{"id":246,"date":"2020-08-21T19:43:20","date_gmt":"2020-08-21T23:43:20","guid":{"rendered":"https:\/\/opentextbc.ca\/introalgebra\/chapter\/multiply-and-divide-integers\/"},"modified":"2021-03-24T10:52:10","modified_gmt":"2021-03-24T14:52:10","slug":"multiply-and-divide-integers","status":"publish","type":"chapter","link":"https:\/\/opentextbc.ca\/introalgebra\/chapter\/multiply-and-divide-integers\/","title":{"raw":"1.5 Multiply and Divide Integers","rendered":"1.5 Multiply and Divide Integers"},"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>Multiply integers<\/li>\n \t<li>Divide integers<\/li>\n \t<li>Simplify expressions with integers<\/li>\n \t<li>Evaluate variable expressions with integers<\/li>\n \t<li>Translate English phrases to algebraic expressions<\/li>\n \t<li>Use integers in applications<\/li>\n<\/ul>\n<\/div>\n<\/div>\n<h1>Multiply Integers<\/h1>\n<p id=\"fs-id1170654047593\">Since multiplication is mathematical shorthand for repeated addition, our model can easily be applied to show <span class=\"no-emphasis\" data-type=\"term\">multiplication<\/span> of <span class=\"no-emphasis\" data-type=\"term\">integers<\/span>. Let\u2019s look at this concrete model to see what patterns we notice. We will use the same examples that we used for addition and subtraction. Here, we will use the model just to help us discover the pattern.<\/p>\n<p id=\"fs-id1170654027710\">We remember that \\(a \\cdot b\\) means add <em data-effect=\"italics\">a<\/em>, <em data-effect=\"italics\">b<\/em> times. Here, we are using the model just to help us discover the pattern.<\/p>\n<span id=\"fs-id1170652629325\" data-type=\"media\" data-alt=\"Two images are shown side-by-side. The image on the left has the equation five times three at the top. Below this it reads \u201cadd 5, 3 times.\u201d Below this depicts three rows of blue counters, with five counters in each row. Under this, it says \u201c15 positives.\u201d Under thisis the equation\u201c5 times 3 equals 15.\u201d The image on the right reads \u201cnegative 5 times three. The three is in parentheses. Below this it reads, \u201cadd negative five, three times.\u201d Under this are fifteen red counters in three rows of five. Below this it reads\u201d \u201c15 negatives\u201d. Below this is the equation negative five times 3 equals negative 15.\u201d\"><img class=\"aligncenter\" src=\"https:\/\/opentextbc.ca\/accessibilitytoolkit\/wp-content\/uploads\/sites\/333\/2020\/08\/CNX_ElemAlg_Figure_01_04_001_img_new.jpg\" alt=\"Two images are shown side-by-side. The image on the left has the equation five times three at the top. Below this it reads \u201cadd 5, 3 times.\u201d Below this depicts three rows of blue counters, with five counters in each row. Under this, it says \u201c15 positives.\u201d Under thisis the equation\u201c5 times 3 equals 15.\u201d The image on the right reads \u201cnegative 5 times three. The three is in parentheses. Below this it reads, \u201cadd negative five, three times.\u201d Under this are fifteen red counters in three rows of five. Below this it reads\u201d \u201c15 negatives\u201d. Below this is the equation negative five times 3 equals negative 15.\u201d\" data-media-type=\"image\/jpeg\"><\/span>\n<p id=\"fs-id1170654235984\">The next two examples are more interesting.<\/p>\n<p id=\"fs-id1171791114068\">What does it mean to multiply 5 by \\(-3?\\) It means subtract 5, 3 times. Looking at subtraction as \u201ctaking away,\u201d it means to take away 5, 3 times. But there is nothing to take away, so we start by adding neutral pairs on the workspace. Then we take away 5 three times.<\/p>\n<span id=\"fs-id1170654116877\" data-type=\"media\" data-alt=\"This figure has two columns. In the top row, the left column contains the expression 5 times negative 3. This means take away 5, three times. Below this, there are three groups of five red negative counters, and below each group of red counters is an identical group of five blue positive counters. What are left are fifteen negatives, represented by 15 red counters. Underneath the counters is the equation 5 times negative 3 equals negative 15. In the top row, the right column contains the expression negative 5 times negative 3. This means take away negative 5, three times. Below this, there are three groups of five blue positive counters, and below each group of blue counters is an identical group of five red negative counters. What are left are fifteen positives, represented by 15 blue counters. Underneath the blue counters is the equation negative 5 times negative 3 equals 15.\"><img class=\"aligncenter\" src=\"https:\/\/opentextbc.ca\/accessibilitytoolkit\/wp-content\/uploads\/sites\/333\/2021\/03\/CNX_ElemAlg_Figure_01_04_002_img_new.jpg\" alt=\"This figure has two columns. In the top row, the left column contains the expression 5 times negative 3. This means take away 5, three times. Below this, there are three groups of five red negative counters, and below each group of red counters is an identical group of five blue positive counters. What are left are fifteen negatives, represented by 15 red counters. Underneath the counters is the equation 5 times negative 3 equals negative 15. In the top row, the right column contains the expression negative 5 times negative 3. This means take away negative 5, three times. Below this, there are three groups of five blue positive counters, and below each group of blue counters is an identical group of five red negative counters. What are left are fifteen positives, represented by 15 blue counters. Underneath the blue counters is the equation negative 5 times negative 3 equals 15.\" data-media-type=\"image\/jpeg\"><\/span>\n<p id=\"fs-id1170654009263\">In summary:<\/p>\n\n<div id=\"fs-id1170653916873\" class=\"unnumbered\" data-type=\"equation\" data-label=\"\">\\(\\begin{array}{cccccccc}\\hfill 5 \\cdot 3&amp; =\\hfill &amp; 15\\hfill &amp; &amp; &amp; \\hfill -5\\left(3\\right)&amp; =\\hfill &amp; -15\\hfill \\\\ \\hfill 5\\left(-3\\right)&amp; =\\hfill &amp; -15\\hfill &amp; &amp; &amp; \\hfill \\left(-5\\right)\\left(-3\\right)&amp; =\\hfill &amp; 15\\hfill \\end{array}\\)<\/div>\n<p id=\"fs-id1170653885621\">Notice that for multiplication of two signed numbers, when the:<\/p>\n\n<ul id=\"fs-id1166425881422\" data-bullet-style=\"bullet\">\n \t<li>signs are the <em data-effect=\"italics\">same<\/em>, the product is <em data-effect=\"italics\">positive<\/em>.<\/li>\n \t<li>signs are <em data-effect=\"italics\">different<\/em>, the product is <em data-effect=\"italics\">negative<\/em>.<\/li>\n<\/ul>\n<p id=\"fs-id1170653867968\">We\u2019ll put this all together in the chart below<\/p>\n\n<div class=\"textbox textbox--key-takeaways\"><header class=\"textbox__header\">\n<p class=\"textbox__title\">Multiplication of Signed Numbers<\/p>\n\n<\/header>\n<div class=\"textbox__content\">\n\nFor multiplication of two signed numbers:\n<table class=\"grid\" style=\"width: 100%;\" border=\"0\">\n<tbody>\n<tr valign=\"top\">\n<th data-valign=\"top\" data-align=\"left\">Same signs<\/th>\n<td><strong>Product<\/strong><\/td>\n<td><strong>Example<\/strong><\/td>\n<\/tr>\n<tr>\n<td>Two positives\nTwo negatives<\/td>\n<td>Positive\nPositive<\/td>\n<td>\\(\\begin{array}{ccc}\\hfill 7\\cdot4&amp; =\\hfill &amp; 28\\hfill \\\\ \\hfill -8\\left(-6\\right)&amp; =\\hfill &amp; 48\\hfill \\end{array}\\)<\/td>\n<\/tr>\n<\/tbody>\n<\/table>\n<table class=\"grid\" style=\"width: 100%;\" border=\"0\">\n<tbody>\n<tr>\n<td><strong>Different signs<\/strong><\/td>\n<td><strong>Product<\/strong><\/td>\n<td><strong>Example<\/strong><\/td>\n<\/tr>\n<tr>\n<td>Positive \\cdot negative\nNegative \\cdot positive<\/td>\n<td>Negative\nNegative<\/td>\n<td>\\(\\begin{array}{ccc}\\hfill 7\\left(-9\\right)&amp; =\\hfill &amp; -63\\hfill \\\\ \\hfill -5\\cdot10&amp; =\\hfill &amp; -50\\hfill \\end{array}\\)<\/td>\n<\/tr>\n<\/tbody>\n<\/table>\n<\/div>\n<\/div>\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-id1170654016481\" data-type=\"problem\">\n<p id=\"fs-id1170653756055\">Multiply: a) \\(-9\\cdot3\\) b) \\(-2\\left(-5\\right)\\) c) \\(4\\left(-8\\right)\\) d) \\(7\\cdot6\\).<\/p>\n\n<\/div>\n<div id=\"fs-id1170654013170\" 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-959\" summary=\".\">\n<tbody>\n<tr>\n<td>a)\nMultiply, noting that the signs are different so the product is negative.<\/td>\n<td>\\(\\begin{array}{c}-9\\cdot3\\\\ -27\\end{array}\\)<\/td>\n<\/tr>\n<tr>\n<td>b)\nMultiply, noting that the signs are the same so the product is positive.<\/td>\n<td>\\(\\begin{array}{c}-2\\left(-5\\right)\\\\ 10\\end{array}\\)<\/td>\n<\/tr>\n<tr>\n<td>c)\nMultiply, with different signs.<\/td>\n<td>\\(\\begin{array}{c}4\\left(-8\\right)\\\\ -32\\end{array}\\)<\/td>\n<\/tr>\n<tr>\n<td>d)\nMultiply, with same signs.<\/td>\n<td>\\(\\begin{array}{c}7\\cdot6\\\\ 42\\end{array}\\)<\/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-id1170654150864\" data-type=\"problem\">\n<p id=\"fs-id1170653870759\">Multiply: a) \\(-6\\cdot8\\) b) \\(-4\\left(-7\\right)\\) c) \\(9\\left(-7\\right)\\) d) \\(5\\cdot12\\).<\/p>\n\n<\/div>\n<div id=\"fs-id1170654034104\" data-type=\"solution\"><details><summary>Show answer<\/summary>\n<p id=\"fs-id1170653885313\">a)\\(-48\\) b) 28 c) \\(-63\\) d) 60<\/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 1.2<\/p>\n\n<\/header>\n<div class=\"textbox__content\">\n<div id=\"fs-id1170654016412\" data-type=\"problem\">\n<p id=\"fs-id1170654116452\">Multiply: a) \\(-8\\cdot7\\) b) \\(-6\\left(-9\\right)\\) c) \\(7\\left(-4\\right)\\) d) \\(3\\cdot13\\).<\/p>\n\n<\/div>\n<div id=\"fs-id1170653741029\" data-type=\"solution\"><details><summary>Show answer<\/summary>\n<p id=\"fs-id1170653795701\">a)\\(-56\\) b) 54 c) \\(-28\\) d) 39<\/p>\n\n<\/details><\/div>\n<\/div>\n<\/div>\n<p id=\"fs-id1170654150913\">When we multiply a number by 1, the result is the same number. What happens when we multiply a number by \\(-1\\)? Let\u2019s multiply a positive number and then a negative number by \\(-1\\) to see what we get.<\/p>\n\\(\\begin{array}{ccccccc}&amp; &amp; &amp; \\hfill -1\\cdot 4\\hfill &amp; &amp; &amp; \\hfill -1\\left(-3\\right)\\hfill \\\\ \\text{Multiply.}\\hfill &amp; &amp; &amp; \\hfill -4\\hfill &amp; &amp; &amp; \\hfill 3\\hfill \\\\ &amp; &amp; &amp; \\hfill -4\\phantom{\\rule{0.2em}{0ex}}\\text{is the opposite of}\\phantom{\\rule{0.2em}{0ex}}4.\\hfill &amp; &amp; &amp; \\hfill 3\\phantom{\\rule{0.2em}{0ex}}\\text{is the opposite of}\\phantom{\\rule{0.2em}{0ex}}-3.\\hfill \\end{array}\\)\n<p id=\"fs-id1170652622975\">Each time we multiply a number by \\(-1\\), we get its opposite!<\/p>\n\n<div id=\"fs-id1170653776943\" data-type=\"note\">\n<div data-type=\"title\">\n<div class=\"textbox textbox--key-takeaways\"><header class=\"textbox__header\">\n<p class=\"textbox__title\">Multiplication by \\(-1\\)<\/p>\n\n<\/header>\n<div class=\"textbox__content\">\n\n\\(-1a=\\text{-}a\\)\n\nMultiplying a number by \\(-1\\) gives its opposite.\n\n<\/div>\n<\/div>\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-id1170654068942\" data-type=\"problem\">\n<p id=\"fs-id1170654036219\">Multiply: a) \\(-1\\cdot7\\) b) \\(-1\\left(-11\\right)\\).<\/p>\n\n<\/div>\n<div id=\"fs-id1170653910210\" data-type=\"solution\">\n<div data-type=\"title\"><\/div>\n<div data-type=\"title\"><strong>Solution<\/strong><\/div>\n<table id=\"eip-228\" summary=\".\">\n<tbody>\n<tr>\n<td>a)\nMultiply, noting that the signs are different so the product is negative.<\/td>\n<td>\\(\\begin{array}{c}-1\\cdot7\\\\ -7\\\\ -7\\phantom{\\rule{0.2em}{0ex}}\\text{is the opposite of}\\phantom{\\rule{0.2em}{0ex}}7.\\end{array}\\)<\/td>\n<\/tr>\n<tr>\n<td>b)\nMultiply, noting that the signs are the same so the product is positive.<\/td>\n<td>\\(\\begin{array}{c}-1\\left(-11\\right)\\\\ 11\\\\ 11\\phantom{\\rule{0.2em}{0ex}}\\text{is the opposite of}\\phantom{\\rule{0.2em}{0ex}}-11.\\end{array}\\)<\/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-id1170654073784\" data-type=\"problem\">\n<p id=\"fs-id1170653851085\">Multiply: a) \\(-1\\cdot9\\) b) \\(-1 \\cdot \\left(-17\\right)\\).<\/p>\n\n<\/div>\n<div id=\"fs-id1170654014381\" data-type=\"solution\"><details><summary>Show answer<\/summary>\n<p id=\"fs-id1170654231240\">a)\\(-9\\) b) 17<\/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 2.2<\/p>\n\n<\/header>\n<div class=\"textbox__content\">\n<div id=\"fs-id1170654047261\" data-type=\"problem\">\n<p id=\"fs-id1170653804423\">Multiply: a) \\(-1\\cdot8\\) b) \\(-1 \\cdot \\left(-16\\right)\\).<\/p>\n\n<\/div>\n<div id=\"fs-id1170654015023\" data-type=\"solution\"><details><summary>Show answer<\/summary>\n<p id=\"fs-id1170653799135\">a)\\(-8\\) b) 16<\/p>\n\n<\/details><\/div>\n<\/div>\n<\/div>\n<\/div>\n<h1>Divide Integers<\/h1>\n<p id=\"fs-id1170654029961\">What about <span class=\"no-emphasis\" data-type=\"term\">division<\/span>? Division is the inverse operation of multiplication. So, \\(15\\div 3=5\\) because \\(5\\cdot3=15\\). In words, this expression says that 15 can be divided into three groups of five each because adding five three times gives 15. Look at some examples of multiplying integers, to figure out the rules for dividing integers.<\/p>\n\\(\\begin{array}{cccccccccccccc}\\hfill 5\\cdot3&amp; =\\hfill &amp; 15\\phantom{\\rule{0.2em}{0ex}}\\text{so}\\phantom{\\rule{0.2em}{0ex}}15\\div 3\\hfill &amp; =\\hfill &amp; 5\\hfill &amp; &amp; &amp; &amp; &amp; \\hfill -5\\left(3\\right)&amp; =\\hfill &amp; -15\\phantom{\\rule{0.2em}{0ex}}\\text{so}\\phantom{\\rule{0.2em}{0ex}}-15\\div3\\hfill &amp; =\\hfill &amp; -5\\hfill \\\\ \\hfill \\left(-5\\right)\\left(-3\\right)&amp; =\\hfill &amp; 15\\phantom{\\rule{0.2em}{0ex}}\\text{so}\\phantom{\\rule{0.2em}{0ex}}15\\div \\left(-3\\right)\\hfill &amp; =\\hfill &amp; -5\\hfill &amp; &amp; &amp; &amp; &amp; \\hfill 5\\left(-3\\right)&amp; =\\hfill &amp; -15\\phantom{\\rule{0.2em}{0ex}}\\text{so}\\phantom{\\rule{0.2em}{0ex}}-15\\div \\left(-3\\right)\\hfill &amp; =\\hfill &amp; 5\\hfill \\end{array}\\)\n<p id=\"fs-id1170654116562\">Division follows the same rules as multiplication!<\/p>\n<p id=\"fs-id1170653915002\">For division of two signed numbers, when the:<\/p>\n\n<ul id=\"fs-id1166426287557\" data-bullet-style=\"bullet\">\n \t<li>signs are the <em data-effect=\"italics\">same<\/em>, the quotient is <em data-effect=\"italics\">positive<\/em>.<\/li>\n \t<li>signs are <em data-effect=\"italics\">different<\/em>, the quotient is <em data-effect=\"italics\">negative<\/em>.<\/li>\n<\/ul>\n<p id=\"fs-id1170653869100\">And remember that we can always check the answer of a division problem by multiplying.<\/p>\n\n<div id=\"fs-id1170654015283\" data-type=\"note\">\n<div data-type=\"title\">\n<div class=\"textbox textbox--key-takeaways\"><header class=\"textbox__header\">\n<p class=\"textbox__title\">Multiplication and Division of Signed Numbers<\/p>\n\n<\/header>\n<div class=\"textbox__content\">\n<p id=\"fs-id1170653774421\">For multiplication and division of two signed numbers:<\/p>\n\n<ul id=\"fs-id1166425927232\" data-bullet-style=\"bullet\">\n \t<li>If the signs are the same, the result is positive.<\/li>\n \t<li>If the signs are different, the result is negative.<\/li>\n<\/ul>\n<table id=\"fs-id1170654154997\" style=\"width: 100%;\" summary=\"No Summary\">\n<thead>\n<tr valign=\"top\">\n<th style=\"width: 50%;\" scope=\"col\" data-valign=\"top\" data-align=\"left\">Same signs<\/th>\n<th style=\"width: 50%;\" scope=\"col\" data-valign=\"top\" data-align=\"left\">Result<\/th>\n<\/tr>\n<\/thead>\n<tbody>\n<tr valign=\"top\">\n<td style=\"width: 50%;\" data-valign=\"top\" data-align=\"left\">Two positives<\/td>\n<td style=\"width: 50%;\" data-valign=\"top\" data-align=\"left\">Positive<\/td>\n<\/tr>\n<tr>\n<td style=\"width: 50%;\">Two negatives<\/td>\n<td style=\"width: 50%;\">Positive<\/td>\n<\/tr>\n<\/tbody>\n<\/table>\nIf the signs are the same, the result is positive.\n<table id=\"fs-id1170653799921\" style=\"width: 100%; height: 48px;\" summary=\"No Summary\">\n<thead>\n<tr style=\"height: 16px;\" valign=\"top\">\n<th style=\"height: 16px; width: 50%;\" scope=\"col\" data-valign=\"top\" data-align=\"left\">Different signs<\/th>\n<th style=\"height: 16px; width: 50%;\" scope=\"col\" data-valign=\"top\" data-align=\"left\">Result<\/th>\n<\/tr>\n<\/thead>\n<tbody>\n<tr style=\"height: 16px;\" valign=\"top\">\n<td style=\"height: 16px; width: 50%;\" data-valign=\"top\" data-align=\"left\">Positive and negative<\/td>\n<td style=\"height: 16px; width: 50%;\" data-valign=\"top\" data-align=\"left\">Negative<\/td>\n<\/tr>\n<tr style=\"height: 16px;\">\n<td style=\"height: 16px; width: 50%;\">Negative and positive<\/td>\n<td style=\"height: 16px; width: 50%;\">Negative<\/td>\n<\/tr>\n<\/tbody>\n<\/table>\nIf the signs are different, the result is negative.\n\n<\/div>\n<\/div>\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-id1170652618826\" data-type=\"problem\">\n<p id=\"fs-id1170654008734\">Divide: a) \\(-27\\div 3\\) b) \\(-100\\div \\left(-4\\right)\\).<\/p>\n\n<\/div>\n<div id=\"fs-id1170654212229\" data-type=\"solution\">\n<div data-type=\"title\"><\/div>\n<div data-type=\"title\"><strong>Solution<\/strong><\/div>\n<table id=\"eip-762\" summary=\".\">\n<tbody>\n<tr>\n<td>a)\nDivide. With different signs, the quotient is negative.<\/td>\n<td>\\(\\begin{array}{c}-27\\div 3\\\\ -9\\end{array}\\)<\/td>\n<\/tr>\n<tr>\n<td>b)\nDivide. With signs that are the same, the quotient is positive.<\/td>\n<td>\\(\\begin{array}{c}-100\\div\\left(-4\\right)\\\\ 25\\end{array}\\)<\/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-id1170653797425\" data-type=\"problem\">\n<p id=\"fs-id1170653906270\">Divide: a) \\(-42\\div 6\\) b) \\(-117\\div\\left(-3\\right)\\).<\/p>\n\n<\/div>\n<div id=\"fs-id1170654149901\" data-type=\"solution\"><details><summary>Show answer<\/summary>\n<p id=\"fs-id1170654047662\">a)\\(-7\\) b) 39<\/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 3.2<\/p>\n\n<\/header>\n<div class=\"textbox__content\">\n<div id=\"fs-id1170654233461\" data-type=\"problem\">\n<p id=\"fs-id1170652622579\">Divide: a) \\(-63\\div 7\\) b) \\(-115\\div\\left(-5\\right)\\).<\/p>\n\n<\/div>\n<div id=\"fs-id1170653897540\" data-type=\"solution\"><details><summary>Show answer<\/summary>\n<p id=\"fs-id1170653910431\">a)\\(-9\\) b) 23<\/p>\n\n<\/details><\/div>\n<\/div>\n<\/div>\n<\/div>\n<\/div>\n<h1>Simplify Expressions with Integers<\/h1>\n<p id=\"fs-id1170653741550\">What happens when there are more than two numbers in an expression? The order of operations still applies when negatives are included. Remember My Dear Aunt Sally?<\/p>\n<p id=\"fs-id1170653790201\">Let\u2019s try some examples. We\u2019ll simplify expressions that use all four operations with integers\u2014addition, subtraction, multiplication, and division. Remember to follow the order of operations.<\/p>\n\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 id=\"fs-id1170654066443\" data-type=\"problem\">\n<p id=\"fs-id1170653768124\">Simplify: \\(7\\left(-2\\right)+4\\left(-7\\right)-6\\).<\/p>\n\n<\/div>\n<div id=\"fs-id1170652623765\" 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-431\" summary=\".\">\n<tbody>\n<tr>\n<td><\/td>\n<td>\\(7\\left(-2\\right)+4\\left(-7\\right)-6\\)<\/td>\n<\/tr>\n<tr>\n<td>Multiply first.<\/td>\n<td>\\(-14+\\left(-28\\right)-6\\)<\/td>\n<\/tr>\n<tr>\n<td>Add.<\/td>\n<td>\\(-42-6\\)<\/td>\n<\/tr>\n<tr>\n<td>Subtract.<\/td>\n<td>\\(-48\\)<\/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-id1170652620764\" data-type=\"problem\">\n<p id=\"fs-id1170653875298\">Simplify: \\(8\\left(-3\\right)+5\\left(-7\\right)-4\\).<\/p>\n\n<\/div>\n<div id=\"fs-id1170654149857\" data-type=\"solution\"><details><summary>Show answer<\/summary>\n<p id=\"fs-id1170654149859\">\\(-63\\)<\/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 4.2<\/p>\n\n<\/header>\n<div class=\"textbox__content\">\n<div id=\"fs-id1170652630283\" data-type=\"problem\">\n<p id=\"fs-id1170653880078\">Simplify: \\(9\\left(-3\\right)+7\\left(-8\\right)-1\\).<\/p>\n\n<\/div>\n<div id=\"fs-id1170652620232\" data-type=\"solution\"><details><summary>Show answer<\/summary>\n<p id=\"fs-id1170654286008\">\\(-84\\)<\/p>\n\n<\/details><\/div>\n<\/div>\n<\/div>\n<div id=\"fs-id1170653871378\" class=\"try\" data-type=\"note\">\n<div id=\"fs-id1170652630281\" data-type=\"exercise\">\n<div id=\"fs-id1170652620232\" data-type=\"solution\">\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-id1170652619970\" data-type=\"problem\">\n<p id=\"fs-id1170653761875\">Simplify: a) \\({\\left(-2\\right)}^{4}\\) b) \\(\\text{-}{2}^{4}\\).<\/p>\n\n<\/div>\n<div id=\"fs-id1170654237484\" 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-217\" summary=\".\">\n<tbody>\n<tr>\n<td>a)\nWrite in expanded form.\nMultiply.\nMultiply.\nMultiply.<\/td>\n<td>\\(\\begin{array}{c}{\\left(-2\\right)}^{4}\\\\ \\left(-2\\right)\\left(-2\\right)\\left(-2\\right)\\left(-2\\right)\\\\ 4\\left(-2\\right)\\left(-2\\right)\\\\ -8\\left(-2\\right)\\\\ 16\\end{array}\\)<\/td>\n<\/tr>\n<tr>\n<td>b)\nWrite in expanded form. We are asked to find the opposite of\\(\\phantom{\\rule{0.2em}{0ex}}{2}^{4}\\).\nMultiply.\nMultiply.\nMultiply.<\/td>\n<td>\\(\\begin{array}{c}\\text{-}{2}^{4}\\\\ \\text{-}\\left(2\\cdot2\\cdot2\\cdot2\\right)\\\\ \\text{-}\\left(4\\cdot2\\cdot2\\right)\\\\ \\text{-}\\left(8\\cdot2\\right)\\\\ 16\\end{array}\\)<\/td>\n<\/tr>\n<\/tbody>\n<\/table>\n<p id=\"fs-id1170653737864\">Notice the difference in parts a) and b). In part a), the exponent means to raise what is in the parentheses, the \\(\\left(-2\\right)\\) to the \\({4}^{\\text{th}}\\) power. In part b), the exponent means to raise just the 2 to the \\({4}^{\\text{th}}\\) power and then take the opposite.<\/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 5.1<\/p>\n\n<\/header>\n<div class=\"textbox__content\">\n<div id=\"fs-id1170652622523\" data-type=\"problem\">\n<p id=\"fs-id1170653790279\">Simplify: a) \\({\\left(-3\\right)}^{4}\\) b) \\(\\text{-}{3}^{4}\\).<\/p>\n\n<\/div>\n<div id=\"fs-id1170654230619\" data-type=\"solution\"><details><summary>Show answer<\/summary>\n<p id=\"fs-id1170654230621\">a) 81 b) \\(-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 5.2<\/p>\n\n<\/header>\n<div class=\"textbox__content\">\n<div id=\"fs-id1170653875785\" data-type=\"problem\">\n<p id=\"fs-id1170654200505\">Simplify: a) \\({\\left(-7\\right)}^{2}\\) b) \\(\\text{-}{7}^{2}\\).<\/p>\n\n<\/div>\n<div id=\"fs-id1170654154361\" data-type=\"solution\"><details><summary>Show answer<\/summary>\n<p id=\"fs-id1170654154363\">a) 49 b) \\(-49\\)<\/p>\n\n<\/details><\/div>\n<\/div>\n<\/div>\n<\/div>\n<\/div>\n<\/div>\n<p id=\"fs-id1170653904816\">The next example reminds us to simplify inside parentheses first.<\/p>\n\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-id1170652622789\" data-type=\"problem\">\n<p id=\"fs-id1170652622791\">Simplify: \\(12-3\\left(9-12\\right)\\).<\/p>\n\n<\/div>\n<div id=\"fs-id1170653905533\" 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-138\" summary=\".\">\n<tbody>\n<tr>\n<td><\/td>\n<td>\\(12-3\\left(9-12\\right)\\)<\/td>\n<\/tr>\n<tr>\n<td>Subtract in parentheses first.<\/td>\n<td>\\(12-3\\left(-3\\right)\\)<\/td>\n<\/tr>\n<tr>\n<td>Multiply.<\/td>\n<td>\\(12-\\left(-9\\right)\\)<\/td>\n<\/tr>\n<tr>\n<td>Subtract.<\/td>\n<td>\\(21\\)<\/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 6.1<\/p>\n\n<\/header>\n<div class=\"textbox__content\">\n<div id=\"fs-id1170654134940\" data-type=\"problem\">\n<p id=\"fs-id1170654134942\">Simplify: \\(17-4\\left(8-11\\right)\\).<\/p>\n\n<\/div>\n<div id=\"fs-id1170652622244\" data-type=\"solution\"><details><summary>Show answer<\/summary>\n<p id=\"fs-id1170654150070\">29<\/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 6.2<\/p>\n\n<\/header>\n<div class=\"textbox__content\">\n<div id=\"fs-id1170652631542\" data-type=\"problem\">\n<p id=\"fs-id1170654239598\">Simplify: \\(16-6\\left(7-13\\right)\\).<\/p>\n\n<\/div>\n<div id=\"fs-id1170653874260\" data-type=\"solution\"><details><summary>Show answer<\/summary>\n<p id=\"fs-id1170653874262\">52<\/p>\n\n<\/details><\/div>\n<\/div>\n<\/div>\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 id=\"fs-id1170652624014\" data-type=\"problem\">\n<p id=\"fs-id1170652624016\">Simplify: \\(8\\left(-9\\right)\\div{\\left(-2\\right)}^{3}\\).<\/p>\n\n<\/div>\n<div id=\"fs-id1170653850514\" 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-410\" style=\"width: 100%;\" summary=\".\">\n<tbody>\n<tr>\n<td><\/td>\n<td>\\(8\\left(-9\\right)\\div{\\left(-2\\right)}^{3}\\)<\/td>\n<\/tr>\n<tr>\n<td>Exponents first.<\/td>\n<td>\\(8\\left(-9\\right)\\div\\left(-8\\right)\\)<\/td>\n<\/tr>\n<tr>\n<td>Multiply.<\/td>\n<td>\\(-72\\div \\left(-8\\right)\\)<\/td>\n<\/tr>\n<tr>\n<td>Divide.<\/td>\n<td>\\(9\\)<\/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-id1170652621179\" data-type=\"problem\">\n<p id=\"fs-id1170652621181\">Simplify: \\(12\\left(-9\\right)\\div{\\left(-3\\right)}^{3}\\).<\/p>\n\n<\/div>\n<div id=\"fs-id1170653797293\" data-type=\"solution\"><details><summary>Show answer<\/summary>\n<p id=\"fs-id1170653797295\">4<\/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 7.2<\/p>\n\n<\/header>\n<div class=\"textbox__content\">\n<div id=\"fs-id1170654071433\" data-type=\"problem\">\n<p id=\"fs-id1170654071435\">Simplify: \\(18\\left(-4\\right)\\div{\\left(-2\\right)}^{3}\\).<\/p>\n\n<\/div>\n<div id=\"fs-id1170652622271\" data-type=\"solution\"><details><summary>Show answer<\/summary>\n<p id=\"fs-id1170652622274\">9<\/p>\n\n<\/details><\/div>\n<\/div>\n<\/div>\n<div id=\"fs-id1170654156593\" class=\"try\" data-type=\"note\">\n<div id=\"fs-id1170652621176\" data-type=\"exercise\">\n<div id=\"fs-id1170652621179\" data-type=\"problem\">\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-id1170654047271\" data-type=\"problem\">\n<p id=\"fs-id1170654047273\">Simplify: \\(-30\\div 2+\\left(-3\\right)\\left(-7\\right)\\).<\/p>\n\n<\/div>\n<div id=\"fs-id1170654233306\" data-type=\"solution\">\n<div data-type=\"title\"><\/div>\n<div data-type=\"title\"><strong>Solution<\/strong><\/div>\n<table id=\"eip-343\" summary=\".\">\n<tbody>\n<tr>\n<td><\/td>\n<td>\\(-30\\div 2+\\left(-3\\right)\\left(-7\\right)\\)<\/td>\n<\/tr>\n<tr>\n<td>Multiply and divide left to right, so divide first.<\/td>\n<td>\\(-15+\\left(-3\\right)\\left(-7\\right)\\)<\/td>\n<\/tr>\n<tr>\n<td>Multiply.<\/td>\n<td>\\(-15+21\\)<\/td>\n<\/tr>\n<tr>\n<td>Add.<\/td>\n<td>\\(6\\)<\/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-id1170654154229\" data-type=\"problem\">\n<p id=\"fs-id1170654154231\">Simplify: \\(-27\\div 3+\\left(-5\\right)\\left(-6\\right)\\).<\/p>\n\n<\/div>\n<div id=\"fs-id1170654079166\" data-type=\"solution\"><details><summary>Show answer<\/summary>\n<p id=\"fs-id1170654079169\">21<\/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 8.2<\/p>\n\n<\/header>\n<div class=\"textbox__content\">\n<div id=\"fs-id1170652622504\" data-type=\"problem\">\n<p id=\"fs-id1170653742352\">Simplify: \\(-32\\div 4+\\left(-2\\right)\\left(-7\\right)\\).<\/p>\n\n<\/div>\n<div id=\"fs-id1170652630484\" data-type=\"solution\"><details><summary>Show answer<\/summary>\n<p id=\"fs-id1170654011846\">6<\/p>\n\n<\/details><\/div>\n<\/div>\n<\/div>\n<\/div>\n<\/div>\n<\/div>\n<h1>Evaluate Variable Expressions with Integers<\/h1>\n<p id=\"fs-id1170653874683\">Remember that to evaluate an expression means to substitute a number for the variable in the expression. Now we can use negative numbers as well as positive numbers.<\/p>\n\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-id1170654236884\" data-type=\"problem\">\n<p id=\"fs-id1170654236886\">When \\(n=-5\\), evaluate: a) \\(n+1\\) b) \\(\\text{-}n+1\\).<\/p>\n\n<\/div>\n<div id=\"fs-id1170653907935\" 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-id1166421949103\">a)<\/p>\n\n<table id=\"fs-id1167836601446\" class=\"unnumbered unstyled\" summary=\"This is a solution table with two columns. The top of the right column has the equation \u201cn plus 1.\u201d The next row down on the left reads, \u201cSubstitute negative 5 for n\u201d. The negative five is in red. Next to this in the right column, it has the equation \u201cnegative 5 plus 1.\u201d The next row down reads, \u201csimplify.\u201d Next to this in the right column is \u201cnegative 4\u201d.\" data-label=\"\">\n<tbody>\n<tr>\n<td><\/td>\n<td><span id=\"fs-id1167836341026\" data-type=\"media\" data-alt=\".\"><img src=\"https:\/\/opentextbc.ca\/accessibilitytoolkit\/wp-content\/uploads\/sites\/333\/2021\/03\/CNX_ElemAlg_Figure_01_04_003b_img_new.jpg\" alt=\".\" data-media-type=\"image\/png\"><\/span><\/td>\n<\/tr>\n<tr>\n<td><span id=\"fs-id1167836692265\" data-type=\"media\" data-alt=\".\"><img src=\"https:\/\/opentextbc.ca\/accessibilitytoolkit\/wp-content\/uploads\/sites\/333\/2021\/03\/CNX_ElemAlg_Figure_01_04_003a_img_new.jpg\" alt=\".\" data-media-type=\"image\/png\"><\/span><\/td>\n<td><span id=\"fs-id1167836606199\" data-type=\"media\" data-alt=\".\"><img src=\"https:\/\/opentextbc.ca\/accessibilitytoolkit\/wp-content\/uploads\/sites\/333\/2021\/03\/CNX_ElemAlg_Figure_01_04_003c_img_new.jpg\" alt=\".\" data-media-type=\"image\/png\"><\/span><\/td>\n<\/tr>\n<tr>\n<td>Simplify.<\/td>\n<td>\u22124<\/td>\n<\/tr>\n<\/tbody>\n<\/table>\n<p id=\"fs-id1167833329031\">b)<\/p>\n\n<table id=\"eip-id1169751873718\" class=\"unnumbered unstyled\" summary=\"This is a solution table with two columns. The top of the right column has the equation \u201cnegative n plus 1.\u201d The next row down on the left reads, \u201cSubstitute negative 5 for n\u201d. The negative five is in red. Next to this in the right column, it has a negative sign outside of parentheses. Negative 5 is in parentheses, then plus 1.\u201d The next row down reads, \u201csimplify.\u201d Next to this in the right column is the equation five plus one. The next row down says \u201cAdd\u201d. Next to this in the right column is \u201c6\u201d.\" data-label=\"\">\n<tbody>\n<tr>\n<td><\/td>\n<td><span id=\"eip-id1169754187288\" data-type=\"media\" data-alt=\".\"><img src=\"https:\/\/opentextbc.ca\/accessibilitytoolkit\/wp-content\/uploads\/sites\/333\/2021\/03\/CNX_ElemAlg_Figure_01_04_004b_img_new.jpg\" alt=\".\" data-media-type=\"image\/png\"><\/span><\/td>\n<\/tr>\n<tr>\n<td><span id=\"eip-id1169754188317\" data-type=\"media\" data-alt=\".\"><img src=\"https:\/\/opentextbc.ca\/accessibilitytoolkit\/wp-content\/uploads\/sites\/333\/2021\/03\/CNX_ElemAlg_Figure_01_04_004a_img_new.jpg\" alt=\".\" data-media-type=\"image\/png\"><\/span><\/td>\n<td><span id=\"eip-id1169754188329\" data-type=\"media\" data-alt=\".\"><img src=\"https:\/\/opentextbc.ca\/accessibilitytoolkit\/wp-content\/uploads\/sites\/333\/2021\/03\/CNX_ElemAlg_Figure_01_04_004c_img_new.jpg\" alt=\".\" data-media-type=\"image\/png\"><\/span><\/td>\n<\/tr>\n<tr>\n<td>Simplify.<\/td>\n<td><span id=\"eip-id1169754018353\" data-type=\"media\" data-alt=\".\"><img src=\"https:\/\/opentextbc.ca\/accessibilitytoolkit\/wp-content\/uploads\/sites\/333\/2021\/03\/CNX_ElemAlg_Figure_01_04_004d_img_new.jpg\" alt=\".\" data-media-type=\"image\/png\"><\/span><\/td>\n<\/tr>\n<tr>\n<td>Add.<\/td>\n<td data-align=\"center\">6<\/td>\n<\/tr>\n<\/tbody>\n<\/table>\n<\/div>\n<\/div>\n<\/div>\n<div id=\"fs-id1170652631263\" class=\"try\" data-type=\"note\">\n<div id=\"fs-id1170652631266\" data-type=\"exercise\">\n<div id=\"fs-id1170653797954\" data-type=\"problem\">\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-id1170653797954\" data-type=\"problem\">\n<p id=\"fs-id1170653797956\">When \\(n=-8\\), evaluate a) \\(n+2\\) b) \\(\\text{-}n+2\\).<\/p>\n\n<\/div>\n<div id=\"fs-id1170652631156\" data-type=\"solution\"><details><summary>Show answer<\/summary>\n<p id=\"fs-id1170652631158\">a)\\(-6\\) b) 10<\/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-id1170653799901\" data-type=\"problem\">\n<p id=\"fs-id1170653799903\">When \\(y=-9\\), evaluate a) \\(y+8\\) b) \\(\\text{-}y+8\\).<\/p>\n\n<\/div>\n<div id=\"fs-id1170654286534\" data-type=\"solution\"><details><summary>Show answer<\/summary>\n<p id=\"fs-id1170654286536\">a)\\(-1\\) b) 17<\/p>\n\n<\/details><\/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-id1170654212321\" data-type=\"problem\">\n<p id=\"fs-id1170654212324\">Evaluate \\({\\left(x+y\\right)}^{2}\\) when \\(x=-18\\) and \\(y=24\\).<\/p>\n\n<\/div>\n<div id=\"fs-id1170653800718\" data-type=\"solution\">\n<div data-type=\"title\"><\/div>\n<div data-type=\"title\"><strong>Solution<\/strong><\/div>\n<table id=\"eip-id1169751902542\" class=\"unnumbered unstyled\" style=\"height: 72px;\" summary=\"This is a solution table with two columns. The top of the right column has the equation \u201cx plus y in parentheses squared.\u201d The next row down on the left reads, \u201cSubstitute negative eighteen for \u201cx\u201d and 24 for \u201cy\u201d. The negative 18 is in red, and \u201c24\u201d is in blue. Next to this in the right column, it has the equation negative eighteen plus 24\u201d in parentheses squared. The next row down reads, \u201cadd inside the parentheses.\u201d Next to this in the right column is the equation \u201c6\u201d in parentheses squared. The next row down says \u201cSimplify\u201d. Next to this in the right column is \u201c36\u201d.\" data-label=\"\">\n<tbody>\n<tr style=\"height: 19px;\">\n<td style=\"height: 19px; width: 458.646px;\"><\/td>\n<td style=\"height: 19px; width: 251.979px;\" data-align=\"center\"><span id=\"eip-id1169754030720\" data-type=\"media\" data-alt=\".\"><img src=\"https:\/\/opentextbc.ca\/accessibilitytoolkit\/wp-content\/uploads\/sites\/333\/2021\/03\/CNX_ElemAlg_Figure_01_04_005b_img_new.jpg\" alt=\".\" data-media-type=\"image\/png\"><\/span><\/td>\n<\/tr>\n<tr style=\"height: 23px;\">\n<td style=\"height: 23px; width: 458.646px;\"><span id=\"eip-id1169752191035\" data-type=\"media\" data-alt=\".\"><img src=\"https:\/\/opentextbc.ca\/accessibilitytoolkit\/wp-content\/uploads\/sites\/333\/2021\/03\/CNX_ElemAlg_Figure_01_04_005a_img_new.jpg\" alt=\".\" data-media-type=\"image\/png\"><\/span><\/td>\n<td style=\"height: 23px; width: 251.979px;\" data-align=\"center\">\\({\\left(-18+24\\right)}^{2}\\)<\/td>\n<\/tr>\n<tr style=\"height: 15px;\">\n<td style=\"height: 15px; width: 458.646px;\">Add inside parenthesis.<\/td>\n<td style=\"height: 15px; width: 251.979px;\" data-align=\"center\">(6)<sup>2<\/sup><\/td>\n<\/tr>\n<tr style=\"height: 15px;\">\n<td style=\"height: 15px; width: 458.646px;\">Simplify.<\/td>\n<td style=\"height: 15px; width: 251.979px;\" data-align=\"center\">36<\/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-id1170652630296\" data-type=\"problem\">\n<p id=\"fs-id1170652630298\">Evaluate \\({\\left(x+y\\right)}^{2}\\) when \\(x=-15\\) and \\(y=29\\).<\/p>\n\n<\/div>\n<div id=\"fs-id1170654285387\" data-type=\"solution\"><details><summary>Show answer<\/summary>\n<p id=\"fs-id1170654061358\">196<\/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-id1170653791775\" data-type=\"problem\">\n<p id=\"fs-id1170653791777\">Evaluate \\({\\left(x+y\\right)}^{3}\\) when \\(x=-8\\) and \\(y=10\\).<\/p>\n\n<\/div>\n<div id=\"fs-id1170652624057\" data-type=\"solution\"><details><summary>Show answer<\/summary>\n<p id=\"fs-id1170652624060\">8<\/p>\n\n<\/details><\/div>\n<\/div>\n<\/div>\n<\/div>\n<\/div>\n<\/div>\n<div id=\"fs-id1170654061364\" class=\"try\" data-type=\"note\">\n<div id=\"fs-id1170653791773\" data-type=\"exercise\">\n<div id=\"fs-id1170652624057\" data-type=\"solution\">\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-id1170652623780\" data-type=\"problem\">\n<p id=\"fs-id1170652623782\">Evaluate \\(20-z\\) when a) \\(z=12\\) and b) \\(z=-12\\).<\/p>\n\n<\/div>\n<div id=\"fs-id1170654165739\" 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-id1166419679240\">a)<\/p>\n\n<table id=\"eip-id1169752967592\" class=\"unnumbered unstyled\" summary=\"This is a solution table with two columns. The top of the right column has the equation \u201ctwenty minus z.\u201d The next row down on the left reads, \u201cSubstitute 12 for \u201cz\u201d. The twelve is in red. Next to this in the right column, it has twenty minus twelve. The next row down reads, \u201csubtract.\u201d Next to this in the right column is \u201c8\u201d.\" data-label=\"\">\n<tbody>\n<tr>\n<td><\/td>\n<td data-align=\"center\"><span id=\"eip-id1169752986908\" data-type=\"media\" data-alt=\".\"><img src=\"https:\/\/opentextbc.ca\/accessibilitytoolkit\/wp-content\/uploads\/sites\/333\/2021\/03\/CNX_ElemAlg_Figure_01_04_006b_img_new.jpg\" alt=\".\" data-media-type=\"image\/png\"><\/span><\/td>\n<\/tr>\n<tr>\n<td><span id=\"eip-id1169751035249\" data-type=\"media\" data-alt=\".\"><img src=\"https:\/\/opentextbc.ca\/accessibilitytoolkit\/wp-content\/uploads\/sites\/333\/2021\/03\/CNX_ElemAlg_Figure_01_04_006a_img_new.jpg\" alt=\".\" data-media-type=\"image\/png\"><\/span><\/td>\n<td data-align=\"center\"><span id=\"eip-id1169753314441\" data-type=\"media\" data-alt=\".\"><img src=\"https:\/\/opentextbc.ca\/accessibilitytoolkit\/wp-content\/uploads\/sites\/333\/2021\/03\/CNX_ElemAlg_Figure_01_04_006c_img_new.jpg\" alt=\".\" data-media-type=\"image\/png\"><\/span><\/td>\n<\/tr>\n<tr>\n<td>Subtract.<\/td>\n<td data-align=\"center\">8<\/td>\n<\/tr>\n<\/tbody>\n<\/table>\nb)\n<table id=\"eip-id1169753284608\" class=\"unnumbered unstyled\" summary=\"This is a solution table with two columns. The top of the right column has the equation \u201ctwenty minus z.\u201d The next row down on the left reads, \u201cSubstitute negative 12 for \u201cz\u201d. The negative twelve is in red. Next to this in the right column, it has twenty minus negative twelve. The negative 12 is in parentheses. The next row down reads, \u201csubtract.\u201d Next to this in the right column is \u201c32\u201d.\" data-label=\"\">\n<tbody>\n<tr>\n<td><\/td>\n<td data-align=\"center\"><span id=\"eip-id1169752818172\" data-type=\"media\" data-alt=\".\"><img src=\"https:\/\/opentextbc.ca\/accessibilitytoolkit\/wp-content\/uploads\/sites\/333\/2021\/03\/CNX_ElemAlg_Figure_01_04_007b_img_new.jpg\" alt=\".\" data-media-type=\"image\/png\"><\/span><\/td>\n<\/tr>\n<tr>\n<td><span id=\"eip-id1169752838416\" data-type=\"media\" data-alt=\".\"><img src=\"https:\/\/opentextbc.ca\/accessibilitytoolkit\/wp-content\/uploads\/sites\/333\/2021\/03\/CNX_ElemAlg_Figure_01_04_007a_img_new.jpg\" alt=\".\" data-media-type=\"image\/png\"><\/span><\/td>\n<td data-align=\"center\"><span id=\"eip-id1169750893297\" data-type=\"media\" data-alt=\".\"><img src=\"https:\/\/opentextbc.ca\/accessibilitytoolkit\/wp-content\/uploads\/sites\/333\/2021\/03\/CNX_ElemAlg_Figure_01_04_007c_img_new.jpg\" alt=\".\" data-media-type=\"image\/png\"><\/span><\/td>\n<\/tr>\n<tr>\n<td>Subtract.<\/td>\n<td data-align=\"center\">32<\/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-id1170654157554\" data-type=\"problem\">\n<p id=\"fs-id1170654157556\">Evaluate: \\(17-k\\) when a) \\(k=19\\) and b) \\(k=-19\\).<\/p>\n\n<\/div>\n<div id=\"fs-id1170652619306\" data-type=\"solution\"><details><summary>Show answer<\/summary>\n<p id=\"fs-id1170652619308\">a)\\(-2\\) b) 36<\/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-id1170652623499\" data-type=\"problem\">\n<p id=\"fs-id1170654138480\">Evaluate: \\(-5-b\\) when a) \\(b=14\\) and b) \\(b=-14\\).<\/p>\n\n<\/div>\n<div id=\"fs-id1170652619277\" data-type=\"solution\"><details><summary>Show answer<\/summary>\n<p id=\"fs-id1170652619279\">a)\\(-19\\) b) 9<\/p>\n\n<\/details><\/div>\n<\/div>\n<\/div>\n<\/div>\n<\/div>\n<\/div>\n<div id=\"fs-id1170654157548\" class=\"try\" data-type=\"note\">\n<div id=\"fs-id1170654157552\" data-type=\"exercise\">\n<div id=\"fs-id1170654157554\" data-type=\"problem\">\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-id1170654287816\" data-type=\"problem\">\n<p id=\"fs-id1170652618176\">Evaluate: \\(2{x}^{2}+3x+8\\) when \\(x=4\\).<\/p>\n\n<\/div>\n<div id=\"fs-id1170654215881\" 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-id1170654164395\">Substitute \\(4\\phantom{\\rule{0.2em}{0ex}}\\text{for}\\phantom{\\rule{0.2em}{0ex}}x\\). Use parentheses to show multiplication.<\/p>\n\n<table id=\"eip-id1169752967487\" class=\"unnumbered unstyled\" summary=\"This is a solution table with two columns. The top of the right column has the equation \u201ctwo \u201cx\u201d squared plus three\u201dx\u201d plus 8.\u201d The next row down on the left reads, \u201cSubstitute.\u201d Next to this in the right column, it has \u201ctwo times 4 squared plus three times four plus eight.\u201d The fours are red. The next row down reads, \u201cevaluate the exponents.\u201d Next to this in the right column is \u201ctwo times 16 squared plus three times 4 plus 8\u201d. The next row down reads, \u201cMultiply.\u201d Next to this in the right column \u201c32 plus 12 plus 8.\u201d The next row down reads \u201cadd\u201d. Next to this in the right column is \u201c52\u201d.\" data-label=\"\">\n<tbody>\n<tr>\n<td><\/td>\n<td data-align=\"center\"><span id=\"eip-id1169753319331\" data-type=\"media\" data-alt=\".\"><img src=\"https:\/\/opentextbc.ca\/accessibilitytoolkit\/wp-content\/uploads\/sites\/333\/2021\/03\/CNX_ElemAlg_Figure_01_04_008a_img_new.jpg\" alt=\".\" data-media-type=\"image\/png\"><\/span><\/td>\n<\/tr>\n<tr>\n<td>Substitute.<\/td>\n<td data-align=\"center\"><span id=\"eip-id1169752839642\" data-type=\"media\" data-alt=\".\"><img src=\"https:\/\/opentextbc.ca\/accessibilitytoolkit\/wp-content\/uploads\/sites\/333\/2021\/03\/CNX_ElemAlg_Figure_01_04_008b_img_new.jpg\" alt=\".\" data-media-type=\"image\/png\"><\/span><\/td>\n<\/tr>\n<tr>\n<td>Evaluate exponents.<\/td>\n<td data-align=\"center\"><span id=\"eip-id1169753138651\" data-type=\"media\" data-alt=\".\"><img src=\"https:\/\/opentextbc.ca\/accessibilitytoolkit\/wp-content\/uploads\/sites\/333\/2021\/03\/CNX_ElemAlg_Figure_01_04_008c_img_new.jpg\" alt=\".\" data-media-type=\"image\/png\"><\/span><\/td>\n<\/tr>\n<tr>\n<td>Multiply.<\/td>\n<td data-align=\"center\"><span id=\"eip-id1169752821475\" data-type=\"media\" data-alt=\".\"><img src=\"https:\/\/opentextbc.ca\/accessibilitytoolkit\/wp-content\/uploads\/sites\/333\/2021\/03\/CNX_ElemAlg_Figure_01_04_008d_img_new.jpg\" alt=\".\" data-media-type=\"image\/png\"><\/span><\/td>\n<\/tr>\n<tr>\n<td>Add.<\/td>\n<td data-align=\"center\">52<\/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-id1170654080966\" data-type=\"problem\">\n<p id=\"fs-id1170654080968\">Evaluate: \\(3{x}^{2}-2x+6\\) when \\(x=-3\\).<\/p>\n\n<\/div>\n<div id=\"fs-id1170653798527\" data-type=\"solution\"><details><summary>Show answer<\/summary>\n<p id=\"fs-id1170653798529\">39<\/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-id1170654129713\" data-type=\"problem\">\n<p id=\"fs-id1170654129715\">Evaluate: \\(4{x}^{2}-x-5\\) when \\(x=-2\\).<\/p>\n\n<\/div>\n<div id=\"fs-id1170653875048\" data-type=\"solution\"><details><summary>Show answer<\/summary>\n<p id=\"fs-id1170653875050\">13<\/p>\n\n<\/details><\/div>\n<\/div>\n<\/div>\n<\/div>\n<\/div>\n<\/div>\n<h1>Translate Phrases to Expressions with Integers<\/h1>\n<p id=\"fs-id1170654080268\">Our earlier work translating English to algebra also applies to phrases that include both positive and negative numbers.<\/p>\n\n<div class=\"textbox textbox--examples\"><header class=\"textbox__header\">\n<p class=\"textbox__title\">EXAMPLE 13<\/p>\n\n<\/header>\n<div class=\"textbox__content\">\n<div id=\"fs-id1170654286415\" data-type=\"problem\">\n<p id=\"fs-id1170654286418\">Translate and simplify: the sum of 8 and \\(-12\\), increased by 3<\/p>\n\n<\/div>\n<div id=\"fs-id1170652630972\" 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-929\" summary=\".\">\n<tbody>\n<tr>\n<td><\/td>\n<td>the <strong>sum<\/strong> of 8 and \\(-12\\), increased by 3.<\/td>\n<\/tr>\n<tr>\n<td>Translate.<\/td>\n<td>\\(\\left[8+\\left(-12\\right)\\right]+3\\)<\/td>\n<\/tr>\n<tr>\n<td>Simplify. Be careful not to confuse the brackets with an absolute value sign.<\/td>\n<td>\\(\\left(-4\\right)+3\\)<\/td>\n<\/tr>\n<tr>\n<td>Add.<\/td>\n<td>\\(-1\\)<\/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 13.1<\/p>\n\n<\/header>\n<div class=\"textbox__content\">\n<div id=\"fs-id1170654285669\" data-type=\"problem\">\n<p id=\"fs-id1170652620473\">Translate and simplify the sum of 9 and \\(-16\\), increased by 4<\/p>\n\n<\/div>\n<div id=\"fs-id1170652622182\" data-type=\"solution\"><details><summary>Show answer<\/summary>\n<p id=\"fs-id1170652622184\">\\(\\left(9+\\left(-16\\right)\\right)+4-3\\)<\/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 13.2<\/p>\n\n<\/header>\n<div class=\"textbox__content\">\n<div id=\"fs-id1170654041776\" data-type=\"problem\">\n<p id=\"fs-id1170654041778\">Translate and simplify the sum of \\(-8\\) and \\(-12\\), increased by 7<\/p>\n\n<\/div>\n<div id=\"fs-id1170653849382\" data-type=\"solution\"><details><summary>Show answer<\/summary>\n<p id=\"fs-id1170654209722\">\\(\\left(-8+\\left(-12\\right)\\right)+7-13\\)<\/p>\n\n<\/details><\/div>\n<\/div>\n<\/div>\n<p id=\"fs-id1170652622623\">When we first introduced the operation symbols, we saw that the expression may be read in several ways. They are listed in the chart below.<\/p>\n\n<table id=\"fs-id1170654190232\" class=\"grid\" summary=\"This table has two cells. In the top cell is the expression: a, minus b. In the bottom cell are the phrases: \u201ca minus b\u201d, \u201cthe difference of a and b\u201d, \u201cb subtracted from a\u201d, and \u201cb less than a\u201d.\" data-label=\"\">\n<thead>\n<tr valign=\"top\">\n<th data-align=\"center\" data-valign=\"top\">\\(a-b\\)<\/th>\n<\/tr>\n<\/thead>\n<tbody>\n<tr valign=\"top\">\n<td data-align=\"center\" data-valign=\"top\">\\(a\\) minus \\(b\\)\nthe difference of \\(a\\) and \\(b\\)\n\\(b\\) subtracted from \\(a\\)\n\\(b\\) less than \\(a\\)<\/td>\n<\/tr>\n<\/tbody>\n<\/table>\n<p id=\"fs-id1170654238524\">Be careful to get <em data-effect=\"italics\">a<\/em> and <em data-effect=\"italics\">b<\/em> in the right order!<\/p>\n\n<div class=\"textbox textbox--examples\"><header class=\"textbox__header\">\n<p class=\"textbox__title\">EXAMPLE 14<\/p>\n\n<\/header>\n<div class=\"textbox__content\">\n<div id=\"fs-id1170653874526\" data-type=\"problem\">\n<p id=\"fs-id1170653874528\">Translate and then simplify a) the difference of 13 and \\(-21\\) b) subtract 24 from \\(-19\\).<\/p>\n\n<\/div>\n<div id=\"fs-id1170654150875\" 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-651\" summary=\".\">\n<tbody>\n<tr>\n<td>a)\nTranslate.\nSimplify.<\/td>\n<td>\\(\\begin{array}{c}\\text{the}\\phantom{\\rule{0.2em}{0ex}}\\mathbf{\\text{difference}}\\phantom{\\rule{0.2em}{0ex}}\\mathit{\\text{of}}\\phantom{\\rule{0.2em}{0ex}}13\\phantom{\\rule{0.2em}{0ex}}\\mathit{\\text{and}}\\phantom{\\rule{0.2em}{0ex}}-21\\\\ 13-\\left(-21\\right)\\\\ 34\\end{array}\\)<\/td>\n<\/tr>\n<tr>\n<td>b)\nTranslate. Remember, \"subtract \\(b\\) from \\(a\\) means \\(a-b\\).\nSimplify.<\/td>\n<td>\\(\\begin{array}{c}\\mathbf{\\text{subtract}}\\phantom{\\rule{0.2em}{0ex}}24\\phantom{\\rule{0.2em}{0ex}}\\mathbf{\\text{from}}\\phantom{\\rule{0.2em}{0ex}}-19\\\\ -19-24\\\\ -43\\end{array}\\)<\/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 14.1<\/p>\n\n<\/header>\n<div class=\"textbox__content\">\n<div id=\"fs-id1170654159530\" data-type=\"problem\">\n<p id=\"fs-id1170654159532\">Translate and simplify a) the difference of 14 and \\(-23\\) b) subtract 21 from \\(-17\\).<\/p>\n\n<\/div>\n<div id=\"fs-id1170652619950\" data-type=\"solution\"><details><summary>Show answer<\/summary>\n<p id=\"fs-id1170652619953\">a)\\(14-\\left(-23\\right);37\\) b)\\(-17-21;-38\\)<\/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 14.2<\/p>\n\n<\/header>\n<div class=\"textbox__content\">\n<div id=\"fs-id1170654285364\" data-type=\"problem\">\n<p id=\"fs-id1170654285366\">Translate and simplify a) the difference of 11 and \\(-19\\) b) subtract 18 from \\(-11\\).<\/p>\n\n<\/div>\n<div id=\"fs-id1170652621632\" data-type=\"solution\"><details><summary>Show answer<\/summary>\n<p id=\"fs-id1170652621634\">a)\\(11-\\left(-19\\right);30\\) b)\\(-11-18;-29\\)<\/p>\n\n<\/details><\/div>\n<\/div>\n<\/div>\n<p id=\"fs-id1170653881059\">Once again, our prior work translating English to algebra transfers to phrases that include both multiplying and dividing integers. Remember that the key word for <span class=\"no-emphasis\" data-type=\"term\">multiplication<\/span> is \u201c<span class=\"no-emphasis\" data-type=\"term\">product<\/span>\u201d and for <span class=\"no-emphasis\" data-type=\"term\">division<\/span> is \u201c<span class=\"no-emphasis\" data-type=\"term\">quotient<\/span>.\u201d<\/p>\n\n<div class=\"textbox textbox--examples\"><header class=\"textbox__header\">\n<p class=\"textbox__title\">EXAMPLE 15<\/p>\n\n<\/header>\n<div class=\"textbox__content\">\n<div id=\"fs-id1170654158684\" data-type=\"problem\">\n<p id=\"fs-id1170654158686\">Translate to an algebraic expression and simplify if possible: the product of \\(-2\\) and 14<\/p>\n\n<\/div>\n<div id=\"fs-id1170654158696\" 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-856\" summary=\".\">\n<tbody>\n<tr>\n<td><\/td>\n<td>\\(\\text{the product}\\phantom{\\rule{0.2em}{0ex}}\\mathit{\\text{of}}\\phantom{\\rule{0.2em}{0ex}}-2\\phantom{\\rule{0.2em}{0ex}}\\mathit{\\text{and}}\\phantom{\\rule{0.2em}{0ex}}14\\)<\/td>\n<\/tr>\n<tr>\n<td>Translate.<\/td>\n<td>\\(\\left(-2\\right)\\left(14\\right)\\)<\/td>\n<\/tr>\n<tr>\n<td>Simplify.<\/td>\n<td>\\(-28\\)<\/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 15.1<\/p>\n\n<\/header>\n<div class=\"textbox__content\">\n<div id=\"fs-id1170652620834\" data-type=\"problem\">\n<p id=\"fs-id1170652620836\">Translate to an algebraic expression and simplify if possible: the product of \\(-5\\) and 12<\/p>\n\n<\/div>\n<div id=\"fs-id1170652623909\" data-type=\"solution\"><details><summary>Show answer<\/summary>\n<p id=\"fs-id1170652623911\">\\(-5\\left(12\\right);-60\\)<\/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 15.2<\/p>\n\n<\/header>\n<div class=\"textbox__content\">\n<div id=\"fs-id1170653797095\" data-type=\"problem\">\n<p id=\"fs-id1170653797097\">Translate to an algebraic expression and simplify if possible: the product of 8 and \\(-13\\).<\/p>\n\n<\/div>\n<div id=\"fs-id1170653868747\" data-type=\"solution\"><details><summary>Show answer<\/summary>\n<p id=\"fs-id1170653868749\">\\(-8\\left(13\\right);-104\\)<\/p>\n\n<\/details><\/div>\n<\/div>\n<\/div>\n<div id=\"fs-id1170653797090\" class=\"try\" data-type=\"note\">\n<div id=\"fs-id1170653797093\" data-type=\"exercise\">\n<div id=\"fs-id1170653868747\" data-type=\"solution\">\n<div class=\"textbox textbox--examples\"><header class=\"textbox__header\">\n<p class=\"textbox__title\">EXAMPLE 16<\/p>\n\n<\/header>\n<div class=\"textbox__content\">\n<div id=\"fs-id1170654158560\" data-type=\"problem\">\n<p id=\"fs-id1170654158562\">Translate to an algebraic expression and simplify if possible: the quotient of \\(-56\\) and \\(-7\\).<\/p>\n\n<\/div>\n<div id=\"fs-id1170653875100\" data-type=\"solution\">\n<div data-type=\"title\"><\/div>\n<div data-type=\"title\"><strong>Solution<\/strong><\/div>\n<table id=\"eip-659\" summary=\".\">\n<tbody>\n<tr>\n<td><\/td>\n<td>\\(\\text{the quotient}\\phantom{\\rule{0.2em}{0ex}}\\mathit{\\text{of}}\\phantom{\\rule{0.2em}{0ex}}-56\\phantom{\\rule{0.2em}{0ex}}\\mathit{\\text{and}}\\phantom{\\rule{0.2em}{0ex}}-7\\)<\/td>\n<\/tr>\n<tr>\n<td>Translate.<\/td>\n<td>\\(-56\\div \\left(-7\\right)\\)<\/td>\n<\/tr>\n<tr>\n<td>Simplify.<\/td>\n<td>\\(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 16.1<\/p>\n\n<\/header>\n<div class=\"textbox__content\">\n<div id=\"fs-id1170652621556\" data-type=\"problem\">\n<p id=\"fs-id1170652621559\">Translate to an algebraic expression and simplify if possible: the quotient of \\(-63\\) and \\(-9\\).<\/p>\n\n<\/div>\n<div id=\"fs-id1170653906972\" data-type=\"solution\"><details><summary>Show answer<\/summary>\n<p id=\"fs-id1170653906974\">\\(-63\\div \\left(-9\\right);7\\)<\/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 16.2<\/p>\n\n<\/header>\n<div class=\"textbox__content\">\n<div id=\"fs-id1170653930632\" data-type=\"problem\">\n<p id=\"fs-id1170652630883\">Translate to an algebraic expression and simplify if possible: the quotient of \\(-72\\) and \\(-9\\).<\/p>\n\n<\/div>\n<div id=\"fs-id1170654164368\" data-type=\"solution\"><details><summary>Show answer<\/summary>\n<p id=\"fs-id1170654164370\">\\(-72\\div \\left(-9\\right);8\\)<\/p>\n\n<\/details><\/div>\n<\/div>\n<\/div>\n<\/div>\n<\/div>\n<\/div>\n<h1>Use Integers in Applications<\/h1>\n<p id=\"fs-id1170653875242\">We\u2019ll outline a plan to solve applications. It\u2019s hard to find something if we don\u2019t know what we\u2019re looking for or what to call it! So when we solve an application, we first need to determine what the problem is asking us to find. Then we\u2019ll write a phrase that gives the information to find it. We\u2019ll translate the phrase into an expression and then simplify the expression to get the answer. Finally, we summarize the answer in a sentence to make sure it makes sense.<\/p>\n\n<div class=\"textbox textbox--examples\"><header class=\"textbox__header\">\n<p class=\"textbox__title\">EXAMPLE 17<\/p>\n\n<\/header>\n<div class=\"textbox__content\">\n<div id=\"fs-id1170653875252\" data-type=\"exercise\">\n<div id=\"fs-id1170653879266\" data-type=\"problem\">\n<p id=\"fs-id1170653879268\">The temperature in Sparwood, British Columbia, one morning was 11 degrees. By mid-afternoon, the temperature had dropped to \\(-9\\) degrees. What was the difference of the morning and afternoon temperatures?<\/p>\n\n<\/div>\n<div id=\"fs-id1170653879279\" 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<span id=\"fs-id1170653797914\" data-type=\"media\" data-alt=\"This is a table with two columns. The left column includes steps to solve the problem. The right column includes the math to solve the problem. In the first row, the left column says \u201cStep 1. Read the problem. Make sure all the words and ideas are understood.\u201d The right column is blank.\"><img src=\"https:\/\/opentextbc.ca\/accessibilitytoolkit\/wp-content\/uploads\/sites\/333\/2021\/03\/CNX_ElemAlg_Figure_01_04_009a_new.jpg\" alt=\"This is a table with two columns. The left column includes steps to solve the problem. The right column includes the math to solve the problem. In the first row, the left column says \u201cStep 1. Read the problem. Make sure all the words and ideas are understood.\u201d The right column is blank.\" data-media-type=\"image\/jpeg\"><\/span><span id=\"fs-id1170653907530\" data-type=\"media\" data-alt=\"In the second row, the left column says \u201cStep 2. Identify what we are asked to find\u201d. The right column says, \u201cthe difference of the morning and afternoon temperatures.\u201d\"><img src=\"https:\/\/opentextbc.ca\/accessibilitytoolkit\/wp-content\/uploads\/sites\/333\/2021\/03\/CNX_ElemAlg_Figure_01_04_009b_new.jpg\" alt=\"In the second row, the left column says \u201cStep 2. Identify what we are asked to find\u201d. The right column says, \u201cthe difference of the morning and afternoon temperatures.\u201d\" data-media-type=\"image\/jpeg\"><\/span><span id=\"fs-id1170654231700\" data-type=\"media\" data-alt=\"In the third row, the left column says, \u201cStep 3. Write a phrase that gives the information to find it.\u201d Next to this in the right column, it says \u201cthe difference of 11 and negative 9.\u201d\"><img src=\"https:\/\/opentextbc.ca\/accessibilitytoolkit\/wp-content\/uploads\/sites\/333\/2021\/03\/CNX_ElemAlg_Figure_01_04_009c_new.jpg\" alt=\"In the third row, the left column says, \u201cStep 3. Write a phrase that gives the information to find it.\u201d Next to this in the right column, it says \u201cthe difference of 11 and negative 9.\u201d\" data-media-type=\"image\/jpeg\"><\/span><span id=\"fs-id1170652751567\" data-type=\"media\" data-alt=\"In the fourth row, the left column says, \u201cStep 4. Translate the phrase to an expression.\u201d The right column contains 11 minus negative 9.\"><img src=\"https:\/\/opentextbc.ca\/accessibilitytoolkit\/wp-content\/uploads\/sites\/333\/2021\/03\/CNX_ElemAlg_Figure_01_04_009d_new.jpg\" alt=\"In the fourth row, the left column says, \u201cStep 4. Translate the phrase to an expression.\u201d The right column contains 11 minus negative 9.\" data-media-type=\"image\/jpeg\"><\/span><span id=\"fs-id1170653837169\" data-type=\"media\" data-alt=\"In the fifth row, the left column says, \u201cStep 5. Simplify the expression.\u201d The right column contains 20.\"><img src=\"https:\/\/opentextbc.ca\/accessibilitytoolkit\/wp-content\/uploads\/sites\/333\/2021\/03\/CNX_ElemAlg_Figure_01_04_009e_new.jpg\" alt=\"In the fifth row, the left column says, \u201cStep 5. Simplify the expression.\u201d The right column contains 20.\" data-media-type=\"image\/jpeg\"><\/span><span id=\"fs-id1171792706468\" data-type=\"media\" data-alt=\"The final row says, \u201cStep five. Write a complete sentence that answers the question.\u201d Next to this in the right column, it says \u201cthe difference in temperatures was 20 degrees.\u201d\"><img src=\"https:\/\/opentextbc.ca\/accessibilitytoolkit\/wp-content\/uploads\/sites\/333\/2021\/03\/CNX_ElemAlg_Figure_01_04_009f_new.jpg\" alt=\"The final row says, \u201cStep five. Write a complete sentence that answers the question.\u201d Next to this in the right column, it says \u201cthe difference in temperatures was 20 degrees.\u201d\" data-media-type=\"image\/jpeg\"><\/span>\n\n<\/div>\n<\/div>\n<\/div>\n<\/div>\n<div class=\"textbox textbox--exercises\"><header class=\"textbox__header\">\n<p class=\"textbox__title\">TRY IT 17.1<\/p>\n\n<\/header>\n<div class=\"textbox__content\">\n<div id=\"fs-id1170652630563\" data-type=\"problem\">\n<p id=\"fs-id1170652630565\">The temperature in Whitehorse, Yukon, one morning was 15 degrees. By mid-afternoon the temperature had dropped to 30 degrees below zero. What was the difference in the morning and afternoon temperatures?<\/p>\n\n<\/div>\n<div id=\"fs-id1170652630571\" data-type=\"solution\"><details><summary>Show answer<\/summary>\n<p id=\"fs-id1170652630574\">The difference in temperatures was 45 degrees.<\/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 17.2<\/p>\n\n<\/header>\n<div class=\"textbox__content\">\n<div id=\"fs-id1170654202594\" data-type=\"problem\">\n<p id=\"fs-id1170654202596\">The temperature in Quesnel, BC, was \\(-6\\) degrees at lunchtime. By sunset the temperature had dropped to \\(-15\\) degrees. What was the difference in the lunchtime and sunset temperatures?<\/p>\n\n<\/div>\n<div id=\"fs-id1170654209698\" data-type=\"solution\"><details><summary>Show answer<\/summary>\n<p id=\"fs-id1170654209700\">The difference in temperatures was 9 degrees.<\/p>\n\n<\/details><\/div>\n<\/div>\n<\/div>\n<div class=\"textbox textbox--key-takeaways\"><header class=\"textbox__header\">\n<p class=\"textbox__title\">HOW TO: Apply a Strategy to Solve Applications with Integers<\/p>\n\n<\/header>\n<div class=\"textbox__content\">\n<ol id=\"fs-id1166426171804\" class=\"stepwise\" type=\"1\">\n \t<li>Read the problem. Make sure all the words and ideas are understood<\/li>\n \t<li>Identify what we are asked to find.<\/li>\n \t<li>Write a phrase that gives the information to find it.<\/li>\n \t<li>Translate the phrase to an expression.<\/li>\n \t<li>Simplify the expression.<\/li>\n \t<li>Answer the question with a complete sentence.<\/li>\n<\/ol>\n<\/div>\n<\/div>\n<div id=\"fs-id1170654209706\" class=\"howto\" data-type=\"note\">\n<div class=\"textbox textbox--examples\"><header class=\"textbox__header\">\n<p class=\"textbox__title\">EXAMPLE 18<\/p>\n\n<\/header>\n<div class=\"textbox__content\">\n<div id=\"fs-id1170652620547\" data-type=\"problem\">\n<p id=\"fs-id1170654154716\">The Mustangs football team received three penalties in the third quarter. Each penalty gave them a loss of fifteen yards. What is the number of yards lost?<\/p>\n\n<\/div>\n<div id=\"fs-id1170654154722\" data-type=\"solution\">\n<div data-type=\"title\"><\/div>\n<div data-type=\"title\"><strong>Solution<\/strong><\/div>\n<table id=\"eip-436\" summary=\".\">\n<tbody>\n<tr>\n<td><strong>Step 1.<\/strong> Read the problem. Make sure all the words and ideas are understood.<\/td>\n<td><\/td>\n<\/tr>\n<tr>\n<td><strong>Step 2.<\/strong> Identify what we are asked to find.<\/td>\n<td>the number of yards lost<\/td>\n<\/tr>\n<tr>\n<td><strong>Step 3.<\/strong> Write a phrase that gives the information to find it.<\/td>\n<td>three times a 15-yard penalty<\/td>\n<\/tr>\n<tr>\n<td><strong>Step 4.<\/strong> Translate the phrase to an expression.<\/td>\n<td>\\(3\\left(-15\\right)\\)<\/td>\n<\/tr>\n<tr>\n<td><strong>Step 5.<\/strong> Simplify the expression.<\/td>\n<td>\\(-45\\)<\/td>\n<\/tr>\n<tr>\n<td><strong>Step 6.<\/strong> Answer the question with a complete sentence.<\/td>\n<td>The team lost 45 yards.<\/td>\n<\/tr>\n<\/tbody>\n<\/table>\n<\/div>\n<\/div>\n<\/div>\n<\/div>\n<div id=\"fs-id1170654185951\" class=\"try\" data-type=\"note\">\n<div id=\"fs-id1170653874319\" data-type=\"exercise\">\n<div id=\"fs-id1170653874322\" data-type=\"problem\">\n<div class=\"textbox textbox--exercises\"><header class=\"textbox__header\">\n<p class=\"textbox__title\">TRY IT 18.1<\/p>\n\n<\/header>\n<div class=\"textbox__content\">\n<div id=\"fs-id1170653874322\" data-type=\"problem\">\n<p id=\"fs-id1170653874324\">The Bears played poorly and had seven penalties in the game. Each penalty resulted in a loss of 15 yards. What is the number of yards lost due to penalties?<\/p>\n\n<\/div>\n<div id=\"fs-id1170653874329\" data-type=\"solution\"><details><summary>Show answer<\/summary>\n<p id=\"fs-id1170653874332\">The Bears lost 105 yards.<\/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 18.2<\/p>\n\n<\/header>\n<div class=\"textbox__content\">\n<div id=\"fs-id1170653874667\" data-type=\"problem\">\n<p id=\"fs-id1170653874669\">Bill uses the ATM on campus because it is convenient. However, each time he uses it he is charged a \\$2 fee. Last month he used the ATM eight times. How much was his total fee for using the ATM?<\/p>\n\n<\/div>\n<div id=\"fs-id1170653874675\" data-type=\"solution\"><details><summary>Show answer<\/summary>\n<p id=\"fs-id1170654239353\">A \\$16 fee was deducted from his checking account.<\/p>\n\n<\/details><\/div>\n<\/div>\n<\/div>\n<\/div>\n<\/div>\n<\/div>\n<h1>Key Concepts<\/h1>\n<ul id=\"fs-id1170654239367\" data-bullet-style=\"bullet\">\n \t<li><strong data-effect=\"bold\">Multiplication and Division of Two Signed Numbers<\/strong>\n<ul id=\"fs-id1170653881237\" data-bullet-style=\"open-circle\">\n \t<li>Same signs\u2014Product is positive<\/li>\n \t<li>Different signs\u2014Product is negative<\/li>\n<\/ul>\n<\/li>\n \t<li><strong data-effect=\"bold\">Strategy for Applications<\/strong>\n<ol id=\"fs-id1170652621952\" class=\"stepwise\" type=\"1\">\n \t<li>Identify what you are asked to find.<\/li>\n \t<li>Write a phrase that gives the information to find it.<\/li>\n \t<li>Translate the phrase to an expression.<\/li>\n \t<li>Simplify the expression.<\/li>\n \t<li>Answer the question with a complete sentence.<\/li>\n<\/ol>\n<\/li>\n<\/ul>\n<h1>Practice Makes Perfect<\/h1>\n<h2>Multiply Integers<\/h2>\n<p id=\"fs-id1166421558397\">In the following exercises, multiply.<\/p>\n\n<table style=\"border-collapse: collapse; width: 100%;\" border=\"0\">\n<tbody>\n<tr>\n<td style=\"width: 50%;\">1. \\(-4\\cdot8\\)<\/td>\n<td style=\"width: 50%;\">2. \\(-3\\cdot9\\)<\/td>\n<\/tr>\n<tr>\n<td style=\"width: 50%;\">3. \\(9\\left(-7\\right)\\)<\/td>\n<td style=\"width: 50%;\">4. \\(13\\left(-5\\right)\\)<\/td>\n<\/tr>\n<tr>\n<td style=\"width: 50%;\">5. \\(-1\\cdot6\\)<\/td>\n<td style=\"width: 50%;\">6. \\(-1\\cdot3\\)<\/td>\n<\/tr>\n<tr>\n<td style=\"width: 50%;\">7. \\(-1\\left(-14\\right)\\)<\/td>\n<td style=\"width: 50%;\">8. \\(-1\\left(-19\\right)\\)<\/td>\n<\/tr>\n<\/tbody>\n<\/table>\n<h2>Divide Integers<\/h2>\n<p id=\"fs-id1166421949046\">In the following exercises, divide.<\/p>\n\n<table style=\"border-collapse: collapse; width: 100%; height: 75px;\" border=\"0\">\n<tbody>\n<tr style=\"height: 15px;\">\n<td style=\"width: 50%; height: 15px;\">9. \\(-24\\div6\\)<\/td>\n<td style=\"width: 50%; height: 15px;\">10. \\(35\\div\\left(-7\\right)\\)<\/td>\n<\/tr>\n<tr style=\"height: 15px;\">\n<td style=\"width: 50%; height: 15px;\">11. \\(-52\\div\\left(-4\\right)\\)<\/td>\n<td style=\"width: 50%; height: 15px;\">12. \\(-84\\div\\left(-6\\right)\\)<\/td>\n<\/tr>\n<tr style=\"height: 15px;\">\n<td style=\"width: 50%; height: 15px;\">13. \\(-180\\div15\\)<\/td>\n<td style=\"width: 50%; height: 15px;\">14. \\(-192\\div12\\)<\/td>\n<\/tr>\n<\/tbody>\n<\/table>\n<h2>Simplify Expressions with Integers<\/h2>\n<p id=\"fs-id1166421486016\">In the following exercises, simplify each expression.<\/p>\n\n<table style=\"border-collapse: collapse; width: 100%;\" border=\"0\">\n<tbody>\n<tr>\n<td style=\"width: 50%;\">15. \\(5\\left(-6\\right)+7\\left(-2\\right)-3\\)<\/td>\n<td style=\"width: 50%;\">16. \\(8\\left(-4\\right)+5\\left(-4\\right)-6\\)<\/td>\n<\/tr>\n<tr>\n<td style=\"width: 50%;\">17. \\({\\left(-2\\right)}^{6}\\)<\/td>\n<td style=\"width: 50%;\">18. \\({\\left(-3\\right)}^{5}\\)<\/td>\n<\/tr>\n<tr>\n<td style=\"width: 50%;\">19. \\(\\text{-}{4}^{2}\\)<\/td>\n<td style=\"width: 50%;\">20. \\(\\text{-}{6}^{2}\\)<\/td>\n<\/tr>\n<tr>\n<td style=\"width: 50%;\">21. \\(-3\\left(-5\\right)\\left(6\\right)\\)<\/td>\n<td style=\"width: 50%;\">22. \\(-4\\left(-6\\right)\\left(3\\right)\\)<\/td>\n<\/tr>\n<tr>\n<td style=\"width: 50%;\">23. \\(\\left(8-11\\right)\\left(9-12\\right)\\)<\/td>\n<td style=\"width: 50%;\">24. \\(\\left(6-11\\right)\\left(8-13\\right)\\)<\/td>\n<\/tr>\n<tr>\n<td style=\"width: 50%;\">25. \\(26-3\\left(2-7\\right)\\)<\/td>\n<td style=\"width: 50%;\">26. \\(23-2\\left(4-6\\right)\\)<\/td>\n<\/tr>\n<tr>\n<td style=\"width: 50%;\">27. \\(65\\div\\left(-5\\right)+\\left(-28\\right)\\div\\left(-7\\right)\\)<\/td>\n<td style=\"width: 50%;\">28. \\(52\\div\\left(-4\\right)+\\left(-32\\right)\\div\\left(-8\\right)\\)<\/td>\n<\/tr>\n<tr>\n<td style=\"width: 50%;\">29. \\(9-2\\left[3-8\\left(-2\\right)\\right]\\)<\/td>\n<td style=\"width: 50%;\">30. \\(11-3\\left[7-4\\left(-2\\right)\\right]\\)<\/td>\n<\/tr>\n<tr>\n<td style=\"width: 50%;\">31. \\({\\left(-3\\right)}^{2}-24\\div\\left(8-2\\right)\\)<\/td>\n<td style=\"width: 50%;\">32. \\({\\left(-4\\right)}^{2}-32\\div\\left(12-4\\right)\\)<\/td>\n<\/tr>\n<\/tbody>\n<\/table>\n<h2>Evaluate Variable Expressions with Integers<\/h2>\n<p id=\"fs-id1166426233230\">In the following exercises, evaluate each expression.<\/p>\n\n<table style=\"border-collapse: collapse; width: 100%;\" border=\"0\">\n<tbody>\n<tr>\n<td style=\"width: 50%;\">33. \\(y+\\left(-14\\right)\\) when\na) \\(y=-33\\)\nb) \\(y=30\\)<\/td>\n<td style=\"width: 50%;\">34. \\(x+\\left(-21\\right)\\) when\na) \\(x=-27\\)\nb) \\(x=44\\)<\/td>\n<\/tr>\n<tr>\n<td style=\"width: 50%;\">35.\na)\\(a+3\\) when \\(a=-7\\)\nb) \\(\\text{-}a+3\\) when \\(a=-7\\)<\/td>\n<td style=\"width: 50%;\">36.\na)\\(d+\\left(-9\\right)\\) when \\(d=-8\\)\nb) \\(\\text{-}d+\\left(-9\\right)\\) when \\(d=-8\\)<\/td>\n<\/tr>\n<tr>\n<td style=\"width: 50%;\">37.\u00a0\\(m+n\\) when\n\\(m=-15,n=7\\)<\/td>\n<td style=\"width: 50%;\">38. \\(p+q\\) when\n\\(p=-9,q=17\\)<\/td>\n<\/tr>\n<tr>\n<td style=\"width: 50%;\">39. \\(r+s\\) when \\(r=-9,s=-7\\)<\/td>\n<td style=\"width: 50%;\">40. \\(t+u\\) when \\(t=-6,u=-5\\)<\/td>\n<\/tr>\n<tr>\n<td style=\"width: 50%;\">41. \\({\\left(x+y\\right)}^{2}\\) when\n\\(x=-3,y=14\\)<\/td>\n<td style=\"width: 50%;\">42. \\({\\left(y+z\\right)}^{2}\\) when\n\\(y=-3,z=15\\)<\/td>\n<\/tr>\n<tr>\n<td style=\"width: 50%;\">43. \\(-2x+17\\) when\na) \\(x=8\\)\nb) \\(x=-8\\)<\/td>\n<td style=\"width: 50%;\">44. \\(-5y+14\\) when\na) \\(y=9\\)\nb) \\(y=-9\\)<\/td>\n<\/tr>\n<tr>\n<td style=\"width: 50%;\">45. \\(10-3m\\) when\na) \\(m=5\\)\nb) \\(m=-5\\)<\/td>\n<td style=\"width: 50%;\">46. \\(18-4n\\) when\na) \\(n=3\\)\nb) \\(n=-3\\)<\/td>\n<\/tr>\n<tr>\n<td style=\"width: 50%;\">47. \\(2{w}^{2}-3w+7\\) when\n\\(w=-2\\)<\/td>\n<td style=\"width: 50%;\">48. \\(3{u}^{2}-4u+5\\) when \\(u=-3\\)<\/td>\n<\/tr>\n<tr>\n<td style=\"width: 50%;\">49. \\(9a-2b-8\\) when\n\\(a=-6\\phantom{\\rule{0.2em}{0ex}}\\text{and}\\phantom{\\rule{0.2em}{0ex}}b=-3\\)<\/td>\n<td style=\"width: 50%;\">50. \\(7m-4n-2\\) when\n\\(m=-4\\phantom{\\rule{0.2em}{0ex}}\\text{and}\\phantom{\\rule{0.2em}{0ex}}n=-9\\)<\/td>\n<\/tr>\n<\/tbody>\n<\/table>\n<h2>Translate English Phrases to Algebraic Expressions<\/h2>\n<p id=\"fs-id1166418098647\">In the following exercises, translate to an algebraic expression and simplify if possible.<\/p>\n\n<table style=\"border-collapse: collapse; width: 100%; height: 120px;\" border=\"0\">\n<tbody>\n<tr style=\"height: 15px;\">\n<td style=\"width: 50%; height: 15px;\">51. the sum of 3 and \\(-15\\), increased by 7<\/td>\n<td style=\"width: 50%; height: 15px;\">52. the sum of \\(-8\\) and \\(-9\\), increased by 23<\/td>\n<\/tr>\n<tr style=\"height: 15px;\">\n<td style=\"width: 50%; height: 15px;\">53. the difference of 10 and \\(-18\\)<\/td>\n<td style=\"width: 50%; height: 15px;\">54. subtract 11 from \\(-25\\)<\/td>\n<\/tr>\n<tr style=\"height: 15px;\">\n<td style=\"width: 50%; height: 15px;\">55. the difference of \\(-5\\) and \\(-30\\)<\/td>\n<td style=\"width: 50%; height: 15px;\">56. subtract \\(-6\\) from \\(-13\\)<\/td>\n<\/tr>\n<tr style=\"height: 15px;\">\n<td style=\"width: 50%; height: 15px;\">57. the product of \\(-3\\) and \\(15\\)<\/td>\n<td style=\"width: 50%; height: 15px;\">58. the product of \\(-4\\) and \\(16\\)<\/td>\n<\/tr>\n<tr style=\"height: 15px;\">\n<td style=\"width: 50%; height: 15px;\">59. the quotient of \\(-60\\) and \\(-20\\)<\/td>\n<td style=\"width: 50%; height: 15px;\">60. the quotient of \\(-40\\) and \\(-20\\)<\/td>\n<\/tr>\n<tr style=\"height: 15px;\">\n<td style=\"width: 50%; height: 15px;\">61. the quotient of \\(-6\\) and the sum of <em data-effect=\"italics\">a<\/em> and <em data-effect=\"italics\">b<\/em><\/td>\n<td style=\"width: 50%; height: 15px;\">62. the quotient of \\(-7\\) and the sum of <em data-effect=\"italics\">m<\/em> and <em data-effect=\"italics\">n<\/em><\/td>\n<\/tr>\n<tr style=\"height: 15px;\">\n<td style=\"width: 50%; height: 15px;\">63. the product of \\(-10\\) and the difference of \\(p\\phantom{\\rule{0.2em}{0ex}}\\text{and}\\phantom{\\rule{0.2em}{0ex}}q\\)<\/td>\n<td style=\"width: 50%; height: 15px;\">64. the product of \\(-13\\) and the difference of \\(c\\phantom{\\rule{0.2em}{0ex}}\\text{and}\\phantom{\\rule{0.2em}{0ex}}d\\)<\/td>\n<\/tr>\n<\/tbody>\n<\/table>\n<h2>Use Integers in Applications<\/h2>\n<p id=\"fs-id1166423907674\">In the following exercises, solve.<\/p>\n\n<table style=\"border-collapse: collapse; width: 100%;\" border=\"0\">\n<tbody>\n<tr>\n<td style=\"width: 50%;\">65. <strong data-effect=\"bold\">Temperature<\/strong> On January \\(15\\), the high temperature in Lytton, British Columbia, was \\(84\\)\u00b0 . That same day, the high temperature in Fort Nelson, British Columbia was \\(-12\\)\u00b0. What was the difference between the temperature in Lytton and the temperature in Embarrass?<\/td>\n<td style=\"width: 50%;\">66.<strong data-effect=\"bold\"> Temperature<\/strong> On January \\(21\\), the high temperature in Palm Springs, California, was \\(89\\)\u00b0, and the high temperature in Whitefield, New Hampshire was \\(-31\\)\u00b0. What was the difference between the temperature in Palm Springs and the temperature in Whitefield?<\/td>\n<\/tr>\n<tr>\n<td style=\"width: 50%;\">67. <strong data-effect=\"bold\">Football<\/strong> At the first down, the Chargers had the ball on their 25 yard line. On the next three downs, they lost 6 yards, gained 10 yards, and lost 8 yards. What was the yard line at the end of the fourth down?<\/td>\n<td style=\"width: 50%;\">68.<strong data-effect=\"bold\"> Football<\/strong> At the first down, the Steelers had the ball on their 30 yard line. On the next three downs, they gained 9 yards, lost 14 yards, and lost 2 yards. What was the yard line at the end of the fourth down?<\/td>\n<\/tr>\n<tr>\n<td style=\"width: 50%;\">69.<strong data-effect=\"bold\"> Checking Account<\/strong> Ester has \\$124 in her checking account. She writes a check for \\$152. What is the new balance in her checking account?<\/td>\n<td style=\"width: 50%;\">70.<strong data-effect=\"bold\"> Checking Account<\/strong> Selina has \\$165 in her checking account. She writes a check for \\$207. What is the new balance in her checking account?<\/td>\n<\/tr>\n<tr>\n<td style=\"width: 50%;\">71. <strong data-effect=\"bold\">Checking Account<\/strong> Kevin has a balance of \\(-\\$38\\) in his checking account. He deposits \\$225 to the account. What is the new balance?<\/td>\n<td style=\"width: 50%;\">72. <strong data-effect=\"bold\">Checking Account<\/strong> Reymonte has a balance of \\(-\\$49\\) in his checking account. He deposits \\$281 to the account. What is the new balance?<\/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%;\">73. <strong data-effect=\"bold\">Stock market<\/strong> Javier owns 300 shares of stock in one company. On Tuesday, the stock price dropped \\$12 per share. What was the total effect on Javier\u2019s portfolio?<\/td>\n<td style=\"width: 50%;\">74. <strong data-effect=\"bold\">Weight loss<\/strong> In the first week of a diet program, eight women lost an average of 3 pounds each. What was the total weight change for the eight women?<\/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%;\">75. In your own words, state the rules for multiplying integers.<\/td>\n<td style=\"width: 50%;\">76. In your own words, state the rules for dividing integers.<\/td>\n<\/tr>\n<tr>\n<td style=\"width: 50%;\">77. Why is \\(-{2}^{4}\\ne {\\left(-2\\right)}^{4}?\\)<\/td>\n<td style=\"width: 50%;\">78. Why is \\(-{4}^{3}={\\left(-4\\right)}^{3}?\\)<\/td>\n<\/tr>\n<\/tbody>\n<\/table>\n<h1>Answers<\/h1>\n<table style=\"border-collapse: collapse; width: 100%; height: 153px;\" border=\"0\">\n<tbody>\n<tr style=\"height: 17px;\">\n<td style=\"width: 33.3333%; height: 17px;\">1. \\(-32\\)<\/td>\n<td style=\"width: 33.3333%; height: 17px;\">3. \\(-63\\)<\/td>\n<td style=\"width: 33.3333%; height: 17px;\">5. \\(-6\\)<\/td>\n<\/tr>\n<tr style=\"height: 17px;\">\n<td style=\"width: 33.3333%; height: 17px;\">7. 14<\/td>\n<td style=\"width: 33.3333%; height: 17px;\">9. \\(-4\\)<\/td>\n<td style=\"width: 33.3333%; height: 17px;\">11. 13<\/td>\n<\/tr>\n<tr style=\"height: 17px;\">\n<td style=\"width: 33.3333%; height: 17px;\">13. \\(-12\\)<\/td>\n<td style=\"width: 33.3333%; height: 17px;\">15. \\(-47\\)<\/td>\n<td style=\"width: 33.3333%; height: 17px;\">17. 64<\/td>\n<\/tr>\n<tr style=\"height: 17px;\">\n<td style=\"width: 33.3333%; height: 17px;\">19. \\(-16\\)<\/td>\n<td style=\"width: 33.3333%; height: 17px;\">21. 90<\/td>\n<td style=\"width: 33.3333%; height: 17px;\">23. 9<\/td>\n<\/tr>\n<tr style=\"height: 17px;\">\n<td style=\"width: 33.3333%; height: 17px;\">25. 41<\/td>\n<td style=\"width: 33.3333%; height: 17px;\">27. \\(-9\\)<\/td>\n<td style=\"width: 33.3333%; height: 17px;\">29. \\(-29\\)<\/td>\n<\/tr>\n<tr style=\"height: 17px;\">\n<td style=\"width: 33.3333%; height: 17px;\">31. 5<\/td>\n<td style=\"width: 33.3333%; height: 17px;\">33. a)\\(-47\\) b) 16<\/td>\n<td style=\"width: 33.3333%; height: 17px;\">35. a)\\(-4\\) b) 10<\/td>\n<\/tr>\n<tr style=\"height: 17px;\">\n<td style=\"width: 33.3333%; height: 17px;\">37. \\(-8\\)<\/td>\n<td style=\"width: 33.3333%; height: 17px;\">39. \\(-16\\)<\/td>\n<td style=\"width: 33.3333%; height: 17px;\">41. 121<\/td>\n<\/tr>\n<tr style=\"height: 17px;\">\n<td style=\"width: 33.3333%; height: 17px;\">43. a) 1 b) 33<\/td>\n<td style=\"width: 33.3333%; height: 17px;\">45. a)\\(-5\\)b) 25<\/td>\n<td style=\"width: 33.3333%; height: 17px;\">47. 21<\/td>\n<\/tr>\n<tr style=\"height: 17px;\">\n<td style=\"width: 33.3333%; height: 17px;\">49. \\(-56\\)<\/td>\n<td style=\"width: 33.3333%; height: 17px;\">51. \\(\\left(3+\\left(-15\\right)\\right)+7;-5\\)<\/td>\n<td style=\"width: 33.3333%; height: 17px;\">53. \\(10-\\left(-18\\right);28\\)<\/td>\n<\/tr>\n<tr>\n<td style=\"width: 33.3333%;\">55. \\(-5-\\left(-30\\right);25\\)<\/td>\n<td style=\"width: 33.3333%;\">57. \\(-3\\cdot 15;-45\\)<\/td>\n<td style=\"width: 33.3333%;\">59. \\(-60\\div\\left(-20\\right);3\\)<\/td>\n<\/tr>\n<tr>\n<td style=\"width: 33.3333%;\">61. \\(\\frac{-6}{a+b}\\)<\/td>\n<td style=\"width: 33.3333%;\">63. \\(-10\\left(p-q\\right)\\)<\/td>\n<td style=\"width: 33.3333%;\">65. \\(96\\)\u00b0<\/td>\n<\/tr>\n<tr>\n<td style=\"width: 33.3333%;\">67. 21<\/td>\n<td style=\"width: 33.3333%;\">69. \\(\\text{-}\\$28\\)<\/td>\n<td style=\"width: 33.3333%;\">71. \\$187<\/td>\n<\/tr>\n<tr>\n<td style=\"width: 33.3333%;\">73. \\(\\text{-}\\$3600\\)<\/td>\n<td style=\"width: 33.3333%;\">75. Answers may vary<\/td>\n<td style=\"width: 33.3333%;\">77.\u00a0Answers may vary<\/td>\n<\/tr>\n<\/tbody>\n<\/table>\n<h1>Attributions<\/h1>\nThis chapter has been adapted from \u201cMultiply and Divide Integers\u201d in <a href=\"https:\/\/openstax.org\/details\/books\/elementary-algebra\"><em>Elementary Algebra<\/em><\/a> (OpenStax) by Lynn Marecek and MaryAnne Anthony-Smith, 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.\n\n<!-- pb_fixme -->","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>Multiply integers<\/li>\n<li>Divide integers<\/li>\n<li>Simplify expressions with integers<\/li>\n<li>Evaluate variable expressions with integers<\/li>\n<li>Translate English phrases to algebraic expressions<\/li>\n<li>Use integers in applications<\/li>\n<\/ul>\n<\/div>\n<\/div>\n<h1>Multiply Integers<\/h1>\n<p id=\"fs-id1170654047593\">Since multiplication is mathematical shorthand for repeated addition, our model can easily be applied to show <span class=\"no-emphasis\" data-type=\"term\">multiplication<\/span> of <span class=\"no-emphasis\" data-type=\"term\">integers<\/span>. Let\u2019s look at this concrete model to see what patterns we notice. We will use the same examples that we used for addition and subtraction. Here, we will use the model just to help us discover the pattern.<\/p>\n<p id=\"fs-id1170654027710\">We remember that <img loading=\"lazy\" decoding=\"async\" src=\"https:\/\/opentextbc.ca\/introalgebra\/wp-content\/ql-cache\/quicklatex.com-3c7ce7788e60e03d2a0376725734513b_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"&#97;&#32;&#92;&#99;&#100;&#111;&#116;&#32;&#98;\" title=\"Rendered by QuickLaTeX.com\" height=\"12\" width=\"30\" style=\"vertical-align: 0px;\" \/> means add <em data-effect=\"italics\">a<\/em>, <em data-effect=\"italics\">b<\/em> times. Here, we are using the model just to help us discover the pattern.<\/p>\n<p><span id=\"fs-id1170652629325\" data-type=\"media\" data-alt=\"Two images are shown side-by-side. The image on the left has the equation five times three at the top. Below this it reads \u201cadd 5, 3 times.\u201d Below this depicts three rows of blue counters, with five counters in each row. Under this, it says \u201c15 positives.\u201d Under thisis the equation\u201c5 times 3 equals 15.\u201d The image on the right reads \u201cnegative 5 times three. The three is in parentheses. Below this it reads, \u201cadd negative five, three times.\u201d Under this are fifteen red counters in three rows of five. Below this it reads\u201d \u201c15 negatives\u201d. Below this is the equation negative five times 3 equals negative 15.\u201d\"><img decoding=\"async\" class=\"aligncenter\" src=\"https:\/\/opentextbc.ca\/accessibilitytoolkit\/wp-content\/uploads\/sites\/333\/2020\/08\/CNX_ElemAlg_Figure_01_04_001_img_new.jpg\" alt=\"Two images are shown side-by-side. The image on the left has the equation five times three at the top. Below this it reads \u201cadd 5, 3 times.\u201d Below this depicts three rows of blue counters, with five counters in each row. Under this, it says \u201c15 positives.\u201d Under thisis the equation\u201c5 times 3 equals 15.\u201d The image on the right reads \u201cnegative 5 times three. The three is in parentheses. Below this it reads, \u201cadd negative five, three times.\u201d Under this are fifteen red counters in three rows of five. Below this it reads\u201d \u201c15 negatives\u201d. Below this is the equation negative five times 3 equals negative 15.\u201d\" data-media-type=\"image\/jpeg\" \/><\/span><\/p>\n<p id=\"fs-id1170654235984\">The next two examples are more interesting.<\/p>\n<p id=\"fs-id1171791114068\">What does it mean to multiply 5 by <img loading=\"lazy\" decoding=\"async\" src=\"https:\/\/opentextbc.ca\/introalgebra\/wp-content\/ql-cache\/quicklatex.com-80cc5c6a8396c9c51a989af972cef479_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"&#45;&#51;&#63;\" title=\"Rendered by QuickLaTeX.com\" height=\"12\" width=\"30\" style=\"vertical-align: 0px;\" \/> It means subtract 5, 3 times. Looking at subtraction as \u201ctaking away,\u201d it means to take away 5, 3 times. But there is nothing to take away, so we start by adding neutral pairs on the workspace. Then we take away 5 three times.<\/p>\n<p><span id=\"fs-id1170654116877\" data-type=\"media\" data-alt=\"This figure has two columns. In the top row, the left column contains the expression 5 times negative 3. This means take away 5, three times. Below this, there are three groups of five red negative counters, and below each group of red counters is an identical group of five blue positive counters. What are left are fifteen negatives, represented by 15 red counters. Underneath the counters is the equation 5 times negative 3 equals negative 15. In the top row, the right column contains the expression negative 5 times negative 3. This means take away negative 5, three times. Below this, there are three groups of five blue positive counters, and below each group of blue counters is an identical group of five red negative counters. What are left are fifteen positives, represented by 15 blue counters. Underneath the blue counters is the equation negative 5 times negative 3 equals 15.\"><img decoding=\"async\" class=\"aligncenter\" src=\"https:\/\/opentextbc.ca\/accessibilitytoolkit\/wp-content\/uploads\/sites\/333\/2021\/03\/CNX_ElemAlg_Figure_01_04_002_img_new.jpg\" alt=\"This figure has two columns. In the top row, the left column contains the expression 5 times negative 3. This means take away 5, three times. Below this, there are three groups of five red negative counters, and below each group of red counters is an identical group of five blue positive counters. What are left are fifteen negatives, represented by 15 red counters. Underneath the counters is the equation 5 times negative 3 equals negative 15. In the top row, the right column contains the expression negative 5 times negative 3. This means take away negative 5, three times. Below this, there are three groups of five blue positive counters, and below each group of blue counters is an identical group of five red negative counters. What are left are fifteen positives, represented by 15 blue counters. Underneath the blue counters is the equation negative 5 times negative 3 equals 15.\" data-media-type=\"image\/jpeg\" \/><\/span><\/p>\n<p id=\"fs-id1170654009263\">In summary:<\/p>\n<div id=\"fs-id1170653916873\" class=\"unnumbered\" data-type=\"equation\" data-label=\"\"><img loading=\"lazy\" decoding=\"async\" src=\"https:\/\/opentextbc.ca\/introalgebra\/wp-content\/ql-cache\/quicklatex.com-e5c974bb2de5b919a80e070a1666c45e_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;&#99;&#99;&#99;&#99;&#125;&#92;&#104;&#102;&#105;&#108;&#108;&#32;&#53;&#32;&#92;&#99;&#100;&#111;&#116;&#32;&#51;&#38;&#32;&#61;&#92;&#104;&#102;&#105;&#108;&#108;&#32;&#38;&#32;&#49;&#53;&#92;&#104;&#102;&#105;&#108;&#108;&#32;&#38;&#32;&#38;&#32;&#38;&#32;&#92;&#104;&#102;&#105;&#108;&#108;&#32;&#45;&#53;&#92;&#108;&#101;&#102;&#116;&#40;&#51;&#92;&#114;&#105;&#103;&#104;&#116;&#41;&#38;&#32;&#61;&#92;&#104;&#102;&#105;&#108;&#108;&#32;&#38;&#32;&#45;&#49;&#53;&#92;&#104;&#102;&#105;&#108;&#108;&#32;&#92;&#92;&#32;&#92;&#104;&#102;&#105;&#108;&#108;&#32;&#53;&#92;&#108;&#101;&#102;&#116;&#40;&#45;&#51;&#92;&#114;&#105;&#103;&#104;&#116;&#41;&#38;&#32;&#61;&#92;&#104;&#102;&#105;&#108;&#108;&#32;&#38;&#32;&#45;&#49;&#53;&#92;&#104;&#102;&#105;&#108;&#108;&#32;&#38;&#32;&#38;&#32;&#38;&#32;&#92;&#104;&#102;&#105;&#108;&#108;&#32;&#92;&#108;&#101;&#102;&#116;&#40;&#45;&#53;&#92;&#114;&#105;&#103;&#104;&#116;&#41;&#92;&#108;&#101;&#102;&#116;&#40;&#45;&#51;&#92;&#114;&#105;&#103;&#104;&#116;&#41;&#38;&#32;&#61;&#92;&#104;&#102;&#105;&#108;&#108;&#32;&#38;&#32;&#49;&#53;&#92;&#104;&#102;&#105;&#108;&#108;&#32;&#92;&#101;&#110;&#100;&#123;&#97;&#114;&#114;&#97;&#121;&#125;\" title=\"Rendered by QuickLaTeX.com\" height=\"41\" width=\"328\" style=\"vertical-align: -16px;\" \/><\/div>\n<p id=\"fs-id1170653885621\">Notice that for multiplication of two signed numbers, when the:<\/p>\n<ul id=\"fs-id1166425881422\" data-bullet-style=\"bullet\">\n<li>signs are the <em data-effect=\"italics\">same<\/em>, the product is <em data-effect=\"italics\">positive<\/em>.<\/li>\n<li>signs are <em data-effect=\"italics\">different<\/em>, the product is <em data-effect=\"italics\">negative<\/em>.<\/li>\n<\/ul>\n<p id=\"fs-id1170653867968\">We\u2019ll put this all together in the chart below<\/p>\n<div class=\"textbox textbox--key-takeaways\">\n<header class=\"textbox__header\">\n<p class=\"textbox__title\">Multiplication of Signed Numbers<\/p>\n<\/header>\n<div class=\"textbox__content\">\n<p>For multiplication of two signed numbers:<\/p>\n<table class=\"grid\" style=\"width: 100%;\">\n<tbody>\n<tr valign=\"top\">\n<th data-valign=\"top\" data-align=\"left\">Same signs<\/th>\n<td><strong>Product<\/strong><\/td>\n<td><strong>Example<\/strong><\/td>\n<\/tr>\n<tr>\n<td>Two positives<br \/>\nTwo negatives<\/td>\n<td>Positive<br \/>\nPositive<\/td>\n<td><img loading=\"lazy\" decoding=\"async\" src=\"https:\/\/opentextbc.ca\/introalgebra\/wp-content\/ql-cache\/quicklatex.com-e6998895f6cc95e93320c3ac8d4e80ec_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;&#125;&#92;&#104;&#102;&#105;&#108;&#108;&#32;&#55;&#92;&#99;&#100;&#111;&#116;&#52;&#38;&#32;&#61;&#92;&#104;&#102;&#105;&#108;&#108;&#32;&#38;&#32;&#50;&#56;&#92;&#104;&#102;&#105;&#108;&#108;&#32;&#92;&#92;&#32;&#92;&#104;&#102;&#105;&#108;&#108;&#32;&#45;&#56;&#92;&#108;&#101;&#102;&#116;&#40;&#45;&#54;&#92;&#114;&#105;&#103;&#104;&#116;&#41;&#38;&#32;&#61;&#92;&#104;&#102;&#105;&#108;&#108;&#32;&#38;&#32;&#52;&#56;&#92;&#104;&#102;&#105;&#108;&#108;&#32;&#92;&#101;&#110;&#100;&#123;&#97;&#114;&#114;&#97;&#121;&#125;\" title=\"Rendered by QuickLaTeX.com\" height=\"40\" width=\"125\" style=\"vertical-align: -16px;\" \/><\/td>\n<\/tr>\n<\/tbody>\n<\/table>\n<table class=\"grid\" style=\"width: 100%;\">\n<tbody>\n<tr>\n<td><strong>Different signs<\/strong><\/td>\n<td><strong>Product<\/strong><\/td>\n<td><strong>Example<\/strong><\/td>\n<\/tr>\n<tr>\n<td>Positive \\cdot negative<br \/>\nNegative \\cdot positive<\/td>\n<td>Negative<br \/>\nNegative<\/td>\n<td><img loading=\"lazy\" decoding=\"async\" src=\"https:\/\/opentextbc.ca\/introalgebra\/wp-content\/ql-cache\/quicklatex.com-8a8bde3e9cb5aa1a04adf7808eb14fb7_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;&#125;&#92;&#104;&#102;&#105;&#108;&#108;&#32;&#55;&#92;&#108;&#101;&#102;&#116;&#40;&#45;&#57;&#92;&#114;&#105;&#103;&#104;&#116;&#41;&#38;&#32;&#61;&#92;&#104;&#102;&#105;&#108;&#108;&#32;&#38;&#32;&#45;&#54;&#51;&#92;&#104;&#102;&#105;&#108;&#108;&#32;&#92;&#92;&#32;&#92;&#104;&#102;&#105;&#108;&#108;&#32;&#45;&#53;&#92;&#99;&#100;&#111;&#116;&#49;&#48;&#38;&#32;&#61;&#92;&#104;&#102;&#105;&#108;&#108;&#32;&#38;&#32;&#45;&#53;&#48;&#92;&#104;&#102;&#105;&#108;&#108;&#32;&#92;&#101;&#110;&#100;&#123;&#97;&#114;&#114;&#97;&#121;&#125;\" title=\"Rendered by QuickLaTeX.com\" height=\"36\" width=\"130\" style=\"vertical-align: -11px;\" \/><\/td>\n<\/tr>\n<\/tbody>\n<\/table>\n<\/div>\n<\/div>\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-id1170654016481\" data-type=\"problem\">\n<p id=\"fs-id1170653756055\">Multiply: a) <img loading=\"lazy\" decoding=\"async\" src=\"https:\/\/opentextbc.ca\/introalgebra\/wp-content\/ql-cache\/quicklatex.com-de7c632208e88535c1777d8c3eea9b90_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"&#45;&#57;&#92;&#99;&#100;&#111;&#116;&#51;\" title=\"Rendered by QuickLaTeX.com\" height=\"12\" width=\"43\" style=\"vertical-align: 0px;\" \/> b) <img loading=\"lazy\" decoding=\"async\" src=\"https:\/\/opentextbc.ca\/introalgebra\/wp-content\/ql-cache\/quicklatex.com-777d7e03559de57012fa6bee17017df6_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"&#45;&#50;&#92;&#108;&#101;&#102;&#116;&#40;&#45;&#53;&#92;&#114;&#105;&#103;&#104;&#116;&#41;\" title=\"Rendered by QuickLaTeX.com\" height=\"18\" width=\"61\" style=\"vertical-align: -4px;\" \/> c) <img loading=\"lazy\" decoding=\"async\" src=\"https:\/\/opentextbc.ca\/introalgebra\/wp-content\/ql-cache\/quicklatex.com-70eabcb64a7d9494be9d191cbf23d11d_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"&#52;&#92;&#108;&#101;&#102;&#116;&#40;&#45;&#56;&#92;&#114;&#105;&#103;&#104;&#116;&#41;\" title=\"Rendered by QuickLaTeX.com\" height=\"18\" width=\"48\" style=\"vertical-align: -4px;\" \/> d) <img loading=\"lazy\" decoding=\"async\" src=\"https:\/\/opentextbc.ca\/introalgebra\/wp-content\/ql-cache\/quicklatex.com-df846a36f642b6bb2be4b32f33f16369_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"&#55;&#92;&#99;&#100;&#111;&#116;&#54;\" title=\"Rendered by QuickLaTeX.com\" height=\"13\" width=\"31\" style=\"vertical-align: 0px;\" \/>.<\/p>\n<\/div>\n<div id=\"fs-id1170654013170\" 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-959\" summary=\".\">\n<tbody>\n<tr>\n<td>a)<br \/>\nMultiply, noting that the signs are different so the product is negative.<\/td>\n<td><img loading=\"lazy\" decoding=\"async\" src=\"https:\/\/opentextbc.ca\/introalgebra\/wp-content\/ql-cache\/quicklatex.com-e77142885052948c1ad2369080360d8e_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;&#125;&#45;&#57;&#92;&#99;&#100;&#111;&#116;&#51;&#92;&#92;&#32;&#45;&#50;&#55;&#92;&#101;&#110;&#100;&#123;&#97;&#114;&#114;&#97;&#121;&#125;\" title=\"Rendered by QuickLaTeX.com\" height=\"34\" width=\"44\" style=\"vertical-align: -11px;\" \/><\/td>\n<\/tr>\n<tr>\n<td>b)<br \/>\nMultiply, noting that the signs are the same so the product is positive.<\/td>\n<td><img loading=\"lazy\" decoding=\"async\" src=\"https:\/\/opentextbc.ca\/introalgebra\/wp-content\/ql-cache\/quicklatex.com-288b5020f6ce0368a272332f7f054c5b_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;&#125;&#45;&#50;&#92;&#108;&#101;&#102;&#116;&#40;&#45;&#53;&#92;&#114;&#105;&#103;&#104;&#116;&#41;&#92;&#92;&#32;&#49;&#48;&#92;&#101;&#110;&#100;&#123;&#97;&#114;&#114;&#97;&#121;&#125;\" title=\"Rendered by QuickLaTeX.com\" height=\"37\" width=\"61\" style=\"vertical-align: -12px;\" \/><\/td>\n<\/tr>\n<tr>\n<td>c)<br \/>\nMultiply, with different signs.<\/td>\n<td><img loading=\"lazy\" decoding=\"async\" src=\"https:\/\/opentextbc.ca\/introalgebra\/wp-content\/ql-cache\/quicklatex.com-5e93a5f4831eda5c57265e0b72c0543f_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;&#125;&#52;&#92;&#108;&#101;&#102;&#116;&#40;&#45;&#56;&#92;&#114;&#105;&#103;&#104;&#116;&#41;&#92;&#92;&#32;&#45;&#51;&#50;&#92;&#101;&#110;&#100;&#123;&#97;&#114;&#114;&#97;&#121;&#125;\" title=\"Rendered by QuickLaTeX.com\" height=\"36\" width=\"48\" style=\"vertical-align: -11px;\" \/><\/td>\n<\/tr>\n<tr>\n<td>d)<br \/>\nMultiply, with same signs.<\/td>\n<td><img loading=\"lazy\" decoding=\"async\" src=\"https:\/\/opentextbc.ca\/introalgebra\/wp-content\/ql-cache\/quicklatex.com-36eedafad1fb35dfb4e5deb1fdcde93e_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;&#125;&#55;&#92;&#99;&#100;&#111;&#116;&#54;&#92;&#92;&#32;&#52;&#50;&#92;&#101;&#110;&#100;&#123;&#97;&#114;&#114;&#97;&#121;&#125;\" title=\"Rendered by QuickLaTeX.com\" height=\"35\" width=\"31\" style=\"vertical-align: -11px;\" \/><\/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-id1170654150864\" data-type=\"problem\">\n<p id=\"fs-id1170653870759\">Multiply: a) <img loading=\"lazy\" decoding=\"async\" src=\"https:\/\/opentextbc.ca\/introalgebra\/wp-content\/ql-cache\/quicklatex.com-753d2b8d68d83e3bbc10f04cace32aa2_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"&#45;&#54;&#92;&#99;&#100;&#111;&#116;&#56;\" title=\"Rendered by QuickLaTeX.com\" height=\"12\" width=\"43\" style=\"vertical-align: 0px;\" \/> b) <img loading=\"lazy\" decoding=\"async\" src=\"https:\/\/opentextbc.ca\/introalgebra\/wp-content\/ql-cache\/quicklatex.com-bc440a9bd341434fbc31c0a84282560e_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"&#45;&#52;&#92;&#108;&#101;&#102;&#116;&#40;&#45;&#55;&#92;&#114;&#105;&#103;&#104;&#116;&#41;\" title=\"Rendered by QuickLaTeX.com\" height=\"18\" width=\"61\" style=\"vertical-align: -4px;\" \/> c) <img loading=\"lazy\" decoding=\"async\" src=\"https:\/\/opentextbc.ca\/introalgebra\/wp-content\/ql-cache\/quicklatex.com-b361129d452a3d90c0bec2bb004052be_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"&#57;&#92;&#108;&#101;&#102;&#116;&#40;&#45;&#55;&#92;&#114;&#105;&#103;&#104;&#116;&#41;\" title=\"Rendered by QuickLaTeX.com\" height=\"18\" width=\"48\" style=\"vertical-align: -4px;\" \/> d) <img loading=\"lazy\" decoding=\"async\" src=\"https:\/\/opentextbc.ca\/introalgebra\/wp-content\/ql-cache\/quicklatex.com-f7778de7e8225296a7b3ab2b07c899a7_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"&#53;&#92;&#99;&#100;&#111;&#116;&#49;&#50;\" title=\"Rendered by QuickLaTeX.com\" height=\"13\" width=\"39\" style=\"vertical-align: 0px;\" \/>.<\/p>\n<\/div>\n<div id=\"fs-id1170654034104\" data-type=\"solution\">\n<details>\n<summary>Show answer<\/summary>\n<p id=\"fs-id1170653885313\">a)<img loading=\"lazy\" decoding=\"async\" src=\"https:\/\/opentextbc.ca\/introalgebra\/wp-content\/ql-cache\/quicklatex.com-08ed8320699be2770837da731d65c7c5_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"&#45;&#52;&#56;\" title=\"Rendered by QuickLaTeX.com\" height=\"13\" width=\"31\" style=\"vertical-align: -1px;\" \/> b) 28 c) <img loading=\"lazy\" decoding=\"async\" src=\"https:\/\/opentextbc.ca\/introalgebra\/wp-content\/ql-cache\/quicklatex.com-c081a4d1588de9f9de1dd7d5282b4c9d_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"&#45;&#54;&#51;\" title=\"Rendered by QuickLaTeX.com\" height=\"12\" width=\"31\" style=\"vertical-align: 0px;\" \/> d) 60<\/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 1.2<\/p>\n<\/header>\n<div class=\"textbox__content\">\n<div id=\"fs-id1170654016412\" data-type=\"problem\">\n<p id=\"fs-id1170654116452\">Multiply: a) <img loading=\"lazy\" decoding=\"async\" src=\"https:\/\/opentextbc.ca\/introalgebra\/wp-content\/ql-cache\/quicklatex.com-a2804bb3d8e2e26c3b9e59f0661f8cb6_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"&#45;&#56;&#92;&#99;&#100;&#111;&#116;&#55;\" title=\"Rendered by QuickLaTeX.com\" height=\"13\" width=\"43\" style=\"vertical-align: 0px;\" \/> b) <img loading=\"lazy\" decoding=\"async\" src=\"https:\/\/opentextbc.ca\/introalgebra\/wp-content\/ql-cache\/quicklatex.com-fb79e6862442da81207cad531c1130a7_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"&#45;&#54;&#92;&#108;&#101;&#102;&#116;&#40;&#45;&#57;&#92;&#114;&#105;&#103;&#104;&#116;&#41;\" title=\"Rendered by QuickLaTeX.com\" height=\"18\" width=\"61\" style=\"vertical-align: -4px;\" \/> c) <img loading=\"lazy\" decoding=\"async\" src=\"https:\/\/opentextbc.ca\/introalgebra\/wp-content\/ql-cache\/quicklatex.com-e99ff919ab15281b2038d914222f91d3_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"&#55;&#92;&#108;&#101;&#102;&#116;&#40;&#45;&#52;&#92;&#114;&#105;&#103;&#104;&#116;&#41;\" title=\"Rendered by QuickLaTeX.com\" height=\"18\" width=\"48\" style=\"vertical-align: -4px;\" \/> d) <img loading=\"lazy\" decoding=\"async\" src=\"https:\/\/opentextbc.ca\/introalgebra\/wp-content\/ql-cache\/quicklatex.com-3a5fc0f8a225cf8e5d6aa84e7c519a7a_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"&#51;&#92;&#99;&#100;&#111;&#116;&#49;&#51;\" title=\"Rendered by QuickLaTeX.com\" height=\"12\" width=\"40\" style=\"vertical-align: 0px;\" \/>.<\/p>\n<\/div>\n<div id=\"fs-id1170653741029\" data-type=\"solution\">\n<details>\n<summary>Show answer<\/summary>\n<p id=\"fs-id1170653795701\">a)<img loading=\"lazy\" decoding=\"async\" src=\"https:\/\/opentextbc.ca\/introalgebra\/wp-content\/ql-cache\/quicklatex.com-eeacf7895c3fd138514ad215aa482af4_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"&#45;&#53;&#54;\" title=\"Rendered by QuickLaTeX.com\" height=\"13\" width=\"31\" style=\"vertical-align: 0px;\" \/> b) 54 c) <img loading=\"lazy\" decoding=\"async\" src=\"https:\/\/opentextbc.ca\/introalgebra\/wp-content\/ql-cache\/quicklatex.com-7eaefbab9f26b55d0afa7f1689372c40_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"&#45;&#50;&#56;\" title=\"Rendered by QuickLaTeX.com\" height=\"12\" width=\"31\" style=\"vertical-align: 0px;\" \/> d) 39<\/p>\n<\/details>\n<\/div>\n<\/div>\n<\/div>\n<p id=\"fs-id1170654150913\">When we multiply a number by 1, the result is the same number. What happens when we multiply a number by <img loading=\"lazy\" decoding=\"async\" src=\"https:\/\/opentextbc.ca\/introalgebra\/wp-content\/ql-cache\/quicklatex.com-7b34c01098c83fa602de54e9d74d63a9_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"&#45;&#49;\" title=\"Rendered by QuickLaTeX.com\" height=\"13\" width=\"21\" style=\"vertical-align: -1px;\" \/>? Let\u2019s multiply a positive number and then a negative number by <img loading=\"lazy\" decoding=\"async\" src=\"https:\/\/opentextbc.ca\/introalgebra\/wp-content\/ql-cache\/quicklatex.com-7b34c01098c83fa602de54e9d74d63a9_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"&#45;&#49;\" title=\"Rendered by QuickLaTeX.com\" height=\"13\" width=\"21\" style=\"vertical-align: -1px;\" \/> to see what we get.<\/p>\n<p><img loading=\"lazy\" decoding=\"async\" src=\"https:\/\/opentextbc.ca\/introalgebra\/wp-content\/ql-cache\/quicklatex.com-51234b5987c36f317662fc30ae7fcc20_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;&#99;&#99;&#99;&#125;&#38;&#32;&#38;&#32;&#38;&#32;&#92;&#104;&#102;&#105;&#108;&#108;&#32;&#45;&#49;&#92;&#99;&#100;&#111;&#116;&#32;&#52;&#92;&#104;&#102;&#105;&#108;&#108;&#32;&#38;&#32;&#38;&#32;&#38;&#32;&#92;&#104;&#102;&#105;&#108;&#108;&#32;&#45;&#49;&#92;&#108;&#101;&#102;&#116;&#40;&#45;&#51;&#92;&#114;&#105;&#103;&#104;&#116;&#41;&#92;&#104;&#102;&#105;&#108;&#108;&#32;&#92;&#92;&#32;&#92;&#116;&#101;&#120;&#116;&#123;&#77;&#117;&#108;&#116;&#105;&#112;&#108;&#121;&#46;&#125;&#92;&#104;&#102;&#105;&#108;&#108;&#32;&#38;&#32;&#38;&#32;&#38;&#32;&#92;&#104;&#102;&#105;&#108;&#108;&#32;&#45;&#52;&#92;&#104;&#102;&#105;&#108;&#108;&#32;&#38;&#32;&#38;&#32;&#38;&#32;&#92;&#104;&#102;&#105;&#108;&#108;&#32;&#51;&#92;&#104;&#102;&#105;&#108;&#108;&#32;&#92;&#92;&#32;&#38;&#32;&#38;&#32;&#38;&#32;&#92;&#104;&#102;&#105;&#108;&#108;&#32;&#45;&#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;&#105;&#115;&#32;&#116;&#104;&#101;&#32;&#111;&#112;&#112;&#111;&#115;&#105;&#116;&#101;&#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;&#52;&#46;&#92;&#104;&#102;&#105;&#108;&#108;&#32;&#38;&#32;&#38;&#32;&#38;&#32;&#92;&#104;&#102;&#105;&#108;&#108;&#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;&#116;&#101;&#120;&#116;&#123;&#105;&#115;&#32;&#116;&#104;&#101;&#32;&#111;&#112;&#112;&#111;&#115;&#105;&#116;&#101;&#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;&#45;&#51;&#46;&#92;&#104;&#102;&#105;&#108;&#108;&#32;&#92;&#101;&#110;&#100;&#123;&#97;&#114;&#114;&#97;&#121;&#125;\" title=\"Rendered by QuickLaTeX.com\" height=\"62\" width=\"528\" style=\"vertical-align: -26px;\" \/><\/p>\n<p id=\"fs-id1170652622975\">Each time we multiply a number by <img loading=\"lazy\" decoding=\"async\" src=\"https:\/\/opentextbc.ca\/introalgebra\/wp-content\/ql-cache\/quicklatex.com-7b34c01098c83fa602de54e9d74d63a9_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"&#45;&#49;\" title=\"Rendered by QuickLaTeX.com\" height=\"13\" width=\"21\" style=\"vertical-align: -1px;\" \/>, we get its opposite!<\/p>\n<div id=\"fs-id1170653776943\" 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\">Multiplication by <img loading=\"lazy\" decoding=\"async\" src=\"https:\/\/opentextbc.ca\/introalgebra\/wp-content\/ql-cache\/quicklatex.com-7b34c01098c83fa602de54e9d74d63a9_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"&#45;&#49;\" title=\"Rendered by QuickLaTeX.com\" height=\"13\" width=\"21\" style=\"vertical-align: -1px;\" \/><\/p>\n<\/header>\n<div class=\"textbox__content\">\n<p><img loading=\"lazy\" decoding=\"async\" src=\"https:\/\/opentextbc.ca\/introalgebra\/wp-content\/ql-cache\/quicklatex.com-160fe5d9875697871f0f4bbf770cd795_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"&#45;&#49;&#97;&#61;&#92;&#116;&#101;&#120;&#116;&#123;&#45;&#125;&#97;\" title=\"Rendered by QuickLaTeX.com\" height=\"12\" width=\"70\" style=\"vertical-align: 0px;\" \/><\/p>\n<p>Multiplying a number by <img loading=\"lazy\" decoding=\"async\" src=\"https:\/\/opentextbc.ca\/introalgebra\/wp-content\/ql-cache\/quicklatex.com-7b34c01098c83fa602de54e9d74d63a9_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"&#45;&#49;\" title=\"Rendered by QuickLaTeX.com\" height=\"13\" width=\"21\" style=\"vertical-align: -1px;\" \/> gives its opposite.<\/p>\n<\/div>\n<\/div>\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-id1170654068942\" data-type=\"problem\">\n<p id=\"fs-id1170654036219\">Multiply: a) <img loading=\"lazy\" decoding=\"async\" src=\"https:\/\/opentextbc.ca\/introalgebra\/wp-content\/ql-cache\/quicklatex.com-4cc02b0dea58170ed1d677175e755a62_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"&#45;&#49;&#92;&#99;&#100;&#111;&#116;&#55;\" title=\"Rendered by QuickLaTeX.com\" height=\"13\" width=\"43\" style=\"vertical-align: 0px;\" \/> b) <img loading=\"lazy\" decoding=\"async\" src=\"https:\/\/opentextbc.ca\/introalgebra\/wp-content\/ql-cache\/quicklatex.com-3d008c149a4735bade76f09f84da99b0_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"&#45;&#49;&#92;&#108;&#101;&#102;&#116;&#40;&#45;&#49;&#49;&#92;&#114;&#105;&#103;&#104;&#116;&#41;\" title=\"Rendered by QuickLaTeX.com\" height=\"18\" width=\"70\" style=\"vertical-align: -4px;\" \/>.<\/p>\n<\/div>\n<div id=\"fs-id1170653910210\" data-type=\"solution\">\n<div data-type=\"title\"><\/div>\n<div data-type=\"title\"><strong>Solution<\/strong><\/div>\n<table id=\"eip-228\" summary=\".\">\n<tbody>\n<tr>\n<td>a)<br \/>\nMultiply, noting that the signs are different so the product is negative.<\/td>\n<td><img loading=\"lazy\" decoding=\"async\" src=\"https:\/\/opentextbc.ca\/introalgebra\/wp-content\/ql-cache\/quicklatex.com-cb90ab6d1f527080952f45666bef6432_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;&#125;&#45;&#49;&#92;&#99;&#100;&#111;&#116;&#55;&#92;&#92;&#32;&#45;&#55;&#92;&#92;&#32;&#45;&#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;&#116;&#104;&#101;&#32;&#111;&#112;&#112;&#111;&#115;&#105;&#116;&#101;&#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;&#55;&#46;&#92;&#101;&#110;&#100;&#123;&#97;&#114;&#114;&#97;&#121;&#125;\" title=\"Rendered by QuickLaTeX.com\" height=\"61\" width=\"175\" style=\"vertical-align: -26px;\" \/><\/td>\n<\/tr>\n<tr>\n<td>b)<br \/>\nMultiply, noting that the signs are the same so the product is positive.<\/td>\n<td><img loading=\"lazy\" decoding=\"async\" src=\"https:\/\/opentextbc.ca\/introalgebra\/wp-content\/ql-cache\/quicklatex.com-5a39f60ffd303d28baf399e762632ec6_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;&#125;&#45;&#49;&#92;&#108;&#101;&#102;&#116;&#40;&#45;&#49;&#49;&#92;&#114;&#105;&#103;&#104;&#116;&#41;&#92;&#92;&#32;&#49;&#49;&#92;&#92;&#32;&#49;&#49;&#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;&#116;&#104;&#101;&#32;&#111;&#112;&#112;&#111;&#115;&#105;&#116;&#101;&#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;&#45;&#49;&#49;&#46;&#92;&#101;&#110;&#100;&#123;&#97;&#114;&#114;&#97;&#121;&#125;\" title=\"Rendered by QuickLaTeX.com\" height=\"61\" width=\"201\" style=\"vertical-align: -25px;\" \/><\/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-id1170654073784\" data-type=\"problem\">\n<p id=\"fs-id1170653851085\">Multiply: a) <img loading=\"lazy\" decoding=\"async\" src=\"https:\/\/opentextbc.ca\/introalgebra\/wp-content\/ql-cache\/quicklatex.com-7ca2da17fc7236aab9ecd4bc8933058a_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"&#45;&#49;&#92;&#99;&#100;&#111;&#116;&#57;\" title=\"Rendered by QuickLaTeX.com\" height=\"12\" width=\"43\" style=\"vertical-align: 0px;\" \/> b) <img loading=\"lazy\" decoding=\"async\" src=\"https:\/\/opentextbc.ca\/introalgebra\/wp-content\/ql-cache\/quicklatex.com-4e5deed80daf9b22b8a48b2e79dafc77_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"&#45;&#49;&#32;&#92;&#99;&#100;&#111;&#116;&#32;&#92;&#108;&#101;&#102;&#116;&#40;&#45;&#49;&#55;&#92;&#114;&#105;&#103;&#104;&#116;&#41;\" title=\"Rendered by QuickLaTeX.com\" height=\"19\" width=\"79\" style=\"vertical-align: -5px;\" \/>.<\/p>\n<\/div>\n<div id=\"fs-id1170654014381\" data-type=\"solution\">\n<details>\n<summary>Show answer<\/summary>\n<p id=\"fs-id1170654231240\">a)<img loading=\"lazy\" decoding=\"async\" src=\"https:\/\/opentextbc.ca\/introalgebra\/wp-content\/ql-cache\/quicklatex.com-9672181aec15f8334b80ada7de4e4fc0_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"&#45;&#57;\" title=\"Rendered by QuickLaTeX.com\" height=\"12\" width=\"22\" style=\"vertical-align: 0px;\" \/> b) 17<\/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 2.2<\/p>\n<\/header>\n<div class=\"textbox__content\">\n<div id=\"fs-id1170654047261\" data-type=\"problem\">\n<p id=\"fs-id1170653804423\">Multiply: a) <img loading=\"lazy\" decoding=\"async\" src=\"https:\/\/opentextbc.ca\/introalgebra\/wp-content\/ql-cache\/quicklatex.com-21320231faabe21b0a91760883f4e94e_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"&#45;&#49;&#92;&#99;&#100;&#111;&#116;&#56;\" title=\"Rendered by QuickLaTeX.com\" height=\"12\" width=\"43\" style=\"vertical-align: 0px;\" \/> b) <img loading=\"lazy\" decoding=\"async\" src=\"https:\/\/opentextbc.ca\/introalgebra\/wp-content\/ql-cache\/quicklatex.com-758d61c8257fc211116d5cd48966202d_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"&#45;&#49;&#32;&#92;&#99;&#100;&#111;&#116;&#32;&#92;&#108;&#101;&#102;&#116;&#40;&#45;&#49;&#54;&#92;&#114;&#105;&#103;&#104;&#116;&#41;\" title=\"Rendered by QuickLaTeX.com\" height=\"19\" width=\"79\" style=\"vertical-align: -5px;\" \/>.<\/p>\n<\/div>\n<div id=\"fs-id1170654015023\" data-type=\"solution\">\n<details>\n<summary>Show answer<\/summary>\n<p id=\"fs-id1170653799135\">a)<img loading=\"lazy\" decoding=\"async\" src=\"https:\/\/opentextbc.ca\/introalgebra\/wp-content\/ql-cache\/quicklatex.com-ca32393b1b5af7c55a95d89cf9d610f2_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"&#45;&#56;\" title=\"Rendered by QuickLaTeX.com\" height=\"12\" width=\"22\" style=\"vertical-align: 0px;\" \/> b) 16<\/p>\n<\/details>\n<\/div>\n<\/div>\n<\/div>\n<\/div>\n<h1>Divide Integers<\/h1>\n<p id=\"fs-id1170654029961\">What about <span class=\"no-emphasis\" data-type=\"term\">division<\/span>? Division is the inverse operation of multiplication. So, <img loading=\"lazy\" decoding=\"async\" src=\"https:\/\/opentextbc.ca\/introalgebra\/wp-content\/ql-cache\/quicklatex.com-259fda24381aa07d31aa2faddde3156e_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"&#49;&#53;&#92;&#100;&#105;&#118;&#32;&#51;&#61;&#53;\" title=\"Rendered by QuickLaTeX.com\" height=\"14\" width=\"79\" style=\"vertical-align: -1px;\" \/> because <img loading=\"lazy\" decoding=\"async\" src=\"https:\/\/opentextbc.ca\/introalgebra\/wp-content\/ql-cache\/quicklatex.com-5b53d8cea1b2e23d1bbfe4264a550e01_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"&#53;&#92;&#99;&#100;&#111;&#116;&#51;&#61;&#49;&#53;\" title=\"Rendered by QuickLaTeX.com\" height=\"13\" width=\"71\" style=\"vertical-align: 0px;\" \/>. In words, this expression says that 15 can be divided into three groups of five each because adding five three times gives 15. Look at some examples of multiplying integers, to figure out the rules for dividing integers.<\/p>\n<p><img loading=\"lazy\" decoding=\"async\" src=\"https:\/\/opentextbc.ca\/introalgebra\/wp-content\/ql-cache\/quicklatex.com-1df1320a6a7d764d3da05dd21adb50fb_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;&#99;&#99;&#99;&#99;&#99;&#99;&#99;&#99;&#99;&#99;&#125;&#92;&#104;&#102;&#105;&#108;&#108;&#32;&#53;&#92;&#99;&#100;&#111;&#116;&#51;&#38;&#32;&#61;&#92;&#104;&#102;&#105;&#108;&#108;&#32;&#38;&#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;&#92;&#116;&#101;&#120;&#116;&#123;&#115;&#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;&#49;&#53;&#92;&#100;&#105;&#118;&#32;&#51;&#92;&#104;&#102;&#105;&#108;&#108;&#32;&#38;&#32;&#61;&#92;&#104;&#102;&#105;&#108;&#108;&#32;&#38;&#32;&#53;&#92;&#104;&#102;&#105;&#108;&#108;&#32;&#38;&#32;&#38;&#32;&#38;&#32;&#38;&#32;&#38;&#32;&#92;&#104;&#102;&#105;&#108;&#108;&#32;&#45;&#53;&#92;&#108;&#101;&#102;&#116;&#40;&#51;&#92;&#114;&#105;&#103;&#104;&#116;&#41;&#38;&#32;&#61;&#92;&#104;&#102;&#105;&#108;&#108;&#32;&#38;&#32;&#45;&#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;&#92;&#116;&#101;&#120;&#116;&#123;&#115;&#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;&#45;&#49;&#53;&#92;&#100;&#105;&#118;&#51;&#92;&#104;&#102;&#105;&#108;&#108;&#32;&#38;&#32;&#61;&#92;&#104;&#102;&#105;&#108;&#108;&#32;&#38;&#32;&#45;&#53;&#92;&#104;&#102;&#105;&#108;&#108;&#32;&#92;&#92;&#32;&#92;&#104;&#102;&#105;&#108;&#108;&#32;&#92;&#108;&#101;&#102;&#116;&#40;&#45;&#53;&#92;&#114;&#105;&#103;&#104;&#116;&#41;&#92;&#108;&#101;&#102;&#116;&#40;&#45;&#51;&#92;&#114;&#105;&#103;&#104;&#116;&#41;&#38;&#32;&#61;&#92;&#104;&#102;&#105;&#108;&#108;&#32;&#38;&#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;&#92;&#116;&#101;&#120;&#116;&#123;&#115;&#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;&#49;&#53;&#92;&#100;&#105;&#118;&#32;&#92;&#108;&#101;&#102;&#116;&#40;&#45;&#51;&#92;&#114;&#105;&#103;&#104;&#116;&#41;&#92;&#104;&#102;&#105;&#108;&#108;&#32;&#38;&#32;&#61;&#92;&#104;&#102;&#105;&#108;&#108;&#32;&#38;&#32;&#45;&#53;&#92;&#104;&#102;&#105;&#108;&#108;&#32;&#38;&#32;&#38;&#32;&#38;&#32;&#38;&#32;&#38;&#32;&#92;&#104;&#102;&#105;&#108;&#108;&#32;&#53;&#92;&#108;&#101;&#102;&#116;&#40;&#45;&#51;&#92;&#114;&#105;&#103;&#104;&#116;&#41;&#38;&#32;&#61;&#92;&#104;&#102;&#105;&#108;&#108;&#32;&#38;&#32;&#45;&#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;&#92;&#116;&#101;&#120;&#116;&#123;&#115;&#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;&#45;&#49;&#53;&#92;&#100;&#105;&#118;&#32;&#92;&#108;&#101;&#102;&#116;&#40;&#45;&#51;&#92;&#114;&#105;&#103;&#104;&#116;&#41;&#92;&#104;&#102;&#105;&#108;&#108;&#32;&#38;&#32;&#61;&#92;&#104;&#102;&#105;&#108;&#108;&#32;&#38;&#32;&#53;&#92;&#104;&#102;&#105;&#108;&#108;&#32;&#92;&#101;&#110;&#100;&#123;&#97;&#114;&#114;&#97;&#121;&#125;\" title=\"Rendered by QuickLaTeX.com\" height=\"41\" width=\"702\" style=\"vertical-align: -16px;\" \/><\/p>\n<p id=\"fs-id1170654116562\">Division follows the same rules as multiplication!<\/p>\n<p id=\"fs-id1170653915002\">For division of two signed numbers, when the:<\/p>\n<ul id=\"fs-id1166426287557\" data-bullet-style=\"bullet\">\n<li>signs are the <em data-effect=\"italics\">same<\/em>, the quotient is <em data-effect=\"italics\">positive<\/em>.<\/li>\n<li>signs are <em data-effect=\"italics\">different<\/em>, the quotient is <em data-effect=\"italics\">negative<\/em>.<\/li>\n<\/ul>\n<p id=\"fs-id1170653869100\">And remember that we can always check the answer of a division problem by multiplying.<\/p>\n<div id=\"fs-id1170654015283\" 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\">Multiplication and Division of Signed Numbers<\/p>\n<\/header>\n<div class=\"textbox__content\">\n<p id=\"fs-id1170653774421\">For multiplication and division of two signed numbers:<\/p>\n<ul id=\"fs-id1166425927232\" data-bullet-style=\"bullet\">\n<li>If the signs are the same, the result is positive.<\/li>\n<li>If the signs are different, the result is negative.<\/li>\n<\/ul>\n<table id=\"fs-id1170654154997\" style=\"width: 100%;\" summary=\"No Summary\">\n<thead>\n<tr valign=\"top\">\n<th style=\"width: 50%;\" scope=\"col\" data-valign=\"top\" data-align=\"left\">Same signs<\/th>\n<th style=\"width: 50%;\" scope=\"col\" data-valign=\"top\" data-align=\"left\">Result<\/th>\n<\/tr>\n<\/thead>\n<tbody>\n<tr valign=\"top\">\n<td style=\"width: 50%;\" data-valign=\"top\" data-align=\"left\">Two positives<\/td>\n<td style=\"width: 50%;\" data-valign=\"top\" data-align=\"left\">Positive<\/td>\n<\/tr>\n<tr>\n<td style=\"width: 50%;\">Two negatives<\/td>\n<td style=\"width: 50%;\">Positive<\/td>\n<\/tr>\n<\/tbody>\n<\/table>\n<p>If the signs are the same, the result is positive.<\/p>\n<table id=\"fs-id1170653799921\" style=\"width: 100%; height: 48px;\" summary=\"No Summary\">\n<thead>\n<tr style=\"height: 16px;\" valign=\"top\">\n<th style=\"height: 16px; width: 50%;\" scope=\"col\" data-valign=\"top\" data-align=\"left\">Different signs<\/th>\n<th style=\"height: 16px; width: 50%;\" scope=\"col\" data-valign=\"top\" data-align=\"left\">Result<\/th>\n<\/tr>\n<\/thead>\n<tbody>\n<tr style=\"height: 16px;\" valign=\"top\">\n<td style=\"height: 16px; width: 50%;\" data-valign=\"top\" data-align=\"left\">Positive and negative<\/td>\n<td style=\"height: 16px; width: 50%;\" data-valign=\"top\" data-align=\"left\">Negative<\/td>\n<\/tr>\n<tr style=\"height: 16px;\">\n<td style=\"height: 16px; width: 50%;\">Negative and positive<\/td>\n<td style=\"height: 16px; width: 50%;\">Negative<\/td>\n<\/tr>\n<\/tbody>\n<\/table>\n<p>If the signs are different, the result is negative.<\/p>\n<\/div>\n<\/div>\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-id1170652618826\" data-type=\"problem\">\n<p id=\"fs-id1170654008734\">Divide: a) <img loading=\"lazy\" decoding=\"async\" src=\"https:\/\/opentextbc.ca\/introalgebra\/wp-content\/ql-cache\/quicklatex.com-b3dbb76a7a3b4b23f8238a05c6710616_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"&#45;&#50;&#55;&#92;&#100;&#105;&#118;&#32;&#51;\" title=\"Rendered by QuickLaTeX.com\" height=\"14\" width=\"61\" style=\"vertical-align: -1px;\" \/> b) <img loading=\"lazy\" decoding=\"async\" src=\"https:\/\/opentextbc.ca\/introalgebra\/wp-content\/ql-cache\/quicklatex.com-3443fdd50bfd8cbef0209c257457ca50_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"&#45;&#49;&#48;&#48;&#92;&#100;&#105;&#118;&#32;&#92;&#108;&#101;&#102;&#116;&#40;&#45;&#52;&#92;&#114;&#105;&#103;&#104;&#116;&#41;\" title=\"Rendered by QuickLaTeX.com\" height=\"19\" width=\"97\" style=\"vertical-align: -5px;\" \/>.<\/p>\n<\/div>\n<div id=\"fs-id1170654212229\" data-type=\"solution\">\n<div data-type=\"title\"><\/div>\n<div data-type=\"title\"><strong>Solution<\/strong><\/div>\n<table id=\"eip-762\" summary=\".\">\n<tbody>\n<tr>\n<td>a)<br \/>\nDivide. With different signs, the quotient is negative.<\/td>\n<td><img loading=\"lazy\" decoding=\"async\" src=\"https:\/\/opentextbc.ca\/introalgebra\/wp-content\/ql-cache\/quicklatex.com-abd0e0180314b3577a7a4ff8d744a8cc_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;&#125;&#45;&#50;&#55;&#92;&#100;&#105;&#118;&#32;&#51;&#92;&#92;&#32;&#45;&#57;&#92;&#101;&#110;&#100;&#123;&#97;&#114;&#114;&#97;&#121;&#125;\" title=\"Rendered by QuickLaTeX.com\" height=\"35\" width=\"61\" style=\"vertical-align: -11px;\" \/><\/td>\n<\/tr>\n<tr>\n<td>b)<br \/>\nDivide. With signs that are the same, the quotient is positive.<\/td>\n<td><img loading=\"lazy\" decoding=\"async\" src=\"https:\/\/opentextbc.ca\/introalgebra\/wp-content\/ql-cache\/quicklatex.com-1b9824277f2d9151cf02a1aaaf207d46_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;&#125;&#45;&#49;&#48;&#48;&#92;&#100;&#105;&#118;&#92;&#108;&#101;&#102;&#116;&#40;&#45;&#52;&#92;&#114;&#105;&#103;&#104;&#116;&#41;&#92;&#92;&#32;&#50;&#53;&#92;&#101;&#110;&#100;&#123;&#97;&#114;&#114;&#97;&#121;&#125;\" title=\"Rendered by QuickLaTeX.com\" height=\"36\" width=\"97\" style=\"vertical-align: -11px;\" \/><\/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-id1170653797425\" data-type=\"problem\">\n<p id=\"fs-id1170653906270\">Divide: a) <img loading=\"lazy\" decoding=\"async\" src=\"https:\/\/opentextbc.ca\/introalgebra\/wp-content\/ql-cache\/quicklatex.com-d2160bf7a3c60d2097ea7ceab482e603_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"&#45;&#52;&#50;&#92;&#100;&#105;&#118;&#32;&#54;\" title=\"Rendered by QuickLaTeX.com\" height=\"13\" width=\"61\" style=\"vertical-align: -1px;\" \/> b) <img loading=\"lazy\" decoding=\"async\" src=\"https:\/\/opentextbc.ca\/introalgebra\/wp-content\/ql-cache\/quicklatex.com-e440c780a9ce4097c4c6094154a91c25_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"&#45;&#49;&#49;&#55;&#92;&#100;&#105;&#118;&#92;&#108;&#101;&#102;&#116;&#40;&#45;&#51;&#92;&#114;&#105;&#103;&#104;&#116;&#41;\" title=\"Rendered by QuickLaTeX.com\" height=\"19\" width=\"97\" style=\"vertical-align: -5px;\" \/>.<\/p>\n<\/div>\n<div id=\"fs-id1170654149901\" data-type=\"solution\">\n<details>\n<summary>Show answer<\/summary>\n<p id=\"fs-id1170654047662\">a)<img loading=\"lazy\" decoding=\"async\" src=\"https:\/\/opentextbc.ca\/introalgebra\/wp-content\/ql-cache\/quicklatex.com-00c6d30c5f7439a21caf981437f64be1_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"&#45;&#55;\" title=\"Rendered by QuickLaTeX.com\" height=\"13\" width=\"22\" style=\"vertical-align: 0px;\" \/> b) 39<\/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 3.2<\/p>\n<\/header>\n<div class=\"textbox__content\">\n<div id=\"fs-id1170654233461\" data-type=\"problem\">\n<p id=\"fs-id1170652622579\">Divide: a) <img loading=\"lazy\" decoding=\"async\" src=\"https:\/\/opentextbc.ca\/introalgebra\/wp-content\/ql-cache\/quicklatex.com-d570c018b7d7e36fe04b0a4ab1dd0955_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"&#45;&#54;&#51;&#92;&#100;&#105;&#118;&#32;&#55;\" title=\"Rendered by QuickLaTeX.com\" height=\"14\" width=\"61\" style=\"vertical-align: -1px;\" \/> b) <img loading=\"lazy\" decoding=\"async\" src=\"https:\/\/opentextbc.ca\/introalgebra\/wp-content\/ql-cache\/quicklatex.com-4a53e49ccc7b3fae267897a2dd311cbf_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"&#45;&#49;&#49;&#53;&#92;&#100;&#105;&#118;&#92;&#108;&#101;&#102;&#116;&#40;&#45;&#53;&#92;&#114;&#105;&#103;&#104;&#116;&#41;\" title=\"Rendered by QuickLaTeX.com\" height=\"19\" width=\"97\" style=\"vertical-align: -5px;\" \/>.<\/p>\n<\/div>\n<div id=\"fs-id1170653897540\" data-type=\"solution\">\n<details>\n<summary>Show answer<\/summary>\n<p id=\"fs-id1170653910431\">a)<img loading=\"lazy\" decoding=\"async\" src=\"https:\/\/opentextbc.ca\/introalgebra\/wp-content\/ql-cache\/quicklatex.com-9672181aec15f8334b80ada7de4e4fc0_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"&#45;&#57;\" title=\"Rendered by QuickLaTeX.com\" height=\"12\" width=\"22\" style=\"vertical-align: 0px;\" \/> b) 23<\/p>\n<\/details>\n<\/div>\n<\/div>\n<\/div>\n<\/div>\n<\/div>\n<h1>Simplify Expressions with Integers<\/h1>\n<p id=\"fs-id1170653741550\">What happens when there are more than two numbers in an expression? The order of operations still applies when negatives are included. Remember My Dear Aunt Sally?<\/p>\n<p id=\"fs-id1170653790201\">Let\u2019s try some examples. We\u2019ll simplify expressions that use all four operations with integers\u2014addition, subtraction, multiplication, and division. Remember to follow the order of operations.<\/p>\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 id=\"fs-id1170654066443\" data-type=\"problem\">\n<p id=\"fs-id1170653768124\">Simplify: <img loading=\"lazy\" decoding=\"async\" src=\"https:\/\/opentextbc.ca\/introalgebra\/wp-content\/ql-cache\/quicklatex.com-24b8f0796e27dc6238f7631b9c932920_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"&#55;&#92;&#108;&#101;&#102;&#116;&#40;&#45;&#50;&#92;&#114;&#105;&#103;&#104;&#116;&#41;&#43;&#52;&#92;&#108;&#101;&#102;&#116;&#40;&#45;&#55;&#92;&#114;&#105;&#103;&#104;&#116;&#41;&#45;&#54;\" title=\"Rendered by QuickLaTeX.com\" height=\"18\" width=\"149\" style=\"vertical-align: -4px;\" \/>.<\/p>\n<\/div>\n<div id=\"fs-id1170652623765\" 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-431\" summary=\".\">\n<tbody>\n<tr>\n<td><\/td>\n<td><img loading=\"lazy\" decoding=\"async\" src=\"https:\/\/opentextbc.ca\/introalgebra\/wp-content\/ql-cache\/quicklatex.com-24b8f0796e27dc6238f7631b9c932920_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"&#55;&#92;&#108;&#101;&#102;&#116;&#40;&#45;&#50;&#92;&#114;&#105;&#103;&#104;&#116;&#41;&#43;&#52;&#92;&#108;&#101;&#102;&#116;&#40;&#45;&#55;&#92;&#114;&#105;&#103;&#104;&#116;&#41;&#45;&#54;\" title=\"Rendered by QuickLaTeX.com\" height=\"18\" width=\"149\" style=\"vertical-align: -4px;\" \/><\/td>\n<\/tr>\n<tr>\n<td>Multiply first.<\/td>\n<td><img loading=\"lazy\" decoding=\"async\" src=\"https:\/\/opentextbc.ca\/introalgebra\/wp-content\/ql-cache\/quicklatex.com-44a4a8f04ead233888dbb3b890d6faf6_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"&#45;&#49;&#52;&#43;&#92;&#108;&#101;&#102;&#116;&#40;&#45;&#50;&#56;&#92;&#114;&#105;&#103;&#104;&#116;&#41;&#45;&#54;\" title=\"Rendered by QuickLaTeX.com\" height=\"18\" width=\"128\" style=\"vertical-align: -4px;\" \/><\/td>\n<\/tr>\n<tr>\n<td>Add.<\/td>\n<td><img loading=\"lazy\" decoding=\"async\" src=\"https:\/\/opentextbc.ca\/introalgebra\/wp-content\/ql-cache\/quicklatex.com-652e950e5cfb123bb379f94f5038aaef_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"&#45;&#52;&#50;&#45;&#54;\" title=\"Rendered by QuickLaTeX.com\" height=\"13\" width=\"61\" style=\"vertical-align: -1px;\" \/><\/td>\n<\/tr>\n<tr>\n<td>Subtract.<\/td>\n<td><img loading=\"lazy\" decoding=\"async\" src=\"https:\/\/opentextbc.ca\/introalgebra\/wp-content\/ql-cache\/quicklatex.com-08ed8320699be2770837da731d65c7c5_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"&#45;&#52;&#56;\" title=\"Rendered by QuickLaTeX.com\" height=\"13\" width=\"31\" 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 4.1<\/p>\n<\/header>\n<div class=\"textbox__content\">\n<div id=\"fs-id1170652620764\" data-type=\"problem\">\n<p id=\"fs-id1170653875298\">Simplify: <img loading=\"lazy\" decoding=\"async\" src=\"https:\/\/opentextbc.ca\/introalgebra\/wp-content\/ql-cache\/quicklatex.com-bdf49d134a670670b6e654be9873bc8d_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"&#56;&#92;&#108;&#101;&#102;&#116;&#40;&#45;&#51;&#92;&#114;&#105;&#103;&#104;&#116;&#41;&#43;&#53;&#92;&#108;&#101;&#102;&#116;&#40;&#45;&#55;&#92;&#114;&#105;&#103;&#104;&#116;&#41;&#45;&#52;\" title=\"Rendered by QuickLaTeX.com\" height=\"18\" width=\"149\" style=\"vertical-align: -4px;\" \/>.<\/p>\n<\/div>\n<div id=\"fs-id1170654149857\" data-type=\"solution\">\n<details>\n<summary>Show answer<\/summary>\n<p id=\"fs-id1170654149859\"><img loading=\"lazy\" decoding=\"async\" src=\"https:\/\/opentextbc.ca\/introalgebra\/wp-content\/ql-cache\/quicklatex.com-c081a4d1588de9f9de1dd7d5282b4c9d_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"&#45;&#54;&#51;\" title=\"Rendered by QuickLaTeX.com\" height=\"12\" width=\"31\" style=\"vertical-align: 0px;\" \/><\/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 4.2<\/p>\n<\/header>\n<div class=\"textbox__content\">\n<div id=\"fs-id1170652630283\" data-type=\"problem\">\n<p id=\"fs-id1170653880078\">Simplify: <img loading=\"lazy\" decoding=\"async\" src=\"https:\/\/opentextbc.ca\/introalgebra\/wp-content\/ql-cache\/quicklatex.com-b251463a49e13db977887354a686b3c5_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"&#57;&#92;&#108;&#101;&#102;&#116;&#40;&#45;&#51;&#92;&#114;&#105;&#103;&#104;&#116;&#41;&#43;&#55;&#92;&#108;&#101;&#102;&#116;&#40;&#45;&#56;&#92;&#114;&#105;&#103;&#104;&#116;&#41;&#45;&#49;\" title=\"Rendered by QuickLaTeX.com\" height=\"18\" width=\"148\" style=\"vertical-align: -4px;\" \/>.<\/p>\n<\/div>\n<div id=\"fs-id1170652620232\" data-type=\"solution\">\n<details>\n<summary>Show answer<\/summary>\n<p id=\"fs-id1170654286008\"><img loading=\"lazy\" decoding=\"async\" src=\"https:\/\/opentextbc.ca\/introalgebra\/wp-content\/ql-cache\/quicklatex.com-1ca0b09b1d64b0c44f550249d0ab3ddf_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"&#45;&#56;&#52;\" title=\"Rendered by QuickLaTeX.com\" height=\"13\" width=\"31\" style=\"vertical-align: -1px;\" \/><\/p>\n<\/details>\n<\/div>\n<\/div>\n<\/div>\n<div id=\"fs-id1170653871378\" class=\"try\" data-type=\"note\">\n<div id=\"fs-id1170652630281\" data-type=\"exercise\">\n<div id=\"fs-id1170652620232\" data-type=\"solution\">\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-id1170652619970\" data-type=\"problem\">\n<p id=\"fs-id1170653761875\">Simplify: a) <img loading=\"lazy\" decoding=\"async\" src=\"https:\/\/opentextbc.ca\/introalgebra\/wp-content\/ql-cache\/quicklatex.com-39e546b1083a74884e4981f6405b861e_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"&#123;&#92;&#108;&#101;&#102;&#116;&#40;&#45;&#50;&#92;&#114;&#105;&#103;&#104;&#116;&#41;&#125;&#94;&#123;&#52;&#125;\" title=\"Rendered by QuickLaTeX.com\" height=\"21\" width=\"42\" style=\"vertical-align: -4px;\" \/> b) <img loading=\"lazy\" decoding=\"async\" src=\"https:\/\/opentextbc.ca\/introalgebra\/wp-content\/ql-cache\/quicklatex.com-f278ff35c8dcfadef48d2edadefd1d3f_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"&#92;&#116;&#101;&#120;&#116;&#123;&#45;&#125;&#123;&#50;&#125;&#94;&#123;&#52;&#125;\" title=\"Rendered by QuickLaTeX.com\" height=\"15\" width=\"22\" style=\"vertical-align: 0px;\" \/>.<\/p>\n<\/div>\n<div id=\"fs-id1170654237484\" 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-217\" summary=\".\">\n<tbody>\n<tr>\n<td>a)<br \/>\nWrite in expanded form.<br \/>\nMultiply.<br \/>\nMultiply.<br \/>\nMultiply.<\/td>\n<td><img loading=\"lazy\" decoding=\"async\" src=\"https:\/\/opentextbc.ca\/introalgebra\/wp-content\/ql-cache\/quicklatex.com-205c076c140d74f350b316871c06b34d_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;&#125;&#123;&#92;&#108;&#101;&#102;&#116;&#40;&#45;&#50;&#92;&#114;&#105;&#103;&#104;&#116;&#41;&#125;&#94;&#123;&#52;&#125;&#92;&#92;&#32;&#92;&#108;&#101;&#102;&#116;&#40;&#45;&#50;&#92;&#114;&#105;&#103;&#104;&#116;&#41;&#92;&#108;&#101;&#102;&#116;&#40;&#45;&#50;&#92;&#114;&#105;&#103;&#104;&#116;&#41;&#92;&#108;&#101;&#102;&#116;&#40;&#45;&#50;&#92;&#114;&#105;&#103;&#104;&#116;&#41;&#92;&#108;&#101;&#102;&#116;&#40;&#45;&#50;&#92;&#114;&#105;&#103;&#104;&#116;&#41;&#92;&#92;&#32;&#52;&#92;&#108;&#101;&#102;&#116;&#40;&#45;&#50;&#92;&#114;&#105;&#103;&#104;&#116;&#41;&#92;&#108;&#101;&#102;&#116;&#40;&#45;&#50;&#92;&#114;&#105;&#103;&#104;&#116;&#41;&#92;&#92;&#32;&#45;&#56;&#92;&#108;&#101;&#102;&#116;&#40;&#45;&#50;&#92;&#114;&#105;&#103;&#104;&#116;&#41;&#92;&#92;&#32;&#49;&#54;&#92;&#101;&#110;&#100;&#123;&#97;&#114;&#114;&#97;&#121;&#125;\" title=\"Rendered by QuickLaTeX.com\" height=\"107\" width=\"153\" style=\"vertical-align: -46px;\" \/><\/td>\n<\/tr>\n<tr>\n<td>b)<br \/>\nWrite in expanded form. We are asked to find the opposite of<img loading=\"lazy\" decoding=\"async\" src=\"https:\/\/opentextbc.ca\/introalgebra\/wp-content\/ql-cache\/quicklatex.com-71f34c438201a6a3b27229dd6727aefc_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;&#50;&#125;&#94;&#123;&#52;&#125;\" title=\"Rendered by QuickLaTeX.com\" height=\"15\" width=\"16\" style=\"vertical-align: 0px;\" \/>.<br \/>\nMultiply.<br \/>\nMultiply.<br \/>\nMultiply.<\/td>\n<td><img loading=\"lazy\" decoding=\"async\" src=\"https:\/\/opentextbc.ca\/introalgebra\/wp-content\/ql-cache\/quicklatex.com-c0f9789031a3c497109479b1171effac_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;&#125;&#92;&#116;&#101;&#120;&#116;&#123;&#45;&#125;&#123;&#50;&#125;&#94;&#123;&#52;&#125;&#92;&#92;&#32;&#92;&#116;&#101;&#120;&#116;&#123;&#45;&#125;&#92;&#108;&#101;&#102;&#116;&#40;&#50;&#92;&#99;&#100;&#111;&#116;&#50;&#92;&#99;&#100;&#111;&#116;&#50;&#92;&#99;&#100;&#111;&#116;&#50;&#92;&#114;&#105;&#103;&#104;&#116;&#41;&#92;&#92;&#32;&#92;&#116;&#101;&#120;&#116;&#123;&#45;&#125;&#92;&#108;&#101;&#102;&#116;&#40;&#52;&#92;&#99;&#100;&#111;&#116;&#50;&#92;&#99;&#100;&#111;&#116;&#50;&#92;&#114;&#105;&#103;&#104;&#116;&#41;&#92;&#92;&#32;&#92;&#116;&#101;&#120;&#116;&#123;&#45;&#125;&#92;&#108;&#101;&#102;&#116;&#40;&#56;&#92;&#99;&#100;&#111;&#116;&#50;&#92;&#114;&#105;&#103;&#104;&#116;&#41;&#92;&#92;&#32;&#49;&#54;&#92;&#101;&#110;&#100;&#123;&#97;&#114;&#114;&#97;&#121;&#125;\" title=\"Rendered by QuickLaTeX.com\" height=\"103\" width=\"96\" style=\"vertical-align: -44px;\" \/><\/td>\n<\/tr>\n<\/tbody>\n<\/table>\n<p id=\"fs-id1170653737864\">Notice the difference in parts a) and b). In part a), the exponent means to raise what is in the parentheses, the <img loading=\"lazy\" decoding=\"async\" src=\"https:\/\/opentextbc.ca\/introalgebra\/wp-content\/ql-cache\/quicklatex.com-5ef599d93da3e39727ed820e5302abcb_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"&#92;&#108;&#101;&#102;&#116;&#40;&#45;&#50;&#92;&#114;&#105;&#103;&#104;&#116;&#41;\" title=\"Rendered by QuickLaTeX.com\" height=\"18\" width=\"35\" style=\"vertical-align: -4px;\" \/> to the <img loading=\"lazy\" decoding=\"async\" src=\"https:\/\/opentextbc.ca\/introalgebra\/wp-content\/ql-cache\/quicklatex.com-bc80ad7a002ec7cb8b7ec5deacae34ab_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"&#123;&#52;&#125;&#94;&#123;&#92;&#116;&#101;&#120;&#116;&#123;&#116;&#104;&#125;&#125;\" title=\"Rendered by QuickLaTeX.com\" height=\"17\" width=\"22\" style=\"vertical-align: -1px;\" \/> power. In part b), the exponent means to raise just the 2 to the <img loading=\"lazy\" decoding=\"async\" src=\"https:\/\/opentextbc.ca\/introalgebra\/wp-content\/ql-cache\/quicklatex.com-bc80ad7a002ec7cb8b7ec5deacae34ab_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"&#123;&#52;&#125;&#94;&#123;&#92;&#116;&#101;&#120;&#116;&#123;&#116;&#104;&#125;&#125;\" title=\"Rendered by QuickLaTeX.com\" height=\"17\" width=\"22\" style=\"vertical-align: -1px;\" \/> power and then take the opposite.<\/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 5.1<\/p>\n<\/header>\n<div class=\"textbox__content\">\n<div id=\"fs-id1170652622523\" data-type=\"problem\">\n<p id=\"fs-id1170653790279\">Simplify: a) <img loading=\"lazy\" decoding=\"async\" src=\"https:\/\/opentextbc.ca\/introalgebra\/wp-content\/ql-cache\/quicklatex.com-7f030f29170d3e23cfadee1ce2e2d79f_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"&#123;&#92;&#108;&#101;&#102;&#116;&#40;&#45;&#51;&#92;&#114;&#105;&#103;&#104;&#116;&#41;&#125;&#94;&#123;&#52;&#125;\" title=\"Rendered by QuickLaTeX.com\" height=\"21\" width=\"42\" style=\"vertical-align: -4px;\" \/> b) <img loading=\"lazy\" decoding=\"async\" src=\"https:\/\/opentextbc.ca\/introalgebra\/wp-content\/ql-cache\/quicklatex.com-91ffa9fdd7ca1075001d7087286a50bb_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"&#92;&#116;&#101;&#120;&#116;&#123;&#45;&#125;&#123;&#51;&#125;&#94;&#123;&#52;&#125;\" title=\"Rendered by QuickLaTeX.com\" height=\"15\" width=\"22\" style=\"vertical-align: 0px;\" \/>.<\/p>\n<\/div>\n<div id=\"fs-id1170654230619\" data-type=\"solution\">\n<details>\n<summary>Show answer<\/summary>\n<p id=\"fs-id1170654230621\">a) 81 b) <img loading=\"lazy\" decoding=\"async\" src=\"https:\/\/opentextbc.ca\/introalgebra\/wp-content\/ql-cache\/quicklatex.com-1e9ef1c6bd7a9b6e2b87026a76cda03b_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"&#45;&#56;&#49;\" title=\"Rendered by QuickLaTeX.com\" height=\"13\" width=\"30\" style=\"vertical-align: -1px;\" \/><\/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-id1170653875785\" data-type=\"problem\">\n<p id=\"fs-id1170654200505\">Simplify: a) <img loading=\"lazy\" decoding=\"async\" src=\"https:\/\/opentextbc.ca\/introalgebra\/wp-content\/ql-cache\/quicklatex.com-fd5486faed5cb7a4ed65fdd9632f24fa_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"&#123;&#92;&#108;&#101;&#102;&#116;&#40;&#45;&#55;&#92;&#114;&#105;&#103;&#104;&#116;&#41;&#125;&#94;&#123;&#50;&#125;\" title=\"Rendered by QuickLaTeX.com\" height=\"21\" width=\"42\" style=\"vertical-align: -4px;\" \/> b) <img loading=\"lazy\" decoding=\"async\" src=\"https:\/\/opentextbc.ca\/introalgebra\/wp-content\/ql-cache\/quicklatex.com-304378da08a035be246729904f95b6dc_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"&#92;&#116;&#101;&#120;&#116;&#123;&#45;&#125;&#123;&#55;&#125;&#94;&#123;&#50;&#125;\" title=\"Rendered by QuickLaTeX.com\" height=\"15\" width=\"22\" style=\"vertical-align: 0px;\" \/>.<\/p>\n<\/div>\n<div id=\"fs-id1170654154361\" data-type=\"solution\">\n<details>\n<summary>Show answer<\/summary>\n<p id=\"fs-id1170654154363\">a) 49 b) <img loading=\"lazy\" decoding=\"async\" src=\"https:\/\/opentextbc.ca\/introalgebra\/wp-content\/ql-cache\/quicklatex.com-87b45b657a37f37cb779527d2a666770_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"&#45;&#52;&#57;\" title=\"Rendered by QuickLaTeX.com\" height=\"13\" width=\"31\" style=\"vertical-align: -1px;\" \/><\/p>\n<\/details>\n<\/div>\n<\/div>\n<\/div>\n<\/div>\n<\/div>\n<\/div>\n<p id=\"fs-id1170653904816\">The next example reminds us to simplify inside parentheses first.<\/p>\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-id1170652622789\" data-type=\"problem\">\n<p id=\"fs-id1170652622791\">Simplify: <img loading=\"lazy\" decoding=\"async\" src=\"https:\/\/opentextbc.ca\/introalgebra\/wp-content\/ql-cache\/quicklatex.com-ec9bc12da033b8553035518caca5ec4c_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"&#49;&#50;&#45;&#51;&#92;&#108;&#101;&#102;&#116;&#40;&#57;&#45;&#49;&#50;&#92;&#114;&#105;&#103;&#104;&#116;&#41;\" title=\"Rendered by QuickLaTeX.com\" height=\"18\" width=\"112\" style=\"vertical-align: -4px;\" \/>.<\/p>\n<\/div>\n<div id=\"fs-id1170653905533\" 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-138\" summary=\".\">\n<tbody>\n<tr>\n<td><\/td>\n<td><img loading=\"lazy\" decoding=\"async\" src=\"https:\/\/opentextbc.ca\/introalgebra\/wp-content\/ql-cache\/quicklatex.com-ec9bc12da033b8553035518caca5ec4c_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"&#49;&#50;&#45;&#51;&#92;&#108;&#101;&#102;&#116;&#40;&#57;&#45;&#49;&#50;&#92;&#114;&#105;&#103;&#104;&#116;&#41;\" title=\"Rendered by QuickLaTeX.com\" height=\"18\" width=\"112\" style=\"vertical-align: -4px;\" \/><\/td>\n<\/tr>\n<tr>\n<td>Subtract in parentheses first.<\/td>\n<td><img loading=\"lazy\" decoding=\"async\" src=\"https:\/\/opentextbc.ca\/introalgebra\/wp-content\/ql-cache\/quicklatex.com-63d263cf0990efbc8163197da5164dc0_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"&#49;&#50;&#45;&#51;&#92;&#108;&#101;&#102;&#116;&#40;&#45;&#51;&#92;&#114;&#105;&#103;&#104;&#116;&#41;\" title=\"Rendered by QuickLaTeX.com\" height=\"18\" width=\"86\" style=\"vertical-align: -4px;\" \/><\/td>\n<\/tr>\n<tr>\n<td>Multiply.<\/td>\n<td><img loading=\"lazy\" decoding=\"async\" src=\"https:\/\/opentextbc.ca\/introalgebra\/wp-content\/ql-cache\/quicklatex.com-fc7cc2bf045888e626ff99795f9cd64a_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"&#49;&#50;&#45;&#92;&#108;&#101;&#102;&#116;&#40;&#45;&#57;&#92;&#114;&#105;&#103;&#104;&#116;&#41;\" title=\"Rendered by QuickLaTeX.com\" height=\"18\" width=\"74\" style=\"vertical-align: -4px;\" \/><\/td>\n<\/tr>\n<tr>\n<td>Subtract.<\/td>\n<td><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<\/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 6.1<\/p>\n<\/header>\n<div class=\"textbox__content\">\n<div id=\"fs-id1170654134940\" data-type=\"problem\">\n<p id=\"fs-id1170654134942\">Simplify: <img loading=\"lazy\" decoding=\"async\" src=\"https:\/\/opentextbc.ca\/introalgebra\/wp-content\/ql-cache\/quicklatex.com-c4be2c0c69667c5427c3624021a9ade1_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"&#49;&#55;&#45;&#52;&#92;&#108;&#101;&#102;&#116;&#40;&#56;&#45;&#49;&#49;&#92;&#114;&#105;&#103;&#104;&#116;&#41;\" title=\"Rendered by QuickLaTeX.com\" height=\"18\" width=\"112\" style=\"vertical-align: -4px;\" \/>.<\/p>\n<\/div>\n<div id=\"fs-id1170652622244\" data-type=\"solution\">\n<details>\n<summary>Show answer<\/summary>\n<p id=\"fs-id1170654150070\">29<\/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 6.2<\/p>\n<\/header>\n<div class=\"textbox__content\">\n<div id=\"fs-id1170652631542\" data-type=\"problem\">\n<p id=\"fs-id1170654239598\">Simplify: <img loading=\"lazy\" decoding=\"async\" src=\"https:\/\/opentextbc.ca\/introalgebra\/wp-content\/ql-cache\/quicklatex.com-fa83e8ee47935082518d99ccfbf953f2_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"&#49;&#54;&#45;&#54;&#92;&#108;&#101;&#102;&#116;&#40;&#55;&#45;&#49;&#51;&#92;&#114;&#105;&#103;&#104;&#116;&#41;\" title=\"Rendered by QuickLaTeX.com\" height=\"18\" width=\"112\" style=\"vertical-align: -4px;\" \/>.<\/p>\n<\/div>\n<div id=\"fs-id1170653874260\" data-type=\"solution\">\n<details>\n<summary>Show answer<\/summary>\n<p id=\"fs-id1170653874262\">52<\/p>\n<\/details>\n<\/div>\n<\/div>\n<\/div>\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 id=\"fs-id1170652624014\" data-type=\"problem\">\n<p id=\"fs-id1170652624016\">Simplify: <img loading=\"lazy\" decoding=\"async\" src=\"https:\/\/opentextbc.ca\/introalgebra\/wp-content\/ql-cache\/quicklatex.com-3fd25bec589215019b11114b5a71de57_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"&#56;&#92;&#108;&#101;&#102;&#116;&#40;&#45;&#57;&#92;&#114;&#105;&#103;&#104;&#116;&#41;&#92;&#100;&#105;&#118;&#123;&#92;&#108;&#101;&#102;&#116;&#40;&#45;&#50;&#92;&#114;&#105;&#103;&#104;&#116;&#41;&#125;&#94;&#123;&#51;&#125;\" title=\"Rendered by QuickLaTeX.com\" height=\"22\" width=\"113\" style=\"vertical-align: -5px;\" \/>.<\/p>\n<\/div>\n<div id=\"fs-id1170653850514\" 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-410\" style=\"width: 100%;\" summary=\".\">\n<tbody>\n<tr>\n<td><\/td>\n<td><img loading=\"lazy\" decoding=\"async\" src=\"https:\/\/opentextbc.ca\/introalgebra\/wp-content\/ql-cache\/quicklatex.com-3fd25bec589215019b11114b5a71de57_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"&#56;&#92;&#108;&#101;&#102;&#116;&#40;&#45;&#57;&#92;&#114;&#105;&#103;&#104;&#116;&#41;&#92;&#100;&#105;&#118;&#123;&#92;&#108;&#101;&#102;&#116;&#40;&#45;&#50;&#92;&#114;&#105;&#103;&#104;&#116;&#41;&#125;&#94;&#123;&#51;&#125;\" title=\"Rendered by QuickLaTeX.com\" height=\"22\" width=\"113\" style=\"vertical-align: -5px;\" \/><\/td>\n<\/tr>\n<tr>\n<td>Exponents first.<\/td>\n<td><img loading=\"lazy\" decoding=\"async\" src=\"https:\/\/opentextbc.ca\/introalgebra\/wp-content\/ql-cache\/quicklatex.com-0bcec5a1521eb6334fca6eb1035f845a_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"&#56;&#92;&#108;&#101;&#102;&#116;&#40;&#45;&#57;&#92;&#114;&#105;&#103;&#104;&#116;&#41;&#92;&#100;&#105;&#118;&#92;&#108;&#101;&#102;&#116;&#40;&#45;&#56;&#92;&#114;&#105;&#103;&#104;&#116;&#41;\" title=\"Rendered by QuickLaTeX.com\" height=\"19\" width=\"106\" style=\"vertical-align: -5px;\" \/><\/td>\n<\/tr>\n<tr>\n<td>Multiply.<\/td>\n<td><img loading=\"lazy\" decoding=\"async\" src=\"https:\/\/opentextbc.ca\/introalgebra\/wp-content\/ql-cache\/quicklatex.com-69278257962ca777f28ae178be1a5764_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"&#45;&#55;&#50;&#92;&#100;&#105;&#118;&#32;&#92;&#108;&#101;&#102;&#116;&#40;&#45;&#56;&#92;&#114;&#105;&#103;&#104;&#116;&#41;\" title=\"Rendered by QuickLaTeX.com\" height=\"19\" width=\"88\" style=\"vertical-align: -5px;\" \/><\/td>\n<\/tr>\n<tr>\n<td>Divide.<\/td>\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;\" \/><\/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-id1170652621179\" data-type=\"problem\">\n<p id=\"fs-id1170652621181\">Simplify: <img loading=\"lazy\" decoding=\"async\" src=\"https:\/\/opentextbc.ca\/introalgebra\/wp-content\/ql-cache\/quicklatex.com-0711635a71c0d1ed162c9ada0c66dd3e_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"&#49;&#50;&#92;&#108;&#101;&#102;&#116;&#40;&#45;&#57;&#92;&#114;&#105;&#103;&#104;&#116;&#41;&#92;&#100;&#105;&#118;&#123;&#92;&#108;&#101;&#102;&#116;&#40;&#45;&#51;&#92;&#114;&#105;&#103;&#104;&#116;&#41;&#125;&#94;&#123;&#51;&#125;\" title=\"Rendered by QuickLaTeX.com\" height=\"22\" width=\"121\" style=\"vertical-align: -5px;\" \/>.<\/p>\n<\/div>\n<div id=\"fs-id1170653797293\" data-type=\"solution\">\n<details>\n<summary>Show answer<\/summary>\n<p id=\"fs-id1170653797295\">4<\/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 7.2<\/p>\n<\/header>\n<div class=\"textbox__content\">\n<div id=\"fs-id1170654071433\" data-type=\"problem\">\n<p id=\"fs-id1170654071435\">Simplify: <img loading=\"lazy\" decoding=\"async\" src=\"https:\/\/opentextbc.ca\/introalgebra\/wp-content\/ql-cache\/quicklatex.com-ea3bbdc0b0a4510631de70cd05fd4d17_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"&#49;&#56;&#92;&#108;&#101;&#102;&#116;&#40;&#45;&#52;&#92;&#114;&#105;&#103;&#104;&#116;&#41;&#92;&#100;&#105;&#118;&#123;&#92;&#108;&#101;&#102;&#116;&#40;&#45;&#50;&#92;&#114;&#105;&#103;&#104;&#116;&#41;&#125;&#94;&#123;&#51;&#125;\" title=\"Rendered by QuickLaTeX.com\" height=\"22\" width=\"121\" style=\"vertical-align: -5px;\" \/>.<\/p>\n<\/div>\n<div id=\"fs-id1170652622271\" data-type=\"solution\">\n<details>\n<summary>Show answer<\/summary>\n<p id=\"fs-id1170652622274\">9<\/p>\n<\/details>\n<\/div>\n<\/div>\n<\/div>\n<div id=\"fs-id1170654156593\" class=\"try\" data-type=\"note\">\n<div id=\"fs-id1170652621176\" data-type=\"exercise\">\n<div id=\"fs-id1170652621179\" data-type=\"problem\">\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-id1170654047271\" data-type=\"problem\">\n<p id=\"fs-id1170654047273\">Simplify: <img loading=\"lazy\" decoding=\"async\" src=\"https:\/\/opentextbc.ca\/introalgebra\/wp-content\/ql-cache\/quicklatex.com-bcc4d59c21f76a152c670ba0d291b91c_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"&#45;&#51;&#48;&#92;&#100;&#105;&#118;&#32;&#50;&#43;&#92;&#108;&#101;&#102;&#116;&#40;&#45;&#51;&#92;&#114;&#105;&#103;&#104;&#116;&#41;&#92;&#108;&#101;&#102;&#116;&#40;&#45;&#55;&#92;&#114;&#105;&#103;&#104;&#116;&#41;\" title=\"Rendered by QuickLaTeX.com\" height=\"19\" width=\"158\" style=\"vertical-align: -5px;\" \/>.<\/p>\n<\/div>\n<div id=\"fs-id1170654233306\" data-type=\"solution\">\n<div data-type=\"title\"><\/div>\n<div data-type=\"title\"><strong>Solution<\/strong><\/div>\n<table id=\"eip-343\" summary=\".\">\n<tbody>\n<tr>\n<td><\/td>\n<td><img loading=\"lazy\" decoding=\"async\" src=\"https:\/\/opentextbc.ca\/introalgebra\/wp-content\/ql-cache\/quicklatex.com-bcc4d59c21f76a152c670ba0d291b91c_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"&#45;&#51;&#48;&#92;&#100;&#105;&#118;&#32;&#50;&#43;&#92;&#108;&#101;&#102;&#116;&#40;&#45;&#51;&#92;&#114;&#105;&#103;&#104;&#116;&#41;&#92;&#108;&#101;&#102;&#116;&#40;&#45;&#55;&#92;&#114;&#105;&#103;&#104;&#116;&#41;\" title=\"Rendered by QuickLaTeX.com\" height=\"19\" width=\"158\" style=\"vertical-align: -5px;\" \/><\/td>\n<\/tr>\n<tr>\n<td>Multiply and divide left to right, so divide first.<\/td>\n<td><img loading=\"lazy\" decoding=\"async\" src=\"https:\/\/opentextbc.ca\/introalgebra\/wp-content\/ql-cache\/quicklatex.com-f745634152aacc8a73f83c4acbc56484_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"&#45;&#49;&#53;&#43;&#92;&#108;&#101;&#102;&#116;&#40;&#45;&#51;&#92;&#114;&#105;&#103;&#104;&#116;&#41;&#92;&#108;&#101;&#102;&#116;&#40;&#45;&#55;&#92;&#114;&#105;&#103;&#104;&#116;&#41;\" title=\"Rendered by QuickLaTeX.com\" height=\"18\" width=\"127\" style=\"vertical-align: -4px;\" \/><\/td>\n<\/tr>\n<tr>\n<td>Multiply.<\/td>\n<td><img loading=\"lazy\" decoding=\"async\" src=\"https:\/\/opentextbc.ca\/introalgebra\/wp-content\/ql-cache\/quicklatex.com-597a535a0f67f119498557f2d72a72c6_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"&#45;&#49;&#53;&#43;&#50;&#49;\" title=\"Rendered by QuickLaTeX.com\" height=\"15\" width=\"69\" style=\"vertical-align: -2px;\" \/><\/td>\n<\/tr>\n<tr>\n<td>Add.<\/td>\n<td><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<\/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-id1170654154229\" data-type=\"problem\">\n<p id=\"fs-id1170654154231\">Simplify: <img loading=\"lazy\" decoding=\"async\" src=\"https:\/\/opentextbc.ca\/introalgebra\/wp-content\/ql-cache\/quicklatex.com-e736de0ffba98fa939559a4e1e80386b_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"&#45;&#50;&#55;&#92;&#100;&#105;&#118;&#32;&#51;&#43;&#92;&#108;&#101;&#102;&#116;&#40;&#45;&#53;&#92;&#114;&#105;&#103;&#104;&#116;&#41;&#92;&#108;&#101;&#102;&#116;&#40;&#45;&#54;&#92;&#114;&#105;&#103;&#104;&#116;&#41;\" title=\"Rendered by QuickLaTeX.com\" height=\"19\" width=\"158\" style=\"vertical-align: -5px;\" \/>.<\/p>\n<\/div>\n<div id=\"fs-id1170654079166\" data-type=\"solution\">\n<details>\n<summary>Show answer<\/summary>\n<p id=\"fs-id1170654079169\">21<\/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 8.2<\/p>\n<\/header>\n<div class=\"textbox__content\">\n<div id=\"fs-id1170652622504\" data-type=\"problem\">\n<p id=\"fs-id1170653742352\">Simplify: <img loading=\"lazy\" decoding=\"async\" src=\"https:\/\/opentextbc.ca\/introalgebra\/wp-content\/ql-cache\/quicklatex.com-4a14468ee357d38211b061d472935fee_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"&#45;&#51;&#50;&#92;&#100;&#105;&#118;&#32;&#52;&#43;&#92;&#108;&#101;&#102;&#116;&#40;&#45;&#50;&#92;&#114;&#105;&#103;&#104;&#116;&#41;&#92;&#108;&#101;&#102;&#116;&#40;&#45;&#55;&#92;&#114;&#105;&#103;&#104;&#116;&#41;\" title=\"Rendered by QuickLaTeX.com\" height=\"19\" width=\"158\" style=\"vertical-align: -5px;\" \/>.<\/p>\n<\/div>\n<div id=\"fs-id1170652630484\" data-type=\"solution\">\n<details>\n<summary>Show answer<\/summary>\n<p id=\"fs-id1170654011846\">6<\/p>\n<\/details>\n<\/div>\n<\/div>\n<\/div>\n<\/div>\n<\/div>\n<\/div>\n<h1>Evaluate Variable Expressions with Integers<\/h1>\n<p id=\"fs-id1170653874683\">Remember that to evaluate an expression means to substitute a number for the variable in the expression. Now we can use negative numbers as well as positive numbers.<\/p>\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-id1170654236884\" data-type=\"problem\">\n<p id=\"fs-id1170654236886\">When <img loading=\"lazy\" decoding=\"async\" src=\"https:\/\/opentextbc.ca\/introalgebra\/wp-content\/ql-cache\/quicklatex.com-d06eda523b0f75b74b4c7d7f11ee69e3_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"&#110;&#61;&#45;&#53;\" title=\"Rendered by QuickLaTeX.com\" height=\"13\" width=\"56\" style=\"vertical-align: 0px;\" \/>, evaluate: a) <img loading=\"lazy\" decoding=\"async\" src=\"https:\/\/opentextbc.ca\/introalgebra\/wp-content\/ql-cache\/quicklatex.com-d72f4e3699652cfc70b8880515893d7c_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"&#110;&#43;&#49;\" title=\"Rendered by QuickLaTeX.com\" height=\"14\" width=\"40\" style=\"vertical-align: -2px;\" \/> b) <img loading=\"lazy\" decoding=\"async\" src=\"https:\/\/opentextbc.ca\/introalgebra\/wp-content\/ql-cache\/quicklatex.com-c91f08388cb82c419c2d0b6bbd563258_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"&#92;&#116;&#101;&#120;&#116;&#123;&#45;&#125;&#110;&#43;&#49;\" title=\"Rendered by QuickLaTeX.com\" height=\"14\" width=\"46\" style=\"vertical-align: -2px;\" \/>.<\/p>\n<\/div>\n<div id=\"fs-id1170653907935\" 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-id1166421949103\">a)<\/p>\n<table id=\"fs-id1167836601446\" class=\"unnumbered unstyled\" summary=\"This is a solution table with two columns. The top of the right column has the equation \u201cn plus 1.\u201d The next row down on the left reads, \u201cSubstitute negative 5 for n\u201d. The negative five is in red. Next to this in the right column, it has the equation \u201cnegative 5 plus 1.\u201d The next row down reads, \u201csimplify.\u201d Next to this in the right column is \u201cnegative 4\u201d.\" data-label=\"\">\n<tbody>\n<tr>\n<td><\/td>\n<td><span id=\"fs-id1167836341026\" data-type=\"media\" data-alt=\".\"><img decoding=\"async\" src=\"https:\/\/opentextbc.ca\/accessibilitytoolkit\/wp-content\/uploads\/sites\/333\/2021\/03\/CNX_ElemAlg_Figure_01_04_003b_img_new.jpg\" alt=\".\" data-media-type=\"image\/png\" \/><\/span><\/td>\n<\/tr>\n<tr>\n<td><span id=\"fs-id1167836692265\" data-type=\"media\" data-alt=\".\"><img decoding=\"async\" src=\"https:\/\/opentextbc.ca\/accessibilitytoolkit\/wp-content\/uploads\/sites\/333\/2021\/03\/CNX_ElemAlg_Figure_01_04_003a_img_new.jpg\" alt=\".\" data-media-type=\"image\/png\" \/><\/span><\/td>\n<td><span id=\"fs-id1167836606199\" data-type=\"media\" data-alt=\".\"><img decoding=\"async\" src=\"https:\/\/opentextbc.ca\/accessibilitytoolkit\/wp-content\/uploads\/sites\/333\/2021\/03\/CNX_ElemAlg_Figure_01_04_003c_img_new.jpg\" alt=\".\" data-media-type=\"image\/png\" \/><\/span><\/td>\n<\/tr>\n<tr>\n<td>Simplify.<\/td>\n<td>\u22124<\/td>\n<\/tr>\n<\/tbody>\n<\/table>\n<p id=\"fs-id1167833329031\">b)<\/p>\n<table id=\"eip-id1169751873718\" class=\"unnumbered unstyled\" summary=\"This is a solution table with two columns. The top of the right column has the equation \u201cnegative n plus 1.\u201d The next row down on the left reads, \u201cSubstitute negative 5 for n\u201d. The negative five is in red. Next to this in the right column, it has a negative sign outside of parentheses. Negative 5 is in parentheses, then plus 1.\u201d The next row down reads, \u201csimplify.\u201d Next to this in the right column is the equation five plus one. The next row down says \u201cAdd\u201d. Next to this in the right column is \u201c6\u201d.\" data-label=\"\">\n<tbody>\n<tr>\n<td><\/td>\n<td><span id=\"eip-id1169754187288\" data-type=\"media\" data-alt=\".\"><img decoding=\"async\" src=\"https:\/\/opentextbc.ca\/accessibilitytoolkit\/wp-content\/uploads\/sites\/333\/2021\/03\/CNX_ElemAlg_Figure_01_04_004b_img_new.jpg\" alt=\".\" data-media-type=\"image\/png\" \/><\/span><\/td>\n<\/tr>\n<tr>\n<td><span id=\"eip-id1169754188317\" data-type=\"media\" data-alt=\".\"><img decoding=\"async\" src=\"https:\/\/opentextbc.ca\/accessibilitytoolkit\/wp-content\/uploads\/sites\/333\/2021\/03\/CNX_ElemAlg_Figure_01_04_004a_img_new.jpg\" alt=\".\" data-media-type=\"image\/png\" \/><\/span><\/td>\n<td><span id=\"eip-id1169754188329\" data-type=\"media\" data-alt=\".\"><img decoding=\"async\" src=\"https:\/\/opentextbc.ca\/accessibilitytoolkit\/wp-content\/uploads\/sites\/333\/2021\/03\/CNX_ElemAlg_Figure_01_04_004c_img_new.jpg\" alt=\".\" data-media-type=\"image\/png\" \/><\/span><\/td>\n<\/tr>\n<tr>\n<td>Simplify.<\/td>\n<td><span id=\"eip-id1169754018353\" data-type=\"media\" data-alt=\".\"><img decoding=\"async\" src=\"https:\/\/opentextbc.ca\/accessibilitytoolkit\/wp-content\/uploads\/sites\/333\/2021\/03\/CNX_ElemAlg_Figure_01_04_004d_img_new.jpg\" alt=\".\" data-media-type=\"image\/png\" \/><\/span><\/td>\n<\/tr>\n<tr>\n<td>Add.<\/td>\n<td data-align=\"center\">6<\/td>\n<\/tr>\n<\/tbody>\n<\/table>\n<\/div>\n<\/div>\n<\/div>\n<div id=\"fs-id1170652631263\" class=\"try\" data-type=\"note\">\n<div id=\"fs-id1170652631266\" data-type=\"exercise\">\n<div id=\"fs-id1170653797954\" data-type=\"problem\">\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-id1170653797954\" data-type=\"problem\">\n<p id=\"fs-id1170653797956\">When <img loading=\"lazy\" decoding=\"async\" src=\"https:\/\/opentextbc.ca\/introalgebra\/wp-content\/ql-cache\/quicklatex.com-4157fd6366183148f1649a496ca05698_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"&#110;&#61;&#45;&#56;\" title=\"Rendered by QuickLaTeX.com\" height=\"12\" width=\"57\" style=\"vertical-align: 0px;\" \/>, evaluate a) <img loading=\"lazy\" decoding=\"async\" src=\"https:\/\/opentextbc.ca\/introalgebra\/wp-content\/ql-cache\/quicklatex.com-47d55edfa96136aa77a4cb02acfcb034_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"&#110;&#43;&#50;\" title=\"Rendered by QuickLaTeX.com\" height=\"14\" width=\"40\" style=\"vertical-align: -2px;\" \/> b) <img loading=\"lazy\" decoding=\"async\" src=\"https:\/\/opentextbc.ca\/introalgebra\/wp-content\/ql-cache\/quicklatex.com-f511e77ba7462f0076e97c6da31a7e58_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"&#92;&#116;&#101;&#120;&#116;&#123;&#45;&#125;&#110;&#43;&#50;\" title=\"Rendered by QuickLaTeX.com\" height=\"14\" width=\"46\" style=\"vertical-align: -2px;\" \/>.<\/p>\n<\/div>\n<div id=\"fs-id1170652631156\" data-type=\"solution\">\n<details>\n<summary>Show answer<\/summary>\n<p id=\"fs-id1170652631158\">a)<img loading=\"lazy\" decoding=\"async\" src=\"https:\/\/opentextbc.ca\/introalgebra\/wp-content\/ql-cache\/quicklatex.com-4797c874a138ca175d7c2cd8b3ed9a98_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"&#45;&#54;\" title=\"Rendered by QuickLaTeX.com\" height=\"12\" width=\"22\" style=\"vertical-align: 0px;\" \/> b) 10<\/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-id1170653799901\" data-type=\"problem\">\n<p id=\"fs-id1170653799903\">When <img loading=\"lazy\" decoding=\"async\" src=\"https:\/\/opentextbc.ca\/introalgebra\/wp-content\/ql-cache\/quicklatex.com-c3a4f9b7fbef4cb8ec29455107f6ac6a_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"&#121;&#61;&#45;&#57;\" title=\"Rendered by QuickLaTeX.com\" height=\"16\" width=\"56\" style=\"vertical-align: -4px;\" \/>, evaluate a) <img loading=\"lazy\" decoding=\"async\" src=\"https:\/\/opentextbc.ca\/introalgebra\/wp-content\/ql-cache\/quicklatex.com-3e134f9374cfd4c18406c0d7a9877bfc_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"&#121;&#43;&#56;\" title=\"Rendered by QuickLaTeX.com\" height=\"16\" width=\"40\" style=\"vertical-align: -4px;\" \/> b) <img loading=\"lazy\" decoding=\"async\" src=\"https:\/\/opentextbc.ca\/introalgebra\/wp-content\/ql-cache\/quicklatex.com-7b7d48c892f510764fec02284cc46147_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"&#92;&#116;&#101;&#120;&#116;&#123;&#45;&#125;&#121;&#43;&#56;\" title=\"Rendered by QuickLaTeX.com\" height=\"16\" width=\"46\" style=\"vertical-align: -4px;\" \/>.<\/p>\n<\/div>\n<div id=\"fs-id1170654286534\" data-type=\"solution\">\n<details>\n<summary>Show answer<\/summary>\n<p id=\"fs-id1170654286536\">a)<img loading=\"lazy\" decoding=\"async\" src=\"https:\/\/opentextbc.ca\/introalgebra\/wp-content\/ql-cache\/quicklatex.com-7b34c01098c83fa602de54e9d74d63a9_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"&#45;&#49;\" title=\"Rendered by QuickLaTeX.com\" height=\"13\" width=\"21\" style=\"vertical-align: -1px;\" \/> b) 17<\/p>\n<\/details>\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-id1170654212321\" data-type=\"problem\">\n<p id=\"fs-id1170654212324\">Evaluate <img loading=\"lazy\" decoding=\"async\" src=\"https:\/\/opentextbc.ca\/introalgebra\/wp-content\/ql-cache\/quicklatex.com-a469f70946862971ba45ee6cb67facc9_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"&#123;&#92;&#108;&#101;&#102;&#116;&#40;&#120;&#43;&#121;&#92;&#114;&#105;&#103;&#104;&#116;&#41;&#125;&#94;&#123;&#50;&#125;\" title=\"Rendered by QuickLaTeX.com\" height=\"21\" width=\"61\" style=\"vertical-align: -4px;\" \/> when <img loading=\"lazy\" decoding=\"async\" src=\"https:\/\/opentextbc.ca\/introalgebra\/wp-content\/ql-cache\/quicklatex.com-6b7a4e1252e519c67c5eb46528677f7c_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"&#120;&#61;&#45;&#49;&#56;\" title=\"Rendered by QuickLaTeX.com\" height=\"13\" width=\"66\" style=\"vertical-align: -1px;\" \/> and <img loading=\"lazy\" decoding=\"async\" src=\"https:\/\/opentextbc.ca\/introalgebra\/wp-content\/ql-cache\/quicklatex.com-672e03bf2648666b6cbcdb4bd4dce9f0_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"&#121;&#61;&#50;&#52;\" title=\"Rendered by QuickLaTeX.com\" height=\"16\" width=\"51\" style=\"vertical-align: -4px;\" \/>.<\/p>\n<\/div>\n<div id=\"fs-id1170653800718\" data-type=\"solution\">\n<div data-type=\"title\"><\/div>\n<div data-type=\"title\"><strong>Solution<\/strong><\/div>\n<table id=\"eip-id1169751902542\" class=\"unnumbered unstyled\" style=\"height: 72px;\" summary=\"This is a solution table with two columns. The top of the right column has the equation \u201cx plus y in parentheses squared.\u201d The next row down on the left reads, \u201cSubstitute negative eighteen for \u201cx\u201d and 24 for \u201cy\u201d. The negative 18 is in red, and \u201c24\u201d is in blue. Next to this in the right column, it has the equation negative eighteen plus 24\u201d in parentheses squared. The next row down reads, \u201cadd inside the parentheses.\u201d Next to this in the right column is the equation \u201c6\u201d in parentheses squared. The next row down says \u201cSimplify\u201d. Next to this in the right column is \u201c36\u201d.\" data-label=\"\">\n<tbody>\n<tr style=\"height: 19px;\">\n<td style=\"height: 19px; width: 458.646px;\"><\/td>\n<td style=\"height: 19px; width: 251.979px;\" data-align=\"center\"><span id=\"eip-id1169754030720\" data-type=\"media\" data-alt=\".\"><img decoding=\"async\" src=\"https:\/\/opentextbc.ca\/accessibilitytoolkit\/wp-content\/uploads\/sites\/333\/2021\/03\/CNX_ElemAlg_Figure_01_04_005b_img_new.jpg\" alt=\".\" data-media-type=\"image\/png\" \/><\/span><\/td>\n<\/tr>\n<tr style=\"height: 23px;\">\n<td style=\"height: 23px; width: 458.646px;\"><span id=\"eip-id1169752191035\" data-type=\"media\" data-alt=\".\"><img decoding=\"async\" src=\"https:\/\/opentextbc.ca\/accessibilitytoolkit\/wp-content\/uploads\/sites\/333\/2021\/03\/CNX_ElemAlg_Figure_01_04_005a_img_new.jpg\" alt=\".\" data-media-type=\"image\/png\" \/><\/span><\/td>\n<td style=\"height: 23px; width: 251.979px;\" data-align=\"center\"><img loading=\"lazy\" decoding=\"async\" src=\"https:\/\/opentextbc.ca\/introalgebra\/wp-content\/ql-cache\/quicklatex.com-adba02a2e5c4ac350afded793801b8d4_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"&#123;&#92;&#108;&#101;&#102;&#116;&#40;&#45;&#49;&#56;&#43;&#50;&#52;&#92;&#114;&#105;&#103;&#104;&#116;&#41;&#125;&#94;&#123;&#50;&#125;\" title=\"Rendered by QuickLaTeX.com\" height=\"21\" width=\"91\" style=\"vertical-align: -4px;\" \/><\/td>\n<\/tr>\n<tr style=\"height: 15px;\">\n<td style=\"height: 15px; width: 458.646px;\">Add inside parenthesis.<\/td>\n<td style=\"height: 15px; width: 251.979px;\" data-align=\"center\">(6)<sup>2<\/sup><\/td>\n<\/tr>\n<tr style=\"height: 15px;\">\n<td style=\"height: 15px; width: 458.646px;\">Simplify.<\/td>\n<td style=\"height: 15px; width: 251.979px;\" data-align=\"center\">36<\/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-id1170652630296\" data-type=\"problem\">\n<p id=\"fs-id1170652630298\">Evaluate <img loading=\"lazy\" decoding=\"async\" src=\"https:\/\/opentextbc.ca\/introalgebra\/wp-content\/ql-cache\/quicklatex.com-a469f70946862971ba45ee6cb67facc9_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"&#123;&#92;&#108;&#101;&#102;&#116;&#40;&#120;&#43;&#121;&#92;&#114;&#105;&#103;&#104;&#116;&#41;&#125;&#94;&#123;&#50;&#125;\" title=\"Rendered by QuickLaTeX.com\" height=\"21\" width=\"61\" style=\"vertical-align: -4px;\" \/> when <img loading=\"lazy\" decoding=\"async\" src=\"https:\/\/opentextbc.ca\/introalgebra\/wp-content\/ql-cache\/quicklatex.com-b4c8f29b4b370d6e1680d2a3cb708771_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"&#120;&#61;&#45;&#49;&#53;\" title=\"Rendered by QuickLaTeX.com\" height=\"14\" width=\"65\" style=\"vertical-align: -1px;\" \/> and <img loading=\"lazy\" decoding=\"async\" src=\"https:\/\/opentextbc.ca\/introalgebra\/wp-content\/ql-cache\/quicklatex.com-1d9ceb72d75740eb264ef8935d8e409e_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"&#121;&#61;&#50;&#57;\" title=\"Rendered by QuickLaTeX.com\" height=\"16\" width=\"51\" style=\"vertical-align: -4px;\" \/>.<\/p>\n<\/div>\n<div id=\"fs-id1170654285387\" data-type=\"solution\">\n<details>\n<summary>Show answer<\/summary>\n<p id=\"fs-id1170654061358\">196<\/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-id1170653791775\" data-type=\"problem\">\n<p id=\"fs-id1170653791777\">Evaluate <img loading=\"lazy\" decoding=\"async\" src=\"https:\/\/opentextbc.ca\/introalgebra\/wp-content\/ql-cache\/quicklatex.com-0b9349de57d1d909e3b5623de66e58d0_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"&#123;&#92;&#108;&#101;&#102;&#116;&#40;&#120;&#43;&#121;&#92;&#114;&#105;&#103;&#104;&#116;&#41;&#125;&#94;&#123;&#51;&#125;\" title=\"Rendered by QuickLaTeX.com\" height=\"21\" width=\"61\" style=\"vertical-align: -4px;\" \/> when <img loading=\"lazy\" decoding=\"async\" src=\"https:\/\/opentextbc.ca\/introalgebra\/wp-content\/ql-cache\/quicklatex.com-7852d0704798164bd2ce5b572ac50cd9_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"&#120;&#61;&#45;&#56;\" title=\"Rendered by QuickLaTeX.com\" height=\"12\" width=\"57\" style=\"vertical-align: 0px;\" \/> and <img loading=\"lazy\" decoding=\"async\" src=\"https:\/\/opentextbc.ca\/introalgebra\/wp-content\/ql-cache\/quicklatex.com-e49d18427ec504a62c9381964d39393c_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"&#121;&#61;&#49;&#48;\" title=\"Rendered by QuickLaTeX.com\" height=\"16\" width=\"51\" style=\"vertical-align: -4px;\" \/>.<\/p>\n<\/div>\n<div id=\"fs-id1170652624057\" data-type=\"solution\">\n<details>\n<summary>Show answer<\/summary>\n<p id=\"fs-id1170652624060\">8<\/p>\n<\/details>\n<\/div>\n<\/div>\n<\/div>\n<\/div>\n<\/div>\n<\/div>\n<div id=\"fs-id1170654061364\" class=\"try\" data-type=\"note\">\n<div id=\"fs-id1170653791773\" data-type=\"exercise\">\n<div id=\"fs-id1170652624057\" data-type=\"solution\">\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-id1170652623780\" data-type=\"problem\">\n<p id=\"fs-id1170652623782\">Evaluate <img loading=\"lazy\" decoding=\"async\" src=\"https:\/\/opentextbc.ca\/introalgebra\/wp-content\/ql-cache\/quicklatex.com-96fa163893ec7754dfb32e67268f354c_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"&#50;&#48;&#45;&#122;\" title=\"Rendered by QuickLaTeX.com\" height=\"12\" width=\"48\" style=\"vertical-align: 0px;\" \/> when a) <img loading=\"lazy\" decoding=\"async\" src=\"https:\/\/opentextbc.ca\/introalgebra\/wp-content\/ql-cache\/quicklatex.com-0e9a9f79659b4d78df01bcabe15215d3_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"&#122;&#61;&#49;&#50;\" title=\"Rendered by QuickLaTeX.com\" height=\"13\" width=\"50\" style=\"vertical-align: -1px;\" \/> and b) <img loading=\"lazy\" decoding=\"async\" src=\"https:\/\/opentextbc.ca\/introalgebra\/wp-content\/ql-cache\/quicklatex.com-47d9db2f88056dd3eba737497637952c_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"&#122;&#61;&#45;&#49;&#50;\" title=\"Rendered by QuickLaTeX.com\" height=\"12\" width=\"64\" style=\"vertical-align: 0px;\" \/>.<\/p>\n<\/div>\n<div id=\"fs-id1170654165739\" 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-id1166419679240\">a)<\/p>\n<table id=\"eip-id1169752967592\" class=\"unnumbered unstyled\" summary=\"This is a solution table with two columns. The top of the right column has the equation \u201ctwenty minus z.\u201d The next row down on the left reads, \u201cSubstitute 12 for \u201cz\u201d. The twelve is in red. Next to this in the right column, it has twenty minus twelve. The next row down reads, \u201csubtract.\u201d Next to this in the right column is \u201c8\u201d.\" data-label=\"\">\n<tbody>\n<tr>\n<td><\/td>\n<td data-align=\"center\"><span id=\"eip-id1169752986908\" data-type=\"media\" data-alt=\".\"><img decoding=\"async\" src=\"https:\/\/opentextbc.ca\/accessibilitytoolkit\/wp-content\/uploads\/sites\/333\/2021\/03\/CNX_ElemAlg_Figure_01_04_006b_img_new.jpg\" alt=\".\" data-media-type=\"image\/png\" \/><\/span><\/td>\n<\/tr>\n<tr>\n<td><span id=\"eip-id1169751035249\" data-type=\"media\" data-alt=\".\"><img decoding=\"async\" src=\"https:\/\/opentextbc.ca\/accessibilitytoolkit\/wp-content\/uploads\/sites\/333\/2021\/03\/CNX_ElemAlg_Figure_01_04_006a_img_new.jpg\" alt=\".\" data-media-type=\"image\/png\" \/><\/span><\/td>\n<td data-align=\"center\"><span id=\"eip-id1169753314441\" data-type=\"media\" data-alt=\".\"><img decoding=\"async\" src=\"https:\/\/opentextbc.ca\/accessibilitytoolkit\/wp-content\/uploads\/sites\/333\/2021\/03\/CNX_ElemAlg_Figure_01_04_006c_img_new.jpg\" alt=\".\" data-media-type=\"image\/png\" \/><\/span><\/td>\n<\/tr>\n<tr>\n<td>Subtract.<\/td>\n<td data-align=\"center\">8<\/td>\n<\/tr>\n<\/tbody>\n<\/table>\n<p>b)<\/p>\n<table id=\"eip-id1169753284608\" class=\"unnumbered unstyled\" summary=\"This is a solution table with two columns. The top of the right column has the equation \u201ctwenty minus z.\u201d The next row down on the left reads, \u201cSubstitute negative 12 for \u201cz\u201d. The negative twelve is in red. Next to this in the right column, it has twenty minus negative twelve. The negative 12 is in parentheses. The next row down reads, \u201csubtract.\u201d Next to this in the right column is \u201c32\u201d.\" data-label=\"\">\n<tbody>\n<tr>\n<td><\/td>\n<td data-align=\"center\"><span id=\"eip-id1169752818172\" data-type=\"media\" data-alt=\".\"><img decoding=\"async\" src=\"https:\/\/opentextbc.ca\/accessibilitytoolkit\/wp-content\/uploads\/sites\/333\/2021\/03\/CNX_ElemAlg_Figure_01_04_007b_img_new.jpg\" alt=\".\" data-media-type=\"image\/png\" \/><\/span><\/td>\n<\/tr>\n<tr>\n<td><span id=\"eip-id1169752838416\" data-type=\"media\" data-alt=\".\"><img decoding=\"async\" src=\"https:\/\/opentextbc.ca\/accessibilitytoolkit\/wp-content\/uploads\/sites\/333\/2021\/03\/CNX_ElemAlg_Figure_01_04_007a_img_new.jpg\" alt=\".\" data-media-type=\"image\/png\" \/><\/span><\/td>\n<td data-align=\"center\"><span id=\"eip-id1169750893297\" data-type=\"media\" data-alt=\".\"><img decoding=\"async\" src=\"https:\/\/opentextbc.ca\/accessibilitytoolkit\/wp-content\/uploads\/sites\/333\/2021\/03\/CNX_ElemAlg_Figure_01_04_007c_img_new.jpg\" alt=\".\" data-media-type=\"image\/png\" \/><\/span><\/td>\n<\/tr>\n<tr>\n<td>Subtract.<\/td>\n<td data-align=\"center\">32<\/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-id1170654157554\" data-type=\"problem\">\n<p id=\"fs-id1170654157556\">Evaluate: <img loading=\"lazy\" decoding=\"async\" src=\"https:\/\/opentextbc.ca\/introalgebra\/wp-content\/ql-cache\/quicklatex.com-a5fdf1c45dbe2c7e2a8e651ca8f6d51c_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"&#49;&#55;&#45;&#107;\" title=\"Rendered by QuickLaTeX.com\" height=\"14\" width=\"47\" style=\"vertical-align: -1px;\" \/> when a) <img loading=\"lazy\" decoding=\"async\" src=\"https:\/\/opentextbc.ca\/introalgebra\/wp-content\/ql-cache\/quicklatex.com-b3295f7a70d244f17de1abf774c538a4_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"&#107;&#61;&#49;&#57;\" title=\"Rendered by QuickLaTeX.com\" height=\"14\" width=\"51\" style=\"vertical-align: -1px;\" \/> and b) <img loading=\"lazy\" decoding=\"async\" src=\"https:\/\/opentextbc.ca\/introalgebra\/wp-content\/ql-cache\/quicklatex.com-aca30dd086e3e2a1ccd24fafae9f66d4_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"&#107;&#61;&#45;&#49;&#57;\" title=\"Rendered by QuickLaTeX.com\" height=\"12\" width=\"65\" style=\"vertical-align: 0px;\" \/>.<\/p>\n<\/div>\n<div id=\"fs-id1170652619306\" data-type=\"solution\">\n<details>\n<summary>Show answer<\/summary>\n<p id=\"fs-id1170652619308\">a)<img loading=\"lazy\" decoding=\"async\" src=\"https:\/\/opentextbc.ca\/introalgebra\/wp-content\/ql-cache\/quicklatex.com-17c33e2329e29a62a80ad2b547b4753d_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"&#45;&#50;\" title=\"Rendered by QuickLaTeX.com\" height=\"12\" width=\"21\" style=\"vertical-align: 0px;\" \/> b) 36<\/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-id1170652623499\" data-type=\"problem\">\n<p id=\"fs-id1170654138480\">Evaluate: <img loading=\"lazy\" decoding=\"async\" src=\"https:\/\/opentextbc.ca\/introalgebra\/wp-content\/ql-cache\/quicklatex.com-1806d9e7cdec8146fa21c480bf42225e_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"&#45;&#53;&#45;&#98;\" title=\"Rendered by QuickLaTeX.com\" height=\"13\" width=\"51\" style=\"vertical-align: 0px;\" \/> when a) <img loading=\"lazy\" decoding=\"async\" src=\"https:\/\/opentextbc.ca\/introalgebra\/wp-content\/ql-cache\/quicklatex.com-ee951a7e5630634730f11f6c2ab8ccc9_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"&#98;&#61;&#49;&#52;\" title=\"Rendered by QuickLaTeX.com\" height=\"14\" width=\"49\" style=\"vertical-align: -1px;\" \/> and b) <img loading=\"lazy\" decoding=\"async\" src=\"https:\/\/opentextbc.ca\/introalgebra\/wp-content\/ql-cache\/quicklatex.com-5bd013d779c2dbbfdeb75abdb853cd62_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"&#98;&#61;&#45;&#49;&#52;\" title=\"Rendered by QuickLaTeX.com\" height=\"12\" width=\"63\" style=\"vertical-align: 0px;\" \/>.<\/p>\n<\/div>\n<div id=\"fs-id1170652619277\" data-type=\"solution\">\n<details>\n<summary>Show answer<\/summary>\n<p id=\"fs-id1170652619279\">a)<img loading=\"lazy\" decoding=\"async\" src=\"https:\/\/opentextbc.ca\/introalgebra\/wp-content\/ql-cache\/quicklatex.com-0e22bf27371ae8e82f2cf9857cc59c29_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"&#45;&#49;&#57;\" title=\"Rendered by QuickLaTeX.com\" height=\"13\" width=\"31\" style=\"vertical-align: -1px;\" \/> b) 9<\/p>\n<\/details>\n<\/div>\n<\/div>\n<\/div>\n<\/div>\n<\/div>\n<\/div>\n<div id=\"fs-id1170654157548\" class=\"try\" data-type=\"note\">\n<div id=\"fs-id1170654157552\" data-type=\"exercise\">\n<div id=\"fs-id1170654157554\" data-type=\"problem\">\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-id1170654287816\" data-type=\"problem\">\n<p id=\"fs-id1170652618176\">Evaluate: <img loading=\"lazy\" decoding=\"async\" src=\"https:\/\/opentextbc.ca\/introalgebra\/wp-content\/ql-cache\/quicklatex.com-3e362c24d22f82d89f3d039864a4892a_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"&#50;&#123;&#120;&#125;&#94;&#123;&#50;&#125;&#43;&#51;&#120;&#43;&#56;\" title=\"Rendered by QuickLaTeX.com\" height=\"17\" width=\"98\" style=\"vertical-align: -2px;\" \/> when <img loading=\"lazy\" decoding=\"async\" src=\"https:\/\/opentextbc.ca\/introalgebra\/wp-content\/ql-cache\/quicklatex.com-2145acc2878ed61214887e120f2485b7_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"&#120;&#61;&#52;\" title=\"Rendered by QuickLaTeX.com\" height=\"13\" width=\"43\" style=\"vertical-align: -1px;\" \/>.<\/p>\n<\/div>\n<div id=\"fs-id1170654215881\" 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-id1170654164395\">Substitute <img loading=\"lazy\" decoding=\"async\" src=\"https:\/\/opentextbc.ca\/introalgebra\/wp-content\/ql-cache\/quicklatex.com-85af046328f5487fbb2d348639b5162c_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;&#116;&#101;&#120;&#116;&#123;&#102;&#111;&#114;&#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;&#120;\" title=\"Rendered by QuickLaTeX.com\" height=\"13\" width=\"47\" style=\"vertical-align: 0px;\" \/>. Use parentheses to show multiplication.<\/p>\n<table id=\"eip-id1169752967487\" class=\"unnumbered unstyled\" summary=\"This is a solution table with two columns. The top of the right column has the equation \u201ctwo \u201cx\u201d squared plus three\u201dx\u201d plus 8.\u201d The next row down on the left reads, \u201cSubstitute.\u201d Next to this in the right column, it has \u201ctwo times 4 squared plus three times four plus eight.\u201d The fours are red. The next row down reads, \u201cevaluate the exponents.\u201d Next to this in the right column is \u201ctwo times 16 squared plus three times 4 plus 8\u201d. The next row down reads, \u201cMultiply.\u201d Next to this in the right column \u201c32 plus 12 plus 8.\u201d The next row down reads \u201cadd\u201d. Next to this in the right column is \u201c52\u201d.\" data-label=\"\">\n<tbody>\n<tr>\n<td><\/td>\n<td data-align=\"center\"><span id=\"eip-id1169753319331\" data-type=\"media\" data-alt=\".\"><img decoding=\"async\" src=\"https:\/\/opentextbc.ca\/accessibilitytoolkit\/wp-content\/uploads\/sites\/333\/2021\/03\/CNX_ElemAlg_Figure_01_04_008a_img_new.jpg\" alt=\".\" data-media-type=\"image\/png\" \/><\/span><\/td>\n<\/tr>\n<tr>\n<td>Substitute.<\/td>\n<td data-align=\"center\"><span id=\"eip-id1169752839642\" data-type=\"media\" data-alt=\".\"><img decoding=\"async\" src=\"https:\/\/opentextbc.ca\/accessibilitytoolkit\/wp-content\/uploads\/sites\/333\/2021\/03\/CNX_ElemAlg_Figure_01_04_008b_img_new.jpg\" alt=\".\" data-media-type=\"image\/png\" \/><\/span><\/td>\n<\/tr>\n<tr>\n<td>Evaluate exponents.<\/td>\n<td data-align=\"center\"><span id=\"eip-id1169753138651\" data-type=\"media\" data-alt=\".\"><img decoding=\"async\" src=\"https:\/\/opentextbc.ca\/accessibilitytoolkit\/wp-content\/uploads\/sites\/333\/2021\/03\/CNX_ElemAlg_Figure_01_04_008c_img_new.jpg\" alt=\".\" data-media-type=\"image\/png\" \/><\/span><\/td>\n<\/tr>\n<tr>\n<td>Multiply.<\/td>\n<td data-align=\"center\"><span id=\"eip-id1169752821475\" data-type=\"media\" data-alt=\".\"><img decoding=\"async\" src=\"https:\/\/opentextbc.ca\/accessibilitytoolkit\/wp-content\/uploads\/sites\/333\/2021\/03\/CNX_ElemAlg_Figure_01_04_008d_img_new.jpg\" alt=\".\" data-media-type=\"image\/png\" \/><\/span><\/td>\n<\/tr>\n<tr>\n<td>Add.<\/td>\n<td data-align=\"center\">52<\/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-id1170654080966\" data-type=\"problem\">\n<p id=\"fs-id1170654080968\">Evaluate: <img loading=\"lazy\" decoding=\"async\" src=\"https:\/\/opentextbc.ca\/introalgebra\/wp-content\/ql-cache\/quicklatex.com-68dec9e0111b2f82a5c083b4fd0c1e1c_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"&#51;&#123;&#120;&#125;&#94;&#123;&#50;&#125;&#45;&#50;&#120;&#43;&#54;\" title=\"Rendered by QuickLaTeX.com\" height=\"17\" width=\"98\" style=\"vertical-align: -2px;\" \/> when <img loading=\"lazy\" decoding=\"async\" src=\"https:\/\/opentextbc.ca\/introalgebra\/wp-content\/ql-cache\/quicklatex.com-7e135cd6350a4c21195c621240f7aee7_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"&#120;&#61;&#45;&#51;\" title=\"Rendered by QuickLaTeX.com\" height=\"12\" width=\"57\" style=\"vertical-align: 0px;\" \/>.<\/p>\n<\/div>\n<div id=\"fs-id1170653798527\" data-type=\"solution\">\n<details>\n<summary>Show answer<\/summary>\n<p id=\"fs-id1170653798529\">39<\/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-id1170654129713\" data-type=\"problem\">\n<p id=\"fs-id1170654129715\">Evaluate: <img loading=\"lazy\" decoding=\"async\" src=\"https:\/\/opentextbc.ca\/introalgebra\/wp-content\/ql-cache\/quicklatex.com-eba611e4a46b976e033fda6c2896ec08_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"&#52;&#123;&#120;&#125;&#94;&#123;&#50;&#125;&#45;&#120;&#45;&#53;\" title=\"Rendered by QuickLaTeX.com\" height=\"16\" width=\"88\" style=\"vertical-align: -1px;\" \/> when <img loading=\"lazy\" decoding=\"async\" src=\"https:\/\/opentextbc.ca\/introalgebra\/wp-content\/ql-cache\/quicklatex.com-01f282abd343bbe6b83c45e54b86c6ed_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"&#120;&#61;&#45;&#50;\" title=\"Rendered by QuickLaTeX.com\" height=\"12\" width=\"56\" style=\"vertical-align: 0px;\" \/>.<\/p>\n<\/div>\n<div id=\"fs-id1170653875048\" data-type=\"solution\">\n<details>\n<summary>Show answer<\/summary>\n<p id=\"fs-id1170653875050\">13<\/p>\n<\/details>\n<\/div>\n<\/div>\n<\/div>\n<\/div>\n<\/div>\n<\/div>\n<h1>Translate Phrases to Expressions with Integers<\/h1>\n<p id=\"fs-id1170654080268\">Our earlier work translating English to algebra also applies to phrases that include both positive and negative numbers.<\/p>\n<div class=\"textbox textbox--examples\">\n<header class=\"textbox__header\">\n<p class=\"textbox__title\">EXAMPLE 13<\/p>\n<\/header>\n<div class=\"textbox__content\">\n<div id=\"fs-id1170654286415\" data-type=\"problem\">\n<p id=\"fs-id1170654286418\">Translate and simplify: the sum of 8 and <img loading=\"lazy\" decoding=\"async\" src=\"https:\/\/opentextbc.ca\/introalgebra\/wp-content\/ql-cache\/quicklatex.com-9eae543c53f9301fa411ef541a1f4433_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"&#45;&#49;&#50;\" title=\"Rendered by QuickLaTeX.com\" height=\"13\" width=\"30\" style=\"vertical-align: -1px;\" \/>, increased by 3<\/p>\n<\/div>\n<div id=\"fs-id1170652630972\" 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-929\" summary=\".\">\n<tbody>\n<tr>\n<td><\/td>\n<td>the <strong>sum<\/strong> of 8 and <img loading=\"lazy\" decoding=\"async\" src=\"https:\/\/opentextbc.ca\/introalgebra\/wp-content\/ql-cache\/quicklatex.com-9eae543c53f9301fa411ef541a1f4433_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"&#45;&#49;&#50;\" title=\"Rendered by QuickLaTeX.com\" height=\"13\" width=\"30\" style=\"vertical-align: -1px;\" \/>, increased by 3.<\/td>\n<\/tr>\n<tr>\n<td>Translate.<\/td>\n<td><img loading=\"lazy\" decoding=\"async\" src=\"https:\/\/opentextbc.ca\/introalgebra\/wp-content\/ql-cache\/quicklatex.com-a09a92a3386daf3ef02efe2b4e1bbfc6_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"&#92;&#108;&#101;&#102;&#116;&#91;&#56;&#43;&#92;&#108;&#101;&#102;&#116;&#40;&#45;&#49;&#50;&#92;&#114;&#105;&#103;&#104;&#116;&#41;&#92;&#114;&#105;&#103;&#104;&#116;&#93;&#43;&#51;\" title=\"Rendered by QuickLaTeX.com\" height=\"19\" width=\"114\" style=\"vertical-align: -5px;\" \/><\/td>\n<\/tr>\n<tr>\n<td>Simplify. Be careful not to confuse the brackets with an absolute value sign.<\/td>\n<td><img loading=\"lazy\" decoding=\"async\" src=\"https:\/\/opentextbc.ca\/introalgebra\/wp-content\/ql-cache\/quicklatex.com-2d0d5d4ddb7f9e4c9928b27ff57b7925_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"&#92;&#108;&#101;&#102;&#116;&#40;&#45;&#52;&#92;&#114;&#105;&#103;&#104;&#116;&#41;&#43;&#51;\" title=\"Rendered by QuickLaTeX.com\" height=\"18\" width=\"66\" style=\"vertical-align: -4px;\" \/><\/td>\n<\/tr>\n<tr>\n<td>Add.<\/td>\n<td><img loading=\"lazy\" decoding=\"async\" src=\"https:\/\/opentextbc.ca\/introalgebra\/wp-content\/ql-cache\/quicklatex.com-7b34c01098c83fa602de54e9d74d63a9_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"&#45;&#49;\" title=\"Rendered by QuickLaTeX.com\" height=\"13\" width=\"21\" 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 13.1<\/p>\n<\/header>\n<div class=\"textbox__content\">\n<div id=\"fs-id1170654285669\" data-type=\"problem\">\n<p id=\"fs-id1170652620473\">Translate and simplify the sum of 9 and <img loading=\"lazy\" decoding=\"async\" src=\"https:\/\/opentextbc.ca\/introalgebra\/wp-content\/ql-cache\/quicklatex.com-60f20f07f8f7c62331f2d8fe388a61b0_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"&#45;&#49;&#54;\" title=\"Rendered by QuickLaTeX.com\" height=\"13\" width=\"31\" style=\"vertical-align: -1px;\" \/>, increased by 4<\/p>\n<\/div>\n<div id=\"fs-id1170652622182\" data-type=\"solution\">\n<details>\n<summary>Show answer<\/summary>\n<p id=\"fs-id1170652622184\"><img loading=\"lazy\" decoding=\"async\" src=\"https:\/\/opentextbc.ca\/introalgebra\/wp-content\/ql-cache\/quicklatex.com-e5de78774ed9d16455eb1df5aa313ff4_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"&#92;&#108;&#101;&#102;&#116;&#40;&#57;&#43;&#92;&#108;&#101;&#102;&#116;&#40;&#45;&#49;&#54;&#92;&#114;&#105;&#103;&#104;&#116;&#41;&#92;&#114;&#105;&#103;&#104;&#116;&#41;&#43;&#52;&#45;&#51;\" title=\"Rendered by QuickLaTeX.com\" height=\"18\" width=\"150\" style=\"vertical-align: -4px;\" \/><\/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 13.2<\/p>\n<\/header>\n<div class=\"textbox__content\">\n<div id=\"fs-id1170654041776\" data-type=\"problem\">\n<p id=\"fs-id1170654041778\">Translate and simplify the sum of <img loading=\"lazy\" decoding=\"async\" src=\"https:\/\/opentextbc.ca\/introalgebra\/wp-content\/ql-cache\/quicklatex.com-ca32393b1b5af7c55a95d89cf9d610f2_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"&#45;&#56;\" title=\"Rendered by QuickLaTeX.com\" height=\"12\" width=\"22\" style=\"vertical-align: 0px;\" \/> and <img loading=\"lazy\" decoding=\"async\" src=\"https:\/\/opentextbc.ca\/introalgebra\/wp-content\/ql-cache\/quicklatex.com-9eae543c53f9301fa411ef541a1f4433_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"&#45;&#49;&#50;\" title=\"Rendered by QuickLaTeX.com\" height=\"13\" width=\"30\" style=\"vertical-align: -1px;\" \/>, increased by 7<\/p>\n<\/div>\n<div id=\"fs-id1170653849382\" data-type=\"solution\">\n<details>\n<summary>Show answer<\/summary>\n<p id=\"fs-id1170654209722\"><img loading=\"lazy\" decoding=\"async\" src=\"https:\/\/opentextbc.ca\/introalgebra\/wp-content\/ql-cache\/quicklatex.com-131523c5b505a2f40f981813cbf5e786_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"&#92;&#108;&#101;&#102;&#116;&#40;&#45;&#56;&#43;&#92;&#108;&#101;&#102;&#116;&#40;&#45;&#49;&#50;&#92;&#114;&#105;&#103;&#104;&#116;&#41;&#92;&#114;&#105;&#103;&#104;&#116;&#41;&#43;&#55;&#45;&#49;&#51;\" title=\"Rendered by QuickLaTeX.com\" height=\"18\" width=\"173\" style=\"vertical-align: -4px;\" \/><\/p>\n<\/details>\n<\/div>\n<\/div>\n<\/div>\n<p id=\"fs-id1170652622623\">When we first introduced the operation symbols, we saw that the expression may be read in several ways. They are listed in the chart below.<\/p>\n<table id=\"fs-id1170654190232\" class=\"grid\" summary=\"This table has two cells. In the top cell is the expression: a, minus b. In the bottom cell are the phrases: \u201ca minus b\u201d, \u201cthe difference of a and b\u201d, \u201cb subtracted from a\u201d, and \u201cb less than a\u201d.\" data-label=\"\">\n<thead>\n<tr valign=\"top\">\n<th data-align=\"center\" data-valign=\"top\"><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;\" \/><\/th>\n<\/tr>\n<\/thead>\n<tbody>\n<tr valign=\"top\">\n<td data-align=\"center\" data-valign=\"top\"><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;\" \/> minus <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;\" \/><br \/>\nthe 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;\" \/><br \/>\n<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;\" \/> subtracted from <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<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;\" \/> less 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;\" \/><\/td>\n<\/tr>\n<\/tbody>\n<\/table>\n<p id=\"fs-id1170654238524\">Be careful to get <em data-effect=\"italics\">a<\/em> and <em data-effect=\"italics\">b<\/em> in the right order!<\/p>\n<div class=\"textbox textbox--examples\">\n<header class=\"textbox__header\">\n<p class=\"textbox__title\">EXAMPLE 14<\/p>\n<\/header>\n<div class=\"textbox__content\">\n<div id=\"fs-id1170653874526\" data-type=\"problem\">\n<p id=\"fs-id1170653874528\">Translate and then simplify a) the difference of 13 and <img loading=\"lazy\" decoding=\"async\" src=\"https:\/\/opentextbc.ca\/introalgebra\/wp-content\/ql-cache\/quicklatex.com-f2cae475c6cc4ade824f228f09d1e1ad_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"&#45;&#50;&#49;\" title=\"Rendered by QuickLaTeX.com\" height=\"13\" width=\"30\" style=\"vertical-align: -1px;\" \/> b) subtract 24 from <img loading=\"lazy\" decoding=\"async\" src=\"https:\/\/opentextbc.ca\/introalgebra\/wp-content\/ql-cache\/quicklatex.com-0e22bf27371ae8e82f2cf9857cc59c29_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"&#45;&#49;&#57;\" title=\"Rendered by QuickLaTeX.com\" height=\"13\" width=\"31\" style=\"vertical-align: -1px;\" \/>.<\/p>\n<\/div>\n<div id=\"fs-id1170654150875\" 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-651\" summary=\".\">\n<tbody>\n<tr>\n<td>a)<br \/>\nTranslate.<br \/>\nSimplify.<\/td>\n<td><img loading=\"lazy\" decoding=\"async\" src=\"https:\/\/opentextbc.ca\/introalgebra\/wp-content\/ql-cache\/quicklatex.com-e7ea6d41ab574940ef2873b51deea121_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;&#125;&#92;&#116;&#101;&#120;&#116;&#123;&#116;&#104;&#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;&#92;&#109;&#97;&#116;&#104;&#98;&#102;&#123;&#92;&#116;&#101;&#120;&#116;&#123;&#100;&#105;&#102;&#102;&#101;&#114;&#101;&#110;&#99;&#101;&#125;&#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;&#109;&#97;&#116;&#104;&#105;&#116;&#123;&#92;&#116;&#101;&#120;&#116;&#123;&#111;&#102;&#125;&#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;&#49;&#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;&#109;&#97;&#116;&#104;&#105;&#116;&#123;&#92;&#116;&#101;&#120;&#116;&#123;&#97;&#110;&#100;&#125;&#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;&#45;&#50;&#49;&#92;&#92;&#32;&#49;&#51;&#45;&#92;&#108;&#101;&#102;&#116;&#40;&#45;&#50;&#49;&#92;&#114;&#105;&#103;&#104;&#116;&#41;&#92;&#92;&#32;&#51;&#52;&#92;&#101;&#110;&#100;&#123;&#97;&#114;&#114;&#97;&#121;&#125;\" title=\"Rendered by QuickLaTeX.com\" height=\"58\" width=\"215\" style=\"vertical-align: -23px;\" \/><\/td>\n<\/tr>\n<tr>\n<td>b)<br \/>\nTranslate. Remember, &#8220;subtract <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;\" \/> from <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;\" \/> means <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;\" \/>.<br \/>\nSimplify.<\/td>\n<td><img loading=\"lazy\" decoding=\"async\" src=\"https:\/\/opentextbc.ca\/introalgebra\/wp-content\/ql-cache\/quicklatex.com-fb91af6db4e39cde91c21a935d8a78ab_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;&#125;&#92;&#109;&#97;&#116;&#104;&#98;&#102;&#123;&#92;&#116;&#101;&#120;&#116;&#123;&#115;&#117;&#98;&#116;&#114;&#97;&#99;&#116;&#125;&#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;&#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;&#109;&#97;&#116;&#104;&#98;&#102;&#123;&#92;&#116;&#101;&#120;&#116;&#123;&#102;&#114;&#111;&#109;&#125;&#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;&#45;&#49;&#57;&#92;&#92;&#32;&#45;&#49;&#57;&#45;&#50;&#52;&#92;&#92;&#32;&#45;&#52;&#51;&#92;&#101;&#110;&#100;&#123;&#97;&#114;&#114;&#97;&#121;&#125;\" title=\"Rendered by QuickLaTeX.com\" height=\"57\" width=\"168\" style=\"vertical-align: -22px;\" \/><\/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 14.1<\/p>\n<\/header>\n<div class=\"textbox__content\">\n<div id=\"fs-id1170654159530\" data-type=\"problem\">\n<p id=\"fs-id1170654159532\">Translate and simplify a) the difference of 14 and <img loading=\"lazy\" decoding=\"async\" src=\"https:\/\/opentextbc.ca\/introalgebra\/wp-content\/ql-cache\/quicklatex.com-dd97a36455222fbbcd36f22967b75707_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"&#45;&#50;&#51;\" title=\"Rendered by QuickLaTeX.com\" height=\"12\" width=\"31\" style=\"vertical-align: 0px;\" \/> b) subtract 21 from <img loading=\"lazy\" decoding=\"async\" src=\"https:\/\/opentextbc.ca\/introalgebra\/wp-content\/ql-cache\/quicklatex.com-0a516826583d9ebf41e251f45bc98b74_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"&#45;&#49;&#55;\" title=\"Rendered by QuickLaTeX.com\" height=\"14\" width=\"31\" style=\"vertical-align: -1px;\" \/>.<\/p>\n<\/div>\n<div id=\"fs-id1170652619950\" data-type=\"solution\">\n<details>\n<summary>Show answer<\/summary>\n<p id=\"fs-id1170652619953\">a)<img loading=\"lazy\" decoding=\"async\" src=\"https:\/\/opentextbc.ca\/introalgebra\/wp-content\/ql-cache\/quicklatex.com-9b770b870a6862b21a9978dbe8e9ac92_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"&#49;&#52;&#45;&#92;&#108;&#101;&#102;&#116;&#40;&#45;&#50;&#51;&#92;&#114;&#105;&#103;&#104;&#116;&#41;&#59;&#51;&#55;\" title=\"Rendered by QuickLaTeX.com\" height=\"18\" width=\"113\" style=\"vertical-align: -4px;\" \/> b)<img loading=\"lazy\" decoding=\"async\" src=\"https:\/\/opentextbc.ca\/introalgebra\/wp-content\/ql-cache\/quicklatex.com-74efd35ca9c98c615222a71714014e2e_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"&#45;&#49;&#55;&#45;&#50;&#49;&#59;&#45;&#51;&#56;\" title=\"Rendered by QuickLaTeX.com\" height=\"16\" width=\"110\" style=\"vertical-align: -3px;\" \/><\/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 14.2<\/p>\n<\/header>\n<div class=\"textbox__content\">\n<div id=\"fs-id1170654285364\" data-type=\"problem\">\n<p id=\"fs-id1170654285366\">Translate and simplify a) the difference of 11 and <img loading=\"lazy\" decoding=\"async\" src=\"https:\/\/opentextbc.ca\/introalgebra\/wp-content\/ql-cache\/quicklatex.com-0e22bf27371ae8e82f2cf9857cc59c29_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"&#45;&#49;&#57;\" title=\"Rendered by QuickLaTeX.com\" height=\"13\" width=\"31\" style=\"vertical-align: -1px;\" \/> b) subtract 18 from <img loading=\"lazy\" decoding=\"async\" src=\"https:\/\/opentextbc.ca\/introalgebra\/wp-content\/ql-cache\/quicklatex.com-2981688f5b26fd15fa08c897afa741ad_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"&#45;&#49;&#49;\" title=\"Rendered by QuickLaTeX.com\" height=\"13\" width=\"30\" style=\"vertical-align: -1px;\" \/>.<\/p>\n<\/div>\n<div id=\"fs-id1170652621632\" data-type=\"solution\">\n<details>\n<summary>Show answer<\/summary>\n<p id=\"fs-id1170652621634\">a)<img loading=\"lazy\" decoding=\"async\" src=\"https:\/\/opentextbc.ca\/introalgebra\/wp-content\/ql-cache\/quicklatex.com-1ec19c9cce1a4c3289312de38b03db08_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"&#49;&#49;&#45;&#92;&#108;&#101;&#102;&#116;&#40;&#45;&#49;&#57;&#92;&#114;&#105;&#103;&#104;&#116;&#41;&#59;&#51;&#48;\" title=\"Rendered by QuickLaTeX.com\" height=\"18\" width=\"113\" style=\"vertical-align: -4px;\" \/> b)<img loading=\"lazy\" decoding=\"async\" src=\"https:\/\/opentextbc.ca\/introalgebra\/wp-content\/ql-cache\/quicklatex.com-fd1396b56752541ae85e7773acd7240c_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"&#45;&#49;&#49;&#45;&#49;&#56;&#59;&#45;&#50;&#57;\" title=\"Rendered by QuickLaTeX.com\" height=\"15\" width=\"110\" style=\"vertical-align: -3px;\" \/><\/p>\n<\/details>\n<\/div>\n<\/div>\n<\/div>\n<p id=\"fs-id1170653881059\">Once again, our prior work translating English to algebra transfers to phrases that include both multiplying and dividing integers. Remember that the key word for <span class=\"no-emphasis\" data-type=\"term\">multiplication<\/span> is \u201c<span class=\"no-emphasis\" data-type=\"term\">product<\/span>\u201d and for <span class=\"no-emphasis\" data-type=\"term\">division<\/span> is \u201c<span class=\"no-emphasis\" data-type=\"term\">quotient<\/span>.\u201d<\/p>\n<div class=\"textbox textbox--examples\">\n<header class=\"textbox__header\">\n<p class=\"textbox__title\">EXAMPLE 15<\/p>\n<\/header>\n<div class=\"textbox__content\">\n<div id=\"fs-id1170654158684\" data-type=\"problem\">\n<p id=\"fs-id1170654158686\">Translate to an algebraic expression and simplify if possible: the product of <img loading=\"lazy\" decoding=\"async\" src=\"https:\/\/opentextbc.ca\/introalgebra\/wp-content\/ql-cache\/quicklatex.com-17c33e2329e29a62a80ad2b547b4753d_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"&#45;&#50;\" title=\"Rendered by QuickLaTeX.com\" height=\"12\" width=\"21\" style=\"vertical-align: 0px;\" \/> and 14<\/p>\n<\/div>\n<div id=\"fs-id1170654158696\" 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-856\" summary=\".\">\n<tbody>\n<tr>\n<td><\/td>\n<td><img loading=\"lazy\" decoding=\"async\" src=\"https:\/\/opentextbc.ca\/introalgebra\/wp-content\/ql-cache\/quicklatex.com-ddba7febf8540e7c33c599a06b2c0c95_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"&#92;&#116;&#101;&#120;&#116;&#123;&#116;&#104;&#101;&#32;&#112;&#114;&#111;&#100;&#117;&#99;&#116;&#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;&#109;&#97;&#116;&#104;&#105;&#116;&#123;&#92;&#116;&#101;&#120;&#116;&#123;&#111;&#102;&#125;&#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;&#45;&#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;&#92;&#109;&#97;&#116;&#104;&#105;&#116;&#123;&#92;&#116;&#101;&#120;&#116;&#123;&#97;&#110;&#100;&#125;&#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;&#49;&#52;\" title=\"Rendered by QuickLaTeX.com\" height=\"16\" width=\"197\" style=\"vertical-align: -3px;\" \/><\/td>\n<\/tr>\n<tr>\n<td>Translate.<\/td>\n<td><img loading=\"lazy\" decoding=\"async\" src=\"https:\/\/opentextbc.ca\/introalgebra\/wp-content\/ql-cache\/quicklatex.com-1722b6d3cb5f6407c198b5960c231b50_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"&#92;&#108;&#101;&#102;&#116;&#40;&#45;&#50;&#92;&#114;&#105;&#103;&#104;&#116;&#41;&#92;&#108;&#101;&#102;&#116;&#40;&#49;&#52;&#92;&#114;&#105;&#103;&#104;&#116;&#41;\" title=\"Rendered by QuickLaTeX.com\" height=\"18\" width=\"69\" style=\"vertical-align: -4px;\" \/><\/td>\n<\/tr>\n<tr>\n<td>Simplify.<\/td>\n<td><img loading=\"lazy\" decoding=\"async\" src=\"https:\/\/opentextbc.ca\/introalgebra\/wp-content\/ql-cache\/quicklatex.com-7eaefbab9f26b55d0afa7f1689372c40_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"&#45;&#50;&#56;\" title=\"Rendered by QuickLaTeX.com\" height=\"12\" width=\"31\" 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 15.1<\/p>\n<\/header>\n<div class=\"textbox__content\">\n<div id=\"fs-id1170652620834\" data-type=\"problem\">\n<p id=\"fs-id1170652620836\">Translate to an algebraic expression and simplify if possible: the product of <img loading=\"lazy\" decoding=\"async\" src=\"https:\/\/opentextbc.ca\/introalgebra\/wp-content\/ql-cache\/quicklatex.com-7b5b9d9f382b11767d19f257afca0019_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"&#45;&#53;\" title=\"Rendered by QuickLaTeX.com\" height=\"13\" width=\"21\" style=\"vertical-align: 0px;\" \/> and 12<\/p>\n<\/div>\n<div id=\"fs-id1170652623909\" data-type=\"solution\">\n<details>\n<summary>Show answer<\/summary>\n<p id=\"fs-id1170652623911\"><img loading=\"lazy\" decoding=\"async\" src=\"https:\/\/opentextbc.ca\/introalgebra\/wp-content\/ql-cache\/quicklatex.com-b3fb5ad0791f34b993e4f3d506bedf3f_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"&#45;&#53;&#92;&#108;&#101;&#102;&#116;&#40;&#49;&#50;&#92;&#114;&#105;&#103;&#104;&#116;&#41;&#59;&#45;&#54;&#48;\" title=\"Rendered by QuickLaTeX.com\" height=\"18\" width=\"99\" style=\"vertical-align: -4px;\" \/><\/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 15.2<\/p>\n<\/header>\n<div class=\"textbox__content\">\n<div id=\"fs-id1170653797095\" data-type=\"problem\">\n<p id=\"fs-id1170653797097\">Translate to an algebraic expression and simplify if possible: the product of 8 and <img loading=\"lazy\" decoding=\"async\" src=\"https:\/\/opentextbc.ca\/introalgebra\/wp-content\/ql-cache\/quicklatex.com-ee7bea24371f97fb5673002404153494_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"&#45;&#49;&#51;\" title=\"Rendered by QuickLaTeX.com\" height=\"13\" width=\"31\" style=\"vertical-align: -1px;\" \/>.<\/p>\n<\/div>\n<div id=\"fs-id1170653868747\" data-type=\"solution\">\n<details>\n<summary>Show answer<\/summary>\n<p id=\"fs-id1170653868749\"><img loading=\"lazy\" decoding=\"async\" src=\"https:\/\/opentextbc.ca\/introalgebra\/wp-content\/ql-cache\/quicklatex.com-3b202311c4e51b1e87ff0229245f89be_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"&#45;&#56;&#92;&#108;&#101;&#102;&#116;&#40;&#49;&#51;&#92;&#114;&#105;&#103;&#104;&#116;&#41;&#59;&#45;&#49;&#48;&#52;\" title=\"Rendered by QuickLaTeX.com\" height=\"18\" width=\"108\" style=\"vertical-align: -4px;\" \/><\/p>\n<\/details>\n<\/div>\n<\/div>\n<\/div>\n<div id=\"fs-id1170653797090\" class=\"try\" data-type=\"note\">\n<div id=\"fs-id1170653797093\" data-type=\"exercise\">\n<div id=\"fs-id1170653868747\" data-type=\"solution\">\n<div class=\"textbox textbox--examples\">\n<header class=\"textbox__header\">\n<p class=\"textbox__title\">EXAMPLE 16<\/p>\n<\/header>\n<div class=\"textbox__content\">\n<div id=\"fs-id1170654158560\" data-type=\"problem\">\n<p id=\"fs-id1170654158562\">Translate to an algebraic expression and simplify if possible: the quotient of <img loading=\"lazy\" decoding=\"async\" src=\"https:\/\/opentextbc.ca\/introalgebra\/wp-content\/ql-cache\/quicklatex.com-eeacf7895c3fd138514ad215aa482af4_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"&#45;&#53;&#54;\" title=\"Rendered by QuickLaTeX.com\" height=\"13\" width=\"31\" style=\"vertical-align: 0px;\" \/> and <img loading=\"lazy\" decoding=\"async\" src=\"https:\/\/opentextbc.ca\/introalgebra\/wp-content\/ql-cache\/quicklatex.com-00c6d30c5f7439a21caf981437f64be1_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"&#45;&#55;\" title=\"Rendered by QuickLaTeX.com\" height=\"13\" width=\"22\" style=\"vertical-align: 0px;\" \/>.<\/p>\n<\/div>\n<div id=\"fs-id1170653875100\" data-type=\"solution\">\n<div data-type=\"title\"><\/div>\n<div data-type=\"title\"><strong>Solution<\/strong><\/div>\n<table id=\"eip-659\" summary=\".\">\n<tbody>\n<tr>\n<td><\/td>\n<td><img loading=\"lazy\" decoding=\"async\" src=\"https:\/\/opentextbc.ca\/introalgebra\/wp-content\/ql-cache\/quicklatex.com-807d8d0bacf9c8e4a7e349f1eec75cee_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"&#92;&#116;&#101;&#120;&#116;&#123;&#116;&#104;&#101;&#32;&#113;&#117;&#111;&#116;&#105;&#101;&#110;&#116;&#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;&#109;&#97;&#116;&#104;&#105;&#116;&#123;&#92;&#116;&#101;&#120;&#116;&#123;&#111;&#102;&#125;&#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;&#45;&#53;&#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;&#109;&#97;&#116;&#104;&#105;&#116;&#123;&#92;&#116;&#101;&#120;&#116;&#123;&#97;&#110;&#100;&#125;&#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;&#45;&#55;\" title=\"Rendered by QuickLaTeX.com\" height=\"16\" width=\"222\" style=\"vertical-align: -3px;\" \/><\/td>\n<\/tr>\n<tr>\n<td>Translate.<\/td>\n<td><img loading=\"lazy\" decoding=\"async\" src=\"https:\/\/opentextbc.ca\/introalgebra\/wp-content\/ql-cache\/quicklatex.com-35af2a5138063eea6a7b7932749dbd2c_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"&#45;&#53;&#54;&#92;&#100;&#105;&#118;&#32;&#92;&#108;&#101;&#102;&#116;&#40;&#45;&#55;&#92;&#114;&#105;&#103;&#104;&#116;&#41;\" title=\"Rendered by QuickLaTeX.com\" height=\"19\" width=\"88\" style=\"vertical-align: -5px;\" \/><\/td>\n<\/tr>\n<tr>\n<td>Simplify.<\/td>\n<td><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<\/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 16.1<\/p>\n<\/header>\n<div class=\"textbox__content\">\n<div id=\"fs-id1170652621556\" data-type=\"problem\">\n<p id=\"fs-id1170652621559\">Translate to an algebraic expression and simplify if possible: the quotient of <img loading=\"lazy\" decoding=\"async\" src=\"https:\/\/opentextbc.ca\/introalgebra\/wp-content\/ql-cache\/quicklatex.com-c081a4d1588de9f9de1dd7d5282b4c9d_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"&#45;&#54;&#51;\" title=\"Rendered by QuickLaTeX.com\" height=\"12\" width=\"31\" style=\"vertical-align: 0px;\" \/> and <img loading=\"lazy\" decoding=\"async\" src=\"https:\/\/opentextbc.ca\/introalgebra\/wp-content\/ql-cache\/quicklatex.com-9672181aec15f8334b80ada7de4e4fc0_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"&#45;&#57;\" title=\"Rendered by QuickLaTeX.com\" height=\"12\" width=\"22\" style=\"vertical-align: 0px;\" \/>.<\/p>\n<\/div>\n<div id=\"fs-id1170653906972\" data-type=\"solution\">\n<details>\n<summary>Show answer<\/summary>\n<p id=\"fs-id1170653906974\"><img loading=\"lazy\" decoding=\"async\" src=\"https:\/\/opentextbc.ca\/introalgebra\/wp-content\/ql-cache\/quicklatex.com-897cdadceea1dbe174270e3f14546138_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"&#45;&#54;&#51;&#92;&#100;&#105;&#118;&#32;&#92;&#108;&#101;&#102;&#116;&#40;&#45;&#57;&#92;&#114;&#105;&#103;&#104;&#116;&#41;&#59;&#55;\" title=\"Rendered by QuickLaTeX.com\" height=\"19\" width=\"108\" style=\"vertical-align: -5px;\" \/><\/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 16.2<\/p>\n<\/header>\n<div class=\"textbox__content\">\n<div id=\"fs-id1170653930632\" data-type=\"problem\">\n<p id=\"fs-id1170652630883\">Translate to an algebraic expression and simplify if possible: the quotient of <img loading=\"lazy\" decoding=\"async\" src=\"https:\/\/opentextbc.ca\/introalgebra\/wp-content\/ql-cache\/quicklatex.com-25756e825613a03f37862f6d7e41bb5b_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"&#45;&#55;&#50;\" title=\"Rendered by QuickLaTeX.com\" height=\"13\" width=\"30\" style=\"vertical-align: 0px;\" \/> and <img loading=\"lazy\" decoding=\"async\" src=\"https:\/\/opentextbc.ca\/introalgebra\/wp-content\/ql-cache\/quicklatex.com-9672181aec15f8334b80ada7de4e4fc0_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"&#45;&#57;\" title=\"Rendered by QuickLaTeX.com\" height=\"12\" width=\"22\" style=\"vertical-align: 0px;\" \/>.<\/p>\n<\/div>\n<div id=\"fs-id1170654164368\" data-type=\"solution\">\n<details>\n<summary>Show answer<\/summary>\n<p id=\"fs-id1170654164370\"><img loading=\"lazy\" decoding=\"async\" src=\"https:\/\/opentextbc.ca\/introalgebra\/wp-content\/ql-cache\/quicklatex.com-beca1204930694a0b1e62e421a3960e1_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"&#45;&#55;&#50;&#92;&#100;&#105;&#118;&#32;&#92;&#108;&#101;&#102;&#116;&#40;&#45;&#57;&#92;&#114;&#105;&#103;&#104;&#116;&#41;&#59;&#56;\" title=\"Rendered by QuickLaTeX.com\" height=\"19\" width=\"108\" style=\"vertical-align: -5px;\" \/><\/p>\n<\/details>\n<\/div>\n<\/div>\n<\/div>\n<\/div>\n<\/div>\n<\/div>\n<h1>Use Integers in Applications<\/h1>\n<p id=\"fs-id1170653875242\">We\u2019ll outline a plan to solve applications. It\u2019s hard to find something if we don\u2019t know what we\u2019re looking for or what to call it! So when we solve an application, we first need to determine what the problem is asking us to find. Then we\u2019ll write a phrase that gives the information to find it. We\u2019ll translate the phrase into an expression and then simplify the expression to get the answer. Finally, we summarize the answer in a sentence to make sure it makes sense.<\/p>\n<div class=\"textbox textbox--examples\">\n<header class=\"textbox__header\">\n<p class=\"textbox__title\">EXAMPLE 17<\/p>\n<\/header>\n<div class=\"textbox__content\">\n<div id=\"fs-id1170653875252\" data-type=\"exercise\">\n<div id=\"fs-id1170653879266\" data-type=\"problem\">\n<p id=\"fs-id1170653879268\">The temperature in Sparwood, British Columbia, one morning was 11 degrees. By mid-afternoon, the temperature had dropped to <img loading=\"lazy\" decoding=\"async\" src=\"https:\/\/opentextbc.ca\/introalgebra\/wp-content\/ql-cache\/quicklatex.com-9672181aec15f8334b80ada7de4e4fc0_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"&#45;&#57;\" title=\"Rendered by QuickLaTeX.com\" height=\"12\" width=\"22\" style=\"vertical-align: 0px;\" \/> degrees. What was the difference of the morning and afternoon temperatures?<\/p>\n<\/div>\n<div id=\"fs-id1170653879279\" 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><span id=\"fs-id1170653797914\" data-type=\"media\" data-alt=\"This is a table with two columns. The left column includes steps to solve the problem. The right column includes the math to solve the problem. In the first row, the left column says \u201cStep 1. Read the problem. Make sure all the words and ideas are understood.\u201d The right column is blank.\"><img decoding=\"async\" src=\"https:\/\/opentextbc.ca\/accessibilitytoolkit\/wp-content\/uploads\/sites\/333\/2021\/03\/CNX_ElemAlg_Figure_01_04_009a_new.jpg\" alt=\"This is a table with two columns. The left column includes steps to solve the problem. The right column includes the math to solve the problem. In the first row, the left column says \u201cStep 1. Read the problem. Make sure all the words and ideas are understood.\u201d The right column is blank.\" data-media-type=\"image\/jpeg\" \/><\/span><span id=\"fs-id1170653907530\" data-type=\"media\" data-alt=\"In the second row, the left column says \u201cStep 2. Identify what we are asked to find\u201d. The right column says, \u201cthe difference of the morning and afternoon temperatures.\u201d\"><img decoding=\"async\" src=\"https:\/\/opentextbc.ca\/accessibilitytoolkit\/wp-content\/uploads\/sites\/333\/2021\/03\/CNX_ElemAlg_Figure_01_04_009b_new.jpg\" alt=\"In the second row, the left column says \u201cStep 2. Identify what we are asked to find\u201d. The right column says, \u201cthe difference of the morning and afternoon temperatures.\u201d\" data-media-type=\"image\/jpeg\" \/><\/span><span id=\"fs-id1170654231700\" data-type=\"media\" data-alt=\"In the third row, the left column says, \u201cStep 3. Write a phrase that gives the information to find it.\u201d Next to this in the right column, it says \u201cthe difference of 11 and negative 9.\u201d\"><img decoding=\"async\" src=\"https:\/\/opentextbc.ca\/accessibilitytoolkit\/wp-content\/uploads\/sites\/333\/2021\/03\/CNX_ElemAlg_Figure_01_04_009c_new.jpg\" alt=\"In the third row, the left column says, \u201cStep 3. Write a phrase that gives the information to find it.\u201d Next to this in the right column, it says \u201cthe difference of 11 and negative 9.\u201d\" data-media-type=\"image\/jpeg\" \/><\/span><span id=\"fs-id1170652751567\" data-type=\"media\" data-alt=\"In the fourth row, the left column says, \u201cStep 4. Translate the phrase to an expression.\u201d The right column contains 11 minus negative 9.\"><img decoding=\"async\" src=\"https:\/\/opentextbc.ca\/accessibilitytoolkit\/wp-content\/uploads\/sites\/333\/2021\/03\/CNX_ElemAlg_Figure_01_04_009d_new.jpg\" alt=\"In the fourth row, the left column says, \u201cStep 4. Translate the phrase to an expression.\u201d The right column contains 11 minus negative 9.\" data-media-type=\"image\/jpeg\" \/><\/span><span id=\"fs-id1170653837169\" data-type=\"media\" data-alt=\"In the fifth row, the left column says, \u201cStep 5. Simplify the expression.\u201d The right column contains 20.\"><img decoding=\"async\" src=\"https:\/\/opentextbc.ca\/accessibilitytoolkit\/wp-content\/uploads\/sites\/333\/2021\/03\/CNX_ElemAlg_Figure_01_04_009e_new.jpg\" alt=\"In the fifth row, the left column says, \u201cStep 5. Simplify the expression.\u201d The right column contains 20.\" data-media-type=\"image\/jpeg\" \/><\/span><span id=\"fs-id1171792706468\" data-type=\"media\" data-alt=\"The final row says, \u201cStep five. Write a complete sentence that answers the question.\u201d Next to this in the right column, it says \u201cthe difference in temperatures was 20 degrees.\u201d\"><img decoding=\"async\" src=\"https:\/\/opentextbc.ca\/accessibilitytoolkit\/wp-content\/uploads\/sites\/333\/2021\/03\/CNX_ElemAlg_Figure_01_04_009f_new.jpg\" alt=\"The final row says, \u201cStep five. Write a complete sentence that answers the question.\u201d Next to this in the right column, it says \u201cthe difference in temperatures was 20 degrees.\u201d\" data-media-type=\"image\/jpeg\" \/><\/span><\/p>\n<\/div>\n<\/div>\n<\/div>\n<\/div>\n<div class=\"textbox textbox--exercises\">\n<header class=\"textbox__header\">\n<p class=\"textbox__title\">TRY IT 17.1<\/p>\n<\/header>\n<div class=\"textbox__content\">\n<div id=\"fs-id1170652630563\" data-type=\"problem\">\n<p id=\"fs-id1170652630565\">The temperature in Whitehorse, Yukon, one morning was 15 degrees. By mid-afternoon the temperature had dropped to 30 degrees below zero. What was the difference in the morning and afternoon temperatures?<\/p>\n<\/div>\n<div id=\"fs-id1170652630571\" data-type=\"solution\">\n<details>\n<summary>Show answer<\/summary>\n<p id=\"fs-id1170652630574\">The difference in temperatures was 45 degrees.<\/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 17.2<\/p>\n<\/header>\n<div class=\"textbox__content\">\n<div id=\"fs-id1170654202594\" data-type=\"problem\">\n<p id=\"fs-id1170654202596\">The temperature in Quesnel, BC, was <img loading=\"lazy\" decoding=\"async\" src=\"https:\/\/opentextbc.ca\/introalgebra\/wp-content\/ql-cache\/quicklatex.com-4797c874a138ca175d7c2cd8b3ed9a98_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"&#45;&#54;\" title=\"Rendered by QuickLaTeX.com\" height=\"12\" width=\"22\" style=\"vertical-align: 0px;\" \/> degrees at lunchtime. By sunset the temperature had dropped to <img loading=\"lazy\" decoding=\"async\" src=\"https:\/\/opentextbc.ca\/introalgebra\/wp-content\/ql-cache\/quicklatex.com-0329d19b932005c996d83dbb9e09ffed_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"&#45;&#49;&#53;\" title=\"Rendered by QuickLaTeX.com\" height=\"14\" width=\"30\" style=\"vertical-align: -1px;\" \/> degrees. What was the difference in the lunchtime and sunset temperatures?<\/p>\n<\/div>\n<div id=\"fs-id1170654209698\" data-type=\"solution\">\n<details>\n<summary>Show answer<\/summary>\n<p id=\"fs-id1170654209700\">The difference in temperatures was 9 degrees.<\/p>\n<\/details>\n<\/div>\n<\/div>\n<\/div>\n<div class=\"textbox textbox--key-takeaways\">\n<header class=\"textbox__header\">\n<p class=\"textbox__title\">HOW TO: Apply a Strategy to Solve Applications with Integers<\/p>\n<\/header>\n<div class=\"textbox__content\">\n<ol id=\"fs-id1166426171804\" class=\"stepwise\" type=\"1\">\n<li>Read the problem. Make sure all the words and ideas are understood<\/li>\n<li>Identify what we are asked to find.<\/li>\n<li>Write a phrase that gives the information to find it.<\/li>\n<li>Translate the phrase to an expression.<\/li>\n<li>Simplify the expression.<\/li>\n<li>Answer the question with a complete sentence.<\/li>\n<\/ol>\n<\/div>\n<\/div>\n<div id=\"fs-id1170654209706\" class=\"howto\" data-type=\"note\">\n<div class=\"textbox textbox--examples\">\n<header class=\"textbox__header\">\n<p class=\"textbox__title\">EXAMPLE 18<\/p>\n<\/header>\n<div class=\"textbox__content\">\n<div id=\"fs-id1170652620547\" data-type=\"problem\">\n<p id=\"fs-id1170654154716\">The Mustangs football team received three penalties in the third quarter. Each penalty gave them a loss of fifteen yards. What is the number of yards lost?<\/p>\n<\/div>\n<div id=\"fs-id1170654154722\" data-type=\"solution\">\n<div data-type=\"title\"><\/div>\n<div data-type=\"title\"><strong>Solution<\/strong><\/div>\n<table id=\"eip-436\" summary=\".\">\n<tbody>\n<tr>\n<td><strong>Step 1.<\/strong> Read the problem. Make sure all the words and ideas are understood.<\/td>\n<td><\/td>\n<\/tr>\n<tr>\n<td><strong>Step 2.<\/strong> Identify what we are asked to find.<\/td>\n<td>the number of yards lost<\/td>\n<\/tr>\n<tr>\n<td><strong>Step 3.<\/strong> Write a phrase that gives the information to find it.<\/td>\n<td>three times a 15-yard penalty<\/td>\n<\/tr>\n<tr>\n<td><strong>Step 4.<\/strong> Translate the phrase to an expression.<\/td>\n<td><img loading=\"lazy\" decoding=\"async\" src=\"https:\/\/opentextbc.ca\/introalgebra\/wp-content\/ql-cache\/quicklatex.com-2cd4178f8b6ebed821e3212e1390689c_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"&#51;&#92;&#108;&#101;&#102;&#116;&#40;&#45;&#49;&#53;&#92;&#114;&#105;&#103;&#104;&#116;&#41;\" title=\"Rendered by QuickLaTeX.com\" height=\"18\" width=\"57\" style=\"vertical-align: -4px;\" \/><\/td>\n<\/tr>\n<tr>\n<td><strong>Step 5.<\/strong> Simplify the expression.<\/td>\n<td><img loading=\"lazy\" decoding=\"async\" src=\"https:\/\/opentextbc.ca\/introalgebra\/wp-content\/ql-cache\/quicklatex.com-5efc88a25eac99bdddb5f279a9640b88_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"&#45;&#52;&#53;\" title=\"Rendered by QuickLaTeX.com\" height=\"14\" width=\"30\" style=\"vertical-align: -1px;\" \/><\/td>\n<\/tr>\n<tr>\n<td><strong>Step 6.<\/strong> Answer the question with a complete sentence.<\/td>\n<td>The team lost 45 yards.<\/td>\n<\/tr>\n<\/tbody>\n<\/table>\n<\/div>\n<\/div>\n<\/div>\n<\/div>\n<div id=\"fs-id1170654185951\" class=\"try\" data-type=\"note\">\n<div id=\"fs-id1170653874319\" data-type=\"exercise\">\n<div id=\"fs-id1170653874322\" data-type=\"problem\">\n<div class=\"textbox textbox--exercises\">\n<header class=\"textbox__header\">\n<p class=\"textbox__title\">TRY IT 18.1<\/p>\n<\/header>\n<div class=\"textbox__content\">\n<div id=\"fs-id1170653874322\" data-type=\"problem\">\n<p id=\"fs-id1170653874324\">The Bears played poorly and had seven penalties in the game. Each penalty resulted in a loss of 15 yards. What is the number of yards lost due to penalties?<\/p>\n<\/div>\n<div id=\"fs-id1170653874329\" data-type=\"solution\">\n<details>\n<summary>Show answer<\/summary>\n<p id=\"fs-id1170653874332\">The Bears lost 105 yards.<\/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 18.2<\/p>\n<\/header>\n<div class=\"textbox__content\">\n<div id=\"fs-id1170653874667\" data-type=\"problem\">\n<p id=\"fs-id1170653874669\">Bill uses the ATM on campus because it is convenient. However, each time he uses it he is charged a &#36;2 fee. Last month he used the ATM eight times. How much was his total fee for using the ATM?<\/p>\n<\/div>\n<div id=\"fs-id1170653874675\" data-type=\"solution\">\n<details>\n<summary>Show answer<\/summary>\n<p id=\"fs-id1170654239353\">A &#36;16 fee was deducted from his checking account.<\/p>\n<\/details>\n<\/div>\n<\/div>\n<\/div>\n<\/div>\n<\/div>\n<\/div>\n<h1>Key Concepts<\/h1>\n<ul id=\"fs-id1170654239367\" data-bullet-style=\"bullet\">\n<li><strong data-effect=\"bold\">Multiplication and Division of Two Signed Numbers<\/strong>\n<ul id=\"fs-id1170653881237\" data-bullet-style=\"open-circle\">\n<li>Same signs\u2014Product is positive<\/li>\n<li>Different signs\u2014Product is negative<\/li>\n<\/ul>\n<\/li>\n<li><strong data-effect=\"bold\">Strategy for Applications<\/strong>\n<ol id=\"fs-id1170652621952\" class=\"stepwise\" type=\"1\">\n<li>Identify what you are asked to find.<\/li>\n<li>Write a phrase that gives the information to find it.<\/li>\n<li>Translate the phrase to an expression.<\/li>\n<li>Simplify the expression.<\/li>\n<li>Answer the question with a complete sentence.<\/li>\n<\/ol>\n<\/li>\n<\/ul>\n<h1>Practice Makes Perfect<\/h1>\n<h2>Multiply Integers<\/h2>\n<p id=\"fs-id1166421558397\">In the following exercises, multiply.<\/p>\n<table style=\"border-collapse: collapse; width: 100%;\">\n<tbody>\n<tr>\n<td style=\"width: 50%;\">1. <img loading=\"lazy\" decoding=\"async\" src=\"https:\/\/opentextbc.ca\/introalgebra\/wp-content\/ql-cache\/quicklatex.com-6c35d4f5986bc5f7c4127a38b882fe2d_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"&#45;&#52;&#92;&#99;&#100;&#111;&#116;&#56;\" title=\"Rendered by QuickLaTeX.com\" height=\"12\" width=\"43\" style=\"vertical-align: 0px;\" \/><\/td>\n<td style=\"width: 50%;\">2. <img loading=\"lazy\" decoding=\"async\" src=\"https:\/\/opentextbc.ca\/introalgebra\/wp-content\/ql-cache\/quicklatex.com-b901bcb2b169813b18844d5310d540a3_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"&#45;&#51;&#92;&#99;&#100;&#111;&#116;&#57;\" title=\"Rendered by QuickLaTeX.com\" height=\"12\" width=\"43\" style=\"vertical-align: 0px;\" \/><\/td>\n<\/tr>\n<tr>\n<td style=\"width: 50%;\">3. <img loading=\"lazy\" decoding=\"async\" src=\"https:\/\/opentextbc.ca\/introalgebra\/wp-content\/ql-cache\/quicklatex.com-b361129d452a3d90c0bec2bb004052be_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"&#57;&#92;&#108;&#101;&#102;&#116;&#40;&#45;&#55;&#92;&#114;&#105;&#103;&#104;&#116;&#41;\" title=\"Rendered by QuickLaTeX.com\" height=\"18\" width=\"48\" style=\"vertical-align: -4px;\" \/><\/td>\n<td style=\"width: 50%;\">4. <img loading=\"lazy\" decoding=\"async\" src=\"https:\/\/opentextbc.ca\/introalgebra\/wp-content\/ql-cache\/quicklatex.com-e26d28a6d9c5af3feb6f409cca797f2d_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"&#49;&#51;&#92;&#108;&#101;&#102;&#116;&#40;&#45;&#53;&#92;&#114;&#105;&#103;&#104;&#116;&#41;\" title=\"Rendered by QuickLaTeX.com\" height=\"18\" width=\"56\" style=\"vertical-align: -4px;\" \/><\/td>\n<\/tr>\n<tr>\n<td style=\"width: 50%;\">5. <img loading=\"lazy\" decoding=\"async\" src=\"https:\/\/opentextbc.ca\/introalgebra\/wp-content\/ql-cache\/quicklatex.com-02d9f5a32b08eb8d149cd6577bcb3d70_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"&#45;&#49;&#92;&#99;&#100;&#111;&#116;&#54;\" title=\"Rendered by QuickLaTeX.com\" height=\"12\" width=\"43\" style=\"vertical-align: 0px;\" \/><\/td>\n<td style=\"width: 50%;\">6. <img loading=\"lazy\" decoding=\"async\" src=\"https:\/\/opentextbc.ca\/introalgebra\/wp-content\/ql-cache\/quicklatex.com-1e5670bdd5d0976864c04f38e0468037_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"&#45;&#49;&#92;&#99;&#100;&#111;&#116;&#51;\" title=\"Rendered by QuickLaTeX.com\" height=\"12\" width=\"43\" style=\"vertical-align: 0px;\" \/><\/td>\n<\/tr>\n<tr>\n<td style=\"width: 50%;\">7. <img loading=\"lazy\" decoding=\"async\" src=\"https:\/\/opentextbc.ca\/introalgebra\/wp-content\/ql-cache\/quicklatex.com-7d398b90f253a04cd8d61419909697cd_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"&#45;&#49;&#92;&#108;&#101;&#102;&#116;&#40;&#45;&#49;&#52;&#92;&#114;&#105;&#103;&#104;&#116;&#41;\" title=\"Rendered by QuickLaTeX.com\" height=\"18\" width=\"70\" style=\"vertical-align: -4px;\" \/><\/td>\n<td style=\"width: 50%;\">8. <img loading=\"lazy\" decoding=\"async\" src=\"https:\/\/opentextbc.ca\/introalgebra\/wp-content\/ql-cache\/quicklatex.com-af4d3e14c40317fc6cb99953de35ec8f_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"&#45;&#49;&#92;&#108;&#101;&#102;&#116;&#40;&#45;&#49;&#57;&#92;&#114;&#105;&#103;&#104;&#116;&#41;\" title=\"Rendered by QuickLaTeX.com\" height=\"18\" width=\"70\" style=\"vertical-align: -4px;\" \/><\/td>\n<\/tr>\n<\/tbody>\n<\/table>\n<h2>Divide Integers<\/h2>\n<p id=\"fs-id1166421949046\">In the following exercises, divide.<\/p>\n<table style=\"border-collapse: collapse; width: 100%; height: 75px;\">\n<tbody>\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-5bf127a98d89e04d3ddc7f28746db24e_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"&#45;&#50;&#52;&#92;&#100;&#105;&#118;&#54;\" title=\"Rendered by QuickLaTeX.com\" height=\"13\" width=\"61\" style=\"vertical-align: -1px;\" \/><\/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-5011828a400115eb798b62fec482f388_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"&#51;&#53;&#92;&#100;&#105;&#118;&#92;&#108;&#101;&#102;&#116;&#40;&#45;&#55;&#92;&#114;&#105;&#103;&#104;&#116;&#41;\" title=\"Rendered by QuickLaTeX.com\" height=\"19\" width=\"75\" style=\"vertical-align: -5px;\" \/><\/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-633a865ee9b7d2b894c6b3e808aa8369_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"&#45;&#53;&#50;&#92;&#100;&#105;&#118;&#92;&#108;&#101;&#102;&#116;&#40;&#45;&#52;&#92;&#114;&#105;&#103;&#104;&#116;&#41;\" title=\"Rendered by QuickLaTeX.com\" height=\"19\" width=\"88\" style=\"vertical-align: -5px;\" \/><\/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-501013f7b77bff54cb04598212791c9c_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"&#45;&#56;&#52;&#92;&#100;&#105;&#118;&#92;&#108;&#101;&#102;&#116;&#40;&#45;&#54;&#92;&#114;&#105;&#103;&#104;&#116;&#41;\" title=\"Rendered by QuickLaTeX.com\" height=\"19\" width=\"88\" style=\"vertical-align: -5px;\" \/><\/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-cba9138f78ae5ea833c8990a4b3ac841_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"&#45;&#49;&#56;&#48;&#92;&#100;&#105;&#118;&#49;&#53;\" title=\"Rendered by QuickLaTeX.com\" height=\"14\" width=\"78\" style=\"vertical-align: -1px;\" \/><\/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-ffe152010c6f96d7c5ebe43cbc75046e_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"&#45;&#49;&#57;&#50;&#92;&#100;&#105;&#118;&#49;&#50;\" title=\"Rendered by QuickLaTeX.com\" height=\"13\" width=\"78\" style=\"vertical-align: -1px;\" \/><\/td>\n<\/tr>\n<\/tbody>\n<\/table>\n<h2>Simplify Expressions with Integers<\/h2>\n<p id=\"fs-id1166421486016\">In the following exercises, simplify each expression.<\/p>\n<table style=\"border-collapse: collapse; width: 100%;\">\n<tbody>\n<tr>\n<td style=\"width: 50%;\">15. <img loading=\"lazy\" decoding=\"async\" src=\"https:\/\/opentextbc.ca\/introalgebra\/wp-content\/ql-cache\/quicklatex.com-85f0f85521a080391f767cabf8d51180_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"&#53;&#92;&#108;&#101;&#102;&#116;&#40;&#45;&#54;&#92;&#114;&#105;&#103;&#104;&#116;&#41;&#43;&#55;&#92;&#108;&#101;&#102;&#116;&#40;&#45;&#50;&#92;&#114;&#105;&#103;&#104;&#116;&#41;&#45;&#51;\" title=\"Rendered by QuickLaTeX.com\" height=\"18\" width=\"149\" style=\"vertical-align: -4px;\" \/><\/td>\n<td style=\"width: 50%;\">16. <img loading=\"lazy\" decoding=\"async\" src=\"https:\/\/opentextbc.ca\/introalgebra\/wp-content\/ql-cache\/quicklatex.com-42d324e2b5ce01d2839a7dd66ec820c0_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"&#56;&#92;&#108;&#101;&#102;&#116;&#40;&#45;&#52;&#92;&#114;&#105;&#103;&#104;&#116;&#41;&#43;&#53;&#92;&#108;&#101;&#102;&#116;&#40;&#45;&#52;&#92;&#114;&#105;&#103;&#104;&#116;&#41;&#45;&#54;\" title=\"Rendered by QuickLaTeX.com\" height=\"18\" width=\"149\" style=\"vertical-align: -4px;\" \/><\/td>\n<\/tr>\n<tr>\n<td style=\"width: 50%;\">17. <img loading=\"lazy\" decoding=\"async\" src=\"https:\/\/opentextbc.ca\/introalgebra\/wp-content\/ql-cache\/quicklatex.com-c3d91d19a200676911902f50f3ee4e43_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"&#123;&#92;&#108;&#101;&#102;&#116;&#40;&#45;&#50;&#92;&#114;&#105;&#103;&#104;&#116;&#41;&#125;&#94;&#123;&#54;&#125;\" title=\"Rendered by QuickLaTeX.com\" height=\"21\" width=\"42\" style=\"vertical-align: -4px;\" \/><\/td>\n<td style=\"width: 50%;\">18. <img loading=\"lazy\" decoding=\"async\" src=\"https:\/\/opentextbc.ca\/introalgebra\/wp-content\/ql-cache\/quicklatex.com-0e00bf55759c5b8bf6723f02ba00afdc_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"&#123;&#92;&#108;&#101;&#102;&#116;&#40;&#45;&#51;&#92;&#114;&#105;&#103;&#104;&#116;&#41;&#125;&#94;&#123;&#53;&#125;\" title=\"Rendered by QuickLaTeX.com\" height=\"21\" width=\"42\" style=\"vertical-align: -4px;\" \/><\/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-6a686631829c9f458dd8dc32b0614e8a_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"&#92;&#116;&#101;&#120;&#116;&#123;&#45;&#125;&#123;&#52;&#125;&#94;&#123;&#50;&#125;\" title=\"Rendered by QuickLaTeX.com\" height=\"15\" width=\"22\" style=\"vertical-align: 0px;\" \/><\/td>\n<td style=\"width: 50%;\">20. <img loading=\"lazy\" decoding=\"async\" src=\"https:\/\/opentextbc.ca\/introalgebra\/wp-content\/ql-cache\/quicklatex.com-b5fa0b7d2e5b888e1613f38515d3244a_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"&#92;&#116;&#101;&#120;&#116;&#123;&#45;&#125;&#123;&#54;&#125;&#94;&#123;&#50;&#125;\" title=\"Rendered by QuickLaTeX.com\" height=\"15\" width=\"22\" style=\"vertical-align: 0px;\" \/><\/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-aa75b0df6dbc1e81f7fd2a16258eb2f5_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"&#45;&#51;&#92;&#108;&#101;&#102;&#116;&#40;&#45;&#53;&#92;&#114;&#105;&#103;&#104;&#116;&#41;&#92;&#108;&#101;&#102;&#116;&#40;&#54;&#92;&#114;&#105;&#103;&#104;&#116;&#41;\" title=\"Rendered by QuickLaTeX.com\" height=\"18\" width=\"86\" 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-92ee7e0dfb4eff0145c51b2c590533bf_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"&#45;&#52;&#92;&#108;&#101;&#102;&#116;&#40;&#45;&#54;&#92;&#114;&#105;&#103;&#104;&#116;&#41;&#92;&#108;&#101;&#102;&#116;&#40;&#51;&#92;&#114;&#105;&#103;&#104;&#116;&#41;\" title=\"Rendered by QuickLaTeX.com\" height=\"18\" width=\"86\" style=\"vertical-align: -4px;\" \/><\/td>\n<\/tr>\n<tr>\n<td style=\"width: 50%;\">23. <img loading=\"lazy\" decoding=\"async\" src=\"https:\/\/opentextbc.ca\/introalgebra\/wp-content\/ql-cache\/quicklatex.com-e0394b023c4f67d69d7a99987647f7f5_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"&#92;&#108;&#101;&#102;&#116;&#40;&#56;&#45;&#49;&#49;&#92;&#114;&#105;&#103;&#104;&#116;&#41;&#92;&#108;&#101;&#102;&#116;&#40;&#57;&#45;&#49;&#50;&#92;&#114;&#105;&#103;&#104;&#116;&#41;\" title=\"Rendered by QuickLaTeX.com\" height=\"18\" width=\"125\" style=\"vertical-align: -4px;\" \/><\/td>\n<td style=\"width: 50%;\">24. <img loading=\"lazy\" decoding=\"async\" src=\"https:\/\/opentextbc.ca\/introalgebra\/wp-content\/ql-cache\/quicklatex.com-b74138c11841b38808f35613eea0d9c1_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"&#92;&#108;&#101;&#102;&#116;&#40;&#54;&#45;&#49;&#49;&#92;&#114;&#105;&#103;&#104;&#116;&#41;&#92;&#108;&#101;&#102;&#116;&#40;&#56;&#45;&#49;&#51;&#92;&#114;&#105;&#103;&#104;&#116;&#41;\" title=\"Rendered by QuickLaTeX.com\" height=\"18\" width=\"125\" style=\"vertical-align: -4px;\" \/><\/td>\n<\/tr>\n<tr>\n<td style=\"width: 50%;\">25. <img loading=\"lazy\" decoding=\"async\" src=\"https:\/\/opentextbc.ca\/introalgebra\/wp-content\/ql-cache\/quicklatex.com-653f4ea6625efc3317803561a1dcf962_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"&#50;&#54;&#45;&#51;&#92;&#108;&#101;&#102;&#116;&#40;&#50;&#45;&#55;&#92;&#114;&#105;&#103;&#104;&#116;&#41;\" title=\"Rendered by QuickLaTeX.com\" height=\"18\" width=\"104\" style=\"vertical-align: -4px;\" \/><\/td>\n<td style=\"width: 50%;\">26. <img loading=\"lazy\" decoding=\"async\" src=\"https:\/\/opentextbc.ca\/introalgebra\/wp-content\/ql-cache\/quicklatex.com-de8aa2f9c3c0b7b1426fbf05a26db1ed_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"&#50;&#51;&#45;&#50;&#92;&#108;&#101;&#102;&#116;&#40;&#52;&#45;&#54;&#92;&#114;&#105;&#103;&#104;&#116;&#41;\" title=\"Rendered by QuickLaTeX.com\" height=\"18\" width=\"104\" style=\"vertical-align: -4px;\" \/><\/td>\n<\/tr>\n<tr>\n<td style=\"width: 50%;\">27. <img loading=\"lazy\" decoding=\"async\" src=\"https:\/\/opentextbc.ca\/introalgebra\/wp-content\/ql-cache\/quicklatex.com-0b6d57327d04caa90d36199cca298b0e_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"&#54;&#53;&#92;&#100;&#105;&#118;&#92;&#108;&#101;&#102;&#116;&#40;&#45;&#53;&#92;&#114;&#105;&#103;&#104;&#116;&#41;&#43;&#92;&#108;&#101;&#102;&#116;&#40;&#45;&#50;&#56;&#92;&#114;&#105;&#103;&#104;&#116;&#41;&#92;&#100;&#105;&#118;&#92;&#108;&#101;&#102;&#116;&#40;&#45;&#55;&#92;&#114;&#105;&#103;&#104;&#116;&#41;\" title=\"Rendered by QuickLaTeX.com\" height=\"19\" width=\"200\" style=\"vertical-align: -5px;\" \/><\/td>\n<td style=\"width: 50%;\">28. <img loading=\"lazy\" decoding=\"async\" src=\"https:\/\/opentextbc.ca\/introalgebra\/wp-content\/ql-cache\/quicklatex.com-da4602be87ee760ed18e37b438f08311_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"&#53;&#50;&#92;&#100;&#105;&#118;&#92;&#108;&#101;&#102;&#116;&#40;&#45;&#52;&#92;&#114;&#105;&#103;&#104;&#116;&#41;&#43;&#92;&#108;&#101;&#102;&#116;&#40;&#45;&#51;&#50;&#92;&#114;&#105;&#103;&#104;&#116;&#41;&#92;&#100;&#105;&#118;&#92;&#108;&#101;&#102;&#116;&#40;&#45;&#56;&#92;&#114;&#105;&#103;&#104;&#116;&#41;\" title=\"Rendered by QuickLaTeX.com\" height=\"19\" width=\"200\" style=\"vertical-align: -5px;\" \/><\/td>\n<\/tr>\n<tr>\n<td style=\"width: 50%;\">29. <img loading=\"lazy\" decoding=\"async\" src=\"https:\/\/opentextbc.ca\/introalgebra\/wp-content\/ql-cache\/quicklatex.com-d53067a8da43befde6f153cea9ad046d_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"&#57;&#45;&#50;&#92;&#108;&#101;&#102;&#116;&#91;&#51;&#45;&#56;&#92;&#108;&#101;&#102;&#116;&#40;&#45;&#50;&#92;&#114;&#105;&#103;&#104;&#116;&#41;&#92;&#114;&#105;&#103;&#104;&#116;&#93;\" title=\"Rendered by QuickLaTeX.com\" height=\"19\" width=\"129\" style=\"vertical-align: -5px;\" \/><\/td>\n<td style=\"width: 50%;\">30. <img loading=\"lazy\" decoding=\"async\" src=\"https:\/\/opentextbc.ca\/introalgebra\/wp-content\/ql-cache\/quicklatex.com-736f06f6d3a1259461be721afeff8c7a_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"&#49;&#49;&#45;&#51;&#92;&#108;&#101;&#102;&#116;&#91;&#55;&#45;&#52;&#92;&#108;&#101;&#102;&#116;&#40;&#45;&#50;&#92;&#114;&#105;&#103;&#104;&#116;&#41;&#92;&#114;&#105;&#103;&#104;&#116;&#93;\" title=\"Rendered by QuickLaTeX.com\" height=\"19\" width=\"137\" style=\"vertical-align: -5px;\" \/><\/td>\n<\/tr>\n<tr>\n<td style=\"width: 50%;\">31. <img loading=\"lazy\" decoding=\"async\" src=\"https:\/\/opentextbc.ca\/introalgebra\/wp-content\/ql-cache\/quicklatex.com-6548c84526f3f5182cb18e9dbea8ff39_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"&#123;&#92;&#108;&#101;&#102;&#116;&#40;&#45;&#51;&#92;&#114;&#105;&#103;&#104;&#116;&#41;&#125;&#94;&#123;&#50;&#125;&#45;&#50;&#52;&#92;&#100;&#105;&#118;&#92;&#108;&#101;&#102;&#116;&#40;&#56;&#45;&#50;&#92;&#114;&#105;&#103;&#104;&#116;&#41;\" title=\"Rendered by QuickLaTeX.com\" height=\"22\" width=\"157\" style=\"vertical-align: -5px;\" \/><\/td>\n<td style=\"width: 50%;\">32. <img loading=\"lazy\" decoding=\"async\" src=\"https:\/\/opentextbc.ca\/introalgebra\/wp-content\/ql-cache\/quicklatex.com-23c207e903f173c6f0bdb98ffb1c1ed8_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"&#123;&#92;&#108;&#101;&#102;&#116;&#40;&#45;&#52;&#92;&#114;&#105;&#103;&#104;&#116;&#41;&#125;&#94;&#123;&#50;&#125;&#45;&#51;&#50;&#92;&#100;&#105;&#118;&#92;&#108;&#101;&#102;&#116;&#40;&#49;&#50;&#45;&#52;&#92;&#114;&#105;&#103;&#104;&#116;&#41;\" title=\"Rendered by QuickLaTeX.com\" height=\"22\" width=\"165\" style=\"vertical-align: -5px;\" \/><\/td>\n<\/tr>\n<\/tbody>\n<\/table>\n<h2>Evaluate Variable Expressions with Integers<\/h2>\n<p id=\"fs-id1166426233230\">In the following exercises, evaluate each expression.<\/p>\n<table style=\"border-collapse: collapse; width: 100%;\">\n<tbody>\n<tr>\n<td style=\"width: 50%;\">33. <img loading=\"lazy\" decoding=\"async\" src=\"https:\/\/opentextbc.ca\/introalgebra\/wp-content\/ql-cache\/quicklatex.com-1d68be4b037a45e488d7b547084f3bd6_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"&#121;&#43;&#92;&#108;&#101;&#102;&#116;&#40;&#45;&#49;&#52;&#92;&#114;&#105;&#103;&#104;&#116;&#41;\" title=\"Rendered by QuickLaTeX.com\" height=\"18\" width=\"76\" style=\"vertical-align: -4px;\" \/> when<br \/>\na) <img loading=\"lazy\" decoding=\"async\" src=\"https:\/\/opentextbc.ca\/introalgebra\/wp-content\/ql-cache\/quicklatex.com-72122a4c8ec17c289eec6cc0fba169c8_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"&#121;&#61;&#45;&#51;&#51;\" title=\"Rendered by QuickLaTeX.com\" height=\"16\" width=\"65\" style=\"vertical-align: -4px;\" \/><br \/>\nb) <img loading=\"lazy\" decoding=\"async\" src=\"https:\/\/opentextbc.ca\/introalgebra\/wp-content\/ql-cache\/quicklatex.com-02d2d43e4042eb1d7c4946f1691acc28_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"&#121;&#61;&#51;&#48;\" title=\"Rendered by QuickLaTeX.com\" height=\"16\" width=\"51\" style=\"vertical-align: -4px;\" \/><\/td>\n<td style=\"width: 50%;\">34. <img loading=\"lazy\" decoding=\"async\" src=\"https:\/\/opentextbc.ca\/introalgebra\/wp-content\/ql-cache\/quicklatex.com-0d2604c0dc262cf6cd9bc6e0cd7644f4_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"&#120;&#43;&#92;&#108;&#101;&#102;&#116;&#40;&#45;&#50;&#49;&#92;&#114;&#105;&#103;&#104;&#116;&#41;\" title=\"Rendered by QuickLaTeX.com\" height=\"18\" width=\"77\" style=\"vertical-align: -4px;\" \/> when<br \/>\na) <img loading=\"lazy\" decoding=\"async\" src=\"https:\/\/opentextbc.ca\/introalgebra\/wp-content\/ql-cache\/quicklatex.com-d50b89d15ab8c25c12da93a6cef1268b_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"&#120;&#61;&#45;&#50;&#55;\" title=\"Rendered by QuickLaTeX.com\" height=\"13\" width=\"66\" style=\"vertical-align: 0px;\" \/><br \/>\nb) <img loading=\"lazy\" decoding=\"async\" src=\"https:\/\/opentextbc.ca\/introalgebra\/wp-content\/ql-cache\/quicklatex.com-8a0c2fd9a040adbffa2b489ee1ed09ca_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"&#120;&#61;&#52;&#52;\" title=\"Rendered by QuickLaTeX.com\" height=\"13\" width=\"52\" style=\"vertical-align: -1px;\" \/><\/td>\n<\/tr>\n<tr>\n<td style=\"width: 50%;\">35.<br \/>\na)<img loading=\"lazy\" decoding=\"async\" src=\"https:\/\/opentextbc.ca\/introalgebra\/wp-content\/ql-cache\/quicklatex.com-103ba5181780b8a6b8fdfcdeb9975164_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"&#97;&#43;&#51;\" title=\"Rendered by QuickLaTeX.com\" height=\"14\" width=\"40\" style=\"vertical-align: -2px;\" \/> when <img loading=\"lazy\" decoding=\"async\" src=\"https:\/\/opentextbc.ca\/introalgebra\/wp-content\/ql-cache\/quicklatex.com-5290584148395560feb2acb793cee254_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"&#97;&#61;&#45;&#55;\" title=\"Rendered by QuickLaTeX.com\" height=\"13\" width=\"56\" style=\"vertical-align: 0px;\" \/><br \/>\nb) <img loading=\"lazy\" decoding=\"async\" src=\"https:\/\/opentextbc.ca\/introalgebra\/wp-content\/ql-cache\/quicklatex.com-9f137b7089f925b3777573e7a3ecc8b4_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"&#92;&#116;&#101;&#120;&#116;&#123;&#45;&#125;&#97;&#43;&#51;\" title=\"Rendered by QuickLaTeX.com\" height=\"14\" width=\"46\" style=\"vertical-align: -2px;\" \/> when <img loading=\"lazy\" decoding=\"async\" src=\"https:\/\/opentextbc.ca\/introalgebra\/wp-content\/ql-cache\/quicklatex.com-5290584148395560feb2acb793cee254_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"&#97;&#61;&#45;&#55;\" title=\"Rendered by QuickLaTeX.com\" height=\"13\" width=\"56\" style=\"vertical-align: 0px;\" \/><\/td>\n<td style=\"width: 50%;\">36.<br \/>\na)<img loading=\"lazy\" decoding=\"async\" src=\"https:\/\/opentextbc.ca\/introalgebra\/wp-content\/ql-cache\/quicklatex.com-7a30dd3bc0372c61edd9e81844822285_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"&#100;&#43;&#92;&#108;&#101;&#102;&#116;&#40;&#45;&#57;&#92;&#114;&#105;&#103;&#104;&#116;&#41;\" title=\"Rendered by QuickLaTeX.com\" height=\"18\" width=\"67\" style=\"vertical-align: -4px;\" \/> when <img loading=\"lazy\" decoding=\"async\" src=\"https:\/\/opentextbc.ca\/introalgebra\/wp-content\/ql-cache\/quicklatex.com-571cb9b58a511d7f6eb61eb09b229027_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"&#100;&#61;&#45;&#56;\" title=\"Rendered by QuickLaTeX.com\" height=\"13\" width=\"56\" style=\"vertical-align: 0px;\" \/><br \/>\nb) <img loading=\"lazy\" decoding=\"async\" src=\"https:\/\/opentextbc.ca\/introalgebra\/wp-content\/ql-cache\/quicklatex.com-f4fc38af0c524fef23027143680c34d6_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"&#92;&#116;&#101;&#120;&#116;&#123;&#45;&#125;&#100;&#43;&#92;&#108;&#101;&#102;&#116;&#40;&#45;&#57;&#92;&#114;&#105;&#103;&#104;&#116;&#41;\" title=\"Rendered by QuickLaTeX.com\" height=\"19\" width=\"73\" style=\"vertical-align: -5px;\" \/> when <img loading=\"lazy\" decoding=\"async\" src=\"https:\/\/opentextbc.ca\/introalgebra\/wp-content\/ql-cache\/quicklatex.com-571cb9b58a511d7f6eb61eb09b229027_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"&#100;&#61;&#45;&#56;\" title=\"Rendered by QuickLaTeX.com\" height=\"13\" width=\"56\" style=\"vertical-align: 0px;\" \/><\/td>\n<\/tr>\n<tr>\n<td style=\"width: 50%;\">37.\u00a0<img loading=\"lazy\" decoding=\"async\" src=\"https:\/\/opentextbc.ca\/introalgebra\/wp-content\/ql-cache\/quicklatex.com-281c1f5441bf02904e1c1f2a3860b2ec_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"&#109;&#43;&#110;\" title=\"Rendered by QuickLaTeX.com\" height=\"13\" width=\"48\" style=\"vertical-align: -2px;\" \/> when<br \/>\n<img loading=\"lazy\" decoding=\"async\" src=\"https:\/\/opentextbc.ca\/introalgebra\/wp-content\/ql-cache\/quicklatex.com-64ccf570d2df3acfc2238e40ed386995_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"&#109;&#61;&#45;&#49;&#53;&#44;&#110;&#61;&#55;\" title=\"Rendered by QuickLaTeX.com\" height=\"17\" width=\"122\" style=\"vertical-align: -4px;\" \/><\/td>\n<td style=\"width: 50%;\">38. <img loading=\"lazy\" decoding=\"async\" src=\"https:\/\/opentextbc.ca\/introalgebra\/wp-content\/ql-cache\/quicklatex.com-a1f6573a971cd3cb4f8b7e7bebbd8c69_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"&#112;&#43;&#113;\" title=\"Rendered by QuickLaTeX.com\" height=\"15\" width=\"40\" style=\"vertical-align: -4px;\" \/> when<br \/>\n<img loading=\"lazy\" decoding=\"async\" src=\"https:\/\/opentextbc.ca\/introalgebra\/wp-content\/ql-cache\/quicklatex.com-c30ca6d65bd1bee60e2117500a419fc6_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"&#112;&#61;&#45;&#57;&#44;&#113;&#61;&#49;&#55;\" title=\"Rendered by QuickLaTeX.com\" height=\"17\" width=\"114\" style=\"vertical-align: -4px;\" \/><\/td>\n<\/tr>\n<tr>\n<td style=\"width: 50%;\">39. <img loading=\"lazy\" decoding=\"async\" src=\"https:\/\/opentextbc.ca\/introalgebra\/wp-content\/ql-cache\/quicklatex.com-6c9c01aeb27d92ce9a549330021d5eeb_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"&#114;&#43;&#115;\" title=\"Rendered by QuickLaTeX.com\" height=\"13\" width=\"38\" style=\"vertical-align: -2px;\" \/> when <img loading=\"lazy\" decoding=\"async\" src=\"https:\/\/opentextbc.ca\/introalgebra\/wp-content\/ql-cache\/quicklatex.com-a2d51f330566d9c6b48d221ce3b989c6_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"&#114;&#61;&#45;&#57;&#44;&#115;&#61;&#45;&#55;\" title=\"Rendered by QuickLaTeX.com\" height=\"17\" width=\"118\" style=\"vertical-align: -4px;\" \/><\/td>\n<td style=\"width: 50%;\">40. <img loading=\"lazy\" decoding=\"async\" src=\"https:\/\/opentextbc.ca\/introalgebra\/wp-content\/ql-cache\/quicklatex.com-2a6daf059dbc01417aaff0cbe5dfd074_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"&#116;&#43;&#117;\" title=\"Rendered by QuickLaTeX.com\" height=\"14\" width=\"38\" style=\"vertical-align: -2px;\" \/> when <img loading=\"lazy\" decoding=\"async\" src=\"https:\/\/opentextbc.ca\/introalgebra\/wp-content\/ql-cache\/quicklatex.com-ae16ef1b9f97f16d5cd73420bf09618a_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"&#116;&#61;&#45;&#54;&#44;&#117;&#61;&#45;&#53;\" title=\"Rendered by QuickLaTeX.com\" height=\"17\" width=\"116\" style=\"vertical-align: -4px;\" \/><\/td>\n<\/tr>\n<tr>\n<td style=\"width: 50%;\">41. <img loading=\"lazy\" decoding=\"async\" src=\"https:\/\/opentextbc.ca\/introalgebra\/wp-content\/ql-cache\/quicklatex.com-a469f70946862971ba45ee6cb67facc9_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"&#123;&#92;&#108;&#101;&#102;&#116;&#40;&#120;&#43;&#121;&#92;&#114;&#105;&#103;&#104;&#116;&#41;&#125;&#94;&#123;&#50;&#125;\" title=\"Rendered by QuickLaTeX.com\" height=\"21\" width=\"61\" style=\"vertical-align: -4px;\" \/> when<br \/>\n<img loading=\"lazy\" decoding=\"async\" src=\"https:\/\/opentextbc.ca\/introalgebra\/wp-content\/ql-cache\/quicklatex.com-f19ccce3cbd3c2f724bc70eab550496e_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"&#120;&#61;&#45;&#51;&#44;&#121;&#61;&#49;&#52;\" title=\"Rendered by QuickLaTeX.com\" height=\"16\" width=\"115\" style=\"vertical-align: -4px;\" \/><\/td>\n<td style=\"width: 50%;\">42. <img loading=\"lazy\" decoding=\"async\" src=\"https:\/\/opentextbc.ca\/introalgebra\/wp-content\/ql-cache\/quicklatex.com-66cbf4f9745ec400cb2d1ada5b287f62_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"&#123;&#92;&#108;&#101;&#102;&#116;&#40;&#121;&#43;&#122;&#92;&#114;&#105;&#103;&#104;&#116;&#41;&#125;&#94;&#123;&#50;&#125;\" title=\"Rendered by QuickLaTeX.com\" height=\"21\" width=\"60\" style=\"vertical-align: -4px;\" \/> when<br \/>\n<img loading=\"lazy\" decoding=\"async\" src=\"https:\/\/opentextbc.ca\/introalgebra\/wp-content\/ql-cache\/quicklatex.com-07e18f1bc07fb0f5cd162592d51d40be_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"&#121;&#61;&#45;&#51;&#44;&#122;&#61;&#49;&#53;\" title=\"Rendered by QuickLaTeX.com\" height=\"17\" width=\"113\" style=\"vertical-align: -4px;\" \/><\/td>\n<\/tr>\n<tr>\n<td style=\"width: 50%;\">43. <img loading=\"lazy\" decoding=\"async\" src=\"https:\/\/opentextbc.ca\/introalgebra\/wp-content\/ql-cache\/quicklatex.com-fc636c66f91c2d104d5bdedbfd729ee9_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"&#45;&#50;&#120;&#43;&#49;&#55;\" title=\"Rendered by QuickLaTeX.com\" height=\"15\" width=\"71\" style=\"vertical-align: -2px;\" \/> when<br \/>\na) <img loading=\"lazy\" decoding=\"async\" src=\"https:\/\/opentextbc.ca\/introalgebra\/wp-content\/ql-cache\/quicklatex.com-1dc438da70f358c2eb1bf64a8b7ea4b5_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"&#120;&#61;&#56;\" title=\"Rendered by QuickLaTeX.com\" height=\"12\" width=\"43\" style=\"vertical-align: 0px;\" \/><br \/>\nb) <img loading=\"lazy\" decoding=\"async\" src=\"https:\/\/opentextbc.ca\/introalgebra\/wp-content\/ql-cache\/quicklatex.com-7852d0704798164bd2ce5b572ac50cd9_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"&#120;&#61;&#45;&#56;\" title=\"Rendered by QuickLaTeX.com\" height=\"12\" width=\"57\" style=\"vertical-align: 0px;\" \/><\/td>\n<td style=\"width: 50%;\">44. <img loading=\"lazy\" decoding=\"async\" src=\"https:\/\/opentextbc.ca\/introalgebra\/wp-content\/ql-cache\/quicklatex.com-a65231a82c224c45330923760fbbf599_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"&#45;&#53;&#121;&#43;&#49;&#52;\" title=\"Rendered by QuickLaTeX.com\" height=\"17\" width=\"71\" style=\"vertical-align: -4px;\" \/> when<br \/>\na) <img loading=\"lazy\" decoding=\"async\" src=\"https:\/\/opentextbc.ca\/introalgebra\/wp-content\/ql-cache\/quicklatex.com-633f747b2de427f7a98de490b31bd0f8_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"&#121;&#61;&#57;\" title=\"Rendered by QuickLaTeX.com\" height=\"16\" width=\"42\" style=\"vertical-align: -4px;\" \/><br \/>\nb) <img loading=\"lazy\" decoding=\"async\" src=\"https:\/\/opentextbc.ca\/introalgebra\/wp-content\/ql-cache\/quicklatex.com-c3a4f9b7fbef4cb8ec29455107f6ac6a_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"&#121;&#61;&#45;&#57;\" title=\"Rendered by QuickLaTeX.com\" height=\"16\" width=\"56\" style=\"vertical-align: -4px;\" \/><\/td>\n<\/tr>\n<tr>\n<td style=\"width: 50%;\">45. <img loading=\"lazy\" decoding=\"async\" src=\"https:\/\/opentextbc.ca\/introalgebra\/wp-content\/ql-cache\/quicklatex.com-b8372c2ce478af16f2f0f2b0a5d4cc29_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"&#49;&#48;&#45;&#51;&#109;\" title=\"Rendered by QuickLaTeX.com\" height=\"13\" width=\"62\" style=\"vertical-align: -1px;\" \/> when<br \/>\na) <img loading=\"lazy\" decoding=\"async\" src=\"https:\/\/opentextbc.ca\/introalgebra\/wp-content\/ql-cache\/quicklatex.com-1f41bbee1ac2908051c4c1e1795f0354_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"&#109;&#61;&#53;\" title=\"Rendered by QuickLaTeX.com\" height=\"13\" width=\"47\" style=\"vertical-align: 0px;\" \/><br \/>\nb) <img loading=\"lazy\" decoding=\"async\" src=\"https:\/\/opentextbc.ca\/introalgebra\/wp-content\/ql-cache\/quicklatex.com-2e18e51d7627b3b5c2941e9ae4338c74_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"&#109;&#61;&#45;&#53;\" title=\"Rendered by QuickLaTeX.com\" height=\"13\" width=\"61\" style=\"vertical-align: 0px;\" \/><\/td>\n<td style=\"width: 50%;\">46. <img loading=\"lazy\" decoding=\"async\" src=\"https:\/\/opentextbc.ca\/introalgebra\/wp-content\/ql-cache\/quicklatex.com-d177829835205a44d52ae4997334b95e_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"&#49;&#56;&#45;&#52;&#110;\" title=\"Rendered by QuickLaTeX.com\" height=\"13\" width=\"58\" style=\"vertical-align: -1px;\" \/> when<br \/>\na) <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;\" \/><br \/>\nb) <img loading=\"lazy\" decoding=\"async\" src=\"https:\/\/opentextbc.ca\/introalgebra\/wp-content\/ql-cache\/quicklatex.com-ac12605a682d0ded7ba7f4ac4a0ab159_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"&#110;&#61;&#45;&#51;\" title=\"Rendered by QuickLaTeX.com\" height=\"12\" width=\"57\" style=\"vertical-align: 0px;\" \/><\/td>\n<\/tr>\n<tr>\n<td style=\"width: 50%;\">47. <img loading=\"lazy\" decoding=\"async\" src=\"https:\/\/opentextbc.ca\/introalgebra\/wp-content\/ql-cache\/quicklatex.com-ff69da810453c4b3978a1e2e9e70d7a9_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"&#50;&#123;&#119;&#125;&#94;&#123;&#50;&#125;&#45;&#51;&#119;&#43;&#55;\" title=\"Rendered by QuickLaTeX.com\" height=\"17\" width=\"104\" style=\"vertical-align: -2px;\" \/> when<br \/>\n<img loading=\"lazy\" decoding=\"async\" src=\"https:\/\/opentextbc.ca\/introalgebra\/wp-content\/ql-cache\/quicklatex.com-161f3d8fef97a4b264c217752183f8c6_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"&#119;&#61;&#45;&#50;\" title=\"Rendered by QuickLaTeX.com\" height=\"12\" width=\"59\" style=\"vertical-align: 0px;\" \/><\/td>\n<td style=\"width: 50%;\">48. <img loading=\"lazy\" decoding=\"async\" src=\"https:\/\/opentextbc.ca\/introalgebra\/wp-content\/ql-cache\/quicklatex.com-745524cfafd4030d888a5482d066c347_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"&#51;&#123;&#117;&#125;&#94;&#123;&#50;&#125;&#45;&#52;&#117;&#43;&#53;\" title=\"Rendered by QuickLaTeX.com\" height=\"17\" width=\"97\" style=\"vertical-align: -2px;\" \/> when <img loading=\"lazy\" decoding=\"async\" src=\"https:\/\/opentextbc.ca\/introalgebra\/wp-content\/ql-cache\/quicklatex.com-a822643b315d2749212bc17a7abb9d6e_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"&#117;&#61;&#45;&#51;\" title=\"Rendered by QuickLaTeX.com\" height=\"12\" width=\"57\" style=\"vertical-align: 0px;\" \/><\/td>\n<\/tr>\n<tr>\n<td style=\"width: 50%;\">49. <img loading=\"lazy\" decoding=\"async\" src=\"https:\/\/opentextbc.ca\/introalgebra\/wp-content\/ql-cache\/quicklatex.com-fed435a1f6e46141f785b1aeee66dece_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"&#57;&#97;&#45;&#50;&#98;&#45;&#56;\" title=\"Rendered by QuickLaTeX.com\" height=\"13\" width=\"87\" style=\"vertical-align: 0px;\" \/> when<br \/>\n<img loading=\"lazy\" decoding=\"async\" src=\"https:\/\/opentextbc.ca\/introalgebra\/wp-content\/ql-cache\/quicklatex.com-4cf1937a6096935f404c1a135bc03207_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"&#97;&#61;&#45;&#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;&#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;&#98;&#61;&#45;&#51;\" title=\"Rendered by QuickLaTeX.com\" height=\"13\" width=\"146\" style=\"vertical-align: 0px;\" \/><\/td>\n<td style=\"width: 50%;\">50. <img loading=\"lazy\" decoding=\"async\" src=\"https:\/\/opentextbc.ca\/introalgebra\/wp-content\/ql-cache\/quicklatex.com-50fa975d04c832a8447a0f621f724e27_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"&#55;&#109;&#45;&#52;&#110;&#45;&#50;\" title=\"Rendered by QuickLaTeX.com\" height=\"14\" width=\"95\" style=\"vertical-align: -1px;\" \/> when<br \/>\n<img loading=\"lazy\" decoding=\"async\" src=\"https:\/\/opentextbc.ca\/introalgebra\/wp-content\/ql-cache\/quicklatex.com-5844826bb67b2da5830217a17b7cd6b2_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"&#109;&#61;&#45;&#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;&#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;&#110;&#61;&#45;&#57;\" title=\"Rendered by QuickLaTeX.com\" height=\"14\" width=\"155\" style=\"vertical-align: -1px;\" \/><\/td>\n<\/tr>\n<\/tbody>\n<\/table>\n<h2>Translate English Phrases to Algebraic Expressions<\/h2>\n<p id=\"fs-id1166418098647\">In the following exercises, translate to an algebraic expression and simplify if possible.<\/p>\n<table style=\"border-collapse: collapse; width: 100%; height: 120px;\">\n<tbody>\n<tr style=\"height: 15px;\">\n<td style=\"width: 50%; height: 15px;\">51. the sum of 3 and <img loading=\"lazy\" decoding=\"async\" src=\"https:\/\/opentextbc.ca\/introalgebra\/wp-content\/ql-cache\/quicklatex.com-0329d19b932005c996d83dbb9e09ffed_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"&#45;&#49;&#53;\" title=\"Rendered by QuickLaTeX.com\" height=\"14\" width=\"30\" style=\"vertical-align: -1px;\" \/>, increased by 7<\/td>\n<td style=\"width: 50%; height: 15px;\">52. the sum of <img loading=\"lazy\" decoding=\"async\" src=\"https:\/\/opentextbc.ca\/introalgebra\/wp-content\/ql-cache\/quicklatex.com-ca32393b1b5af7c55a95d89cf9d610f2_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"&#45;&#56;\" title=\"Rendered by QuickLaTeX.com\" height=\"12\" width=\"22\" style=\"vertical-align: 0px;\" \/> and <img loading=\"lazy\" decoding=\"async\" src=\"https:\/\/opentextbc.ca\/introalgebra\/wp-content\/ql-cache\/quicklatex.com-9672181aec15f8334b80ada7de4e4fc0_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"&#45;&#57;\" title=\"Rendered by QuickLaTeX.com\" height=\"12\" width=\"22\" style=\"vertical-align: 0px;\" \/>, increased by 23<\/td>\n<\/tr>\n<tr style=\"height: 15px;\">\n<td style=\"width: 50%; height: 15px;\">53. the difference of 10 and <img loading=\"lazy\" decoding=\"async\" src=\"https:\/\/opentextbc.ca\/introalgebra\/wp-content\/ql-cache\/quicklatex.com-bb9e52ddecc045b16dbf509b1c89f11b_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"&#45;&#49;&#56;\" title=\"Rendered by QuickLaTeX.com\" height=\"13\" width=\"31\" style=\"vertical-align: -1px;\" \/><\/td>\n<td style=\"width: 50%; height: 15px;\">54. subtract 11 from <img loading=\"lazy\" decoding=\"async\" src=\"https:\/\/opentextbc.ca\/introalgebra\/wp-content\/ql-cache\/quicklatex.com-170b493658855d7211748be1a7029d86_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"&#45;&#50;&#53;\" title=\"Rendered by QuickLaTeX.com\" height=\"13\" width=\"30\" style=\"vertical-align: 0px;\" \/><\/td>\n<\/tr>\n<tr style=\"height: 15px;\">\n<td style=\"width: 50%; height: 15px;\">55. the difference of <img loading=\"lazy\" decoding=\"async\" src=\"https:\/\/opentextbc.ca\/introalgebra\/wp-content\/ql-cache\/quicklatex.com-7b5b9d9f382b11767d19f257afca0019_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"&#45;&#53;\" title=\"Rendered by QuickLaTeX.com\" height=\"13\" width=\"21\" style=\"vertical-align: 0px;\" \/> and <img loading=\"lazy\" decoding=\"async\" src=\"https:\/\/opentextbc.ca\/introalgebra\/wp-content\/ql-cache\/quicklatex.com-ec1795c5af248d148a298ec6e4785280_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"&#45;&#51;&#48;\" title=\"Rendered by QuickLaTeX.com\" height=\"12\" width=\"31\" style=\"vertical-align: 0px;\" \/><\/td>\n<td style=\"width: 50%; height: 15px;\">56. subtract <img loading=\"lazy\" decoding=\"async\" src=\"https:\/\/opentextbc.ca\/introalgebra\/wp-content\/ql-cache\/quicklatex.com-4797c874a138ca175d7c2cd8b3ed9a98_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"&#45;&#54;\" title=\"Rendered by QuickLaTeX.com\" height=\"12\" width=\"22\" style=\"vertical-align: 0px;\" \/> from <img loading=\"lazy\" decoding=\"async\" src=\"https:\/\/opentextbc.ca\/introalgebra\/wp-content\/ql-cache\/quicklatex.com-ee7bea24371f97fb5673002404153494_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"&#45;&#49;&#51;\" title=\"Rendered by QuickLaTeX.com\" height=\"13\" width=\"31\" style=\"vertical-align: -1px;\" \/><\/td>\n<\/tr>\n<tr style=\"height: 15px;\">\n<td style=\"width: 50%; height: 15px;\">57. the product of <img loading=\"lazy\" decoding=\"async\" src=\"https:\/\/opentextbc.ca\/introalgebra\/wp-content\/ql-cache\/quicklatex.com-470cb162cf92c55d139f4f69216225e5_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"&#45;&#51;\" title=\"Rendered by QuickLaTeX.com\" height=\"12\" width=\"22\" style=\"vertical-align: 0px;\" \/> and <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<td style=\"width: 50%; height: 15px;\">58. the product of <img loading=\"lazy\" decoding=\"async\" src=\"https:\/\/opentextbc.ca\/introalgebra\/wp-content\/ql-cache\/quicklatex.com-00b9cce9021441b203ec0271d72e6ba2_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"&#45;&#52;\" title=\"Rendered by QuickLaTeX.com\" height=\"13\" width=\"22\" style=\"vertical-align: -1px;\" \/> and <img loading=\"lazy\" decoding=\"async\" src=\"https:\/\/opentextbc.ca\/introalgebra\/wp-content\/ql-cache\/quicklatex.com-8dde8d4cade60a4f3ca0e779512b974c_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"&#49;&#54;\" title=\"Rendered by QuickLaTeX.com\" height=\"13\" width=\"17\" style=\"vertical-align: -1px;\" \/><\/td>\n<\/tr>\n<tr style=\"height: 15px;\">\n<td style=\"width: 50%; height: 15px;\">59. the quotient of <img loading=\"lazy\" decoding=\"async\" src=\"https:\/\/opentextbc.ca\/introalgebra\/wp-content\/ql-cache\/quicklatex.com-212f5b2401cf3e4defaf1949abd4591a_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"&#45;&#54;&#48;\" title=\"Rendered by QuickLaTeX.com\" height=\"12\" width=\"31\" style=\"vertical-align: 0px;\" \/> and <img loading=\"lazy\" decoding=\"async\" src=\"https:\/\/opentextbc.ca\/introalgebra\/wp-content\/ql-cache\/quicklatex.com-9b93660fe4bfeaf9a69e38dd0cba4d18_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"&#45;&#50;&#48;\" title=\"Rendered by QuickLaTeX.com\" height=\"12\" width=\"31\" style=\"vertical-align: 0px;\" \/><\/td>\n<td style=\"width: 50%; height: 15px;\">60. the quotient of <img loading=\"lazy\" decoding=\"async\" src=\"https:\/\/opentextbc.ca\/introalgebra\/wp-content\/ql-cache\/quicklatex.com-e9e8668f98ca5c439e8df86b7e3360a5_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"&#45;&#52;&#48;\" title=\"Rendered by QuickLaTeX.com\" height=\"13\" width=\"31\" style=\"vertical-align: -1px;\" \/> and <img loading=\"lazy\" decoding=\"async\" src=\"https:\/\/opentextbc.ca\/introalgebra\/wp-content\/ql-cache\/quicklatex.com-9b93660fe4bfeaf9a69e38dd0cba4d18_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"&#45;&#50;&#48;\" 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;\">61. the quotient of <img loading=\"lazy\" decoding=\"async\" src=\"https:\/\/opentextbc.ca\/introalgebra\/wp-content\/ql-cache\/quicklatex.com-4797c874a138ca175d7c2cd8b3ed9a98_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"&#45;&#54;\" title=\"Rendered by QuickLaTeX.com\" height=\"12\" width=\"22\" style=\"vertical-align: 0px;\" \/> and the sum of <em data-effect=\"italics\">a<\/em> and <em data-effect=\"italics\">b<\/em><\/td>\n<td style=\"width: 50%; height: 15px;\">62. the quotient of <img loading=\"lazy\" decoding=\"async\" src=\"https:\/\/opentextbc.ca\/introalgebra\/wp-content\/ql-cache\/quicklatex.com-00c6d30c5f7439a21caf981437f64be1_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"&#45;&#55;\" title=\"Rendered by QuickLaTeX.com\" height=\"13\" width=\"22\" style=\"vertical-align: 0px;\" \/> and the sum of <em data-effect=\"italics\">m<\/em> and <em data-effect=\"italics\">n<\/em><\/td>\n<\/tr>\n<tr style=\"height: 15px;\">\n<td style=\"width: 50%; height: 15px;\">63. the product of <img loading=\"lazy\" decoding=\"async\" src=\"https:\/\/opentextbc.ca\/introalgebra\/wp-content\/ql-cache\/quicklatex.com-24329a36a4e10288288979f77a565ca2_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"&#45;&#49;&#48;\" title=\"Rendered by QuickLaTeX.com\" height=\"13\" width=\"31\" style=\"vertical-align: -1px;\" \/> and the difference of <img loading=\"lazy\" decoding=\"async\" src=\"https:\/\/opentextbc.ca\/introalgebra\/wp-content\/ql-cache\/quicklatex.com-ddda4f13c3540844cbe9dbbe49f0db38_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"&#112;&#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;&#113;\" title=\"Rendered by QuickLaTeX.com\" height=\"17\" width=\"54\" style=\"vertical-align: -4px;\" \/><\/td>\n<td style=\"width: 50%; height: 15px;\">64. the product of <img loading=\"lazy\" decoding=\"async\" src=\"https:\/\/opentextbc.ca\/introalgebra\/wp-content\/ql-cache\/quicklatex.com-ee7bea24371f97fb5673002404153494_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"&#45;&#49;&#51;\" title=\"Rendered by QuickLaTeX.com\" height=\"13\" width=\"31\" style=\"vertical-align: -1px;\" \/> and the difference of <img loading=\"lazy\" decoding=\"async\" src=\"https:\/\/opentextbc.ca\/introalgebra\/wp-content\/ql-cache\/quicklatex.com-24fc7739b2b57fbb4d6ed30365a39f0b_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"&#99;&#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;&#100;\" title=\"Rendered by QuickLaTeX.com\" height=\"13\" width=\"53\" style=\"vertical-align: 0px;\" \/><\/td>\n<\/tr>\n<\/tbody>\n<\/table>\n<h2>Use Integers in Applications<\/h2>\n<p id=\"fs-id1166423907674\">In the following exercises, solve.<\/p>\n<table style=\"border-collapse: collapse; width: 100%;\">\n<tbody>\n<tr>\n<td style=\"width: 50%;\">65. <strong data-effect=\"bold\">Temperature<\/strong> On January <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;\" \/>, the high temperature in Lytton, British Columbia, was <img loading=\"lazy\" decoding=\"async\" src=\"https:\/\/opentextbc.ca\/introalgebra\/wp-content\/ql-cache\/quicklatex.com-2044c4aefe2adfc3b277146852400fd1_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"&#56;&#52;\" title=\"Rendered by QuickLaTeX.com\" height=\"13\" width=\"18\" style=\"vertical-align: -1px;\" \/>\u00b0 . That same day, the high temperature in Fort Nelson, British Columbia was <img loading=\"lazy\" decoding=\"async\" src=\"https:\/\/opentextbc.ca\/introalgebra\/wp-content\/ql-cache\/quicklatex.com-9eae543c53f9301fa411ef541a1f4433_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"&#45;&#49;&#50;\" title=\"Rendered by QuickLaTeX.com\" height=\"13\" width=\"30\" style=\"vertical-align: -1px;\" \/>\u00b0. What was the difference between the temperature in Lytton and the temperature in Embarrass?<\/td>\n<td style=\"width: 50%;\">66.<strong data-effect=\"bold\"> Temperature<\/strong> On January <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;\" \/>, the high temperature in Palm Springs, California, was <img loading=\"lazy\" decoding=\"async\" src=\"https:\/\/opentextbc.ca\/introalgebra\/wp-content\/ql-cache\/quicklatex.com-b98da7c985053d158d19790d72a1f782_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"&#56;&#57;\" title=\"Rendered by QuickLaTeX.com\" height=\"12\" width=\"18\" style=\"vertical-align: 0px;\" \/>\u00b0, and the high temperature in Whitefield, New Hampshire was <img loading=\"lazy\" decoding=\"async\" src=\"https:\/\/opentextbc.ca\/introalgebra\/wp-content\/ql-cache\/quicklatex.com-aef29fb3b7f163a804596c378eba113f_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"&#45;&#51;&#49;\" title=\"Rendered by QuickLaTeX.com\" height=\"12\" width=\"30\" style=\"vertical-align: 0px;\" \/>\u00b0. What was the difference between the temperature in Palm Springs and the temperature in Whitefield?<\/td>\n<\/tr>\n<tr>\n<td style=\"width: 50%;\">67. <strong data-effect=\"bold\">Football<\/strong> At the first down, the Chargers had the ball on their 25 yard line. On the next three downs, they lost 6 yards, gained 10 yards, and lost 8 yards. What was the yard line at the end of the fourth down?<\/td>\n<td style=\"width: 50%;\">68.<strong data-effect=\"bold\"> Football<\/strong> At the first down, the Steelers had the ball on their 30 yard line. On the next three downs, they gained 9 yards, lost 14 yards, and lost 2 yards. What was the yard line at the end of the fourth down?<\/td>\n<\/tr>\n<tr>\n<td style=\"width: 50%;\">69.<strong data-effect=\"bold\"> Checking Account<\/strong> Ester has &#36;124 in her checking account. She writes a check for &#36;152. What is the new balance in her checking account?<\/td>\n<td style=\"width: 50%;\">70.<strong data-effect=\"bold\"> Checking Account<\/strong> Selina has &#36;165 in her checking account. She writes a check for &#36;207. What is the new balance in her checking account?<\/td>\n<\/tr>\n<tr>\n<td style=\"width: 50%;\">71. <strong data-effect=\"bold\">Checking Account<\/strong> Kevin has a balance of <img loading=\"lazy\" decoding=\"async\" src=\"https:\/\/opentextbc.ca\/introalgebra\/wp-content\/ql-cache\/quicklatex.com-c09bd1dab7b4ad4642548bdff771c81a_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"&#45;&#92;&#36;&#51;&#56;\" title=\"Rendered by QuickLaTeX.com\" height=\"14\" width=\"40\" style=\"vertical-align: -1px;\" \/> in his checking account. He deposits &#36;225 to the account. What is the new balance?<\/td>\n<td style=\"width: 50%;\">72. <strong data-effect=\"bold\">Checking Account<\/strong> Reymonte has a balance of <img loading=\"lazy\" decoding=\"async\" src=\"https:\/\/opentextbc.ca\/introalgebra\/wp-content\/ql-cache\/quicklatex.com-70d0d6f122ac2525ee0d7f8b268d8722_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"&#45;&#92;&#36;&#52;&#57;\" title=\"Rendered by QuickLaTeX.com\" height=\"14\" width=\"40\" style=\"vertical-align: -1px;\" \/> in his checking account. He deposits &#36;281 to the account. What is the new balance?<\/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%;\">73. <strong data-effect=\"bold\">Stock market<\/strong> Javier owns 300 shares of stock in one company. On Tuesday, the stock price dropped &#36;12 per share. What was the total effect on Javier\u2019s portfolio?<\/td>\n<td style=\"width: 50%;\">74. <strong data-effect=\"bold\">Weight loss<\/strong> In the first week of a diet program, eight women lost an average of 3 pounds each. What was the total weight change for the eight women?<\/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%;\">75. In your own words, state the rules for multiplying integers.<\/td>\n<td style=\"width: 50%;\">76. In your own words, state the rules for dividing integers.<\/td>\n<\/tr>\n<tr>\n<td style=\"width: 50%;\">77. Why is <img loading=\"lazy\" decoding=\"async\" src=\"https:\/\/opentextbc.ca\/introalgebra\/wp-content\/ql-cache\/quicklatex.com-a0048d3d18807f95afb6795eea8191e3_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"&#45;&#123;&#50;&#125;&#94;&#123;&#52;&#125;&#92;&#110;&#101;&#32;&#123;&#92;&#108;&#101;&#102;&#116;&#40;&#45;&#50;&#92;&#114;&#105;&#103;&#104;&#116;&#41;&#125;&#94;&#123;&#52;&#125;&#63;\" title=\"Rendered by QuickLaTeX.com\" height=\"22\" width=\"105\" style=\"vertical-align: -5px;\" \/><\/td>\n<td style=\"width: 50%;\">78. Why is <img loading=\"lazy\" decoding=\"async\" src=\"https:\/\/opentextbc.ca\/introalgebra\/wp-content\/ql-cache\/quicklatex.com-6834660c7c62973d322b57725380e85b_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"&#45;&#123;&#52;&#125;&#94;&#123;&#51;&#125;&#61;&#123;&#92;&#108;&#101;&#102;&#116;&#40;&#45;&#52;&#92;&#114;&#105;&#103;&#104;&#116;&#41;&#125;&#94;&#123;&#51;&#125;&#63;\" title=\"Rendered by QuickLaTeX.com\" height=\"22\" width=\"105\" style=\"vertical-align: -5px;\" \/><\/td>\n<\/tr>\n<\/tbody>\n<\/table>\n<h1>Answers<\/h1>\n<table style=\"border-collapse: collapse; width: 100%; height: 153px;\">\n<tbody>\n<tr style=\"height: 17px;\">\n<td style=\"width: 33.3333%; height: 17px;\">1. <img loading=\"lazy\" decoding=\"async\" src=\"https:\/\/opentextbc.ca\/introalgebra\/wp-content\/ql-cache\/quicklatex.com-fce2979511e6a27a1bd61ca970c655b6_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"&#45;&#51;&#50;\" title=\"Rendered by QuickLaTeX.com\" height=\"12\" width=\"30\" style=\"vertical-align: 0px;\" \/><\/td>\n<td style=\"width: 33.3333%; height: 17px;\">3. <img loading=\"lazy\" decoding=\"async\" src=\"https:\/\/opentextbc.ca\/introalgebra\/wp-content\/ql-cache\/quicklatex.com-c081a4d1588de9f9de1dd7d5282b4c9d_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"&#45;&#54;&#51;\" title=\"Rendered by QuickLaTeX.com\" height=\"12\" width=\"31\" style=\"vertical-align: 0px;\" \/><\/td>\n<td style=\"width: 33.3333%; height: 17px;\">5. <img loading=\"lazy\" decoding=\"async\" src=\"https:\/\/opentextbc.ca\/introalgebra\/wp-content\/ql-cache\/quicklatex.com-4797c874a138ca175d7c2cd8b3ed9a98_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"&#45;&#54;\" title=\"Rendered by QuickLaTeX.com\" height=\"12\" width=\"22\" style=\"vertical-align: 0px;\" \/><\/td>\n<\/tr>\n<tr style=\"height: 17px;\">\n<td style=\"width: 33.3333%; height: 17px;\">7. 14<\/td>\n<td style=\"width: 33.3333%; height: 17px;\">9. <img loading=\"lazy\" decoding=\"async\" src=\"https:\/\/opentextbc.ca\/introalgebra\/wp-content\/ql-cache\/quicklatex.com-00b9cce9021441b203ec0271d72e6ba2_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"&#45;&#52;\" title=\"Rendered by QuickLaTeX.com\" height=\"13\" width=\"22\" style=\"vertical-align: -1px;\" \/><\/td>\n<td style=\"width: 33.3333%; height: 17px;\">11. 13<\/td>\n<\/tr>\n<tr style=\"height: 17px;\">\n<td style=\"width: 33.3333%; height: 17px;\">13. <img loading=\"lazy\" decoding=\"async\" src=\"https:\/\/opentextbc.ca\/introalgebra\/wp-content\/ql-cache\/quicklatex.com-9eae543c53f9301fa411ef541a1f4433_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"&#45;&#49;&#50;\" title=\"Rendered by QuickLaTeX.com\" height=\"13\" width=\"30\" style=\"vertical-align: -1px;\" \/><\/td>\n<td style=\"width: 33.3333%; height: 17px;\">15. <img loading=\"lazy\" decoding=\"async\" src=\"https:\/\/opentextbc.ca\/introalgebra\/wp-content\/ql-cache\/quicklatex.com-6193f2be927539d70e972d662785fd1e_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"&#45;&#52;&#55;\" title=\"Rendered by QuickLaTeX.com\" height=\"14\" width=\"31\" style=\"vertical-align: -1px;\" \/><\/td>\n<td style=\"width: 33.3333%; height: 17px;\">17. 64<\/td>\n<\/tr>\n<tr style=\"height: 17px;\">\n<td style=\"width: 33.3333%; height: 17px;\">19. <img loading=\"lazy\" decoding=\"async\" src=\"https:\/\/opentextbc.ca\/introalgebra\/wp-content\/ql-cache\/quicklatex.com-60f20f07f8f7c62331f2d8fe388a61b0_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"&#45;&#49;&#54;\" title=\"Rendered by QuickLaTeX.com\" height=\"13\" width=\"31\" style=\"vertical-align: -1px;\" \/><\/td>\n<td style=\"width: 33.3333%; height: 17px;\">21. 90<\/td>\n<td style=\"width: 33.3333%; height: 17px;\">23. 9<\/td>\n<\/tr>\n<tr style=\"height: 17px;\">\n<td style=\"width: 33.3333%; height: 17px;\">25. 41<\/td>\n<td style=\"width: 33.3333%; height: 17px;\">27. <img loading=\"lazy\" decoding=\"async\" src=\"https:\/\/opentextbc.ca\/introalgebra\/wp-content\/ql-cache\/quicklatex.com-9672181aec15f8334b80ada7de4e4fc0_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"&#45;&#57;\" title=\"Rendered by QuickLaTeX.com\" height=\"12\" width=\"22\" style=\"vertical-align: 0px;\" \/><\/td>\n<td style=\"width: 33.3333%; height: 17px;\">29. <img loading=\"lazy\" decoding=\"async\" src=\"https:\/\/opentextbc.ca\/introalgebra\/wp-content\/ql-cache\/quicklatex.com-94535250d2f2556f9c0cb93ff04db6e0_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"&#45;&#50;&#57;\" title=\"Rendered by QuickLaTeX.com\" height=\"12\" width=\"31\" style=\"vertical-align: 0px;\" \/><\/td>\n<\/tr>\n<tr style=\"height: 17px;\">\n<td style=\"width: 33.3333%; height: 17px;\">31. 5<\/td>\n<td style=\"width: 33.3333%; height: 17px;\">33. a)<img loading=\"lazy\" decoding=\"async\" src=\"https:\/\/opentextbc.ca\/introalgebra\/wp-content\/ql-cache\/quicklatex.com-6193f2be927539d70e972d662785fd1e_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"&#45;&#52;&#55;\" title=\"Rendered by QuickLaTeX.com\" height=\"14\" width=\"31\" style=\"vertical-align: -1px;\" \/> b) 16<\/td>\n<td style=\"width: 33.3333%; height: 17px;\">35. a)<img loading=\"lazy\" decoding=\"async\" src=\"https:\/\/opentextbc.ca\/introalgebra\/wp-content\/ql-cache\/quicklatex.com-00b9cce9021441b203ec0271d72e6ba2_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"&#45;&#52;\" title=\"Rendered by QuickLaTeX.com\" height=\"13\" width=\"22\" style=\"vertical-align: -1px;\" \/> b) 10<\/td>\n<\/tr>\n<tr style=\"height: 17px;\">\n<td style=\"width: 33.3333%; height: 17px;\">37. <img loading=\"lazy\" decoding=\"async\" src=\"https:\/\/opentextbc.ca\/introalgebra\/wp-content\/ql-cache\/quicklatex.com-ca32393b1b5af7c55a95d89cf9d610f2_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"&#45;&#56;\" title=\"Rendered by QuickLaTeX.com\" height=\"12\" width=\"22\" style=\"vertical-align: 0px;\" \/><\/td>\n<td style=\"width: 33.3333%; height: 17px;\">39. <img loading=\"lazy\" decoding=\"async\" src=\"https:\/\/opentextbc.ca\/introalgebra\/wp-content\/ql-cache\/quicklatex.com-60f20f07f8f7c62331f2d8fe388a61b0_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"&#45;&#49;&#54;\" title=\"Rendered by QuickLaTeX.com\" height=\"13\" width=\"31\" style=\"vertical-align: -1px;\" \/><\/td>\n<td style=\"width: 33.3333%; height: 17px;\">41. 121<\/td>\n<\/tr>\n<tr style=\"height: 17px;\">\n<td style=\"width: 33.3333%; height: 17px;\">43. a) 1 b) 33<\/td>\n<td style=\"width: 33.3333%; height: 17px;\">45. a)<img loading=\"lazy\" decoding=\"async\" src=\"https:\/\/opentextbc.ca\/introalgebra\/wp-content\/ql-cache\/quicklatex.com-7b5b9d9f382b11767d19f257afca0019_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"&#45;&#53;\" title=\"Rendered by QuickLaTeX.com\" height=\"13\" width=\"21\" style=\"vertical-align: 0px;\" \/>b) 25<\/td>\n<td style=\"width: 33.3333%; height: 17px;\">47. 21<\/td>\n<\/tr>\n<tr style=\"height: 17px;\">\n<td style=\"width: 33.3333%; height: 17px;\">49. <img loading=\"lazy\" decoding=\"async\" src=\"https:\/\/opentextbc.ca\/introalgebra\/wp-content\/ql-cache\/quicklatex.com-eeacf7895c3fd138514ad215aa482af4_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"&#45;&#53;&#54;\" title=\"Rendered by QuickLaTeX.com\" height=\"13\" width=\"31\" style=\"vertical-align: 0px;\" \/><\/td>\n<td style=\"width: 33.3333%; height: 17px;\">51. <img loading=\"lazy\" decoding=\"async\" src=\"https:\/\/opentextbc.ca\/introalgebra\/wp-content\/ql-cache\/quicklatex.com-04b4413671d3707a89c0e1f126f09c5f_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"&#92;&#108;&#101;&#102;&#116;&#40;&#51;&#43;&#92;&#108;&#101;&#102;&#116;&#40;&#45;&#49;&#53;&#92;&#114;&#105;&#103;&#104;&#116;&#41;&#92;&#114;&#105;&#103;&#104;&#116;&#41;&#43;&#55;&#59;&#45;&#53;\" title=\"Rendered by QuickLaTeX.com\" height=\"18\" width=\"149\" style=\"vertical-align: -4px;\" \/><\/td>\n<td style=\"width: 33.3333%; height: 17px;\">53. <img loading=\"lazy\" decoding=\"async\" src=\"https:\/\/opentextbc.ca\/introalgebra\/wp-content\/ql-cache\/quicklatex.com-09017fbbaa0316e319972d53dd1367c3_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"&#49;&#48;&#45;&#92;&#108;&#101;&#102;&#116;&#40;&#45;&#49;&#56;&#92;&#114;&#105;&#103;&#104;&#116;&#41;&#59;&#50;&#56;\" title=\"Rendered by QuickLaTeX.com\" height=\"18\" width=\"113\" style=\"vertical-align: -4px;\" \/><\/td>\n<\/tr>\n<tr>\n<td style=\"width: 33.3333%;\">55. <img loading=\"lazy\" decoding=\"async\" src=\"https:\/\/opentextbc.ca\/introalgebra\/wp-content\/ql-cache\/quicklatex.com-c066e2e3c10a98f09793984015822a4b_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"&#45;&#53;&#45;&#92;&#108;&#101;&#102;&#116;&#40;&#45;&#51;&#48;&#92;&#114;&#105;&#103;&#104;&#116;&#41;&#59;&#50;&#53;\" title=\"Rendered by QuickLaTeX.com\" height=\"18\" width=\"116\" style=\"vertical-align: -4px;\" \/><\/td>\n<td style=\"width: 33.3333%;\">57. <img loading=\"lazy\" decoding=\"async\" src=\"https:\/\/opentextbc.ca\/introalgebra\/wp-content\/ql-cache\/quicklatex.com-956a563927add17ca942010c00eba2c4_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"&#45;&#51;&#92;&#99;&#100;&#111;&#116;&#32;&#49;&#53;&#59;&#45;&#52;&#53;\" title=\"Rendered by QuickLaTeX.com\" height=\"17\" width=\"91\" style=\"vertical-align: -4px;\" \/><\/td>\n<td style=\"width: 33.3333%;\">59. <img loading=\"lazy\" decoding=\"async\" src=\"https:\/\/opentextbc.ca\/introalgebra\/wp-content\/ql-cache\/quicklatex.com-fc4ccf76ec6f44b0594248d2297c665b_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"&#45;&#54;&#48;&#92;&#100;&#105;&#118;&#92;&#108;&#101;&#102;&#116;&#40;&#45;&#50;&#48;&#92;&#114;&#105;&#103;&#104;&#116;&#41;&#59;&#51;\" title=\"Rendered by QuickLaTeX.com\" height=\"19\" width=\"117\" style=\"vertical-align: -5px;\" \/><\/td>\n<\/tr>\n<tr>\n<td style=\"width: 33.3333%;\">61. <img loading=\"lazy\" decoding=\"async\" src=\"https:\/\/opentextbc.ca\/introalgebra\/wp-content\/ql-cache\/quicklatex.com-107bf84796215066792d64ae12f51759_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"&#92;&#102;&#114;&#97;&#99;&#123;&#45;&#54;&#125;&#123;&#97;&#43;&#98;&#125;\" title=\"Rendered by QuickLaTeX.com\" height=\"24\" width=\"24\" style=\"vertical-align: -8px;\" \/><\/td>\n<td style=\"width: 33.3333%;\">63. <img loading=\"lazy\" decoding=\"async\" src=\"https:\/\/opentextbc.ca\/introalgebra\/wp-content\/ql-cache\/quicklatex.com-95a01e98d1bed3dfaf3a358e7ecf4983_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"&#45;&#49;&#48;&#92;&#108;&#101;&#102;&#116;&#40;&#112;&#45;&#113;&#92;&#114;&#105;&#103;&#104;&#116;&#41;\" title=\"Rendered by QuickLaTeX.com\" height=\"18\" width=\"86\" style=\"vertical-align: -4px;\" \/><\/td>\n<td style=\"width: 33.3333%;\">65. <img loading=\"lazy\" decoding=\"async\" src=\"https:\/\/opentextbc.ca\/introalgebra\/wp-content\/ql-cache\/quicklatex.com-662f6ae8c8d225801ecf7f82bc73ef62_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"&#57;&#54;\" title=\"Rendered by QuickLaTeX.com\" height=\"12\" width=\"18\" style=\"vertical-align: 0px;\" \/>\u00b0<\/td>\n<\/tr>\n<tr>\n<td style=\"width: 33.3333%;\">67. 21<\/td>\n<td style=\"width: 33.3333%;\">69. <img loading=\"lazy\" decoding=\"async\" src=\"https:\/\/opentextbc.ca\/introalgebra\/wp-content\/ql-cache\/quicklatex.com-226998950c838b119f4d4b6149934a1d_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"&#92;&#116;&#101;&#120;&#116;&#123;&#45;&#125;&#92;&#36;&#50;&#56;\" title=\"Rendered by QuickLaTeX.com\" height=\"14\" width=\"33\" style=\"vertical-align: -1px;\" \/><\/td>\n<td style=\"width: 33.3333%;\">71. &#36;187<\/td>\n<\/tr>\n<tr>\n<td style=\"width: 33.3333%;\">73. <img loading=\"lazy\" decoding=\"async\" src=\"https:\/\/opentextbc.ca\/introalgebra\/wp-content\/ql-cache\/quicklatex.com-dfa7487e335cd882ecd30126be86d3ae_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"&#92;&#116;&#101;&#120;&#116;&#123;&#45;&#125;&#92;&#36;&#51;&#54;&#48;&#48;\" title=\"Rendered by QuickLaTeX.com\" height=\"14\" width=\"51\" style=\"vertical-align: -1px;\" \/><\/td>\n<td style=\"width: 33.3333%;\">75. Answers may vary<\/td>\n<td style=\"width: 33.3333%;\">77.\u00a0Answers may vary<\/td>\n<\/tr>\n<\/tbody>\n<\/table>\n<h1>Attributions<\/h1>\n<p>This chapter has been adapted from \u201cMultiply and Divide Integers\u201d in <a href=\"https:\/\/openstax.org\/details\/books\/elementary-algebra\"><em>Elementary Algebra<\/em><\/a> (OpenStax) by Lynn Marecek and MaryAnne Anthony-Smith, which is under a <a href=\"https:\/\/creativecommons.org\/licenses\/by\/4.0\/\">CC BY 4.0 Licence<\/a>. Adapted by Izabela Mazur. 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