{"id":189,"date":"2022-10-07T12:57:14","date_gmt":"2022-10-07T16:57:14","guid":{"rendered":"https:\/\/opentextbc.ca\/alfm5\/chapter\/topic-b-subtracting-common-fractions-2\/"},"modified":"2025-12-15T12:57:46","modified_gmt":"2025-12-15T17:57:46","slug":"subtracting-common-fractions","status":"publish","type":"chapter","link":"https:\/\/opentextbc.ca\/alfm5\/chapter\/subtracting-common-fractions\/","title":{"raw":"Topic B: Subtracting Common Fractions","rendered":"Topic B: Subtracting Common Fractions"},"content":{"raw":"Good news!\r\n\r\nThere is only one new thing to learn in this topic. Everything else uses skills and knowledge you already have.\r\n\r\n<strong>Let's look at subtraction:<\/strong>\r\n<div class=\"textbox textbox--examples\"><header class=\"textbox__header\">\r\n<p class=\"textbox__title\">Example A<\/p>\r\n\r\n<\/header>\r\n<div class=\"textbox__content\">\r\n\r\n<img class=\"size-full wp-image-179 aligncenter\" src=\"https:\/\/opentextbc.ca\/busstatsancillary\/wp-content\/uploads\/sites\/437\/2022\/10\/Picture-4-B-1.jpg\" alt=\"A rectangle divided in 5 equal parts. 4 parts and shaded and one unshaded.\" width=\"263\" height=\"63\" \/>\r\n\r\nThe shaded part [latex]\\left(\\dfrac{4}{5}\\right)[\/latex] is the amount that you are starting with.\r\n\r\nNow cross out (pretend you are <em>taking away<\/em>) 3 shaded parts [latex]\\left(\\dfrac{3}{5}\\right)[\/latex].\r\n\r\n<\/div>\r\n<div class=\"textbox__content\">\r\n\r\n<img class=\"size-full wp-image-180 aligncenter\" src=\"https:\/\/opentextbc.ca\/busstatsancillary\/wp-content\/uploads\/sites\/437\/2023\/08\/Picture-4-B-2.jpg\" alt=\"Repeat of rectangle divided in 5 equal parts. 4 of 5 shaded. One unshaded. Three 'x' es applied to 3 of the boxes.\" width=\"267\" height=\"64\" \/>\r\n\r\n<\/div>\r\n<\/div>\r\n<div class=\"textbox textbox--examples\" style=\"break-before: page;\"><header class=\"textbox__header\">\r\n<p class=\"textbox__title\">Example B<\/p>\r\n\r\n<\/header>\r\n<div class=\"textbox__content\">\r\n\r\nDraw a pizza.\r\n\r\n&nbsp;\r\n\r\n<\/div>\r\n<div class=\"textbox__content\">\r\n<ul>\r\n \t<li>Slice it into 8 equal pieces.<\/li>\r\n \t<li>Draw pieces of pineapple on 5 pieces.<\/li>\r\n \t<li>What fraction of the pizza has pineapple?\u00a0 [latex]\\dfrac{5}{8}[\/latex]<\/li>\r\n \t<li>Cross out 2 pineapple pieces to show they have been eaten.<\/li>\r\n \t<li>How much of the pineapple pizza is left?<\/li>\r\n \t<li>[latex]\\begin{array}{rrl}&amp;\\dfrac{5}{8}&amp;\\text{(amount you started with)}\\\\-&amp;\\dfrac{2}{8}&amp;\\text{(amount eaten, \"taken away\")}\\\\ \\hline&amp;\\dfrac{3}{8}&amp;\\text {of the pizza is left with pineapple on it}\\end{array}[\/latex]<\/li>\r\n<\/ul>\r\n<\/div>\r\n<\/div>\r\nCommon fractions must have the same denominator when you subtract one from the other. <strong>Subtract the numerators<\/strong> and keep the same denominators.\r\n<div class=\"textbox textbox--exercises\"><header class=\"textbox__header\">\r\n<p class=\"textbox__title\">Exercise 1<\/p>\r\n\r\n<\/header>\r\n<div class=\"textbox__content\">\r\n\r\nSubtract to find the [pb_glossary id=\"277\"]difference[\/pb_glossary].\r\n\r\nTIP: Express the difference in lowest terms.\r\n<ol class=\"twocolumn bigspace\" type=\"a\">\r\n \t<li>[latex]\\begin{array}{rr}&amp;\\dfrac{3}{5}\\\\-&amp;\\dfrac{1}{5}\\\\\\hline&amp;\\dfrac{2}{5}\\end{array}[\/latex]<\/li>\r\n \t<li>[latex]\\begin{array}{rrrr}&amp;\\dfrac{7}{8} &amp;&amp;\\\\-&amp;\\dfrac{3}{8}&amp;&amp;\\\\ \\hline &amp;\\dfrac{4}{8}&amp;=&amp;\\dfrac{1}{2}\\\\ \\end{array}[\/latex]<\/li>\r\n \t<li>[latex]\\begin{array}{rr}&amp;\\dfrac{2}{3}\\\\-&amp;\\dfrac{1}{3}\\\\ \\hline&amp;\\end{array}[\/latex]<\/li>\r\n \t<li>[latex]\\begin{array}{rr}&amp;\\dfrac{5}{9}\\\\-&amp;\\dfrac{2}{9}\\\\ \\hline&amp;\\end{array}[\/latex]<\/li>\r\n \t<li>[latex]\\begin{array}{rr}&amp;\\dfrac{6}{7}\\\\-&amp;\\dfrac{1}{7}\\\\ \\hline&amp;\\end{array}[\/latex]<\/li>\r\n \t<li>[latex]\\begin{array}{rr}&amp;\\dfrac{3}{4}\\\\-&amp;\\dfrac{1}{4}\\\\ \\hline&amp;\\end{array}[\/latex]<\/li>\r\n \t<li>[latex]\\begin{array}{rr}&amp;\\dfrac{3}{2}\\\\-&amp;\\dfrac{1}{2}\\\\ \\hline&amp;\\end{array}[\/latex]<\/li>\r\n<\/ol>\r\n<\/div>\r\n<div class=\"textbox__content\">\r\n\r\n<strong>Answers to Exercise 1<\/strong>\r\n<ol class=\"threecolumn\" start=\"3\" type=\"a\">\r\n \t<li>[latex]\\dfrac{1}{3}[\/latex]<\/li>\r\n \t<li>[latex]\\dfrac{1}{3}[\/latex]<\/li>\r\n \t<li>[latex]\\dfrac{5}{7}[\/latex]<\/li>\r\n \t<li>[latex]\\dfrac{1}{2}[\/latex]<\/li>\r\n \t<li>[latex]\\dfrac{2}{2}[\/latex] = 1<\/li>\r\n<\/ol>\r\n<\/div>\r\n<\/div>\r\nYou know how to find the <strong>least common denominator (LCD)<\/strong> and to <strong>rewrite fractions in an equivalent form<\/strong> using the <strong>LCD<\/strong>.\r\n\r\nYou must use those skills when you wish to subtract fractions with different denominators.\r\n<div class=\"textbox textbox--examples\"><header class=\"textbox__header\">\r\n<p class=\"textbox__title\">Example C<\/p>\r\n\r\n<\/header>\r\n<div class=\"textbox__content\">\r\n\r\n[latex]\\dfrac{4}{5}-\\dfrac{3}{10} = [\/latex]\r\n\r\nDenominators are 5 and 10. The least common multiple is 10, so the least common denominator is 10.\r\n\r\n[latex]\\begin{array}{rrrr}&amp;\\dfrac{4}{5}\\left(\\dfrac{\u00d72}{\u00d72}\\right) =&amp;\\dfrac{8}{10}&amp;&amp;\\text{Write equivalent fractions using the LCD}\\\\ -&amp;\\dfrac{3}{10}=&amp;\\dfrac{3}{10} &amp;&amp;\\text{Subtract the numerators}\\\\ \\hline&amp;=&amp;\\dfrac{5}{10}\\left(\\dfrac{\u00f75}{\u00f75}\\right)&amp;=\\dfrac{1}{2}&amp;\\text{Simplify the answer.}\\end{array}[\/latex]\r\n\r\n<\/div>\r\n<\/div>\r\n<div class=\"textbox textbox--exercises\"><header class=\"textbox__header\">\r\n<p class=\"textbox__title\">Exercise 2<\/p>\r\n\r\n<\/header>\r\n<div class=\"textbox__content\">\r\n\r\n<strong>Subtract and simplify the answers.<\/strong>\r\n<ol class=\"twocolumn bigspace\" type=\"a\">\r\n \t<li>[latex]\\begin{array}{rr}&amp;\\dfrac{5}{6}\\\\-&amp;\\dfrac{2}{3}\\\\ \\hline&amp;\\dfrac{1}{6}\\end{array}[\/latex]<\/li>\r\n \t<li>[latex]\\begin{array}{rr}&amp;\\dfrac{9}{10}\\\\-&amp;\\dfrac{1}{5}\\\\ \\hline&amp;\\dfrac{7}{10}\\end{array}[\/latex]<\/li>\r\n \t<li>[latex]\\begin{array}{rr}&amp;\\dfrac{1}{4}\\\\-&amp;\\dfrac{1}{12}\\\\ \\hline&amp;\\end{array}[\/latex]<\/li>\r\n \t<li>[latex]\\begin{array}{rr}&amp;\\dfrac{7}{10}\\\\-&amp;\\dfrac{3}{5}\\\\ \\hline&amp;\\end{array}[\/latex]<\/li>\r\n \t<li>[latex]\\begin{array}{rr}&amp;\\dfrac{15}{16}\\\\-&amp;\\dfrac{5}{8}\\\\ \\hline&amp;\\end{array}[\/latex]<\/li>\r\n \t<li>[latex]\\begin{array}{rr}&amp;\\dfrac{7}{16}\\\\-&amp;\\dfrac{1}{4}\\\\ \\hline&amp;\\end{array}[\/latex]<\/li>\r\n \t<li>[latex]\\begin{array}{rr}&amp;\\dfrac{3}{8}\\\\-&amp;\\dfrac{1}{4}\\\\ \\hline&amp;\\end{array}[\/latex]<\/li>\r\n \t<li>[latex]\\begin{array}{rr}&amp;\\dfrac{5}{6}\\\\-&amp;\\dfrac{1}{2}\\\\ \\hline&amp;\\end{array}[\/latex]<\/li>\r\n \t<li>[latex]\\begin{array}{rr}&amp;\\dfrac{7}{8}\\\\-&amp;\\dfrac{1}{2}\\\\ \\hline&amp;\\end{array}[\/latex]<\/li>\r\n \t<li>[latex]\\begin{array}{rr}&amp;\\dfrac{5}{8}\\\\-&amp;\\dfrac{1}{3}\\\\ \\hline&amp;\\end{array}[\/latex]<\/li>\r\n \t<li>[latex]\\begin{array}{rr}&amp;\\dfrac{2}{3}\\\\-&amp;\\dfrac{1}{8}\\\\ \\hline&amp;\\end{array}[\/latex]<\/li>\r\n \t<li>[latex]\\begin{array}{rr}&amp;\\dfrac{5}{12}\\\\-&amp;\\dfrac{1}{4}\\\\ \\hline&amp;\\end{array}[\/latex]<\/li>\r\n \t<li>[latex]\\begin{array}{rr}&amp;\\dfrac{1}{2}\\\\-&amp;\\dfrac{1}{6}\\\\ \\hline&amp;\\end{array}[\/latex]<\/li>\r\n \t<li>[latex]\\begin{array}{rr}&amp;\\dfrac{3}{4}\\\\-&amp;\\dfrac{1}{10}\\\\ \\hline&amp;\\end{array}[\/latex]<\/li>\r\n \t<li>[latex]\\begin{array}{rr}&amp;\\dfrac{1}{8}\\\\-&amp;\\dfrac{1}{16}\\\\ \\hline&amp;\\end{array}[\/latex]<\/li>\r\n \t<li>[latex]\\begin{array}{rr}&amp;\\dfrac{4}{5}\\\\-&amp;\\dfrac{1}{2}\\\\ \\hline&amp;\\end{array}[\/latex]<\/li>\r\n<\/ol>\r\n<strong>Answers to Exercise 2<\/strong>\r\n<ol class=\"threecolumn\" start=\"3\" type=\"a\">\r\n \t<li>[latex]\\dfrac{1}{6}[\/latex]<\/li>\r\n \t<li>[latex]\\dfrac{1}{10}[\/latex]<\/li>\r\n \t<li>[latex]\\dfrac{5}{16}[\/latex]<\/li>\r\n \t<li>[latex]\\dfrac{3}{16}[\/latex]<\/li>\r\n \t<li>[latex]\\dfrac{1}{8}[\/latex]<\/li>\r\n \t<li>[latex]\\dfrac{1}{3}[\/latex]<\/li>\r\n \t<li>[latex]\\dfrac{3}{8}[\/latex]<\/li>\r\n \t<li>[latex]\\dfrac{7}{24}[\/latex]<\/li>\r\n \t<li>[latex]\\dfrac{13}{24}[\/latex]<\/li>\r\n \t<li>[latex]\\dfrac{1}{6}[\/latex]<\/li>\r\n \t<li>[latex]\\dfrac{1}{3}[\/latex]<\/li>\r\n \t<li>[latex]\\dfrac{13}{20}[\/latex]<\/li>\r\n \t<li>[latex]\\dfrac{1}{16}[\/latex]<\/li>\r\n \t<li>[latex]\\dfrac{3}{10}[\/latex]<\/li>\r\n<\/ol>\r\n<\/div>\r\n<\/div>\r\n<p style=\"break-before: page;\"><strong>Subtracting mixed numbers<\/strong> is very similar to adding mixed numbers.<\/p>\r\n\r\n<div class=\"textbox\">\r\n<ul>\r\n \t<li>Find the least common denominator if the fractions do not have the same denominator already.<\/li>\r\n \t<li>Rename the fractions as equivalent fractions using the <strong>LCD. Don\u2019t forget to keep whole number with the problem.<\/strong><\/li>\r\n \t<li>Subtract the second denominator from the first. Keep the same denominator. Subtract the whole numbers.<\/li>\r\n \t<li>Simplify the answer.<\/li>\r\n<\/ul>\r\n<\/div>\r\n<div class=\"textbox textbox--examples\"><header class=\"textbox__header\">\r\n<p class=\"textbox__title\">Example D<\/p>\r\n\r\n<\/header>\r\n<div class=\"textbox__content\">[latex]\\begin{array}{rrr}&amp;4\\dfrac{1}{2}\\left(\\dfrac{\\times3}{\\times3}\\right)&amp;=&amp;4\\dfrac{3}{6}&amp;\\\\-&amp;3\\dfrac{1}{6}&amp;=&amp; 3\\dfrac{1}{6}\\\\ \\hline\\\\&amp;&amp;&amp;1\\dfrac{2}{6}&amp;=1\\dfrac{1}{3} \\end{array}[\/latex]<\/div>\r\n<\/div>\r\n<div class=\"textbox textbox--examples\"><header class=\"textbox__header\">\r\n<p class=\"textbox__title\">Example E<\/p>\r\n\r\n<\/header>\r\n<div class=\"textbox__content\">[latex]\\begin{array}{rrr}&amp;12\\dfrac{3}{4}\\left(\\dfrac{\\times3}{\\times3}\\right)&amp;=&amp;12\\dfrac{9}{12}\\\\-&amp;\\dfrac{2}{3}\\left(\\dfrac{\\times4}{\\times4}\\right)&amp;=&amp; \\dfrac{8}{12}\\\\ \\hline\\\\&amp;&amp;&amp;12\\dfrac{1}{12}\\end{array}[\/latex]<\/div>\r\n<\/div>\r\n<div class=\"textbox textbox--exercises\"><header class=\"textbox__header\">\r\n<p class=\"textbox__title\">Exercise 3<\/p>\r\n\r\n<\/header>\r\n<div class=\"textbox__content\">\r\n\r\nWork through all these questions carefully.\r\n<ol class=\"twocolumn bigspace\" type=\"a\">\r\n \t<li>[latex]\\begin{array}{rrr}&amp;16\\dfrac{2}{3}=&amp;16\\dfrac{16}{24}\\\\-&amp;4\\dfrac{3}{8}=&amp;4\\dfrac{9}{24}\\\\ \\hline\\\\&amp;&amp;12\\dfrac{7}{24}\\end{array}[\/latex]<\/li>\r\n \t<li>[latex]\\begin{array}{rr}&amp;9\\dfrac{7}{12}\\\\-&amp;9\\dfrac{5}{12}\\\\ \\hline&amp;\\end{array}[\/latex]<\/li>\r\n \t<li>[latex]\\begin{array}{rr}&amp;6\\dfrac{3}{4}\\\\-&amp;2\\dfrac{1}{3}\\\\ \\hline&amp;\\end{array}[\/latex]<\/li>\r\n \t<li>[latex]\\begin{array}{rr}&amp;22\\dfrac{5}{6}\\\\-&amp;18\\dfrac{2}{5}\\\\ \\hline&amp;\\end{array}[\/latex]<\/li>\r\n \t<li>[latex]\\begin{array}{rr}&amp;3\\dfrac{7}{8}\\\\-&amp;2\\dfrac{3}{4}\\\\ \\hline&amp;\\end{array}[\/latex]<\/li>\r\n \t<li>[latex]\\begin{array}{rr}&amp;1\\dfrac{7}{10}\\\\-&amp;\\dfrac{1}{2}\\\\ \\hline&amp;\\end{array}[\/latex]<\/li>\r\n \t<li>[latex]\\begin{array}{rr}&amp;9\\dfrac{1}{4}\\\\-&amp;7\\\\ \\hline&amp;\\end{array}[\/latex]<\/li>\r\n \t<li>[latex]\\begin{array}{rr}&amp;1\\dfrac{5}{8}\\\\-&amp;\\dfrac{1}{3}\\\\ \\hline&amp;\\end{array}[\/latex]<\/li>\r\n \t<li>[latex]\\begin{array}{rr}&amp;19\\dfrac{5}{6}\\\\-&amp;11\\dfrac{5}{12}\\\\ \\hline&amp;\\end{array}[\/latex]<\/li>\r\n<\/ol>\r\n<\/div>\r\n<div class=\"textbox__content\">\r\n\r\n<strong>Answ<\/strong><strong>er<\/strong><strong>s to Exercise 3<\/strong>\r\n<ol class=\"threecolumn\" start=\"2\" type=\"a\">\r\n \t<li>[latex]\\dfrac{1}{6}[\/latex]<\/li>\r\n \t<li>[latex]4\\dfrac{5}{12}[\/latex]<\/li>\r\n \t<li>[latex]4\\dfrac{13}{30}[\/latex]<\/li>\r\n \t<li>[latex]1\\dfrac{1}{8}[\/latex]<\/li>\r\n \t<li>[latex]1\\dfrac{1}{5}[\/latex]<\/li>\r\n \t<li>[latex]2\\dfrac{1}{4}[\/latex]<\/li>\r\n \t<li>[latex]1\\dfrac{7}{24}[\/latex]<\/li>\r\n \t<li>[latex]8\\dfrac{5}{12}[\/latex]<\/li>\r\n<\/ol>\r\n<\/div>\r\n<\/div>\r\n<h1>Subtracting Mixed Numbers from Whole Numbers<\/h1>\r\nThis is the start of a new process! You already have all the skills to do this, but the process is new.\r\n<div class=\"textbox textbox--examples\"><header class=\"textbox__header\">\r\n<p class=\"textbox__title\">Example F<\/p>\r\n\r\n<\/header>\r\n<div class=\"textbox__content\">\r\n\r\n<strong>Let's look at some apples.<\/strong>\r\n\r\nYou have 3 whole apples and you want to give your son 1 apple and your daughter half an apple. How will you do this?\r\n<p style=\"text-align: center;\"><img class=\"aligncenter wp-image-181 size-full\" style=\"text-align: start;\" src=\"https:\/\/opentextbc.ca\/busstatsancillary\/wp-content\/uploads\/sites\/437\/2023\/08\/Picture-4-1-e1680809952450.png\" alt=\"Row of 3 apples.\" width=\"412\" height=\"108\" \/><\/p>\r\n<p style=\"break-before: page;\">Yes! You will cut one apple in half.<\/p>\r\n\r\n<\/div>\r\n<img class=\"aligncenter wp-image-182 size-full\" src=\"https:\/\/opentextbc.ca\/busstatsancillary\/wp-content\/uploads\/sites\/437\/2023\/08\/Picture-4-2-e1680810013273.png\" alt=\"Row of 3 apples. Last apple is cut into two pieces.\" width=\"419\" height=\"108\" \/>\r\n<div class=\"textbox__content\">\r\n\r\nNow you have [latex]2 \\tfrac{2}{2}[\/latex] apples. And you can easily give away [latex]1 \\tfrac{1}{2}[\/latex] of them. Cross out [latex]1 \\tfrac{1}{2}[\/latex] apples in the drawing. How much is left?\r\n\r\nHere is the arithmetic for what you just did.\r\n<p style=\"text-align: center;\">[latex]3=2\\dfrac{2}{2}-1\\dfrac{1}{2}=1\\dfrac{1}{2}[\/latex]<\/p>\r\n[latex]1\\tfrac{1}{2} [\/latex]apples are left\r\n\r\n<\/div>\r\n<\/div>\r\n<div class=\"textbox textbox--examples\"><header class=\"textbox__header\">\r\n<p class=\"textbox__title\">Example G<\/p>\r\n\r\n<\/header>\r\n<div class=\"textbox__content\">\r\n\r\nHere are 6 cans of pop to share among your friends.\r\n\r\n<img class=\"aligncenter wp-image-183 size-full\" src=\"https:\/\/opentextbc.ca\/busstatsancillary\/wp-content\/uploads\/sites\/437\/2023\/08\/Picture-4-3.png\" alt=\"6 cans of pop\" width=\"502\" height=\"194\" \/>\r\n\r\n4 people want a whole can, but one person is on a diet and only wants [latex]\\tfrac{1}{4}[\/latex] of a can. How much pop will be left?\r\n\r\nWhat will you do? You will open a can and think of that can as [latex]\\tfrac{4}{4}[\/latex].\r\n\r\n<\/div>\r\n<p style=\"text-align: center;\"><img class=\"aligncenter wp-image-184 size-full\" src=\"https:\/\/opentextbc.ca\/busstatsancillary\/wp-content\/uploads\/sites\/437\/2023\/08\/Picture-4-4.png\" alt=\"6 cans of pop. Last can is divided in 4.\" width=\"553\" height=\"199\" \/><\/p>\r\n\r\n<div class=\"textbox__content\">\r\n\r\nYou have [latex]5 \\tfrac{4}{4} [\/latex] cans of pop and you can give out 4 whole cans and [latex]\\tfrac{1}{4}[\/latex] can of pop. Cross out the 4 whole cans and [latex]\\tfrac{1}{4}[\/latex] of a can in the drawing.\r\n\r\nHow many cans are left?\r\n\r\nHere is the arithmetic:\r\n<p style=\"text-align: center;\">[latex]\\begin{array}{rr} 6 =&amp; 5 \\dfrac{4}{4} \\\\ -&amp; 4\\dfrac{1}{4} \\\\ \\hline &amp; 1 \\dfrac{3}{4} \\end{array}[\/latex]<\/p>\r\n\r\n<\/div>\r\n<\/div>\r\n<div class=\"textbox textbox--examples\"><header class=\"textbox__header\">\r\n<p class=\"textbox__title\">Example H<\/p>\r\n\r\n<\/header>\r\n<div class=\"textbox__content\">\r\n\r\nDraw five apple pies. If you plan to give away [latex]3\\dfrac{2}{3}[\/latex] of the pies, how many pies are you keeping?\r\n\r\nTo do that, cut one pie into thirds. Then cross out 3 whole pies and [latex]\\dfrac{2}{3}[\/latex].\r\n\r\nHere is the arithmetic:\r\n<p style=\"text-align: center;\">[latex]\\begin{array}{rr}5=&amp;4\\dfrac{3}{3}\\\\-&amp;3\\dfrac{2}{3}\\\\ \\hline&amp;1\\dfrac{1}{3}&amp;\\text{pies kept}\\end{array}[\/latex]<\/p>\r\n\r\n<\/div>\r\n<\/div>\r\nRemember [latex]1 = \\dfrac{1}{1} = \\dfrac{2}{2} = \\dfrac{3}{3} = \\dfrac{4}{4} = \\dfrac{5}{5} = \\dfrac{6}{6} =\\dfrac{7}{7} = \\dfrac{8}{8} = \\dfrac{9}{9} =\\dfrac{10}{10}[\/latex] and so on.\r\n\r\n<strong>T<\/strong><strong>o subtract a mixed number from a whole number, follow these steps:<\/strong>\r\n<ol>\r\n \t<li>\"Borrow\" <strong>one<\/strong> from the whole number.<\/li>\r\n \t<li>Rewrite the one as an improper fraction with the same denominator as the fraction you are subtracting from the whole number. <strong>(Remember to change the whole number to one less.)<\/strong><\/li>\r\n \t<li>Subtract the mixed numbers.<\/li>\r\n<\/ol>\r\n<div class=\"textbox textbox--examples\"><header class=\"textbox__header\">\r\n<p class=\"textbox__title\">Example I<\/p>\r\n\r\n<\/header>\r\n<div class=\"textbox__content\">\r\n\r\n[latex]18 - 12 \\dfrac{3}{4} =[\/latex]\r\n\r\n\"Borrow\" 1 from 18 and change to [latex]\\tfrac{4}{4}[\/latex].\r\n<p style=\"text-align: center;\">[latex]\\begin{array}{rr} \\cancel{18}17 = &amp; 17 \\dfrac{4}{4} \\\\ -&amp; 12 \\dfrac{3}{4} \\\\ \\hline &amp; 5 \\dfrac{1}{4} \\end{array}[\/latex]<\/p>\r\nTry it yourself:\r\n\r\n[latex]1 - \\dfrac{4}{5} =[\/latex]\r\n\r\n<\/div>\r\n<\/div>\r\n<div class=\"textbox textbox--exercises\" style=\"break-before: page;\"><header class=\"textbox__header\">\r\n<p class=\"textbox__title\">Exercise 4<\/p>\r\n\r\n<\/header>\r\n<div class=\"textbox__content\">\r\n\r\nSubtract and express in lowest terms. <strong>TIP:<\/strong> Remember to change your whole number to a mixed numeral.\r\n<ol class=\"twocolumn bigspace\" type=\"a\">\r\n \t<li>[latex]\\begin{array}{rr}5=&amp;4\\dfrac{2}{2}\\\\-&amp;1\\dfrac{1}{2}\\\\ \\hline&amp;3\\dfrac{1}{2}\\end{array}[\/latex]<\/li>\r\n \t<li>[latex]\\begin{array}{rr}&amp;9\\\\-&amp;4\\dfrac{3}{10}\\\\ \\hline&amp;\\end{array}[\/latex]<\/li>\r\n \t<li>[latex]\\begin{array}{rr}&amp;12\\\\-&amp;11\\dfrac{5}{8}\\\\ \\hline&amp;\\end{array}[\/latex]<\/li>\r\n \t<li>[latex]\\begin{array}{rr}&amp;25\\\\-&amp;20\\dfrac{1}{4}\\\\ \\hline&amp;\\end{array}[\/latex]<\/li>\r\n \t<li>[latex]\\begin{array}{rr}&amp;3\\\\-&amp;2\\dfrac{2}{3}\\\\ \\hline&amp;\\end{array}[\/latex]<\/li>\r\n \t<li>[latex]\\begin{array}{rr}&amp;8\\\\-&amp;\\dfrac{3}{4}\\\\ \\hline&amp;\\end{array}[\/latex]<\/li>\r\n \t<li>[latex]\\begin{array}{rr}&amp;32\\\\-&amp;28\\dfrac{1}{2}\\\\ \\hline&amp;\\end{array}[\/latex]<\/li>\r\n \t<li>[latex]\\begin{array}{rr}&amp;5\\\\-&amp;3\\dfrac{1}{3}\\\\ \\hline&amp;\\end{array}[\/latex]<\/li>\r\n \t<li>[latex]\\begin{array}{rr}&amp;8\\\\-&amp;4\\dfrac{4}{9}\\\\ \\hline&amp;\\end{array}[\/latex]<\/li>\r\n<\/ol>\r\n<strong>Answers to Exercise 4<\/strong>\r\n<ol class=\"threecolumn\" start=\"2\" type=\"a\">\r\n \t<li>[latex]4\\dfrac{7}{10}[\/latex]<\/li>\r\n \t<li>[latex]\\dfrac{3}{8}[\/latex]<\/li>\r\n \t<li>[latex]4\\dfrac{3}{4}[\/latex]<\/li>\r\n \t<li>[latex]\\dfrac{1}{3}[\/latex]<\/li>\r\n \t<li>[latex]7\\dfrac{1}{4}[\/latex]<\/li>\r\n \t<li>[latex]3\\dfrac{1}{2}[\/latex]<\/li>\r\n \t<li>[latex]1\\dfrac{2}{3}[\/latex]<\/li>\r\n \t<li>[latex]3\\dfrac{5}{9}[\/latex]<\/li>\r\n<\/ol>\r\n<\/div>\r\n<\/div>\r\n<h1>Renaming to Subtract Mixed Numbers<\/h1>\r\n<div class=\"textbox textbox--examples\"><header class=\"textbox__header\">\r\n<p class=\"textbox__title\">Example J<\/p>\r\n\r\n<\/header>\r\n<div class=\"textbox__content\">\r\n\r\nLook at the [latex]3\\tfrac{1}{4}[\/latex] chocolate bars.\r\n\r\n<img class=\"aligncenter wp-image-185 size-full\" src=\"https:\/\/opentextbc.ca\/busstatsancillary\/wp-content\/uploads\/sites\/437\/2023\/08\/Picture-4-5.png\" alt=\"3 whole chocolate bars. One quarter of a bar.\" width=\"574\" height=\"65\" \/>\r\n\r\nYou need to give [latex]2\\tfrac{3}{4}[\/latex] chocolate bars to the kids on the soccer team. How will you do this?\r\n\r\nYou will have to cut up one of the whole chocolate bars into 4 pieces, or [latex]\\tfrac{4}{4}[\/latex].\r\n\r\n<\/div>\r\n<p style=\"text-align: center;\"><img class=\"aligncenter wp-image-186 size-full\" title=\"2 whole chocolate bars. 4 quarters of a chocolate bar. One quarter of a chocolate bar.\" src=\"https:\/\/opentextbc.ca\/busstatsancillary\/wp-content\/uploads\/sites\/437\/2023\/08\/Picture-4-6.png\" alt=\"2 whole chocolate bars. 4 quarters of a chocolate bar. One quarter of a chocolate bar.\" width=\"613\" height=\"71\" data-popupalt-original-title=\"null\" \/><\/p>\r\n\r\n<div class=\"textbox__content\">\r\n\r\nNow you have 2 whole bars, [latex]\\tfrac{4}{4}[\/latex] of a bar and [latex]\\tfrac{1}{4}[\/latex] of a bar which equals [latex]2\\tfrac{5}{4}[\/latex] of a bar. It will be easy to give away (subtract) [latex]2\\tfrac{3}{4}[\/latex] bars. Cross out [latex]2\\tfrac{3}{4}[\/latex] bars. How much is left?\r\n\r\nHere is the arithmetic:\r\n\r\n[latex]3\\dfrac{1}{4}-2\\dfrac{3}{4}=[\/latex]\r\n\r\n[latex]\\begin{array}{rrr} 3 \\dfrac{1}{4} = &amp; 2 \\dfrac{4}{4} + \\dfrac{1}{4} = &amp; 2 \\dfrac{5}{4} \\\\ &amp; - &amp; 2 \\dfrac{3}{4} \\\\ \\hline &amp;&amp; \\dfrac{2}{4} &amp; = \\dfrac{1}{2} \\text{ chocolate bar left} \\end{array}[\/latex]\r\n\r\n<\/div>\r\n<\/div>\r\n<div class=\"textbox textbox--examples\"><header class=\"textbox__header\">\r\n<p class=\"textbox__title\">Example K<\/p>\r\n\r\n<\/header>\r\n<div class=\"textbox__content\">\r\n\r\nLook at these [latex]5\\dfrac{1}{8}[\/latex] cherry pies.\r\n\r\n<img class=\"size-medium wp-image-187 aligncenter\" title=\"Illustration of 5 cherry pies and one slice that is one eighth of a pie\" src=\"https:\/\/opentextbc.ca\/busstatsancillary\/wp-content\/uploads\/sites\/437\/2023\/08\/Picture-4-7-300x117.png\" alt=\"Illustration of 5 cherry pies and one slice that is one eighth of a pie\" width=\"300\" height=\"117\" data-popupalt-original-title=\"null\" \/>\r\n\r\nYou promised to send [latex]3\\dfrac{5}{8}[\/latex] pies to the spring party at school. How will you do this?\r\n\r\nCut one of the whole pies into eighths.\r\n\r\n<img class=\"size-medium wp-image-188 aligncenter\" title=\"Illustration of four cherry pies, plain. One cherry pie with cross hashes indicating eighths lines. And then a slice of pie that is one eighth. Illustration of problem to solve. \" src=\"https:\/\/opentextbc.ca\/busstatsancillary\/wp-content\/uploads\/sites\/437\/2023\/08\/Picture-4-8-300x111.png\" alt=\"Illustration of four cherry pies, plain. One cherry pie with cross hashes indicating eighths lines. And then a slice of pie that is one eighth. Illustration of problem to solve. \" width=\"300\" height=\"111\" data-popupalt-original-title=\"null\" \/>\r\n\r\nThen, cross out [latex]3\\dfrac{5}{8}[\/latex] pies.\r\n\r\nHow much pie is left?\r\n\r\n[latex]\\begin{array}{rr} 5\\dfrac{1}{8}=4\\dfrac{8}{8}+\\dfrac{1}{8}=&amp;4\\dfrac{9}{8}\\\\\r\n-&amp;3\\dfrac{5}{8}\\\\\r\n\\hline\r\n&amp;1\\dfrac{4}{8}&amp;=1\\dfrac{1}{2}\\text{ pies left}\\end{array}[\/latex]\r\n\r\n<\/div>\r\n<\/div>\r\n<h1>Steps for rewriting a mixed number for subtraction<\/h1>\r\n<ol>\r\n \t<li>Check to see if rewriting is needed. That is, check that the fraction in the mixed number you are starting with is less than the fraction you want to take away.\r\n<ul>\r\n \t<li>Question: [latex]4\\dfrac{1}{3}-2\\dfrac{2}{3}[\/latex]<\/li>\r\n \t<li>[latex]\\dfrac{1}{3}\\text{ is less than }\\dfrac{2}{3}[\/latex]<\/li>\r\n<\/ul>\r\n<\/li>\r\n \t<li>\"Borrow\" 1 from the whole number in the first mixed number. TIP: Remember to change the whole number to 1 less.<\/li>\r\n \t<li>Rewrite the \"borrowed\" 1 as an improper fraction with the same denominator as the other fractions.\r\n<ul>\r\n \t<li>[latex]4\\dfrac{1}{3}=3\\dfrac{3}{3}+\\dfrac{1}{3}[\/latex]<\/li>\r\n \t<li>[latex]\\dfrac{3}{3}[\/latex] is the 1 that you borrowed from the 4.<\/li>\r\n<\/ul>\r\n<\/li>\r\n \t<li>Add the rewritten 1 to the fraction that is part of the same mixed number.\r\n<ul>\r\n \t<li>[latex]3\\dfrac{3}{3}+\\dfrac{1}{3}=3\\dfrac{4}{3}[\/latex]<\/li>\r\n<\/ul>\r\n<\/li>\r\n \t<li>Subtract as usual, expressing your answer in lowest terms.\r\n<ul>\r\n \t<li>[latex]\\begin{array}{rrr}&amp;4\\dfrac{1}{3}=&amp;3\\dfrac{4}{3}\\\\-&amp;2\\dfrac{2}{3}=&amp;2\\dfrac{2}{3}\\\\ \\hline&amp;&amp;1\\dfrac{2}{3}\\end{array}[\/latex]<\/li>\r\n<\/ul>\r\n<\/li>\r\n<\/ol>\r\n<div>\r\n<div class=\"textbox textbox--examples\" style=\"break-before: page;\"><header class=\"textbox__header\">\r\n<p class=\"textbox__title\">Example L<\/p>\r\n\r\n<\/header>\r\n<div class=\"textbox__content\">\r\n\r\n[latex]5\\dfrac{2}{5}-2\\dfrac{4}{5}[\/latex]\r\n\r\n<strong>Step 1: <\/strong>[latex]\\dfrac{2}{5}[\/latex] is less than [latex]\\dfrac{4}{5}[\/latex], so it's necessary to rewrite.\r\n\r\n<strong>Step 2 and 3:<\/strong> Borrow 1.\r\n\r\n[latex]5\\dfrac{2}{5}=4\\dfrac{5}{5}+\\dfrac{2}{5}=4\\dfrac{7}{5}[\/latex]\r\n\r\n<strong>Step 4 and 5:<\/strong>\r\n\r\n[latex]\\begin{array}{rr}5\\dfrac{2}{5}=&amp;4\\dfrac{5}{5}+\\dfrac{2}{5}=&amp;4\\dfrac{7}{5} \\\\ -&amp;2\\dfrac{4}{5}=&amp;2\\dfrac{4}{5}\\\\\\hline&amp;&amp;2\\dfrac{3}{5}\\end{array}[\/latex]\r\n\r\n<\/div>\r\n<\/div>\r\n<\/div>\r\n<div class=\"textbox textbox--examples\"><header class=\"textbox__header\">\r\n<p class=\"textbox__title\">Example M<\/p>\r\n\r\n<\/header>\r\n<div class=\"textbox__content\">\r\n\r\n[latex]1\\dfrac{2}{4}-\\dfrac{3}{4}[\/latex]\r\n\r\n<strong>Step 1:<\/strong> [latex]\\dfrac{2}{4}[\/latex] is less than [latex]\\dfrac{3}{4}[\/latex], so we need to rewrite to subtract.\r\n\r\n<strong>Step 2, 3, 4 and 5:<\/strong>\r\n\r\n[latex]\\begin{array}{rrr}1\\dfrac{2}{4} =&amp;\\dfrac{4}{4} +\\dfrac{2}{4}=&amp;\\dfrac{6}{4} \\\\ -&amp; \\dfrac{3}{4} =&amp; \\dfrac{3}{4} \\\\ \\hline &amp;&amp;\\dfrac{3}{4} \\end{array}[\/latex]\r\n\r\n<\/div>\r\n<\/div>\r\n<div class=\"textbox textbox--exercises\"><header class=\"textbox__header\">\r\n<p class=\"textbox__title\">Exercise 5<\/p>\r\n\r\n<\/header>\r\n<div class=\"textbox__content\">\r\n\r\nSubtract. Be sure the answers are in lowest terms.\r\n<ol class=\"twocolumn bigspace\" type=\"a\">\r\n \t<li>[latex]\\begin{array}{rrr}20\\dfrac{1}{4} =&amp; 19 \\dfrac{5}{4}\\\\-&amp;10\\dfrac{3}{4}\\\\ \\hline&amp;9\\dfrac{2}{4}&amp;=9\\dfrac{1}{2} \\end{array}[\/latex]<\/li>\r\n \t<li>[latex]\\begin{array}{rr}&amp;3\\dfrac{1}{3}\\\\-&amp;1\\dfrac{2}{3}\\\\ \\hline&amp;\\end{array}[\/latex]<\/li>\r\n \t<li>[latex]\\begin{array}{rr}&amp;56\\dfrac{2}{5}\\\\-&amp;20\\dfrac{4}{5}\\\\ \\hline&amp;\\end{array}[\/latex]<\/li>\r\n \t<li>[latex]\\begin{array}{rr}&amp;8\\dfrac{1}{3}\\\\-&amp;1\\dfrac{2}{3}\\\\ \\hline&amp;\\end{array}[\/latex]<\/li>\r\n \t<li>[latex]\\begin{array}{rr}&amp;4\\dfrac{1}{5}\\\\-&amp;2\\dfrac{3}{5}\\\\ \\hline&amp;\\end{array}[\/latex]<\/li>\r\n \t<li>[latex]\\begin{array}{rr}&amp;5\\dfrac{2}{7}\\\\-&amp;1\\dfrac{3}{7}\\\\ \\hline&amp;\\end{array}[\/latex]<\/li>\r\n \t<li>[latex]\\begin{array}{rr}&amp;12\\dfrac{5}{9}\\\\-&amp;10\\dfrac{7}{9}\\\\ \\hline&amp;\\end{array}[\/latex]<\/li>\r\n \t<li>\u00a0[latex]\\begin{array}{rr}&amp;9\\dfrac{3}{5}\\\\-&amp;\\dfrac{4}{5}\\\\ \\hline&amp;\\end{array}[\/latex]<\/li>\r\n \t<li>[latex]\\begin{array}{rr}&amp;15\\dfrac{3}{8}\\\\-&amp;14\\dfrac{7}{8}\\\\ \\hline&amp;\\end{array}[\/latex]<\/li>\r\n<\/ol>\r\n<strong>Answers to Exercise 5<\/strong>\r\n<ol class=\"threecolumn\" start=\"2\" type=\"a\">\r\n \t<li>[latex]1\\dfrac{2}{3}[\/latex]<\/li>\r\n \t<li>[latex]35\\dfrac{3}{5}[\/latex]<\/li>\r\n \t<li>[latex]6\\dfrac{2}{3}[\/latex]<\/li>\r\n \t<li>[latex]1\\dfrac{3}{5}[\/latex]<\/li>\r\n \t<li>[latex]3\\dfrac{6}{7}[\/latex]<\/li>\r\n \t<li>[latex]1\\dfrac{7}{9}[\/latex]<\/li>\r\n \t<li>[latex]8\\dfrac{4}{5}[\/latex]<\/li>\r\n \t<li>[latex]\\dfrac{1}{2}[\/latex]<\/li>\r\n<\/ol>\r\n<\/div>\r\n<\/div>\r\nHere is the last step for subtraction of fractions. Mixed numbers to be subtracted often do not have the same denominators-they are [pb_glossary id=\"270\"]unlike fractions[\/pb_glossary].\r\n\r\nYou must\r\n<ul>\r\n \t<li>Write equivalent fractions using the LCD.<\/li>\r\n \t<li>Decide if you need to \"borrow\" or rename before you subtract.<\/li>\r\n \t<li>Subtract and simplify the answer.<\/li>\r\n<\/ul>\r\n<div class=\"textbox textbox--examples\"><header class=\"textbox__header\">\r\n<p class=\"textbox__title\">Example N<\/p>\r\n\r\n<\/header>\r\n<div class=\"textbox__content\">\r\n\r\n[latex]4\\dfrac{1}{3}-2\\dfrac{5}{6}=[\/latex]\r\n\r\n&nbsp;\r\n\r\n[latex]\\begin{array}{rrr}\r\n&amp;4\\dfrac{1}{3}=4\\dfrac{2}{6}=3\\dfrac{6}{6} + \\dfrac{2}{6}=&amp;3\\dfrac{8}{6}\\\\&amp;-&amp;2\\dfrac{5}{6}\\\\ \\hline&amp;&amp;1\\dfrac{3}{6}&amp;=1\\dfrac{1}{2}\\end{array}[\/latex]\r\n\r\n<\/div>\r\n<\/div>\r\n<div class=\"textbox textbox--examples\"><header class=\"textbox__header\">\r\n<p class=\"textbox__title\">Example O<\/p>\r\n\r\n<\/header>\r\n<div class=\"textbox__content\">\r\n\r\n[latex]9\\dfrac{1}{10} - 4\\dfrac{1}{4}=[\/latex]\r\n\r\n&nbsp;\r\n\r\n[latex]\\begin{array}{rrrr}9\\dfrac{1}{10}=&amp;9\\dfrac{2}{20}=&amp;8\\dfrac{20}{20} + \\dfrac{2}{20}= &amp;8\\dfrac{22}{20}\\\\ -&amp;4\\dfrac{1}{4} = &amp;4\\dfrac{5}{20} =&amp; 4\\dfrac{5}{20}\\\\ \\hline&amp;&amp;&amp;4\\dfrac{17}{20}\\end{array}[\/latex]\r\n\r\n<\/div>\r\n<\/div>\r\n<div class=\"textbox textbox--exercises\" style=\"break-before: page;\"><header class=\"textbox__header\">\r\n<p class=\"textbox__title\">Exercise 6<\/p>\r\n\r\n<\/header>\r\n<div class=\"textbox__content\">\r\n\r\nSubtract. Be sure the answers are in lowest terms.\r\n<ol class=\"twocolumn bigspace\" type=\"a\">\r\n \t<li>[latex]\\begin{array}{rr}&amp;9\\dfrac{3}{8}=&amp;9\\dfrac{3}{8}=&amp;8\\dfrac{11}{8}\\\\-&amp;7\\dfrac{1}{2}=&amp;7\\dfrac{4}{8}=&amp;7\\dfrac{4}{8}\\\\ \\hline&amp;&amp;&amp; 1 \\dfrac{7}{8} \\end{array}[\/latex]<\/li>\r\n \t<li>[latex]\\begin{array}{rr}&amp;7\\dfrac{1}{16}\\\\-&amp;4\\dfrac{1}{8}\\\\ \\hline&amp;\\end{array}[\/latex]<\/li>\r\n \t<li>[latex]\\begin{array}{rr}&amp;15\\dfrac{1}{6}\\\\-&amp;12\\dfrac{7}{8}\\\\ \\hline&amp;\\end{array}[\/latex]<\/li>\r\n \t<li>[latex]\\begin{array}{rr}&amp;20\\dfrac{2}{6}\\\\-&amp;16\\dfrac{2}{3}\\\\ \\hline&amp;\\end{array}[\/latex]<\/li>\r\n \t<li>[latex]\\begin{array}{rr}&amp;6\\dfrac{3}{5}\\\\-&amp;4\\dfrac{1}{4}\\\\ \\hline&amp;\\end{array}[\/latex]<\/li>\r\n \t<li>[latex]\\begin{array}{rr}&amp;9\\dfrac{1}{4}\\\\-&amp;7\\dfrac{3}{8}\\\\ \\hline&amp;\\end{array}[\/latex]<\/li>\r\n \t<li>[latex]\\begin{array}{rr}&amp;5\\dfrac{1}{3}\\\\-&amp;2\\dfrac{1}{2}\\\\ \\hline&amp;\\end{array}[\/latex]<\/li>\r\n \t<li>[latex]\\begin{array}{rr}&amp;18\\dfrac{1}{6}\\\\-&amp;12\\dfrac{2}{3}\\\\ \\hline&amp;\\end{array}[\/latex]<\/li>\r\n<\/ol>\r\n<strong>Answers to Exercise 6<\/strong>\r\n<ol class=\"threecolumn\" start=\"2\" type=\"a\">\r\n \t<li>[latex]2\\dfrac{15}{16}[\/latex]<\/li>\r\n \t<li>[latex]2\\dfrac{7}{24}[\/latex]<\/li>\r\n \t<li>[latex]3\\dfrac{2}{3}[\/latex]<\/li>\r\n \t<li>[latex]2\\dfrac{7}{20}[\/latex]<\/li>\r\n \t<li>[latex]1\\dfrac{7}{8}[\/latex]<\/li>\r\n \t<li>[latex]2\\dfrac{5}{6}[\/latex]<\/li>\r\n \t<li>[latex]5\\dfrac{1}{2}[\/latex]<\/li>\r\n<\/ol>\r\n<\/div>\r\n<\/div>\r\n<div class=\"textbox textbox--exercises\"><header class=\"textbox__header\">\r\n<p class=\"textbox__title\">Exercise 7<\/p>\r\n\r\n<\/header>\r\n<div class=\"textbox__content\">\r\n\r\nA Subtraction Review.\r\n<ol class=\"twocolumn bigspace\" type=\"a\">\r\n \t<li>[latex]\\begin{array}{rr}&amp;\\dfrac{5}{8}\\\\-&amp;\\dfrac{1}{4}\\\\ \\hline&amp;\\end{array}[\/latex]<\/li>\r\n \t<li>[latex]\\begin{array}{rr}&amp;8\\dfrac{3}{4}\\\\-&amp;4\\dfrac{1}{3}\\\\ \\hline&amp;\\end{array}[\/latex]<\/li>\r\n \t<li>[latex]\\begin{array}{rr}&amp;13\\dfrac{1}{3}\\\\-&amp;12\\dfrac{5}{6}\\\\ \\hline&amp;\\end{array}[\/latex]<\/li>\r\n \t<li>[latex]\\begin{array}{rr}&amp;7\\dfrac{1}{3}\\\\-&amp;4\\dfrac{5}{6}\\\\ \\hline&amp;\\end{array}[\/latex]<\/li>\r\n \t<li>[latex]\\begin{array}{rr}&amp;9\\dfrac{1}{5}\\\\-&amp;6\\dfrac{1}{3}\\\\ \\hline&amp;\\end{array}[\/latex]<\/li>\r\n \t<li>[latex]\\begin{array}{rr}&amp;7\\\\-&amp;1\\dfrac{7}{8}\\\\ \\hline&amp;\\end{array}[\/latex]<\/li>\r\n \t<li>[latex]\\begin{array}{rr}&amp;19\\dfrac{2}{3}\\\\-&amp;18\\\\ \\hline&amp;\\end{array}[\/latex]<\/li>\r\n \t<li>[latex]\\begin{array}{rr}&amp;\\dfrac{5}{8}\\\\-&amp;\\dfrac{1}{2}\\\\ \\hline&amp;\\end{array}[\/latex]<\/li>\r\n<\/ol>\r\n<strong>Answers to Exercise 7<\/strong>\r\n<ol class=\"threecolumn\" type=\"a\">\r\n \t<li>[latex]\\dfrac{3}{8}[\/latex]<\/li>\r\n \t<li>[latex]4\\dfrac{5}{12}[\/latex]<\/li>\r\n \t<li>[latex]\\dfrac{1}{2}[\/latex]<\/li>\r\n \t<li>[latex]2\\dfrac{1}{2}[\/latex]<\/li>\r\n \t<li>[latex]2\\dfrac{13}{15}[\/latex]<\/li>\r\n \t<li>[latex]5\\dfrac{1}{8}[\/latex]<\/li>\r\n \t<li>[latex]1\\dfrac{2}{3}[\/latex]<\/li>\r\n \t<li>[latex]\\dfrac{1}{8}[\/latex]<\/li>\r\n<\/ol>\r\n<\/div>\r\n<\/div>\r\n<h1>Problems Using Subtraction of Common Fractions<\/h1>\r\nSubtraction problems may ask you to:\r\n<div class=\"textbox\">\r\n<ul>\r\n \t<li>find the difference between two amounts.\r\n<ul>\r\n \t<li>\"how much more is...\"<\/li>\r\n \t<li>\"how much less is...\"<\/li>\r\n<\/ul>\r\n<\/li>\r\n \t<li>take away, give away, or lose.<\/li>\r\n<\/ul>\r\n<ul>\r\n \t<li>decide how much is left or how much remains.<\/li>\r\n<\/ul>\r\n<\/div>\r\nRead over the subtraction problems that you did in Unit Two with decimals. The wording and problem situations will be similar.\r\n\r\nDrawing a sketch and estimating the answer using whole numbers may also be helpful.\r\n<div class=\"textbox textbox--exercises\"><header class=\"textbox__header\">\r\n<p class=\"textbox__title\">Exercise 8<\/p>\r\n\r\n<\/header>\r\n<div class=\"textbox__content\">\r\n<ol type=\"a\">\r\n \t<li>The New Earth Diaper Company stocks went from [latex]5\\tfrac{7}{8}[\/latex] to [latex]7\\tfrac{3}{8} [\/latex]this week. How much did the stocks increase in value?<\/li>\r\n \t<li>Jean is knitting an afghan which will be made from 5 long pieces. She has finished [latex]3\\tfrac{2}{3}[\/latex] of the pieces. How many pieces does she still have to knit?<\/li>\r\n \t<li>Dave said he worked in the garden for [latex]6\\tfrac{1}{4}[\/latex] hours, but his wife saw him snoozing under a tree for [latex]1\\tfrac{1}{2}[\/latex] hours! How long did Dave really work?<\/li>\r\n \t<li>Maureen left [latex]\\tfrac{2}{3}[\/latex] of a big lasagne casserole in the fridge hoping it would be enough for a quick dinner that night. But alas, when she got home, only [latex]\\tfrac{1}{4}[\/latex] of the big lasagne casserole remained. How much of the lasagne was eaten while she was out?<\/li>\r\n \t<li>In the first half of 1992, the Bank of Canada Prime Rate dropped steadily. It started the year at [latex]8\\tfrac{1}{2}[\/latex] % and was at a low [latex]6\\tfrac{3}{4} [\/latex]% in July. How many percentage points did the prime rate drop? (Note: treat the % just like a unit in this problem.)<\/li>\r\n \t<li>Mark is [latex]1\\tfrac{3}{4}[\/latex] metres tall. His partner is [latex]1\\tfrac{1}{3}[\/latex] metres tall. How much taller is Mark than his partner?<\/li>\r\n \t<li>A teenager can drink [latex]3\\tfrac{3}{4}[\/latex] litres of water each day. If this teenager drinks [latex]2\\tfrac{1}{2}[\/latex] litres of water by lunch, how much more water will he drink in the day?<\/li>\r\n \t<li>Joan bought [latex]13\\tfrac{1}{2}[\/latex] metres to do her sewing project. She has used [latex]8\\tfrac{1}{5}[\/latex] metres so far. How much material does she have left?<\/li>\r\n<\/ol>\r\n<strong>Answers to Exercise 8<\/strong>\r\n<ol class=\"threecolumn\" type=\"a\">\r\n \t<li>[latex]1\\dfrac{1}{2}[\/latex] or $1.50<\/li>\r\n \t<li>[latex]1\\dfrac{1}{3}[\/latex] pieces<\/li>\r\n \t<li>[latex]4\\dfrac{3}{4}[\/latex] hours<\/li>\r\n \t<li>[latex]\\dfrac{5}{12}[\/latex] of the lasagna<\/li>\r\n \t<li>[latex]1\\dfrac{3}{4}[\/latex]\u00a0percentage points<\/li>\r\n \t<li>[latex]\\dfrac{5}{12}[\/latex] metres taller<\/li>\r\n \t<li>[latex]1\\dfrac{1}{4}[\/latex] litres left to drink<\/li>\r\n \t<li>[latex]5\\dfrac{3}{10}[\/latex] metres left<\/li>\r\n<\/ol>\r\n<\/div>\r\n<\/div>\r\n<h1>Topic B Self-Test<\/h1>\r\n<strong>Mark\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0 \/15\u00a0 \u00a0Aim 12\/15<\/strong>\r\n<ol type=\"A\">\r\n \t<li>Subtract these fractions. Simplify the answers when necessary (15 marks).\r\n<ol class=\"twocolumn bigspace\" type=\"a\">\r\n \t<li>[latex]\\begin{array}{rr}&amp;\\dfrac{7}{8}\\\\-&amp;\\dfrac{1}{8}\\\\ \\hline&amp;\\end{array}[\/latex]<\/li>\r\n \t<li>[latex]\\begin{array}{rr}&amp;\\dfrac{11}{15}\\\\-&amp;\\dfrac{4}{15}\\\\ \\hline&amp;\\end{array}[\/latex]<\/li>\r\n \t<li>[latex]\\begin{array}{rr}&amp;\\dfrac{7}{8}\\\\-&amp;\\dfrac{3}{16}\\\\ \\hline&amp;\\end{array}[\/latex]<\/li>\r\n \t<li>[latex]\\begin{array}{rr}&amp;\\dfrac{2}{3}\\\\-&amp;\\dfrac{1}{6}\\\\ \\hline\\end{array}[\/latex]<\/li>\r\n \t<li>[latex]\\begin{array}{rr}&amp;\\dfrac{4}{7}\\\\-&amp;\\dfrac{1}{14}\\\\ \\hline\\end{array}[\/latex]<\/li>\r\n \t<li>[latex]\\begin{array}{rr}&amp;\\dfrac{4}{5}\\\\-&amp;\\dfrac{3}{8}\\\\ \\hline\\end{array}[\/latex]<\/li>\r\n \t<li>[latex]\\begin{array}{rr}&amp;4\\\\-&amp;2\\dfrac{1}{2}\\\\ \\hline\\end{array}[\/latex]<\/li>\r\n \t<li>[latex]\\begin{array}{rr}&amp;5\\\\-&amp;4\\dfrac{7}{8}\\\\ \\hline\\end{array}[\/latex]<\/li>\r\n \t<li>[latex]\\begin{array}{rr}&amp;10\\dfrac{3}{5}\\\\-&amp;3\\dfrac{3}{10}\\\\ \\hline\\end{array}[\/latex]<\/li>\r\n \t<li>[latex]\\begin{array}{rr}&amp;7\\dfrac{1}{5}\\\\-&amp;3\\dfrac{4}{5}\\\\ \\hline\\end{array}[\/latex]<\/li>\r\n \t<li>[latex]\\begin{array}{rr}&amp;12\\dfrac{1}{8}\\\\-&amp;11\\\\ \\hline\\end{array}[\/latex]<\/li>\r\n \t<li>[latex]\\begin{array}{rr}&amp;9\\dfrac{1}{5}\\\\-&amp;\\dfrac{1}{4}\\\\ \\hline\\end{array}[\/latex]<\/li>\r\n \t<li>[latex]\\begin{array}{rr}&amp;5\\dfrac{1}{4}\\\\-&amp;1\\dfrac{2}{3}\\\\ \\hline\\end{array}[\/latex]<\/li>\r\n \t<li>[latex]\\begin{array}{rr}&amp;10\\dfrac{1}{2}\\\\-&amp;2\\dfrac{2}{5}\\\\ \\hline\\end{array}[\/latex]<\/li>\r\n \t<li>[latex]\\begin{array}{rr}&amp;6\\dfrac{2}{3}\\\\-&amp;4\\dfrac{3}{8}\\\\ \\hline\\end{array}[\/latex]<\/li>\r\n<\/ol>\r\n<\/li>\r\n<\/ol>\r\n<strong>Answers to Topic B Self-Test<\/strong>\r\n<ol class=\"threecolumn\" type=\"A\">\r\n \t<li style=\"list-style-type: none;\">\r\n<ol type=\"a\">\r\n \t<li>[latex]\\dfrac{3}{4}[\/latex]<\/li>\r\n \t<li>[latex]\\dfrac{7}{15}[\/latex]<\/li>\r\n \t<li>[latex]\\dfrac{11}{16}[\/latex]<\/li>\r\n \t<li>[latex]\\dfrac{1}{2}[\/latex]<\/li>\r\n \t<li>[latex]\\dfrac{1}{2}[\/latex]<\/li>\r\n \t<li>[latex]\\dfrac{17}{40}[\/latex]<\/li>\r\n \t<li>[latex]1\\dfrac{1}{2}[\/latex]<\/li>\r\n \t<li>[latex]\\dfrac{1}{8}[\/latex]<\/li>\r\n \t<li>[latex]7\\dfrac{3}{10}[\/latex]<\/li>\r\n \t<li>[latex]3\\dfrac{2}{5}[\/latex]<\/li>\r\n \t<li>[latex]1\\dfrac{1}{8}[\/latex]<\/li>\r\n \t<li>[latex]8\\dfrac{19}{20}[\/latex]<\/li>\r\n \t<li>[latex]3\\dfrac{7}{12}[\/latex]<\/li>\r\n \t<li>[latex]8\\dfrac{1}{10}[\/latex]<\/li>\r\n \t<li>[latex]2\\dfrac{7}{24}[\/latex]<\/li>\r\n<\/ol>\r\n<\/li>\r\n<\/ol>","rendered":"<p>Good news!<\/p>\n<p>There is only one new thing to learn in this topic. Everything else uses skills and knowledge you already have.<\/p>\n<p><strong>Let&#8217;s look at subtraction:<\/strong><\/p>\n<div class=\"textbox textbox--examples\">\n<header class=\"textbox__header\">\n<p class=\"textbox__title\">Example A<\/p>\n<\/header>\n<div class=\"textbox__content\">\n<p><img loading=\"lazy\" decoding=\"async\" class=\"size-full wp-image-179 aligncenter\" src=\"https:\/\/opentextbc.ca\/busstatsancillary\/wp-content\/uploads\/sites\/437\/2022\/10\/Picture-4-B-1.jpg\" alt=\"A rectangle divided in 5 equal parts. 4 parts and shaded and one unshaded.\" width=\"263\" height=\"63\" srcset=\"https:\/\/opentextbc.ca\/alfm5\/wp-content\/uploads\/sites\/437\/2022\/10\/Picture-4-B-1.jpg 263w, https:\/\/opentextbc.ca\/alfm5\/wp-content\/uploads\/sites\/437\/2022\/10\/Picture-4-B-1-65x16.jpg 65w, https:\/\/opentextbc.ca\/alfm5\/wp-content\/uploads\/sites\/437\/2022\/10\/Picture-4-B-1-225x54.jpg 225w\" sizes=\"auto, (max-width: 263px) 100vw, 263px\" \/><\/p>\n<p>The shaded part [latex]\\left(\\dfrac{4}{5}\\right)[\/latex] is the amount that you are starting with.<\/p>\n<p>Now cross out (pretend you are <em>taking away<\/em>) 3 shaded parts [latex]\\left(\\dfrac{3}{5}\\right)[\/latex].<\/p>\n<\/div>\n<div class=\"textbox__content\">\n<p><img loading=\"lazy\" decoding=\"async\" class=\"size-full wp-image-180 aligncenter\" src=\"https:\/\/opentextbc.ca\/busstatsancillary\/wp-content\/uploads\/sites\/437\/2023\/08\/Picture-4-B-2.jpg\" alt=\"Repeat of rectangle divided in 5 equal parts. 4 of 5 shaded. One unshaded. Three 'x' es applied to 3 of the boxes.\" width=\"267\" height=\"64\" srcset=\"https:\/\/opentextbc.ca\/alfm5\/wp-content\/uploads\/sites\/437\/2023\/08\/Picture-4-B-2.jpg 267w, https:\/\/opentextbc.ca\/alfm5\/wp-content\/uploads\/sites\/437\/2023\/08\/Picture-4-B-2-65x16.jpg 65w, https:\/\/opentextbc.ca\/alfm5\/wp-content\/uploads\/sites\/437\/2023\/08\/Picture-4-B-2-225x54.jpg 225w\" sizes=\"auto, (max-width: 267px) 100vw, 267px\" \/><\/p>\n<\/div>\n<\/div>\n<div class=\"textbox textbox--examples\" style=\"break-before: page;\">\n<header class=\"textbox__header\">\n<p class=\"textbox__title\">Example B<\/p>\n<\/header>\n<div class=\"textbox__content\">\n<p>Draw a pizza.<\/p>\n<p>&nbsp;<\/p>\n<\/div>\n<div class=\"textbox__content\">\n<ul>\n<li>Slice it into 8 equal pieces.<\/li>\n<li>Draw pieces of pineapple on 5 pieces.<\/li>\n<li>What fraction of the pizza has pineapple?\u00a0 [latex]\\dfrac{5}{8}[\/latex]<\/li>\n<li>Cross out 2 pineapple pieces to show they have been eaten.<\/li>\n<li>How much of the pineapple pizza is left?<\/li>\n<li>[latex]\\begin{array}{rrl}&\\dfrac{5}{8}&\\text{(amount you started with)}\\\\-&\\dfrac{2}{8}&\\text{(amount eaten, \"taken away\")}\\\\ \\hline&\\dfrac{3}{8}&\\text {of the pizza is left with pineapple on it}\\end{array}[\/latex]<\/li>\n<\/ul>\n<\/div>\n<\/div>\n<p>Common fractions must have the same denominator when you subtract one from the other. <strong>Subtract the numerators<\/strong> and keep the same denominators.<\/p>\n<div class=\"textbox textbox--exercises\">\n<header class=\"textbox__header\">\n<p class=\"textbox__title\">Exercise 1<\/p>\n<\/header>\n<div class=\"textbox__content\">\n<p>Subtract to find the <a class=\"glossary-term\" aria-haspopup=\"dialog\" aria-describedby=\"definition\" href=\"#term_189_277\">difference<\/a>.<\/p>\n<p>TIP: Express the difference in lowest terms.<\/p>\n<ol class=\"twocolumn bigspace\" type=\"a\">\n<li>[latex]\\begin{array}{rr}&\\dfrac{3}{5}\\\\-&\\dfrac{1}{5}\\\\\\hline&\\dfrac{2}{5}\\end{array}[\/latex]<\/li>\n<li>[latex]\\begin{array}{rrrr}&\\dfrac{7}{8} &&\\\\-&\\dfrac{3}{8}&&\\\\ \\hline &\\dfrac{4}{8}&=&\\dfrac{1}{2}\\\\ \\end{array}[\/latex]<\/li>\n<li>[latex]\\begin{array}{rr}&\\dfrac{2}{3}\\\\-&\\dfrac{1}{3}\\\\ \\hline&\\end{array}[\/latex]<\/li>\n<li>[latex]\\begin{array}{rr}&\\dfrac{5}{9}\\\\-&\\dfrac{2}{9}\\\\ \\hline&\\end{array}[\/latex]<\/li>\n<li>[latex]\\begin{array}{rr}&\\dfrac{6}{7}\\\\-&\\dfrac{1}{7}\\\\ \\hline&\\end{array}[\/latex]<\/li>\n<li>[latex]\\begin{array}{rr}&\\dfrac{3}{4}\\\\-&\\dfrac{1}{4}\\\\ \\hline&\\end{array}[\/latex]<\/li>\n<li>[latex]\\begin{array}{rr}&\\dfrac{3}{2}\\\\-&\\dfrac{1}{2}\\\\ \\hline&\\end{array}[\/latex]<\/li>\n<\/ol>\n<\/div>\n<div class=\"textbox__content\">\n<p><strong>Answers to Exercise 1<\/strong><\/p>\n<ol class=\"threecolumn\" start=\"3\" type=\"a\">\n<li>[latex]\\dfrac{1}{3}[\/latex]<\/li>\n<li>[latex]\\dfrac{1}{3}[\/latex]<\/li>\n<li>[latex]\\dfrac{5}{7}[\/latex]<\/li>\n<li>[latex]\\dfrac{1}{2}[\/latex]<\/li>\n<li>[latex]\\dfrac{2}{2}[\/latex] = 1<\/li>\n<\/ol>\n<\/div>\n<\/div>\n<p>You know how to find the <strong>least common denominator (LCD)<\/strong> and to <strong>rewrite fractions in an equivalent form<\/strong> using the <strong>LCD<\/strong>.<\/p>\n<p>You must use those skills when you wish to subtract fractions with different denominators.<\/p>\n<div class=\"textbox textbox--examples\">\n<header class=\"textbox__header\">\n<p class=\"textbox__title\">Example C<\/p>\n<\/header>\n<div class=\"textbox__content\">\n<p>[latex]\\dfrac{4}{5}-\\dfrac{3}{10} =[\/latex]<\/p>\n<p>Denominators are 5 and 10. The least common multiple is 10, so the least common denominator is 10.<\/p>\n<p>[latex]\\begin{array}{rrrr}&\\dfrac{4}{5}\\left(\\dfrac{\u00d72}{\u00d72}\\right) =&\\dfrac{8}{10}&&\\text{Write equivalent fractions using the LCD}\\\\ -&\\dfrac{3}{10}=&\\dfrac{3}{10} &&\\text{Subtract the numerators}\\\\ \\hline&=&\\dfrac{5}{10}\\left(\\dfrac{\u00f75}{\u00f75}\\right)&=\\dfrac{1}{2}&\\text{Simplify the answer.}\\end{array}[\/latex]<\/p>\n<\/div>\n<\/div>\n<div class=\"textbox textbox--exercises\">\n<header class=\"textbox__header\">\n<p class=\"textbox__title\">Exercise 2<\/p>\n<\/header>\n<div class=\"textbox__content\">\n<p><strong>Subtract and simplify the answers.<\/strong><\/p>\n<ol class=\"twocolumn bigspace\" type=\"a\">\n<li>[latex]\\begin{array}{rr}&\\dfrac{5}{6}\\\\-&\\dfrac{2}{3}\\\\ \\hline&\\dfrac{1}{6}\\end{array}[\/latex]<\/li>\n<li>[latex]\\begin{array}{rr}&\\dfrac{9}{10}\\\\-&\\dfrac{1}{5}\\\\ \\hline&\\dfrac{7}{10}\\end{array}[\/latex]<\/li>\n<li>[latex]\\begin{array}{rr}&\\dfrac{1}{4}\\\\-&\\dfrac{1}{12}\\\\ \\hline&\\end{array}[\/latex]<\/li>\n<li>[latex]\\begin{array}{rr}&\\dfrac{7}{10}\\\\-&\\dfrac{3}{5}\\\\ \\hline&\\end{array}[\/latex]<\/li>\n<li>[latex]\\begin{array}{rr}&\\dfrac{15}{16}\\\\-&\\dfrac{5}{8}\\\\ \\hline&\\end{array}[\/latex]<\/li>\n<li>[latex]\\begin{array}{rr}&\\dfrac{7}{16}\\\\-&\\dfrac{1}{4}\\\\ \\hline&\\end{array}[\/latex]<\/li>\n<li>[latex]\\begin{array}{rr}&\\dfrac{3}{8}\\\\-&\\dfrac{1}{4}\\\\ \\hline&\\end{array}[\/latex]<\/li>\n<li>[latex]\\begin{array}{rr}&\\dfrac{5}{6}\\\\-&\\dfrac{1}{2}\\\\ \\hline&\\end{array}[\/latex]<\/li>\n<li>[latex]\\begin{array}{rr}&\\dfrac{7}{8}\\\\-&\\dfrac{1}{2}\\\\ \\hline&\\end{array}[\/latex]<\/li>\n<li>[latex]\\begin{array}{rr}&\\dfrac{5}{8}\\\\-&\\dfrac{1}{3}\\\\ \\hline&\\end{array}[\/latex]<\/li>\n<li>[latex]\\begin{array}{rr}&\\dfrac{2}{3}\\\\-&\\dfrac{1}{8}\\\\ \\hline&\\end{array}[\/latex]<\/li>\n<li>[latex]\\begin{array}{rr}&\\dfrac{5}{12}\\\\-&\\dfrac{1}{4}\\\\ \\hline&\\end{array}[\/latex]<\/li>\n<li>[latex]\\begin{array}{rr}&\\dfrac{1}{2}\\\\-&\\dfrac{1}{6}\\\\ \\hline&\\end{array}[\/latex]<\/li>\n<li>[latex]\\begin{array}{rr}&\\dfrac{3}{4}\\\\-&\\dfrac{1}{10}\\\\ \\hline&\\end{array}[\/latex]<\/li>\n<li>[latex]\\begin{array}{rr}&\\dfrac{1}{8}\\\\-&\\dfrac{1}{16}\\\\ \\hline&\\end{array}[\/latex]<\/li>\n<li>[latex]\\begin{array}{rr}&\\dfrac{4}{5}\\\\-&\\dfrac{1}{2}\\\\ \\hline&\\end{array}[\/latex]<\/li>\n<\/ol>\n<p><strong>Answers to Exercise 2<\/strong><\/p>\n<ol class=\"threecolumn\" start=\"3\" type=\"a\">\n<li>[latex]\\dfrac{1}{6}[\/latex]<\/li>\n<li>[latex]\\dfrac{1}{10}[\/latex]<\/li>\n<li>[latex]\\dfrac{5}{16}[\/latex]<\/li>\n<li>[latex]\\dfrac{3}{16}[\/latex]<\/li>\n<li>[latex]\\dfrac{1}{8}[\/latex]<\/li>\n<li>[latex]\\dfrac{1}{3}[\/latex]<\/li>\n<li>[latex]\\dfrac{3}{8}[\/latex]<\/li>\n<li>[latex]\\dfrac{7}{24}[\/latex]<\/li>\n<li>[latex]\\dfrac{13}{24}[\/latex]<\/li>\n<li>[latex]\\dfrac{1}{6}[\/latex]<\/li>\n<li>[latex]\\dfrac{1}{3}[\/latex]<\/li>\n<li>[latex]\\dfrac{13}{20}[\/latex]<\/li>\n<li>[latex]\\dfrac{1}{16}[\/latex]<\/li>\n<li>[latex]\\dfrac{3}{10}[\/latex]<\/li>\n<\/ol>\n<\/div>\n<\/div>\n<p style=\"break-before: page;\"><strong>Subtracting mixed numbers<\/strong> is very similar to adding mixed numbers.<\/p>\n<div class=\"textbox\">\n<ul>\n<li>Find the least common denominator if the fractions do not have the same denominator already.<\/li>\n<li>Rename the fractions as equivalent fractions using the <strong>LCD. Don\u2019t forget to keep whole number with the problem.<\/strong><\/li>\n<li>Subtract the second denominator from the first. Keep the same denominator. Subtract the whole numbers.<\/li>\n<li>Simplify the answer.<\/li>\n<\/ul>\n<\/div>\n<div class=\"textbox textbox--examples\">\n<header class=\"textbox__header\">\n<p class=\"textbox__title\">Example D<\/p>\n<\/header>\n<div class=\"textbox__content\">[latex]\\begin{array}{rrr}&4\\dfrac{1}{2}\\left(\\dfrac{\\times3}{\\times3}\\right)&=&4\\dfrac{3}{6}&\\\\-&3\\dfrac{1}{6}&=& 3\\dfrac{1}{6}\\\\ \\hline\\\\&&&1\\dfrac{2}{6}&=1\\dfrac{1}{3} \\end{array}[\/latex]<\/div>\n<\/div>\n<div class=\"textbox textbox--examples\">\n<header class=\"textbox__header\">\n<p class=\"textbox__title\">Example E<\/p>\n<\/header>\n<div class=\"textbox__content\">[latex]\\begin{array}{rrr}&12\\dfrac{3}{4}\\left(\\dfrac{\\times3}{\\times3}\\right)&=&12\\dfrac{9}{12}\\\\-&\\dfrac{2}{3}\\left(\\dfrac{\\times4}{\\times4}\\right)&=& \\dfrac{8}{12}\\\\ \\hline\\\\&&&12\\dfrac{1}{12}\\end{array}[\/latex]<\/div>\n<\/div>\n<div class=\"textbox textbox--exercises\">\n<header class=\"textbox__header\">\n<p class=\"textbox__title\">Exercise 3<\/p>\n<\/header>\n<div class=\"textbox__content\">\n<p>Work through all these questions carefully.<\/p>\n<ol class=\"twocolumn bigspace\" type=\"a\">\n<li>[latex]\\begin{array}{rrr}&16\\dfrac{2}{3}=&16\\dfrac{16}{24}\\\\-&4\\dfrac{3}{8}=&4\\dfrac{9}{24}\\\\ \\hline\\\\&&12\\dfrac{7}{24}\\end{array}[\/latex]<\/li>\n<li>[latex]\\begin{array}{rr}&9\\dfrac{7}{12}\\\\-&9\\dfrac{5}{12}\\\\ \\hline&\\end{array}[\/latex]<\/li>\n<li>[latex]\\begin{array}{rr}&6\\dfrac{3}{4}\\\\-&2\\dfrac{1}{3}\\\\ \\hline&\\end{array}[\/latex]<\/li>\n<li>[latex]\\begin{array}{rr}&22\\dfrac{5}{6}\\\\-&18\\dfrac{2}{5}\\\\ \\hline&\\end{array}[\/latex]<\/li>\n<li>[latex]\\begin{array}{rr}&3\\dfrac{7}{8}\\\\-&2\\dfrac{3}{4}\\\\ \\hline&\\end{array}[\/latex]<\/li>\n<li>[latex]\\begin{array}{rr}&1\\dfrac{7}{10}\\\\-&\\dfrac{1}{2}\\\\ \\hline&\\end{array}[\/latex]<\/li>\n<li>[latex]\\begin{array}{rr}&9\\dfrac{1}{4}\\\\-&7\\\\ \\hline&\\end{array}[\/latex]<\/li>\n<li>[latex]\\begin{array}{rr}&1\\dfrac{5}{8}\\\\-&\\dfrac{1}{3}\\\\ \\hline&\\end{array}[\/latex]<\/li>\n<li>[latex]\\begin{array}{rr}&19\\dfrac{5}{6}\\\\-&11\\dfrac{5}{12}\\\\ \\hline&\\end{array}[\/latex]<\/li>\n<\/ol>\n<\/div>\n<div class=\"textbox__content\">\n<p><strong>Answ<\/strong><strong>er<\/strong><strong>s to Exercise 3<\/strong><\/p>\n<ol class=\"threecolumn\" start=\"2\" type=\"a\">\n<li>[latex]\\dfrac{1}{6}[\/latex]<\/li>\n<li>[latex]4\\dfrac{5}{12}[\/latex]<\/li>\n<li>[latex]4\\dfrac{13}{30}[\/latex]<\/li>\n<li>[latex]1\\dfrac{1}{8}[\/latex]<\/li>\n<li>[latex]1\\dfrac{1}{5}[\/latex]<\/li>\n<li>[latex]2\\dfrac{1}{4}[\/latex]<\/li>\n<li>[latex]1\\dfrac{7}{24}[\/latex]<\/li>\n<li>[latex]8\\dfrac{5}{12}[\/latex]<\/li>\n<\/ol>\n<\/div>\n<\/div>\n<h1>Subtracting Mixed Numbers from Whole Numbers<\/h1>\n<p>This is the start of a new process! You already have all the skills to do this, but the process is new.<\/p>\n<div class=\"textbox textbox--examples\">\n<header class=\"textbox__header\">\n<p class=\"textbox__title\">Example F<\/p>\n<\/header>\n<div class=\"textbox__content\">\n<p><strong>Let&#8217;s look at some apples.<\/strong><\/p>\n<p>You have 3 whole apples and you want to give your son 1 apple and your daughter half an apple. How will you do this?<\/p>\n<p style=\"text-align: center;\"><img loading=\"lazy\" decoding=\"async\" class=\"aligncenter wp-image-181 size-full\" style=\"text-align: start;\" src=\"https:\/\/opentextbc.ca\/busstatsancillary\/wp-content\/uploads\/sites\/437\/2023\/08\/Picture-4-1-e1680809952450.png\" alt=\"Row of 3 apples.\" width=\"412\" height=\"108\" srcset=\"https:\/\/opentextbc.ca\/alfm5\/wp-content\/uploads\/sites\/437\/2023\/08\/Picture-4-1-e1680809952450.png 412w, https:\/\/opentextbc.ca\/alfm5\/wp-content\/uploads\/sites\/437\/2023\/08\/Picture-4-1-e1680809952450-300x79.png 300w, https:\/\/opentextbc.ca\/alfm5\/wp-content\/uploads\/sites\/437\/2023\/08\/Picture-4-1-e1680809952450-65x17.png 65w, https:\/\/opentextbc.ca\/alfm5\/wp-content\/uploads\/sites\/437\/2023\/08\/Picture-4-1-e1680809952450-225x59.png 225w, https:\/\/opentextbc.ca\/alfm5\/wp-content\/uploads\/sites\/437\/2023\/08\/Picture-4-1-e1680809952450-350x92.png 350w\" sizes=\"auto, (max-width: 412px) 100vw, 412px\" \/><\/p>\n<p style=\"break-before: page;\">Yes! You will cut one apple in half.<\/p>\n<\/div>\n<p><img loading=\"lazy\" decoding=\"async\" class=\"aligncenter wp-image-182 size-full\" src=\"https:\/\/opentextbc.ca\/busstatsancillary\/wp-content\/uploads\/sites\/437\/2023\/08\/Picture-4-2-e1680810013273.png\" alt=\"Row of 3 apples. Last apple is cut into two pieces.\" width=\"419\" height=\"108\" srcset=\"https:\/\/opentextbc.ca\/alfm5\/wp-content\/uploads\/sites\/437\/2023\/08\/Picture-4-2-e1680810013273.png 419w, https:\/\/opentextbc.ca\/alfm5\/wp-content\/uploads\/sites\/437\/2023\/08\/Picture-4-2-e1680810013273-300x77.png 300w, https:\/\/opentextbc.ca\/alfm5\/wp-content\/uploads\/sites\/437\/2023\/08\/Picture-4-2-e1680810013273-65x17.png 65w, https:\/\/opentextbc.ca\/alfm5\/wp-content\/uploads\/sites\/437\/2023\/08\/Picture-4-2-e1680810013273-225x58.png 225w, https:\/\/opentextbc.ca\/alfm5\/wp-content\/uploads\/sites\/437\/2023\/08\/Picture-4-2-e1680810013273-350x90.png 350w\" sizes=\"auto, (max-width: 419px) 100vw, 419px\" \/><\/p>\n<div class=\"textbox__content\">\n<p>Now you have [latex]2 \\tfrac{2}{2}[\/latex] apples. And you can easily give away [latex]1 \\tfrac{1}{2}[\/latex] of them. Cross out [latex]1 \\tfrac{1}{2}[\/latex] apples in the drawing. How much is left?<\/p>\n<p>Here is the arithmetic for what you just did.<\/p>\n<p style=\"text-align: center;\">[latex]3=2\\dfrac{2}{2}-1\\dfrac{1}{2}=1\\dfrac{1}{2}[\/latex]<\/p>\n<p>[latex]1\\tfrac{1}{2}[\/latex]apples are left<\/p>\n<\/div>\n<\/div>\n<div class=\"textbox textbox--examples\">\n<header class=\"textbox__header\">\n<p class=\"textbox__title\">Example G<\/p>\n<\/header>\n<div class=\"textbox__content\">\n<p>Here are 6 cans of pop to share among your friends.<\/p>\n<p><img loading=\"lazy\" decoding=\"async\" class=\"aligncenter wp-image-183 size-full\" src=\"https:\/\/opentextbc.ca\/busstatsancillary\/wp-content\/uploads\/sites\/437\/2023\/08\/Picture-4-3.png\" alt=\"6 cans of pop\" width=\"502\" height=\"194\" srcset=\"https:\/\/opentextbc.ca\/alfm5\/wp-content\/uploads\/sites\/437\/2023\/08\/Picture-4-3.png 502w, https:\/\/opentextbc.ca\/alfm5\/wp-content\/uploads\/sites\/437\/2023\/08\/Picture-4-3-300x116.png 300w, https:\/\/opentextbc.ca\/alfm5\/wp-content\/uploads\/sites\/437\/2023\/08\/Picture-4-3-65x25.png 65w, https:\/\/opentextbc.ca\/alfm5\/wp-content\/uploads\/sites\/437\/2023\/08\/Picture-4-3-225x87.png 225w, https:\/\/opentextbc.ca\/alfm5\/wp-content\/uploads\/sites\/437\/2023\/08\/Picture-4-3-350x135.png 350w\" sizes=\"auto, (max-width: 502px) 100vw, 502px\" \/><\/p>\n<p>4 people want a whole can, but one person is on a diet and only wants [latex]\\tfrac{1}{4}[\/latex] of a can. How much pop will be left?<\/p>\n<p>What will you do? You will open a can and think of that can as [latex]\\tfrac{4}{4}[\/latex].<\/p>\n<\/div>\n<p style=\"text-align: center;\"><img loading=\"lazy\" decoding=\"async\" class=\"aligncenter wp-image-184 size-full\" src=\"https:\/\/opentextbc.ca\/busstatsancillary\/wp-content\/uploads\/sites\/437\/2023\/08\/Picture-4-4.png\" alt=\"6 cans of pop. Last can is divided in 4.\" width=\"553\" height=\"199\" srcset=\"https:\/\/opentextbc.ca\/alfm5\/wp-content\/uploads\/sites\/437\/2023\/08\/Picture-4-4.png 553w, https:\/\/opentextbc.ca\/alfm5\/wp-content\/uploads\/sites\/437\/2023\/08\/Picture-4-4-300x108.png 300w, https:\/\/opentextbc.ca\/alfm5\/wp-content\/uploads\/sites\/437\/2023\/08\/Picture-4-4-65x23.png 65w, https:\/\/opentextbc.ca\/alfm5\/wp-content\/uploads\/sites\/437\/2023\/08\/Picture-4-4-225x81.png 225w, https:\/\/opentextbc.ca\/alfm5\/wp-content\/uploads\/sites\/437\/2023\/08\/Picture-4-4-350x126.png 350w\" sizes=\"auto, (max-width: 553px) 100vw, 553px\" \/><\/p>\n<div class=\"textbox__content\">\n<p>You have [latex]5 \\tfrac{4}{4}[\/latex] cans of pop and you can give out 4 whole cans and [latex]\\tfrac{1}{4}[\/latex] can of pop. Cross out the 4 whole cans and [latex]\\tfrac{1}{4}[\/latex] of a can in the drawing.<\/p>\n<p>How many cans are left?<\/p>\n<p>Here is the arithmetic:<\/p>\n<p style=\"text-align: center;\">[latex]\\begin{array}{rr} 6 =& 5 \\dfrac{4}{4} \\\\ -& 4\\dfrac{1}{4} \\\\ \\hline & 1 \\dfrac{3}{4} \\end{array}[\/latex]<\/p>\n<\/div>\n<\/div>\n<div class=\"textbox textbox--examples\">\n<header class=\"textbox__header\">\n<p class=\"textbox__title\">Example H<\/p>\n<\/header>\n<div class=\"textbox__content\">\n<p>Draw five apple pies. If you plan to give away [latex]3\\dfrac{2}{3}[\/latex] of the pies, how many pies are you keeping?<\/p>\n<p>To do that, cut one pie into thirds. Then cross out 3 whole pies and [latex]\\dfrac{2}{3}[\/latex].<\/p>\n<p>Here is the arithmetic:<\/p>\n<p style=\"text-align: center;\">[latex]\\begin{array}{rr}5=&4\\dfrac{3}{3}\\\\-&3\\dfrac{2}{3}\\\\ \\hline&1\\dfrac{1}{3}&\\text{pies kept}\\end{array}[\/latex]<\/p>\n<\/div>\n<\/div>\n<p>Remember [latex]1 = \\dfrac{1}{1} = \\dfrac{2}{2} = \\dfrac{3}{3} = \\dfrac{4}{4} = \\dfrac{5}{5} = \\dfrac{6}{6} =\\dfrac{7}{7} = \\dfrac{8}{8} = \\dfrac{9}{9} =\\dfrac{10}{10}[\/latex] and so on.<\/p>\n<p><strong>T<\/strong><strong>o subtract a mixed number from a whole number, follow these steps:<\/strong><\/p>\n<ol>\n<li>&#8220;Borrow&#8221; <strong>one<\/strong> from the whole number.<\/li>\n<li>Rewrite the one as an improper fraction with the same denominator as the fraction you are subtracting from the whole number. <strong>(Remember to change the whole number to one less.)<\/strong><\/li>\n<li>Subtract the mixed numbers.<\/li>\n<\/ol>\n<div class=\"textbox textbox--examples\">\n<header class=\"textbox__header\">\n<p class=\"textbox__title\">Example I<\/p>\n<\/header>\n<div class=\"textbox__content\">\n<p>[latex]18 - 12 \\dfrac{3}{4} =[\/latex]<\/p>\n<p>&#8220;Borrow&#8221; 1 from 18 and change to [latex]\\tfrac{4}{4}[\/latex].<\/p>\n<p style=\"text-align: center;\">[latex]\\begin{array}{rr} \\cancel{18}17 = & 17 \\dfrac{4}{4} \\\\ -& 12 \\dfrac{3}{4} \\\\ \\hline & 5 \\dfrac{1}{4} \\end{array}[\/latex]<\/p>\n<p>Try it yourself:<\/p>\n<p>[latex]1 - \\dfrac{4}{5} =[\/latex]<\/p>\n<\/div>\n<\/div>\n<div class=\"textbox textbox--exercises\" style=\"break-before: page;\">\n<header class=\"textbox__header\">\n<p class=\"textbox__title\">Exercise 4<\/p>\n<\/header>\n<div class=\"textbox__content\">\n<p>Subtract and express in lowest terms. <strong>TIP:<\/strong> Remember to change your whole number to a mixed numeral.<\/p>\n<ol class=\"twocolumn bigspace\" type=\"a\">\n<li>[latex]\\begin{array}{rr}5=&4\\dfrac{2}{2}\\\\-&1\\dfrac{1}{2}\\\\ \\hline&3\\dfrac{1}{2}\\end{array}[\/latex]<\/li>\n<li>[latex]\\begin{array}{rr}&9\\\\-&4\\dfrac{3}{10}\\\\ \\hline&\\end{array}[\/latex]<\/li>\n<li>[latex]\\begin{array}{rr}&12\\\\-&11\\dfrac{5}{8}\\\\ \\hline&\\end{array}[\/latex]<\/li>\n<li>[latex]\\begin{array}{rr}&25\\\\-&20\\dfrac{1}{4}\\\\ \\hline&\\end{array}[\/latex]<\/li>\n<li>[latex]\\begin{array}{rr}&3\\\\-&2\\dfrac{2}{3}\\\\ \\hline&\\end{array}[\/latex]<\/li>\n<li>[latex]\\begin{array}{rr}&8\\\\-&\\dfrac{3}{4}\\\\ \\hline&\\end{array}[\/latex]<\/li>\n<li>[latex]\\begin{array}{rr}&32\\\\-&28\\dfrac{1}{2}\\\\ \\hline&\\end{array}[\/latex]<\/li>\n<li>[latex]\\begin{array}{rr}&5\\\\-&3\\dfrac{1}{3}\\\\ \\hline&\\end{array}[\/latex]<\/li>\n<li>[latex]\\begin{array}{rr}&8\\\\-&4\\dfrac{4}{9}\\\\ \\hline&\\end{array}[\/latex]<\/li>\n<\/ol>\n<p><strong>Answers to Exercise 4<\/strong><\/p>\n<ol class=\"threecolumn\" start=\"2\" type=\"a\">\n<li>[latex]4\\dfrac{7}{10}[\/latex]<\/li>\n<li>[latex]\\dfrac{3}{8}[\/latex]<\/li>\n<li>[latex]4\\dfrac{3}{4}[\/latex]<\/li>\n<li>[latex]\\dfrac{1}{3}[\/latex]<\/li>\n<li>[latex]7\\dfrac{1}{4}[\/latex]<\/li>\n<li>[latex]3\\dfrac{1}{2}[\/latex]<\/li>\n<li>[latex]1\\dfrac{2}{3}[\/latex]<\/li>\n<li>[latex]3\\dfrac{5}{9}[\/latex]<\/li>\n<\/ol>\n<\/div>\n<\/div>\n<h1>Renaming to Subtract Mixed Numbers<\/h1>\n<div class=\"textbox textbox--examples\">\n<header class=\"textbox__header\">\n<p class=\"textbox__title\">Example J<\/p>\n<\/header>\n<div class=\"textbox__content\">\n<p>Look at the [latex]3\\tfrac{1}{4}[\/latex] chocolate bars.<\/p>\n<p><img loading=\"lazy\" decoding=\"async\" class=\"aligncenter wp-image-185 size-full\" src=\"https:\/\/opentextbc.ca\/busstatsancillary\/wp-content\/uploads\/sites\/437\/2023\/08\/Picture-4-5.png\" alt=\"3 whole chocolate bars. One quarter of a bar.\" width=\"574\" height=\"65\" srcset=\"https:\/\/opentextbc.ca\/alfm5\/wp-content\/uploads\/sites\/437\/2023\/08\/Picture-4-5.png 574w, https:\/\/opentextbc.ca\/alfm5\/wp-content\/uploads\/sites\/437\/2023\/08\/Picture-4-5-300x34.png 300w, https:\/\/opentextbc.ca\/alfm5\/wp-content\/uploads\/sites\/437\/2023\/08\/Picture-4-5-65x7.png 65w, https:\/\/opentextbc.ca\/alfm5\/wp-content\/uploads\/sites\/437\/2023\/08\/Picture-4-5-225x25.png 225w, https:\/\/opentextbc.ca\/alfm5\/wp-content\/uploads\/sites\/437\/2023\/08\/Picture-4-5-350x40.png 350w\" sizes=\"auto, (max-width: 574px) 100vw, 574px\" \/><\/p>\n<p>You need to give [latex]2\\tfrac{3}{4}[\/latex] chocolate bars to the kids on the soccer team. How will you do this?<\/p>\n<p>You will have to cut up one of the whole chocolate bars into 4 pieces, or [latex]\\tfrac{4}{4}[\/latex].<\/p>\n<\/div>\n<p style=\"text-align: center;\"><img loading=\"lazy\" decoding=\"async\" class=\"aligncenter wp-image-186 size-full\" title=\"2 whole chocolate bars. 4 quarters of a chocolate bar. One quarter of a chocolate bar.\" src=\"https:\/\/opentextbc.ca\/busstatsancillary\/wp-content\/uploads\/sites\/437\/2023\/08\/Picture-4-6.png\" alt=\"2 whole chocolate bars. 4 quarters of a chocolate bar. One quarter of a chocolate bar.\" width=\"613\" height=\"71\" data-popupalt-original-title=\"null\" srcset=\"https:\/\/opentextbc.ca\/alfm5\/wp-content\/uploads\/sites\/437\/2023\/08\/Picture-4-6.png 613w, https:\/\/opentextbc.ca\/alfm5\/wp-content\/uploads\/sites\/437\/2023\/08\/Picture-4-6-300x35.png 300w, https:\/\/opentextbc.ca\/alfm5\/wp-content\/uploads\/sites\/437\/2023\/08\/Picture-4-6-65x8.png 65w, https:\/\/opentextbc.ca\/alfm5\/wp-content\/uploads\/sites\/437\/2023\/08\/Picture-4-6-225x26.png 225w, https:\/\/opentextbc.ca\/alfm5\/wp-content\/uploads\/sites\/437\/2023\/08\/Picture-4-6-350x41.png 350w\" sizes=\"auto, (max-width: 613px) 100vw, 613px\" \/><\/p>\n<div class=\"textbox__content\">\n<p>Now you have 2 whole bars, [latex]\\tfrac{4}{4}[\/latex] of a bar and [latex]\\tfrac{1}{4}[\/latex] of a bar which equals [latex]2\\tfrac{5}{4}[\/latex] of a bar. It will be easy to give away (subtract) [latex]2\\tfrac{3}{4}[\/latex] bars. Cross out [latex]2\\tfrac{3}{4}[\/latex] bars. How much is left?<\/p>\n<p>Here is the arithmetic:<\/p>\n<p>[latex]3\\dfrac{1}{4}-2\\dfrac{3}{4}=[\/latex]<\/p>\n<p>[latex]\\begin{array}{rrr} 3 \\dfrac{1}{4} = & 2 \\dfrac{4}{4} + \\dfrac{1}{4} = & 2 \\dfrac{5}{4} \\\\ & - & 2 \\dfrac{3}{4} \\\\ \\hline && \\dfrac{2}{4} & = \\dfrac{1}{2} \\text{ chocolate bar left} \\end{array}[\/latex]<\/p>\n<\/div>\n<\/div>\n<div class=\"textbox textbox--examples\">\n<header class=\"textbox__header\">\n<p class=\"textbox__title\">Example K<\/p>\n<\/header>\n<div class=\"textbox__content\">\n<p>Look at these [latex]5\\dfrac{1}{8}[\/latex] cherry pies.<\/p>\n<p><img loading=\"lazy\" decoding=\"async\" class=\"size-medium wp-image-187 aligncenter\" title=\"Illustration of 5 cherry pies and one slice that is one eighth of a pie\" src=\"https:\/\/opentextbc.ca\/busstatsancillary\/wp-content\/uploads\/sites\/437\/2023\/08\/Picture-4-7-300x117.png\" alt=\"Illustration of 5 cherry pies and one slice that is one eighth of a pie\" width=\"300\" height=\"117\" data-popupalt-original-title=\"null\" srcset=\"https:\/\/opentextbc.ca\/alfm5\/wp-content\/uploads\/sites\/437\/2023\/08\/Picture-4-7-300x117.png 300w, https:\/\/opentextbc.ca\/alfm5\/wp-content\/uploads\/sites\/437\/2023\/08\/Picture-4-7-65x25.png 65w, https:\/\/opentextbc.ca\/alfm5\/wp-content\/uploads\/sites\/437\/2023\/08\/Picture-4-7-225x88.png 225w, https:\/\/opentextbc.ca\/alfm5\/wp-content\/uploads\/sites\/437\/2023\/08\/Picture-4-7-350x137.png 350w, https:\/\/opentextbc.ca\/alfm5\/wp-content\/uploads\/sites\/437\/2023\/08\/Picture-4-7.png 520w\" sizes=\"auto, (max-width: 300px) 100vw, 300px\" \/><\/p>\n<p>You promised to send [latex]3\\dfrac{5}{8}[\/latex] pies to the spring party at school. How will you do this?<\/p>\n<p>Cut one of the whole pies into eighths.<\/p>\n<p><img loading=\"lazy\" decoding=\"async\" class=\"size-medium wp-image-188 aligncenter\" title=\"Illustration of four cherry pies, plain. One cherry pie with cross hashes indicating eighths lines. And then a slice of pie that is one eighth. Illustration of problem to solve.\" src=\"https:\/\/opentextbc.ca\/busstatsancillary\/wp-content\/uploads\/sites\/437\/2023\/08\/Picture-4-8-300x111.png\" alt=\"Illustration of four cherry pies, plain. One cherry pie with cross hashes indicating eighths lines. And then a slice of pie that is one eighth. Illustration of problem to solve.\" width=\"300\" height=\"111\" data-popupalt-original-title=\"null\" srcset=\"https:\/\/opentextbc.ca\/alfm5\/wp-content\/uploads\/sites\/437\/2023\/08\/Picture-4-8-300x111.png 300w, https:\/\/opentextbc.ca\/alfm5\/wp-content\/uploads\/sites\/437\/2023\/08\/Picture-4-8-65x24.png 65w, https:\/\/opentextbc.ca\/alfm5\/wp-content\/uploads\/sites\/437\/2023\/08\/Picture-4-8-225x83.png 225w, https:\/\/opentextbc.ca\/alfm5\/wp-content\/uploads\/sites\/437\/2023\/08\/Picture-4-8-350x130.png 350w, https:\/\/opentextbc.ca\/alfm5\/wp-content\/uploads\/sites\/437\/2023\/08\/Picture-4-8.png 540w\" sizes=\"auto, (max-width: 300px) 100vw, 300px\" \/><\/p>\n<p>Then, cross out [latex]3\\dfrac{5}{8}[\/latex] pies.<\/p>\n<p>How much pie is left?<\/p>\n<p>[latex]\\begin{array}{rr} 5\\dfrac{1}{8}=4\\dfrac{8}{8}+\\dfrac{1}{8}=&4\\dfrac{9}{8}\\\\  -&3\\dfrac{5}{8}\\\\  \\hline  &1\\dfrac{4}{8}&=1\\dfrac{1}{2}\\text{ pies left}\\end{array}[\/latex]<\/p>\n<\/div>\n<\/div>\n<h1>Steps for rewriting a mixed number for subtraction<\/h1>\n<ol>\n<li>Check to see if rewriting is needed. That is, check that the fraction in the mixed number you are starting with is less than the fraction you want to take away.\n<ul>\n<li>Question: [latex]4\\dfrac{1}{3}-2\\dfrac{2}{3}[\/latex]<\/li>\n<li>[latex]\\dfrac{1}{3}\\text{ is less than }\\dfrac{2}{3}[\/latex]<\/li>\n<\/ul>\n<\/li>\n<li>&#8220;Borrow&#8221; 1 from the whole number in the first mixed number. TIP: Remember to change the whole number to 1 less.<\/li>\n<li>Rewrite the &#8220;borrowed&#8221; 1 as an improper fraction with the same denominator as the other fractions.\n<ul>\n<li>[latex]4\\dfrac{1}{3}=3\\dfrac{3}{3}+\\dfrac{1}{3}[\/latex]<\/li>\n<li>[latex]\\dfrac{3}{3}[\/latex] is the 1 that you borrowed from the 4.<\/li>\n<\/ul>\n<\/li>\n<li>Add the rewritten 1 to the fraction that is part of the same mixed number.\n<ul>\n<li>[latex]3\\dfrac{3}{3}+\\dfrac{1}{3}=3\\dfrac{4}{3}[\/latex]<\/li>\n<\/ul>\n<\/li>\n<li>Subtract as usual, expressing your answer in lowest terms.\n<ul>\n<li>[latex]\\begin{array}{rrr}&4\\dfrac{1}{3}=&3\\dfrac{4}{3}\\\\-&2\\dfrac{2}{3}=&2\\dfrac{2}{3}\\\\ \\hline&&1\\dfrac{2}{3}\\end{array}[\/latex]<\/li>\n<\/ul>\n<\/li>\n<\/ol>\n<div>\n<div class=\"textbox textbox--examples\" style=\"break-before: page;\">\n<header class=\"textbox__header\">\n<p class=\"textbox__title\">Example L<\/p>\n<\/header>\n<div class=\"textbox__content\">\n<p>[latex]5\\dfrac{2}{5}-2\\dfrac{4}{5}[\/latex]<\/p>\n<p><strong>Step 1: <\/strong>[latex]\\dfrac{2}{5}[\/latex] is less than [latex]\\dfrac{4}{5}[\/latex], so it&#8217;s necessary to rewrite.<\/p>\n<p><strong>Step 2 and 3:<\/strong> Borrow 1.<\/p>\n<p>[latex]5\\dfrac{2}{5}=4\\dfrac{5}{5}+\\dfrac{2}{5}=4\\dfrac{7}{5}[\/latex]<\/p>\n<p><strong>Step 4 and 5:<\/strong><\/p>\n<p>[latex]\\begin{array}{rr}5\\dfrac{2}{5}=&4\\dfrac{5}{5}+\\dfrac{2}{5}=&4\\dfrac{7}{5} \\\\ -&2\\dfrac{4}{5}=&2\\dfrac{4}{5}\\\\\\hline&&2\\dfrac{3}{5}\\end{array}[\/latex]<\/p>\n<\/div>\n<\/div>\n<\/div>\n<div class=\"textbox textbox--examples\">\n<header class=\"textbox__header\">\n<p class=\"textbox__title\">Example M<\/p>\n<\/header>\n<div class=\"textbox__content\">\n<p>[latex]1\\dfrac{2}{4}-\\dfrac{3}{4}[\/latex]<\/p>\n<p><strong>Step 1:<\/strong> [latex]\\dfrac{2}{4}[\/latex] is less than [latex]\\dfrac{3}{4}[\/latex], so we need to rewrite to subtract.<\/p>\n<p><strong>Step 2, 3, 4 and 5:<\/strong><\/p>\n<p>[latex]\\begin{array}{rrr}1\\dfrac{2}{4} =&\\dfrac{4}{4} +\\dfrac{2}{4}=&\\dfrac{6}{4} \\\\ -& \\dfrac{3}{4} =& \\dfrac{3}{4} \\\\ \\hline &&\\dfrac{3}{4} \\end{array}[\/latex]<\/p>\n<\/div>\n<\/div>\n<div class=\"textbox textbox--exercises\">\n<header class=\"textbox__header\">\n<p class=\"textbox__title\">Exercise 5<\/p>\n<\/header>\n<div class=\"textbox__content\">\n<p>Subtract. Be sure the answers are in lowest terms.<\/p>\n<ol class=\"twocolumn bigspace\" type=\"a\">\n<li>[latex]\\begin{array}{rrr}20\\dfrac{1}{4} =& 19 \\dfrac{5}{4}\\\\-&10\\dfrac{3}{4}\\\\ \\hline&9\\dfrac{2}{4}&=9\\dfrac{1}{2} \\end{array}[\/latex]<\/li>\n<li>[latex]\\begin{array}{rr}&3\\dfrac{1}{3}\\\\-&1\\dfrac{2}{3}\\\\ \\hline&\\end{array}[\/latex]<\/li>\n<li>[latex]\\begin{array}{rr}&56\\dfrac{2}{5}\\\\-&20\\dfrac{4}{5}\\\\ \\hline&\\end{array}[\/latex]<\/li>\n<li>[latex]\\begin{array}{rr}&8\\dfrac{1}{3}\\\\-&1\\dfrac{2}{3}\\\\ \\hline&\\end{array}[\/latex]<\/li>\n<li>[latex]\\begin{array}{rr}&4\\dfrac{1}{5}\\\\-&2\\dfrac{3}{5}\\\\ \\hline&\\end{array}[\/latex]<\/li>\n<li>[latex]\\begin{array}{rr}&5\\dfrac{2}{7}\\\\-&1\\dfrac{3}{7}\\\\ \\hline&\\end{array}[\/latex]<\/li>\n<li>[latex]\\begin{array}{rr}&12\\dfrac{5}{9}\\\\-&10\\dfrac{7}{9}\\\\ \\hline&\\end{array}[\/latex]<\/li>\n<li>\u00a0[latex]\\begin{array}{rr}&9\\dfrac{3}{5}\\\\-&\\dfrac{4}{5}\\\\ \\hline&\\end{array}[\/latex]<\/li>\n<li>[latex]\\begin{array}{rr}&15\\dfrac{3}{8}\\\\-&14\\dfrac{7}{8}\\\\ \\hline&\\end{array}[\/latex]<\/li>\n<\/ol>\n<p><strong>Answers to Exercise 5<\/strong><\/p>\n<ol class=\"threecolumn\" start=\"2\" type=\"a\">\n<li>[latex]1\\dfrac{2}{3}[\/latex]<\/li>\n<li>[latex]35\\dfrac{3}{5}[\/latex]<\/li>\n<li>[latex]6\\dfrac{2}{3}[\/latex]<\/li>\n<li>[latex]1\\dfrac{3}{5}[\/latex]<\/li>\n<li>[latex]3\\dfrac{6}{7}[\/latex]<\/li>\n<li>[latex]1\\dfrac{7}{9}[\/latex]<\/li>\n<li>[latex]8\\dfrac{4}{5}[\/latex]<\/li>\n<li>[latex]\\dfrac{1}{2}[\/latex]<\/li>\n<\/ol>\n<\/div>\n<\/div>\n<p>Here is the last step for subtraction of fractions. Mixed numbers to be subtracted often do not have the same denominators-they are <a class=\"glossary-term\" aria-haspopup=\"dialog\" aria-describedby=\"definition\" href=\"#term_189_270\">unlike fractions<\/a>.<\/p>\n<p>You must<\/p>\n<ul>\n<li>Write equivalent fractions using the LCD.<\/li>\n<li>Decide if you need to &#8220;borrow&#8221; or rename before you subtract.<\/li>\n<li>Subtract and simplify the answer.<\/li>\n<\/ul>\n<div class=\"textbox textbox--examples\">\n<header class=\"textbox__header\">\n<p class=\"textbox__title\">Example N<\/p>\n<\/header>\n<div class=\"textbox__content\">\n<p>[latex]4\\dfrac{1}{3}-2\\dfrac{5}{6}=[\/latex]<\/p>\n<p>&nbsp;<\/p>\n<p>[latex]\\begin{array}{rrr}  &4\\dfrac{1}{3}=4\\dfrac{2}{6}=3\\dfrac{6}{6} + \\dfrac{2}{6}=&3\\dfrac{8}{6}\\\\&-&2\\dfrac{5}{6}\\\\ \\hline&&1\\dfrac{3}{6}&=1\\dfrac{1}{2}\\end{array}[\/latex]<\/p>\n<\/div>\n<\/div>\n<div class=\"textbox textbox--examples\">\n<header class=\"textbox__header\">\n<p class=\"textbox__title\">Example O<\/p>\n<\/header>\n<div class=\"textbox__content\">\n<p>[latex]9\\dfrac{1}{10} - 4\\dfrac{1}{4}=[\/latex]<\/p>\n<p>&nbsp;<\/p>\n<p>[latex]\\begin{array}{rrrr}9\\dfrac{1}{10}=&9\\dfrac{2}{20}=&8\\dfrac{20}{20} + \\dfrac{2}{20}= &8\\dfrac{22}{20}\\\\ -&4\\dfrac{1}{4} = &4\\dfrac{5}{20} =& 4\\dfrac{5}{20}\\\\ \\hline&&&4\\dfrac{17}{20}\\end{array}[\/latex]<\/p>\n<\/div>\n<\/div>\n<div class=\"textbox textbox--exercises\" style=\"break-before: page;\">\n<header class=\"textbox__header\">\n<p class=\"textbox__title\">Exercise 6<\/p>\n<\/header>\n<div class=\"textbox__content\">\n<p>Subtract. Be sure the answers are in lowest terms.<\/p>\n<ol class=\"twocolumn bigspace\" type=\"a\">\n<li>[latex]\\begin{array}{rr}&9\\dfrac{3}{8}=&9\\dfrac{3}{8}=&8\\dfrac{11}{8}\\\\-&7\\dfrac{1}{2}=&7\\dfrac{4}{8}=&7\\dfrac{4}{8}\\\\ \\hline&&& 1 \\dfrac{7}{8} \\end{array}[\/latex]<\/li>\n<li>[latex]\\begin{array}{rr}&7\\dfrac{1}{16}\\\\-&4\\dfrac{1}{8}\\\\ \\hline&\\end{array}[\/latex]<\/li>\n<li>[latex]\\begin{array}{rr}&15\\dfrac{1}{6}\\\\-&12\\dfrac{7}{8}\\\\ \\hline&\\end{array}[\/latex]<\/li>\n<li>[latex]\\begin{array}{rr}&20\\dfrac{2}{6}\\\\-&16\\dfrac{2}{3}\\\\ \\hline&\\end{array}[\/latex]<\/li>\n<li>[latex]\\begin{array}{rr}&6\\dfrac{3}{5}\\\\-&4\\dfrac{1}{4}\\\\ \\hline&\\end{array}[\/latex]<\/li>\n<li>[latex]\\begin{array}{rr}&9\\dfrac{1}{4}\\\\-&7\\dfrac{3}{8}\\\\ \\hline&\\end{array}[\/latex]<\/li>\n<li>[latex]\\begin{array}{rr}&5\\dfrac{1}{3}\\\\-&2\\dfrac{1}{2}\\\\ \\hline&\\end{array}[\/latex]<\/li>\n<li>[latex]\\begin{array}{rr}&18\\dfrac{1}{6}\\\\-&12\\dfrac{2}{3}\\\\ \\hline&\\end{array}[\/latex]<\/li>\n<\/ol>\n<p><strong>Answers to Exercise 6<\/strong><\/p>\n<ol class=\"threecolumn\" start=\"2\" type=\"a\">\n<li>[latex]2\\dfrac{15}{16}[\/latex]<\/li>\n<li>[latex]2\\dfrac{7}{24}[\/latex]<\/li>\n<li>[latex]3\\dfrac{2}{3}[\/latex]<\/li>\n<li>[latex]2\\dfrac{7}{20}[\/latex]<\/li>\n<li>[latex]1\\dfrac{7}{8}[\/latex]<\/li>\n<li>[latex]2\\dfrac{5}{6}[\/latex]<\/li>\n<li>[latex]5\\dfrac{1}{2}[\/latex]<\/li>\n<\/ol>\n<\/div>\n<\/div>\n<div class=\"textbox textbox--exercises\">\n<header class=\"textbox__header\">\n<p class=\"textbox__title\">Exercise 7<\/p>\n<\/header>\n<div class=\"textbox__content\">\n<p>A Subtraction Review.<\/p>\n<ol class=\"twocolumn bigspace\" type=\"a\">\n<li>[latex]\\begin{array}{rr}&\\dfrac{5}{8}\\\\-&\\dfrac{1}{4}\\\\ \\hline&\\end{array}[\/latex]<\/li>\n<li>[latex]\\begin{array}{rr}&8\\dfrac{3}{4}\\\\-&4\\dfrac{1}{3}\\\\ \\hline&\\end{array}[\/latex]<\/li>\n<li>[latex]\\begin{array}{rr}&13\\dfrac{1}{3}\\\\-&12\\dfrac{5}{6}\\\\ \\hline&\\end{array}[\/latex]<\/li>\n<li>[latex]\\begin{array}{rr}&7\\dfrac{1}{3}\\\\-&4\\dfrac{5}{6}\\\\ \\hline&\\end{array}[\/latex]<\/li>\n<li>[latex]\\begin{array}{rr}&9\\dfrac{1}{5}\\\\-&6\\dfrac{1}{3}\\\\ \\hline&\\end{array}[\/latex]<\/li>\n<li>[latex]\\begin{array}{rr}&7\\\\-&1\\dfrac{7}{8}\\\\ \\hline&\\end{array}[\/latex]<\/li>\n<li>[latex]\\begin{array}{rr}&19\\dfrac{2}{3}\\\\-&18\\\\ \\hline&\\end{array}[\/latex]<\/li>\n<li>[latex]\\begin{array}{rr}&\\dfrac{5}{8}\\\\-&\\dfrac{1}{2}\\\\ \\hline&\\end{array}[\/latex]<\/li>\n<\/ol>\n<p><strong>Answers to Exercise 7<\/strong><\/p>\n<ol class=\"threecolumn\" type=\"a\">\n<li>[latex]\\dfrac{3}{8}[\/latex]<\/li>\n<li>[latex]4\\dfrac{5}{12}[\/latex]<\/li>\n<li>[latex]\\dfrac{1}{2}[\/latex]<\/li>\n<li>[latex]2\\dfrac{1}{2}[\/latex]<\/li>\n<li>[latex]2\\dfrac{13}{15}[\/latex]<\/li>\n<li>[latex]5\\dfrac{1}{8}[\/latex]<\/li>\n<li>[latex]1\\dfrac{2}{3}[\/latex]<\/li>\n<li>[latex]\\dfrac{1}{8}[\/latex]<\/li>\n<\/ol>\n<\/div>\n<\/div>\n<h1>Problems Using Subtraction of Common Fractions<\/h1>\n<p>Subtraction problems may ask you to:<\/p>\n<div class=\"textbox\">\n<ul>\n<li>find the difference between two amounts.\n<ul>\n<li>&#8220;how much more is&#8230;&#8221;<\/li>\n<li>&#8220;how much less is&#8230;&#8221;<\/li>\n<\/ul>\n<\/li>\n<li>take away, give away, or lose.<\/li>\n<\/ul>\n<ul>\n<li>decide how much is left or how much remains.<\/li>\n<\/ul>\n<\/div>\n<p>Read over the subtraction problems that you did in Unit Two with decimals. The wording and problem situations will be similar.<\/p>\n<p>Drawing a sketch and estimating the answer using whole numbers may also be helpful.<\/p>\n<div class=\"textbox textbox--exercises\">\n<header class=\"textbox__header\">\n<p class=\"textbox__title\">Exercise 8<\/p>\n<\/header>\n<div class=\"textbox__content\">\n<ol type=\"a\">\n<li>The New Earth Diaper Company stocks went from [latex]5\\tfrac{7}{8}[\/latex] to [latex]7\\tfrac{3}{8}[\/latex]this week. How much did the stocks increase in value?<\/li>\n<li>Jean is knitting an afghan which will be made from 5 long pieces. She has finished [latex]3\\tfrac{2}{3}[\/latex] of the pieces. How many pieces does she still have to knit?<\/li>\n<li>Dave said he worked in the garden for [latex]6\\tfrac{1}{4}[\/latex] hours, but his wife saw him snoozing under a tree for [latex]1\\tfrac{1}{2}[\/latex] hours! How long did Dave really work?<\/li>\n<li>Maureen left [latex]\\tfrac{2}{3}[\/latex] of a big lasagne casserole in the fridge hoping it would be enough for a quick dinner that night. But alas, when she got home, only [latex]\\tfrac{1}{4}[\/latex] of the big lasagne casserole remained. How much of the lasagne was eaten while she was out?<\/li>\n<li>In the first half of 1992, the Bank of Canada Prime Rate dropped steadily. It started the year at [latex]8\\tfrac{1}{2}[\/latex] % and was at a low [latex]6\\tfrac{3}{4}[\/latex]% in July. How many percentage points did the prime rate drop? (Note: treat the % just like a unit in this problem.)<\/li>\n<li>Mark is [latex]1\\tfrac{3}{4}[\/latex] metres tall. His partner is [latex]1\\tfrac{1}{3}[\/latex] metres tall. How much taller is Mark than his partner?<\/li>\n<li>A teenager can drink [latex]3\\tfrac{3}{4}[\/latex] litres of water each day. If this teenager drinks [latex]2\\tfrac{1}{2}[\/latex] litres of water by lunch, how much more water will he drink in the day?<\/li>\n<li>Joan bought [latex]13\\tfrac{1}{2}[\/latex] metres to do her sewing project. She has used [latex]8\\tfrac{1}{5}[\/latex] metres so far. How much material does she have left?<\/li>\n<\/ol>\n<p><strong>Answers to Exercise 8<\/strong><\/p>\n<ol class=\"threecolumn\" type=\"a\">\n<li>[latex]1\\dfrac{1}{2}[\/latex] or $1.50<\/li>\n<li>[latex]1\\dfrac{1}{3}[\/latex] pieces<\/li>\n<li>[latex]4\\dfrac{3}{4}[\/latex] hours<\/li>\n<li>[latex]\\dfrac{5}{12}[\/latex] of the lasagna<\/li>\n<li>[latex]1\\dfrac{3}{4}[\/latex]\u00a0percentage points<\/li>\n<li>[latex]\\dfrac{5}{12}[\/latex] metres taller<\/li>\n<li>[latex]1\\dfrac{1}{4}[\/latex] litres left to drink<\/li>\n<li>[latex]5\\dfrac{3}{10}[\/latex] metres left<\/li>\n<\/ol>\n<\/div>\n<\/div>\n<h1>Topic B Self-Test<\/h1>\n<p><strong>Mark\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0 \/15\u00a0 \u00a0Aim 12\/15<\/strong><\/p>\n<ol type=\"A\">\n<li>Subtract these fractions. Simplify the answers when necessary (15 marks).\n<ol class=\"twocolumn bigspace\" type=\"a\">\n<li>[latex]\\begin{array}{rr}&\\dfrac{7}{8}\\\\-&\\dfrac{1}{8}\\\\ \\hline&\\end{array}[\/latex]<\/li>\n<li>[latex]\\begin{array}{rr}&\\dfrac{11}{15}\\\\-&\\dfrac{4}{15}\\\\ \\hline&\\end{array}[\/latex]<\/li>\n<li>[latex]\\begin{array}{rr}&\\dfrac{7}{8}\\\\-&\\dfrac{3}{16}\\\\ \\hline&\\end{array}[\/latex]<\/li>\n<li>[latex]\\begin{array}{rr}&\\dfrac{2}{3}\\\\-&\\dfrac{1}{6}\\\\ \\hline\\end{array}[\/latex]<\/li>\n<li>[latex]\\begin{array}{rr}&\\dfrac{4}{7}\\\\-&\\dfrac{1}{14}\\\\ \\hline\\end{array}[\/latex]<\/li>\n<li>[latex]\\begin{array}{rr}&\\dfrac{4}{5}\\\\-&\\dfrac{3}{8}\\\\ \\hline\\end{array}[\/latex]<\/li>\n<li>[latex]\\begin{array}{rr}&4\\\\-&2\\dfrac{1}{2}\\\\ \\hline\\end{array}[\/latex]<\/li>\n<li>[latex]\\begin{array}{rr}&5\\\\-&4\\dfrac{7}{8}\\\\ \\hline\\end{array}[\/latex]<\/li>\n<li>[latex]\\begin{array}{rr}&10\\dfrac{3}{5}\\\\-&3\\dfrac{3}{10}\\\\ \\hline\\end{array}[\/latex]<\/li>\n<li>[latex]\\begin{array}{rr}&7\\dfrac{1}{5}\\\\-&3\\dfrac{4}{5}\\\\ \\hline\\end{array}[\/latex]<\/li>\n<li>[latex]\\begin{array}{rr}&12\\dfrac{1}{8}\\\\-&11\\\\ \\hline\\end{array}[\/latex]<\/li>\n<li>[latex]\\begin{array}{rr}&9\\dfrac{1}{5}\\\\-&\\dfrac{1}{4}\\\\ \\hline\\end{array}[\/latex]<\/li>\n<li>[latex]\\begin{array}{rr}&5\\dfrac{1}{4}\\\\-&1\\dfrac{2}{3}\\\\ \\hline\\end{array}[\/latex]<\/li>\n<li>[latex]\\begin{array}{rr}&10\\dfrac{1}{2}\\\\-&2\\dfrac{2}{5}\\\\ \\hline\\end{array}[\/latex]<\/li>\n<li>[latex]\\begin{array}{rr}&6\\dfrac{2}{3}\\\\-&4\\dfrac{3}{8}\\\\ \\hline\\end{array}[\/latex]<\/li>\n<\/ol>\n<\/li>\n<\/ol>\n<p><strong>Answers to Topic B Self-Test<\/strong><\/p>\n<ol class=\"threecolumn\" type=\"A\">\n<li style=\"list-style-type: none;\">\n<ol type=\"a\">\n<li>[latex]\\dfrac{3}{4}[\/latex]<\/li>\n<li>[latex]\\dfrac{7}{15}[\/latex]<\/li>\n<li>[latex]\\dfrac{11}{16}[\/latex]<\/li>\n<li>[latex]\\dfrac{1}{2}[\/latex]<\/li>\n<li>[latex]\\dfrac{1}{2}[\/latex]<\/li>\n<li>[latex]\\dfrac{17}{40}[\/latex]<\/li>\n<li>[latex]1\\dfrac{1}{2}[\/latex]<\/li>\n<li>[latex]\\dfrac{1}{8}[\/latex]<\/li>\n<li>[latex]7\\dfrac{3}{10}[\/latex]<\/li>\n<li>[latex]3\\dfrac{2}{5}[\/latex]<\/li>\n<li>[latex]1\\dfrac{1}{8}[\/latex]<\/li>\n<li>[latex]8\\dfrac{19}{20}[\/latex]<\/li>\n<li>[latex]3\\dfrac{7}{12}[\/latex]<\/li>\n<li>[latex]8\\dfrac{1}{10}[\/latex]<\/li>\n<li>[latex]2\\dfrac{7}{24}[\/latex]<\/li>\n<\/ol>\n<\/li>\n<\/ol>\n<div class=\"glossary\"><span class=\"screen-reader-text\" id=\"definition\">definition<\/span><template id=\"term_189_277\"><div class=\"glossary__definition\" role=\"dialog\" data-id=\"term_189_277\"><div tabindex=\"-1\"><p>The result of a subtraction question, the answer. Subtraction gives the difference between two numbers.<\/p>\n<\/div><button><span aria-hidden=\"true\">&times;<\/span><span class=\"screen-reader-text\">Close definition<\/span><\/button><\/div><\/template><template id=\"term_189_270\"><div class=\"glossary__definition\" role=\"dialog\" data-id=\"term_189_270\"><div tabindex=\"-1\"><p>Fractions which have different denominators.<\/p>\n<\/div><button><span aria-hidden=\"true\">&times;<\/span><span class=\"screen-reader-text\">Close definition<\/span><\/button><\/div><\/template><\/div>","protected":false},"author":123,"menu_order":2,"template":"","meta":{"pb_show_title":"on","pb_short_title":"","pb_subtitle":"","pb_authors":[],"pb_section_license":""},"chapter-type":[],"contributor":[],"license":[],"class_list":["post-189","chapter","type-chapter","status-publish","hentry"],"part":154,"_links":{"self":[{"href":"https:\/\/opentextbc.ca\/alfm5\/wp-json\/pressbooks\/v2\/chapters\/189","targetHints":{"allow":["GET"]}}],"collection":[{"href":"https:\/\/opentextbc.ca\/alfm5\/wp-json\/pressbooks\/v2\/chapters"}],"about":[{"href":"https:\/\/opentextbc.ca\/alfm5\/wp-json\/wp\/v2\/types\/chapter"}],"author":[{"embeddable":true,"href":"https:\/\/opentextbc.ca\/alfm5\/wp-json\/wp\/v2\/users\/123"}],"version-history":[{"count":21,"href":"https:\/\/opentextbc.ca\/alfm5\/wp-json\/pressbooks\/v2\/chapters\/189\/revisions"}],"predecessor-version":[{"id":537,"href":"https:\/\/opentextbc.ca\/alfm5\/wp-json\/pressbooks\/v2\/chapters\/189\/revisions\/537"}],"part":[{"href":"https:\/\/opentextbc.ca\/alfm5\/wp-json\/pressbooks\/v2\/parts\/154"}],"metadata":[{"href":"https:\/\/opentextbc.ca\/alfm5\/wp-json\/pressbooks\/v2\/chapters\/189\/metadata\/"}],"wp:attachment":[{"href":"https:\/\/opentextbc.ca\/alfm5\/wp-json\/wp\/v2\/media?parent=189"}],"wp:term":[{"taxonomy":"chapter-type","embeddable":true,"href":"https:\/\/opentextbc.ca\/alfm5\/wp-json\/pressbooks\/v2\/chapter-type?post=189"},{"taxonomy":"contributor","embeddable":true,"href":"https:\/\/opentextbc.ca\/alfm5\/wp-json\/wp\/v2\/contributor?post=189"},{"taxonomy":"license","embeddable":true,"href":"https:\/\/opentextbc.ca\/alfm5\/wp-json\/wp\/v2\/license?post=189"}],"curies":[{"name":"wp","href":"https:\/\/api.w.org\/{rel}","templated":true}]}}