data-align=\"center\">27____27<\/td>\n<\/tr>\n<tr>\n<td>Compare.<\/td>\n<td data-align=\"center\">27 = 27<\/td>\n<\/tr>\n<tr>\n<td><\/td>\n<td data-align=\"center\">MPG of Mini Cooper = MPG of Fit<\/td>\n<\/tr>\n<\/tbody>\n<\/table>\n<table id=\"eip-id1164755231773\" style=\"width: 100%; height: 70px;\" summary=\".\" data-label=\"\">\n<tbody>\n<tr style=\"height: 14px;\">\n<td style=\"height: 14px;\">d.<\/td>\n<td style=\"height: 14px;\"><\/td>\n<\/tr>\n<tr style=\"height: 14px;\">\n<td style=\"height: 14px;\"><\/td>\n<td style=\"height: 14px;\" data-align=\"center\">MPG of Corolla____MPG of Versa<\/td>\n<\/tr>\n<tr style=\"height: 14px;\">\n<td style=\"height: 14px;\">Find the values in the chart.<\/td>\n<td style=\"height: 14px;\" data-align=\"center\">28____26<\/td>\n<\/tr>\n<tr style=\"height: 14px;\">\n<td style=\"height: 14px;\">Compare.<\/td>\n<td style=\"height: 14px;\" data-align=\"center\">28 &gt; 26<\/td>\n<\/tr>\n<tr style=\"height: 14px;\">\n<td style=\"height: 14px;\"><\/td>\n<td style=\"height: 14px;\" data-align=\"center\">MPG of Corolla &gt; MPG of Versa<\/td>\n<\/tr>\n<\/tbody>\n<\/table>\n<table id=\"eip-id1164755231845\" style=\"width: 100%;\" summary=\".\" data-label=\"\">\n<tbody>\n<tr>\n<td>e.<\/td>\n<td><\/td>\n<\/tr>\n<tr>\n<td><\/td>\n<td data-align=\"center\">MPG of Corolla____MPG of Prius<\/td>\n<\/tr>\n<tr>\n<td>Find the values in the chart.<\/td>\n<td data-align=\"center\">28____48<\/td>\n<\/tr>\n<tr>\n<td>Compare.<\/td>\n<td data-align=\"center\">28 &lt; 48<\/td>\n<\/tr>\n<tr>\n<td><\/td>\n<td data-align=\"center\">MPG of Corolla &lt; MPG of Prius<\/td>\n<\/tr>\n<\/tbody>\n<\/table>\n<\/div>\n<\/div>\n<\/div>\n<div class=\"textbox textbox--exercises\">\n<header class=\"textbox__header\">\n<p class=\"textbox__title\">TRY IT 3.1<\/p>\n<\/header>\n<div class=\"textbox__content\">\n<div id=\"fs-id1567666\" data-type=\"problem\">\n<p id=\"fs-id2173921\">Use <a class=\"autogenerated-content\" href=\"#CNX_BMath_Figure_02_01_003\">Figure 1<\/a> to fill in the appropriate <img loading=\"lazy\" decoding=\"async\" src=\"https:\/\/opentextbc.ca\/introalgebra\/wp-content\/ql-cache\/quicklatex.com-fefddd3656bfbfe5250ca84d77b0a7a2_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"&#92;&#116;&#101;&#120;&#116;&#123;&#115;&#121;&#109;&#98;&#111;&#108;&#125;&#44;&#92;&#116;&#101;&#120;&#116;&#123;&#61;&#125;&#44;\" title=\"Rendered by QuickLaTeX.com\" height=\"16\" width=\"80\" style=\"vertical-align: -4px;\" \/> &lt; <img loading=\"lazy\" decoding=\"async\" src=\"https:\/\/opentextbc.ca\/introalgebra\/wp-content\/ql-cache\/quicklatex.com-3a2d99fc726cd1dd8743213eeaeac0e3_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"&#44;&#92;&#116;&#101;&#120;&#116;&#123;&#111;&#114;&#125;\" title=\"Rendered by QuickLaTeX.com\" height=\"12\" width=\"23\" style=\"vertical-align: -4px;\" \/> &gt;.<\/p>\n<ol id=\"eip-id1168468772318\" class=\"circled\" type=\"a\">\n<li>MPG of Prius_____MPG of Versa<\/li>\n<li>MPG of Mini Cooper_____ MPG of Corolla<\/li>\n<\/ol>\n<\/div>\n<div id=\"fs-id611660\" data-type=\"solution\">\n<details>\n<summary>Show Answer<\/summary>\n<ol id=\"eip-id1168468400876\" class=\"circled\" type=\"a\">\n<li>&gt;<\/li>\n<li>&lt;<\/li>\n<\/ol>\n<\/details>\n<\/div>\n<\/div>\n<\/div>\n<div class=\"textbox textbox--exercises\">\n<header class=\"textbox__header\">\n<p class=\"textbox__title\">TRY IT 3.2<\/p>\n<\/header>\n<div class=\"textbox__content\">\n<div id=\"fs-id1824239\" data-type=\"problem\">\n<p id=\"fs-id1171104004719\">Use <a class=\"autogenerated-content\" href=\"#CNX_BMath_Figure_02_01_003\">Figure 1<\/a> to fill in the appropriate <img loading=\"lazy\" decoding=\"async\" src=\"https:\/\/opentextbc.ca\/introalgebra\/wp-content\/ql-cache\/quicklatex.com-fefddd3656bfbfe5250ca84d77b0a7a2_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"&#92;&#116;&#101;&#120;&#116;&#123;&#115;&#121;&#109;&#98;&#111;&#108;&#125;&#44;&#92;&#116;&#101;&#120;&#116;&#123;&#61;&#125;&#44;\" title=\"Rendered by QuickLaTeX.com\" height=\"16\" width=\"80\" style=\"vertical-align: -4px;\" \/> &lt; <img loading=\"lazy\" decoding=\"async\" src=\"https:\/\/opentextbc.ca\/introalgebra\/wp-content\/ql-cache\/quicklatex.com-3a2d99fc726cd1dd8743213eeaeac0e3_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"&#44;&#92;&#116;&#101;&#120;&#116;&#123;&#111;&#114;&#125;\" title=\"Rendered by QuickLaTeX.com\" height=\"12\" width=\"23\" style=\"vertical-align: -4px;\" \/> &gt;.<\/p>\n<ol id=\"eip-id1168467211692\" class=\"circled\" type=\"a\">\n<li>MPG of Fit_____ MPG of Prius<\/li>\n<li>MPG of Corolla _____ MPG of Fit<\/li>\n<\/ol>\n<\/div>\n<div id=\"fs-id2270408\" data-type=\"solution\">\n<details>\n<summary>Show Answer<\/summary>\n<ol id=\"eip-id1168468505851\" class=\"circled\" type=\"a\">\n<li>&lt;<\/li>\n<li>&lt;<\/li>\n<\/ol>\n<\/details>\n<\/div>\n<\/div>\n<\/div>\n<p>Grouping symbols in algebra are much like the commas, colons, and other punctuation marks in written language. They indicate which expressions are to be kept together and separate from other expressions. The table below lists three of the most commonly used grouping symbols in algebra.<\/p>\n<\/div>\n<\/div>\n<\/div>\n<table id=\"fs-id2856176\" class=\"grid\" style=\"width: 100%;\" summary=\"This table has four rows and two columns. The first row spans both columns and is a header reading \u201cCommon Grouping Symbols\u201d. The second row is labeled \u201cparentheses\u201d in the first column and the shows the open parentheses symbol followed by the close parentheses symbol. The third row is labeled \u201cBrackets\u201d in the first column and the shows the open square bracket symbol followed by the close square bracket symbol. The third row is labeled \u201cbraces\u201d in the first column and the shows the open curly brace symbol followed by the close curly brace symbol.\">\n<caption>Common Grouping Symbols<\/caption>\n<tbody>\n<tr valign=\"top\">\n<td style=\"text-align: left;\" data-align=\"left\">parentheses<\/td>\n<td style=\"text-align: left;\" data-align=\"center\"><img loading=\"lazy\" decoding=\"async\" src=\"https:\/\/opentextbc.ca\/introalgebra\/wp-content\/ql-cache\/quicklatex.com-6e6dea679189f864ebb36ac42159ea16_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"&#92;&#108;&#101;&#102;&#116;&#40;&#92;&#112;&#104;&#97;&#110;&#116;&#111;&#109;&#123;&#92;&#114;&#117;&#108;&#101;&#123;&#48;&#46;&#53;&#101;&#109;&#125;&#123;&#48;&#101;&#120;&#125;&#125;&#92;&#114;&#105;&#103;&#104;&#116;&#41;\" title=\"Rendered by QuickLaTeX.com\" height=\"18\" width=\"21\" style=\"vertical-align: -4px;\" \/><\/td>\n<\/tr>\n<tr valign=\"top\">\n<td style=\"text-align: left;\" data-align=\"left\">brackets<\/td>\n<td style=\"text-align: left;\" data-align=\"center\"><img loading=\"lazy\" decoding=\"async\" src=\"https:\/\/opentextbc.ca\/introalgebra\/wp-content\/ql-cache\/quicklatex.com-6366aa9031ead5bd088fb8b907907f10_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"&#92;&#108;&#101;&#102;&#116;&#091;&#92;&#112;&#104;&#97;&#110;&#116;&#111;&#109;&#123;&#92;&#114;&#117;&#108;&#101;&#123;&#48;&#46;&#53;&#101;&#109;&#125;&#123;&#48;&#101;&#120;&#125;&#125;&#92;&#114;&#105;&#103;&#104;&#116;&#093;\" title=\"Rendered by QuickLaTeX.com\" height=\"18\" width=\"15\" style=\"vertical-align: -5px;\" \/><\/td>\n<\/tr>\n<tr valign=\"top\">\n<td style=\"text-align: left;\" data-align=\"left\">braces<\/td>\n<td style=\"text-align: left;\" data-align=\"center\"><img loading=\"lazy\" decoding=\"async\" src=\"https:\/\/opentextbc.ca\/introalgebra\/wp-content\/ql-cache\/quicklatex.com-d1a935744eae2523b7d685715069ba6c_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"&#92;&#108;&#101;&#102;&#116;&#92;&#123;&#92;&#112;&#104;&#97;&#110;&#116;&#111;&#109;&#123;&#92;&#114;&#117;&#108;&#101;&#123;&#48;&#46;&#53;&#101;&#109;&#125;&#123;&#48;&#101;&#120;&#125;&#125;&#92;&#114;&#105;&#103;&#104;&#116;&#92;&#125;\" title=\"Rendered by QuickLaTeX.com\" height=\"18\" width=\"25\" style=\"vertical-align: -5px;\" \/><\/td>\n<\/tr>\n<\/tbody>\n<\/table>\n<p>Here are some examples of expressions that include grouping symbols. We will simplify expressions like these later in this section.<\/p>\n<div id=\"fs-id2221712\" class=\"unnumbered\" data-type=\"equation\" data-label=\"\"><img loading=\"lazy\" decoding=\"async\" src=\"https:\/\/opentextbc.ca\/introalgebra\/wp-content\/ql-cache\/quicklatex.com-7598f6833080f5808d041872936979d0_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"&#56;&#92;&#108;&#101;&#102;&#116;&#40;&#49;&#52;&#45;&#56;&#92;&#114;&#105;&#103;&#104;&#116;&#41;&#92;&#112;&#104;&#97;&#110;&#116;&#111;&#109;&#123;&#92;&#114;&#117;&#108;&#101;&#123;&#52;&#101;&#109;&#125;&#123;&#48;&#101;&#120;&#125;&#125;&#50;&#49;&#45;&#51;&#92;&#108;&#101;&#102;&#116;&#091;&#50;&#43;&#52;&#92;&#108;&#101;&#102;&#116;&#40;&#57;&#45;&#56;&#92;&#114;&#105;&#103;&#104;&#116;&#41;&#92;&#114;&#105;&#103;&#104;&#116;&#093;&#92;&#112;&#104;&#97;&#110;&#116;&#111;&#109;&#123;&#92;&#114;&#117;&#108;&#101;&#123;&#52;&#101;&#109;&#125;&#123;&#48;&#101;&#120;&#125;&#125;&#50;&#52;&#92;&#100;&#105;&#118;&#32;&#92;&#108;&#101;&#102;&#116;&#92;&#123;&#49;&#51;&#45;&#50;&#92;&#108;&#101;&#102;&#116;&#091;&#49;&#92;&#108;&#101;&#102;&#116;&#40;&#54;&#45;&#53;&#92;&#114;&#105;&#103;&#104;&#116;&#41;&#43;&#52;&#92;&#114;&#105;&#103;&#104;&#116;&#093;&#92;&#114;&#105;&#103;&#104;&#116;&#92;&#125;\" title=\"Rendered by QuickLaTeX.com\" height=\"19\" width=\"591\" style=\"vertical-align: -5px;\" \/><\/div>\n<h1>Identify Expressions and Equations<\/h1>\n<p id=\"fs-id2139102\">What is the difference in English between a phrase and a sentence? A phrase expresses a single thought that is incomplete by itself, but a sentence makes a complete statement. \u201cRunning very fast\u201d is a phrase, but \u201cThe football player was running very fast\u201d is a sentence. A sentence has a subject and a verb.<\/p>\n<p id=\"fs-id1171104014483\">In algebra, we have <em data-effect=\"italics\">expressions<\/em> and <em data-effect=\"italics\">equations<\/em>. An <span class=\"no-emphasis\" data-type=\"term\">expression<\/span> is like a phrase. Here are some examples of expressions and how they relate to word phrases:<\/p>\n<table id=\"fs-id2472125\" style=\"width: 100%;\" summary=\"This table has five rows and three columns. The first row is a header row and it labels each column. The first column is labeled \u201cExpression\u201d, the second \u201cWords\u201d and the third \u201cPhrase\u201d. In the second row, under the \u201cExpression\u201d column is three plus five. Under the \u201cWords\u201d column is the phrase \u201cthree plus five\u201d. Under the \u201cPhrase\u201d column is the phrase \u201cthe sum of three and five\u201d. In the third row, under the \u201cExpression\u201d column is n minus one. Under the \u201cWords\u201d column is the phrase \u201cn minus one.\u201d Under the \u201cPhrase\u201d column is the phrase \u201cthe difference of n and one.\u201d In the fourth row, under the \u201cExpression\u201d column is six times seven. Under the \u201cWords\u201d column is the phrase \u201csix times seven.\u201d Under the \u201cPhrase\u201d column is the phrase \u201cthe product of six and seven.\u201d In the fifth row, under the \u201cExpression\u201d column is x divided by y. Under the \u201cWords\u201d column is the phrase \u201cx divided by y.\u201d Under the \u201cPhrase\u201d column is the phrase \u201cthe quotient of x and y.\u201d\" data-label=\"\">\n<thead>\n<tr valign=\"top\">\n<th style=\"text-align: left;\" scope=\"col\" data-align=\"left\">Expression<\/th>\n<th style=\"text-align: left;\" scope=\"col\" data-align=\"left\">Words<\/th>\n<th style=\"text-align: left;\" scope=\"col\" data-align=\"left\">Phrase<\/th>\n<\/tr>\n<\/thead>\n<tbody>\n<tr valign=\"top\">\n<td style=\"text-align: left;\" data-align=\"left\"><img loading=\"lazy\" decoding=\"async\" src=\"https:\/\/opentextbc.ca\/introalgebra\/wp-content\/ql-cache\/quicklatex.com-cf4c2a80a2ff2ee7907cea5334d164d6_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"&#51;&#43;&#53;\" title=\"Rendered by QuickLaTeX.com\" height=\"15\" width=\"39\" style=\"vertical-align: -2px;\" \/><\/td>\n<td style=\"text-align: left;\" data-align=\"left\"><img loading=\"lazy\" decoding=\"async\" src=\"https:\/\/opentextbc.ca\/introalgebra\/wp-content\/ql-cache\/quicklatex.com-762867bb15efea281f5d64de25ffebdd_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"&#51;&#92;&#112;&#104;&#97;&#110;&#116;&#111;&#109;&#123;&#92;&#114;&#117;&#108;&#101;&#123;&#48;&#46;&#50;&#101;&#109;&#125;&#123;&#48;&#101;&#120;&#125;&#125;&#92;&#116;&#101;&#120;&#116;&#123;&#112;&#108;&#117;&#115;&#125;&#92;&#112;&#104;&#97;&#110;&#116;&#111;&#109;&#123;&#92;&#114;&#117;&#108;&#101;&#123;&#48;&#46;&#50;&#101;&#109;&#125;&#123;&#48;&#101;&#120;&#125;&#125;&#53;\" title=\"Rendered by QuickLaTeX.com\" height=\"16\" width=\"56\" style=\"vertical-align: -3px;\" \/><\/td>\n<td style=\"text-align: left;\" data-align=\"left\">the sum of three and five<\/td>\n<\/tr>\n<tr valign=\"top\">\n<td style=\"text-align: left;\" data-align=\"left\"><img loading=\"lazy\" decoding=\"async\" src=\"https:\/\/opentextbc.ca\/introalgebra\/wp-content\/ql-cache\/quicklatex.com-f30b71e7fcec69d119f30f67cf09c975_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"&#110;&#45;&#49;\" title=\"Rendered by QuickLaTeX.com\" height=\"13\" width=\"40\" style=\"vertical-align: -1px;\" \/><\/td>\n<td style=\"text-align: left;\" data-align=\"left\"><img loading=\"lazy\" decoding=\"async\" src=\"https:\/\/opentextbc.ca\/introalgebra\/wp-content\/ql-cache\/quicklatex.com-b170995d512c659d8668b4e42e1fef6b_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"&#110;\" title=\"Rendered by QuickLaTeX.com\" height=\"8\" width=\"11\" style=\"vertical-align: 0px;\" \/> minus one<\/td>\n<td style=\"text-align: left;\" data-align=\"left\">the difference of <img loading=\"lazy\" decoding=\"async\" src=\"https:\/\/opentextbc.ca\/introalgebra\/wp-content\/ql-cache\/quicklatex.com-b170995d512c659d8668b4e42e1fef6b_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"&#110;\" title=\"Rendered by QuickLaTeX.com\" height=\"8\" width=\"11\" style=\"vertical-align: 0px;\" \/> and one<\/td>\n<\/tr>\n<tr valign=\"top\">\n<td style=\"text-align: left;\" data-align=\"left\"><img loading=\"lazy\" decoding=\"async\" src=\"https:\/\/opentextbc.ca\/introalgebra\/wp-content\/ql-cache\/quicklatex.com-c5cb7d583240ff955f68f8efcb5977a3_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"&#54;&#92;&#99;&#100;&#111;&#116;&#32;&#55;\" title=\"Rendered by QuickLaTeX.com\" height=\"13\" width=\"31\" style=\"vertical-align: 0px;\" \/><\/td>\n<td style=\"text-align: left;\" data-align=\"left\"><img loading=\"lazy\" decoding=\"async\" src=\"https:\/\/opentextbc.ca\/introalgebra\/wp-content\/ql-cache\/quicklatex.com-adb8738f2ddf7a3a9576b69d8d89e6c4_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"&#54;&#92;&#112;&#104;&#97;&#110;&#116;&#111;&#109;&#123;&#92;&#114;&#117;&#108;&#101;&#123;&#48;&#46;&#50;&#101;&#109;&#125;&#123;&#48;&#101;&#120;&#125;&#125;&#92;&#116;&#101;&#120;&#116;&#123;&#116;&#105;&#109;&#101;&#115;&#125;&#92;&#112;&#104;&#97;&#110;&#116;&#111;&#109;&#123;&#92;&#114;&#117;&#108;&#101;&#123;&#48;&#46;&#50;&#101;&#109;&#125;&#123;&#48;&#101;&#120;&#125;&#125;&#55;\" title=\"Rendered by QuickLaTeX.com\" height=\"13\" width=\"66\" style=\"vertical-align: 0px;\" \/><\/td>\n<td style=\"text-align: left;\" data-align=\"left\">the product of six and seven<\/td>\n<\/tr>\n<tr valign=\"top\">\n<td style=\"text-align: left;\" data-align=\"left\"><img loading=\"lazy\" decoding=\"async\" src=\"https:\/\/opentextbc.ca\/introalgebra\/wp-content\/ql-cache\/quicklatex.com-5156593683f791fcfc08d98d0045ea64_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"&#92;&#102;&#114;&#97;&#99;&#123;&#120;&#125;&#123;&#121;&#125;\" title=\"Rendered by QuickLaTeX.com\" height=\"22\" width=\"8\" style=\"vertical-align: -9px;\" \/><\/td>\n<td style=\"text-align: left;\" data-align=\"left\"><img loading=\"lazy\" decoding=\"async\" src=\"https:\/\/opentextbc.ca\/introalgebra\/wp-content\/ql-cache\/quicklatex.com-ede05c264bba0eda080918aaa09c4658_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"&#120;\" title=\"Rendered by QuickLaTeX.com\" height=\"8\" width=\"10\" style=\"vertical-align: 0px;\" \/> divided by <img loading=\"lazy\" decoding=\"async\" src=\"https:\/\/opentextbc.ca\/introalgebra\/wp-content\/ql-cache\/quicklatex.com-0af556714940c351c933bba8cf840796_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"&#121;\" title=\"Rendered by QuickLaTeX.com\" height=\"12\" width=\"9\" style=\"vertical-align: -4px;\" \/><\/td>\n<td style=\"text-align: left;\" data-align=\"left\">the quotient of <img loading=\"lazy\" decoding=\"async\" src=\"https:\/\/opentextbc.ca\/introalgebra\/wp-content\/ql-cache\/quicklatex.com-ede05c264bba0eda080918aaa09c4658_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"&#120;\" title=\"Rendered by QuickLaTeX.com\" height=\"8\" width=\"10\" style=\"vertical-align: 0px;\" \/> and <img loading=\"lazy\" decoding=\"async\" src=\"https:\/\/opentextbc.ca\/introalgebra\/wp-content\/ql-cache\/quicklatex.com-0af556714940c351c933bba8cf840796_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"&#121;\" title=\"Rendered by QuickLaTeX.com\" height=\"12\" width=\"9\" style=\"vertical-align: -4px;\" \/><\/td>\n<\/tr>\n<\/tbody>\n<\/table>\n<p>Notice that the phrases do not form a complete sentence because the phrase does not have a verb. An <span class=\"no-emphasis\" data-type=\"term\">equation<\/span> is two expressions linked with an equal sign. When you read the words the symbols represent in an equation, you have a complete sentence in English. The equal sign gives the verb. Here are some examples of equations:<\/p>\n<table id=\"fs-id2658369\" style=\"width: 100%;\" summary=\"This table has six rows and two columns. The first row is a header row labeling each column. The first column is labeled \u201cEquation\u201d and the second \u201cSentence\u201d. In the second row, under the \u201cEquation\u201d column is three plus five equals eight. Under the \u201cSentence\u201d column is the sentence \u201cThe sum of three and five is equal to eight\u201d. In the third row, under the \u201cEquation\u201d column is n minus one equals fourteen. Under the \u201cSentence\u201d column is the Sentence \u201cThe difference of n and one equals fourteen.\u201d In the fourth row, under the \u201cEquation\u201d column is six times seven equals forty-two. Under the \u201cSentence\u201d column is the sentence \u201cThe product of six and seven is equal to forty-two.\u201d In the fifth row, under the \u201cEquation\u201d column is x equals fifty-three. Under the \u201cSentence\u201d column is the sentence \u201cx is equal to fifty-three.\u201d In the sixth row, under the \u201cEquation\u201d column is y plus nine equals two times y minus 3. Under the \u201cSentence\u201d column is the sentence \u201cy plus nine is equal to two y minus three.\u201d\" data-label=\"\">\n<thead>\n<tr valign=\"top\">\n<th style=\"text-align: left;\" scope=\"col\" data-align=\"left\">Equation<\/th>\n<th style=\"text-align: left;\" scope=\"col\" data-align=\"left\">Sentence<\/th>\n<\/tr>\n<\/thead>\n<tbody>\n<tr valign=\"top\">\n<td style=\"text-align: left;\" data-align=\"left\"><img loading=\"lazy\" decoding=\"async\" src=\"https:\/\/opentextbc.ca\/introalgebra\/wp-content\/ql-cache\/quicklatex.com-f251b590557dcb19113fbdb2ed254a90_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"&#51;&#43;&#53;&#61;&#56;\" title=\"Rendered by QuickLaTeX.com\" height=\"15\" width=\"72\" style=\"vertical-align: -2px;\" \/><\/td>\n<td style=\"text-align: left;\" data-align=\"left\">The sum of three and five is equal to eight.<\/td>\n<\/tr>\n<tr valign=\"top\">\n<td style=\"text-align: left;\" data-align=\"left\"><img loading=\"lazy\" decoding=\"async\" src=\"https:\/\/opentextbc.ca\/introalgebra\/wp-content\/ql-cache\/quicklatex.com-f05c27bbfe4c10679cf87e80eb4691e4_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"&#110;&#45;&#49;&#61;&#49;&#52;\" title=\"Rendered by QuickLaTeX.com\" height=\"13\" width=\"83\" style=\"vertical-align: -1px;\" \/><\/td>\n<td style=\"text-align: left;\" data-align=\"left\"><img loading=\"lazy\" decoding=\"async\" src=\"https:\/\/opentextbc.ca\/introalgebra\/wp-content\/ql-cache\/quicklatex.com-b170995d512c659d8668b4e42e1fef6b_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"&#110;\" title=\"Rendered by QuickLaTeX.com\" height=\"8\" width=\"11\" style=\"vertical-align: 0px;\" \/> minus one equals fourteen.<\/td>\n<\/tr>\n<tr valign=\"top\">\n<td style=\"text-align: left;\" data-align=\"left\"><img loading=\"lazy\" decoding=\"async\" src=\"https:\/\/opentextbc.ca\/introalgebra\/wp-content\/ql-cache\/quicklatex.com-d318b4958469c6ee37c85dbd39d45f0c_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"&#54;&#92;&#99;&#100;&#111;&#116;&#32;&#55;&#61;&#52;&#50;\" title=\"Rendered by QuickLaTeX.com\" height=\"13\" width=\"71\" style=\"vertical-align: 0px;\" \/><\/td>\n<td style=\"text-align: left;\" data-align=\"left\">The product of six and seven is equal to forty-two.<\/td>\n<\/tr>\n<tr valign=\"top\">\n<td style=\"text-align: left;\" data-align=\"left\"><img loading=\"lazy\" decoding=\"async\" src=\"https:\/\/opentextbc.ca\/introalgebra\/wp-content\/ql-cache\/quicklatex.com-4eeb41e4a9dbb3013f1ac9d84c50015b_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"&#120;&#61;&#53;&#51;\" title=\"Rendered by QuickLaTeX.com\" height=\"13\" width=\"52\" style=\"vertical-align: 0px;\" \/><\/td>\n<td style=\"text-align: left;\" data-align=\"left\"><img loading=\"lazy\" decoding=\"async\" src=\"https:\/\/opentextbc.ca\/introalgebra\/wp-content\/ql-cache\/quicklatex.com-ede05c264bba0eda080918aaa09c4658_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"&#120;\" title=\"Rendered by QuickLaTeX.com\" height=\"8\" width=\"10\" style=\"vertical-align: 0px;\" \/> is equal to fifty-three.<\/td>\n<\/tr>\n<tr valign=\"top\">\n<td style=\"text-align: left;\" data-align=\"left\"><img loading=\"lazy\" decoding=\"async\" src=\"https:\/\/opentextbc.ca\/introalgebra\/wp-content\/ql-cache\/quicklatex.com-9f1807d0072c0bdf9e3edb59dc1e9cb2_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"&#121;&#43;&#57;&#61;&#50;&#121;&#45;&#51;\" title=\"Rendered by QuickLaTeX.com\" height=\"16\" width=\"112\" style=\"vertical-align: -4px;\" \/><\/td>\n<td style=\"text-align: left;\" data-align=\"left\"><img loading=\"lazy\" decoding=\"async\" src=\"https:\/\/opentextbc.ca\/introalgebra\/wp-content\/ql-cache\/quicklatex.com-0af556714940c351c933bba8cf840796_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"&#121;\" title=\"Rendered by QuickLaTeX.com\" height=\"12\" width=\"9\" style=\"vertical-align: -4px;\" \/> plus nine is equal to two <img loading=\"lazy\" decoding=\"async\" src=\"https:\/\/opentextbc.ca\/introalgebra\/wp-content\/ql-cache\/quicklatex.com-0af556714940c351c933bba8cf840796_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"&#121;\" title=\"Rendered by QuickLaTeX.com\" height=\"12\" width=\"9\" style=\"vertical-align: -4px;\" \/> minus three.<\/td>\n<\/tr>\n<\/tbody>\n<\/table>\n<div id=\"fs-id1365219\" data-type=\"note\">\n<div data-type=\"title\">\n<div class=\"textbox textbox--key-takeaways\">\n<header class=\"textbox__header\">\n<p class=\"textbox__title\">Expressions and Equations<\/p>\n<\/header>\n<div class=\"textbox__content\">\n<p>An expression is a number, a variable, or a combination of numbers and variables and operation symbols.<\/p>\n<p id=\"fs-id2451266\">An equation is made up of two expressions connected by an equal sign.<\/p>\n<\/div>\n<\/div>\n<\/div>\n<div class=\"textbox textbox--examples\">\n<header class=\"textbox__header\">\n<p class=\"textbox__title\">EXAMPLE 4<\/p>\n<\/header>\n<div class=\"textbox__content\">\n<div data-type=\"problem\">\n<p id=\"fs-id1544580\">Determine if each is an expression or an equation:<\/p>\n<ol id=\"eip-id1168469631637\" class=\"circled\" type=\"a\">\n<li><img loading=\"lazy\" decoding=\"async\" src=\"https:\/\/opentextbc.ca\/introalgebra\/wp-content\/ql-cache\/quicklatex.com-50c2b0b49d1dc61ada00090a1abf73b8_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"&#92;&#112;&#104;&#97;&#110;&#116;&#111;&#109;&#123;&#92;&#114;&#117;&#108;&#101;&#123;&#48;&#46;&#50;&#101;&#109;&#125;&#123;&#48;&#101;&#120;&#125;&#125;&#49;&#54;&#45;&#54;&#61;&#49;&#48;\" title=\"Rendered by QuickLaTeX.com\" height=\"13\" width=\"88\" style=\"vertical-align: -1px;\" \/><\/li>\n<li><img loading=\"lazy\" decoding=\"async\" src=\"https:\/\/opentextbc.ca\/introalgebra\/wp-content\/ql-cache\/quicklatex.com-bb6a0cdd1ffdceb123f2c31b46cff1b3_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"&#92;&#112;&#104;&#97;&#110;&#116;&#111;&#109;&#123;&#92;&#114;&#117;&#108;&#101;&#123;&#48;&#46;&#50;&#101;&#109;&#125;&#123;&#48;&#101;&#120;&#125;&#125;&#52;&#92;&#99;&#100;&#111;&#116;&#32;&#50;&#43;&#49;\" title=\"Rendered by QuickLaTeX.com\" height=\"14\" width=\"60\" style=\"vertical-align: -2px;\" \/><\/li>\n<li><img loading=\"lazy\" decoding=\"async\" src=\"https:\/\/opentextbc.ca\/introalgebra\/wp-content\/ql-cache\/quicklatex.com-1ce9a2882a3fcc95c02f071706cd7a08_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"&#92;&#112;&#104;&#97;&#110;&#116;&#111;&#109;&#123;&#92;&#114;&#117;&#108;&#101;&#123;&#48;&#46;&#50;&#101;&#109;&#125;&#123;&#48;&#101;&#120;&#125;&#125;&#120;&#92;&#100;&#105;&#118;&#32;&#50;&#53;\" title=\"Rendered by QuickLaTeX.com\" height=\"14\" width=\"48\" style=\"vertical-align: -1px;\" \/><\/li>\n<li><img loading=\"lazy\" decoding=\"async\" src=\"https:\/\/opentextbc.ca\/introalgebra\/wp-content\/ql-cache\/quicklatex.com-abe813531d91d3fd774fbe5e6174deee_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"&#92;&#112;&#104;&#97;&#110;&#116;&#111;&#109;&#123;&#92;&#114;&#117;&#108;&#101;&#123;&#48;&#46;&#50;&#101;&#109;&#125;&#123;&#48;&#101;&#120;&#125;&#125;&#121;&#43;&#56;&#61;&#52;&#48;\" title=\"Rendered by QuickLaTeX.com\" height=\"16\" width=\"81\" style=\"vertical-align: -4px;\" \/><\/li>\n<\/ol>\n<\/div>\n<div id=\"fs-id1584678\" data-type=\"solution\">\n<div data-type=\"title\"><\/div>\n<div data-type=\"title\"><strong>Solution<\/strong><\/div>\n<div data-type=\"title\"><\/div>\n<table id=\"eip-id1166346957031\" class=\"unnumbered unstyled\" summary=\".\" data-label=\"\">\n<tbody>\n<tr>\n<td>a. <img loading=\"lazy\" decoding=\"async\" src=\"https:\/\/opentextbc.ca\/introalgebra\/wp-content\/ql-cache\/quicklatex.com-50c2b0b49d1dc61ada00090a1abf73b8_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"&#92;&#112;&#104;&#97;&#110;&#116;&#111;&#109;&#123;&#92;&#114;&#117;&#108;&#101;&#123;&#48;&#46;&#50;&#101;&#109;&#125;&#123;&#48;&#101;&#120;&#125;&#125;&#49;&#54;&#45;&#54;&#61;&#49;&#48;\" title=\"Rendered by QuickLaTeX.com\" height=\"13\" width=\"88\" style=\"vertical-align: -1px;\" \/><\/td>\n<td>This is an equation\u2014two expressions are connected with an equal sign.<\/td>\n<\/tr>\n<tr>\n<td>b. <img loading=\"lazy\" decoding=\"async\" src=\"https:\/\/opentextbc.ca\/introalgebra\/wp-content\/ql-cache\/quicklatex.com-bb6a0cdd1ffdceb123f2c31b46cff1b3_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"&#92;&#112;&#104;&#97;&#110;&#116;&#111;&#109;&#123;&#92;&#114;&#117;&#108;&#101;&#123;&#48;&#46;&#50;&#101;&#109;&#125;&#123;&#48;&#101;&#120;&#125;&#125;&#52;&#92;&#99;&#100;&#111;&#116;&#32;&#50;&#43;&#49;\" title=\"Rendered by QuickLaTeX.com\" height=\"14\" width=\"60\" style=\"vertical-align: -2px;\" \/><\/td>\n<td>This is an expression\u2014no equal sign.<\/td>\n<\/tr>\n<tr>\n<td>c. <img loading=\"lazy\" decoding=\"async\" src=\"https:\/\/opentextbc.ca\/introalgebra\/wp-content\/ql-cache\/quicklatex.com-1ce9a2882a3fcc95c02f071706cd7a08_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"&#92;&#112;&#104;&#97;&#110;&#116;&#111;&#109;&#123;&#92;&#114;&#117;&#108;&#101;&#123;&#48;&#46;&#50;&#101;&#109;&#125;&#123;&#48;&#101;&#120;&#125;&#125;&#120;&#92;&#100;&#105;&#118;&#32;&#50;&#53;\" title=\"Rendered by QuickLaTeX.com\" height=\"14\" width=\"48\" style=\"vertical-align: -1px;\" \/><\/td>\n<td>This is an expression\u2014no equal sign.<\/td>\n<\/tr>\n<tr>\n<td>d. <img loading=\"lazy\" decoding=\"async\" src=\"https:\/\/opentextbc.ca\/introalgebra\/wp-content\/ql-cache\/quicklatex.com-abe813531d91d3fd774fbe5e6174deee_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"&#92;&#112;&#104;&#97;&#110;&#116;&#111;&#109;&#123;&#92;&#114;&#117;&#108;&#101;&#123;&#48;&#46;&#50;&#101;&#109;&#125;&#123;&#48;&#101;&#120;&#125;&#125;&#121;&#43;&#56;&#61;&#52;&#48;\" title=\"Rendered by QuickLaTeX.com\" height=\"16\" width=\"81\" style=\"vertical-align: -4px;\" \/><\/td>\n<td>This is an equation\u2014two expressions are connected with an equal sign.<\/td>\n<\/tr>\n<\/tbody>\n<\/table>\n<\/div>\n<\/div>\n<\/div>\n<div class=\"textbox textbox--exercises\">\n<header class=\"textbox__header\">\n<p class=\"textbox__title\">TRY IT 4.1<\/p>\n<\/header>\n<div class=\"textbox__content\">\n<div id=\"fs-id2650086\" data-type=\"problem\">\n<p id=\"fs-id1619065\">Determine if each is an expression or an equation:<\/p>\n<ol id=\"eip-id1168468600384\" class=\"circled\" type=\"a\">\n<li><img loading=\"lazy\" decoding=\"async\" src=\"https:\/\/opentextbc.ca\/introalgebra\/wp-content\/ql-cache\/quicklatex.com-a558290ed20394aca20efb1db37f2be9_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"&#92;&#112;&#104;&#97;&#110;&#116;&#111;&#109;&#123;&#92;&#114;&#117;&#108;&#101;&#123;&#48;&#46;&#50;&#101;&#109;&#125;&#123;&#48;&#101;&#120;&#125;&#125;&#50;&#51;&#43;&#54;&#61;&#50;&#57;&#92;&#112;&#104;&#97;&#110;&#116;&#111;&#109;&#123;&#92;&#114;&#117;&#108;&#101;&#123;&#48;&#46;&#52;&#101;&#109;&#125;&#123;&#48;&#101;&#120;&#125;&#125;\" title=\"Rendered by QuickLaTeX.com\" height=\"14\" width=\"89\" style=\"vertical-align: -2px;\" \/><\/li>\n<li><img loading=\"lazy\" decoding=\"async\" src=\"https:\/\/opentextbc.ca\/introalgebra\/wp-content\/ql-cache\/quicklatex.com-ec827f55d20f8525312cdb1c1a54dc3f_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"&#92;&#112;&#104;&#97;&#110;&#116;&#111;&#109;&#123;&#92;&#114;&#117;&#108;&#101;&#123;&#48;&#46;&#50;&#101;&#109;&#125;&#123;&#48;&#101;&#120;&#125;&#125;&#55;&#92;&#99;&#100;&#111;&#116;&#32;&#51;&#45;&#55;\" title=\"Rendered by QuickLaTeX.com\" height=\"13\" width=\"61\" style=\"vertical-align: 0px;\" \/><\/li>\n<\/ol>\n<\/div>\n<div id=\"fs-id1346095\" data-type=\"solution\">\n<details>\n<summary>Show Answer<\/summary>\n<ol id=\"eip-id1168468285584\" class=\"circled\" type=\"a\">\n<li>equation<\/li>\n<li>expression<\/li>\n<\/ol>\n<\/details>\n<\/div>\n<\/div>\n<\/div>\n<div class=\"textbox textbox--exercises\">\n<header class=\"textbox__header\">\n<p class=\"textbox__title\">TRY IT 4.2<\/p>\n<\/header>\n<div class=\"textbox__content\">\n<div id=\"fs-id1789247\" data-type=\"problem\">\n<p id=\"fs-id1171103307873\">Determine if each is an expression or an equation:<\/p>\n<ol id=\"eip-id1168469631624\" class=\"circled\" type=\"a\">\n<li><img loading=\"lazy\" decoding=\"async\" src=\"https:\/\/opentextbc.ca\/introalgebra\/wp-content\/ql-cache\/quicklatex.com-6e4af365cd659ceb9ca751cf4f65ce52_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"&#92;&#112;&#104;&#97;&#110;&#116;&#111;&#109;&#123;&#92;&#114;&#117;&#108;&#101;&#123;&#48;&#46;&#50;&#101;&#109;&#125;&#123;&#48;&#101;&#120;&#125;&#125;&#121;&#92;&#100;&#105;&#118;&#32;&#49;&#52;&#92;&#112;&#104;&#97;&#110;&#116;&#111;&#109;&#123;&#92;&#114;&#117;&#108;&#101;&#123;&#48;&#46;&#52;&#101;&#109;&#125;&#123;&#48;&#101;&#120;&#125;&#125;\" title=\"Rendered by QuickLaTeX.com\" height=\"16\" width=\"49\" style=\"vertical-align: -4px;\" \/><\/li>\n<li><img loading=\"lazy\" decoding=\"async\" src=\"https:\/\/opentextbc.ca\/introalgebra\/wp-content\/ql-cache\/quicklatex.com-b7f328b94064d1b96b89456b2dd8bb85_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"&#92;&#112;&#104;&#97;&#110;&#116;&#111;&#109;&#123;&#92;&#114;&#117;&#108;&#101;&#123;&#48;&#46;&#50;&#101;&#109;&#125;&#123;&#48;&#101;&#120;&#125;&#125;&#120;&#45;&#54;&#61;&#50;&#49;\" title=\"Rendered by QuickLaTeX.com\" height=\"13\" width=\"81\" style=\"vertical-align: -1px;\" \/><\/li>\n<\/ol>\n<\/div>\n<div id=\"fs-id1577444\" data-type=\"solution\">\n<details>\n<summary>Show Answer<\/summary>\n<ol id=\"eip-id1168469631663\" class=\"circled\" type=\"a\">\n<li>expression<\/li>\n<li>equation<\/li>\n<\/ol>\n<\/details>\n<\/div>\n<\/div>\n<\/div>\n<\/div>\n<h1>Simplify Expressions with Exponents<\/h1>\n<p id=\"fs-id1392631\">To simplify a numerical expression means to do all the math possible. For example, to simplify <img loading=\"lazy\" decoding=\"async\" src=\"https:\/\/opentextbc.ca\/introalgebra\/wp-content\/ql-cache\/quicklatex.com-0e5bcdefd1364fe53e1d9f55e26c39b7_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"&#52;&#92;&#99;&#100;&#111;&#116;&#50;&#43;&#49;\" title=\"Rendered by QuickLaTeX.com\" height=\"14\" width=\"60\" style=\"vertical-align: -2px;\" \/> we\u2019d first multiply <img loading=\"lazy\" decoding=\"async\" src=\"https:\/\/opentextbc.ca\/introalgebra\/wp-content\/ql-cache\/quicklatex.com-4b63cc3704237b82061627522aa907fd_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"&#52;&#92;&#99;&#100;&#111;&#116;&#50;\" title=\"Rendered by QuickLaTeX.com\" height=\"12\" width=\"30\" style=\"vertical-align: 0px;\" \/> to get <img loading=\"lazy\" decoding=\"async\" src=\"https:\/\/opentextbc.ca\/introalgebra\/wp-content\/ql-cache\/quicklatex.com-23212a120eb92d226d44696a0b80bead_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"&#56;\" title=\"Rendered by QuickLaTeX.com\" height=\"12\" width=\"9\" style=\"vertical-align: 0px;\" \/> and then add the <img loading=\"lazy\" decoding=\"async\" src=\"https:\/\/opentextbc.ca\/introalgebra\/wp-content\/ql-cache\/quicklatex.com-4868771cbc422b5818f85500909ce433_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"&#49;\" title=\"Rendered by QuickLaTeX.com\" height=\"13\" width=\"7\" style=\"vertical-align: -1px;\" \/> to get <img loading=\"lazy\" decoding=\"async\" src=\"https:\/\/opentextbc.ca\/introalgebra\/wp-content\/ql-cache\/quicklatex.com-e99b7c7ddd421682faf67e5b5f865882_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"&#57;\" title=\"Rendered by QuickLaTeX.com\" height=\"12\" width=\"9\" style=\"vertical-align: 0px;\" \/>. A good habit to develop is to work down the page, writing each step of the process below the previous step. The example just described would look like this:<\/p>\n<div id=\"fs-id1308315\" class=\"unnumbered\" data-type=\"equation\" data-label=\"\"><img loading=\"lazy\" decoding=\"async\" src=\"https:\/\/opentextbc.ca\/introalgebra\/wp-content\/ql-cache\/quicklatex.com-0e5bcdefd1364fe53e1d9f55e26c39b7_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"&#52;&#92;&#99;&#100;&#111;&#116;&#50;&#43;&#49;\" title=\"Rendered by QuickLaTeX.com\" height=\"14\" width=\"60\" style=\"vertical-align: -2px;\" \/><\/div>\n<div id=\"fs-id2495596\" class=\"unnumbered\" data-type=\"equation\" data-label=\"\"><img loading=\"lazy\" decoding=\"async\" src=\"https:\/\/opentextbc.ca\/introalgebra\/wp-content\/ql-cache\/quicklatex.com-da4cd73586f94b2e8aa3caaa55128212_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"&#56;&#43;&#49;\" title=\"Rendered by QuickLaTeX.com\" height=\"14\" width=\"39\" style=\"vertical-align: -2px;\" \/><\/div>\n<div id=\"fs-id3016728\" class=\"unnumbered\" data-type=\"equation\" data-label=\"\"><img loading=\"lazy\" decoding=\"async\" src=\"https:\/\/opentextbc.ca\/introalgebra\/wp-content\/ql-cache\/quicklatex.com-e99b7c7ddd421682faf67e5b5f865882_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"&#57;\" title=\"Rendered by QuickLaTeX.com\" height=\"12\" width=\"9\" style=\"vertical-align: 0px;\" \/><\/div>\n<p id=\"fs-id2144760\">Suppose we have the expression <img loading=\"lazy\" decoding=\"async\" src=\"https:\/\/opentextbc.ca\/introalgebra\/wp-content\/ql-cache\/quicklatex.com-708f52894b212c80d74774828823b151_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"&#50;&#92;&#99;&#100;&#111;&#116;&#50;&#92;&#99;&#100;&#111;&#116;&#50;&#92;&#99;&#100;&#111;&#116;&#50;&#92;&#99;&#100;&#111;&#116;&#50;&#92;&#99;&#100;&#111;&#116;&#50;&#92;&#99;&#100;&#111;&#116;&#50;&#92;&#99;&#100;&#111;&#116;&#50;&#92;&#99;&#100;&#111;&#116;&#50;\" title=\"Rendered by QuickLaTeX.com\" height=\"12\" width=\"181\" style=\"vertical-align: 0px;\" \/>. We could write this more compactly using exponential notation. Exponential notation is used in algebra to represent a quantity multiplied by itself several times. We write <img loading=\"lazy\" decoding=\"async\" src=\"https:\/\/opentextbc.ca\/introalgebra\/wp-content\/ql-cache\/quicklatex.com-a6fa2186368e6575cca8d555edfdf6f0_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"&#50;&#92;&#99;&#100;&#111;&#116;&#50;&#92;&#99;&#100;&#111;&#116;&#50;\" title=\"Rendered by QuickLaTeX.com\" height=\"12\" width=\"51\" style=\"vertical-align: 0px;\" \/> as <img loading=\"lazy\" decoding=\"async\" src=\"https:\/\/opentextbc.ca\/introalgebra\/wp-content\/ql-cache\/quicklatex.com-3a402f8a62a07dd1eb366927c0a3e64f_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"&#123;&#50;&#125;&#94;&#123;&#51;&#125;\" title=\"Rendered by QuickLaTeX.com\" height=\"15\" width=\"16\" style=\"vertical-align: 0px;\" \/> and <img loading=\"lazy\" decoding=\"async\" src=\"https:\/\/opentextbc.ca\/introalgebra\/wp-content\/ql-cache\/quicklatex.com-708f52894b212c80d74774828823b151_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"&#50;&#92;&#99;&#100;&#111;&#116;&#50;&#92;&#99;&#100;&#111;&#116;&#50;&#92;&#99;&#100;&#111;&#116;&#50;&#92;&#99;&#100;&#111;&#116;&#50;&#92;&#99;&#100;&#111;&#116;&#50;&#92;&#99;&#100;&#111;&#116;&#50;&#92;&#99;&#100;&#111;&#116;&#50;&#92;&#99;&#100;&#111;&#116;&#50;\" title=\"Rendered by QuickLaTeX.com\" height=\"12\" width=\"181\" style=\"vertical-align: 0px;\" \/> as <img loading=\"lazy\" decoding=\"async\" src=\"https:\/\/opentextbc.ca\/introalgebra\/wp-content\/ql-cache\/quicklatex.com-5b90f99714c54357ddf7d3aea0e1d1fa_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"&#123;&#50;&#125;&#94;&#123;&#57;&#125;\" title=\"Rendered by QuickLaTeX.com\" height=\"15\" width=\"16\" style=\"vertical-align: 0px;\" \/>. In expressions such as <img loading=\"lazy\" decoding=\"async\" src=\"https:\/\/opentextbc.ca\/introalgebra\/wp-content\/ql-cache\/quicklatex.com-3a402f8a62a07dd1eb366927c0a3e64f_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"&#123;&#50;&#125;&#94;&#123;&#51;&#125;\" title=\"Rendered by QuickLaTeX.com\" height=\"15\" width=\"16\" style=\"vertical-align: 0px;\" \/>, the <img loading=\"lazy\" decoding=\"async\" src=\"https:\/\/opentextbc.ca\/introalgebra\/wp-content\/ql-cache\/quicklatex.com-e584dd0bab4e6c8efc164939c28db757_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"&#50;\" title=\"Rendered by QuickLaTeX.com\" height=\"12\" width=\"8\" style=\"vertical-align: 0px;\" \/> is called the base and the <img loading=\"lazy\" decoding=\"async\" src=\"https:\/\/opentextbc.ca\/introalgebra\/wp-content\/ql-cache\/quicklatex.com-4a1d3ea4963f568cabd97329456036b6_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"&#51;\" title=\"Rendered by QuickLaTeX.com\" height=\"12\" width=\"9\" style=\"vertical-align: 0px;\" \/> is called the exponent. The exponent tells us how many factors of the base we have to multiply.<\/p>\n<p><span id=\"fs-id2149605\" data-type=\"media\" data-alt=\"The image shows the number two with the number three, in superscript, to the right of the two. The number two is labeled as \u201cbase\u201d and the number three is labeled as \u201cexponent\u201d.\"><img decoding=\"async\" class=\"aligncenter\" src=\"https:\/\/opentextbc.ca\/accessibilitytoolkit\/wp-content\/uploads\/sites\/333\/2021\/03\/CNX_BMath_Figure_02_01_003_img-1.jpg\" alt=\"The image shows the number two with the number three, in superscript, to the right of the two. The number two is labeled as \u201cbase\u201d and the number three is labeled as \u201cexponent\u201d.\" data-media-type=\"image\/jpeg\" \/><\/span><\/p>\n<div id=\"fs-id2669230\" class=\"unnumbered\" data-type=\"equation\" data-label=\"\"><img loading=\"lazy\" decoding=\"async\" src=\"https:\/\/opentextbc.ca\/introalgebra\/wp-content\/ql-cache\/quicklatex.com-f6310f7ab8a428d88b06bce703ff5b1a_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"&#92;&#116;&#101;&#120;&#116;&#123;&#109;&#101;&#97;&#110;&#115;&#32;&#109;&#117;&#108;&#116;&#105;&#112;&#108;&#121;&#32;&#116;&#104;&#114;&#101;&#101;&#32;&#102;&#97;&#99;&#116;&#111;&#114;&#115;&#32;&#111;&#102;&#32;&#50;&#125;\" title=\"Rendered by QuickLaTeX.com\" height=\"16\" width=\"256\" style=\"vertical-align: -3px;\" \/><\/div>\n<p id=\"fs-id2295676\">We say <img loading=\"lazy\" decoding=\"async\" src=\"https:\/\/opentextbc.ca\/introalgebra\/wp-content\/ql-cache\/quicklatex.com-3a402f8a62a07dd1eb366927c0a3e64f_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"&#123;&#50;&#125;&#94;&#123;&#51;&#125;\" title=\"Rendered by QuickLaTeX.com\" height=\"15\" width=\"16\" style=\"vertical-align: 0px;\" \/> is in exponential notation and <img loading=\"lazy\" decoding=\"async\" src=\"https:\/\/opentextbc.ca\/introalgebra\/wp-content\/ql-cache\/quicklatex.com-a6fa2186368e6575cca8d555edfdf6f0_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"&#50;&#92;&#99;&#100;&#111;&#116;&#50;&#92;&#99;&#100;&#111;&#116;&#50;\" title=\"Rendered by QuickLaTeX.com\" height=\"12\" width=\"51\" style=\"vertical-align: 0px;\" \/> is in expanded notation.<\/p>\n<div id=\"fs-id1243267\" data-type=\"note\">\n<div data-type=\"title\">\n<div class=\"textbox textbox--key-takeaways\">\n<header class=\"textbox__header\">\n<p class=\"textbox__title\">Exponential Notation<\/p>\n<\/header>\n<div class=\"textbox__content\">\n<p id=\"fs-id2283832\">For any expression <img loading=\"lazy\" decoding=\"async\" src=\"https:\/\/opentextbc.ca\/introalgebra\/wp-content\/ql-cache\/quicklatex.com-e4bb51256ecc9ffb84be2f323eb6bf7e_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"&#123;&#97;&#125;&#94;&#123;&#110;&#125;&#44;&#97;\" title=\"Rendered by QuickLaTeX.com\" height=\"16\" width=\"35\" style=\"vertical-align: -4px;\" \/> is a factor multiplied by itself <img loading=\"lazy\" decoding=\"async\" src=\"https:\/\/opentextbc.ca\/introalgebra\/wp-content\/ql-cache\/quicklatex.com-b170995d512c659d8668b4e42e1fef6b_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"&#110;\" title=\"Rendered by QuickLaTeX.com\" height=\"8\" width=\"11\" style=\"vertical-align: 0px;\" \/> times if <img loading=\"lazy\" decoding=\"async\" src=\"https:\/\/opentextbc.ca\/introalgebra\/wp-content\/ql-cache\/quicklatex.com-b170995d512c659d8668b4e42e1fef6b_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"&#110;\" title=\"Rendered by QuickLaTeX.com\" height=\"8\" width=\"11\" style=\"vertical-align: 0px;\" \/> is a positive integer.<\/p>\n<div id=\"fs-id1882026\" class=\"unnumbered\" data-type=\"equation\" data-label=\"\"><img loading=\"lazy\" decoding=\"async\" src=\"https:\/\/opentextbc.ca\/introalgebra\/wp-content\/ql-cache\/quicklatex.com-f5975a21738a00b5a3947d0fc69fc644_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"&#123;&#97;&#125;&#94;&#123;&#110;&#125;&#92;&#116;&#101;&#120;&#116;&#123;&#109;&#101;&#97;&#110;&#115;&#32;&#109;&#117;&#108;&#116;&#105;&#112;&#108;&#121;&#125;&#92;&#112;&#104;&#97;&#110;&#116;&#111;&#109;&#123;&#92;&#114;&#117;&#108;&#101;&#123;&#48;&#46;&#50;&#101;&#109;&#125;&#123;&#48;&#101;&#120;&#125;&#125;&#110;&#92;&#112;&#104;&#97;&#110;&#116;&#111;&#109;&#123;&#92;&#114;&#117;&#108;&#101;&#123;&#48;&#46;&#50;&#101;&#109;&#125;&#123;&#48;&#101;&#120;&#125;&#125;&#92;&#116;&#101;&#120;&#116;&#123;&#102;&#97;&#99;&#116;&#111;&#114;&#115;&#32;&#111;&#102;&#125;&#92;&#112;&#104;&#97;&#110;&#116;&#111;&#109;&#123;&#92;&#114;&#117;&#108;&#101;&#123;&#48;&#46;&#50;&#101;&#109;&#125;&#123;&#48;&#101;&#120;&#125;&#125;&#97;\" title=\"Rendered by QuickLaTeX.com\" height=\"16\" width=\"240\" style=\"vertical-align: -3px;\" \/><\/div>\n<p><span id=\"fs-id2284773\" data-type=\"media\" data-alt=\"At the top of the image is the letter a with the letter n, in superscript, to the right of the a. The letter a is labeled as \u201cbase\u201d and the letter n is labeled as \u201cexponent\u201d. Below this is the letter a with the letter n, in superscript, to the right of the a set equal to n factors of a.\"><img decoding=\"async\" class=\"aligncenter\" src=\"https:\/\/opentextbc.ca\/accessibilitytoolkit\/wp-content\/uploads\/sites\/333\/2021\/03\/CNX_BMath_Figure_02_01_010_img-1.jpg\" alt=\"At the top of the image is the letter a with the letter n, in superscript, to the right of the a. The letter a is labeled as \u201cbase\u201d and the letter n is labeled as \u201cexponent\u201d. Below this is the letter a with the letter n, in superscript, to the right of the a set equal to n factors of a.\" data-media-type=\"image\/jpeg\" \/><\/span><\/p>\n<p id=\"fs-id2786021\">The expression <img loading=\"lazy\" decoding=\"async\" src=\"https:\/\/opentextbc.ca\/introalgebra\/wp-content\/ql-cache\/quicklatex.com-ef78644f25c125ead81d3c69ef32dee0_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"&#123;&#97;&#125;&#94;&#123;&#110;&#125;\" title=\"Rendered by QuickLaTeX.com\" height=\"12\" width=\"17\" style=\"vertical-align: 0px;\" \/> is read <img loading=\"lazy\" decoding=\"async\" src=\"https:\/\/opentextbc.ca\/introalgebra\/wp-content\/ql-cache\/quicklatex.com-5c53d6ebabdbcfa4e107550ea60b1b19_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"&#97;\" title=\"Rendered by QuickLaTeX.com\" height=\"8\" width=\"9\" style=\"vertical-align: 0px;\" \/> to the <img loading=\"lazy\" decoding=\"async\" src=\"https:\/\/opentextbc.ca\/introalgebra\/wp-content\/ql-cache\/quicklatex.com-02553ae49d720703c253c7bcbf008617_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"&#123;&#110;&#125;&#94;&#123;&#116;&#104;&#125;\" title=\"Rendered by QuickLaTeX.com\" height=\"15\" width=\"24\" style=\"vertical-align: 0px;\" \/> power.<\/p>\n<\/div>\n<\/div>\n<p>For powers of <img loading=\"lazy\" decoding=\"async\" src=\"https:\/\/opentextbc.ca\/introalgebra\/wp-content\/ql-cache\/quicklatex.com-8b4c6cd9d27ba344abe355a47d378bb2_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"&#110;&#61;&#50;\" title=\"Rendered by QuickLaTeX.com\" height=\"12\" width=\"42\" style=\"vertical-align: 0px;\" \/> and <img loading=\"lazy\" decoding=\"async\" src=\"https:\/\/opentextbc.ca\/introalgebra\/wp-content\/ql-cache\/quicklatex.com-85761a607075b960ff00638d721cfe9c_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"&#110;&#61;&#51;\" title=\"Rendered by QuickLaTeX.com\" height=\"12\" width=\"43\" style=\"vertical-align: 0px;\" \/>, we have special names.<\/p>\n<\/div>\n<\/div>\n<div id=\"fs-id1547556\" class=\"unnumbered\" data-type=\"equation\" data-label=\"\"><img loading=\"lazy\" decoding=\"async\" src=\"https:\/\/opentextbc.ca\/introalgebra\/wp-content\/ql-cache\/quicklatex.com-d24124a58990e4ace21c3431f8dac79c_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"&#92;&#98;&#101;&#103;&#105;&#110;&#123;&#97;&#114;&#114;&#97;&#121;&#125;&#123;&#108;&#125;&#123;&#97;&#125;&#94;&#123;&#50;&#125;&#92;&#112;&#104;&#97;&#110;&#116;&#111;&#109;&#123;&#92;&#114;&#117;&#108;&#101;&#123;&#48;&#46;&#50;&#101;&#109;&#125;&#123;&#48;&#101;&#120;&#125;&#125;&#92;&#116;&#101;&#120;&#116;&#123;&#105;&#115;&#32;&#114;&#101;&#97;&#100;&#32;&#97;&#115;&#125;&#92;&#112;&#104;&#97;&#110;&#116;&#111;&#109;&#123;&#92;&#114;&#117;&#108;&#101;&#123;&#48;&#46;&#50;&#101;&#109;&#125;&#123;&#48;&#101;&#120;&#125;&#125;&#92;&#116;&#101;&#120;&#116;&#123;&#34;&#125;&#97;&#92;&#112;&#104;&#97;&#110;&#116;&#111;&#109;&#123;&#92;&#114;&#117;&#108;&#101;&#123;&#48;&#46;&#50;&#101;&#109;&#125;&#123;&#48;&#101;&#120;&#125;&#125;&#92;&#116;&#101;&#120;&#116;&#123;&#115;&#113;&#117;&#97;&#114;&#101;&#100;&#34;&#125;&#92;&#92;&#32;&#123;&#97;&#125;&#94;&#123;&#51;&#125;&#92;&#112;&#104;&#97;&#110;&#116;&#111;&#109;&#123;&#92;&#114;&#117;&#108;&#101;&#123;&#48;&#46;&#50;&#101;&#109;&#125;&#123;&#48;&#101;&#120;&#125;&#125;&#92;&#116;&#101;&#120;&#116;&#123;&#105;&#115;&#32;&#114;&#101;&#97;&#100;&#32;&#97;&#115;&#125;&#92;&#112;&#104;&#97;&#110;&#116;&#111;&#109;&#123;&#92;&#114;&#117;&#108;&#101;&#123;&#48;&#46;&#50;&#101;&#109;&#125;&#123;&#48;&#101;&#120;&#125;&#125;&#92;&#116;&#101;&#120;&#116;&#123;&#34;&#125;&#97;&#92;&#112;&#104;&#97;&#110;&#116;&#111;&#109;&#123;&#92;&#114;&#117;&#108;&#101;&#123;&#48;&#46;&#50;&#101;&#109;&#125;&#123;&#48;&#101;&#120;&#125;&#125;&#92;&#116;&#101;&#120;&#116;&#123;&#99;&#117;&#98;&#101;&#100;&#34;&#125;&#92;&#101;&#110;&#100;&#123;&#97;&#114;&#114;&#97;&#121;&#125;\" title=\"Rendered by QuickLaTeX.com\" height=\"38\" width=\"186\" style=\"vertical-align: -12px;\" \/><\/div>\n<p id=\"fs-id1387277\">The table below lists some examples of expressions written in exponential notation.<\/p>\n<table id=\"fs-id1830286\" style=\"width: 100%;\" summary=\"This table has five rows and two columns. The first row is a header row and it labels each column. The first column is labeled \u201cExponential Notation\u201d and the second \u201cIn Words\u201d. The second row shows the number seven followed by the superscript two in the first column and the phrase \u201cseven to the second power, or seven squared\u201d in the second column. The next row shows the number five followed by the superscript three in the first column and the phrase \u201cfive to the third power, or five cubed\u201d in the second column. The next row shows the number nine followed by the superscript four in the first column and the phrase \u201cnine to the fourth power\u201d in the second column. The last row shows the number twelve followed by the superscript five in the first column and the phrase \u201ctwelve to the fifth power\u201d in the second column.\">\n<thead>\n<tr valign=\"top\">\n<th style=\"text-align: left;\" scope=\"col\" data-align=\"left\">Exponential Notation<\/th>\n<th style=\"text-align: left;\" scope=\"col\" data-align=\"center\">In Words<\/th>\n<\/tr>\n<\/thead>\n<tbody>\n<tr valign=\"top\">\n<td style=\"text-align: left;\" data-align=\"left\"><img loading=\"lazy\" decoding=\"async\" src=\"https:\/\/opentextbc.ca\/introalgebra\/wp-content\/ql-cache\/quicklatex.com-d832ca5a71393670c83317b52a256157_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"&#123;&#55;&#125;&#94;&#123;&#50;&#125;\" title=\"Rendered by QuickLaTeX.com\" height=\"15\" width=\"16\" style=\"vertical-align: 0px;\" \/><\/td>\n<td style=\"text-align: left;\" data-align=\"left\"><img loading=\"lazy\" decoding=\"async\" src=\"https:\/\/opentextbc.ca\/introalgebra\/wp-content\/ql-cache\/quicklatex.com-aca3387e59afe477960eabc2f23b3db5_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"&#55;\" title=\"Rendered by QuickLaTeX.com\" height=\"13\" width=\"9\" style=\"vertical-align: 0px;\" \/> to the second power, or <img loading=\"lazy\" decoding=\"async\" src=\"https:\/\/opentextbc.ca\/introalgebra\/wp-content\/ql-cache\/quicklatex.com-aca3387e59afe477960eabc2f23b3db5_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"&#55;\" title=\"Rendered by QuickLaTeX.com\" height=\"13\" width=\"9\" style=\"vertical-align: 0px;\" \/> squared<\/td>\n<\/tr>\n<tr valign=\"top\">\n<td style=\"text-align: left;\" data-align=\"left\"><img loading=\"lazy\" decoding=\"async\" src=\"https:\/\/opentextbc.ca\/introalgebra\/wp-content\/ql-cache\/quicklatex.com-22a6de91ce40f10ddb25e6ea195347ce_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"&#123;&#53;&#125;&#94;&#123;&#51;&#125;\" title=\"Rendered by QuickLaTeX.com\" height=\"15\" width=\"16\" style=\"vertical-align: 0px;\" \/><\/td>\n<td style=\"text-align: left;\" data-align=\"left\"><img loading=\"lazy\" decoding=\"async\" src=\"https:\/\/opentextbc.ca\/introalgebra\/wp-content\/ql-cache\/quicklatex.com-8995e2084120c1c1f4b53f490d281bc4_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"&#53;\" title=\"Rendered by QuickLaTeX.com\" height=\"13\" width=\"8\" style=\"vertical-align: 0px;\" \/> to the third power, or <img loading=\"lazy\" decoding=\"async\" src=\"https:\/\/opentextbc.ca\/introalgebra\/wp-content\/ql-cache\/quicklatex.com-8995e2084120c1c1f4b53f490d281bc4_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"&#53;\" title=\"Rendered by QuickLaTeX.com\" height=\"13\" width=\"8\" style=\"vertical-align: 0px;\" \/> cubed<\/td>\n<\/tr>\n<tr valign=\"top\">\n<td style=\"text-align: left;\" data-align=\"left\"><img loading=\"lazy\" decoding=\"async\" src=\"https:\/\/opentextbc.ca\/introalgebra\/wp-content\/ql-cache\/quicklatex.com-8075dfc642680f4c4a50ad4e0ba4b830_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"&#123;&#57;&#125;&#94;&#123;&#52;&#125;\" title=\"Rendered by QuickLaTeX.com\" height=\"15\" width=\"16\" style=\"vertical-align: 0px;\" \/><\/td>\n<td style=\"text-align: left;\" data-align=\"left\"><img loading=\"lazy\" decoding=\"async\" src=\"https:\/\/opentextbc.ca\/introalgebra\/wp-content\/ql-cache\/quicklatex.com-e99b7c7ddd421682faf67e5b5f865882_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"&#57;\" title=\"Rendered by QuickLaTeX.com\" height=\"12\" width=\"9\" style=\"vertical-align: 0px;\" \/> to the fourth power<\/td>\n<\/tr>\n<tr valign=\"top\">\n<td style=\"text-align: left;\" data-align=\"left\"><img loading=\"lazy\" decoding=\"async\" src=\"https:\/\/opentextbc.ca\/introalgebra\/wp-content\/ql-cache\/quicklatex.com-e2a89f6a2f2291b0852fd67c1b816441_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"&#123;&#49;&#50;&#125;&#94;&#123;&#53;&#125;\" title=\"Rendered by QuickLaTeX.com\" height=\"16\" width=\"24\" style=\"vertical-align: -1px;\" \/><\/td>\n<td style=\"text-align: left;\" data-align=\"left\"><img loading=\"lazy\" decoding=\"async\" src=\"https:\/\/opentextbc.ca\/introalgebra\/wp-content\/ql-cache\/quicklatex.com-40f7428479801bf4ef27a5149e9df526_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"&#49;&#50;\" title=\"Rendered by QuickLaTeX.com\" height=\"13\" width=\"16\" style=\"vertical-align: -1px;\" \/> to the fifth power<\/td>\n<\/tr>\n<\/tbody>\n<\/table>\n<div data-type=\"example\">\n<div class=\"textbox textbox--examples\">\n<header class=\"textbox__header\">\n<p class=\"textbox__title\">EXAMPLE 5<\/p>\n<\/header>\n<div class=\"textbox__content\">\n<div id=\"fs-id2692026\" data-type=\"problem\">\n<p id=\"fs-id1969755\">Write each expression in exponential form:<\/p>\n<ol id=\"eip-id1168469525719\" class=\"circled\" type=\"a\">\n<li><img loading=\"lazy\" decoding=\"async\" src=\"https:\/\/opentextbc.ca\/introalgebra\/wp-content\/ql-cache\/quicklatex.com-0033b10a6dd7d2b27b7ef7c36d7e29ce_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"&#92;&#112;&#104;&#97;&#110;&#116;&#111;&#109;&#123;&#92;&#114;&#117;&#108;&#101;&#123;&#48;&#46;&#50;&#101;&#109;&#125;&#123;&#48;&#101;&#120;&#125;&#125;&#49;&#54;&#92;&#99;&#100;&#111;&#116;&#49;&#54;&#92;&#99;&#100;&#111;&#116;&#49;&#54;&#92;&#99;&#100;&#111;&#116;&#49;&#54;&#92;&#99;&#100;&#111;&#116;&#49;&#54;&#92;&#99;&#100;&#111;&#116;&#49;&#54;&#92;&#99;&#100;&#111;&#116;&#49;&#54;\" title=\"Rendered by QuickLaTeX.com\" height=\"12\" width=\"200\" style=\"vertical-align: 0px;\" \/><\/li>\n<li><img loading=\"lazy\" decoding=\"async\" src=\"https:\/\/opentextbc.ca\/introalgebra\/wp-content\/ql-cache\/quicklatex.com-60be981d520594c1e2873bc95f7ffdcd_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"&#92;&#112;&#104;&#97;&#110;&#116;&#111;&#109;&#123;&#92;&#114;&#117;&#108;&#101;&#123;&#48;&#46;&#50;&#101;&#109;&#125;&#123;&#48;&#101;&#120;&#125;&#125;&#57;&#92;&#99;&#100;&#111;&#116;&#57;&#92;&#99;&#100;&#111;&#116;&#57;&#92;&#99;&#100;&#111;&#116;&#57;&#92;&#99;&#100;&#111;&#116;&#57;\" title=\"Rendered by QuickLaTeX.com\" height=\"12\" width=\"95\" style=\"vertical-align: 0px;\" \/><\/li>\n<li><img loading=\"lazy\" decoding=\"async\" src=\"https:\/\/opentextbc.ca\/introalgebra\/wp-content\/ql-cache\/quicklatex.com-be9e23551c8a64813bb22553097a687a_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"&#92;&#112;&#104;&#97;&#110;&#116;&#111;&#109;&#123;&#92;&#114;&#117;&#108;&#101;&#123;&#48;&#46;&#50;&#101;&#109;&#125;&#123;&#48;&#101;&#120;&#125;&#125;&#120;&#92;&#99;&#100;&#111;&#116;&#32;&#120;&#92;&#99;&#100;&#111;&#116;&#32;&#120;&#92;&#99;&#100;&#111;&#116;&#32;&#120;\" title=\"Rendered by QuickLaTeX.com\" height=\"8\" width=\"78\" style=\"vertical-align: 0px;\" \/><\/li>\n<li><img loading=\"lazy\" decoding=\"async\" src=\"https:\/\/opentextbc.ca\/introalgebra\/wp-content\/ql-cache\/quicklatex.com-755235106995d203b2927c20a8e47ffd_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"&#92;&#112;&#104;&#97;&#110;&#116;&#111;&#109;&#123;&#92;&#114;&#117;&#108;&#101;&#123;&#48;&#46;&#50;&#101;&#109;&#125;&#123;&#48;&#101;&#120;&#125;&#125;&#97;&#92;&#99;&#100;&#111;&#116;&#32;&#97;&#92;&#99;&#100;&#111;&#116;&#32;&#97;&#92;&#99;&#100;&#111;&#116;&#32;&#97;&#92;&#99;&#100;&#111;&#116;&#32;&#97;&#92;&#99;&#100;&#111;&#116;&#32;&#97;&#92;&#99;&#100;&#111;&#116;&#32;&#97;&#92;&#99;&#100;&#111;&#116;&#32;&#97;\" title=\"Rendered by QuickLaTeX.com\" height=\"8\" width=\"164\" style=\"vertical-align: 0px;\" \/><\/li>\n<\/ol>\n<\/div>\n<div id=\"fs-id4124564\" data-type=\"solution\">\n<div data-type=\"title\"><\/div>\n<div data-type=\"title\"><strong>Solution<\/strong><\/div>\n<div data-type=\"title\"><\/div>\n<table id=\"eip-id1168469627334\" style=\"width: 100%;\" summary=\".\" data-label=\"\">\n<tbody>\n<tr>\n<td>a. The base 16 is a factor 7 times.<\/td>\n<td><img loading=\"lazy\" decoding=\"async\" src=\"https:\/\/opentextbc.ca\/introalgebra\/wp-content\/ql-cache\/quicklatex.com-97a1705bd17af21623aedf88d3bac62b_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"&#123;&#49;&#54;&#125;&#94;&#123;&#55;&#125;\" title=\"Rendered by QuickLaTeX.com\" height=\"16\" width=\"24\" style=\"vertical-align: -1px;\" \/><\/td>\n<\/tr>\n<tr>\n<td>b. The base 9 is a factor 5 times.<\/td>\n<td><img loading=\"lazy\" decoding=\"async\" src=\"https:\/\/opentextbc.ca\/introalgebra\/wp-content\/ql-cache\/quicklatex.com-e51308d1f57d7b304d32e225017a6f97_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"&#123;&#57;&#125;&#94;&#123;&#53;&#125;\" title=\"Rendered by QuickLaTeX.com\" height=\"15\" width=\"16\" style=\"vertical-align: 0px;\" \/><\/td>\n<\/tr>\n<tr>\n<td>c. The base <img loading=\"lazy\" decoding=\"async\" src=\"https:\/\/opentextbc.ca\/introalgebra\/wp-content\/ql-cache\/quicklatex.com-ede05c264bba0eda080918aaa09c4658_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"&#120;\" title=\"Rendered by QuickLaTeX.com\" height=\"8\" width=\"10\" style=\"vertical-align: 0px;\" \/> is a factor 4 times.<\/td>\n<td><img loading=\"lazy\" decoding=\"async\" src=\"https:\/\/opentextbc.ca\/introalgebra\/wp-content\/ql-cache\/quicklatex.com-159899034a68d14dd24abc2121923568_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"&#123;&#120;&#125;&#94;&#123;&#52;&#125;\" title=\"Rendered by QuickLaTeX.com\" height=\"15\" width=\"17\" style=\"vertical-align: 0px;\" \/><\/td>\n<\/tr>\n<tr>\n<td>d. The base <img loading=\"lazy\" decoding=\"async\" src=\"https:\/\/opentextbc.ca\/introalgebra\/wp-content\/ql-cache\/quicklatex.com-5c53d6ebabdbcfa4e107550ea60b1b19_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"&#97;\" title=\"Rendered by QuickLaTeX.com\" height=\"8\" width=\"9\" style=\"vertical-align: 0px;\" \/> is a factor 8 times.<\/td>\n<td><img loading=\"lazy\" decoding=\"async\" src=\"https:\/\/opentextbc.ca\/introalgebra\/wp-content\/ql-cache\/quicklatex.com-429724eba970bc2bdecc03d1e9142f7d_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"&#123;&#97;&#125;&#94;&#123;&#56;&#125;\" title=\"Rendered by QuickLaTeX.com\" height=\"15\" width=\"16\" style=\"vertical-align: 0px;\" \/><\/td>\n<\/tr>\n<\/tbody>\n<\/table>\n<\/div>\n<\/div>\n<\/div>\n<div class=\"textbox textbox--exercises\">\n<header class=\"textbox__header\">\n<p class=\"textbox__title\">TRY IT 5.1<\/p>\n<\/header>\n<div class=\"textbox__content\">\n<div id=\"fs-id2214154\" data-type=\"problem\">\n<p id=\"fs-id1859717\">Write each expression in exponential form:<\/p>\n<p id=\"fs-id1611515\"><img loading=\"lazy\" decoding=\"async\" src=\"https:\/\/opentextbc.ca\/introalgebra\/wp-content\/ql-cache\/quicklatex.com-7c10328136ee46620d4de81d7ff5364c_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"&#52;&#49;&#92;&#99;&#100;&#111;&#116;&#52;&#49;&#92;&#99;&#100;&#111;&#116;&#52;&#49;&#92;&#99;&#100;&#111;&#116;&#52;&#49;&#92;&#99;&#100;&#111;&#116;&#52;&#49;\" title=\"Rendered by QuickLaTeX.com\" height=\"12\" width=\"139\" style=\"vertical-align: 0px;\" \/><\/p>\n<\/div>\n<div id=\"fs-id2276750\" data-type=\"solution\">\n<details>\n<summary>Show Answer<\/summary>\n<p id=\"fs-id1377278\">41<sup>5<\/sup><\/p>\n<\/details>\n<\/div>\n<\/div>\n<\/div>\n<div class=\"textbox textbox--exercises\">\n<header class=\"textbox__header\">\n<p class=\"textbox__title\">TRY IT 5.2<\/p>\n<\/header>\n<div class=\"textbox__content\">\n<div id=\"fs-id1345426\" data-type=\"problem\">\n<p id=\"fs-id1171104403843\">Write each expression in exponential form:<\/p>\n<p id=\"fs-id2216220\"><img loading=\"lazy\" decoding=\"async\" src=\"https:\/\/opentextbc.ca\/introalgebra\/wp-content\/ql-cache\/quicklatex.com-3cb1cc660afc36cb56212a4f7fb07d83_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"&#55;&#92;&#99;&#100;&#111;&#116;&#55;&#92;&#99;&#100;&#111;&#116;&#55;&#92;&#99;&#100;&#111;&#116;&#55;&#92;&#99;&#100;&#111;&#116;&#55;&#92;&#99;&#100;&#111;&#116;&#55;&#92;&#99;&#100;&#111;&#116;&#55;&#92;&#99;&#100;&#111;&#116;&#55;&#92;&#99;&#100;&#111;&#116;&#55;\" title=\"Rendered by QuickLaTeX.com\" height=\"13\" width=\"182\" style=\"vertical-align: 0px;\" \/><\/p>\n<\/div>\n<div id=\"fs-id2782287\" data-type=\"solution\">\n<details>\n<summary>Show Answer<\/summary>\n<p id=\"fs-id1390717\">7<sup>9<\/sup><\/p>\n<\/details>\n<\/div>\n<\/div>\n<\/div>\n<\/div>\n<div id=\"fs-id1171103024968\" class=\"try\" data-type=\"note\">\n<div id=\"fs-id2669743\" data-type=\"exercise\">\n<div id=\"fs-id1345426\" data-type=\"problem\">\n<div class=\"textbox textbox--examples\">\n<header class=\"textbox__header\">\n<p class=\"textbox__title\">EXAMPLE 6<\/p>\n<\/header>\n<div class=\"textbox__content\">\n<div id=\"fs-id1842666\" data-type=\"problem\">\n<p id=\"fs-id2270606\">Write each exponential expression in expanded form:<\/p>\n<ol id=\"eip-id1168469513220\" class=\"circled\" type=\"a\">\n<li><img loading=\"lazy\" decoding=\"async\" src=\"https:\/\/opentextbc.ca\/introalgebra\/wp-content\/ql-cache\/quicklatex.com-631f93fc40c0b634d6d162c6cb67a109_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"&#92;&#112;&#104;&#97;&#110;&#116;&#111;&#109;&#123;&#92;&#114;&#117;&#108;&#101;&#123;&#48;&#46;&#50;&#101;&#109;&#125;&#123;&#48;&#101;&#120;&#125;&#125;&#123;&#56;&#125;&#94;&#123;&#54;&#125;&#92;&#112;&#104;&#97;&#110;&#116;&#111;&#109;&#123;&#92;&#114;&#117;&#108;&#101;&#123;&#48;&#46;&#50;&#101;&#109;&#125;&#123;&#48;&#101;&#120;&#125;&#125;\" title=\"Rendered by QuickLaTeX.com\" height=\"15\" width=\"16\" style=\"vertical-align: 0px;\" \/><\/li>\n<li><img loading=\"lazy\" decoding=\"async\" src=\"https:\/\/opentextbc.ca\/introalgebra\/wp-content\/ql-cache\/quicklatex.com-b8832c40f001cb86061449db5d5a297b_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"&#92;&#112;&#104;&#97;&#110;&#116;&#111;&#109;&#123;&#92;&#114;&#117;&#108;&#101;&#123;&#48;&#46;&#50;&#101;&#109;&#125;&#123;&#48;&#101;&#120;&#125;&#125;&#123;&#120;&#125;&#94;&#123;&#53;&#125;\" title=\"Rendered by QuickLaTeX.com\" height=\"15\" width=\"17\" style=\"vertical-align: 0px;\" \/><\/li>\n<\/ol>\n<\/div>\n<div id=\"fs-id2150233\" data-type=\"solution\">\n<div data-type=\"title\"><\/div>\n<div data-type=\"title\"><strong>Solution<\/strong><\/div>\n<div data-type=\"title\"><\/div>\n<p id=\"fs-id3177573\">a. The base is <img loading=\"lazy\" decoding=\"async\" src=\"https:\/\/opentextbc.ca\/introalgebra\/wp-content\/ql-cache\/quicklatex.com-23212a120eb92d226d44696a0b80bead_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"&#56;\" title=\"Rendered by QuickLaTeX.com\" height=\"12\" width=\"9\" style=\"vertical-align: 0px;\" \/> and the exponent is <img loading=\"lazy\" decoding=\"async\" src=\"https:\/\/opentextbc.ca\/introalgebra\/wp-content\/ql-cache\/quicklatex.com-b5c3e12330dabaeec7413281aba0f134_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"&#54;\" title=\"Rendered by QuickLaTeX.com\" height=\"12\" width=\"9\" style=\"vertical-align: 0px;\" \/>, so <img loading=\"lazy\" decoding=\"async\" src=\"https:\/\/opentextbc.ca\/introalgebra\/wp-content\/ql-cache\/quicklatex.com-387099948263518cacda9166ae83f7db_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"&#123;&#56;&#125;&#94;&#123;&#54;&#125;\" title=\"Rendered by QuickLaTeX.com\" height=\"15\" width=\"16\" style=\"vertical-align: 0px;\" \/> means <img loading=\"lazy\" decoding=\"async\" src=\"https:\/\/opentextbc.ca\/introalgebra\/wp-content\/ql-cache\/quicklatex.com-e14ec2337a4f0583515b91ada307afb1_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"&#56;&#92;&#99;&#100;&#111;&#116;&#32;&#56;&#92;&#99;&#100;&#111;&#116;&#32;&#56;&#92;&#99;&#100;&#111;&#116;&#32;&#56;&#92;&#99;&#100;&#111;&#116;&#32;&#56;&#92;&#99;&#100;&#111;&#116;&#32;&#56;\" title=\"Rendered by QuickLaTeX.com\" height=\"12\" width=\"117\" style=\"vertical-align: 0px;\" \/><\/p>\n<p id=\"fs-id2845374\">b. The base is <img loading=\"lazy\" decoding=\"async\" src=\"https:\/\/opentextbc.ca\/introalgebra\/wp-content\/ql-cache\/quicklatex.com-ede05c264bba0eda080918aaa09c4658_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"&#120;\" title=\"Rendered by QuickLaTeX.com\" height=\"8\" width=\"10\" style=\"vertical-align: 0px;\" \/> and the exponent is <img loading=\"lazy\" decoding=\"async\" src=\"https:\/\/opentextbc.ca\/introalgebra\/wp-content\/ql-cache\/quicklatex.com-8995e2084120c1c1f4b53f490d281bc4_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"&#53;\" title=\"Rendered by QuickLaTeX.com\" height=\"13\" width=\"8\" style=\"vertical-align: 0px;\" \/>, so <img loading=\"lazy\" decoding=\"async\" src=\"https:\/\/opentextbc.ca\/introalgebra\/wp-content\/ql-cache\/quicklatex.com-48541f82788d9b97a870606bd6257cd7_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"&#123;&#120;&#125;&#94;&#123;&#53;&#125;\" title=\"Rendered by QuickLaTeX.com\" height=\"15\" width=\"17\" style=\"vertical-align: 0px;\" \/> means <img loading=\"lazy\" decoding=\"async\" src=\"https:\/\/opentextbc.ca\/introalgebra\/wp-content\/ql-cache\/quicklatex.com-2adb5a63ea93ccbbb7c1ebd935c511d3_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"&#120;&#92;&#99;&#100;&#111;&#116;&#32;&#120;&#92;&#99;&#100;&#111;&#116;&#32;&#120;&#92;&#99;&#100;&#111;&#116;&#32;&#120;&#92;&#99;&#100;&#111;&#116;&#32;&#120;\" title=\"Rendered by QuickLaTeX.com\" height=\"8\" width=\"102\" style=\"vertical-align: 0px;\" \/><\/p>\n<\/div>\n<\/div>\n<\/div>\n<div class=\"textbox textbox--exercises\">\n<header class=\"textbox__header\">\n<p class=\"textbox__title\">TRY IT 6.1<\/p>\n<\/header>\n<div class=\"textbox__content\">\n<div id=\"fs-id2150329\" data-type=\"problem\">\n<p id=\"fs-id1337149\">Write each exponential expression in expanded form:<\/p>\n<ol id=\"eip-id1168466675879\" class=\"circled\" type=\"a\">\n<li><img loading=\"lazy\" decoding=\"async\" src=\"https:\/\/opentextbc.ca\/introalgebra\/wp-content\/ql-cache\/quicklatex.com-27c49982b6230f50688b7fc841426899_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"&#92;&#112;&#104;&#97;&#110;&#116;&#111;&#109;&#123;&#92;&#114;&#117;&#108;&#101;&#123;&#48;&#46;&#50;&#101;&#109;&#125;&#123;&#48;&#101;&#120;&#125;&#125;&#123;&#52;&#125;&#94;&#123;&#56;&#125;\" title=\"Rendered by QuickLaTeX.com\" height=\"16\" width=\"16\" style=\"vertical-align: -1px;\" \/><\/li>\n<li><img loading=\"lazy\" decoding=\"async\" src=\"https:\/\/opentextbc.ca\/introalgebra\/wp-content\/ql-cache\/quicklatex.com-067d5fcc21aa848b50db34270ff4737d_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"&#92;&#112;&#104;&#97;&#110;&#116;&#111;&#109;&#123;&#92;&#114;&#117;&#108;&#101;&#123;&#48;&#46;&#50;&#101;&#109;&#125;&#123;&#48;&#101;&#120;&#125;&#125;&#123;&#97;&#125;&#94;&#123;&#55;&#125;\" title=\"Rendered by QuickLaTeX.com\" height=\"15\" width=\"16\" style=\"vertical-align: 0px;\" \/><\/li>\n<\/ol>\n<\/div>\n<div id=\"fs-id1245764\" data-type=\"solution\">\n<details>\n<summary>Show Answer<\/summary>\n<ol id=\"eip-id1168466512417\" class=\"circled\" type=\"a\">\n<li><img loading=\"lazy\" decoding=\"async\" src=\"https:\/\/opentextbc.ca\/introalgebra\/wp-content\/ql-cache\/quicklatex.com-d563189c27adf553abd8a7535a563263_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"&#52;&#32;&#92;&#99;&#100;&#111;&#116;&#32;&#52;&#32;&#92;&#99;&#100;&#111;&#116;&#32;&#52;&#32;&#92;&#99;&#100;&#111;&#116;&#32;&#52;&#32;&#92;&#99;&#100;&#111;&#116;&#32;&#52;&#32;&#92;&#99;&#100;&#111;&#116;&#32;&#52;&#32;&#92;&#99;&#100;&#111;&#116;&#32;&#52;&#32;&#92;&#99;&#100;&#111;&#116;&#32;&#52;\" title=\"Rendered by QuickLaTeX.com\" height=\"12\" width=\"161\" style=\"vertical-align: 0px;\" \/><\/li>\n<li><img loading=\"lazy\" decoding=\"async\" src=\"https:\/\/opentextbc.ca\/introalgebra\/wp-content\/ql-cache\/quicklatex.com-9cfdc1c5410ac923ab039ed098198433_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"&#97;&#32;&#92;&#99;&#100;&#111;&#116;&#32;&#97;&#32;&#92;&#99;&#100;&#111;&#116;&#32;&#97;&#32;&#92;&#99;&#100;&#111;&#116;&#32;&#97;&#32;&#92;&#99;&#100;&#111;&#116;&#32;&#97;&#32;&#92;&#99;&#100;&#111;&#116;&#32;&#97;&#32;&#92;&#99;&#100;&#111;&#116;&#32;&#97;\" title=\"Rendered by QuickLaTeX.com\" height=\"8\" width=\"142\" style=\"vertical-align: 0px;\" \/><\/li>\n<\/ol>\n<\/details>\n<\/div>\n<\/div>\n<\/div>\n<div class=\"textbox textbox--exercises\">\n<header class=\"textbox__header\">\n<p class=\"textbox__title\">TRY IT 6.2<\/p>\n<\/header>\n<div class=\"textbox__content\">\n<div id=\"fs-id1215612\" data-type=\"problem\">\n<p id=\"fs-id1171103315685\">Write each exponential expression in expanded form:<\/p>\n<ol id=\"eip-id1168467437310\" class=\"circled\" type=\"a\">\n<li><img loading=\"lazy\" decoding=\"async\" src=\"https:\/\/opentextbc.ca\/introalgebra\/wp-content\/ql-cache\/quicklatex.com-f33eea4709da9b7b4e5b5b18226ac1f9_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"&#123;&#92;&#112;&#104;&#97;&#110;&#116;&#111;&#109;&#123;&#92;&#114;&#117;&#108;&#101;&#123;&#48;&#46;&#50;&#101;&#109;&#125;&#123;&#48;&#101;&#120;&#125;&#125;&#56;&#125;&#94;&#123;&#56;&#125;&#92;&#112;&#104;&#97;&#110;&#116;&#111;&#109;&#123;&#92;&#114;&#117;&#108;&#101;&#123;&#48;&#46;&#52;&#101;&#109;&#125;&#123;&#48;&#101;&#120;&#125;&#125;\" title=\"Rendered by QuickLaTeX.com\" height=\"15\" width=\"15\" style=\"vertical-align: 0px;\" \/><\/li>\n<li><img loading=\"lazy\" decoding=\"async\" src=\"https:\/\/opentextbc.ca\/introalgebra\/wp-content\/ql-cache\/quicklatex.com-2f564849d26bc9423824e0bdacb98e09_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"&#92;&#112;&#104;&#97;&#110;&#116;&#111;&#109;&#123;&#92;&#114;&#117;&#108;&#101;&#123;&#48;&#46;&#50;&#101;&#109;&#125;&#123;&#48;&#101;&#120;&#125;&#125;&#123;&#98;&#125;&#94;&#123;&#54;&#125;\" title=\"Rendered by QuickLaTeX.com\" height=\"15\" width=\"15\" style=\"vertical-align: 0px;\" \/><\/li>\n<\/ol>\n<\/div>\n<div id=\"fs-id1302295\" data-type=\"solution\">\n<details>\n<summary>Show Answer<\/summary>\n<ol id=\"eip-id1168468532157\" class=\"circled\" type=\"a\">\n<li><img loading=\"lazy\" decoding=\"async\" src=\"https:\/\/opentextbc.ca\/introalgebra\/wp-content\/ql-cache\/quicklatex.com-1922a093a0ce2181ecb48dd32ed7d8fa_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"&#56;&#32;&#92;&#99;&#100;&#111;&#116;&#32;&#56;&#32;&#92;&#99;&#100;&#111;&#116;&#32;&#56;&#32;&#92;&#99;&#100;&#111;&#116;&#32;&#56;&#32;&#92;&#99;&#100;&#111;&#116;&#32;&#56;&#32;&#92;&#99;&#100;&#111;&#116;&#32;&#56;&#32;&#92;&#99;&#100;&#111;&#116;&#32;&#56;&#32;&#92;&#99;&#100;&#111;&#116;&#32;&#56;\" title=\"Rendered by QuickLaTeX.com\" height=\"12\" width=\"161\" style=\"vertical-align: 0px;\" \/><\/li>\n<li><img loading=\"lazy\" decoding=\"async\" src=\"https:\/\/opentextbc.ca\/introalgebra\/wp-content\/ql-cache\/quicklatex.com-2208c269b37f0a3a4bbd8a4810c2eca3_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"&#98;&#32;&#92;&#99;&#100;&#111;&#116;&#32;&#98;&#32;&#92;&#99;&#100;&#111;&#116;&#32;&#98;&#32;&#92;&#99;&#100;&#111;&#116;&#32;&#98;&#32;&#92;&#99;&#100;&#111;&#116;&#32;&#98;&#32;&#92;&#99;&#100;&#111;&#116;&#32;&#98;\" title=\"Rendered by QuickLaTeX.com\" height=\"12\" width=\"110\" style=\"vertical-align: 0px;\" \/><\/li>\n<\/ol>\n<\/details>\n<\/div>\n<\/div>\n<\/div>\n<\/div>\n<\/div>\n<\/div>\n<p id=\"fs-id2661619\">To simplify an exponential expression without using a calculator, we write it in expanded form and then multiply the factors.<\/p>\n<div class=\"textbox textbox--examples\">\n<header class=\"textbox__header\">\n<p class=\"textbox__title\">EXAMPLE 7<\/p>\n<\/header>\n<div class=\"textbox__content\">\n<div data-type=\"problem\">\n<p id=\"fs-id1603288\">Simplify: <img loading=\"lazy\" decoding=\"async\" src=\"https:\/\/opentextbc.ca\/introalgebra\/wp-content\/ql-cache\/quicklatex.com-3e51d6feba44ebe62d8639ff84d02323_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"&#123;&#51;&#125;&#94;&#123;&#52;&#125;\" title=\"Rendered by QuickLaTeX.com\" height=\"15\" width=\"16\" style=\"vertical-align: 0px;\" \/>.<\/p>\n<\/div>\n<div id=\"fs-id1762208\" data-type=\"solution\">\n<div data-type=\"title\"><\/div>\n<div data-type=\"title\"><strong>Solution<\/strong><\/div>\n<div data-type=\"title\"><\/div>\n<table id=\"eip-id1164752752096\" style=\"width: 100%;\" summary=\".\" data-label=\"\">\n<tbody>\n<tr>\n<td><\/td>\n<td data-align=\"center\"><img loading=\"lazy\" decoding=\"async\" src=\"https:\/\/opentextbc.ca\/introalgebra\/wp-content\/ql-cache\/quicklatex.com-3e51d6feba44ebe62d8639ff84d02323_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"&#123;&#51;&#125;&#94;&#123;&#52;&#125;\" title=\"Rendered by QuickLaTeX.com\" height=\"15\" width=\"16\" style=\"vertical-align: 0px;\" \/><\/td>\n<\/tr>\n<tr>\n<td>Expand the expression.<\/td>\n<td data-align=\"center\"><img loading=\"lazy\" decoding=\"async\" src=\"https:\/\/opentextbc.ca\/introalgebra\/wp-content\/ql-cache\/quicklatex.com-8d2978629f9062b8c180d8a21001968f_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"&#51;&#92;&#99;&#100;&#111;&#116;&#32;&#51;&#92;&#99;&#100;&#111;&#116;&#32;&#51;&#92;&#99;&#100;&#111;&#116;&#32;&#51;\" title=\"Rendered by QuickLaTeX.com\" height=\"12\" width=\"74\" style=\"vertical-align: 0px;\" \/><\/td>\n<\/tr>\n<tr>\n<td>Multiply left to right.<\/td>\n<td data-align=\"center\"><img loading=\"lazy\" decoding=\"async\" src=\"https:\/\/opentextbc.ca\/introalgebra\/wp-content\/ql-cache\/quicklatex.com-3e62258d03d957521f030ebd19cf3735_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"&#57;&#92;&#99;&#100;&#111;&#116;&#32;&#51;&#92;&#99;&#100;&#111;&#116;&#32;&#51;\" title=\"Rendered by QuickLaTeX.com\" height=\"12\" width=\"52\" style=\"vertical-align: 0px;\" \/><\/td>\n<\/tr>\n<tr>\n<td><\/td>\n<td data-align=\"center\"><img loading=\"lazy\" decoding=\"async\" src=\"https:\/\/opentextbc.ca\/introalgebra\/wp-content\/ql-cache\/quicklatex.com-5a00c7742fac01808aa384b1961e5823_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"&#50;&#55;&#92;&#99;&#100;&#111;&#116;&#32;&#51;\" title=\"Rendered by QuickLaTeX.com\" height=\"13\" width=\"40\" style=\"vertical-align: 0px;\" \/><\/td>\n<\/tr>\n<tr>\n<td>Multiply.<\/td>\n<td data-align=\"center\"><img loading=\"lazy\" decoding=\"async\" src=\"https:\/\/opentextbc.ca\/introalgebra\/wp-content\/ql-cache\/quicklatex.com-2fddb0fc050fd5cd8cec81b9bb162aa9_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"&#56;&#49;\" title=\"Rendered by QuickLaTeX.com\" height=\"13\" width=\"17\" style=\"vertical-align: -1px;\" \/><\/td>\n<\/tr>\n<\/tbody>\n<\/table>\n<\/div>\n<\/div>\n<\/div>\n<div class=\"textbox textbox--exercises\">\n<header class=\"textbox__header\">\n<p class=\"textbox__title\">TRY IT 7.1<\/p>\n<\/header>\n<div class=\"textbox__content\">\n<div id=\"fs-id1578312\" data-type=\"problem\">\n<p id=\"fs-id2784369\">Simplify:<\/p>\n<ol id=\"eip-id1168466339424\" class=\"circled\" type=\"a\">\n<li><img loading=\"lazy\" decoding=\"async\" src=\"https:\/\/opentextbc.ca\/introalgebra\/wp-content\/ql-cache\/quicklatex.com-52be7f73b3501ccbfc2e4f6cb3721784_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"&#92;&#112;&#104;&#97;&#110;&#116;&#111;&#109;&#123;&#92;&#114;&#117;&#108;&#101;&#123;&#48;&#46;&#50;&#101;&#109;&#125;&#123;&#48;&#101;&#120;&#125;&#125;&#123;&#53;&#125;&#94;&#123;&#51;&#125;&#92;&#112;&#104;&#97;&#110;&#116;&#111;&#109;&#123;&#92;&#114;&#117;&#108;&#101;&#123;&#48;&#46;&#52;&#101;&#109;&#125;&#123;&#48;&#101;&#120;&#125;&#125;\" title=\"Rendered by QuickLaTeX.com\" height=\"15\" width=\"16\" style=\"vertical-align: 0px;\" \/><\/li>\n<li><img loading=\"lazy\" decoding=\"async\" src=\"https:\/\/opentextbc.ca\/introalgebra\/wp-content\/ql-cache\/quicklatex.com-ac97f89dd380a5501d405daf59b7f589_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"&#92;&#112;&#104;&#97;&#110;&#116;&#111;&#109;&#123;&#92;&#114;&#117;&#108;&#101;&#123;&#48;&#46;&#50;&#101;&#109;&#125;&#123;&#48;&#101;&#120;&#125;&#125;&#123;&#49;&#125;&#94;&#123;&#55;&#125;\" title=\"Rendered by QuickLaTeX.com\" height=\"16\" width=\"15\" style=\"vertical-align: -1px;\" \/><\/li>\n<\/ol>\n<\/div>\n<div id=\"fs-id3294286\" data-type=\"solution\">\n<details>\n<summary>Show Answer<\/summary>\n<ol id=\"eip-id1168466339465\" class=\"circled\" type=\"a\">\n<li>125<\/li>\n<li>1<\/li>\n<\/ol>\n<\/details>\n<\/div>\n<\/div>\n<\/div>\n<div class=\"textbox textbox--exercises\">\n<header class=\"textbox__header\">\n<p class=\"textbox__title\">TRY IT 7.2<\/p>\n<\/header>\n<div class=\"textbox__content\">\n<div id=\"fs-id1917006\" data-type=\"problem\">\n<p id=\"fs-id1171103315179\">Simplify:<\/p>\n<ol id=\"eip-id1168467189297\" class=\"circled\" type=\"a\">\n<li><img loading=\"lazy\" decoding=\"async\" src=\"https:\/\/opentextbc.ca\/introalgebra\/wp-content\/ql-cache\/quicklatex.com-c122624fe8c9dd475bac3badbfa98545_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"&#92;&#112;&#104;&#97;&#110;&#116;&#111;&#109;&#123;&#92;&#114;&#117;&#108;&#101;&#123;&#48;&#46;&#50;&#101;&#109;&#125;&#123;&#48;&#101;&#120;&#125;&#125;&#123;&#55;&#125;&#94;&#123;&#50;&#125;&#92;&#112;&#104;&#97;&#110;&#116;&#111;&#109;&#123;&#92;&#114;&#117;&#108;&#101;&#123;&#48;&#46;&#52;&#101;&#109;&#125;&#123;&#48;&#101;&#120;&#125;&#125;\" title=\"Rendered by QuickLaTeX.com\" height=\"15\" width=\"16\" style=\"vertical-align: 0px;\" \/><\/li>\n<li><img loading=\"lazy\" decoding=\"async\" src=\"https:\/\/opentextbc.ca\/introalgebra\/wp-content\/ql-cache\/quicklatex.com-129eac5c7a4a763f18a9570946b034ce_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"&#92;&#112;&#104;&#97;&#110;&#116;&#111;&#109;&#123;&#92;&#114;&#117;&#108;&#101;&#123;&#48;&#46;&#50;&#101;&#109;&#125;&#123;&#48;&#101;&#120;&#125;&#125;&#123;&#48;&#125;&#94;&#123;&#53;&#125;\" title=\"Rendered by QuickLaTeX.com\" height=\"15\" width=\"16\" style=\"vertical-align: 0px;\" \/><\/li>\n<\/ol>\n<\/div>\n<div id=\"fs-id1152934\" data-type=\"solution\">\n<details>\n<summary>Show Answer<\/summary>\n<ol id=\"eip-id1168467343038\" class=\"circled\" type=\"a\">\n<li>49<\/li>\n<li>0<\/li>\n<\/ol>\n<\/details>\n<\/div>\n<\/div>\n<\/div>\n<h1>Simplify Expressions Using the Order of Operations<\/h1>\n<p id=\"fs-id1357642\">We\u2019ve introduced most of the symbols and notation used in algebra, but now we need to clarify the <span class=\"no-emphasis\" data-type=\"term\">order of operations<\/span>. Otherwise, expressions may have different meanings, and they may result in different values.<\/p>\n<p id=\"fs-id1171101101203\">For example, consider the expression:<\/p>\n<div id=\"fs-id1171101101206\" class=\"unnumbered\" data-type=\"equation\" data-label=\"\"><img loading=\"lazy\" decoding=\"async\" src=\"https:\/\/opentextbc.ca\/introalgebra\/wp-content\/ql-cache\/quicklatex.com-3f76903033453bfd676449bc26cf98e4_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"&#52;&#43;&#51;&#92;&#99;&#100;&#111;&#116;&#32;&#55;\" title=\"Rendered by QuickLaTeX.com\" height=\"15\" width=\"61\" style=\"vertical-align: -2px;\" \/><\/div>\n<div id=\"fs-id1171103305974\" class=\"unnumbered\" data-type=\"equation\" data-label=\"\"><img loading=\"lazy\" decoding=\"async\" src=\"https:\/\/opentextbc.ca\/introalgebra\/wp-content\/ql-cache\/quicklatex.com-905a3391614c3d47c5b299936895f3bb_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"&#92;&#98;&#101;&#103;&#105;&#110;&#123;&#97;&#114;&#114;&#97;&#121;&#125;&#123;&#99;&#99;&#99;&#99;&#125;&#92;&#104;&#102;&#105;&#108;&#108;&#32;&#92;&#116;&#101;&#120;&#116;&#123;&#83;&#111;&#109;&#101;&#32;&#115;&#116;&#117;&#100;&#101;&#110;&#116;&#115;&#32;&#115;&#97;&#121;&#32;&#105;&#116;&#32;&#115;&#105;&#109;&#112;&#108;&#105;&#102;&#105;&#101;&#115;&#32;&#116;&#111;&#32;&#52;&#57;&#46;&#125;&#92;&#104;&#102;&#105;&#108;&#108;&#32;&#38;&#32;&#92;&#112;&#104;&#97;&#110;&#116;&#111;&#109;&#123;&#92;&#114;&#117;&#108;&#101;&#123;&#50;&#101;&#109;&#125;&#123;&#48;&#101;&#120;&#125;&#125;&#38;&#32;&#38;&#32;&#92;&#104;&#102;&#105;&#108;&#108;&#32;&#92;&#116;&#101;&#120;&#116;&#123;&#83;&#111;&#109;&#101;&#32;&#115;&#116;&#117;&#100;&#101;&#110;&#116;&#115;&#32;&#115;&#97;&#121;&#32;&#105;&#116;&#32;&#115;&#105;&#109;&#112;&#108;&#105;&#102;&#105;&#101;&#115;&#32;&#116;&#111;&#32;&#50;&#53;&#46;&#125;&#92;&#104;&#102;&#105;&#108;&#108;&#32;&#92;&#92;&#32;&#92;&#98;&#101;&#103;&#105;&#110;&#123;&#97;&#114;&#114;&#97;&#121;&#125;&#123;&#99;&#99;&#99;&#125;&#38;&#32;&#38;&#32;&#92;&#104;&#102;&#105;&#108;&#108;&#32;&#52;&#43;&#51;&#92;&#99;&#100;&#111;&#116;&#32;&#55;&#92;&#104;&#102;&#105;&#108;&#108;&#32;&#92;&#92;&#32;&#92;&#116;&#101;&#120;&#116;&#123;&#83;&#105;&#110;&#99;&#101;&#125;&#92;&#112;&#104;&#97;&#110;&#116;&#111;&#109;&#123;&#92;&#114;&#117;&#108;&#101;&#123;&#48;&#46;&#50;&#101;&#109;&#125;&#123;&#48;&#101;&#120;&#125;&#125;&#52;&#43;&#51;&#92;&#112;&#104;&#97;&#110;&#116;&#111;&#109;&#123;&#92;&#114;&#117;&#108;&#101;&#123;&#48;&#46;&#50;&#101;&#109;&#125;&#123;&#48;&#101;&#120;&#125;&#125;&#92;&#116;&#101;&#120;&#116;&#123;&#103;&#105;&#118;&#101;&#115;&#32;&#55;&#46;&#125;&#92;&#104;&#102;&#105;&#108;&#108;&#32;&#38;&#32;&#92;&#112;&#104;&#97;&#110;&#116;&#111;&#109;&#123;&#92;&#114;&#117;&#108;&#101;&#123;&#50;&#101;&#109;&#125;&#123;&#48;&#101;&#120;&#125;&#125;&#38;&#32;&#92;&#104;&#102;&#105;&#108;&#108;&#32;&#55;&#92;&#99;&#100;&#111;&#116;&#32;&#55;&#92;&#104;&#102;&#105;&#108;&#108;&#32;&#92;&#92;&#32;&#92;&#116;&#101;&#120;&#116;&#123;&#65;&#110;&#100;&#125;&#92;&#112;&#104;&#97;&#110;&#116;&#111;&#109;&#123;&#92;&#114;&#117;&#108;&#101;&#123;&#48;&#46;&#50;&#101;&#109;&#125;&#123;&#48;&#101;&#120;&#125;&#125;&#55;&#92;&#99;&#100;&#111;&#116;&#32;&#55;&#92;&#112;&#104;&#97;&#110;&#116;&#111;&#109;&#123;&#92;&#114;&#117;&#108;&#101;&#123;&#48;&#46;&#50;&#101;&#109;&#125;&#123;&#48;&#101;&#120;&#125;&#125;&#92;&#116;&#101;&#120;&#116;&#123;&#105;&#115;&#32;&#52;&#57;&#46;&#125;&#92;&#104;&#102;&#105;&#108;&#108;&#32;&#38;&#32;&#92;&#112;&#104;&#97;&#110;&#116;&#111;&#109;&#123;&#92;&#114;&#117;&#108;&#101;&#123;&#50;&#101;&#109;&#125;&#123;&#48;&#101;&#120;&#125;&#125;&#38;&#32;&#92;&#104;&#102;&#105;&#108;&#108;&#32;&#52;&#57;&#92;&#104;&#102;&#105;&#108;&#108;&#32;&#92;&#101;&#110;&#100;&#123;&#97;&#114;&#114;&#97;&#121;&#125;&#38;&#32;&#38;&#32;&#38;&#32;&#92;&#98;&#101;&#103;&#105;&#110;&#123;&#97;&#114;&#114;&#97;&#121;&#125;&#123;&#99;&#99;&#99;&#125;&#38;&#32;&#38;&#32;&#92;&#104;&#102;&#105;&#108;&#108;&#32;&#52;&#43;&#51;&#92;&#99;&#100;&#111;&#116;&#32;&#55;&#92;&#104;&#102;&#105;&#108;&#108;&#32;&#92;&#92;&#32;&#92;&#112;&#104;&#97;&#110;&#116;&#111;&#109;&#123;&#92;&#114;&#117;&#108;&#101;&#123;&#48;&#46;&#50;&#101;&#109;&#125;&#123;&#48;&#101;&#120;&#125;&#125;&#92;&#116;&#101;&#120;&#116;&#123;&#83;&#105;&#110;&#99;&#101;&#125;&#92;&#112;&#104;&#97;&#110;&#116;&#111;&#109;&#123;&#92;&#114;&#117;&#108;&#101;&#123;&#48;&#46;&#50;&#101;&#109;&#125;&#123;&#48;&#101;&#120;&#125;&#125;&#51;&#92;&#99;&#100;&#111;&#116;&#32;&#55;&#92;&#112;&#104;&#97;&#110;&#116;&#111;&#109;&#123;&#92;&#114;&#117;&#108;&#101;&#123;&#48;&#46;&#50;&#101;&#109;&#125;&#123;&#48;&#101;&#120;&#125;&#125;&#92;&#116;&#101;&#120;&#116;&#123;&#105;&#115;&#32;&#50;&#49;&#46;&#125;&#92;&#104;&#102;&#105;&#108;&#108;&#32;&#38;&#32;&#38;&#32;&#92;&#104;&#102;&#105;&#108;&#108;&#32;&#52;&#43;&#50;&#49;&#92;&#104;&#102;&#105;&#108;&#108;&#32;&#92;&#92;&#32;&#92;&#112;&#104;&#97;&#110;&#116;&#111;&#109;&#123;&#92;&#114;&#117;&#108;&#101;&#123;&#48;&#46;&#50;&#101;&#109;&#125;&#123;&#48;&#101;&#120;&#125;&#125;&#92;&#116;&#101;&#120;&#116;&#123;&#65;&#110;&#100;&#125;&#92;&#112;&#104;&#97;&#110;&#116;&#111;&#109;&#123;&#92;&#114;&#117;&#108;&#101;&#123;&#48;&#46;&#50;&#101;&#109;&#125;&#123;&#48;&#101;&#120;&#125;&#125;&#50;&#49;&#43;&#52;&#92;&#112;&#104;&#97;&#110;&#116;&#111;&#109;&#123;&#92;&#114;&#117;&#108;&#101;&#123;&#48;&#46;&#50;&#101;&#109;&#125;&#123;&#48;&#101;&#120;&#125;&#125;&#92;&#116;&#101;&#120;&#116;&#123;&#109;&#97;&#107;&#101;&#115;&#32;&#50;&#53;&#46;&#125;&#92;&#104;&#102;&#105;&#108;&#108;&#32;&#38;&#32;&#38;&#32;&#92;&#104;&#102;&#105;&#108;&#108;&#32;&#50;&#53;&#92;&#104;&#102;&#105;&#108;&#108;&#32;&#92;&#101;&#110;&#100;&#123;&#97;&#114;&#114;&#97;&#121;&#125;&#92;&#104;&#102;&#105;&#108;&#108;&#32;&#92;&#101;&#110;&#100;&#123;&#97;&#114;&#114;&#97;&#121;&#125;\" title=\"Rendered by QuickLaTeX.com\" height=\"81\" width=\"659\" style=\"vertical-align: -35px;\" \/><\/div>\n<p id=\"fs-id1530117\">Imagine the confusion that could result if every problem had several different correct answers. The same expression should give the same result. So mathematicians established some guidelines called the order of operations, which outlines the order in which parts of an expression must be simplified.<\/p>\n<div id=\"fs-id1715524\" data-type=\"note\">\n<div data-type=\"title\">\n<div class=\"textbox textbox--key-takeaways\">\n<header class=\"textbox__header\">\n<p class=\"textbox__title\">Order of Operations<\/p>\n<\/header>\n<div class=\"textbox__content\">\n<p id=\"fs-id2750738\">When simplifying mathematical expressions perform the operations in the following order:<\/p>\n<p id=\"fs-id1834652\">1. <strong data-effect=\"bold\">P<\/strong>arentheses and other Grouping Symbols<\/p>\n<ul id=\"fs-id1171104029952\" data-bullet-style=\"bullet\">\n<li>Simplify all expressions inside the parentheses or other grouping symbols, working on the innermost parentheses first.<\/li>\n<\/ul>\n<p id=\"fs-id1570796\">2. <strong data-effect=\"bold\">E<\/strong>xponents<\/p>\n<ul id=\"fs-id1171104407077\" data-bullet-style=\"bullet\">\n<li>Simplify all expressions with exponents.<\/li>\n<\/ul>\n<p id=\"fs-id1894922\">3. <strong data-effect=\"bold\">M<\/strong>ultiplication and <strong data-effect=\"bold\">D<\/strong>ivision<\/p>\n<ul id=\"fs-id1171103140103\" data-bullet-style=\"bullet\">\n<li>Perform all multiplication and division in order from left to right. These operations have equal priority.<\/li>\n<\/ul>\n<p id=\"fs-id3402451\">4. <strong data-effect=\"bold\">A<\/strong>ddition and <strong data-effect=\"bold\">S<\/strong>ubtraction<\/p>\n<ul id=\"fs-id1171104002792\" data-bullet-style=\"bullet\">\n<li>Perform all addition and subtraction in order from left to right. These operations have equal priority.<\/li>\n<\/ul>\n<p>Students often ask, \u201cHow will I remember the order?\u201d Here is a way to help you remember: Take the first letter of each key word and substitute the silly phrase.<\/p>\n<p id=\"fs-id1269648\" style=\"text-align: center;\"><strong data-effect=\"bold\">P<\/strong>lease <strong data-effect=\"bold\">E<\/strong>xcuse <strong data-effect=\"bold\">M<\/strong>y <strong data-effect=\"bold\">D<\/strong>ear <strong data-effect=\"bold\">A<\/strong>unt <strong data-effect=\"bold\">S<\/strong>ally.<\/p>\n<table id=\"fs-id1786633\" class=\"grid\" style=\"width: 100%;\" summary=\"This table has five rows and two columns. The first row spans both columns and is a header reading \u201cOrder of Operations\u201d. In the second row the first column contains the word please with the p in bold and the second column contains the word parentheses with the p in bold. In the next row the first column contains the word excuse with the first e in bold and the second column contains the word exponents with the first e in bold. The next row contains the phrase \u201cmy dear\u201d in the first column with the m in my and the d in dear in bold and the second column contains the phrase \u201cmultiplication and division\u201d with the m in multiplication and the d in division in bold. The last row contains the phrase \u201cAunt Sally\u201d in the first column with the a in aunt and the s in Sally in bold and the second column contains the phrase \u201caddition and subtraction with the a in addition and the s in subtraction in bold.\" data-label=\"\">\n<tbody>\n<tr valign=\"top\">\n<td style=\"width: 50%;\" data-align=\"left\"><strong data-effect=\"bold\">P<\/strong>lease<\/td>\n<td style=\"width: 50%;\" data-align=\"left\"><strong data-effect=\"bold\">P<\/strong>arentheses<\/td>\n<\/tr>\n<tr valign=\"top\">\n<td style=\"width: 50%;\" data-align=\"left\"><strong data-effect=\"bold\">E<\/strong>xcuse<\/td>\n<td style=\"width: 50%;\" data-align=\"left\"><strong data-effect=\"bold\">E<\/strong>xponents<\/td>\n<\/tr>\n<tr valign=\"top\">\n<td style=\"width: 50%;\" data-align=\"left\"><strong data-effect=\"bold\">M<\/strong>y <strong data-effect=\"bold\">D<\/strong>ear<\/td>\n<td style=\"width: 50%;\" data-align=\"left\"><strong data-effect=\"bold\">M<\/strong>ultiplication and <strong data-effect=\"bold\">D<\/strong>ivision<\/td>\n<\/tr>\n<tr valign=\"top\">\n<td style=\"width: 50%;\" data-align=\"left\"><strong data-effect=\"bold\">A<\/strong>unt <strong data-effect=\"bold\">S<\/strong>ally<\/td>\n<td style=\"width: 50%;\" data-align=\"left\"><strong data-effect=\"bold\">A<\/strong>ddition and <strong data-effect=\"bold\">S<\/strong>ubtraction<\/td>\n<\/tr>\n<\/tbody>\n<\/table>\n<p id=\"fs-id1785127\">It\u2019s good that \u2018<strong data-effect=\"bold\">M<\/strong>y <strong data-effect=\"bold\">D<\/strong>ear\u2019 goes together, as this reminds us that <strong data-effect=\"bold\">m<\/strong>ultiplication and <strong data-effect=\"bold\">d<\/strong>ivision have equal priority. We do not always do multiplication before division or always do division before multiplication. We do them in order from left to right.<\/p>\n<p id=\"fs-id1389767\">Similarly, \u2018<strong data-effect=\"bold\">A<\/strong>unt <strong data-effect=\"bold\">S<\/strong>ally\u2019 goes together and so reminds us that <strong data-effect=\"bold\">a<\/strong>ddition and <strong data-effect=\"bold\">s<\/strong>ubtraction also have equal priority and we do them in order from left to right.<\/p>\n<\/div>\n<\/div>\n<\/div>\n<\/div>\n<div id=\"eip-313\" class=\"manipulative-math\" data-type=\"note\">\n<div class=\"textbox textbox--examples\">\n<header class=\"textbox__header\">\n<p class=\"textbox__title\">EXAMPLE 8<\/p>\n<\/header>\n<div class=\"textbox__content\">\n<div id=\"fs-id2588260\" data-type=\"problem\">\n<p id=\"fs-id1270576\">Simplify the expressions:<\/p>\n<ol id=\"eip-id1168467381591\" class=\"circled\" type=\"a\">\n<li><img loading=\"lazy\" decoding=\"async\" src=\"https:\/\/opentextbc.ca\/introalgebra\/wp-content\/ql-cache\/quicklatex.com-218a3ed8eae38e558ab408222ffecff5_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"&#92;&#112;&#104;&#97;&#110;&#116;&#111;&#109;&#123;&#92;&#114;&#117;&#108;&#101;&#123;&#48;&#46;&#50;&#101;&#109;&#125;&#123;&#48;&#101;&#120;&#125;&#125;&#52;&#43;&#51;&#92;&#99;&#100;&#111;&#116;&#32;&#55;&#92;&#112;&#104;&#97;&#110;&#116;&#111;&#109;&#123;&#92;&#114;&#117;&#108;&#101;&#123;&#48;&#46;&#50;&#101;&#109;&#125;&#123;&#48;&#101;&#120;&#125;&#125;\" title=\"Rendered by QuickLaTeX.com\" height=\"15\" width=\"61\" style=\"vertical-align: -2px;\" \/><\/li>\n<li><img loading=\"lazy\" decoding=\"async\" src=\"https:\/\/opentextbc.ca\/introalgebra\/wp-content\/ql-cache\/quicklatex.com-3ea15cc34a5bdcd99b5e1abb3e0ca576_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"&#92;&#112;&#104;&#97;&#110;&#116;&#111;&#109;&#123;&#92;&#114;&#117;&#108;&#101;&#123;&#48;&#46;&#50;&#101;&#109;&#125;&#123;&#48;&#101;&#120;&#125;&#125;&#92;&#108;&#101;&#102;&#116;&#40;&#52;&#43;&#51;&#92;&#114;&#105;&#103;&#104;&#116;&#41;&#92;&#99;&#100;&#111;&#116;&#32;&#55;\" title=\"Rendered by QuickLaTeX.com\" height=\"19\" width=\"73\" style=\"vertical-align: -5px;\" \/><\/li>\n<\/ol>\n<\/div>\n<div data-type=\"solution\">\n<div data-type=\"title\"><\/div>\n<div data-type=\"title\"><strong>Solution<\/strong><\/div>\n<div data-type=\"title\"><\/div>\n<table id=\"eip-id1164750479370\" class=\"unnumbered unstyled\" summary=\"The table shows the expression four plus three times seven. On the next line it states are there any parentheses in the expression? No. The line below that states are there any exponents in the expression? No. The next line states is there any multiplication or division in the expression? Yes. The next line states Multiply first and is followed by the expression of four plus three times seven. The expression is now four plus twenty-one. The last operation is addition. Add four and twenty-one to get twenty-five.\" data-label=\"\">\n<tbody>\n<tr>\n<td>a.<\/td>\n<td><\/td>\n<\/tr>\n<tr>\n<td><\/td>\n<td><span id=\"eip-id1164750479401\" data-type=\"media\" data-alt=\".\"><img decoding=\"async\" src=\"https:\/\/opentextbc.ca\/accessibilitytoolkit\/wp-content\/uploads\/sites\/333\/2021\/03\/CNX_BMath_Figure_02_01_011_img-01-1.png\" alt=\".\" data-media-type=\"image\/png\" \/><\/span><\/td>\n<\/tr>\n<tr>\n<td>Are there any <strong>p<\/strong>arentheses? No.<\/td>\n<td><\/td>\n<\/tr>\n<tr>\n<td>Are there any <strong>e<\/strong>xponents? No.<\/td>\n<td><\/td>\n<\/tr>\n<tr>\n<td>Is there any <strong>m<\/strong>ultiplication or <strong>d<\/strong>ivision? Yes.<\/td>\n<td><\/td>\n<\/tr>\n<tr>\n<td>Multiply first.<\/td>\n<td><span id=\"eip-id1164754094653\" data-type=\"media\" data-alt=\".\"><img decoding=\"async\" src=\"https:\/\/opentextbc.ca\/accessibilitytoolkit\/wp-content\/uploads\/sites\/333\/2021\/03\/CNX_BMath_Figure_02_01_011_img-02-1.png\" alt=\".\" data-media-type=\"image\/png\" \/><\/span><\/td>\n<\/tr>\n<tr>\n<td>Add.<\/td>\n<td><span id=\"eip-id1164754094670\" data-type=\"media\" data-alt=\".\"><img decoding=\"async\" src=\"https:\/\/opentextbc.ca\/accessibilitytoolkit\/wp-content\/uploads\/sites\/333\/2021\/03\/CNX_BMath_Figure_02_01_011_img-03-1.png\" alt=\".\" data-media-type=\"image\/png\" \/><\/span><\/td>\n<\/tr>\n<tr>\n<td><\/td>\n<td><span id=\"eip-id1164754094685\" data-type=\"media\" data-alt=\".\"><img decoding=\"async\" src=\"https:\/\/opentextbc.ca\/accessibilitytoolkit\/wp-content\/uploads\/sites\/333\/2021\/03\/CNX_BMath_Figure_02_01_011_img-04-1.png\" alt=\".\" data-media-type=\"image\/png\" \/><\/span><\/td>\n<\/tr>\n<\/tbody>\n<\/table>\n<table id=\"eip-id1164754514704\" class=\"unnumbered unstyled\" summary=\"The image shows the expression four plus three in parentheses times seven. Are there any parentheses? Yes, simplify inside the parentheses by adding four and three to get seven. The expression is now seven times seven. Is there any multiplication or division? Yes, multiply seven by seven to get forty-nine.\" data-label=\"\">\n<tbody>\n<tr>\n<td>b.<\/td>\n<td><\/td>\n<\/tr>\n<tr>\n<td><\/td>\n<td><span id=\"eip-id1164754514734\" data-type=\"media\" data-alt=\".\"><img decoding=\"async\" src=\"https:\/\/opentextbc.ca\/accessibilitytoolkit\/wp-content\/uploads\/sites\/333\/2021\/03\/CNX_BMath_Figure_02_01_012_img-01-1.png\" alt=\".\" data-media-type=\"image\/png\" \/><\/span><\/td>\n<\/tr>\n<tr>\n<td>Are there any <strong>p<\/strong>arentheses? Yes.<\/td>\n<td><span id=\"eip-id1164754514754\" data-type=\"media\" data-alt=\".\"><img decoding=\"async\" src=\"https:\/\/opentextbc.ca\/accessibilitytoolkit\/wp-content\/uploads\/sites\/333\/2021\/03\/CNX_BMath_Figure_02_01_012_img-02-1.png\" alt=\".\" data-media-type=\"image\/png\" \/><\/span><\/td>\n<\/tr>\n<tr>\n<td>Simplify inside the parentheses.<\/td>\n<td><span id=\"eip-id1164754514771\" data-type=\"media\" data-alt=\".\"><img decoding=\"async\" src=\"https:\/\/opentextbc.ca\/accessibilitytoolkit\/wp-content\/uploads\/sites\/333\/2021\/03\/CNX_BMath_Figure_02_01_012_img-03-1.png\" alt=\".\" data-media-type=\"image\/png\" \/><\/span><\/td>\n<\/tr>\n<tr>\n<td>Are there any <strong>e<\/strong>xponents? No.<\/td>\n<td><\/td>\n<\/tr>\n<tr>\n<td>Is there any <strong>m<\/strong>ultiplication or <strong>d<\/strong>ivision? Yes.<\/td>\n<td><\/td>\n<\/tr>\n<tr>\n<td>Multiply.<\/td>\n<td><span id=\"eip-id1164754514814\" data-type=\"media\" data-alt=\".\"><img decoding=\"async\" src=\"https:\/\/opentextbc.ca\/accessibilitytoolkit\/wp-content\/uploads\/sites\/333\/2021\/03\/CNX_BMath_Figure_02_01_012_img-04-1.png\" alt=\".\" data-media-type=\"image\/png\" \/><\/span><\/td>\n<\/tr>\n<\/tbody>\n<\/table>\n<\/div>\n<\/div>\n<\/div>\n<div class=\"textbox textbox--exercises\">\n<header class=\"textbox__header\">\n<p class=\"textbox__title\">TRY IT 8.1<\/p>\n<\/header>\n<div class=\"textbox__content\">\n<div id=\"fs-id1496028\" data-type=\"problem\">\n<p id=\"fs-id2132962\">Simplify the expressions:<\/p>\n<ol id=\"eip-id1168467165875\" class=\"circled\" type=\"a\">\n<li><img loading=\"lazy\" decoding=\"async\" src=\"https:\/\/opentextbc.ca\/introalgebra\/wp-content\/ql-cache\/quicklatex.com-038b41cfc44a53c72e6db00269cb21a0_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"&#92;&#112;&#104;&#97;&#110;&#116;&#111;&#109;&#123;&#92;&#114;&#117;&#108;&#101;&#123;&#48;&#46;&#50;&#101;&#109;&#125;&#123;&#48;&#101;&#120;&#125;&#125;&#49;&#50;&#45;&#53;&#92;&#99;&#100;&#111;&#116;&#32;&#50;&#92;&#112;&#104;&#97;&#110;&#116;&#111;&#109;&#123;&#92;&#114;&#117;&#108;&#101;&#123;&#48;&#46;&#52;&#101;&#109;&#125;&#123;&#48;&#101;&#120;&#125;&#125;\" title=\"Rendered by QuickLaTeX.com\" height=\"13\" width=\"68\" style=\"vertical-align: 0px;\" \/><\/li>\n<li><img loading=\"lazy\" decoding=\"async\" src=\"https:\/\/opentextbc.ca\/introalgebra\/wp-content\/ql-cache\/quicklatex.com-9def8d2f4eea68e91aaad4b4f0a7d6ed_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"&#92;&#112;&#104;&#97;&#110;&#116;&#111;&#109;&#123;&#92;&#114;&#117;&#108;&#101;&#123;&#48;&#46;&#50;&#101;&#109;&#125;&#123;&#48;&#101;&#120;&#125;&#125;&#92;&#108;&#101;&#102;&#116;&#40;&#49;&#50;&#45;&#53;&#92;&#114;&#105;&#103;&#104;&#116;&#41;&#92;&#99;&#100;&#111;&#116;&#32;&#50;\" title=\"Rendered by QuickLaTeX.com\" height=\"19\" width=\"81\" style=\"vertical-align: -5px;\" \/><\/li>\n<\/ol>\n<\/div>\n<div id=\"fs-id1732185\" data-type=\"solution\">\n<details>\n<summary>Show Answer<\/summary>\n<ol id=\"eip-id1168468411163\" class=\"circled\" type=\"a\">\n<li>2<\/li>\n<li>14<\/li>\n<\/ol>\n<\/details>\n<\/div>\n<\/div>\n<\/div>\n<div class=\"textbox textbox--exercises\">\n<header class=\"textbox__header\">\n<p class=\"textbox__title\">TRY IT 8.2<\/p>\n<\/header>\n<div class=\"textbox__content\">\n<div id=\"fs-id1622271\" data-type=\"problem\">\n<p id=\"fs-id1171100608975\">Simplify the expressions:<\/p>\n<ol id=\"eip-id1168468535071\" class=\"circled\" type=\"a\">\n<li><img loading=\"lazy\" decoding=\"async\" src=\"https:\/\/opentextbc.ca\/introalgebra\/wp-content\/ql-cache\/quicklatex.com-86783b60e9e2efd8faece9a4cb772c9d_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"&#92;&#112;&#104;&#97;&#110;&#116;&#111;&#109;&#123;&#92;&#114;&#117;&#108;&#101;&#123;&#48;&#46;&#50;&#101;&#109;&#125;&#123;&#48;&#101;&#120;&#125;&#125;&#56;&#43;&#51;&#92;&#99;&#100;&#111;&#116;&#32;&#57;&#92;&#112;&#104;&#97;&#110;&#116;&#111;&#109;&#123;&#92;&#114;&#117;&#108;&#101;&#123;&#48;&#46;&#52;&#101;&#109;&#125;&#123;&#48;&#101;&#120;&#125;&#125;\" title=\"Rendered by QuickLaTeX.com\" height=\"14\" width=\"61\" style=\"vertical-align: -2px;\" \/><\/li>\n<li><img loading=\"lazy\" decoding=\"async\" src=\"https:\/\/opentextbc.ca\/introalgebra\/wp-content\/ql-cache\/quicklatex.com-837fc57e820e70abcc704bda49508d55_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"&#92;&#108;&#101;&#102;&#116;&#40;&#56;&#43;&#51;&#92;&#114;&#105;&#103;&#104;&#116;&#41;&#92;&#99;&#100;&#111;&#116;&#32;&#57;\" title=\"Rendered by QuickLaTeX.com\" height=\"19\" width=\"74\" style=\"vertical-align: -5px;\" \/><\/li>\n<\/ol>\n<\/div>\n<div id=\"fs-id2265132\" data-type=\"solution\">\n<details>\n<summary>Show Answer<\/summary>\n<ol id=\"eip-id1168467599044\" class=\"circled\" type=\"a\">\n<li>35<\/li>\n<li>99<\/li>\n<\/ol>\n<\/details>\n<\/div>\n<\/div>\n<\/div>\n<\/div>\n<div id=\"fs-id1171104389195\" class=\"try\" data-type=\"note\">\n<div id=\"fs-id2478161\" data-type=\"exercise\">\n<div id=\"fs-id1622271\" data-type=\"problem\">\n<div class=\"textbox textbox--examples\">\n<header class=\"textbox__header\">\n<p class=\"textbox__title\">EXAMPLE 9<\/p>\n<\/header>\n<div class=\"textbox__content\">\n<div id=\"fs-id3340653\" data-type=\"problem\">\n<p id=\"fs-id1714375\">Simplify:<\/p>\n<ol id=\"eip-id1168468508209\" class=\"circled\" type=\"a\">\n<li><img loading=\"lazy\" decoding=\"async\" src=\"https:\/\/opentextbc.ca\/introalgebra\/wp-content\/ql-cache\/quicklatex.com-85a41386dc9fae443afaf08eb49326cb_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"&#92;&#112;&#104;&#97;&#110;&#116;&#111;&#109;&#123;&#92;&#114;&#117;&#108;&#101;&#123;&#48;&#46;&#50;&#101;&#109;&#125;&#123;&#48;&#101;&#120;&#125;&#125;&#92;&#116;&#101;&#120;&#116;&#123;&#49;&#56;&#125;&#92;&#100;&#105;&#118;&#32;&#92;&#116;&#101;&#120;&#116;&#123;&#57;&#125;&#92;&#99;&#100;&#111;&#116;&#32;&#92;&#116;&#101;&#120;&#116;&#123;&#50;&#125;&#92;&#112;&#104;&#97;&#110;&#116;&#111;&#109;&#123;&#92;&#114;&#117;&#108;&#101;&#123;&#48;&#46;&#50;&#101;&#109;&#125;&#123;&#48;&#101;&#120;&#125;&#125;\" title=\"Rendered by QuickLaTeX.com\" height=\"13\" width=\"68\" style=\"vertical-align: -1px;\" \/><\/li>\n<li><img loading=\"lazy\" decoding=\"async\" src=\"https:\/\/opentextbc.ca\/introalgebra\/wp-content\/ql-cache\/quicklatex.com-aa3ed5c99af19cb6fd4523e3759b59b0_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"&#92;&#112;&#104;&#97;&#110;&#116;&#111;&#109;&#123;&#92;&#114;&#117;&#108;&#101;&#123;&#48;&#46;&#50;&#101;&#109;&#125;&#123;&#48;&#101;&#120;&#125;&#125;&#92;&#116;&#101;&#120;&#116;&#123;&#49;&#56;&#125;&#92;&#99;&#100;&#111;&#116;&#32;&#92;&#116;&#101;&#120;&#116;&#123;&#57;&#125;&#92;&#100;&#105;&#118;&#32;&#92;&#116;&#101;&#120;&#116;&#123;&#50;&#125;\" title=\"Rendered by QuickLaTeX.com\" height=\"13\" width=\"68\" style=\"vertical-align: -1px;\" \/><\/li>\n<\/ol>\n<\/div>\n<div id=\"fs-id1231784\" data-type=\"solution\">\n<div data-type=\"title\"><\/div>\n<div data-type=\"title\"><strong>Solution<\/strong><\/div>\n<div data-type=\"title\"><\/div>\n<table id=\"eip-id1164754213884\" class=\"unnumbered unstyled\" summary=\"The table shows the expression eighteen divided by nine times two. Are there any parentheses? No. Are there any exponents? No. Is there any multiplication or division? Yes, there is both multiplication and division. Perform multiplication and division from left to right so, divide first. Divide eighteen by nine to get two. The expression is now two times two. The last operation is multiplication. Multiply two by two to get four.\" data-label=\"\">\n<tbody>\n<tr>\n<td>a.<\/td>\n<td><\/td>\n<\/tr>\n<tr>\n<td><\/td>\n<td><span id=\"eip-id1164754213914\" data-type=\"media\" data-alt=\".\"><img decoding=\"async\" src=\"https:\/\/opentextbc.ca\/accessibilitytoolkit\/wp-content\/uploads\/sites\/333\/2021\/03\/CNX_BMath_Figure_02_01_013_img-01-1.png\" alt=\".\" data-media-type=\"image\/png\" \/><\/span><\/td>\n<\/tr>\n<tr>\n<td>Are there any <strong>p<\/strong>arentheses? No.<\/td>\n<td><\/td>\n<\/tr>\n<tr>\n<td>Are there any <strong>e<\/strong>xponents? No.<\/td>\n<td><\/td>\n<\/tr>\n<tr>\n<td>Is there any <strong>m<\/strong>ultiplication or <strong>d<\/strong>ivision? Yes.<\/td>\n<td><\/td>\n<\/tr>\n<tr>\n<td>Multiply and divide from left to right. Divide.<\/td>\n<td><span id=\"eip-id1164752720013\" data-type=\"media\" data-alt=\".\"><img decoding=\"async\" src=\"https:\/\/opentextbc.ca\/accessibilitytoolkit\/wp-content\/uploads\/sites\/333\/2021\/03\/CNX_BMath_Figure_02_01_013_img-02-1.png\" alt=\".\" data-media-type=\"image\/png\" \/><\/span><\/td>\n<\/tr>\n<tr>\n<td>Multiply.<\/td>\n<td><span id=\"eip-id1164752720030\" data-type=\"media\" data-alt=\".\"><img decoding=\"async\" src=\"https:\/\/opentextbc.ca\/accessibilitytoolkit\/wp-content\/uploads\/sites\/333\/2021\/03\/CNX_BMath_Figure_02_01_013_img-03-1.png\" alt=\".\" data-media-type=\"image\/png\" \/><\/span><\/td>\n<\/tr>\n<\/tbody>\n<\/table>\n<table id=\"eip-id1164752720001\" class=\"unnumbered unstyled\" summary=\"The table shows the expression eighteen times nine divided by two. Are there any parentheses? No. Are there any exponents? No. Is there any multiplication or division? Yes, there is both multiplication and division. Perform multiplication and division from left to right so, multiply first. Multiply eighteen by nine to get one hundred sixty-two. The expression is now one hundred sixty-two divided by two. The last operation is division. divide one hundred sixty-two by two to get eighty-one.\" data-label=\"\">\n<tbody>\n<tr>\n<td>b.<\/td>\n<td><\/td>\n<\/tr>\n<tr>\n<td><\/td>\n<td><span id=\"eip-id1164752720032\" data-type=\"media\" data-alt=\".\"><img decoding=\"async\" src=\"https:\/\/opentextbc.ca\/accessibilitytoolkit\/wp-content\/uploads\/sites\/333\/2021\/03\/CNX_BMath_Figure_02_01_014_img-01-1.png\" alt=\".\" data-media-type=\"image\/png\" \/><\/span><\/td>\n<\/tr>\n<tr>\n<td>Are there any <strong>p<\/strong>arentheses? No.<\/td>\n<td><\/td>\n<\/tr>\n<tr>\n<td>Are there any <strong>e<\/strong>xponents? No.<\/td>\n<td><\/td>\n<\/tr>\n<tr>\n<td>Is there any <strong>m<\/strong>ultiplication or <strong>d<\/strong>ivision? Yes.<\/td>\n<td><\/td>\n<\/tr>\n<tr>\n<td>Multiply and divide from left to right.<\/td>\n<td><\/td>\n<\/tr>\n<tr>\n<td>Multiply.<\/td>\n<td><span id=\"eip-id1164752720096\" data-type=\"media\" data-alt=\".\"><img decoding=\"async\" src=\"https:\/\/opentextbc.ca\/accessibilitytoolkit\/wp-content\/uploads\/sites\/333\/2021\/03\/CNX_BMath_Figure_02_01_014_img-02-1.png\" alt=\".\" data-media-type=\"image\/png\" \/><\/span><\/td>\n<\/tr>\n<tr>\n<td>Divide.<\/td>\n<td><span id=\"eip-id1164752720113\" data-type=\"media\" data-alt=\".\"><img decoding=\"async\" src=\"https:\/\/opentextbc.ca\/accessibilitytoolkit\/wp-content\/uploads\/sites\/333\/2021\/03\/CNX_BMath_Figure_02_01_014_img-03-1.png\" alt=\".\" data-media-type=\"image\/png\" \/><\/span><\/td>\n<\/tr>\n<\/tbody>\n<\/table>\n<\/div>\n<\/div>\n<\/div>\n<div class=\"textbox textbox--exercises\">\n<header class=\"textbox__header\">\n<p class=\"textbox__title\">TRY IT 9.1<\/p>\n<\/header>\n<div class=\"textbox__content\">\n<div id=\"fs-id2626286\" data-type=\"problem\">\n<p id=\"fs-id1632084\">Simplify:<\/p>\n<p id=\"fs-id2626288\"><img loading=\"lazy\" decoding=\"async\" src=\"https:\/\/opentextbc.ca\/introalgebra\/wp-content\/ql-cache\/quicklatex.com-9c67866921d2720c7989513be4ddfb42_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"&#52;&#50;&#92;&#100;&#105;&#118;&#32;&#55;&#92;&#99;&#100;&#111;&#116;&#32;&#51;\" title=\"Rendered by QuickLaTeX.com\" height=\"14\" width=\"70\" style=\"vertical-align: -1px;\" \/><\/p>\n<\/div>\n<div id=\"fs-id2755325\" data-type=\"solution\">\n<details>\n<summary>Show Answer<\/summary>\n<p id=\"fs-id2755327\">18<\/p>\n<\/details>\n<\/div>\n<\/div>\n<\/div>\n<div class=\"textbox textbox--exercises\">\n<header class=\"textbox__header\">\n<p class=\"textbox__title\">TRY IT 9.2<\/p>\n<\/header>\n<div class=\"textbox__content\">\n<div id=\"fs-id2877181\" data-type=\"problem\">\n<p id=\"fs-id1171097539626\">Simplify:<\/p>\n<p id=\"fs-id2877183\"><img loading=\"lazy\" decoding=\"async\" src=\"https:\/\/opentextbc.ca\/introalgebra\/wp-content\/ql-cache\/quicklatex.com-9b17c567a09a954b89c9b00c82fffb7b_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"&#49;&#50;&#92;&#99;&#100;&#111;&#116;&#32;&#51;&#92;&#100;&#105;&#118;&#32;&#52;\" title=\"Rendered by QuickLaTeX.com\" height=\"13\" width=\"69\" style=\"vertical-align: -1px;\" \/><\/p>\n<\/div>\n<div id=\"fs-id2877202\" data-type=\"solution\">\n<details>\n<summary>Show Answer<\/summary>\n<p id=\"fs-id2877204\">9<\/p>\n<\/details>\n<\/div>\n<\/div>\n<\/div>\n<\/div>\n<\/div>\n<\/div>\n<div class=\"textbox textbox--examples\">\n<header class=\"textbox__header\">\n<p class=\"textbox__title\">EXAMPLE 10<\/p>\n<\/header>\n<div class=\"textbox__content\">\n<div id=\"fs-id2877215\" data-type=\"problem\">\n<p id=\"fs-id2308683\">Simplify: <img loading=\"lazy\" decoding=\"async\" src=\"https:\/\/opentextbc.ca\/introalgebra\/wp-content\/ql-cache\/quicklatex.com-aed2528509154128b4468a54a02337b0_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"&#49;&#56;&#92;&#100;&#105;&#118;&#32;&#54;&#43;&#52;&#92;&#108;&#101;&#102;&#116;&#40;&#53;&#45;&#50;&#92;&#114;&#105;&#103;&#104;&#116;&#41;\" title=\"Rendered by QuickLaTeX.com\" height=\"19\" width=\"133\" style=\"vertical-align: -5px;\" \/>.<\/p>\n<\/div>\n<div id=\"fs-id4127406\" data-type=\"solution\">\n<div data-type=\"title\"><\/div>\n<div data-type=\"title\"><strong>Solution<\/strong><\/div>\n<div data-type=\"title\"><\/div>\n<table id=\"eip-id1164754213917\" class=\"unnumbered unstyled\" summary=\"The image shows the expression eighteen divided by six plus four, in parentheses, five minus two. Are there any parentheses? Yes, perform the subtraction inside the parentheses. Five minus two becomes three inside the parentheses. The expression is now eighteen divided by six plus four, in parentheses, three. Are there any exponents? No. Is there any multiplication or division? Yes, there is both multiplication and division. Divide first because multiplication and division are performed left to right. Divide eighteen by six to get three. The expression is now three plus four, in parentheses, three. Now multiply four by the three in parentheses to get twelve. The expression becomes three plus twelve. Add three and twelve to get fifteen.\" data-label=\"\">\n<tbody>\n<tr>\n<td><\/td>\n<td><span id=\"eip-id1164754213936\" data-type=\"media\" data-alt=\".\"><img decoding=\"async\" src=\"https:\/\/opentextbc.ca\/accessibilitytoolkit\/wp-content\/uploads\/sites\/333\/2021\/03\/CNX_BMath_Figure_02_01_015_img-01-1.png\" alt=\".\" data-media-type=\"image\/png\" \/><\/span><\/td>\n<\/tr>\n<tr>\n<td>Parentheses? Yes, subtract first.<\/td>\n<td><span id=\"eip-id1164752719997\" data-type=\"media\" data-alt=\".\"><img decoding=\"async\" src=\"https:\/\/opentextbc.ca\/accessibilitytoolkit\/wp-content\/uploads\/sites\/333\/2021\/03\/CNX_BMath_Figure_02_01_015_img-02-1.png\" alt=\".\" data-media-type=\"image\/png\" \/><\/span><\/td>\n<\/tr>\n<tr>\n<td>Exponents? No.<\/td>\n<td><\/td>\n<\/tr>\n<tr>\n<td>Multiplication or division? Yes.<\/td>\n<td><\/td>\n<\/tr>\n<tr>\n<td>Divide first because we multiply and divide left to right.<\/td>\n<td><span id=\"fs-id1166567548482\" data-type=\"media\" data-alt=\".\"><img decoding=\"async\" src=\"https:\/\/opentextbc.ca\/accessibilitytoolkit\/wp-content\/uploads\/sites\/333\/2021\/03\/CNX_BMath_Figure_02_01_015_img-03-1.png\" alt=\".\" data-media-type=\"image\/png\" \/><\/span><\/td>\n<\/tr>\n<tr>\n<td>Any other multiplication or division? Yes.<\/td>\n<td><\/td>\n<\/tr>\n<tr>\n<td>Multiply.<\/td>\n<td><span id=\"eip-id1164752720057\" data-type=\"media\" data-alt=\".\"><img decoding=\"async\" src=\"https:\/\/opentextbc.ca\/accessibilitytoolkit\/wp-content\/uploads\/sites\/333\/2021\/03\/CNX_BMath_Figure_02_01_015_img-04-1.png\" alt=\".\" data-media-type=\"image\/png\" \/><\/span><\/td>\n<\/tr>\n<tr>\n<td>Any other multiplication or division? No.<\/td>\n<td><\/td>\n<\/tr>\n<tr>\n<td>Any addition or subtraction? Yes.<\/td>\n<td><span id=\"eip-id1164752720083\" data-type=\"media\" data-alt=\".\"><img decoding=\"async\" src=\"https:\/\/opentextbc.ca\/accessibilitytoolkit\/wp-content\/uploads\/sites\/333\/2021\/03\/CNX_BMath_Figure_02_01_015_img-05-1.png\" alt=\".\" data-media-type=\"image\/png\" \/><\/span><\/td>\n<\/tr>\n<\/tbody>\n<\/table>\n<\/div>\n<\/div>\n<\/div>\n<div class=\"textbox textbox--exercises\">\n<header class=\"textbox__header\">\n<p class=\"textbox__title\">TRY IT 10.1<\/p>\n<\/header>\n<div class=\"textbox__content\">\n<div id=\"fs-id2876989\" data-type=\"problem\">\n<p id=\"fs-id2876984\">Simplify:<\/p>\n<p id=\"fs-id2876991\"><img loading=\"lazy\" decoding=\"async\" src=\"https:\/\/opentextbc.ca\/introalgebra\/wp-content\/ql-cache\/quicklatex.com-5b2557a2acec25cbc5ca292a9ae3c8f9_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"&#51;&#48;&#92;&#100;&#105;&#118;&#32;&#53;&#43;&#49;&#48;&#92;&#108;&#101;&#102;&#116;&#40;&#51;&#45;&#50;&#92;&#114;&#105;&#103;&#104;&#116;&#41;\" title=\"Rendered by QuickLaTeX.com\" height=\"19\" width=\"143\" style=\"vertical-align: -5px;\" \/><\/p>\n<\/div>\n<div id=\"fs-id2626124\" data-type=\"solution\">\n<details>\n<summary>Show Answer<\/summary>\n<p id=\"fs-id2626126\">16<\/p>\n<\/details>\n<\/div>\n<\/div>\n<\/div>\n<div class=\"textbox textbox--exercises\">\n<header class=\"textbox__header\">\n<p class=\"textbox__title\">TRY IT 10.2<\/p>\n<\/header>\n<div class=\"textbox__content\">\n<div id=\"fs-id2626133\" data-type=\"problem\">\n<p id=\"fs-id1171103163957\">Simplify:<\/p>\n<p id=\"fs-id2626135\"><img loading=\"lazy\" decoding=\"async\" src=\"https:\/\/opentextbc.ca\/introalgebra\/wp-content\/ql-cache\/quicklatex.com-ee8684e453f3d412681e28c5cc9990c0_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"&#55;&#48;&#92;&#100;&#105;&#118;&#32;&#49;&#48;&#43;&#52;&#92;&#108;&#101;&#102;&#116;&#40;&#54;&#45;&#50;&#92;&#114;&#105;&#103;&#104;&#116;&#41;\" title=\"Rendered by QuickLaTeX.com\" height=\"19\" width=\"143\" style=\"vertical-align: -5px;\" \/><\/p>\n<\/div>\n<div id=\"fs-id2562999\" data-type=\"solution\">\n<details>\n<summary>Show Answer<\/summary>\n<p id=\"fs-id2563001\">23<\/p>\n<\/details>\n<\/div>\n<\/div>\n<\/div>\n<p id=\"fs-id2563008\">When there are multiple grouping symbols, we simplify the innermost parentheses first and work outward.<\/p>\n<div class=\"textbox textbox--examples\">\n<header class=\"textbox__header\">\n<p class=\"textbox__title\">EXAMPLE 11<\/p>\n<\/header>\n<div class=\"textbox__content\">\n<div id=\"fs-id2563015\" data-type=\"problem\">\n<p id=\"fs-id2563017\"><img loading=\"lazy\" decoding=\"async\" src=\"https:\/\/opentextbc.ca\/introalgebra\/wp-content\/ql-cache\/quicklatex.com-0925a6ac1373608a585730b984c7311e_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"&#92;&#116;&#101;&#120;&#116;&#123;&#83;&#105;&#109;&#112;&#108;&#105;&#102;&#121;&#58;&#125;&#92;&#112;&#104;&#97;&#110;&#116;&#111;&#109;&#123;&#92;&#114;&#117;&#108;&#101;&#123;&#48;&#46;&#50;&#101;&#109;&#125;&#123;&#48;&#101;&#120;&#125;&#125;&#53;&#43;&#123;&#50;&#125;&#94;&#123;&#51;&#125;&#43;&#51;&#92;&#108;&#101;&#102;&#116;&#091;&#54;&#45;&#51;&#92;&#108;&#101;&#102;&#116;&#40;&#52;&#45;&#50;&#92;&#114;&#105;&#103;&#104;&#116;&#41;&#92;&#114;&#105;&#103;&#104;&#116;&#093;\" title=\"Rendered by QuickLaTeX.com\" height=\"20\" width=\"257\" style=\"vertical-align: -5px;\" \/>.<\/p>\n<\/div>\n<div id=\"fs-id2308936\" data-type=\"solution\">\n<div data-type=\"title\"><\/div>\n<div data-type=\"title\"><strong>Solution<\/strong><\/div>\n<div data-type=\"title\"><\/div>\n<table id=\"eip-id1164754129434\" class=\"unnumbered unstyled\" summary=\"The image shows the expression five plus two cubed plus three, open bracket, six minus three, open parentheses, four minus two close parentheses, close bracket. Are there any parentheses (or other grouping symbols)? Yes, there are parentheses within brackets. Start with the innermost grouping, the parentheses. Inside the parentheses subtract two from four to get two. The expression becomes five plus two cubed plus three, open bracket, six minus three, in parentheses, two, close bracket. Within the brackets is six minus three, in parentheses, two. Multiply three by two since multiplication comes before subtraction. The expression becomes five plus two cubed plus three, in brackets, six minus six. Finish simplifying inside the brackets by performing the subtraction. Six minus six leaves zero. The expression is now five plus two cubed plus three, in brackets, zero. Are there exponents? Yes, two cubed is eight and the expression becomes five plus eight plus three, in brackets, zero. Is there any multiplication or division? Yes, multiply three by zero to get zero. The expression is now five plus eight plus zero. The remaining operations are both addition. Perform the addition from left to right. five plus eight is thirteen. Thirteen plus zero is thirteen.\" data-label=\"\">\n<tbody>\n<tr>\n<td><\/td>\n<td><span id=\"eip-id1164754129452\" data-type=\"media\" data-alt=\".\"><img decoding=\"async\" src=\"https:\/\/opentextbc.ca\/accessibilitytoolkit\/wp-content\/uploads\/sites\/333\/2021\/03\/CNX_BMath_Figure_02_01_016_img-01-1.png\" alt=\".\" data-media-type=\"image\/png\" \/><\/span><\/td>\n<\/tr>\n<tr>\n<td>Are there any parentheses (or other grouping symbol)? Yes.<\/td>\n<td><\/td>\n<\/tr>\n<tr>\n<td>Focus on the parentheses that are inside the brackets.<\/td>\n<td><span id=\"eip-id1164754129478\" data-type=\"media\" data-alt=\".\"><img decoding=\"async\" src=\"https:\/\/opentextbc.ca\/accessibilitytoolkit\/wp-content\/uploads\/sites\/333\/2021\/03\/CNX_BMath_Figure_02_01_016_img-02-1.png\" alt=\".\" data-media-type=\"image\/png\" \/><\/span><\/td>\n<\/tr>\n<tr>\n<td>Subtract.<\/td>\n<td><span id=\"eip-id1164754129495\" data-type=\"media\" data-alt=\".\"><img decoding=\"async\" src=\"https:\/\/opentextbc.ca\/accessibilitytoolkit\/wp-content\/uploads\/sites\/333\/2021\/03\/CNX_BMath_Figure_02_01_016_img-03-1.png\" alt=\".\" data-media-type=\"image\/png\" \/><\/span><\/td>\n<\/tr>\n<tr>\n<td>Continue inside the brackets and multiply.<\/td>\n<td><span id=\"eip-id1164754129512\" data-type=\"media\" data-alt=\".\"><img decoding=\"async\" src=\"https:\/\/opentextbc.ca\/accessibilitytoolkit\/wp-content\/uploads\/sites\/333\/2021\/03\/CNX_BMath_Figure_02_01_016_img-04-1.png\" alt=\".\" data-media-type=\"image\/png\" \/><\/span><\/td>\n<\/tr>\n<tr>\n<td>Continue inside the brackets and subtract.<\/td>\n<td><span id=\"eip-id1164754129529\" data-type=\"media\" data-alt=\".\"><img decoding=\"async\" src=\"https:\/\/opentextbc.ca\/accessibilitytoolkit\/wp-content\/uploads\/sites\/333\/2021\/03\/CNX_BMath_Figure_02_01_016_img-05-1.png\" alt=\".\" data-media-type=\"image\/png\" \/><\/span><\/td>\n<\/tr>\n<tr>\n<td>The expression inside the brackets requires no further simplification.<\/td>\n<td><\/td>\n<\/tr>\n<tr>\n<td>Are there any exponents? Yes.<\/td>\n<td><\/td>\n<\/tr>\n<tr>\n<td>Simplify exponents.<\/td>\n<td><span id=\"eip-id1164752650667\" data-type=\"media\" data-alt=\".\"><img decoding=\"async\" src=\"https:\/\/opentextbc.ca\/accessibilitytoolkit\/wp-content\/uploads\/sites\/333\/2021\/03\/CNX_BMath_Figure_02_01_016_img-06-1.png\" alt=\".\" data-media-type=\"image\/png\" \/><\/span><\/td>\n<\/tr>\n<tr>\n<td>Is there any multiplication or division? Yes.<\/td>\n<td><\/td>\n<\/tr>\n<tr>\n<td>Multiply.<\/td>\n<td><span id=\"eip-id1164752650693\" data-type=\"media\" data-alt=\".\"><img decoding=\"async\" src=\"https:\/\/opentextbc.ca\/accessibilitytoolkit\/wp-content\/uploads\/sites\/333\/2021\/03\/CNX_BMath_Figure_02_01_016_img-07-1.png\" alt=\".\" data-media-type=\"image\/png\" \/><\/span><\/td>\n<\/tr>\n<tr>\n<td>Is there any addition or subtraction? Yes.<\/td>\n<td><\/td>\n<\/tr>\n<tr>\n<td>Add.<\/td>\n<td><span id=\"eip-id1164752650718\" data-type=\"media\" data-alt=\".\"><img decoding=\"async\" src=\"https:\/\/opentextbc.ca\/accessibilitytoolkit\/wp-content\/uploads\/sites\/333\/2021\/03\/CNX_BMath_Figure_02_01_016_img-08-1.png\" alt=\".\" data-media-type=\"image\/png\" \/><\/span><\/td>\n<\/tr>\n<tr>\n<td>Add.<\/td>\n<td><span id=\"eip-id1164752650735\" data-type=\"media\" data-alt=\".\"><img decoding=\"async\" src=\"https:\/\/opentextbc.ca\/accessibilitytoolkit\/wp-content\/uploads\/sites\/333\/2021\/03\/CNX_BMath_Figure_02_01_016_img-09-1.png\" alt=\".\" data-media-type=\"image\/png\" \/><\/span><\/td>\n<\/tr>\n<tr>\n<td><\/td>\n<td><span id=\"eip-id1164752650751\" data-type=\"media\" data-alt=\".\"><img decoding=\"async\" src=\"https:\/\/opentextbc.ca\/accessibilitytoolkit\/wp-content\/uploads\/sites\/333\/2021\/03\/CNX_BMath_Figure_02_01_016_img-10-1.png\" alt=\".\" data-media-type=\"image\/png\" \/><\/span><\/td>\n<\/tr>\n<\/tbody>\n<\/table>\n<\/div>\n<\/div>\n<\/div>\n<div class=\"textbox textbox--exercises\">\n<header class=\"textbox__header\">\n<p class=\"textbox__title\">TRY IT 11.1<\/p>\n<\/header>\n<div class=\"textbox__content\">\n<div id=\"fs-id2308958\" data-type=\"problem\">\n<p id=\"fs-id2308953\">Simplify:<\/p>\n<p id=\"fs-id2308960\"><img loading=\"lazy\" decoding=\"async\" src=\"https:\/\/opentextbc.ca\/introalgebra\/wp-content\/ql-cache\/quicklatex.com-0c738327e6a736035e5d49618465c2cc_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"&#57;&#43;&#123;&#53;&#125;&#94;&#123;&#51;&#125;&#45;&#92;&#108;&#101;&#102;&#116;&#091;&#52;&#92;&#108;&#101;&#102;&#116;&#40;&#57;&#43;&#51;&#92;&#114;&#105;&#103;&#104;&#116;&#41;&#92;&#114;&#105;&#103;&#104;&#116;&#093;\" title=\"Rendered by QuickLaTeX.com\" height=\"20\" width=\"142\" style=\"vertical-align: -5px;\" \/><\/p>\n<\/div>\n<div id=\"fs-id1956245\" data-type=\"solution\">\n<details>\n<summary>Show Answer<\/summary>\n<p id=\"fs-id1956247\">86<\/p>\n<\/details>\n<\/div>\n<\/div>\n<\/div>\n<div class=\"textbox textbox--exercises\">\n<header class=\"textbox__header\">\n<p class=\"textbox__title\">TRY IT 11.2<\/p>\n<\/header>\n<div class=\"textbox__content\">\n<div id=\"fs-id1956255\" data-type=\"problem\">\n<p id=\"fs-id1171101067875\">Simplify:<\/p>\n<p id=\"fs-id1956257\"><img loading=\"lazy\" decoding=\"async\" src=\"https:\/\/opentextbc.ca\/introalgebra\/wp-content\/ql-cache\/quicklatex.com-840c7c00f2c5c201a98f023f0bb13613_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"&#123;&#55;&#125;&#94;&#123;&#50;&#125;&#45;&#50;&#92;&#108;&#101;&#102;&#116;&#091;&#52;&#92;&#108;&#101;&#102;&#116;&#40;&#53;&#43;&#49;&#92;&#114;&#105;&#103;&#104;&#116;&#41;&#92;&#114;&#105;&#103;&#104;&#116;&#093;\" title=\"Rendered by QuickLaTeX.com\" height=\"20\" width=\"123\" style=\"vertical-align: -5px;\" \/><\/p>\n<\/div>\n<div id=\"fs-id1956294\" data-type=\"solution\">\n<details>\n<summary>Show Answer<\/summary>\n<p id=\"fs-id1956296\">1<\/p>\n<\/details>\n<\/div>\n<\/div>\n<\/div>\n<div id=\"fs-id2308949\" class=\"try\" data-type=\"note\">\n<div id=\"fs-id2308956\" data-type=\"exercise\">\n<div id=\"fs-id1956245\" data-type=\"solution\">\n<div class=\"textbox textbox--examples\">\n<header class=\"textbox__header\">\n<p class=\"textbox__title\">EXAMPLE 12<\/p>\n<\/header>\n<div class=\"textbox__content\">\n<div id=\"fs-id1956307\" data-type=\"problem\">\n<p id=\"fs-id1956309\">Simplify: <img loading=\"lazy\" decoding=\"async\" src=\"https:\/\/opentextbc.ca\/introalgebra\/wp-content\/ql-cache\/quicklatex.com-307f9f50feea41acbfdeb58a5bdf6429_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"&#123;&#50;&#125;&#94;&#123;&#51;&#125;&#43;&#123;&#51;&#125;&#94;&#123;&#52;&#125;&#92;&#100;&#105;&#118;&#32;&#51;&#45;&#123;&#53;&#125;&#94;&#123;&#50;&#125;\" title=\"Rendered by QuickLaTeX.com\" height=\"17\" width=\"123\" style=\"vertical-align: -2px;\" \/>.<\/p>\n<\/div>\n<div id=\"fs-id1956342\" data-type=\"solution\">\n<div data-type=\"title\"><\/div>\n<div data-type=\"title\"><strong>Solution<\/strong><\/div>\n<div data-type=\"title\"><\/div>\n<table id=\"eip-id1164754324162\" class=\"unnumbered unstyled\" summary=\"The image shows the expression two cubed plus three to the fourth divided by three minus five squared. Are there any parentheses? No. Are there any exponents? Yes, several. Simplify each exponent. Two cubed is eight, three to the fourth is eighty-one, and five squared is twenty-five. The expression becomes eight plus eighty-one divided by three minus twenty-five. Is there any multiplication or division? Yes, just division. Divide eighty-one by three to get twenty-seven. The expression is now eight plus twenty-seven minus five. There is both addition and subtraction left. Perform these from left to right. Eight plus twenty-seven is thirty-five. Now the expression is thirty-five minus twenty five which leaves ten.\" data-label=\"\">\n<tbody>\n<tr>\n<td><\/td>\n<td><span id=\"eip-id1164754324181\" data-type=\"media\" data-alt=\".\"><img decoding=\"async\" src=\"https:\/\/opentextbc.ca\/accessibilitytoolkit\/wp-content\/uploads\/sites\/333\/2021\/03\/CNX_BMath_Figure_02_01_017_img-01-1.png\" alt=\".\" data-media-type=\"image\/png\" \/><\/span><\/td>\n<\/tr>\n<tr>\n<td>If an expression has several exponents, they may be simplified in the same step.<\/td>\n<td><\/td>\n<\/tr>\n<tr>\n<td>Simplify exponents.<\/td>\n<td><span id=\"eip-id1164754324206\" data-type=\"media\" data-alt=\".\"><img decoding=\"async\" src=\"https:\/\/opentextbc.ca\/accessibilitytoolkit\/wp-content\/uploads\/sites\/333\/2021\/03\/CNX_BMath_Figure_02_01_017_img-02-1.png\" alt=\".\" data-media-type=\"image\/png\" \/><\/span><\/td>\n<\/tr>\n<tr>\n<td>Divide.<\/td>\n<td><span id=\"eip-id1164754324223\" data-type=\"media\" data-alt=\".\"><img decoding=\"async\" src=\"https:\/\/opentextbc.ca\/accessibilitytoolkit\/wp-content\/uploads\/sites\/333\/2021\/03\/CNX_BMath_Figure_02_01_017_img-03-1.png\" alt=\".\" data-media-type=\"image\/png\" \/><\/span><\/td>\n<\/tr>\n<tr>\n<td>Add.<\/td>\n<td><span id=\"eip-id1164754324240\" data-type=\"media\" data-alt=\".\"><img decoding=\"async\" src=\"https:\/\/opentextbc.ca\/accessibilitytoolkit\/wp-content\/uploads\/sites\/333\/2021\/03\/CNX_BMath_Figure_02_01_017_img-04-1.png\" alt=\".\" data-media-type=\"image\/png\" \/><\/span><\/td>\n<\/tr>\n<tr>\n<td>Subtract.<\/td>\n<td><span id=\"eip-id1164754324256\" data-type=\"media\" data-alt=\".\"><img decoding=\"async\" src=\"https:\/\/opentextbc.ca\/accessibilitytoolkit\/wp-content\/uploads\/sites\/333\/2021\/03\/CNX_BMath_Figure_02_01_017_img-05-1.png\" alt=\".\" data-media-type=\"image\/png\" \/><\/span><\/td>\n<\/tr>\n<tr>\n<td><\/td>\n<td><span id=\"eip-id1164754324272\" data-type=\"media\" data-alt=\".\"><img decoding=\"async\" src=\"https:\/\/opentextbc.ca\/accessibilitytoolkit\/wp-content\/uploads\/sites\/333\/2021\/03\/CNX_BMath_Figure_02_01_017_img-06-1.png\" alt=\".\" data-media-type=\"image\/png\" \/><\/span><\/td>\n<\/tr>\n<\/tbody>\n<\/table>\n<\/div>\n<\/div>\n<\/div>\n<div class=\"textbox textbox--exercises\">\n<header class=\"textbox__header\">\n<p class=\"textbox__title\">TRY IT 12.1<\/p>\n<\/header>\n<div class=\"textbox__content\">\n<div id=\"fs-id1956364\" data-type=\"problem\">\n<p id=\"fs-id1956359\">Simplify:<\/p>\n<p><img loading=\"lazy\" decoding=\"async\" src=\"https:\/\/opentextbc.ca\/introalgebra\/wp-content\/ql-cache\/quicklatex.com-188136b69a995071d61c1c511245fc67_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"&#123;&#51;&#125;&#94;&#123;&#50;&#125;&#43;&#123;&#50;&#125;&#94;&#123;&#52;&#125;&#92;&#100;&#105;&#118;&#32;&#50;&#43;&#123;&#52;&#125;&#94;&#123;&#51;&#125;\" title=\"Rendered by QuickLaTeX.com\" height=\"17\" width=\"123\" style=\"vertical-align: -2px;\" \/><\/p>\n<\/div>\n<div id=\"fs-id1956396\" data-type=\"solution\">\n<details open=\"open\">\n<summary>Show Answer<\/summary>\n<p id=\"fs-id1956399\">81<\/p>\n<\/details>\n<\/div>\n<\/div>\n<\/div>\n<div class=\"textbox textbox--exercises\">\n<header class=\"textbox__header\">\n<p class=\"textbox__title\">TRY IT 12.2<\/p>\n<\/header>\n<div class=\"textbox__content\">\n<div id=\"fs-id1956406\" data-type=\"problem\">\n<p id=\"fs-id1171104064837\">Simplify:<\/p>\n<p id=\"fs-id1956408\"><img loading=\"lazy\" decoding=\"async\" src=\"https:\/\/opentextbc.ca\/introalgebra\/wp-content\/ql-cache\/quicklatex.com-0c3891c6d7e5645a4a109e380d7b9f3a_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"&#123;&#54;&#125;&#94;&#123;&#50;&#125;&#45;&#123;&#53;&#125;&#94;&#123;&#51;&#125;&#92;&#100;&#105;&#118;&#32;&#53;&#43;&#123;&#56;&#125;&#94;&#123;&#50;&#125;\" title=\"Rendered by QuickLaTeX.com\" height=\"17\" width=\"123\" style=\"vertical-align: -2px;\" \/><\/p>\n<\/div>\n<div id=\"fs-id2327292\" data-type=\"solution\">\n<details open=\"open\">\n<summary>Show Answer<\/summary>\n<p id=\"fs-id2327294\">75<\/p>\n<\/details>\n<\/div>\n<\/div>\n<\/div>\n<p>ACCESS ADDITIONAL ONLINE RESOURCES<\/p>\n<\/div>\n<\/div>\n<\/div>\n<div id=\"fs-id2327301\" class=\"media-2\" data-type=\"note\">\n<ul id=\"fs-id2327307\" data-display=\"block\">\n<li><a href=\"http:\/\/openstaxcollege.org\/l\/24orderoperate\">Order of Operations<\/a><\/li>\n<li><a href=\"http:\/\/openstaxcollege.org\/l\/24orderbasic\">Order of Operations \u2013 The Basics<\/a><\/li>\n<li><a href=\"http:\/\/openstaxcollege.org\/l\/24Evalexpress\">Ex: Evaluate an Expression Using the Order of Operations<\/a><\/li>\n<li><a href=\"http:\/\/openstaxcollege.org\/l\/24evalexpress3\">Example 3: Evaluate an Expression Using The Order of Operations<\/a><\/li>\n<\/ul>\n<\/div>\n<h1>Key Concepts<\/h1>\n<table id=\"eip-id1168265095050\" class=\"grid\" summary=\"This table has five rows and four columns. The first row is a header row. Each column is labeled accordingly: the first is labeled \u201cOperation\u201d, the second \u201cNotation\u201d, the third \u201cSay\u201d and the last \u201cThe result is...\u201d. Under the \u201cOperation\u201d column are the words: addition, multiplication, subtraction and division. Under the \u201cNotation\u201d column are algebraic expressions. The first row shows the letter a, the plus symbol, and the letter b. The next row shows four algebraic expressions. The first is the letter a, dot multiplication symbol, and the letter b. The second expression is the letter a in parentheses and the letter b in parentheses. The third expression is the letter a in parentheses and the letter b. The fourth expression is the letter a and the letter b in parentheses. The next row shows the letter a, the minus symbol, and the letter b. The last row shows four algebraic expressions. The first is the letter a, division symbol, and the letter b. The second expression is the letter a, the backslash symbol and the letter b. The third expression is the letter a above the fraction bar and the letter b below the fraction bar. The fourth expression is the letter b outside the division bracket and the letter a inside the division bracket.\" data-label=\"\">\n<thead>\n<tr valign=\"top\">\n<th data-align=\"left\"><strong data-effect=\"bold\">Operation<\/strong><\/th>\n<th data-align=\"left\"><strong data-effect=\"bold\">Notation<\/strong><\/th>\n<th data-align=\"left\"><strong data-effect=\"bold\">Say:<\/strong><\/th>\n<th data-align=\"left\"><strong data-effect=\"bold\">The result is\u2026<\/strong><\/th>\n<\/tr>\n<\/thead>\n<tbody>\n<tr valign=\"top\">\n<td data-align=\"left\">Addition<\/td>\n<td data-align=\"left\"><img loading=\"lazy\" decoding=\"async\" src=\"https:\/\/opentextbc.ca\/introalgebra\/wp-content\/ql-cache\/quicklatex.com-38830949a60ce6786a6fdf6309482002_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"&#97;&#43;&#98;\" title=\"Rendered by QuickLaTeX.com\" height=\"15\" width=\"39\" style=\"vertical-align: -2px;\" \/><\/td>\n<td data-align=\"left\"><img loading=\"lazy\" decoding=\"async\" src=\"https:\/\/opentextbc.ca\/introalgebra\/wp-content\/ql-cache\/quicklatex.com-04ba1b81da8ae280d26d1991b56eec6d_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"&#97;&#92;&#112;&#104;&#97;&#110;&#116;&#111;&#109;&#123;&#92;&#114;&#117;&#108;&#101;&#123;&#48;&#46;&#50;&#101;&#109;&#125;&#123;&#48;&#101;&#120;&#125;&#125;&#92;&#116;&#101;&#120;&#116;&#123;&#112;&#108;&#117;&#115;&#125;&#92;&#112;&#104;&#97;&#110;&#116;&#111;&#109;&#123;&#92;&#114;&#117;&#108;&#101;&#123;&#48;&#46;&#50;&#101;&#109;&#125;&#123;&#48;&#101;&#120;&#125;&#125;&#98;\" title=\"Rendered by QuickLaTeX.com\" height=\"16\" width=\"56\" style=\"vertical-align: -3px;\" \/><\/td>\n<td data-align=\"left\">the sum of <img loading=\"lazy\" decoding=\"async\" src=\"https:\/\/opentextbc.ca\/introalgebra\/wp-content\/ql-cache\/quicklatex.com-5c53d6ebabdbcfa4e107550ea60b1b19_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"&#97;\" title=\"Rendered by QuickLaTeX.com\" height=\"8\" width=\"9\" style=\"vertical-align: 0px;\" \/> and <img loading=\"lazy\" decoding=\"async\" src=\"https:\/\/opentextbc.ca\/introalgebra\/wp-content\/ql-cache\/quicklatex.com-f56d50c26583f9a035ff6b4e3c0ca5c0_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"&#98;\" title=\"Rendered by QuickLaTeX.com\" height=\"13\" width=\"8\" style=\"vertical-align: 0px;\" \/><\/td>\n<\/tr>\n<tr valign=\"top\">\n<td data-align=\"left\">Multiplication<\/td>\n<td data-align=\"left\"><img loading=\"lazy\" decoding=\"async\" src=\"https:\/\/opentextbc.ca\/introalgebra\/wp-content\/ql-cache\/quicklatex.com-7c63a9888ac8ae036ae37309dee0451c_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"&#97;&#92;&#99;&#100;&#111;&#116;&#32;&#98;&#44;&#92;&#108;&#101;&#102;&#116;&#40;&#97;&#92;&#114;&#105;&#103;&#104;&#116;&#41;&#92;&#108;&#101;&#102;&#116;&#40;&#98;&#92;&#114;&#105;&#103;&#104;&#116;&#41;&#44;&#92;&#108;&#101;&#102;&#116;&#40;&#97;&#92;&#114;&#105;&#103;&#104;&#116;&#41;&#98;&#44;&#97;&#92;&#108;&#101;&#102;&#116;&#40;&#98;&#92;&#114;&#105;&#103;&#104;&#116;&#41;\" title=\"Rendered by QuickLaTeX.com\" height=\"19\" width=\"171\" style=\"vertical-align: -5px;\" \/><\/td>\n<td data-align=\"left\"><img loading=\"lazy\" decoding=\"async\" src=\"https:\/\/opentextbc.ca\/introalgebra\/wp-content\/ql-cache\/quicklatex.com-6e4e96a7e0e7b4b2dc622423b51fc66b_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"&#97;&#92;&#112;&#104;&#97;&#110;&#116;&#111;&#109;&#123;&#92;&#114;&#117;&#108;&#101;&#123;&#48;&#46;&#50;&#101;&#109;&#125;&#123;&#48;&#101;&#120;&#125;&#125;&#92;&#116;&#101;&#120;&#116;&#123;&#116;&#105;&#109;&#101;&#115;&#125;&#92;&#112;&#104;&#97;&#110;&#116;&#111;&#109;&#123;&#92;&#114;&#117;&#108;&#101;&#123;&#48;&#46;&#50;&#101;&#109;&#125;&#123;&#48;&#101;&#120;&#125;&#125;&#98;\" title=\"Rendered by QuickLaTeX.com\" height=\"13\" width=\"66\" style=\"vertical-align: 0px;\" \/><\/td>\n<td data-align=\"left\">The product of <img loading=\"lazy\" decoding=\"async\" src=\"https:\/\/opentextbc.ca\/introalgebra\/wp-content\/ql-cache\/quicklatex.com-5c53d6ebabdbcfa4e107550ea60b1b19_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"&#97;\" title=\"Rendered by QuickLaTeX.com\" height=\"8\" width=\"9\" style=\"vertical-align: 0px;\" \/> and <img loading=\"lazy\" decoding=\"async\" src=\"https:\/\/opentextbc.ca\/introalgebra\/wp-content\/ql-cache\/quicklatex.com-f56d50c26583f9a035ff6b4e3c0ca5c0_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"&#98;\" title=\"Rendered by QuickLaTeX.com\" height=\"13\" width=\"8\" style=\"vertical-align: 0px;\" \/><\/td>\n<\/tr>\n<tr valign=\"top\">\n<td data-align=\"left\">Subtraction<\/td>\n<td data-align=\"left\"><img loading=\"lazy\" decoding=\"async\" src=\"https:\/\/opentextbc.ca\/introalgebra\/wp-content\/ql-cache\/quicklatex.com-b644d18119c5701b308f883bd50656d9_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"&#97;&#45;&#98;\" title=\"Rendered by QuickLaTeX.com\" height=\"13\" width=\"39\" style=\"vertical-align: 0px;\" \/><\/td>\n<td data-align=\"left\"><img loading=\"lazy\" decoding=\"async\" src=\"https:\/\/opentextbc.ca\/introalgebra\/wp-content\/ql-cache\/quicklatex.com-d626cdf4753df75818707f16d7b6dc4e_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"&#97;&#92;&#112;&#104;&#97;&#110;&#116;&#111;&#109;&#123;&#92;&#114;&#117;&#108;&#101;&#123;&#48;&#46;&#50;&#101;&#109;&#125;&#123;&#48;&#101;&#120;&#125;&#125;&#92;&#116;&#101;&#120;&#116;&#123;&#109;&#105;&#110;&#117;&#115;&#125;&#92;&#112;&#104;&#97;&#110;&#116;&#111;&#109;&#123;&#92;&#114;&#117;&#108;&#101;&#123;&#48;&#46;&#50;&#101;&#109;&#125;&#123;&#48;&#101;&#120;&#125;&#125;&#98;\" title=\"Rendered by QuickLaTeX.com\" height=\"13\" width=\"70\" style=\"vertical-align: 0px;\" \/><\/td>\n<td data-align=\"left\">the difference of <img loading=\"lazy\" decoding=\"async\" src=\"https:\/\/opentextbc.ca\/introalgebra\/wp-content\/ql-cache\/quicklatex.com-5c53d6ebabdbcfa4e107550ea60b1b19_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"&#97;\" title=\"Rendered by QuickLaTeX.com\" height=\"8\" width=\"9\" style=\"vertical-align: 0px;\" \/> and <img loading=\"lazy\" decoding=\"async\" src=\"https:\/\/opentextbc.ca\/introalgebra\/wp-content\/ql-cache\/quicklatex.com-f56d50c26583f9a035ff6b4e3c0ca5c0_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"&#98;\" title=\"Rendered by QuickLaTeX.com\" height=\"13\" width=\"8\" style=\"vertical-align: 0px;\" \/><\/td>\n<\/tr>\n<tr valign=\"top\">\n<td data-align=\"left\">Division<\/td>\n<td data-align=\"left\"><img loading=\"lazy\" decoding=\"async\" src=\"https:\/\/opentextbc.ca\/introalgebra\/wp-content\/ql-cache\/quicklatex.com-1dc71412a2af9fb0a0b48f86c64005ed_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"&#97;&#92;&#100;&#105;&#118;&#32;&#98;&#44;&#97;&#47;&#98;&#44;&#92;&#112;&#104;&#97;&#110;&#116;&#111;&#109;&#123;&#92;&#114;&#117;&#108;&#101;&#123;&#48;&#46;&#50;&#101;&#109;&#125;&#123;&#48;&#101;&#120;&#125;&#125;&#92;&#102;&#114;&#97;&#99;&#123;&#97;&#125;&#123;&#98;&#125;&#44;&#98;&#92;&#111;&#118;&#101;&#114;&#108;&#105;&#110;&#101;&#123;&#41;&#97;&#125;\" title=\"Rendered by QuickLaTeX.com\" height=\"22\" width=\"128\" style=\"vertical-align: -6px;\" \/><\/td>\n<td data-align=\"left\"><img loading=\"lazy\" decoding=\"async\" src=\"https:\/\/opentextbc.ca\/introalgebra\/wp-content\/ql-cache\/quicklatex.com-5c53d6ebabdbcfa4e107550ea60b1b19_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"&#97;\" title=\"Rendered by QuickLaTeX.com\" height=\"8\" width=\"9\" style=\"vertical-align: 0px;\" \/> divided by <img loading=\"lazy\" decoding=\"async\" src=\"https:\/\/opentextbc.ca\/introalgebra\/wp-content\/ql-cache\/quicklatex.com-f56d50c26583f9a035ff6b4e3c0ca5c0_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"&#98;\" title=\"Rendered by QuickLaTeX.com\" height=\"13\" width=\"8\" style=\"vertical-align: 0px;\" \/><\/td>\n<td data-align=\"left\">The quotient of <img loading=\"lazy\" decoding=\"async\" src=\"https:\/\/opentextbc.ca\/introalgebra\/wp-content\/ql-cache\/quicklatex.com-5c53d6ebabdbcfa4e107550ea60b1b19_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"&#97;\" title=\"Rendered by QuickLaTeX.com\" height=\"8\" width=\"9\" style=\"vertical-align: 0px;\" \/> and <img loading=\"lazy\" decoding=\"async\" src=\"https:\/\/opentextbc.ca\/introalgebra\/wp-content\/ql-cache\/quicklatex.com-f56d50c26583f9a035ff6b4e3c0ca5c0_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"&#98;\" title=\"Rendered by QuickLaTeX.com\" height=\"13\" width=\"8\" style=\"vertical-align: 0px;\" \/><\/td>\n<\/tr>\n<\/tbody>\n<\/table>\n<ul id=\"eip-740\">\n<li><strong>Equality Symbol<\/strong>\n<ul id=\"eip-id1168262501679\">\n<li><img loading=\"lazy\" decoding=\"async\" src=\"https:\/\/opentextbc.ca\/introalgebra\/wp-content\/ql-cache\/quicklatex.com-e69295ccf8d8ca292abcc97f861e345f_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"&#97;&#61;&#98;\" title=\"Rendered by QuickLaTeX.com\" height=\"13\" width=\"41\" style=\"vertical-align: 0px;\" \/> is read as <img loading=\"lazy\" decoding=\"async\" src=\"https:\/\/opentextbc.ca\/introalgebra\/wp-content\/ql-cache\/quicklatex.com-5c53d6ebabdbcfa4e107550ea60b1b19_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"&#97;\" title=\"Rendered by QuickLaTeX.com\" height=\"8\" width=\"9\" style=\"vertical-align: 0px;\" \/> is equal to <img loading=\"lazy\" decoding=\"async\" src=\"https:\/\/opentextbc.ca\/introalgebra\/wp-content\/ql-cache\/quicklatex.com-f56d50c26583f9a035ff6b4e3c0ca5c0_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"&#98;\" title=\"Rendered by QuickLaTeX.com\" height=\"13\" width=\"8\" style=\"vertical-align: 0px;\" \/><\/li>\n<li>The symbol <img loading=\"lazy\" decoding=\"async\" src=\"https:\/\/opentextbc.ca\/introalgebra\/wp-content\/ql-cache\/quicklatex.com-b8690b7efd237bfe32a6e92e3b699b96_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"&#61;\" title=\"Rendered by QuickLaTeX.com\" height=\"4\" width=\"13\" style=\"vertical-align: 2px;\" \/> is called the equal sign.<\/li>\n<\/ul>\n<\/li>\n<li><strong>Inequality<\/strong>\n<ul id=\"eip-id1168263909662\">\n<li><img loading=\"lazy\" decoding=\"async\" src=\"https:\/\/opentextbc.ca\/introalgebra\/wp-content\/ql-cache\/quicklatex.com-5c53d6ebabdbcfa4e107550ea60b1b19_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"&#97;\" title=\"Rendered by QuickLaTeX.com\" height=\"8\" width=\"9\" style=\"vertical-align: 0px;\" \/> &lt; <img loading=\"lazy\" decoding=\"async\" src=\"https:\/\/opentextbc.ca\/introalgebra\/wp-content\/ql-cache\/quicklatex.com-f56d50c26583f9a035ff6b4e3c0ca5c0_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"&#98;\" title=\"Rendered by QuickLaTeX.com\" height=\"13\" width=\"8\" style=\"vertical-align: 0px;\" \/> is read <img loading=\"lazy\" decoding=\"async\" src=\"https:\/\/opentextbc.ca\/introalgebra\/wp-content\/ql-cache\/quicklatex.com-5c53d6ebabdbcfa4e107550ea60b1b19_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"&#97;\" title=\"Rendered by QuickLaTeX.com\" height=\"8\" width=\"9\" style=\"vertical-align: 0px;\" \/> is less than <img loading=\"lazy\" decoding=\"async\" src=\"https:\/\/opentextbc.ca\/introalgebra\/wp-content\/ql-cache\/quicklatex.com-f56d50c26583f9a035ff6b4e3c0ca5c0_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"&#98;\" title=\"Rendered by QuickLaTeX.com\" height=\"13\" width=\"8\" style=\"vertical-align: 0px;\" \/><\/li>\n<li><img loading=\"lazy\" decoding=\"async\" src=\"https:\/\/opentextbc.ca\/introalgebra\/wp-content\/ql-cache\/quicklatex.com-5c53d6ebabdbcfa4e107550ea60b1b19_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"&#97;\" title=\"Rendered by QuickLaTeX.com\" height=\"8\" width=\"9\" style=\"vertical-align: 0px;\" \/> is to the left of <img loading=\"lazy\" decoding=\"async\" src=\"https:\/\/opentextbc.ca\/introalgebra\/wp-content\/ql-cache\/quicklatex.com-f56d50c26583f9a035ff6b4e3c0ca5c0_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"&#98;\" title=\"Rendered by QuickLaTeX.com\" height=\"13\" width=\"8\" style=\"vertical-align: 0px;\" \/> on the number line<br \/>\n<span id=\"eip-id1168264918525\" data-type=\"media\" data-alt=\"..\"><img decoding=\"async\" src=\"https:\/\/opentextbc.ca\/accessibilitytoolkit\/wp-content\/uploads\/sites\/333\/2021\/03\/CNX_BMath_Figure_02_01_018_img-1.jpg\" alt=\"..\" data-media-type=\"image\/jpg\" \/><\/span><\/li>\n<li><img loading=\"lazy\" decoding=\"async\" src=\"https:\/\/opentextbc.ca\/introalgebra\/wp-content\/ql-cache\/quicklatex.com-5c53d6ebabdbcfa4e107550ea60b1b19_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"&#97;\" title=\"Rendered by QuickLaTeX.com\" height=\"8\" width=\"9\" style=\"vertical-align: 0px;\" \/> &gt; <img loading=\"lazy\" decoding=\"async\" src=\"https:\/\/opentextbc.ca\/introalgebra\/wp-content\/ql-cache\/quicklatex.com-f56d50c26583f9a035ff6b4e3c0ca5c0_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"&#98;\" title=\"Rendered by QuickLaTeX.com\" height=\"13\" width=\"8\" style=\"vertical-align: 0px;\" \/> is read <img loading=\"lazy\" decoding=\"async\" src=\"https:\/\/opentextbc.ca\/introalgebra\/wp-content\/ql-cache\/quicklatex.com-5c53d6ebabdbcfa4e107550ea60b1b19_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"&#97;\" title=\"Rendered by QuickLaTeX.com\" height=\"8\" width=\"9\" style=\"vertical-align: 0px;\" \/> is greater than <img loading=\"lazy\" decoding=\"async\" src=\"https:\/\/opentextbc.ca\/introalgebra\/wp-content\/ql-cache\/quicklatex.com-f56d50c26583f9a035ff6b4e3c0ca5c0_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"&#98;\" title=\"Rendered by QuickLaTeX.com\" height=\"13\" width=\"8\" style=\"vertical-align: 0px;\" \/><\/li>\n<li><img loading=\"lazy\" decoding=\"async\" src=\"https:\/\/opentextbc.ca\/introalgebra\/wp-content\/ql-cache\/quicklatex.com-5c53d6ebabdbcfa4e107550ea60b1b19_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"&#97;\" title=\"Rendered by QuickLaTeX.com\" height=\"8\" width=\"9\" style=\"vertical-align: 0px;\" \/> is to the right of <img loading=\"lazy\" decoding=\"async\" src=\"https:\/\/opentextbc.ca\/introalgebra\/wp-content\/ql-cache\/quicklatex.com-f56d50c26583f9a035ff6b4e3c0ca5c0_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"&#98;\" title=\"Rendered by QuickLaTeX.com\" height=\"13\" width=\"8\" style=\"vertical-align: 0px;\" \/> on the number line<br \/>\n<span id=\"eip-id1168264785219\" data-type=\"media\" data-alt=\"..\"><img decoding=\"async\" src=\"https:\/\/opentextbc.ca\/accessibilitytoolkit\/wp-content\/uploads\/sites\/333\/2021\/03\/CNX_BMath_Figure_02_01_019_img-1.jpg\" alt=\"..\" data-media-type=\"image\/jpg\" \/><\/span><\/li>\n<\/ul>\n<\/li>\n<\/ul>\n<table id=\"eip-455\" summary=\"This table has seven rows and two columns. The first row is a header row and it labels each column. The first column is labeled \u201cAlgebraic Notation\u201d, the second \u201cSay\u201d. Under the \u201cAlgebraic Notation\u201d column are the algebraic expressions: a equals b; a is not equal to b; a is less than b; a is greater than b; a is less than or equal to b; a is greater than or equal to b. Under the \u201cSay\u201d column are the phrases: \u201ca is equal to b\u201d, \u201ca is not equal to b\u201d, \u201ca is less than b\u201d, \u201ca is greater than b\u201d, \u201ca is less than or equal to b\u201d, and \u201ca is greater than or equal to b\u201d.\">\n<thead>\n<tr valign=\"top\">\n<th data-align=\"center\">Algebraic Notation<\/th>\n<th data-align=\"center\">Say<\/th>\n<\/tr>\n<\/thead>\n<tbody>\n<tr valign=\"top\">\n<td data-align=\"left\"><img loading=\"lazy\" decoding=\"async\" src=\"https:\/\/opentextbc.ca\/introalgebra\/wp-content\/ql-cache\/quicklatex.com-e69295ccf8d8ca292abcc97f861e345f_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"&#97;&#61;&#98;\" title=\"Rendered by QuickLaTeX.com\" height=\"13\" width=\"41\" style=\"vertical-align: 0px;\" \/><\/td>\n<td data-align=\"left\"><img loading=\"lazy\" decoding=\"async\" src=\"https:\/\/opentextbc.ca\/introalgebra\/wp-content\/ql-cache\/quicklatex.com-5c53d6ebabdbcfa4e107550ea60b1b19_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"&#97;\" title=\"Rendered by QuickLaTeX.com\" height=\"8\" width=\"9\" style=\"vertical-align: 0px;\" \/> is equal to <img loading=\"lazy\" decoding=\"async\" src=\"https:\/\/opentextbc.ca\/introalgebra\/wp-content\/ql-cache\/quicklatex.com-f56d50c26583f9a035ff6b4e3c0ca5c0_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"&#98;\" title=\"Rendered by QuickLaTeX.com\" height=\"13\" width=\"8\" style=\"vertical-align: 0px;\" \/><\/td>\n<\/tr>\n<tr valign=\"top\">\n<td data-align=\"left\"><img loading=\"lazy\" decoding=\"async\" src=\"https:\/\/opentextbc.ca\/introalgebra\/wp-content\/ql-cache\/quicklatex.com-8740efbef2c653ea7d353859ecc91afd_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"&#97;&#92;&#110;&#101;&#32;&#98;\" title=\"Rendered by QuickLaTeX.com\" height=\"17\" width=\"41\" style=\"vertical-align: -4px;\" \/><\/td>\n<td data-align=\"left\"><img loading=\"lazy\" decoding=\"async\" src=\"https:\/\/opentextbc.ca\/introalgebra\/wp-content\/ql-cache\/quicklatex.com-5c53d6ebabdbcfa4e107550ea60b1b19_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"&#97;\" title=\"Rendered by QuickLaTeX.com\" height=\"8\" width=\"9\" style=\"vertical-align: 0px;\" \/> is not equal to <img loading=\"lazy\" decoding=\"async\" src=\"https:\/\/opentextbc.ca\/introalgebra\/wp-content\/ql-cache\/quicklatex.com-f56d50c26583f9a035ff6b4e3c0ca5c0_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"&#98;\" title=\"Rendered by QuickLaTeX.com\" height=\"13\" width=\"8\" style=\"vertical-align: 0px;\" \/><\/td>\n<\/tr>\n<tr valign=\"top\">\n<td data-align=\"left\"><img loading=\"lazy\" decoding=\"async\" src=\"https:\/\/opentextbc.ca\/introalgebra\/wp-content\/ql-cache\/quicklatex.com-5c53d6ebabdbcfa4e107550ea60b1b19_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"&#97;\" title=\"Rendered by QuickLaTeX.com\" height=\"8\" width=\"9\" style=\"vertical-align: 0px;\" \/> &lt; <img loading=\"lazy\" decoding=\"async\" src=\"https:\/\/opentextbc.ca\/introalgebra\/wp-content\/ql-cache\/quicklatex.com-f56d50c26583f9a035ff6b4e3c0ca5c0_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"&#98;\" title=\"Rendered by QuickLaTeX.com\" height=\"13\" width=\"8\" style=\"vertical-align: 0px;\" \/><\/td>\n<td data-align=\"left\"><img loading=\"lazy\" decoding=\"async\" src=\"https:\/\/opentextbc.ca\/introalgebra\/wp-content\/ql-cache\/quicklatex.com-5c53d6ebabdbcfa4e107550ea60b1b19_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"&#97;\" title=\"Rendered by QuickLaTeX.com\" height=\"8\" width=\"9\" style=\"vertical-align: 0px;\" \/> is less than <img loading=\"lazy\" decoding=\"async\" src=\"https:\/\/opentextbc.ca\/introalgebra\/wp-content\/ql-cache\/quicklatex.com-f56d50c26583f9a035ff6b4e3c0ca5c0_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"&#98;\" title=\"Rendered by QuickLaTeX.com\" height=\"13\" width=\"8\" style=\"vertical-align: 0px;\" \/><\/td>\n<\/tr>\n<tr valign=\"top\">\n<td data-align=\"left\"><img loading=\"lazy\" decoding=\"async\" src=\"https:\/\/opentextbc.ca\/introalgebra\/wp-content\/ql-cache\/quicklatex.com-5c53d6ebabdbcfa4e107550ea60b1b19_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"&#97;\" title=\"Rendered by QuickLaTeX.com\" height=\"8\" width=\"9\" style=\"vertical-align: 0px;\" \/> &gt; <img loading=\"lazy\" decoding=\"async\" src=\"https:\/\/opentextbc.ca\/introalgebra\/wp-content\/ql-cache\/quicklatex.com-f56d50c26583f9a035ff6b4e3c0ca5c0_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"&#98;\" title=\"Rendered by QuickLaTeX.com\" height=\"13\" width=\"8\" style=\"vertical-align: 0px;\" \/><\/td>\n<td data-align=\"left\"><img loading=\"lazy\" decoding=\"async\" src=\"https:\/\/opentextbc.ca\/introalgebra\/wp-content\/ql-cache\/quicklatex.com-5c53d6ebabdbcfa4e107550ea60b1b19_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"&#97;\" title=\"Rendered by QuickLaTeX.com\" height=\"8\" width=\"9\" style=\"vertical-align: 0px;\" \/> is greater than <img loading=\"lazy\" decoding=\"async\" src=\"https:\/\/opentextbc.ca\/introalgebra\/wp-content\/ql-cache\/quicklatex.com-f56d50c26583f9a035ff6b4e3c0ca5c0_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"&#98;\" title=\"Rendered by QuickLaTeX.com\" height=\"13\" width=\"8\" style=\"vertical-align: 0px;\" \/><\/td>\n<\/tr>\n<tr valign=\"top\">\n<td data-align=\"left\"><img loading=\"lazy\" decoding=\"async\" src=\"https:\/\/opentextbc.ca\/introalgebra\/wp-content\/ql-cache\/quicklatex.com-22bb7f496e0a4516393886afb53ffa7c_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"&#97;&#92;&#108;&#101;&#32;&#98;\" title=\"Rendered by QuickLaTeX.com\" height=\"16\" width=\"41\" style=\"vertical-align: -3px;\" \/><\/td>\n<td data-align=\"left\"><img loading=\"lazy\" decoding=\"async\" src=\"https:\/\/opentextbc.ca\/introalgebra\/wp-content\/ql-cache\/quicklatex.com-5c53d6ebabdbcfa4e107550ea60b1b19_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"&#97;\" title=\"Rendered by QuickLaTeX.com\" height=\"8\" width=\"9\" style=\"vertical-align: 0px;\" \/> is less than or equal to <img loading=\"lazy\" decoding=\"async\" src=\"https:\/\/opentextbc.ca\/introalgebra\/wp-content\/ql-cache\/quicklatex.com-f56d50c26583f9a035ff6b4e3c0ca5c0_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"&#98;\" title=\"Rendered by QuickLaTeX.com\" height=\"13\" width=\"8\" style=\"vertical-align: 0px;\" \/><\/td>\n<\/tr>\n<tr valign=\"top\">\n<td data-align=\"left\"><img loading=\"lazy\" decoding=\"async\" src=\"https:\/\/opentextbc.ca\/introalgebra\/wp-content\/ql-cache\/quicklatex.com-4925aae9d8237338b0824392ba2d182a_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"&#97;&#92;&#103;&#101;&#32;&#98;\" title=\"Rendered by QuickLaTeX.com\" height=\"16\" width=\"41\" style=\"vertical-align: -3px;\" \/><\/td>\n<td data-align=\"left\"><img loading=\"lazy\" decoding=\"async\" src=\"https:\/\/opentextbc.ca\/introalgebra\/wp-content\/ql-cache\/quicklatex.com-5c53d6ebabdbcfa4e107550ea60b1b19_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"&#97;\" title=\"Rendered by QuickLaTeX.com\" height=\"8\" width=\"9\" style=\"vertical-align: 0px;\" \/> is greater than or equal to <img loading=\"lazy\" decoding=\"async\" src=\"https:\/\/opentextbc.ca\/introalgebra\/wp-content\/ql-cache\/quicklatex.com-f56d50c26583f9a035ff6b4e3c0ca5c0_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"&#98;\" title=\"Rendered by QuickLaTeX.com\" height=\"13\" width=\"8\" style=\"vertical-align: 0px;\" \/><\/td>\n<\/tr>\n<\/tbody>\n<\/table>\n<ul id=\"eip-910\">\n<li><strong>Exponential Notation<\/strong>\n<ul id=\"eip-id1168266330675\">\n<li>For any expression <img loading=\"lazy\" decoding=\"async\" src=\"https:\/\/opentextbc.ca\/introalgebra\/wp-content\/ql-cache\/quicklatex.com-ef78644f25c125ead81d3c69ef32dee0_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"&#123;&#97;&#125;&#94;&#123;&#110;&#125;\" title=\"Rendered by QuickLaTeX.com\" height=\"12\" width=\"17\" style=\"vertical-align: 0px;\" \/> is a factor multiplied by itself <img loading=\"lazy\" decoding=\"async\" src=\"https:\/\/opentextbc.ca\/introalgebra\/wp-content\/ql-cache\/quicklatex.com-b170995d512c659d8668b4e42e1fef6b_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"&#110;\" title=\"Rendered by QuickLaTeX.com\" height=\"8\" width=\"11\" style=\"vertical-align: 0px;\" \/> times, if <img loading=\"lazy\" decoding=\"async\" src=\"https:\/\/opentextbc.ca\/introalgebra\/wp-content\/ql-cache\/quicklatex.com-b170995d512c659d8668b4e42e1fef6b_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"&#110;\" title=\"Rendered by QuickLaTeX.com\" height=\"8\" width=\"11\" style=\"vertical-align: 0px;\" \/> is a positive integer.<\/li>\n<li><img loading=\"lazy\" decoding=\"async\" src=\"https:\/\/opentextbc.ca\/introalgebra\/wp-content\/ql-cache\/quicklatex.com-ef78644f25c125ead81d3c69ef32dee0_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"&#123;&#97;&#125;&#94;&#123;&#110;&#125;\" title=\"Rendered by QuickLaTeX.com\" height=\"12\" width=\"17\" style=\"vertical-align: 0px;\" \/> means multiply <img loading=\"lazy\" decoding=\"async\" src=\"https:\/\/opentextbc.ca\/introalgebra\/wp-content\/ql-cache\/quicklatex.com-b170995d512c659d8668b4e42e1fef6b_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"&#110;\" title=\"Rendered by QuickLaTeX.com\" height=\"8\" width=\"11\" style=\"vertical-align: 0px;\" \/> factors of <img loading=\"lazy\" decoding=\"async\" src=\"https:\/\/opentextbc.ca\/introalgebra\/wp-content\/ql-cache\/quicklatex.com-5c53d6ebabdbcfa4e107550ea60b1b19_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"&#97;\" title=\"Rendered by QuickLaTeX.com\" height=\"8\" width=\"9\" style=\"vertical-align: 0px;\" \/><br \/>\n<span id=\"eip-id1168266330736\" data-type=\"media\" data-alt=\"..\"><img decoding=\"async\" class=\"aligncenter\" src=\"https:\/\/opentextbc.ca\/accessibilitytoolkit\/wp-content\/uploads\/sites\/333\/2021\/03\/CNX_BMath_Figure_02_01_020_img-1.jpg\" alt=\"..\" data-media-type=\"image\/jpg\" \/><\/span><\/li>\n<li>The expression of <img loading=\"lazy\" decoding=\"async\" src=\"https:\/\/opentextbc.ca\/introalgebra\/wp-content\/ql-cache\/quicklatex.com-ef78644f25c125ead81d3c69ef32dee0_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"&#123;&#97;&#125;&#94;&#123;&#110;&#125;\" title=\"Rendered by QuickLaTeX.com\" height=\"12\" width=\"17\" style=\"vertical-align: 0px;\" \/> is read <img loading=\"lazy\" decoding=\"async\" src=\"https:\/\/opentextbc.ca\/introalgebra\/wp-content\/ql-cache\/quicklatex.com-5c53d6ebabdbcfa4e107550ea60b1b19_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"&#97;\" title=\"Rendered by QuickLaTeX.com\" height=\"8\" width=\"9\" style=\"vertical-align: 0px;\" \/> to the <img loading=\"lazy\" decoding=\"async\" src=\"https:\/\/opentextbc.ca\/introalgebra\/wp-content\/ql-cache\/quicklatex.com-11349328cd25470084f3e0e831b97cc4_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"&#110;&#92;&#116;&#101;&#120;&#116;&#123;&#116;&#104;&#125;\" title=\"Rendered by QuickLaTeX.com\" height=\"13\" width=\"28\" style=\"vertical-align: 0px;\" \/> power.<\/li>\n<\/ul>\n<\/li>\n<\/ul>\n<p id=\"eip-908\"><strong>Order of Operations<\/strong> When simplifying mathematical expressions perform the operations in the following order:<\/p>\n<ul id=\"eip-id1168264820124\" data-bullet-style=\"bullet\">\n<li>Parentheses and other Grouping Symbols: Simplify all expressions inside the parentheses or other grouping symbols, working on the innermost parentheses first.<\/li>\n<li>Exponents: Simplify all expressions with exponents.<\/li>\n<li>Multiplication and Division: Perform all multiplication and division in order from left to right. These operations have equal priority.<\/li>\n<li>Addition and Subtraction: Perform all addition and subtraction in order from left to right. These operations have equal priority.<\/li>\n<\/ul>\n<h1>Glossary<\/h1>\n<div class=\"textbox shaded\">\n<dl id=\"fs-id2645686\">\n<dt>expressions<\/dt>\n<dd id=\"fs-id2645692\">An expression is a number, a variable, or a combination of numbers and variables and operation symbols.<\/dd>\n<\/dl>\n<dl id=\"fs-id2645696\">\n<dt>equation<\/dt>\n<dd id=\"fs-id2645701\">An equation is made up of two expressions connected by an equal sign.<\/dd>\n<\/dl>\n<\/div>\n<h1>Practice Makes Perfect<\/h1>\n<h2>Use Variables and Algebraic Symbols<\/h2>\n<p>In the following exercises, translate from algebraic notation to words.<\/p>\n<table style=\"border-collapse: collapse; width: 100%; height: 135px;\">\n<tbody>\n<tr style=\"height: 15px;\">\n<td style=\"width: 50%; height: 15px;\">1. <img loading=\"lazy\" decoding=\"async\" src=\"https:\/\/opentextbc.ca\/introalgebra\/wp-content\/ql-cache\/quicklatex.com-68205bbb783b837657b04a38470f5591_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"&#49;&#54;&#45;&#57;\" title=\"Rendered by QuickLaTeX.com\" height=\"13\" width=\"47\" style=\"vertical-align: -1px;\" \/><\/td>\n<td style=\"width: 50%; height: 15px;\">2. <img loading=\"lazy\" decoding=\"async\" src=\"https:\/\/opentextbc.ca\/introalgebra\/wp-content\/ql-cache\/quicklatex.com-216535d066d50ba7f5f136fa1092e9aa_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"&#50;&#53;&#45;&#55;\" title=\"Rendered by QuickLaTeX.com\" height=\"13\" width=\"48\" style=\"vertical-align: 0px;\" \/><\/td>\n<\/tr>\n<tr style=\"height: 15px;\">\n<td style=\"width: 50%; height: 15px;\">3. <img loading=\"lazy\" decoding=\"async\" src=\"https:\/\/opentextbc.ca\/introalgebra\/wp-content\/ql-cache\/quicklatex.com-1cadcc6a2552129720f2159b22e01000_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"&#53;&#32;&#92;&#99;&#100;&#111;&#116;&#32;&#54;\" title=\"Rendered by QuickLaTeX.com\" height=\"13\" width=\"31\" style=\"vertical-align: 0px;\" \/><\/td>\n<td style=\"width: 50%; height: 15px;\">4. <img loading=\"lazy\" decoding=\"async\" src=\"https:\/\/opentextbc.ca\/introalgebra\/wp-content\/ql-cache\/quicklatex.com-7e59bc0337a0fafb55e6eea03a57ccdd_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"&#51;&#32;&#92;&#99;&#100;&#111;&#116;&#32;&#57;\" title=\"Rendered by QuickLaTeX.com\" height=\"12\" width=\"31\" style=\"vertical-align: 0px;\" \/><\/td>\n<\/tr>\n<tr style=\"height: 15px;\">\n<td style=\"width: 50%; height: 15px;\">5. <img loading=\"lazy\" decoding=\"async\" src=\"https:\/\/opentextbc.ca\/introalgebra\/wp-content\/ql-cache\/quicklatex.com-187ae9fdb69dd61d67cb85375e8a2d96_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"&#50;&#56;&#32;&#92;&#100;&#105;&#118;&#32;&#52;\" title=\"Rendered by QuickLaTeX.com\" height=\"13\" width=\"48\" style=\"vertical-align: -1px;\" \/><\/td>\n<td style=\"width: 50%; height: 15px;\"><span style=\"text-align: initial; background-color: initial;\">6. <img loading=\"lazy\" decoding=\"async\" src=\"https:\/\/opentextbc.ca\/introalgebra\/wp-content\/ql-cache\/quicklatex.com-a97f90f56d07988cbbd957c05e76e48e_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"&#52;&#53;&#32;&#92;&#100;&#105;&#118;&#32;&#53;\" title=\"Rendered by QuickLaTeX.com\" height=\"14\" width=\"47\" style=\"vertical-align: -1px;\" \/><\/span><\/td>\n<\/tr>\n<tr style=\"height: 15px;\">\n<td style=\"width: 50%; height: 15px;\">7. <img loading=\"lazy\" decoding=\"async\" src=\"https:\/\/opentextbc.ca\/introalgebra\/wp-content\/ql-cache\/quicklatex.com-68e7d089f1965e1b1205eaec03417c79_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"&#120;&#43;&#56;\" title=\"Rendered by QuickLaTeX.com\" height=\"14\" width=\"41\" style=\"vertical-align: -2px;\" \/><\/td>\n<td style=\"width: 50%; height: 15px;\">8. <img loading=\"lazy\" decoding=\"async\" src=\"https:\/\/opentextbc.ca\/introalgebra\/wp-content\/ql-cache\/quicklatex.com-339028354620d2bf8b9638e51b7c9347_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"&#120;&#43;&#49;&#49;\" title=\"Rendered by QuickLaTeX.com\" height=\"14\" width=\"49\" style=\"vertical-align: -2px;\" \/><\/td>\n<\/tr>\n<tr style=\"height: 15px;\">\n<td style=\"width: 50%; height: 15px;\">9. <img loading=\"lazy\" decoding=\"async\" src=\"https:\/\/opentextbc.ca\/introalgebra\/wp-content\/ql-cache\/quicklatex.com-ff41a39168ebeb615ff11a7672598aa9_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"&#92;&#108;&#101;&#102;&#116;&#40;&#50;&#92;&#114;&#105;&#103;&#104;&#116;&#41;&#92;&#108;&#101;&#102;&#116;&#40;&#55;&#92;&#114;&#105;&#103;&#104;&#116;&#41;\" title=\"Rendered by QuickLaTeX.com\" height=\"18\" width=\"47\" style=\"vertical-align: -4px;\" \/><\/td>\n<td style=\"width: 50%; height: 15px;\">10. <img loading=\"lazy\" decoding=\"async\" src=\"https:\/\/opentextbc.ca\/introalgebra\/wp-content\/ql-cache\/quicklatex.com-879e086393fe18d33c889fe588881045_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"&#92;&#108;&#101;&#102;&#116;&#40;&#52;&#92;&#114;&#105;&#103;&#104;&#116;&#41;&#92;&#108;&#101;&#102;&#116;&#40;&#56;&#92;&#114;&#105;&#103;&#104;&#116;&#41;\" title=\"Rendered by QuickLaTeX.com\" height=\"18\" width=\"47\" style=\"vertical-align: -4px;\" \/><\/td>\n<\/tr>\n<tr style=\"height: 15px;\">\n<td style=\"width: 50%; height: 15px;\">11. <img loading=\"lazy\" decoding=\"async\" src=\"https:\/\/opentextbc.ca\/introalgebra\/wp-content\/ql-cache\/quicklatex.com-38826cadfc5dbf2d92abbbfd6d370410_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"&#49;&#52;\" title=\"Rendered by QuickLaTeX.com\" height=\"13\" width=\"17\" style=\"vertical-align: -1px;\" \/> &lt; <img loading=\"lazy\" decoding=\"async\" src=\"https:\/\/opentextbc.ca\/introalgebra\/wp-content\/ql-cache\/quicklatex.com-1b44aa122f73c22d86f2d764af01f919_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"&#50;&#49;\" title=\"Rendered by QuickLaTeX.com\" height=\"13\" width=\"17\" style=\"vertical-align: -1px;\" \/><\/td>\n<td style=\"width: 50%; height: 15px;\">12. <img loading=\"lazy\" decoding=\"async\" src=\"https:\/\/opentextbc.ca\/introalgebra\/wp-content\/ql-cache\/quicklatex.com-b976c8c10558ac50c42d953f3ee38707_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"&#49;&#55;\" title=\"Rendered by QuickLaTeX.com\" height=\"14\" width=\"17\" style=\"vertical-align: -1px;\" \/> &lt; <img loading=\"lazy\" decoding=\"async\" src=\"https:\/\/opentextbc.ca\/introalgebra\/wp-content\/ql-cache\/quicklatex.com-6bff01d8c87d130da6950c561718ce13_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"&#51;&#53;\" title=\"Rendered by QuickLaTeX.com\" height=\"13\" width=\"17\" style=\"vertical-align: 0px;\" \/><\/td>\n<\/tr>\n<tr style=\"height: 15px;\">\n<td style=\"width: 50%; height: 15px;\">13. <img loading=\"lazy\" decoding=\"async\" src=\"https:\/\/opentextbc.ca\/introalgebra\/wp-content\/ql-cache\/quicklatex.com-13319028616140a4ba95bea6db2e815a_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"&#51;&#54;&#92;&#103;&#101;&#32;&#49;&#57;\" title=\"Rendered by QuickLaTeX.com\" height=\"15\" width=\"59\" style=\"vertical-align: -3px;\" \/><\/td>\n<td style=\"width: 50%; height: 15px;\">14. <img loading=\"lazy\" decoding=\"async\" src=\"https:\/\/opentextbc.ca\/introalgebra\/wp-content\/ql-cache\/quicklatex.com-aaf66ad7fce1ef603a0052482eb2deee_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"&#52;&#50;&#92;&#103;&#101;&#32;&#50;&#55;\" title=\"Rendered by QuickLaTeX.com\" height=\"16\" width=\"59\" style=\"vertical-align: -3px;\" \/><\/td>\n<\/tr>\n<tr style=\"height: 15px;\">\n<td style=\"width: 50%; height: 15px;\">15. <img loading=\"lazy\" decoding=\"async\" src=\"https:\/\/opentextbc.ca\/introalgebra\/wp-content\/ql-cache\/quicklatex.com-c653dc757f5c9b9149092f4eeb5af1a9_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"&#51;&#110;&#61;&#50;&#52;\" title=\"Rendered by QuickLaTeX.com\" height=\"13\" width=\"61\" style=\"vertical-align: -1px;\" \/><\/td>\n<td style=\"width: 50%; height: 15px;\">16. <img loading=\"lazy\" decoding=\"async\" src=\"https:\/\/opentextbc.ca\/introalgebra\/wp-content\/ql-cache\/quicklatex.com-41850378ffaf2a73d81feb4bf3766c3a_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"&#54;&#110;&#61;&#51;&#54;\" title=\"Rendered by QuickLaTeX.com\" height=\"12\" width=\"61\" style=\"vertical-align: 0px;\" \/><\/td>\n<\/tr>\n<tr style=\"height: 15px;\">\n<td style=\"width: 50%; height: 15px;\">17. <img loading=\"lazy\" decoding=\"async\" src=\"https:\/\/opentextbc.ca\/introalgebra\/wp-content\/ql-cache\/quicklatex.com-90e5f9ccaf5dcf5c488d021c720edc6b_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"&#121;&#45;&#49;\" title=\"Rendered by QuickLaTeX.com\" height=\"16\" width=\"39\" style=\"vertical-align: -4px;\" \/> &gt; <img loading=\"lazy\" decoding=\"async\" src=\"https:\/\/opentextbc.ca\/introalgebra\/wp-content\/ql-cache\/quicklatex.com-b5c3e12330dabaeec7413281aba0f134_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"&#54;\" title=\"Rendered by QuickLaTeX.com\" height=\"12\" width=\"9\" style=\"vertical-align: 0px;\" \/><\/td>\n<td style=\"width: 50%; height: 15px;\">18. <img loading=\"lazy\" decoding=\"async\" src=\"https:\/\/opentextbc.ca\/introalgebra\/wp-content\/ql-cache\/quicklatex.com-e9151933df43f050ab288f4b49522993_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"&#121;&#45;&#52;\" title=\"Rendered by QuickLaTeX.com\" height=\"16\" width=\"40\" style=\"vertical-align: -4px;\" \/> &gt; <img loading=\"lazy\" decoding=\"async\" src=\"https:\/\/opentextbc.ca\/introalgebra\/wp-content\/ql-cache\/quicklatex.com-23212a120eb92d226d44696a0b80bead_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"&#56;\" title=\"Rendered by QuickLaTeX.com\" height=\"12\" width=\"9\" style=\"vertical-align: 0px;\" \/><\/td>\n<\/tr>\n<tr>\n<td style=\"width: 50%;\">19. <img loading=\"lazy\" decoding=\"async\" src=\"https:\/\/opentextbc.ca\/introalgebra\/wp-content\/ql-cache\/quicklatex.com-edfd11c5c5b24238c0d4f9e3d05b3a13_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"&#50;&#92;&#108;&#101;&#32;&#49;&#56;&#32;&#92;&#100;&#105;&#118;&#32;&#54;\" title=\"Rendered by QuickLaTeX.com\" height=\"15\" width=\"81\" style=\"vertical-align: -3px;\" \/><\/td>\n<td style=\"width: 50%;\">20. <img loading=\"lazy\" decoding=\"async\" src=\"https:\/\/opentextbc.ca\/introalgebra\/wp-content\/ql-cache\/quicklatex.com-f77e0df3d55d69204604f748db885d56_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"&#51;&#92;&#108;&#101;&#32;&#50;&#48;&#32;&#92;&#100;&#105;&#118;&#32;&#52;\" title=\"Rendered by QuickLaTeX.com\" height=\"15\" width=\"81\" style=\"vertical-align: -3px;\" \/><\/td>\n<\/tr>\n<tr>\n<td style=\"width: 50%;\">21. <img loading=\"lazy\" decoding=\"async\" src=\"https:\/\/opentextbc.ca\/introalgebra\/wp-content\/ql-cache\/quicklatex.com-5d8baee74c14984601598ef997df320e_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"&#97;&#92;&#110;&#101;&#32;&#55;&#92;&#99;&#100;&#111;&#116;&#32;&#52;\" title=\"Rendered by QuickLaTeX.com\" height=\"17\" width=\"64\" style=\"vertical-align: -4px;\" \/><\/td>\n<td style=\"width: 50%;\">22. <img loading=\"lazy\" decoding=\"async\" src=\"https:\/\/opentextbc.ca\/introalgebra\/wp-content\/ql-cache\/quicklatex.com-22b01f9ebebcb74f9887cdbcacbdd924_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"&#97;&#92;&#110;&#101;&#32;&#49;&#92;&#99;&#100;&#111;&#116;&#32;&#49;&#50;\" title=\"Rendered by QuickLaTeX.com\" height=\"17\" width=\"72\" style=\"vertical-align: -4px;\" \/><\/td>\n<\/tr>\n<\/tbody>\n<\/table>\n<h2>Identify Expressions and Equations<\/h2>\n<p id=\"eip-578\">In the following exercises, determine if each is an expression or an equation.<\/p>\n<table style=\"border-collapse: collapse; width: 100%; height: 90px;\">\n<tbody>\n<tr style=\"height: 15px;\">\n<td style=\"width: 50%; height: 15px;\">23. <img loading=\"lazy\" decoding=\"async\" src=\"https:\/\/opentextbc.ca\/introalgebra\/wp-content\/ql-cache\/quicklatex.com-7a39d1b47a661ee2eb192fe0ab13fa9c_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"&#57;&#92;&#99;&#100;&#111;&#116;&#32;&#54;&#61;&#53;&#52;\" title=\"Rendered by QuickLaTeX.com\" height=\"13\" width=\"72\" style=\"vertical-align: 0px;\" \/><\/td>\n<td style=\"width: 50%; height: 15px;\">24. <img loading=\"lazy\" decoding=\"async\" src=\"https:\/\/opentextbc.ca\/introalgebra\/wp-content\/ql-cache\/quicklatex.com-9e48799e74b2b4b2d00a1870ef735161_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"&#55;&#92;&#99;&#100;&#111;&#116;&#32;&#57;&#61;&#54;&#51;\" title=\"Rendered by QuickLaTeX.com\" height=\"13\" width=\"72\" style=\"vertical-align: 0px;\" \/><\/td>\n<\/tr>\n<tr style=\"height: 15px;\">\n<td style=\"width: 50%; height: 15px;\">25. <img loading=\"lazy\" decoding=\"async\" src=\"https:\/\/opentextbc.ca\/introalgebra\/wp-content\/ql-cache\/quicklatex.com-342de3ffda17fdd03f01c8e849111391_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"&#53;&#92;&#99;&#100;&#111;&#116;&#32;&#52;&#43;&#51;\" title=\"Rendered by QuickLaTeX.com\" height=\"15\" width=\"61\" style=\"vertical-align: -2px;\" \/><\/td>\n<td style=\"width: 50%; height: 15px;\">26. <img loading=\"lazy\" decoding=\"async\" src=\"https:\/\/opentextbc.ca\/introalgebra\/wp-content\/ql-cache\/quicklatex.com-c1e65798d3953812da77e60b59860415_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"&#54;&#92;&#99;&#100;&#111;&#116;&#32;&#51;&#43;&#53;\" title=\"Rendered by QuickLaTeX.com\" height=\"15\" width=\"60\" style=\"vertical-align: -2px;\" \/><\/td>\n<\/tr>\n<tr style=\"height: 15px;\">\n<td style=\"width: 50%; height: 15px;\">27. <img loading=\"lazy\" decoding=\"async\" src=\"https:\/\/opentextbc.ca\/introalgebra\/wp-content\/ql-cache\/quicklatex.com-dc75694098649a22421bc1ec912c0b09_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"&#120;&#43;&#55;\" title=\"Rendered by QuickLaTeX.com\" height=\"15\" width=\"41\" style=\"vertical-align: -2px;\" \/><\/td>\n<td style=\"width: 50%; height: 15px;\">28. <img loading=\"lazy\" decoding=\"async\" src=\"https:\/\/opentextbc.ca\/introalgebra\/wp-content\/ql-cache\/quicklatex.com-1b880e60eb5f7fe8366d9841426117de_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"&#120;&#43;&#57;\" title=\"Rendered by QuickLaTeX.com\" height=\"14\" width=\"41\" style=\"vertical-align: -2px;\" \/><\/td>\n<\/tr>\n<tr style=\"height: 15px;\">\n<td style=\"width: 50%; height: 15px;\">29. <img loading=\"lazy\" decoding=\"async\" src=\"https:\/\/opentextbc.ca\/introalgebra\/wp-content\/ql-cache\/quicklatex.com-f2829365cb54d13a68be79ab7be40b72_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"&#121;&#45;&#53;&#61;&#50;&#53;\" title=\"Rendered by QuickLaTeX.com\" height=\"17\" width=\"80\" style=\"vertical-align: -4px;\" \/><\/td>\n<td style=\"width: 50%; height: 15px;\">30. <img loading=\"lazy\" decoding=\"async\" src=\"https:\/\/opentextbc.ca\/introalgebra\/wp-content\/ql-cache\/quicklatex.com-4ca1ff1ffef53d3e1abf05e465fbf1fd_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"&#121;&#45;&#56;&#61;&#51;&#50;\" title=\"Rendered by QuickLaTeX.com\" height=\"16\" width=\"80\" style=\"vertical-align: -4px;\" \/><\/td>\n<\/tr>\n<\/tbody>\n<\/table>\n<h2>Simplify Expressions with Exponents<\/h2>\n<p id=\"eip-595\">In the following exercises, write in exponential form.<\/p>\n<table style=\"border-collapse: collapse; width: 100%;\">\n<tbody>\n<tr>\n<td style=\"width: 50%;\">31. <img loading=\"lazy\" decoding=\"async\" src=\"https:\/\/opentextbc.ca\/introalgebra\/wp-content\/ql-cache\/quicklatex.com-b2d3785d6d191a86edd0c6ec5a1914b7_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"&#51;&#92;&#99;&#100;&#111;&#116;&#32;&#51;&#92;&#99;&#100;&#111;&#116;&#32;&#51;&#92;&#99;&#100;&#111;&#116;&#32;&#51;&#92;&#99;&#100;&#111;&#116;&#32;&#51;&#92;&#99;&#100;&#111;&#116;&#32;&#51;&#92;&#99;&#100;&#111;&#116;&#32;&#51;\" title=\"Rendered by QuickLaTeX.com\" height=\"12\" width=\"139\" style=\"vertical-align: 0px;\" \/><\/td>\n<td style=\"width: 50%;\">32. <img loading=\"lazy\" decoding=\"async\" src=\"https:\/\/opentextbc.ca\/introalgebra\/wp-content\/ql-cache\/quicklatex.com-e7029bd6a56e81d6d26c7e6eb30e5c08_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"&#52;&#92;&#99;&#100;&#111;&#116;&#32;&#52;&#92;&#99;&#100;&#111;&#116;&#32;&#52;&#92;&#99;&#100;&#111;&#116;&#32;&#52;&#92;&#99;&#100;&#111;&#116;&#32;&#52;&#92;&#99;&#100;&#111;&#116;&#32;&#52;\" title=\"Rendered by QuickLaTeX.com\" height=\"12\" width=\"117\" style=\"vertical-align: 0px;\" \/><\/td>\n<\/tr>\n<tr>\n<td style=\"width: 50%;\">33. <img loading=\"lazy\" decoding=\"async\" src=\"https:\/\/opentextbc.ca\/introalgebra\/wp-content\/ql-cache\/quicklatex.com-2adb5a63ea93ccbbb7c1ebd935c511d3_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"&#120;&#92;&#99;&#100;&#111;&#116;&#32;&#120;&#92;&#99;&#100;&#111;&#116;&#32;&#120;&#92;&#99;&#100;&#111;&#116;&#32;&#120;&#92;&#99;&#100;&#111;&#116;&#32;&#120;\" title=\"Rendered by QuickLaTeX.com\" height=\"8\" width=\"102\" style=\"vertical-align: 0px;\" \/><\/td>\n<td style=\"width: 50%;\">34. <img loading=\"lazy\" decoding=\"async\" src=\"https:\/\/opentextbc.ca\/introalgebra\/wp-content\/ql-cache\/quicklatex.com-7f67f40e00bfb28a8e6de7bb724e2161_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"&#121;&#92;&#99;&#100;&#111;&#116;&#32;&#121;&#92;&#99;&#100;&#111;&#116;&#32;&#121;&#92;&#99;&#100;&#111;&#116;&#32;&#121;&#92;&#99;&#100;&#111;&#116;&#32;&#121;&#92;&#99;&#100;&#111;&#116;&#32;&#121;\" title=\"Rendered by QuickLaTeX.com\" height=\"12\" width=\"120\" style=\"vertical-align: -4px;\" \/><\/td>\n<\/tr>\n<\/tbody>\n<\/table>\n<p id=\"fs-id4333539\">In the following exercises, write in expanded form.<\/p>\n<table style=\"border-collapse: collapse; width: 100%;\">\n<tbody>\n<tr>\n<td style=\"width: 50%;\">35. <img loading=\"lazy\" decoding=\"async\" src=\"https:\/\/opentextbc.ca\/introalgebra\/wp-content\/ql-cache\/quicklatex.com-22a6de91ce40f10ddb25e6ea195347ce_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"&#123;&#53;&#125;&#94;&#123;&#51;&#125;\" title=\"Rendered by QuickLaTeX.com\" height=\"15\" width=\"16\" style=\"vertical-align: 0px;\" \/><\/td>\n<td style=\"width: 50%;\">36. <img loading=\"lazy\" decoding=\"async\" src=\"https:\/\/opentextbc.ca\/introalgebra\/wp-content\/ql-cache\/quicklatex.com-7d37f7552ef609926a3d2fb08b1d5e0d_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"&#123;&#56;&#125;&#94;&#123;&#51;&#125;\" title=\"Rendered by QuickLaTeX.com\" height=\"15\" width=\"16\" style=\"vertical-align: 0px;\" \/><\/td>\n<\/tr>\n<tr>\n<td style=\"width: 50%;\">37. <img loading=\"lazy\" decoding=\"async\" src=\"https:\/\/opentextbc.ca\/introalgebra\/wp-content\/ql-cache\/quicklatex.com-202cb81727487a115a9ecd3ead290a93_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"&#123;&#50;&#125;&#94;&#123;&#56;&#125;\" title=\"Rendered by QuickLaTeX.com\" height=\"15\" width=\"16\" style=\"vertical-align: 0px;\" \/><\/td>\n<td style=\"width: 50%;\">38. <img loading=\"lazy\" decoding=\"async\" src=\"https:\/\/opentextbc.ca\/introalgebra\/wp-content\/ql-cache\/quicklatex.com-b9cec61dc94a9878e732625734f19af6_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"&#123;&#49;&#48;&#125;&#94;&#123;&#53;&#125;\" title=\"Rendered by QuickLaTeX.com\" height=\"16\" width=\"24\" style=\"vertical-align: -1px;\" \/><\/td>\n<\/tr>\n<\/tbody>\n<\/table>\n<h2>Simplify Expressions Using the Order of Operations<\/h2>\n<p id=\"eip-246\">In the following exercises, simplify.<\/p>\n<table style=\"border-collapse: collapse; width: 100%; height: 274px;\">\n<tbody>\n<tr style=\"height: 109px;\">\n<td style=\"width: 50%; height: 109px;\">39.<\/p>\n<p>a.<img loading=\"lazy\" decoding=\"async\" src=\"https:\/\/opentextbc.ca\/introalgebra\/wp-content\/ql-cache\/quicklatex.com-81a36dbe71f4a460c0529815d6d51ece_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"&#92;&#112;&#104;&#97;&#110;&#116;&#111;&#109;&#123;&#92;&#114;&#117;&#108;&#101;&#123;&#48;&#46;&#50;&#101;&#109;&#125;&#123;&#48;&#101;&#120;&#125;&#125;&#51;&#43;&#56;&#92;&#99;&#100;&#111;&#116;&#32;&#53;&#92;&#112;&#104;&#97;&#110;&#116;&#111;&#109;&#123;&#92;&#114;&#117;&#108;&#101;&#123;&#48;&#46;&#50;&#101;&#109;&#125;&#123;&#48;&#101;&#120;&#125;&#125;&#92;&#112;&#104;&#97;&#110;&#116;&#111;&#109;&#123;&#92;&#114;&#117;&#108;&#101;&#123;&#48;&#46;&#52;&#101;&#109;&#125;&#123;&#48;&#101;&#120;&#125;&#125;\" title=\"Rendered by QuickLaTeX.com\" height=\"15\" width=\"60\" style=\"vertical-align: -2px;\" \/><\/p>\n<p>b.<img loading=\"lazy\" decoding=\"async\" src=\"https:\/\/opentextbc.ca\/introalgebra\/wp-content\/ql-cache\/quicklatex.com-3937db2bf9317f1e4ad06463de0ac410_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"&#92;&#112;&#104;&#97;&#110;&#116;&#111;&#109;&#123;&#92;&#114;&#117;&#108;&#101;&#123;&#48;&#46;&#50;&#101;&#109;&#125;&#123;&#48;&#101;&#120;&#125;&#125;&#92;&#116;&#101;&#120;&#116;&#123;&#40;&#51;&#43;&#56;&#41;&#125;&#92;&#99;&#100;&#111;&#116;&#32;&#92;&#116;&#101;&#120;&#116;&#123;&#53;&#125;\" title=\"Rendered by QuickLaTeX.com\" height=\"19\" width=\"65\" style=\"vertical-align: -5px;\" \/><\/td>\n<td style=\"width: 50%; height: 109px;\">40.<\/p>\n<p>a.<img loading=\"lazy\" decoding=\"async\" src=\"https:\/\/opentextbc.ca\/introalgebra\/wp-content\/ql-cache\/quicklatex.com-60f2d33a6b04e577a8c4bcac20a1fd70_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"&#92;&#112;&#104;&#97;&#110;&#116;&#111;&#109;&#123;&#92;&#114;&#117;&#108;&#101;&#123;&#48;&#46;&#50;&#101;&#109;&#125;&#123;&#48;&#101;&#120;&#125;&#125;&#50;&#43;&#54;&#92;&#99;&#100;&#111;&#116;&#32;&#51;&#92;&#112;&#104;&#97;&#110;&#116;&#111;&#109;&#123;&#92;&#114;&#117;&#108;&#101;&#123;&#48;&#46;&#50;&#101;&#109;&#125;&#123;&#48;&#101;&#120;&#125;&#125;&#92;&#112;&#104;&#97;&#110;&#116;&#111;&#109;&#123;&#92;&#114;&#117;&#108;&#101;&#123;&#48;&#46;&#52;&#101;&#109;&#125;&#123;&#48;&#101;&#120;&#125;&#125;\" title=\"Rendered by QuickLaTeX.com\" height=\"14\" width=\"61\" style=\"vertical-align: -2px;\" \/><\/p>\n<p>b.<img loading=\"lazy\" decoding=\"async\" src=\"https:\/\/opentextbc.ca\/introalgebra\/wp-content\/ql-cache\/quicklatex.com-99096d9452159d9c5652391316c1cb9a_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"&#92;&#112;&#104;&#97;&#110;&#116;&#111;&#109;&#123;&#92;&#114;&#117;&#108;&#101;&#123;&#48;&#46;&#50;&#101;&#109;&#125;&#123;&#48;&#101;&#120;&#125;&#125;&#92;&#116;&#101;&#120;&#116;&#123;&#40;&#50;&#43;&#54;&#41;&#125;&#92;&#99;&#100;&#111;&#116;&#32;&#92;&#116;&#101;&#120;&#116;&#123;&#51;&#125;\" title=\"Rendered by QuickLaTeX.com\" height=\"19\" width=\"66\" style=\"vertical-align: -5px;\" \/><\/td>\n<\/tr>\n<tr style=\"height: 15px;\">\n<td style=\"width: 50%; height: 15px;\">41. <img loading=\"lazy\" decoding=\"async\" src=\"https:\/\/opentextbc.ca\/introalgebra\/wp-content\/ql-cache\/quicklatex.com-3a0ba3b058f7091614276649859a7fe1_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"&#123;&#50;&#125;&#94;&#123;&#51;&#125;&#45;&#49;&#50;&#32;&#92;&#100;&#105;&#118;&#32;&#92;&#108;&#101;&#102;&#116;&#40;&#57;&#45;&#53;&#92;&#114;&#105;&#103;&#104;&#116;&#41;\" title=\"Rendered by QuickLaTeX.com\" height=\"20\" width=\"130\" style=\"vertical-align: -5px;\" \/><\/td>\n<td style=\"width: 50%; height: 15px;\">42. <img loading=\"lazy\" decoding=\"async\" src=\"https:\/\/opentextbc.ca\/introalgebra\/wp-content\/ql-cache\/quicklatex.com-baad777d088980f41604505932e3dac1_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"&#123;&#51;&#125;&#94;&#123;&#50;&#125;&#45;&#49;&#56;&#92;&#100;&#105;&#118;&#32;&#92;&#108;&#101;&#102;&#116;&#40;&#49;&#49;&#45;&#53;&#92;&#114;&#105;&#103;&#104;&#116;&#41;\" title=\"Rendered by QuickLaTeX.com\" height=\"20\" width=\"139\" style=\"vertical-align: -5px;\" \/><\/td>\n<\/tr>\n<tr style=\"height: 15px;\">\n<td style=\"width: 50%; height: 15px;\">43. <img loading=\"lazy\" decoding=\"async\" src=\"https:\/\/opentextbc.ca\/introalgebra\/wp-content\/ql-cache\/quicklatex.com-6988096d0f42cb96bcecb6061adb6b05_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"&#51;&#92;&#99;&#100;&#111;&#116;&#32;&#56;&#43;&#53;&#92;&#99;&#100;&#111;&#116;&#32;&#50;\" title=\"Rendered by QuickLaTeX.com\" height=\"15\" width=\"82\" style=\"vertical-align: -2px;\" \/><\/td>\n<td style=\"width: 50%; height: 15px;\">44. <img loading=\"lazy\" decoding=\"async\" src=\"https:\/\/opentextbc.ca\/introalgebra\/wp-content\/ql-cache\/quicklatex.com-447e1f6e25fcb1d50f0007da414fd44c_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"&#52;&#92;&#99;&#100;&#111;&#116;&#32;&#55;&#43;&#51;&#92;&#99;&#100;&#111;&#116;&#32;&#53;\" title=\"Rendered by QuickLaTeX.com\" height=\"15\" width=\"82\" style=\"vertical-align: -2px;\" \/><\/td>\n<\/tr>\n<tr style=\"height: 15px;\">\n<td style=\"width: 50%; height: 15px;\">45. <img loading=\"lazy\" decoding=\"async\" src=\"https:\/\/opentextbc.ca\/introalgebra\/wp-content\/ql-cache\/quicklatex.com-d1ad557dac274b0cecd3d0f2409d2881_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"&#50;&#43;&#56;&#92;&#108;&#101;&#102;&#116;&#40;&#54;&#43;&#49;&#92;&#114;&#105;&#103;&#104;&#116;&#41;\" title=\"Rendered by QuickLaTeX.com\" height=\"18\" width=\"95\" style=\"vertical-align: -4px;\" \/><\/td>\n<td style=\"width: 50%; height: 15px;\">46. <img loading=\"lazy\" decoding=\"async\" src=\"https:\/\/opentextbc.ca\/introalgebra\/wp-content\/ql-cache\/quicklatex.com-568d3450e122c24e54da096592650583_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"&#52;&#43;&#54;&#92;&#108;&#101;&#102;&#116;&#40;&#51;&#43;&#54;&#92;&#114;&#105;&#103;&#104;&#116;&#41;\" title=\"Rendered by QuickLaTeX.com\" height=\"18\" width=\"95\" style=\"vertical-align: -4px;\" \/><\/td>\n<\/tr>\n<tr style=\"height: 15px;\">\n<td style=\"width: 50%; height: 15px;\">47. <img loading=\"lazy\" decoding=\"async\" src=\"https:\/\/opentextbc.ca\/introalgebra\/wp-content\/ql-cache\/quicklatex.com-49e6efc78d7d5105a0a12a8e2a7b0802_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"&#52;&#92;&#99;&#100;&#111;&#116;&#32;&#49;&#50;&#47;&#56;\" title=\"Rendered by QuickLaTeX.com\" height=\"19\" width=\"58\" style=\"vertical-align: -5px;\" \/><\/td>\n<td style=\"width: 50%; height: 15px;\">48. <img loading=\"lazy\" decoding=\"async\" src=\"https:\/\/opentextbc.ca\/introalgebra\/wp-content\/ql-cache\/quicklatex.com-64338cbb502fb407e3e8637fcb1a128a_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"&#50;&#92;&#99;&#100;&#111;&#116;&#32;&#51;&#54;&#47;&#54;\" title=\"Rendered by QuickLaTeX.com\" height=\"19\" width=\"58\" style=\"vertical-align: -5px;\" \/><\/td>\n<\/tr>\n<tr style=\"height: 15px;\">\n<td style=\"width: 50%; height: 15px;\">49. <img loading=\"lazy\" decoding=\"async\" src=\"https:\/\/opentextbc.ca\/introalgebra\/wp-content\/ql-cache\/quicklatex.com-3c0309e2eddc9d9daaa38348b30a1ee3_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"&#54;&#43;&#49;&#48;&#47;&#50;&#43;&#50;\" title=\"Rendered by QuickLaTeX.com\" height=\"18\" width=\"96\" style=\"vertical-align: -5px;\" \/><\/td>\n<td style=\"width: 50%; height: 15px;\">50. <img loading=\"lazy\" decoding=\"async\" src=\"https:\/\/opentextbc.ca\/introalgebra\/wp-content\/ql-cache\/quicklatex.com-a4991275d8b5ce311cf5082c0c619e6b_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"&#57;&#43;&#49;&#50;&#47;&#51;&#43;&#52;\" title=\"Rendered by QuickLaTeX.com\" height=\"18\" width=\"97\" style=\"vertical-align: -5px;\" \/><\/td>\n<\/tr>\n<tr style=\"height: 15px;\">\n<td style=\"width: 50%; height: 15px;\">51. <img loading=\"lazy\" decoding=\"async\" src=\"https:\/\/opentextbc.ca\/introalgebra\/wp-content\/ql-cache\/quicklatex.com-bec6a099237ebd5279a1b29f8a24c095_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"&#92;&#108;&#101;&#102;&#116;&#40;&#54;&#43;&#49;&#48;&#92;&#114;&#105;&#103;&#104;&#116;&#41;&#92;&#100;&#105;&#118;&#32;&#92;&#108;&#101;&#102;&#116;&#40;&#50;&#43;&#50;&#92;&#114;&#105;&#103;&#104;&#116;&#41;\" title=\"Rendered by QuickLaTeX.com\" height=\"19\" width=\"135\" style=\"vertical-align: -5px;\" \/><\/td>\n<td style=\"width: 50%; height: 15px;\">52. <img loading=\"lazy\" decoding=\"async\" src=\"https:\/\/opentextbc.ca\/introalgebra\/wp-content\/ql-cache\/quicklatex.com-688f271e228a2ca99df1dca3018474a6_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"&#92;&#108;&#101;&#102;&#116;&#40;&#57;&#43;&#49;&#50;&#92;&#114;&#105;&#103;&#104;&#116;&#41;&#92;&#100;&#105;&#118;&#32;&#92;&#108;&#101;&#102;&#116;&#40;&#51;&#43;&#52;&#92;&#114;&#105;&#103;&#104;&#116;&#41;\" title=\"Rendered by QuickLaTeX.com\" height=\"19\" width=\"135\" style=\"vertical-align: -5px;\" \/><\/td>\n<\/tr>\n<tr style=\"height: 15px;\">\n<td style=\"width: 50%; height: 15px;\">53. <img loading=\"lazy\" decoding=\"async\" src=\"https:\/\/opentextbc.ca\/introalgebra\/wp-content\/ql-cache\/quicklatex.com-d73e8be75a139e1f66b3303cba6dd553_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"&#50;&#48;&#92;&#100;&#105;&#118;&#32;&#52;&#43;&#54;&#92;&#99;&#100;&#111;&#116;&#53;\" title=\"Rendered by QuickLaTeX.com\" height=\"15\" width=\"100\" style=\"vertical-align: -2px;\" \/><\/td>\n<td style=\"width: 50%; height: 15px;\">54. <img loading=\"lazy\" decoding=\"async\" src=\"https:\/\/opentextbc.ca\/introalgebra\/wp-content\/ql-cache\/quicklatex.com-2d46d2719b2822b00112cab7bb4f03ee_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"&#51;&#51;&#92;&#100;&#105;&#118;&#32;&#51;&#43;&#56;&#92;&#99;&#100;&#111;&#116;&#50;\" title=\"Rendered by QuickLaTeX.com\" height=\"14\" width=\"100\" style=\"vertical-align: -2px;\" \/><\/td>\n<\/tr>\n<tr style=\"height: 15px;\">\n<td style=\"width: 50%; height: 15px;\">55. <img loading=\"lazy\" decoding=\"async\" src=\"https:\/\/opentextbc.ca\/introalgebra\/wp-content\/ql-cache\/quicklatex.com-decc556ae96382595bd947a469a05e8d_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"&#50;&#48;&#92;&#100;&#105;&#118;&#32;&#92;&#108;&#101;&#102;&#116;&#40;&#52;&#43;&#54;&#92;&#114;&#105;&#103;&#104;&#116;&#41;&#92;&#99;&#100;&#111;&#116;&#32;&#53;\" title=\"Rendered by QuickLaTeX.com\" height=\"19\" width=\"113\" style=\"vertical-align: -5px;\" \/><\/td>\n<td style=\"width: 50%; height: 15px;\">56. <img loading=\"lazy\" decoding=\"async\" src=\"https:\/\/opentextbc.ca\/introalgebra\/wp-content\/ql-cache\/quicklatex.com-ff452d4db7e3dfb554d6cf420e0fcb41_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"&#51;&#51;&#92;&#100;&#105;&#118;&#32;&#92;&#108;&#101;&#102;&#116;&#40;&#51;&#43;&#56;&#92;&#114;&#105;&#103;&#104;&#116;&#41;&#92;&#99;&#100;&#111;&#116;&#32;&#50;\" title=\"Rendered by QuickLaTeX.com\" height=\"19\" width=\"113\" style=\"vertical-align: -5px;\" \/><\/td>\n<\/tr>\n<tr style=\"height: 15px;\">\n<td style=\"width: 50%; height: 15px;\">57. <img loading=\"lazy\" decoding=\"async\" src=\"https:\/\/opentextbc.ca\/introalgebra\/wp-content\/ql-cache\/quicklatex.com-c63b437879b41a5f9d2b03e2395729f1_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"&#123;&#52;&#125;&#94;&#123;&#50;&#125;&#43;&#123;&#53;&#125;&#94;&#123;&#50;&#125;\" title=\"Rendered by QuickLaTeX.com\" height=\"17\" width=\"54\" style=\"vertical-align: -2px;\" \/><\/td>\n<td style=\"width: 50%; height: 15px;\">58. <img loading=\"lazy\" decoding=\"async\" src=\"https:\/\/opentextbc.ca\/introalgebra\/wp-content\/ql-cache\/quicklatex.com-ece530e594c9fbce63a97464020cfb5f_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"&#123;&#51;&#125;&#94;&#123;&#50;&#125;&#43;&#123;&#55;&#125;&#94;&#123;&#50;&#125;\" title=\"Rendered by QuickLaTeX.com\" height=\"17\" width=\"54\" style=\"vertical-align: -2px;\" \/><\/td>\n<\/tr>\n<tr style=\"height: 15px;\">\n<td style=\"width: 50%; height: 15px;\">59. <img loading=\"lazy\" decoding=\"async\" src=\"https:\/\/opentextbc.ca\/introalgebra\/wp-content\/ql-cache\/quicklatex.com-714768b56fa6f5935338e9e13d4a2ec8_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"&#123;&#92;&#108;&#101;&#102;&#116;&#40;&#52;&#43;&#53;&#92;&#114;&#105;&#103;&#104;&#116;&#41;&#125;&#94;&#123;&#50;&#125;\" title=\"Rendered by QuickLaTeX.com\" height=\"21\" width=\"59\" style=\"vertical-align: -4px;\" \/><\/td>\n<td style=\"width: 50%; height: 15px;\">60. <img loading=\"lazy\" decoding=\"async\" src=\"https:\/\/opentextbc.ca\/introalgebra\/wp-content\/ql-cache\/quicklatex.com-19697a7ea62ed9409fdc4b6d9ff47acd_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"&#123;&#92;&#108;&#101;&#102;&#116;&#40;&#51;&#43;&#55;&#92;&#114;&#105;&#103;&#104;&#116;&#41;&#125;&#94;&#123;&#50;&#125;\" title=\"Rendered by QuickLaTeX.com\" height=\"21\" width=\"59\" style=\"vertical-align: -4px;\" \/><\/td>\n<\/tr>\n<tr style=\"height: 15px;\">\n<td style=\"width: 50%; height: 15px;\">61. <img loading=\"lazy\" decoding=\"async\" src=\"https:\/\/opentextbc.ca\/introalgebra\/wp-content\/ql-cache\/quicklatex.com-50afced7de346e9f24e899c17c7754a7_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"&#51;&#92;&#108;&#101;&#102;&#116;&#40;&#49;&#43;&#57;&#92;&#99;&#100;&#111;&#116;&#32;&#54;&#92;&#114;&#105;&#103;&#104;&#116;&#41;&#45;&#123;&#52;&#125;&#94;&#123;&#50;&#125;\" title=\"Rendered by QuickLaTeX.com\" height=\"20\" width=\"124\" style=\"vertical-align: -5px;\" \/><\/td>\n<td style=\"width: 50%; height: 15px;\">62. <img loading=\"lazy\" decoding=\"async\" src=\"https:\/\/opentextbc.ca\/introalgebra\/wp-content\/ql-cache\/quicklatex.com-39ec77677c3f14ca3fdc33f0e4edd198_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"&#53;&#92;&#108;&#101;&#102;&#116;&#40;&#50;&#43;&#56;&#92;&#99;&#100;&#111;&#116;&#32;&#52;&#92;&#114;&#105;&#103;&#104;&#116;&#41;&#45;&#123;&#55;&#125;&#94;&#123;&#50;&#125;\" title=\"Rendered by QuickLaTeX.com\" height=\"20\" width=\"124\" style=\"vertical-align: -5px;\" \/><\/td>\n<\/tr>\n<tr>\n<td style=\"width: 50%;\">63. <img loading=\"lazy\" decoding=\"async\" src=\"https:\/\/opentextbc.ca\/introalgebra\/wp-content\/ql-cache\/quicklatex.com-30e1bf8798a5926bd4107059d2e499ad_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"&#50;&#92;&#108;&#101;&#102;&#116;&#091;&#49;&#43;&#51;&#92;&#108;&#101;&#102;&#116;&#40;&#49;&#48;&#45;&#50;&#92;&#114;&#105;&#103;&#104;&#116;&#41;&#92;&#114;&#105;&#103;&#104;&#116;&#093;\" title=\"Rendered by QuickLaTeX.com\" height=\"19\" width=\"124\" style=\"vertical-align: -5px;\" \/><\/td>\n<td style=\"width: 50%;\"><span style=\"text-align: initial; background-color: initial;\">64. <img loading=\"lazy\" decoding=\"async\" src=\"https:\/\/opentextbc.ca\/introalgebra\/wp-content\/ql-cache\/quicklatex.com-139b3764e45e3e513fa3cc4300f08ade_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"&#53;&#92;&#108;&#101;&#102;&#116;&#091;&#50;&#43;&#52;&#92;&#108;&#101;&#102;&#116;&#40;&#51;&#45;&#50;&#92;&#114;&#105;&#103;&#104;&#116;&#41;&#92;&#114;&#105;&#103;&#104;&#116;&#093;\" title=\"Rendered by QuickLaTeX.com\" height=\"19\" width=\"115\" style=\"vertical-align: -5px;\" \/><\/span><\/td>\n<\/tr>\n<\/tbody>\n<\/table>\n<h2>Everyday Math<\/h2>\n<table style=\"border-collapse: collapse; width: 100%;\">\n<tbody>\n<tr>\n<td style=\"width: 50%;\">\n<p id=\"fs-id2757048\"><strong data-effect=\"bold\">65. Basketball<\/strong> In the 2014 NBA playoffs, the San Antonio Spurs beat the Miami Heat. The table below shows the heights of the starters on each team. Use this table to fill in the appropriate symbol ( = ,&lt;,\u00a0 &gt;).<\/p>\n<table id=\"fs-id2757058\" class=\"unnumbered\" summary=\"This table has six rows and five columns. The first row is a header row and it labels each column. The first column is labeled \u201cSpurs\u201d, the next \u201cHeight\u201d, the third column is blank to distinguish the next column labeled \u201cHeat\u201d and the last column is also labeled \u201cHeight\u201d. Under the \u201cSpurs\u201d column are names of players: Tim Duncan, Boris Diaw, Kawhi Leonard, Tony Parker, and Danny Green. Under the \u201cHeight\u201d column are the heights of the five spurs players: eighty-three inches, eighty inches, seventy-nine inches, seventy four inches and seventy-eight inches. Under the \u201cHeat\u201d column are names of players: Rashard Lewis, LeBron James, Chris Bosh, Dwayne Wade, and Ray Allen. Under the \u201cHeight\u201d column are the heights of the five Heat players: eighty-two inches, eighty inches, eighty-three inches, seventy-six inches and seventy-seven inches.\" data-label=\"\">\n<thead>\n<tr valign=\"top\">\n<th data-align=\"center\"><strong data-effect=\"bold\">Spurs<\/strong><\/th>\n<th data-align=\"center\"><strong data-effect=\"bold\">Height<\/strong><\/th>\n<th><\/th>\n<th data-align=\"center\"><strong data-effect=\"bold\">Heat<\/strong><\/th>\n<th data-align=\"center\"><strong data-effect=\"bold\">Height<\/strong><\/th>\n<\/tr>\n<\/thead>\n<tbody>\n<tr valign=\"top\">\n<td data-align=\"left\">Tim Duncan<\/td>\n<td data-align=\"center\"><img loading=\"lazy\" decoding=\"async\" src=\"https:\/\/opentextbc.ca\/introalgebra\/wp-content\/ql-cache\/quicklatex.com-dc7f0211832711f5ec0f19934d82acbf_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"&#56;&#51;&#39;&#39;\" title=\"Rendered by QuickLaTeX.com\" height=\"14\" width=\"26\" style=\"vertical-align: 0px;\" \/><\/td>\n<td rowspan=\"6\"><\/td>\n<td data-align=\"left\">Rashard Lewis<\/td>\n<td data-align=\"center\"><img loading=\"lazy\" decoding=\"async\" src=\"https:\/\/opentextbc.ca\/introalgebra\/wp-content\/ql-cache\/quicklatex.com-46009a6d9f0056a9ad6f4f4b6e9adda5_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"&#56;&#50;&#39;&#39;\" title=\"Rendered by QuickLaTeX.com\" height=\"14\" width=\"26\" style=\"vertical-align: 0px;\" \/><\/td>\n<\/tr>\n<tr valign=\"top\">\n<td data-align=\"left\">Boris Diaw<\/td>\n<td data-align=\"center\"><img loading=\"lazy\" decoding=\"async\" src=\"https:\/\/opentextbc.ca\/introalgebra\/wp-content\/ql-cache\/quicklatex.com-872629c1d11478c01758ab51d108039d_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"&#56;&#48;&#39;&#39;\" title=\"Rendered by QuickLaTeX.com\" height=\"14\" width=\"26\" style=\"vertical-align: 0px;\" \/><\/td>\n<td data-align=\"left\">LeBron James<\/td>\n<td data-align=\"center\"><img loading=\"lazy\" decoding=\"async\" src=\"https:\/\/opentextbc.ca\/introalgebra\/wp-content\/ql-cache\/quicklatex.com-872629c1d11478c01758ab51d108039d_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"&#56;&#48;&#39;&#39;\" title=\"Rendered by QuickLaTeX.com\" height=\"14\" width=\"26\" style=\"vertical-align: 0px;\" \/><\/td>\n<\/tr>\n<tr valign=\"top\">\n<td data-align=\"left\">Kawhi Leonard<\/td>\n<td data-align=\"center\"><img loading=\"lazy\" decoding=\"async\" src=\"https:\/\/opentextbc.ca\/introalgebra\/wp-content\/ql-cache\/quicklatex.com-96cfc34382787f269c1e3e21dd4e8054_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"&#55;&#57;&#39;&#39;\" title=\"Rendered by QuickLaTeX.com\" height=\"14\" width=\"26\" style=\"vertical-align: 0px;\" \/><\/td>\n<td data-align=\"left\">Chris Bosh<\/td>\n<td data-align=\"center\"><img loading=\"lazy\" decoding=\"async\" src=\"https:\/\/opentextbc.ca\/introalgebra\/wp-content\/ql-cache\/quicklatex.com-dc7f0211832711f5ec0f19934d82acbf_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"&#56;&#51;&#39;&#39;\" title=\"Rendered by QuickLaTeX.com\" height=\"14\" width=\"26\" style=\"vertical-align: 0px;\" \/><\/td>\n<\/tr>\n<tr valign=\"top\">\n<td data-align=\"left\">Tony Parker<\/td>\n<td data-align=\"center\"><img loading=\"lazy\" decoding=\"async\" src=\"https:\/\/opentextbc.ca\/introalgebra\/wp-content\/ql-cache\/quicklatex.com-00507e5fbb0a9f1f5d4aa971839159eb_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"&#55;&#52;&#39;&#39;\" title=\"Rendered by QuickLaTeX.com\" height=\"14\" width=\"26\" style=\"vertical-align: 0px;\" \/><\/td>\n<td data-align=\"left\">Dwyane Wade<\/td>\n<td data-align=\"center\"><img loading=\"lazy\" decoding=\"async\" src=\"https:\/\/opentextbc.ca\/introalgebra\/wp-content\/ql-cache\/quicklatex.com-bc77a9c1d6bf9807e763d3dfe4ba1cf3_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"&#55;&#54;&#39;&#39;\" title=\"Rendered by QuickLaTeX.com\" height=\"14\" width=\"26\" style=\"vertical-align: 0px;\" \/><\/td>\n<\/tr>\n<tr valign=\"top\">\n<td data-align=\"left\">Danny Green<\/td>\n<td data-align=\"center\"><img loading=\"lazy\" decoding=\"async\" src=\"https:\/\/opentextbc.ca\/introalgebra\/wp-content\/ql-cache\/quicklatex.com-2ad7c9f24b537c13b183c6920b1d7324_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"&#55;&#56;&#39;&#39;\" title=\"Rendered by QuickLaTeX.com\" height=\"14\" width=\"26\" style=\"vertical-align: 0px;\" \/><\/td>\n<td data-align=\"left\">Ray Allen<\/td>\n<td data-align=\"center\"><img loading=\"lazy\" decoding=\"async\" src=\"https:\/\/opentextbc.ca\/introalgebra\/wp-content\/ql-cache\/quicklatex.com-3f022c12078c2ce6bd9a1882ff754559_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"&#55;&#55;&#39;&#39;\" title=\"Rendered by QuickLaTeX.com\" height=\"14\" width=\"26\" style=\"vertical-align: 0px;\" \/><\/td>\n<\/tr>\n<\/tbody>\n<\/table>\n<ol id=\"eip-id1168466360092\" class=\"circled\" type=\"a\">\n<li>Height of Tim Duncan____Height of Rashard Lewis<\/li>\n<li>Height of Boris Diaw____Height of LeBron James<\/li>\n<li>Height of Kawhi Leonard____Height of Chris Bosh<\/li>\n<li>Height of Tony Parker____Height of Dwyane Wade<\/li>\n<li>Height of Danny Green____Height of Ray Allen<\/li>\n<\/ol>\n<\/td>\n<td style=\"width: 50%;\">\n<p id=\"fs-id2935753\"><strong data-effect=\"bold\">66. Elevation<\/strong> In Colorado there are more than <img loading=\"lazy\" decoding=\"async\" src=\"https:\/\/opentextbc.ca\/introalgebra\/wp-content\/ql-cache\/quicklatex.com-39e5271c62d377c7a347b4eb07f74ab2_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"&#53;&#48;\" title=\"Rendered by QuickLaTeX.com\" height=\"13\" width=\"18\" style=\"vertical-align: 0px;\" \/> mountains with an elevation of over <img loading=\"lazy\" decoding=\"async\" src=\"https:\/\/opentextbc.ca\/introalgebra\/wp-content\/ql-cache\/quicklatex.com-30b15b923751980f337b658be4e88775_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"&#49;&#52;&#44;&#48;&#48;&#48;&#92;&#112;&#104;&#97;&#110;&#116;&#111;&#109;&#123;&#92;&#114;&#117;&#108;&#101;&#123;&#48;&#46;&#50;&#101;&#109;&#125;&#123;&#48;&#101;&#120;&#125;&#125;&#92;&#116;&#101;&#120;&#116;&#123;&#102;&#101;&#101;&#116;&#46;&#125;\" title=\"Rendered by QuickLaTeX.com\" height=\"16\" width=\"87\" style=\"vertical-align: -4px;\" \/> The table shows the ten tallest. Use this table to fill in the appropriate inequality symbol.<\/p>\n<table id=\"fs-id2935762\" class=\"unnumbered\" summary=\"This table has eleven rows and two columns. The first row is a header row and labels the first column \u201cMountain\u201d and the second column \u201cElevation\u201d. Under the \u201cMountain\u201d column are the mountain names: Mt. Elbert, Mt Massive, Mt. Harvard, Blanca Peak, La Plata Peak, Uncompahgre Peak, Crestone Peak, Mt. Lincoln, Grays Peak and Mt. Antero. Under the \u201cElevation\u201d column are the heights: 14,433 feet, 14,421 feet, 14,420 feet, 14,345 feet, 14,336 feet, 14,309 feet, 14,294 feet, 14,286 feet, 14,270 feet, and 14269 feet.\" data-label=\"\">\n<thead>\n<tr valign=\"top\">\n<th data-align=\"left\">Mountain<\/th>\n<th data-align=\"left\">Elevation<\/th>\n<\/tr>\n<\/thead>\n<tbody>\n<tr valign=\"top\">\n<td data-align=\"left\">Mt. Elbert<\/td>\n<td data-align=\"left\"><img loading=\"lazy\" decoding=\"async\" src=\"https:\/\/opentextbc.ca\/introalgebra\/wp-content\/ql-cache\/quicklatex.com-5466658b96c9452133b7a1a6cf242b65_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"&#49;&#52;&#44;&#52;&#51;&#51;&#39;\" title=\"Rendered by QuickLaTeX.com\" height=\"18\" width=\"56\" style=\"vertical-align: -4px;\" \/><\/td>\n<\/tr>\n<tr valign=\"top\">\n<td data-align=\"left\">Mt. Massive<\/td>\n<td data-align=\"left\"><img loading=\"lazy\" decoding=\"async\" src=\"https:\/\/opentextbc.ca\/introalgebra\/wp-content\/ql-cache\/quicklatex.com-c36a4a2091037124a93e156d8454a3c0_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"&#49;&#52;&#44;&#52;&#50;&#49;&#39;\" title=\"Rendered by QuickLaTeX.com\" height=\"18\" width=\"56\" style=\"vertical-align: -4px;\" \/><\/td>\n<\/tr>\n<tr valign=\"top\">\n<td data-align=\"left\">Mt. Harvard<\/td>\n<td data-align=\"left\"><img loading=\"lazy\" decoding=\"async\" src=\"https:\/\/opentextbc.ca\/introalgebra\/wp-content\/ql-cache\/quicklatex.com-887bf19c923dffaeecf1efe8e3e78aaf_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"&#49;&#52;&#44;&#52;&#50;&#48;&#39;\" title=\"Rendered by QuickLaTeX.com\" height=\"18\" width=\"56\" style=\"vertical-align: -4px;\" \/><\/td>\n<\/tr>\n<tr valign=\"top\">\n<td data-align=\"left\">Blanca Peak<\/td>\n<td data-align=\"left\"><img loading=\"lazy\" decoding=\"async\" src=\"https:\/\/opentextbc.ca\/introalgebra\/wp-content\/ql-cache\/quicklatex.com-6efff3a3be667d5955a24637bbe9487c_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"&#49;&#52;&#44;&#51;&#52;&#53;&#39;\" title=\"Rendered by QuickLaTeX.com\" height=\"18\" width=\"56\" style=\"vertical-align: -4px;\" \/><\/td>\n<\/tr>\n<tr valign=\"top\">\n<td data-align=\"left\">La Plata Peak<\/td>\n<td data-align=\"left\"><img loading=\"lazy\" decoding=\"async\" src=\"https:\/\/opentextbc.ca\/introalgebra\/wp-content\/ql-cache\/quicklatex.com-73db37198984e574af31ae288fff7968_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"&#49;&#52;&#44;&#51;&#51;&#54;&#39;\" title=\"Rendered by QuickLaTeX.com\" height=\"18\" width=\"56\" style=\"vertical-align: -4px;\" \/><\/td>\n<\/tr>\n<tr valign=\"top\">\n<td data-align=\"left\">Uncompahgre Peak<\/td>\n<td data-align=\"left\"><img loading=\"lazy\" decoding=\"async\" src=\"https:\/\/opentextbc.ca\/introalgebra\/wp-content\/ql-cache\/quicklatex.com-69984c2a4623399fd7d523ce9a85a6fa_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"&#49;&#52;&#44;&#51;&#48;&#57;&#39;\" title=\"Rendered by QuickLaTeX.com\" height=\"18\" width=\"56\" style=\"vertical-align: -4px;\" \/><\/td>\n<\/tr>\n<tr valign=\"top\">\n<td data-align=\"left\">Crestone Peak<\/td>\n<td data-align=\"left\"><img loading=\"lazy\" decoding=\"async\" src=\"https:\/\/opentextbc.ca\/introalgebra\/wp-content\/ql-cache\/quicklatex.com-12799c00a3fb83f3e8645ff9e02e0f48_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"&#49;&#52;&#44;&#50;&#57;&#52;&#39;\" title=\"Rendered by QuickLaTeX.com\" height=\"18\" width=\"56\" style=\"vertical-align: -4px;\" \/><\/td>\n<\/tr>\n<tr valign=\"top\">\n<td data-align=\"left\">Mt. Lincoln<\/td>\n<td data-align=\"left\"><img loading=\"lazy\" decoding=\"async\" src=\"https:\/\/opentextbc.ca\/introalgebra\/wp-content\/ql-cache\/quicklatex.com-c34f528242b8986d4b6004915db1dbf8_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"&#49;&#52;&#44;&#50;&#56;&#54;&#39;\" title=\"Rendered by QuickLaTeX.com\" height=\"18\" width=\"56\" style=\"vertical-align: -4px;\" \/><\/td>\n<\/tr>\n<tr valign=\"top\">\n<td data-align=\"left\">Grays Peak<\/td>\n<td data-align=\"left\"><img loading=\"lazy\" decoding=\"async\" src=\"https:\/\/opentextbc.ca\/introalgebra\/wp-content\/ql-cache\/quicklatex.com-98dcb8eb35b1877824605fc517015c07_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"&#49;&#52;&#44;&#50;&#55;&#48;&#39;\" title=\"Rendered by QuickLaTeX.com\" height=\"18\" width=\"56\" style=\"vertical-align: -4px;\" \/><\/td>\n<\/tr>\n<tr valign=\"top\">\n<td data-align=\"left\">Mt. Antero<\/td>\n<td data-align=\"left\"><img loading=\"lazy\" decoding=\"async\" src=\"https:\/\/opentextbc.ca\/introalgebra\/wp-content\/ql-cache\/quicklatex.com-f32c47939f2f33257559729b2927c33b_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"&#49;&#52;&#44;&#50;&#54;&#57;&#39;\" title=\"Rendered by QuickLaTeX.com\" height=\"18\" width=\"56\" style=\"vertical-align: -4px;\" \/><\/td>\n<\/tr>\n<\/tbody>\n<\/table>\n<ol id=\"eip-id1168468729595\" class=\"circled\" type=\"a\">\n<li>Elevation of La Plata Peak____Elevation of Mt. Antero<\/li>\n<li>Elevation of Blanca Peak____Elevation of Mt. Elbert<\/li>\n<li>Elevation of Gray\u2019s Peak____Elevation of Mt. Lincoln<\/li>\n<li>Elevation of Mt. Massive____Elevation of Crestone Peak<\/li>\n<li>Elevation of Mt. Harvard____Elevation of Uncompahgre Peak<\/li>\n<\/ol>\n<\/td>\n<\/tr>\n<\/tbody>\n<\/table>\n<h2>Writing Exercises<\/h2>\n<table style=\"border-collapse: collapse; width: 100%;\">\n<tbody>\n<tr>\n<td style=\"width: 50%;\">67.Explain the difference between an expression and an equation.<\/td>\n<td style=\"width: 50%;\">68. Why is it important to use the order of operations to simplify an expression?<\/td>\n<\/tr>\n<\/tbody>\n<\/table>\n<h1>Answers<\/h1>\n<table style=\"border-collapse: collapse; width: 100%;\">\n<tbody>\n<tr>\n<td style=\"width: 33.3333%;\">1. 16 minus 9, the difference of sixteen and nine<\/td>\n<td style=\"width: 33.3333%;\">3. 5 times 6, the product of five and six<\/td>\n<td style=\"width: 33.3333%;\">5. 28 divided by 4, the quotient of twenty-eight and four<\/td>\n<\/tr>\n<tr>\n<td style=\"width: 33.3333%;\">7<em data-effect=\"italics\">. x<\/em> plus 8, the sum of <em data-effect=\"italics\">x<\/em> and eight<\/td>\n<td style=\"width: 33.3333%;\">9. 2 times 7, the product of two and seven<\/td>\n<td style=\"width: 33.3333%;\">11. fourteen is less than twenty-one<\/td>\n<\/tr>\n<tr>\n<td style=\"width: 33.3333%;\">13. thirty-six is greater than or equal to nineteen<\/td>\n<td style=\"width: 33.3333%;\">15. 3 times n equals 24, the product of three and n equals twenty-four<\/td>\n<td style=\"width: 33.3333%;\">17.<em data-effect=\"italics\"> y<\/em> minus 1 is greater than 6, the difference of <em data-effect=\"italics\">y<\/em> and one is greater than six<\/td>\n<\/tr>\n<tr>\n<td style=\"width: 33.3333%;\">19. 2 is less than or equal to 18 divided by 6; 2 is less than or equal to the quotient of eighteen and six<\/td>\n<td style=\"width: 33.3333%;\">21<em data-effect=\"italics\">. a<\/em> is not equal to 7 times 4, <em data-effect=\"italics\">a<\/em> is not equal to the product of seven and four<\/td>\n<td style=\"width: 33.3333%;\">23. equation<\/td>\n<\/tr>\n<tr>\n<td style=\"width: 33.3333%;\">25. expression<\/td>\n<td style=\"width: 33.3333%;\">27. expression<\/td>\n<td style=\"width: 33.3333%;\">29. equation<\/td>\n<\/tr>\n<tr>\n<td style=\"width: 33.3333%;\">31. 3<sup>7<\/sup><\/td>\n<td style=\"width: 33.3333%;\">33<em data-effect=\"italics\">. x<\/em><sup>5<\/sup><\/td>\n<td style=\"width: 33.3333%;\">35. 125<\/td>\n<\/tr>\n<tr>\n<td style=\"width: 33.3333%;\">37. 256<\/td>\n<td style=\"width: 33.3333%;\">39.<\/p>\n<p>a. 43<\/p>\n<p>b. 55<\/td>\n<td style=\"width: 33.3333%;\">41. 5<\/td>\n<\/tr>\n<tr>\n<td style=\"width: 33.3333%;\">43. 34<\/td>\n<td style=\"width: 33.3333%;\">45. 58<\/td>\n<td style=\"width: 33.3333%;\">47. 6<\/td>\n<\/tr>\n<tr>\n<td style=\"width: 33.3333%;\">49. 13<\/td>\n<td style=\"width: 33.3333%;\">51. 4<\/td>\n<td style=\"width: 33.3333%;\">53. 35<\/td>\n<\/tr>\n<tr>\n<td style=\"width: 33.3333%;\">55. 10<\/td>\n<td style=\"width: 33.3333%;\">57. 41<\/td>\n<td style=\"width: 33.3333%;\">59. 81<\/td>\n<\/tr>\n<tr>\n<td style=\"width: 33.3333%;\">61. 149<\/td>\n<td style=\"width: 33.3333%;\">63. 50<\/td>\n<td style=\"width: 33.3333%;\">65. a. &gt; b. <img loading=\"lazy\" decoding=\"async\" src=\"https:\/\/opentextbc.ca\/introalgebra\/wp-content\/ql-cache\/quicklatex.com-b8690b7efd237bfe32a6e92e3b699b96_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"&#61;\" title=\"Rendered by QuickLaTeX.com\" height=\"4\" width=\"13\" style=\"vertical-align: 2px;\" \/> c. &lt; d. &lt; e. &gt;<\/td>\n<\/tr>\n<tr>\n<td style=\"width: 33.3333%;\">67. Answer may vary.<\/td>\n<td style=\"width: 33.3333%;\"><\/td>\n<td style=\"width: 33.3333%;\"><\/td>\n<\/tr>\n<\/tbody>\n<\/table>\n<h1>Attributions<\/h1>\n<p>This chapter has been adapted from \u201cUse the Language of Algebra\u201d in <a href=\"https:\/\/openstax.org\/details\/books\/prealgebra-2e\"><em>Prealgebra<\/em><\/a> (OpenStax) by Lynn Marecek, MaryAnne Anthony-Smith, and Andrea Honeycutt Mathis, which is under a <a href=\"https:\/\/creativecommons.org\/licenses\/by\/4.0\/\">CC BY 4.0 Licence<\/a>. Adapted by Izabela Mazur. See the Copyright page for more information.<\/p>\n","protected":false},"author":90,"menu_order":2,"template":"","meta":{"pb_show_title":"on","pb_short_title":"","pb_subtitle":"","pb_authors":[],"pb_section_license":""},"chapter-type":[],"contributor":[],"license":[],"class_list":["post-101","chapter","type-chapter","status-publish","hentry"],"part":20,"_links":{"self":[{"href":"https:\/\/opentextbc.ca\/introalgebra\/wp-json\/pressbooks\/v2\/chapters\/101","targetHints":{"allow":["GET"]}}],"collection":[{"href":"https:\/\/opentextbc.ca\/introalgebra\/wp-json\/pressbooks\/v2\/chapters"}],"about":[{"href":"https:\/\/opentextbc.ca\/introalgebra\/wp-json\/wp\/v2\/types\/chapter"}],"author":[{"embeddable":true,"href":"https:\/\/opentextbc.ca\/introalgebra\/wp-json\/wp\/v2\/users\/90"}],"version-history":[{"count":1,"href":"https:\/\/opentextbc.ca\/introalgebra\/wp-json\/pressbooks\/v2\/chapters\/101\/revisions"}],"predecessor-version":[{"id":102,"href":"https:\/\/opentextbc.ca\/introalgebra\/wp-json\/pressbooks\/v2\/chapters\/101\/revisions\/102"}],"part":[{"href":"https:\/\/opentextbc.ca\/introalgebra\/wp-json\/pressbooks\/v2\/parts\/20"}],"metadata":[{"href":"https:\/\/opentextbc.ca\/introalgebra\/wp-json\/pressbooks\/v2\/chapters\/101\/metadata\/"}],"wp:attachment":[{"href":"https:\/\/opentextbc.ca\/introalgebra\/wp-json\/wp\/v2\/media?parent=101"}],"wp:term":[{"taxonomy":"chapter-type","embeddable":true,"href":"https:\/\/opentextbc.ca\/introalgebra\/wp-json\/pressbooks\/v2\/chapter-type?post=101"},{"taxonomy":"contributor","embeddable":true,"href":"https:\/\/opentextbc.ca\/introalgebra\/wp-json\/wp\/v2\/contributor?post=101"},{"taxonomy":"license","embeddable":true,"href":"https:\/\/opentextbc.ca\/introalgebra\/wp-json\/wp\/v2\/license?post=101"}],"curies":[{"name":"wp","href":"https:\/\/api.w.org\/{rel}","templated":true}]}}