{"id":98,"date":"2021-10-22T21:05:10","date_gmt":"2021-10-23T01:05:10","guid":{"rendered":"https:\/\/pressbooks.bccampus.ca\/math025\/chapter\/common-fractions\/"},"modified":"2025-06-26T22:02:13","modified_gmt":"2025-06-27T02:02:13","slug":"common-fractions","status":"publish","type":"chapter","link":"https:\/\/pressbooks.bccampus.ca\/math025\/chapter\/common-fractions\/","title":{"raw":"Topic B: Common Fractions","rendered":"Topic B: Common Fractions"},"content":{"raw":"<div class=\"textbox shaded\">\r\n\r\nThere are three types of fractions:\r\n<ul>\r\n \t<li>[pb_glossary id=\"282\"]Proper fractions[\/pb_glossary] are part of the whole thing.<\/li>\r\n \t<li>[pb_glossary id=\"285\"]Improper fractions\u00a0[\/pb_glossary]\u00a0are equal to 1 or are greater than 1.<\/li>\r\n \t<li>[pb_glossary id=\"286\"]Mixed numbers[\/pb_glossary] are greater than one.<\/li>\r\n<\/ul>\r\n<\/div>\r\nIn a [pb_glossary id=\"282\"]proper fraction[\/pb_glossary], the numerator is smaller than the denominator. Proper fractions are less than one.\r\n<ul class=\"twocolumn\">\r\n \t<li>[latex]\\dfrac{3}{4}&lt;1[\/latex]<\/li>\r\n \t<li>[latex]\\dfrac{2}{5}&lt;1[\/latex]<\/li>\r\n \t<li>[latex]\\dfrac{9}{10}&lt;1[\/latex]<\/li>\r\n \t<li>[latex]\\dfrac{4}{7}&lt;1[\/latex]<\/li>\r\n<\/ul>\r\nIn <strong>improper fractions<\/strong>, the numerator is the same or larger than the denominator.\r\n<ul class=\"twocolumn\">\r\n \t<li>[latex]\\dfrac{4}{4}=1[\/latex]<\/li>\r\n \t<li>[latex]\\dfrac{3}{3}=1[\/latex]<\/li>\r\n \t<li>[latex]\\dfrac{8}{3}&gt;1[\/latex]<\/li>\r\n \t<li>[latex]\\dfrac{9}{7}&gt;1[\/latex]<\/li>\r\n<\/ul>\r\nIn <strong>mixed numbers<\/strong>, a whole number and a proper fraction are used together.\r\n<ul class=\"twocolumn\">\r\n \t<li>[latex]1\\dfrac{1}{2}&gt;1[\/latex]<\/li>\r\n \t<li>[latex]4\\dfrac{3}{7}&gt;1[\/latex]<\/li>\r\n \t<li>[latex]3\\dfrac{2}{5}&gt;1[\/latex]<\/li>\r\n \t<li>[latex]1\\dfrac{9}{10}&gt;1[\/latex]<\/li>\r\n<\/ul>\r\nHere are some pictures to visualize mixed numbers:\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=\"aligncenter wp-image-67\" src=\"https:\/\/pressbooks.bccampus.ca\/wp-content\/uploads\/sites\/2383\/2021\/10\/three-apple-halfs.jpg\" alt=\"Three apple halves.\" width=\"300\" height=\"149\" \/>\r\n\r\nYou want to give three small children only [latex]\\tfrac{1}{2}[\/latex] an apple each. You need three half apples. You can write that as [latex]\\tfrac{3}{2}[\/latex] (three-halves). How will you get [latex]\\tfrac{3}{2}[\/latex] of an apple?\r\n\r\nYou must use <strong>more than one apple<\/strong>.\r\n<p style=\"text-align: center\">[latex]\\tfrac{3}{2} = 1\\tfrac{1}{2}[\/latex] apples<\/p>\r\nThis is one whole apple and [latex]\\tfrac{1}{2}[\/latex] of another one.\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 B<\/p>\r\n\r\n<\/header>\r\n<div class=\"textbox__content\">\r\n\r\n<img class=\"aligncenter wp-image-68\" src=\"https:\/\/pressbooks.bccampus.ca\/wp-content\/uploads\/sites\/2383\/2025\/01\/10-eighths.jpg\" alt=\"10 slices of pizza. One whole pizza with eight slices and two additional slices from another pizza.\" width=\"300\" height=\"138\" \/>\r\n\r\n10 pieces of pizza are shown. Each pizza was cut into 8 pieces, so the fraction can be written as [latex]\\tfrac{10}{8}[\/latex]. This is an <strong>improper fraction<\/strong>; it can also be written as a <strong>mixed number:<\/strong> [latex]1\\tfrac{2}{8}[\/latex]. This is 1 whole pizza, and [latex]\\tfrac{2}{8}[\/latex] of another one.\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 1<\/p>\r\n\r\n<\/header>\r\n<div class=\"textbox__content\">\r\n\r\nAnswer these questions.\r\n<ol type=\"a\">\r\n \t<li><img class=\"alignnone wp-image-69\" src=\"https:\/\/pressbooks.bccampus.ca\/wp-content\/uploads\/sites\/2383\/2025\/01\/seven-fourths-apples.jpg\" alt=\"Two apples cut into quarters. There are seven pieces of apple left.\" width=\"300\" height=\"163\" \/>\r\n<ol type=\"i\">\r\n \t<li>How many pieces of apple are shown?<\/li>\r\n \t<li>Each apple was cut into 4 pieces, so the denominator is <span style=\"text-decoration: underline\" aria-label=\"blank;\">\u00a0 \u00a0 \u00a0 \u00a0 \u00a0 \u00a0 \u00a0 \u00a0 \u00a0 \u00a0<\/span>.<\/li>\r\n \t<li>Write the improper fraction that describes the photo.<\/li>\r\n \t<li>The photo shows <span style=\"text-decoration: underline\" aria-label=\"blank;\">\u00a0 \u00a0 \u00a0 \u00a0 \u00a0 \u00a0 \u00a0 \u00a0 \u00a0 \u00a0<\/span> whole apple and <span style=\"text-decoration: underline\" aria-label=\"blank;\">\u00a0 \u00a0 \u00a0 \u00a0 \u00a0 \u00a0 \u00a0 \u00a0 \u00a0 \u00a0<\/span> of a second apple.<\/li>\r\n \t<li>Write the mixed number that describes the apple.<\/li>\r\n<\/ol>\r\n<\/li>\r\n \t<li><img class=\"alignnone wp-image-70\" src=\"https:\/\/pressbooks.bccampus.ca\/wp-content\/uploads\/sites\/2383\/2025\/01\/3-5-8-pizza.jpg\" alt=\"Three pizzas cut into 8 pieces. There are two whole pizzas. The third pizza has 5 slices left.\" width=\"300\" height=\"93\" \/>\r\n<ol type=\"i\">\r\n \t<li>How many pieces of pizza are shown?<\/li>\r\n \t<li>Each pizza was cut into 8 pieces, so the denominator is <span style=\"text-decoration: underline\" aria-label=\"blank;\">\u00a0 \u00a0 \u00a0 \u00a0 \u00a0 \u00a0 \u00a0 \u00a0 \u00a0 \u00a0<\/span>.<\/li>\r\n \t<li>Write the improper fraction that describes the photo.<\/li>\r\n \t<li>The photo shows <span style=\"text-decoration: underline\" aria-label=\"blank;\">\u00a0 \u00a0 \u00a0 \u00a0 \u00a0 \u00a0 \u00a0 \u00a0 \u00a0 \u00a0<\/span> whole pizzas and <span style=\"text-decoration: underline\" aria-label=\"blank;\">\u00a0 \u00a0 \u00a0 \u00a0 \u00a0 \u00a0 \u00a0 \u00a0 \u00a0 \u00a0<\/span> of a third pizza.<\/li>\r\n \t<li>Write the mixed number that describes the pizza.<\/li>\r\n<\/ol>\r\n<\/li>\r\n<\/ol>\r\n<strong>Answers to Exercise 1<\/strong>\r\n<ol class=\"twocolumn\" type=\"a\">\r\n \t<li>Apples.\r\n<ol type=\"i\">\r\n \t<li>[latex]7[\/latex]<\/li>\r\n \t<li>[latex]4[\/latex]<\/li>\r\n \t<li>[latex]\\dfrac{7}{4}[\/latex]<\/li>\r\n \t<li>[latex]1\\text{ and }\\dfrac{3}{4}[\/latex]<\/li>\r\n \t<li>[latex]1\\dfrac{3}{4}[\/latex]<\/li>\r\n<\/ol>\r\n<\/li>\r\n \t<li>Pizza.\r\n<ol type=\"i\">\r\n \t<li>[latex]21[\/latex]<\/li>\r\n \t<li>[latex]8[\/latex]<\/li>\r\n \t<li>[latex]\\dfrac{21}{8}[\/latex]<\/li>\r\n \t<li>[latex]2\\text{ and }\\dfrac{5}{8}[\/latex]<\/li>\r\n \t<li>[latex]2\\dfrac{5}{8}[\/latex]<\/li>\r\n<\/ol>\r\n<\/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 2<\/p>\r\n\r\n<\/header>\r\n<div class=\"textbox__content\">\r\n\r\nWrite the <strong>improper fraction<\/strong> and the <strong>mixed number<\/strong> that describe the shaded part in each drawing. First decide on the denominator. The denominator is what one whole thing has been divided into.\r\n<ol type=\"a\">\r\n \t<li><img class=\"alignnone wp-image-71\" src=\"https:\/\/pressbooks.bccampus.ca\/wp-content\/uploads\/sites\/2383\/2025\/01\/three-halves-circles.jpg\" alt=\"Two circles divided in half. One circle is entirely shaded in. The other circle only has one half shaded in.\" width=\"300\" height=\"155\" \/>\r\nAnswer: [latex]\\dfrac{3}{2}=1\\dfrac{1}{2}[\/latex]<\/li>\r\n \t<li><img class=\"alignnone wp-image-72\" src=\"https:\/\/pressbooks.bccampus.ca\/wp-content\/uploads\/sites\/2383\/2025\/01\/27-eighths.jpg\" alt=\"Four shapes divided into eight. Three shapes are all shaded in. One shape has three sections shaded.\" width=\"300\" height=\"277\" \/><\/li>\r\n \t<li><img class=\"alignnone wp-image-304 size-medium\" src=\"https:\/\/pressbooks.bccampus.ca\/math025\/wp-content\/uploads\/sites\/2383\/2021\/10\/unit1_topicB_exampleB-300x119.jpg\" alt=\"6 rectangles divided into 6. 5 rectangles are all shaded in. One rectangle has two section shaded in.\" width=\"300\" height=\"119\" \/><\/li>\r\n \t<li><img class=\"alignnone wp-image-74\" src=\"https:\/\/pressbooks.bccampus.ca\/wp-content\/uploads\/sites\/2383\/2025\/01\/14-ninths.jpg\" alt=\"2 shapes divided into 9 sections. One shape is all shaded in. The other shape has 5 sections shaded in.\" width=\"300\" height=\"138\" \/><\/li>\r\n \t<li><img class=\"alignnone wp-image-75\" src=\"https:\/\/pressbooks.bccampus.ca\/wp-content\/uploads\/sites\/2383\/2025\/01\/11-fourths.jpg\" alt=\"3 squares divided into 4. Two squares are all shaded in. One square has three sections shaded in.\" width=\"300\" height=\"97\" \/><\/li>\r\n<\/ol>\r\n<strong>Answers to Exercise 2<\/strong>\r\n<ol class=\"twocolumn\" start=\"2\" type=\"a\">\r\n \t<li>[latex]\\dfrac{27}{8} = 3\\dfrac{3}{8}[\/latex]<\/li>\r\n \t<li>[latex]\\dfrac{32}{6} = 5\\dfrac{2}{6}[\/latex]<\/li>\r\n \t<li>[latex]\\dfrac{14}{9} = 1\\dfrac{5}{9}[\/latex]<\/li>\r\n \t<li>[latex]\\dfrac{11}{4} = 2\\dfrac{3}{4}[\/latex]<\/li>\r\n<\/ol>\r\n<\/div>\r\n<\/div>\r\nNow it is your turn to draw some <strong>mixed numbers<\/strong>. The following is an example of how to do that.\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\nShade in this fraction: [latex]4\\dfrac{3}{4}[\/latex]\r\n\r\n(Note: you will not need to use all the squares drawn below.)\r\n\r\n<img class=\"alignnone wp-image-76 size-full\" src=\"https:\/\/pressbooks.bccampus.ca\/wp-content\/uploads\/sites\/2383\/2025\/01\/4-and-3-4ths-e1673977191854.jpg\" alt=\"Six squares divided into 4 sections. Four squares are all shaded in. One square has three sections shaded in. The last square is not shaded in.\" width=\"654\" height=\"96\" \/>\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 3<\/p>\r\n\r\n<\/header>\r\n<div class=\"textbox__content\">\r\n\r\nShade the following mixed fractions in the given shapes.\r\n<ol type=\"a\">\r\n \t<li>[latex]2\\dfrac{3}{5}\\hspace{1cm}[\/latex]<img class=\"wp-image-77 alignnone\" src=\"https:\/\/pressbooks.bccampus.ca\/wp-content\/uploads\/sites\/2383\/2025\/01\/5-5.jpg\" alt=\"Four rectangles, each divided into five sections.\" width=\"300\" height=\"47\" \/><\/li>\r\n \t<li>[latex]3\\dfrac{2}{3}\\hspace{1cm}[\/latex]<img class=\"wp-image-78 alignnone\" src=\"https:\/\/pressbooks.bccampus.ca\/wp-content\/uploads\/sites\/2383\/2025\/01\/Five-circles-in-thirds.jpg\" alt=\"Five circles each divided into thirds.\" width=\"300\" height=\"54\" \/><\/li>\r\n \t<li>[latex]5\\dfrac{1}{4}\\hspace{1cm}[\/latex]<img class=\"alignnone wp-image-79\" src=\"https:\/\/pressbooks.bccampus.ca\/wp-content\/uploads\/sites\/2383\/2025\/01\/9-4-rectangle.jpg\" alt=\"9 rectangles each divided into four sections.\" width=\"300\" height=\"51\" \/><\/li>\r\n \t<li>[latex]1\\dfrac{1}{2}\\hspace{1cm}[\/latex]<img class=\"alignnone wp-image-80\" src=\"https:\/\/pressbooks.bccampus.ca\/wp-content\/uploads\/sites\/2383\/2025\/01\/4-2-rectangle.jpg\" alt=\"Four rectangles each divided in half.\" width=\"300\" height=\"25\" \/><\/li>\r\n<\/ol>\r\nDraw the following mixed fractions:\r\n<ol class=\"bigspace twocolumn\" start=\"5\" type=\"a\">\r\n \t<li>[latex]4\\dfrac{1}{2}[\/latex]<\/li>\r\n \t<li>[latex]3\\dfrac{4}{5}[\/latex]<\/li>\r\n \t<li>[latex]2\\dfrac{2}{3}[\/latex]<\/li>\r\n \t<li>[latex]5\\dfrac{3}{4}[\/latex]<\/li>\r\n<\/ol>\r\n<strong>Answers to Exercise 3<\/strong>\r\n<ol type=\"a\">\r\n \t<li><img class=\"alignnone wp-image-81 size-medium\" src=\"https:\/\/pressbooks.bccampus.ca\/wp-content\/uploads\/sites\/2383\/2025\/01\/5-5-answers-300x29.jpg\" alt=\"5 rectangles divided into 5 sections. 2 are fully shaded. One has three sections shaded. Two are not shaded.\" width=\"300\" height=\"29\" \/><\/li>\r\n \t<li><img class=\"alignnone wp-image-82 size-medium\" src=\"https:\/\/pressbooks.bccampus.ca\/wp-content\/uploads\/sites\/2383\/2025\/01\/5-3-answers-e1673978083703-300x42.jpg\" alt=\"5 circles divided into 3 sections. 3 are fully shaded. 1 has 2 sections shaded. 2 are not shaded.\" width=\"300\" height=\"42\" \/><\/li>\r\n \t<li><img class=\"alignnone wp-image-83 size-medium\" src=\"https:\/\/pressbooks.bccampus.ca\/wp-content\/uploads\/sites\/2383\/2025\/01\/9-4-rectangle-answers-300x40.jpg\" alt=\"9 rectangles divided into 4 sections. 5 are fully shaded. 1 has 1 section shaded. 3 are not shaded.\" width=\"300\" height=\"40\" \/><\/li>\r\n \t<li><img class=\"alignnone wp-image-84 size-medium\" src=\"https:\/\/pressbooks.bccampus.ca\/wp-content\/uploads\/sites\/2383\/2025\/01\/4-2-rectangle-answers-300x22.jpg\" alt=\"4 rectangles divided into 2 sections. 1 is fully shaded. 1 has 1 section shaded. 2 are not shaded.\" width=\"300\" height=\"22\" \/><\/li>\r\n \t<li><img class=\"alignnone wp-image-85 size-medium\" src=\"https:\/\/pressbooks.bccampus.ca\/wp-content\/uploads\/sites\/2383\/2025\/01\/5-2-answers-300x37.jpg\" alt=\"5 circles divided into 2 sections. 4 are fully shaded. 1 has 1 section shaded.\" width=\"300\" height=\"37\" \/><\/li>\r\n \t<li><img class=\"alignnone wp-image-86 size-medium\" src=\"https:\/\/pressbooks.bccampus.ca\/wp-content\/uploads\/sites\/2383\/2025\/01\/5-5-answers2-300x32.jpg\" alt=\"5 rectangles divided into 5 sections. 3 are fully shaded. 1 has 4 sections shaded. 1 is not shaded.\" width=\"300\" height=\"32\" \/><\/li>\r\n \t<li><img class=\"alignnone wp-image-87 size-medium\" src=\"https:\/\/pressbooks.bccampus.ca\/wp-content\/uploads\/sites\/2383\/2025\/01\/3-3-answers-300x80.jpg\" alt=\"3 circles divided into 3 sections. 2 are fully shaded. 1 has 2 sections shaded.\" width=\"300\" height=\"80\" \/><\/li>\r\n \t<li><img class=\"alignnone wp-image-88 size-medium\" src=\"https:\/\/pressbooks.bccampus.ca\/wp-content\/uploads\/sites\/2383\/2025\/01\/6-4-answers-300x41.jpg\" alt=\"6 rectangles divided into 4 sections. 5 are fully shaded. 1 has 3 sections shaded.\" width=\"300\" height=\"41\" \/><\/li>\r\n<\/ol>\r\n<\/div>\r\n<\/div>\r\n<h1>Writing Improper Fractions as Mixed Numbers<\/h1>\r\nIn the last exercise you were able to write (rename) an improper fraction as a mixed number by looking at the drawing - you could see how many whole things were represented. You could see that if the denominator was 3, every time you had [latex]\\tfrac{3}{3}[\/latex] <img class=\"alignnone size-full wp-image-154\" src=\"https:\/\/pressbooks.bccampus.ca\/wp-content\/uploads\/sites\/2383\/2025\/01\/inline-circle-3-3-1.png\" alt=\"A circle split into three equal segments. All segments are shaded green.\" width=\"35\" height=\"29\" \/> that was one whole. If the denominator was 6, every time you had [latex]\\tfrac{6}{6}[\/latex] <img class=\"alignnone size-full wp-image-90\" src=\"https:\/\/pressbooks.bccampus.ca\/wp-content\/uploads\/sites\/2383\/2025\/01\/inline-rectangle-6-6.png\" alt=\"A rectangle split into six equal segments. All segments are shaded grey.\" width=\"81\" height=\"18\" \/> that was one whole, and so on. An improper fraction is written (renamed) as a mixed number by <strong>dividing<\/strong> the <strong>numerator<\/strong> by the <strong>number of parts in the whole<\/strong> (the <strong>denominator<\/strong>).\r\n<div class=\"textbox shaded\">To write (rename) an improper fraction as a mixed number, <strong>divide<\/strong> the <strong>numerator<\/strong> by the <strong>denominator<\/strong>.<\/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\">\r\n\r\nWrite [latex]\\tfrac{8}{5}[\/latex] as a mixed number.\r\n\r\nFirst, write as a long division problem or as a short division question.\r\n<p style=\"text-align: center\">[latex]\\require{enclose}\\text{denominator}\\enclose{longdiv}{\\text{numerator}}=5\\enclose{longdiv}{8}[\/latex]<\/p>\r\n<p style=\"text-align: center\">[latex]\\text{numerator}\\div\\text{denominator} = 8\\div5[\/latex]<\/p>\r\nSecond, divide. Write the remainder as a fraction, using the same denominator.\r\n<ol>\r\n \t<li>The 1 becomes the whole number.<\/li>\r\n \t<li>Use the [pb_glossary id=\"265\"]remainder[\/pb_glossary] (3) as the numerator<\/li>\r\n \t<li>Use the divisor (5) as the denominator.<\/li>\r\n<\/ol>\r\n<p style=\"text-align: center\">[latex]\\begin{array}{r}1\\\\ 5\\enclose{longdiv}{8}\\\\-5\\\\ \\hline\\text{R }3\\end{array}[\/latex]\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0 or \u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0 [latex]8\\div5=1\\text{ R }3[\/latex]<\/p>\r\n<p style=\"text-align: center\">[latex]\\dfrac{8}{5}=1\\dfrac{3}{5}[\/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 E<\/p>\r\n\r\n<\/header>\r\n<div class=\"textbox__content\">\r\n\r\nWrite [latex]\\tfrac{16}{4}[\/latex] as a mixed number.\r\n\r\n[latex]4\\enclose{longdiv}{16}[\/latex] or [latex]16\\div4[\/latex]\r\n<p style=\"text-align: center\">[latex]\\begin{array}{r}4\\\\ 4\\enclose{longdiv}{16}\\\\-16\\\\ \\hline0\\end{array}[\/latex] \u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0 or \u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0 [latex]16\\div4=4[\/latex]<\/p>\r\n<p style=\"text-align: center\">[latex]\\dfrac{16}{4}=4[\/latex]<\/p>\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 4<\/p>\r\n\r\n<\/header>\r\n<div class=\"textbox__content\">\r\n\r\nRewrite each improper fraction as an equivalent mixed number or whole number.\r\n<ol class=\"twocolumn\" type=\"a\">\r\n \t<li>[latex]\\dfrac{9}{2}=[\/latex]<\/li>\r\n \t<li>[latex]\\dfrac{11}{10}=[\/latex]<\/li>\r\n \t<li>[latex]\\dfrac{20}{4}=[\/latex]<\/li>\r\n \t<li>[latex]\\dfrac{17}{6}=[\/latex]<\/li>\r\n \t<li>[latex]\\dfrac{13}{3}=[\/latex]<\/li>\r\n \t<li>[latex]\\dfrac{20}{10}=[\/latex]<\/li>\r\n \t<li>[latex]\\dfrac{7}{4}=[\/latex]<\/li>\r\n<\/ol>\r\n<strong>Answers to Exercise 4<\/strong>\r\n<ol class=\"twocolumn\" type=\"a\">\r\n \t<li>[latex]4\\dfrac{1}{2}[\/latex]<\/li>\r\n \t<li>[latex]1\\dfrac{1}{10}[\/latex]<\/li>\r\n \t<li>[latex]5[\/latex]<\/li>\r\n \t<li>[latex]2\\dfrac{5}{6}[\/latex]<\/li>\r\n \t<li>[latex]4\\dfrac{1}{3}[\/latex]<\/li>\r\n \t<li>[latex]2[\/latex]<\/li>\r\n \t<li>[latex]1\\dfrac{3}{4}[\/latex]<\/li>\r\n<\/ol>\r\n<\/div>\r\n<\/div>\r\n<h1>Renaming Mixed Numbers as Improper Fractions<\/h1>\r\nThis process will be used when you multiply and divide common fractions and when you \"borrow\" in subtraction.\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\nTake the whole number 2.\r\n\r\nHere are 2 equal shapes.\r\n\r\n<img class=\"aligncenter wp-image-91\" src=\"https:\/\/pressbooks.bccampus.ca\/wp-content\/uploads\/sites\/2383\/2025\/01\/Two-shapes.jpg\" alt=\"Two squares.\" width=\"300\" height=\"130\" \/>\r\n\r\nThe shapes are each divided into 3 parts (thirds).\r\n\r\n<img class=\"aligncenter wp-image-92\" src=\"https:\/\/pressbooks.bccampus.ca\/wp-content\/uploads\/sites\/2383\/2025\/01\/Two-shapes-in-three-parts.jpg\" alt=\"Two squares, each divided into three parts.\" width=\"300\" height=\"128\" \/>\r\n\r\nHow many thirds are there? 6 thirds.\r\n<p style=\"text-align: center\">[latex]2 =\\dfrac{6}{3}[\/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 G<\/p>\r\n\r\n<\/header>\r\n<div class=\"textbox__content\">\r\n\r\nTake the whole number 1.\r\n\r\nDraw one shape (a circle or a box).\r\n\r\n<img class=\"aligncenter wp-image-93\" src=\"https:\/\/pressbooks.bccampus.ca\/wp-content\/uploads\/sites\/2383\/2025\/01\/circle.jpg\" alt=\"A circle.\" width=\"100\" height=\"99\" \/>\r\n\r\nNow divide the shape into half.\r\n\r\n<img class=\"aligncenter wp-image-94\" src=\"https:\/\/pressbooks.bccampus.ca\/wp-content\/uploads\/sites\/2383\/2025\/01\/circle-two-parts.jpg\" alt=\"A circle divided into two parts.\" width=\"100\" height=\"97\" \/>\r\n\r\nHow many halves are there? [latex]1=\\dfrac{2}{2}[\/latex]\r\n\r\n<\/div>\r\n<\/div>\r\n<h2>Have you found the shortcut?<\/h2>\r\nThe shortcut to rename a whole number as an improper fraction is to <strong>multiply<\/strong> the <strong>whole number by the denominator<\/strong>.\r\n<ul>\r\n \t<li>[latex]2 = \\dfrac{}{4}\\hspace{1cm}[\/latex]Each whole number has 4 equal parts (4 quarters) in it,\r\n<ul type=\"none\">\r\n \t<li>so [latex]2\\text{ (whole numbers)}\\times4\\text{ (parts)} = 8\\text{ parts}[\/latex]<\/li>\r\n \t<li>so [latex]2 = \\dfrac{8}{4}[\/latex]<\/li>\r\n<\/ul>\r\n<\/li>\r\n \t<li>[latex]6 = \\dfrac{}{2}\\hspace{1cm}[\/latex]Each whole number has 2 equal parts (2 halves),\r\n<ul type=\"none\">\r\n \t<li>so [latex]6\\text{ (whole numbers)}\\times2\\text{ (parts)}=12\\text{ parts}[\/latex]<\/li>\r\n \t<li>so [latex]6= \\dfrac{12}{2}[\/latex]<\/li>\r\n<\/ul>\r\n<\/li>\r\n \t<li>[latex]8 = \\dfrac{}{3}[\/latex]\r\n<ul>\r\n \t<li>[latex]8\\times3=24[\/latex]<\/li>\r\n \t<li>so [latex]8 = \\dfrac{24}{3}[\/latex]<\/li>\r\n<\/ul>\r\n<\/li>\r\n<\/ul>\r\n<div class=\"textbox shaded\">Until you are comfortable, draw a little sketch like you did in the example.<\/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\nRename each whole number as an improper fraction using the denominator shown.\r\n<ol type=\"a\">\r\n \t<li>[latex]6 = \\dfrac{24}{4}[\/latex],\u00a0 \u00a0 \u00a0 [latex]2 = \\dfrac{}{3}[\/latex],\u00a0 \u00a0 \u00a0 \u00a0[latex]4 = \\dfrac{}{3}[\/latex],\u00a0 \u00a0 \u00a0 [latex]8 = \\dfrac{}{10}[\/latex]<\/li>\r\n \t<li>[latex]7 = \\dfrac{}{3}[\/latex],\u00a0 \u00a0 \u00a0 [latex]1 = \\dfrac{}{4}[\/latex],\u00a0 \u00a0 \u00a0 [latex]6 = \\dfrac{}{10}[\/latex],\u00a0 \u00a0 \u00a0 [latex]5 = \\dfrac{}{6}[\/latex]<\/li>\r\n<\/ol>\r\n<strong>Answers to Exercise 5<\/strong>\r\n<ol class=\"twocolumn\" type=\"a\">\r\n \t<li>[latex]\\dfrac{24}{4}[\/latex],[latex]\\dfrac{6}{3}[\/latex],[latex]\\dfrac{12}{3}[\/latex],[latex]\\dfrac{80}{10}[\/latex]<\/li>\r\n \t<li>[latex]\\dfrac{21}{3}[\/latex],[latex]\\dfrac{4}{4}[\/latex],[latex]\\dfrac{60}{10}[\/latex],[latex]\\dfrac{30}{6}[\/latex]<\/li>\r\n<\/ol>\r\n<\/div>\r\n<\/div>\r\nNow let's take this idea further. How can you rename a <strong>mixed number<\/strong> as an improper fraction?\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\nTake the mixed number [latex]2\\tfrac{1}{4}[\/latex]. This is two whole things and <strong>part of a third<\/strong> whole thing.\r\n\r\nHere are three equal shapes divided into fourths.\r\n\r\n<img class=\"aligncenter wp-image-95 size-full\" src=\"https:\/\/pressbooks.bccampus.ca\/wp-content\/uploads\/sites\/2383\/2025\/01\/3-squares-in-quarters-e1673981542487.jpg\" alt=\"Three squares each divided into fourths.\" width=\"472\" height=\"107\" \/>\r\n\r\nShade in two whole shapes [latex]\\tfrac{8}{4}[\/latex] and [latex]\\tfrac{1}{4}[\/latex] of the third shape.\r\n\r\nHow many fourths have you shaded in all? <strong>9<\/strong> fourths\r\n<p style=\"text-align: center\">[latex]2\\dfrac{1}{4} = \\dfrac{9}{4}[\/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 I<\/p>\r\n\r\n<\/header>\r\n<div class=\"textbox__content\">\r\n\r\nTake the mixed number [latex]1\\tfrac{2}{3}[\/latex]. This is one whole thing and part of a second whole thing.\r\n\r\nDraw two equal shapes and divide them into thirds.\r\n\r\nShade in one whole shape [latex]\\tfrac{3}{3}[\/latex] and [latex]\\tfrac{2}{3}[\/latex] of the second shape.\r\n\r\n<img class=\"aligncenter wp-image-92\" src=\"https:\/\/pressbooks.bccampus.ca\/wp-content\/uploads\/sites\/2383\/2025\/01\/Two-shapes-in-three-parts.jpg\" alt=\"Two squares, each divided into three parts.\" width=\"300\" height=\"128\" \/>\r\n\r\nHow many thirds have you shaded in all? <span style=\"text-decoration: underline\" aria-label=\"blank\">\u00a0 \u00a0 \u00a0\u00a0<\/span> thirds\r\n<p style=\"text-align: center\">[latex]1\\dfrac{2}{3}=\\dfrac{}{3}[\/latex]<\/p>\r\n\r\n<\/div>\r\n<\/div>\r\nTo rename a mixed number as an improper fraction, multiply the whole number by the denominator of the fraction and then add this to the numerator. Write the [pb_glossary id=\"272\"]total[\/pb_glossary] as the new numerator over the denominator.\r\n<table class=\"no-border-table\" border=\"0\" width=\"100%\">\r\n<tbody>\r\n<tr>\r\n<td>[latex]3\\dfrac{1}{4}=\\dfrac{?}{4}[\/latex]<\/td>\r\n<td>\u00a0[latex]3=\\dfrac{12}{4}[\/latex]<\/td>\r\n<td>so<\/td>\r\n<td>[latex] 3\\dfrac{1}{4}=\\dfrac{12}{4}+\\dfrac{1}{4}=\\dfrac{13}{4}[\/latex]<\/td>\r\n<\/tr>\r\n<tr>\r\n<td>[latex]2\\dfrac{1}{2}=\\dfrac{?}{2}[\/latex]<\/td>\r\n<td>\u00a0[latex]2=\\dfrac{4}{2}[\/latex]<\/td>\r\n<td>so<\/td>\r\n<td>[latex]2\\dfrac{1}{2}=\\dfrac{4}{2}+\\dfrac{1}{2}=\\dfrac{5}{2}[\/latex]<\/td>\r\n<\/tr>\r\n<\/tbody>\r\n<\/table>\r\n<div class=\"textbox textbox--exercises\"><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\nRename each mixed number as an improper fraction.\r\n<ol class=\"twocolumn\" type=\"a\">\r\n \t<li>[latex]2\\dfrac{4}{5} = \\dfrac{14}{5}[\/latex]<\/li>\r\n \t<li>[latex]8\\dfrac{3}{8} = \\dfrac{67}{8}[\/latex]<\/li>\r\n \t<li>[latex]6\\dfrac{5}{8} = \\dfrac{}{8}[\/latex]<\/li>\r\n \t<li>[latex]5\\dfrac{1}{2} = \\dfrac{}{2}[\/latex]<\/li>\r\n \t<li>[latex]8\\dfrac{4}{5} = [\/latex]<\/li>\r\n \t<li>[latex]6\\dfrac{1}{8} = [\/latex]<\/li>\r\n \t<li>[latex]5\\dfrac{3}{6} = [\/latex]<\/li>\r\n \t<li>[latex]2\\dfrac{7}{8} = [\/latex]<\/li>\r\n \t<li>[latex]1\\dfrac{8}{10} = [\/latex]<\/li>\r\n \t<li>[latex]3\\dfrac{6}{8} = [\/latex]<\/li>\r\n<\/ol>\r\n<strong>Answers to Exercise 6<\/strong>\r\n<ol class=\"twocolumn\" type=\"a\">\r\n \t<li>[latex]\\dfrac{14}{5}[\/latex]<\/li>\r\n \t<li>[latex]\\dfrac{67}{8}[\/latex]<\/li>\r\n \t<li>[latex]\\dfrac{53}{8}[\/latex]<\/li>\r\n \t<li>[latex]\\dfrac{11}{2}[\/latex]<\/li>\r\n \t<li>[latex]\\dfrac{44}{5}[\/latex]<\/li>\r\n \t<li>[latex]\\dfrac{49}{8}[\/latex]<\/li>\r\n \t<li>[latex]\\dfrac{33}{6}[\/latex]<\/li>\r\n \t<li>[latex]\\dfrac{23}{8}[\/latex]<\/li>\r\n \t<li>[latex]\\dfrac{18}{10}[\/latex]<\/li>\r\n \t<li>[latex]\\dfrac{30}{8}[\/latex]<\/li>\r\n<\/ol>\r\n<\/div>\r\n<\/div>\r\n<h1>To Say or Write a Mixed Number<\/h1>\r\nIf you want to say these strange looking fractions out loud, do as follows.\r\n\r\nWrite or say: the whole number + and + the fraction\r\n<ul type=\"none\">\r\n \t<li>[latex]3\\tfrac{2}{5} = [\/latex] three and two fifths<\/li>\r\n \t<li>[latex]5\\tfrac{1}{6} = [\/latex] five and one sixth<\/li>\r\n<\/ul>\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\nWrite the following fractions as words.\r\n<ol class=\"twocolumn\" type=\"a\">\r\n \t<li>[latex]2\\dfrac{1}{8}[\/latex]<\/li>\r\n \t<li>[latex]4\\dfrac{3}{4}[\/latex]<\/li>\r\n \t<li>[latex]1\\dfrac{1}{2}[\/latex]<\/li>\r\n \t<li>[latex]3\\dfrac{3}{4}[\/latex]<\/li>\r\n<\/ol>\r\n<strong>Answers to Exercise 7<\/strong>\r\n<ol class=\"twocolumn\" type=\"a\">\r\n \t<li>Two and one eighth<\/li>\r\n \t<li>Four and three fourths (or four and three quarters)<\/li>\r\n \t<li>One and one half<\/li>\r\n \t<li>Three and three fourths (or three and three quarters)<\/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\/12\u00a0 \u00a0 \u00a0 \u00a0 \u00a0 \u00a0 \u00a0 \u00a0 \u00a0 Aim\u00a0 \u00a0 \u00a0 \u00a0 9\/12<\/strong>\r\n<ol type=\"A\">\r\n \t<li>Write the improper fraction and the mixed number that describe the shaded part of the drawings in each question (4 marks).\r\n<ol type=\"a\">\r\n \t<li><img class=\"alignnone wp-image-96\" src=\"https:\/\/pressbooks.bccampus.ca\/wp-content\/uploads\/sites\/2383\/2025\/01\/4-1-3-circles.jpg\" alt=\"4 circles each divided into 3 parts. Three circles are fully shaded. One circle has one part shaded.\" width=\"300\" height=\"47\" \/><\/li>\r\n \t<li><img class=\"alignnone wp-image-97\" src=\"https:\/\/pressbooks.bccampus.ca\/wp-content\/uploads\/sites\/2383\/2025\/01\/2-3-4-banner.jpg\" alt=\"Two shapes each divided into four parts. The first shape is fully shaded. The second shape has three parts shaded.\" width=\"168\" height=\"47\" \/><\/li>\r\n<\/ol>\r\n<\/li>\r\n \t<li>Rename each improper fraction as an equivalent mixed number or whole number (4 marks).\r\n<ol class=\"twocolumn\" type=\"a\">\r\n \t<li>[latex]\\dfrac{9}{4}=[\/latex]<\/li>\r\n \t<li>[latex]\\dfrac{12}{3}=[\/latex]<\/li>\r\n \t<li>[latex]\\dfrac{5}{3}=[\/latex]<\/li>\r\n \t<li>[latex]\\dfrac{7}{2}=[\/latex]<\/li>\r\n<\/ol>\r\n<\/li>\r\n \t<li>Rename as improper fractions (4 marks).\r\n<ol class=\"twocolumn\" type=\"a\">\r\n \t<li>[latex]3\\dfrac{1}{2}=[\/latex]<\/li>\r\n \t<li>[latex]4\\dfrac{3}{8}=[\/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<\/ol>\r\n<\/li>\r\n<\/ol>\r\n<h2>Answers to Topic B Self-Test<\/h2>\r\n<ol type=\"A\">\r\n \t<li>Write the improper fraction and the mixed number that describe the shaded part of the drawings in each question.\r\n<ol type=\"a\">\r\n \t<li>[latex]\\dfrac{10}{3} = 3\\dfrac{1}{3}[\/latex]<\/li>\r\n \t<li>[latex]\\dfrac{7}{4} = 1\\dfrac{3}{4}[\/latex]<\/li>\r\n<\/ol>\r\n<\/li>\r\n \t<li>Rename each improper fraction as an equivalent mixed number or whole number.\r\n<ol class=\"twocolumn\" type=\"a\">\r\n \t<li>[latex]2\\dfrac{1}{4}[\/latex]<\/li>\r\n \t<li>[latex]4[\/latex]<\/li>\r\n \t<li>[latex]1\\dfrac{2}{3}[\/latex]<\/li>\r\n \t<li>[latex]3\\dfrac{1}{2}[\/latex]<\/li>\r\n<\/ol>\r\n<\/li>\r\n \t<li>Rename as improper fractions.\r\n<ol class=\"twocolumn\" type=\"a\">\r\n \t<li>[latex]\\dfrac{7}{2}[\/latex]<\/li>\r\n \t<li>[latex]\\dfrac{35}{8}[\/latex]<\/li>\r\n \t<li>[latex]\\dfrac{15}{8}[\/latex]<\/li>\r\n \t<li>[latex]\\dfrac{17}{6}[\/latex]<\/li>\r\n<\/ol>\r\n<\/li>\r\n<\/ol>","rendered":"<div class=\"textbox shaded\">\n<p>There are three types of fractions:<\/p>\n<ul>\n<li><a class=\"glossary-term\" aria-haspopup=\"dialog\" aria-describedby=\"definition\" href=\"#term_98_282\">Proper fractions<\/a> are part of the whole thing.<\/li>\n<li><a class=\"glossary-term\" aria-haspopup=\"dialog\" aria-describedby=\"definition\" href=\"#term_98_285\">Improper fractions\u00a0<\/a>\u00a0are equal to 1 or are greater than 1.<\/li>\n<li><a class=\"glossary-term\" aria-haspopup=\"dialog\" aria-describedby=\"definition\" href=\"#term_98_286\">Mixed numbers<\/a> are greater than one.<\/li>\n<\/ul>\n<\/div>\n<p>In a <a class=\"glossary-term\" aria-haspopup=\"dialog\" aria-describedby=\"definition\" href=\"#term_98_282\">proper fraction<\/a>, the numerator is smaller than the denominator. Proper fractions are less than one.<\/p>\n<ul class=\"twocolumn\">\n<li>[latex]\\dfrac{3}{4}<1[\/latex]<\/li>\n<li>[latex]\\dfrac{2}{5}<1[\/latex]<\/li>\n<li>[latex]\\dfrac{9}{10}<1[\/latex]<\/li>\n<li>[latex]\\dfrac{4}{7}<1[\/latex]<\/li>\n<\/ul>\n<p>In <strong>improper fractions<\/strong>, the numerator is the same or larger than the denominator.<\/p>\n<ul class=\"twocolumn\">\n<li>[latex]\\dfrac{4}{4}=1[\/latex]<\/li>\n<li>[latex]\\dfrac{3}{3}=1[\/latex]<\/li>\n<li>[latex]\\dfrac{8}{3}>1[\/latex]<\/li>\n<li>[latex]\\dfrac{9}{7}>1[\/latex]<\/li>\n<\/ul>\n<p>In <strong>mixed numbers<\/strong>, a whole number and a proper fraction are used together.<\/p>\n<ul class=\"twocolumn\">\n<li>[latex]1\\dfrac{1}{2}>1[\/latex]<\/li>\n<li>[latex]4\\dfrac{3}{7}>1[\/latex]<\/li>\n<li>[latex]3\\dfrac{2}{5}>1[\/latex]<\/li>\n<li>[latex]1\\dfrac{9}{10}>1[\/latex]<\/li>\n<\/ul>\n<p>Here are some pictures to visualize mixed numbers:<\/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=\"aligncenter wp-image-67\" src=\"https:\/\/pressbooks.bccampus.ca\/wp-content\/uploads\/sites\/2383\/2021\/10\/three-apple-halfs.jpg\" alt=\"Three apple halves.\" width=\"300\" height=\"149\" srcset=\"https:\/\/pressbooks.bccampus.ca\/math025\/wp-content\/uploads\/sites\/2383\/2021\/10\/three-apple-halfs.jpg 364w, https:\/\/pressbooks.bccampus.ca\/math025\/wp-content\/uploads\/sites\/2383\/2021\/10\/three-apple-halfs-300x149.jpg 300w, https:\/\/pressbooks.bccampus.ca\/math025\/wp-content\/uploads\/sites\/2383\/2021\/10\/three-apple-halfs-65x32.jpg 65w, https:\/\/pressbooks.bccampus.ca\/math025\/wp-content\/uploads\/sites\/2383\/2021\/10\/three-apple-halfs-225x112.jpg 225w, https:\/\/pressbooks.bccampus.ca\/math025\/wp-content\/uploads\/sites\/2383\/2021\/10\/three-apple-halfs-350x174.jpg 350w\" sizes=\"auto, (max-width: 300px) 100vw, 300px\" \/><\/p>\n<p>You want to give three small children only [latex]\\tfrac{1}{2}[\/latex] an apple each. You need three half apples. You can write that as [latex]\\tfrac{3}{2}[\/latex] (three-halves). How will you get [latex]\\tfrac{3}{2}[\/latex] of an apple?<\/p>\n<p>You must use <strong>more than one apple<\/strong>.<\/p>\n<p style=\"text-align: center\">[latex]\\tfrac{3}{2} = 1\\tfrac{1}{2}[\/latex] apples<\/p>\n<p>This is one whole apple and [latex]\\tfrac{1}{2}[\/latex] of another one.<\/p>\n<\/div>\n<\/div>\n<div class=\"textbox textbox--examples\">\n<header class=\"textbox__header\">\n<p class=\"textbox__title\">Example B<\/p>\n<\/header>\n<div class=\"textbox__content\">\n<p><img loading=\"lazy\" decoding=\"async\" class=\"aligncenter wp-image-68\" src=\"https:\/\/pressbooks.bccampus.ca\/wp-content\/uploads\/sites\/2383\/2025\/01\/10-eighths.jpg\" alt=\"10 slices of pizza. One whole pizza with eight slices and two additional slices from another pizza.\" width=\"300\" height=\"138\" srcset=\"https:\/\/pressbooks.bccampus.ca\/math025\/wp-content\/uploads\/sites\/2383\/2025\/01\/10-eighths.jpg 399w, https:\/\/pressbooks.bccampus.ca\/math025\/wp-content\/uploads\/sites\/2383\/2025\/01\/10-eighths-300x138.jpg 300w, https:\/\/pressbooks.bccampus.ca\/math025\/wp-content\/uploads\/sites\/2383\/2025\/01\/10-eighths-65x30.jpg 65w, https:\/\/pressbooks.bccampus.ca\/math025\/wp-content\/uploads\/sites\/2383\/2025\/01\/10-eighths-225x103.jpg 225w, https:\/\/pressbooks.bccampus.ca\/math025\/wp-content\/uploads\/sites\/2383\/2025\/01\/10-eighths-350x161.jpg 350w\" sizes=\"auto, (max-width: 300px) 100vw, 300px\" \/><\/p>\n<p>10 pieces of pizza are shown. Each pizza was cut into 8 pieces, so the fraction can be written as [latex]\\tfrac{10}{8}[\/latex]. This is an <strong>improper fraction<\/strong>; it can also be written as a <strong>mixed number:<\/strong> [latex]1\\tfrac{2}{8}[\/latex]. This is 1 whole pizza, and [latex]\\tfrac{2}{8}[\/latex] of another one.<\/p>\n<\/div>\n<\/div>\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>Answer these questions.<\/p>\n<ol type=\"a\">\n<li><img loading=\"lazy\" decoding=\"async\" class=\"alignnone wp-image-69\" src=\"https:\/\/pressbooks.bccampus.ca\/wp-content\/uploads\/sites\/2383\/2025\/01\/seven-fourths-apples.jpg\" alt=\"Two apples cut into quarters. There are seven pieces of apple left.\" width=\"300\" height=\"163\" srcset=\"https:\/\/pressbooks.bccampus.ca\/math025\/wp-content\/uploads\/sites\/2383\/2025\/01\/seven-fourths-apples.jpg 333w, https:\/\/pressbooks.bccampus.ca\/math025\/wp-content\/uploads\/sites\/2383\/2025\/01\/seven-fourths-apples-300x163.jpg 300w, https:\/\/pressbooks.bccampus.ca\/math025\/wp-content\/uploads\/sites\/2383\/2025\/01\/seven-fourths-apples-65x35.jpg 65w, https:\/\/pressbooks.bccampus.ca\/math025\/wp-content\/uploads\/sites\/2383\/2025\/01\/seven-fourths-apples-225x122.jpg 225w\" sizes=\"auto, (max-width: 300px) 100vw, 300px\" \/>\n<ol type=\"i\">\n<li>How many pieces of apple are shown?<\/li>\n<li>Each apple was cut into 4 pieces, so the denominator is <span style=\"text-decoration: underline\" aria-label=\"blank;\">\u00a0 \u00a0 \u00a0 \u00a0 \u00a0 \u00a0 \u00a0 \u00a0 \u00a0 \u00a0<\/span>.<\/li>\n<li>Write the improper fraction that describes the photo.<\/li>\n<li>The photo shows <span style=\"text-decoration: underline\" aria-label=\"blank;\">\u00a0 \u00a0 \u00a0 \u00a0 \u00a0 \u00a0 \u00a0 \u00a0 \u00a0 \u00a0<\/span> whole apple and <span style=\"text-decoration: underline\" aria-label=\"blank;\">\u00a0 \u00a0 \u00a0 \u00a0 \u00a0 \u00a0 \u00a0 \u00a0 \u00a0 \u00a0<\/span> of a second apple.<\/li>\n<li>Write the mixed number that describes the apple.<\/li>\n<\/ol>\n<\/li>\n<li><img loading=\"lazy\" decoding=\"async\" class=\"alignnone wp-image-70\" src=\"https:\/\/pressbooks.bccampus.ca\/wp-content\/uploads\/sites\/2383\/2025\/01\/3-5-8-pizza.jpg\" alt=\"Three pizzas cut into 8 pieces. There are two whole pizzas. The third pizza has 5 slices left.\" width=\"300\" height=\"93\" srcset=\"https:\/\/pressbooks.bccampus.ca\/math025\/wp-content\/uploads\/sites\/2383\/2025\/01\/3-5-8-pizza.jpg 883w, https:\/\/pressbooks.bccampus.ca\/math025\/wp-content\/uploads\/sites\/2383\/2025\/01\/3-5-8-pizza-300x93.jpg 300w, https:\/\/pressbooks.bccampus.ca\/math025\/wp-content\/uploads\/sites\/2383\/2025\/01\/3-5-8-pizza-768x238.jpg 768w, https:\/\/pressbooks.bccampus.ca\/math025\/wp-content\/uploads\/sites\/2383\/2025\/01\/3-5-8-pizza-65x20.jpg 65w, https:\/\/pressbooks.bccampus.ca\/math025\/wp-content\/uploads\/sites\/2383\/2025\/01\/3-5-8-pizza-225x70.jpg 225w, https:\/\/pressbooks.bccampus.ca\/math025\/wp-content\/uploads\/sites\/2383\/2025\/01\/3-5-8-pizza-350x109.jpg 350w\" sizes=\"auto, (max-width: 300px) 100vw, 300px\" \/>\n<ol type=\"i\">\n<li>How many pieces of pizza are shown?<\/li>\n<li>Each pizza was cut into 8 pieces, so the denominator is <span style=\"text-decoration: underline\" aria-label=\"blank;\">\u00a0 \u00a0 \u00a0 \u00a0 \u00a0 \u00a0 \u00a0 \u00a0 \u00a0 \u00a0<\/span>.<\/li>\n<li>Write the improper fraction that describes the photo.<\/li>\n<li>The photo shows <span style=\"text-decoration: underline\" aria-label=\"blank;\">\u00a0 \u00a0 \u00a0 \u00a0 \u00a0 \u00a0 \u00a0 \u00a0 \u00a0 \u00a0<\/span> whole pizzas and <span style=\"text-decoration: underline\" aria-label=\"blank;\">\u00a0 \u00a0 \u00a0 \u00a0 \u00a0 \u00a0 \u00a0 \u00a0 \u00a0 \u00a0<\/span> of a third pizza.<\/li>\n<li>Write the mixed number that describes the pizza.<\/li>\n<\/ol>\n<\/li>\n<\/ol>\n<p><strong>Answers to Exercise 1<\/strong><\/p>\n<ol class=\"twocolumn\" type=\"a\">\n<li>Apples.\n<ol type=\"i\">\n<li>[latex]7[\/latex]<\/li>\n<li>[latex]4[\/latex]<\/li>\n<li>[latex]\\dfrac{7}{4}[\/latex]<\/li>\n<li>[latex]1\\text{ and }\\dfrac{3}{4}[\/latex]<\/li>\n<li>[latex]1\\dfrac{3}{4}[\/latex]<\/li>\n<\/ol>\n<\/li>\n<li>Pizza.\n<ol type=\"i\">\n<li>[latex]21[\/latex]<\/li>\n<li>[latex]8[\/latex]<\/li>\n<li>[latex]\\dfrac{21}{8}[\/latex]<\/li>\n<li>[latex]2\\text{ and }\\dfrac{5}{8}[\/latex]<\/li>\n<li>[latex]2\\dfrac{5}{8}[\/latex]<\/li>\n<\/ol>\n<\/li>\n<\/ol>\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>Write the <strong>improper fraction<\/strong> and the <strong>mixed number<\/strong> that describe the shaded part in each drawing. First decide on the denominator. The denominator is what one whole thing has been divided into.<\/p>\n<ol type=\"a\">\n<li><img loading=\"lazy\" decoding=\"async\" class=\"alignnone wp-image-71\" src=\"https:\/\/pressbooks.bccampus.ca\/wp-content\/uploads\/sites\/2383\/2025\/01\/three-halves-circles.jpg\" alt=\"Two circles divided in half. One circle is entirely shaded in. The other circle only has one half shaded in.\" width=\"300\" height=\"155\" srcset=\"https:\/\/pressbooks.bccampus.ca\/math025\/wp-content\/uploads\/sites\/2383\/2025\/01\/three-halves-circles.jpg 310w, https:\/\/pressbooks.bccampus.ca\/math025\/wp-content\/uploads\/sites\/2383\/2025\/01\/three-halves-circles-300x155.jpg 300w, https:\/\/pressbooks.bccampus.ca\/math025\/wp-content\/uploads\/sites\/2383\/2025\/01\/three-halves-circles-65x34.jpg 65w, https:\/\/pressbooks.bccampus.ca\/math025\/wp-content\/uploads\/sites\/2383\/2025\/01\/three-halves-circles-225x116.jpg 225w\" sizes=\"auto, (max-width: 300px) 100vw, 300px\" \/><br \/>\nAnswer: [latex]\\dfrac{3}{2}=1\\dfrac{1}{2}[\/latex]<\/li>\n<li><img loading=\"lazy\" decoding=\"async\" class=\"alignnone wp-image-72\" src=\"https:\/\/pressbooks.bccampus.ca\/wp-content\/uploads\/sites\/2383\/2025\/01\/27-eighths.jpg\" alt=\"Four shapes divided into eight. Three shapes are all shaded in. One shape has three sections shaded.\" width=\"300\" height=\"277\" srcset=\"https:\/\/pressbooks.bccampus.ca\/math025\/wp-content\/uploads\/sites\/2383\/2025\/01\/27-eighths.jpg 447w, https:\/\/pressbooks.bccampus.ca\/math025\/wp-content\/uploads\/sites\/2383\/2025\/01\/27-eighths-300x277.jpg 300w, https:\/\/pressbooks.bccampus.ca\/math025\/wp-content\/uploads\/sites\/2383\/2025\/01\/27-eighths-65x60.jpg 65w, https:\/\/pressbooks.bccampus.ca\/math025\/wp-content\/uploads\/sites\/2383\/2025\/01\/27-eighths-225x207.jpg 225w, https:\/\/pressbooks.bccampus.ca\/math025\/wp-content\/uploads\/sites\/2383\/2025\/01\/27-eighths-350x323.jpg 350w\" sizes=\"auto, (max-width: 300px) 100vw, 300px\" \/><\/li>\n<li><img loading=\"lazy\" decoding=\"async\" class=\"alignnone wp-image-304 size-medium\" src=\"https:\/\/pressbooks.bccampus.ca\/math025\/wp-content\/uploads\/sites\/2383\/2021\/10\/unit1_topicB_exampleB-300x119.jpg\" alt=\"6 rectangles divided into 6. 5 rectangles are all shaded in. One rectangle has two section shaded in.\" width=\"300\" height=\"119\" srcset=\"https:\/\/pressbooks.bccampus.ca\/math025\/wp-content\/uploads\/sites\/2383\/2021\/10\/unit1_topicB_exampleB-300x119.jpg 300w, https:\/\/pressbooks.bccampus.ca\/math025\/wp-content\/uploads\/sites\/2383\/2021\/10\/unit1_topicB_exampleB-65x26.jpg 65w, https:\/\/pressbooks.bccampus.ca\/math025\/wp-content\/uploads\/sites\/2383\/2021\/10\/unit1_topicB_exampleB-225x89.jpg 225w, https:\/\/pressbooks.bccampus.ca\/math025\/wp-content\/uploads\/sites\/2383\/2021\/10\/unit1_topicB_exampleB-350x138.jpg 350w, https:\/\/pressbooks.bccampus.ca\/math025\/wp-content\/uploads\/sites\/2383\/2021\/10\/unit1_topicB_exampleB.jpg 491w\" sizes=\"auto, (max-width: 300px) 100vw, 300px\" \/><\/li>\n<li><img loading=\"lazy\" decoding=\"async\" class=\"alignnone wp-image-74\" src=\"https:\/\/pressbooks.bccampus.ca\/wp-content\/uploads\/sites\/2383\/2025\/01\/14-ninths.jpg\" alt=\"2 shapes divided into 9 sections. One shape is all shaded in. The other shape has 5 sections shaded in.\" width=\"300\" height=\"138\" srcset=\"https:\/\/pressbooks.bccampus.ca\/math025\/wp-content\/uploads\/sites\/2383\/2025\/01\/14-ninths.jpg 348w, https:\/\/pressbooks.bccampus.ca\/math025\/wp-content\/uploads\/sites\/2383\/2025\/01\/14-ninths-300x138.jpg 300w, https:\/\/pressbooks.bccampus.ca\/math025\/wp-content\/uploads\/sites\/2383\/2025\/01\/14-ninths-65x30.jpg 65w, https:\/\/pressbooks.bccampus.ca\/math025\/wp-content\/uploads\/sites\/2383\/2025\/01\/14-ninths-225x103.jpg 225w\" sizes=\"auto, (max-width: 300px) 100vw, 300px\" \/><\/li>\n<li><img loading=\"lazy\" decoding=\"async\" class=\"alignnone wp-image-75\" src=\"https:\/\/pressbooks.bccampus.ca\/wp-content\/uploads\/sites\/2383\/2025\/01\/11-fourths.jpg\" alt=\"3 squares divided into 4. Two squares are all shaded in. One square has three sections shaded in.\" width=\"300\" height=\"97\" srcset=\"https:\/\/pressbooks.bccampus.ca\/math025\/wp-content\/uploads\/sites\/2383\/2025\/01\/11-fourths.jpg 348w, https:\/\/pressbooks.bccampus.ca\/math025\/wp-content\/uploads\/sites\/2383\/2025\/01\/11-fourths-300x97.jpg 300w, https:\/\/pressbooks.bccampus.ca\/math025\/wp-content\/uploads\/sites\/2383\/2025\/01\/11-fourths-65x21.jpg 65w, https:\/\/pressbooks.bccampus.ca\/math025\/wp-content\/uploads\/sites\/2383\/2025\/01\/11-fourths-225x72.jpg 225w\" sizes=\"auto, (max-width: 300px) 100vw, 300px\" \/><\/li>\n<\/ol>\n<p><strong>Answers to Exercise 2<\/strong><\/p>\n<ol class=\"twocolumn\" start=\"2\" type=\"a\">\n<li>[latex]\\dfrac{27}{8} = 3\\dfrac{3}{8}[\/latex]<\/li>\n<li>[latex]\\dfrac{32}{6} = 5\\dfrac{2}{6}[\/latex]<\/li>\n<li>[latex]\\dfrac{14}{9} = 1\\dfrac{5}{9}[\/latex]<\/li>\n<li>[latex]\\dfrac{11}{4} = 2\\dfrac{3}{4}[\/latex]<\/li>\n<\/ol>\n<\/div>\n<\/div>\n<p>Now it is your turn to draw some <strong>mixed numbers<\/strong>. The following is an example of how to do that.<\/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>Shade in this fraction: [latex]4\\dfrac{3}{4}[\/latex]<\/p>\n<p>(Note: you will not need to use all the squares drawn below.)<\/p>\n<p><img loading=\"lazy\" decoding=\"async\" class=\"alignnone wp-image-76 size-full\" src=\"https:\/\/pressbooks.bccampus.ca\/wp-content\/uploads\/sites\/2383\/2025\/01\/4-and-3-4ths-e1673977191854.jpg\" alt=\"Six squares divided into 4 sections. Four squares are all shaded in. One square has three sections shaded in. The last square is not shaded in.\" width=\"654\" height=\"96\" srcset=\"https:\/\/pressbooks.bccampus.ca\/math025\/wp-content\/uploads\/sites\/2383\/2025\/01\/4-and-3-4ths-e1673977191854.jpg 654w, https:\/\/pressbooks.bccampus.ca\/math025\/wp-content\/uploads\/sites\/2383\/2025\/01\/4-and-3-4ths-e1673977191854-300x44.jpg 300w, https:\/\/pressbooks.bccampus.ca\/math025\/wp-content\/uploads\/sites\/2383\/2025\/01\/4-and-3-4ths-e1673977191854-65x10.jpg 65w, https:\/\/pressbooks.bccampus.ca\/math025\/wp-content\/uploads\/sites\/2383\/2025\/01\/4-and-3-4ths-e1673977191854-225x33.jpg 225w, https:\/\/pressbooks.bccampus.ca\/math025\/wp-content\/uploads\/sites\/2383\/2025\/01\/4-and-3-4ths-e1673977191854-350x51.jpg 350w\" sizes=\"auto, (max-width: 654px) 100vw, 654px\" \/><\/p>\n<\/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>Shade the following mixed fractions in the given shapes.<\/p>\n<ol type=\"a\">\n<li>[latex]2\\dfrac{3}{5}\\hspace{1cm}[\/latex]<img loading=\"lazy\" decoding=\"async\" class=\"wp-image-77 alignnone\" src=\"https:\/\/pressbooks.bccampus.ca\/wp-content\/uploads\/sites\/2383\/2025\/01\/5-5.jpg\" alt=\"Four rectangles, each divided into five sections.\" width=\"300\" height=\"47\" srcset=\"https:\/\/pressbooks.bccampus.ca\/math025\/wp-content\/uploads\/sites\/2383\/2025\/01\/5-5.jpg 507w, https:\/\/pressbooks.bccampus.ca\/math025\/wp-content\/uploads\/sites\/2383\/2025\/01\/5-5-300x47.jpg 300w, https:\/\/pressbooks.bccampus.ca\/math025\/wp-content\/uploads\/sites\/2383\/2025\/01\/5-5-65x10.jpg 65w, https:\/\/pressbooks.bccampus.ca\/math025\/wp-content\/uploads\/sites\/2383\/2025\/01\/5-5-225x35.jpg 225w, https:\/\/pressbooks.bccampus.ca\/math025\/wp-content\/uploads\/sites\/2383\/2025\/01\/5-5-350x55.jpg 350w\" sizes=\"auto, (max-width: 300px) 100vw, 300px\" \/><\/li>\n<li>[latex]3\\dfrac{2}{3}\\hspace{1cm}[\/latex]<img loading=\"lazy\" decoding=\"async\" class=\"wp-image-78 alignnone\" src=\"https:\/\/pressbooks.bccampus.ca\/wp-content\/uploads\/sites\/2383\/2025\/01\/Five-circles-in-thirds.jpg\" alt=\"Five circles each divided into thirds.\" width=\"300\" height=\"54\" srcset=\"https:\/\/pressbooks.bccampus.ca\/math025\/wp-content\/uploads\/sites\/2383\/2025\/01\/Five-circles-in-thirds.jpg 556w, https:\/\/pressbooks.bccampus.ca\/math025\/wp-content\/uploads\/sites\/2383\/2025\/01\/Five-circles-in-thirds-300x54.jpg 300w, https:\/\/pressbooks.bccampus.ca\/math025\/wp-content\/uploads\/sites\/2383\/2025\/01\/Five-circles-in-thirds-65x12.jpg 65w, https:\/\/pressbooks.bccampus.ca\/math025\/wp-content\/uploads\/sites\/2383\/2025\/01\/Five-circles-in-thirds-225x40.jpg 225w, https:\/\/pressbooks.bccampus.ca\/math025\/wp-content\/uploads\/sites\/2383\/2025\/01\/Five-circles-in-thirds-350x63.jpg 350w\" sizes=\"auto, (max-width: 300px) 100vw, 300px\" \/><\/li>\n<li>[latex]5\\dfrac{1}{4}\\hspace{1cm}[\/latex]<img loading=\"lazy\" decoding=\"async\" class=\"alignnone wp-image-79\" src=\"https:\/\/pressbooks.bccampus.ca\/wp-content\/uploads\/sites\/2383\/2025\/01\/9-4-rectangle.jpg\" alt=\"9 rectangles each divided into four sections.\" width=\"300\" height=\"51\" srcset=\"https:\/\/pressbooks.bccampus.ca\/math025\/wp-content\/uploads\/sites\/2383\/2025\/01\/9-4-rectangle.jpg 630w, https:\/\/pressbooks.bccampus.ca\/math025\/wp-content\/uploads\/sites\/2383\/2025\/01\/9-4-rectangle-300x51.jpg 300w, https:\/\/pressbooks.bccampus.ca\/math025\/wp-content\/uploads\/sites\/2383\/2025\/01\/9-4-rectangle-65x11.jpg 65w, https:\/\/pressbooks.bccampus.ca\/math025\/wp-content\/uploads\/sites\/2383\/2025\/01\/9-4-rectangle-225x39.jpg 225w, https:\/\/pressbooks.bccampus.ca\/math025\/wp-content\/uploads\/sites\/2383\/2025\/01\/9-4-rectangle-350x60.jpg 350w\" sizes=\"auto, (max-width: 300px) 100vw, 300px\" \/><\/li>\n<li>[latex]1\\dfrac{1}{2}\\hspace{1cm}[\/latex]<img loading=\"lazy\" decoding=\"async\" class=\"alignnone wp-image-80\" src=\"https:\/\/pressbooks.bccampus.ca\/wp-content\/uploads\/sites\/2383\/2025\/01\/4-2-rectangle.jpg\" alt=\"Four rectangles each divided in half.\" width=\"300\" height=\"25\" srcset=\"https:\/\/pressbooks.bccampus.ca\/math025\/wp-content\/uploads\/sites\/2383\/2025\/01\/4-2-rectangle.jpg 619w, https:\/\/pressbooks.bccampus.ca\/math025\/wp-content\/uploads\/sites\/2383\/2025\/01\/4-2-rectangle-300x25.jpg 300w, https:\/\/pressbooks.bccampus.ca\/math025\/wp-content\/uploads\/sites\/2383\/2025\/01\/4-2-rectangle-65x5.jpg 65w, https:\/\/pressbooks.bccampus.ca\/math025\/wp-content\/uploads\/sites\/2383\/2025\/01\/4-2-rectangle-225x19.jpg 225w, https:\/\/pressbooks.bccampus.ca\/math025\/wp-content\/uploads\/sites\/2383\/2025\/01\/4-2-rectangle-350x29.jpg 350w\" sizes=\"auto, (max-width: 300px) 100vw, 300px\" \/><\/li>\n<\/ol>\n<p>Draw the following mixed fractions:<\/p>\n<ol class=\"bigspace twocolumn\" start=\"5\" type=\"a\">\n<li>[latex]4\\dfrac{1}{2}[\/latex]<\/li>\n<li>[latex]3\\dfrac{4}{5}[\/latex]<\/li>\n<li>[latex]2\\dfrac{2}{3}[\/latex]<\/li>\n<li>[latex]5\\dfrac{3}{4}[\/latex]<\/li>\n<\/ol>\n<p><strong>Answers to Exercise 3<\/strong><\/p>\n<ol type=\"a\">\n<li><img loading=\"lazy\" decoding=\"async\" class=\"alignnone wp-image-81 size-medium\" src=\"https:\/\/pressbooks.bccampus.ca\/wp-content\/uploads\/sites\/2383\/2025\/01\/5-5-answers-300x29.jpg\" alt=\"5 rectangles divided into 5 sections. 2 are fully shaded. One has three sections shaded. Two are not shaded.\" width=\"300\" height=\"29\" srcset=\"https:\/\/pressbooks.bccampus.ca\/math025\/wp-content\/uploads\/sites\/2383\/2025\/01\/5-5-answers-300x29.jpg 300w, https:\/\/pressbooks.bccampus.ca\/math025\/wp-content\/uploads\/sites\/2383\/2025\/01\/5-5-answers-65x6.jpg 65w, https:\/\/pressbooks.bccampus.ca\/math025\/wp-content\/uploads\/sites\/2383\/2025\/01\/5-5-answers-225x21.jpg 225w, https:\/\/pressbooks.bccampus.ca\/math025\/wp-content\/uploads\/sites\/2383\/2025\/01\/5-5-answers-350x33.jpg 350w, https:\/\/pressbooks.bccampus.ca\/math025\/wp-content\/uploads\/sites\/2383\/2025\/01\/5-5-answers.jpg 640w\" sizes=\"auto, (max-width: 300px) 100vw, 300px\" \/><\/li>\n<li><img loading=\"lazy\" decoding=\"async\" class=\"alignnone wp-image-82 size-medium\" src=\"https:\/\/pressbooks.bccampus.ca\/wp-content\/uploads\/sites\/2383\/2025\/01\/5-3-answers-e1673978083703-300x42.jpg\" alt=\"5 circles divided into 3 sections. 3 are fully shaded. 1 has 2 sections shaded. 2 are not shaded.\" width=\"300\" height=\"42\" srcset=\"https:\/\/pressbooks.bccampus.ca\/math025\/wp-content\/uploads\/sites\/2383\/2025\/01\/5-3-answers-e1673978083703-300x42.jpg 300w, https:\/\/pressbooks.bccampus.ca\/math025\/wp-content\/uploads\/sites\/2383\/2025\/01\/5-3-answers-e1673978083703-65x9.jpg 65w, https:\/\/pressbooks.bccampus.ca\/math025\/wp-content\/uploads\/sites\/2383\/2025\/01\/5-3-answers-e1673978083703-225x31.jpg 225w, https:\/\/pressbooks.bccampus.ca\/math025\/wp-content\/uploads\/sites\/2383\/2025\/01\/5-3-answers-e1673978083703-350x49.jpg 350w, https:\/\/pressbooks.bccampus.ca\/math025\/wp-content\/uploads\/sites\/2383\/2025\/01\/5-3-answers-e1673978083703.jpg 643w\" sizes=\"auto, (max-width: 300px) 100vw, 300px\" \/><\/li>\n<li><img loading=\"lazy\" decoding=\"async\" class=\"alignnone wp-image-83 size-medium\" src=\"https:\/\/pressbooks.bccampus.ca\/wp-content\/uploads\/sites\/2383\/2025\/01\/9-4-rectangle-answers-300x40.jpg\" alt=\"9 rectangles divided into 4 sections. 5 are fully shaded. 1 has 1 section shaded. 3 are not shaded.\" width=\"300\" height=\"40\" srcset=\"https:\/\/pressbooks.bccampus.ca\/math025\/wp-content\/uploads\/sites\/2383\/2025\/01\/9-4-rectangle-answers-300x40.jpg 300w, https:\/\/pressbooks.bccampus.ca\/math025\/wp-content\/uploads\/sites\/2383\/2025\/01\/9-4-rectangle-answers-65x9.jpg 65w, https:\/\/pressbooks.bccampus.ca\/math025\/wp-content\/uploads\/sites\/2383\/2025\/01\/9-4-rectangle-answers-225x30.jpg 225w, https:\/\/pressbooks.bccampus.ca\/math025\/wp-content\/uploads\/sites\/2383\/2025\/01\/9-4-rectangle-answers-350x47.jpg 350w, https:\/\/pressbooks.bccampus.ca\/math025\/wp-content\/uploads\/sites\/2383\/2025\/01\/9-4-rectangle-answers.jpg 631w\" sizes=\"auto, (max-width: 300px) 100vw, 300px\" \/><\/li>\n<li><img loading=\"lazy\" decoding=\"async\" class=\"alignnone wp-image-84 size-medium\" src=\"https:\/\/pressbooks.bccampus.ca\/wp-content\/uploads\/sites\/2383\/2025\/01\/4-2-rectangle-answers-300x22.jpg\" alt=\"4 rectangles divided into 2 sections. 1 is fully shaded. 1 has 1 section shaded. 2 are not shaded.\" width=\"300\" height=\"22\" srcset=\"https:\/\/pressbooks.bccampus.ca\/math025\/wp-content\/uploads\/sites\/2383\/2025\/01\/4-2-rectangle-answers-300x22.jpg 300w, https:\/\/pressbooks.bccampus.ca\/math025\/wp-content\/uploads\/sites\/2383\/2025\/01\/4-2-rectangle-answers-65x5.jpg 65w, https:\/\/pressbooks.bccampus.ca\/math025\/wp-content\/uploads\/sites\/2383\/2025\/01\/4-2-rectangle-answers-225x16.jpg 225w, https:\/\/pressbooks.bccampus.ca\/math025\/wp-content\/uploads\/sites\/2383\/2025\/01\/4-2-rectangle-answers-350x25.jpg 350w, https:\/\/pressbooks.bccampus.ca\/math025\/wp-content\/uploads\/sites\/2383\/2025\/01\/4-2-rectangle-answers.jpg 619w\" sizes=\"auto, (max-width: 300px) 100vw, 300px\" \/><\/li>\n<li><img loading=\"lazy\" decoding=\"async\" class=\"alignnone wp-image-85 size-medium\" src=\"https:\/\/pressbooks.bccampus.ca\/wp-content\/uploads\/sites\/2383\/2025\/01\/5-2-answers-300x37.jpg\" alt=\"5 circles divided into 2 sections. 4 are fully shaded. 1 has 1 section shaded.\" width=\"300\" height=\"37\" srcset=\"https:\/\/pressbooks.bccampus.ca\/math025\/wp-content\/uploads\/sites\/2383\/2025\/01\/5-2-answers-300x37.jpg 300w, https:\/\/pressbooks.bccampus.ca\/math025\/wp-content\/uploads\/sites\/2383\/2025\/01\/5-2-answers-65x8.jpg 65w, https:\/\/pressbooks.bccampus.ca\/math025\/wp-content\/uploads\/sites\/2383\/2025\/01\/5-2-answers-225x28.jpg 225w, https:\/\/pressbooks.bccampus.ca\/math025\/wp-content\/uploads\/sites\/2383\/2025\/01\/5-2-answers-350x43.jpg 350w, https:\/\/pressbooks.bccampus.ca\/math025\/wp-content\/uploads\/sites\/2383\/2025\/01\/5-2-answers.jpg 646w\" sizes=\"auto, (max-width: 300px) 100vw, 300px\" \/><\/li>\n<li><img loading=\"lazy\" decoding=\"async\" class=\"alignnone wp-image-86 size-medium\" src=\"https:\/\/pressbooks.bccampus.ca\/wp-content\/uploads\/sites\/2383\/2025\/01\/5-5-answers2-300x32.jpg\" alt=\"5 rectangles divided into 5 sections. 3 are fully shaded. 1 has 4 sections shaded. 1 is not shaded.\" width=\"300\" height=\"32\" srcset=\"https:\/\/pressbooks.bccampus.ca\/math025\/wp-content\/uploads\/sites\/2383\/2025\/01\/5-5-answers2-300x32.jpg 300w, https:\/\/pressbooks.bccampus.ca\/math025\/wp-content\/uploads\/sites\/2383\/2025\/01\/5-5-answers2-65x7.jpg 65w, https:\/\/pressbooks.bccampus.ca\/math025\/wp-content\/uploads\/sites\/2383\/2025\/01\/5-5-answers2-225x24.jpg 225w, https:\/\/pressbooks.bccampus.ca\/math025\/wp-content\/uploads\/sites\/2383\/2025\/01\/5-5-answers2-350x38.jpg 350w, https:\/\/pressbooks.bccampus.ca\/math025\/wp-content\/uploads\/sites\/2383\/2025\/01\/5-5-answers2.jpg 597w\" sizes=\"auto, (max-width: 300px) 100vw, 300px\" \/><\/li>\n<li><img loading=\"lazy\" decoding=\"async\" class=\"alignnone wp-image-87 size-medium\" src=\"https:\/\/pressbooks.bccampus.ca\/wp-content\/uploads\/sites\/2383\/2025\/01\/3-3-answers-300x80.jpg\" alt=\"3 circles divided into 3 sections. 2 are fully shaded. 1 has 2 sections shaded.\" width=\"300\" height=\"80\" srcset=\"https:\/\/pressbooks.bccampus.ca\/math025\/wp-content\/uploads\/sites\/2383\/2025\/01\/3-3-answers-300x80.jpg 300w, https:\/\/pressbooks.bccampus.ca\/math025\/wp-content\/uploads\/sites\/2383\/2025\/01\/3-3-answers-65x17.jpg 65w, https:\/\/pressbooks.bccampus.ca\/math025\/wp-content\/uploads\/sites\/2383\/2025\/01\/3-3-answers-225x60.jpg 225w, https:\/\/pressbooks.bccampus.ca\/math025\/wp-content\/uploads\/sites\/2383\/2025\/01\/3-3-answers-350x93.jpg 350w, https:\/\/pressbooks.bccampus.ca\/math025\/wp-content\/uploads\/sites\/2383\/2025\/01\/3-3-answers.jpg 376w\" sizes=\"auto, (max-width: 300px) 100vw, 300px\" \/><\/li>\n<li><img loading=\"lazy\" decoding=\"async\" class=\"alignnone wp-image-88 size-medium\" src=\"https:\/\/pressbooks.bccampus.ca\/wp-content\/uploads\/sites\/2383\/2025\/01\/6-4-answers-300x41.jpg\" alt=\"6 rectangles divided into 4 sections. 5 are fully shaded. 1 has 3 sections shaded.\" width=\"300\" height=\"41\" srcset=\"https:\/\/pressbooks.bccampus.ca\/math025\/wp-content\/uploads\/sites\/2383\/2025\/01\/6-4-answers-300x41.jpg 300w, https:\/\/pressbooks.bccampus.ca\/math025\/wp-content\/uploads\/sites\/2383\/2025\/01\/6-4-answers-65x9.jpg 65w, https:\/\/pressbooks.bccampus.ca\/math025\/wp-content\/uploads\/sites\/2383\/2025\/01\/6-4-answers-225x31.jpg 225w, https:\/\/pressbooks.bccampus.ca\/math025\/wp-content\/uploads\/sites\/2383\/2025\/01\/6-4-answers-350x47.jpg 350w, https:\/\/pressbooks.bccampus.ca\/math025\/wp-content\/uploads\/sites\/2383\/2025\/01\/6-4-answers.jpg 472w\" sizes=\"auto, (max-width: 300px) 100vw, 300px\" \/><\/li>\n<\/ol>\n<\/div>\n<\/div>\n<h1>Writing Improper Fractions as Mixed Numbers<\/h1>\n<p>In the last exercise you were able to write (rename) an improper fraction as a mixed number by looking at the drawing &#8211; you could see how many whole things were represented. You could see that if the denominator was 3, every time you had [latex]\\tfrac{3}{3}[\/latex] <img loading=\"lazy\" decoding=\"async\" class=\"alignnone size-full wp-image-154\" src=\"https:\/\/pressbooks.bccampus.ca\/wp-content\/uploads\/sites\/2383\/2025\/01\/inline-circle-3-3-1.png\" alt=\"A circle split into three equal segments. All segments are shaded green.\" width=\"35\" height=\"29\" \/> that was one whole. If the denominator was 6, every time you had [latex]\\tfrac{6}{6}[\/latex] <img loading=\"lazy\" decoding=\"async\" class=\"alignnone size-full wp-image-90\" src=\"https:\/\/pressbooks.bccampus.ca\/wp-content\/uploads\/sites\/2383\/2025\/01\/inline-rectangle-6-6.png\" alt=\"A rectangle split into six equal segments. All segments are shaded grey.\" width=\"81\" height=\"18\" srcset=\"https:\/\/pressbooks.bccampus.ca\/math025\/wp-content\/uploads\/sites\/2383\/2025\/01\/inline-rectangle-6-6.png 81w, https:\/\/pressbooks.bccampus.ca\/math025\/wp-content\/uploads\/sites\/2383\/2025\/01\/inline-rectangle-6-6-65x14.png 65w\" sizes=\"auto, (max-width: 81px) 100vw, 81px\" \/> that was one whole, and so on. An improper fraction is written (renamed) as a mixed number by <strong>dividing<\/strong> the <strong>numerator<\/strong> by the <strong>number of parts in the whole<\/strong> (the <strong>denominator<\/strong>).<\/p>\n<div class=\"textbox shaded\">To write (rename) an improper fraction as a mixed number, <strong>divide<\/strong> the <strong>numerator<\/strong> by the <strong>denominator<\/strong>.<\/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\">\n<p>Write [latex]\\tfrac{8}{5}[\/latex] as a mixed number.<\/p>\n<p>First, write as a long division problem or as a short division question.<\/p>\n<p style=\"text-align: center\">[latex]\\require{enclose}\\text{denominator}\\enclose{longdiv}{\\text{numerator}}=5\\enclose{longdiv}{8}[\/latex]<\/p>\n<p style=\"text-align: center\">[latex]\\text{numerator}\\div\\text{denominator} = 8\\div5[\/latex]<\/p>\n<p>Second, divide. Write the remainder as a fraction, using the same denominator.<\/p>\n<ol>\n<li>The 1 becomes the whole number.<\/li>\n<li>Use the <a class=\"glossary-term\" aria-haspopup=\"dialog\" aria-describedby=\"definition\" href=\"#term_98_265\">remainder<\/a> (3) as the numerator<\/li>\n<li>Use the divisor (5) as the denominator.<\/li>\n<\/ol>\n<p style=\"text-align: center\">[latex]\\begin{array}{r}1\\\\ 5\\enclose{longdiv}{8}\\\\-5\\\\ \\hline\\text{R }3\\end{array}[\/latex]\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0 or \u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0 [latex]8\\div5=1\\text{ R }3[\/latex]<\/p>\n<p style=\"text-align: center\">[latex]\\dfrac{8}{5}=1\\dfrac{3}{5}[\/latex]<\/p>\n<\/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\">\n<p>Write [latex]\\tfrac{16}{4}[\/latex] as a mixed number.<\/p>\n<p>[latex]4\\enclose{longdiv}{16}[\/latex] or [latex]16\\div4[\/latex]<\/p>\n<p style=\"text-align: center\">[latex]\\begin{array}{r}4\\\\ 4\\enclose{longdiv}{16}\\\\-16\\\\ \\hline0\\end{array}[\/latex] \u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0 or \u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0 [latex]16\\div4=4[\/latex]<\/p>\n<p style=\"text-align: center\">[latex]\\dfrac{16}{4}=4[\/latex]<\/p>\n<\/div>\n<\/div>\n<div class=\"textbox textbox--exercises\">\n<header class=\"textbox__header\">\n<p class=\"textbox__title\">Exercise 4<\/p>\n<\/header>\n<div class=\"textbox__content\">\n<p>Rewrite each improper fraction as an equivalent mixed number or whole number.<\/p>\n<ol class=\"twocolumn\" type=\"a\">\n<li>[latex]\\dfrac{9}{2}=[\/latex]<\/li>\n<li>[latex]\\dfrac{11}{10}=[\/latex]<\/li>\n<li>[latex]\\dfrac{20}{4}=[\/latex]<\/li>\n<li>[latex]\\dfrac{17}{6}=[\/latex]<\/li>\n<li>[latex]\\dfrac{13}{3}=[\/latex]<\/li>\n<li>[latex]\\dfrac{20}{10}=[\/latex]<\/li>\n<li>[latex]\\dfrac{7}{4}=[\/latex]<\/li>\n<\/ol>\n<p><strong>Answers to Exercise 4<\/strong><\/p>\n<ol class=\"twocolumn\" type=\"a\">\n<li>[latex]4\\dfrac{1}{2}[\/latex]<\/li>\n<li>[latex]1\\dfrac{1}{10}[\/latex]<\/li>\n<li>[latex]5[\/latex]<\/li>\n<li>[latex]2\\dfrac{5}{6}[\/latex]<\/li>\n<li>[latex]4\\dfrac{1}{3}[\/latex]<\/li>\n<li>[latex]2[\/latex]<\/li>\n<li>[latex]1\\dfrac{3}{4}[\/latex]<\/li>\n<\/ol>\n<\/div>\n<\/div>\n<h1>Renaming Mixed Numbers as Improper Fractions<\/h1>\n<p>This process will be used when you multiply and divide common fractions and when you &#8220;borrow&#8221; in subtraction.<\/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>Take the whole number 2.<\/p>\n<p>Here are 2 equal shapes.<\/p>\n<p><img loading=\"lazy\" decoding=\"async\" class=\"aligncenter wp-image-91\" src=\"https:\/\/pressbooks.bccampus.ca\/wp-content\/uploads\/sites\/2383\/2025\/01\/Two-shapes.jpg\" alt=\"Two squares.\" width=\"300\" height=\"130\" srcset=\"https:\/\/pressbooks.bccampus.ca\/math025\/wp-content\/uploads\/sites\/2383\/2025\/01\/Two-shapes.jpg 676w, https:\/\/pressbooks.bccampus.ca\/math025\/wp-content\/uploads\/sites\/2383\/2025\/01\/Two-shapes-300x130.jpg 300w, https:\/\/pressbooks.bccampus.ca\/math025\/wp-content\/uploads\/sites\/2383\/2025\/01\/Two-shapes-65x28.jpg 65w, https:\/\/pressbooks.bccampus.ca\/math025\/wp-content\/uploads\/sites\/2383\/2025\/01\/Two-shapes-225x97.jpg 225w, https:\/\/pressbooks.bccampus.ca\/math025\/wp-content\/uploads\/sites\/2383\/2025\/01\/Two-shapes-350x151.jpg 350w\" sizes=\"auto, (max-width: 300px) 100vw, 300px\" \/><\/p>\n<p>The shapes are each divided into 3 parts (thirds).<\/p>\n<p><img loading=\"lazy\" decoding=\"async\" class=\"aligncenter wp-image-92\" src=\"https:\/\/pressbooks.bccampus.ca\/wp-content\/uploads\/sites\/2383\/2025\/01\/Two-shapes-in-three-parts.jpg\" alt=\"Two squares, each divided into three parts.\" width=\"300\" height=\"128\" srcset=\"https:\/\/pressbooks.bccampus.ca\/math025\/wp-content\/uploads\/sites\/2383\/2025\/01\/Two-shapes-in-three-parts.jpg 670w, https:\/\/pressbooks.bccampus.ca\/math025\/wp-content\/uploads\/sites\/2383\/2025\/01\/Two-shapes-in-three-parts-300x128.jpg 300w, https:\/\/pressbooks.bccampus.ca\/math025\/wp-content\/uploads\/sites\/2383\/2025\/01\/Two-shapes-in-three-parts-65x28.jpg 65w, https:\/\/pressbooks.bccampus.ca\/math025\/wp-content\/uploads\/sites\/2383\/2025\/01\/Two-shapes-in-three-parts-225x96.jpg 225w, https:\/\/pressbooks.bccampus.ca\/math025\/wp-content\/uploads\/sites\/2383\/2025\/01\/Two-shapes-in-three-parts-350x149.jpg 350w\" sizes=\"auto, (max-width: 300px) 100vw, 300px\" \/><\/p>\n<p>How many thirds are there? 6 thirds.<\/p>\n<p style=\"text-align: center\">[latex]2 =\\dfrac{6}{3}[\/latex]<\/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>Take the whole number 1.<\/p>\n<p>Draw one shape (a circle or a box).<\/p>\n<p><img loading=\"lazy\" decoding=\"async\" class=\"aligncenter wp-image-93\" src=\"https:\/\/pressbooks.bccampus.ca\/wp-content\/uploads\/sites\/2383\/2025\/01\/circle.jpg\" alt=\"A circle.\" width=\"100\" height=\"99\" srcset=\"https:\/\/pressbooks.bccampus.ca\/math025\/wp-content\/uploads\/sites\/2383\/2025\/01\/circle.jpg 216w, https:\/\/pressbooks.bccampus.ca\/math025\/wp-content\/uploads\/sites\/2383\/2025\/01\/circle-150x150.jpg 150w, https:\/\/pressbooks.bccampus.ca\/math025\/wp-content\/uploads\/sites\/2383\/2025\/01\/circle-65x64.jpg 65w\" sizes=\"auto, (max-width: 100px) 100vw, 100px\" \/><\/p>\n<p>Now divide the shape into half.<\/p>\n<p><img loading=\"lazy\" decoding=\"async\" class=\"aligncenter wp-image-94\" src=\"https:\/\/pressbooks.bccampus.ca\/wp-content\/uploads\/sites\/2383\/2025\/01\/circle-two-parts.jpg\" alt=\"A circle divided into two parts.\" width=\"100\" height=\"97\" srcset=\"https:\/\/pressbooks.bccampus.ca\/math025\/wp-content\/uploads\/sites\/2383\/2025\/01\/circle-two-parts.jpg 220w, https:\/\/pressbooks.bccampus.ca\/math025\/wp-content\/uploads\/sites\/2383\/2025\/01\/circle-two-parts-65x63.jpg 65w\" sizes=\"auto, (max-width: 100px) 100vw, 100px\" \/><\/p>\n<p>How many halves are there? [latex]1=\\dfrac{2}{2}[\/latex]<\/p>\n<\/div>\n<\/div>\n<h2>Have you found the shortcut?<\/h2>\n<p>The shortcut to rename a whole number as an improper fraction is to <strong>multiply<\/strong> the <strong>whole number by the denominator<\/strong>.<\/p>\n<ul>\n<li>[latex]2 = \\dfrac{}{4}\\hspace{1cm}[\/latex]Each whole number has 4 equal parts (4 quarters) in it,\n<ul type=\"none\">\n<li>so [latex]2\\text{ (whole numbers)}\\times4\\text{ (parts)} = 8\\text{ parts}[\/latex]<\/li>\n<li>so [latex]2 = \\dfrac{8}{4}[\/latex]<\/li>\n<\/ul>\n<\/li>\n<li>[latex]6 = \\dfrac{}{2}\\hspace{1cm}[\/latex]Each whole number has 2 equal parts (2 halves),\n<ul type=\"none\">\n<li>so [latex]6\\text{ (whole numbers)}\\times2\\text{ (parts)}=12\\text{ parts}[\/latex]<\/li>\n<li>so [latex]6= \\dfrac{12}{2}[\/latex]<\/li>\n<\/ul>\n<\/li>\n<li>[latex]8 = \\dfrac{}{3}[\/latex]\n<ul>\n<li>[latex]8\\times3=24[\/latex]<\/li>\n<li>so [latex]8 = \\dfrac{24}{3}[\/latex]<\/li>\n<\/ul>\n<\/li>\n<\/ul>\n<div class=\"textbox shaded\">Until you are comfortable, draw a little sketch like you did in the example.<\/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>Rename each whole number as an improper fraction using the denominator shown.<\/p>\n<ol type=\"a\">\n<li>[latex]6 = \\dfrac{24}{4}[\/latex],\u00a0 \u00a0 \u00a0 [latex]2 = \\dfrac{}{3}[\/latex],\u00a0 \u00a0 \u00a0 \u00a0[latex]4 = \\dfrac{}{3}[\/latex],\u00a0 \u00a0 \u00a0 [latex]8 = \\dfrac{}{10}[\/latex]<\/li>\n<li>[latex]7 = \\dfrac{}{3}[\/latex],\u00a0 \u00a0 \u00a0 [latex]1 = \\dfrac{}{4}[\/latex],\u00a0 \u00a0 \u00a0 [latex]6 = \\dfrac{}{10}[\/latex],\u00a0 \u00a0 \u00a0 [latex]5 = \\dfrac{}{6}[\/latex]<\/li>\n<\/ol>\n<p><strong>Answers to Exercise 5<\/strong><\/p>\n<ol class=\"twocolumn\" type=\"a\">\n<li>[latex]\\dfrac{24}{4}[\/latex],[latex]\\dfrac{6}{3}[\/latex],[latex]\\dfrac{12}{3}[\/latex],[latex]\\dfrac{80}{10}[\/latex]<\/li>\n<li>[latex]\\dfrac{21}{3}[\/latex],[latex]\\dfrac{4}{4}[\/latex],[latex]\\dfrac{60}{10}[\/latex],[latex]\\dfrac{30}{6}[\/latex]<\/li>\n<\/ol>\n<\/div>\n<\/div>\n<p>Now let&#8217;s take this idea further. How can you rename a <strong>mixed number<\/strong> as an improper fraction?<\/p>\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>Take the mixed number [latex]2\\tfrac{1}{4}[\/latex]. This is two whole things and <strong>part of a third<\/strong> whole thing.<\/p>\n<p>Here are three equal shapes divided into fourths.<\/p>\n<p><img loading=\"lazy\" decoding=\"async\" class=\"aligncenter wp-image-95 size-full\" src=\"https:\/\/pressbooks.bccampus.ca\/wp-content\/uploads\/sites\/2383\/2025\/01\/3-squares-in-quarters-e1673981542487.jpg\" alt=\"Three squares each divided into fourths.\" width=\"472\" height=\"107\" srcset=\"https:\/\/pressbooks.bccampus.ca\/math025\/wp-content\/uploads\/sites\/2383\/2025\/01\/3-squares-in-quarters-e1673981542487.jpg 472w, https:\/\/pressbooks.bccampus.ca\/math025\/wp-content\/uploads\/sites\/2383\/2025\/01\/3-squares-in-quarters-e1673981542487-300x68.jpg 300w, https:\/\/pressbooks.bccampus.ca\/math025\/wp-content\/uploads\/sites\/2383\/2025\/01\/3-squares-in-quarters-e1673981542487-65x15.jpg 65w, https:\/\/pressbooks.bccampus.ca\/math025\/wp-content\/uploads\/sites\/2383\/2025\/01\/3-squares-in-quarters-e1673981542487-225x51.jpg 225w, https:\/\/pressbooks.bccampus.ca\/math025\/wp-content\/uploads\/sites\/2383\/2025\/01\/3-squares-in-quarters-e1673981542487-350x79.jpg 350w\" sizes=\"auto, (max-width: 472px) 100vw, 472px\" \/><\/p>\n<p>Shade in two whole shapes [latex]\\tfrac{8}{4}[\/latex] and [latex]\\tfrac{1}{4}[\/latex] of the third shape.<\/p>\n<p>How many fourths have you shaded in all? <strong>9<\/strong> fourths<\/p>\n<p style=\"text-align: center\">[latex]2\\dfrac{1}{4} = \\dfrac{9}{4}[\/latex]<\/p>\n<\/div>\n<\/div>\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>Take the mixed number [latex]1\\tfrac{2}{3}[\/latex]. This is one whole thing and part of a second whole thing.<\/p>\n<p>Draw two equal shapes and divide them into thirds.<\/p>\n<p>Shade in one whole shape [latex]\\tfrac{3}{3}[\/latex] and [latex]\\tfrac{2}{3}[\/latex] of the second shape.<\/p>\n<p><img loading=\"lazy\" decoding=\"async\" class=\"aligncenter wp-image-92\" src=\"https:\/\/pressbooks.bccampus.ca\/wp-content\/uploads\/sites\/2383\/2025\/01\/Two-shapes-in-three-parts.jpg\" alt=\"Two squares, each divided into three parts.\" width=\"300\" height=\"128\" srcset=\"https:\/\/pressbooks.bccampus.ca\/math025\/wp-content\/uploads\/sites\/2383\/2025\/01\/Two-shapes-in-three-parts.jpg 670w, https:\/\/pressbooks.bccampus.ca\/math025\/wp-content\/uploads\/sites\/2383\/2025\/01\/Two-shapes-in-three-parts-300x128.jpg 300w, https:\/\/pressbooks.bccampus.ca\/math025\/wp-content\/uploads\/sites\/2383\/2025\/01\/Two-shapes-in-three-parts-65x28.jpg 65w, https:\/\/pressbooks.bccampus.ca\/math025\/wp-content\/uploads\/sites\/2383\/2025\/01\/Two-shapes-in-three-parts-225x96.jpg 225w, https:\/\/pressbooks.bccampus.ca\/math025\/wp-content\/uploads\/sites\/2383\/2025\/01\/Two-shapes-in-three-parts-350x149.jpg 350w\" sizes=\"auto, (max-width: 300px) 100vw, 300px\" \/><\/p>\n<p>How many thirds have you shaded in all? <span style=\"text-decoration: underline\" aria-label=\"blank\">\u00a0 \u00a0 \u00a0\u00a0<\/span> thirds<\/p>\n<p style=\"text-align: center\">[latex]1\\dfrac{2}{3}=\\dfrac{}{3}[\/latex]<\/p>\n<\/div>\n<\/div>\n<p>To rename a mixed number as an improper fraction, multiply the whole number by the denominator of the fraction and then add this to the numerator. Write the <a class=\"glossary-term\" aria-haspopup=\"dialog\" aria-describedby=\"definition\" href=\"#term_98_272\">total<\/a> as the new numerator over the denominator.<\/p>\n<table class=\"no-border-table\" style=\"width: 100%;\">\n<tbody>\n<tr>\n<td>[latex]3\\dfrac{1}{4}=\\dfrac{?}{4}[\/latex]<\/td>\n<td>\u00a0[latex]3=\\dfrac{12}{4}[\/latex]<\/td>\n<td>so<\/td>\n<td>[latex]3\\dfrac{1}{4}=\\dfrac{12}{4}+\\dfrac{1}{4}=\\dfrac{13}{4}[\/latex]<\/td>\n<\/tr>\n<tr>\n<td>[latex]2\\dfrac{1}{2}=\\dfrac{?}{2}[\/latex]<\/td>\n<td>\u00a0[latex]2=\\dfrac{4}{2}[\/latex]<\/td>\n<td>so<\/td>\n<td>[latex]2\\dfrac{1}{2}=\\dfrac{4}{2}+\\dfrac{1}{2}=\\dfrac{5}{2}[\/latex]<\/td>\n<\/tr>\n<\/tbody>\n<\/table>\n<div class=\"textbox textbox--exercises\">\n<header class=\"textbox__header\">\n<p class=\"textbox__title\">Exercise 6<\/p>\n<\/header>\n<div class=\"textbox__content\">\n<p>Rename each mixed number as an improper fraction.<\/p>\n<ol class=\"twocolumn\" type=\"a\">\n<li>[latex]2\\dfrac{4}{5} = \\dfrac{14}{5}[\/latex]<\/li>\n<li>[latex]8\\dfrac{3}{8} = \\dfrac{67}{8}[\/latex]<\/li>\n<li>[latex]6\\dfrac{5}{8} = \\dfrac{}{8}[\/latex]<\/li>\n<li>[latex]5\\dfrac{1}{2} = \\dfrac{}{2}[\/latex]<\/li>\n<li>[latex]8\\dfrac{4}{5} =[\/latex]<\/li>\n<li>[latex]6\\dfrac{1}{8} =[\/latex]<\/li>\n<li>[latex]5\\dfrac{3}{6} =[\/latex]<\/li>\n<li>[latex]2\\dfrac{7}{8} =[\/latex]<\/li>\n<li>[latex]1\\dfrac{8}{10} =[\/latex]<\/li>\n<li>[latex]3\\dfrac{6}{8} =[\/latex]<\/li>\n<\/ol>\n<p><strong>Answers to Exercise 6<\/strong><\/p>\n<ol class=\"twocolumn\" type=\"a\">\n<li>[latex]\\dfrac{14}{5}[\/latex]<\/li>\n<li>[latex]\\dfrac{67}{8}[\/latex]<\/li>\n<li>[latex]\\dfrac{53}{8}[\/latex]<\/li>\n<li>[latex]\\dfrac{11}{2}[\/latex]<\/li>\n<li>[latex]\\dfrac{44}{5}[\/latex]<\/li>\n<li>[latex]\\dfrac{49}{8}[\/latex]<\/li>\n<li>[latex]\\dfrac{33}{6}[\/latex]<\/li>\n<li>[latex]\\dfrac{23}{8}[\/latex]<\/li>\n<li>[latex]\\dfrac{18}{10}[\/latex]<\/li>\n<li>[latex]\\dfrac{30}{8}[\/latex]<\/li>\n<\/ol>\n<\/div>\n<\/div>\n<h1>To Say or Write a Mixed Number<\/h1>\n<p>If you want to say these strange looking fractions out loud, do as follows.<\/p>\n<p>Write or say: the whole number + and + the fraction<\/p>\n<ul type=\"none\">\n<li>[latex]3\\tfrac{2}{5} =[\/latex] three and two fifths<\/li>\n<li>[latex]5\\tfrac{1}{6} =[\/latex] five and one sixth<\/li>\n<\/ul>\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>Write the following fractions as words.<\/p>\n<ol class=\"twocolumn\" type=\"a\">\n<li>[latex]2\\dfrac{1}{8}[\/latex]<\/li>\n<li>[latex]4\\dfrac{3}{4}[\/latex]<\/li>\n<li>[latex]1\\dfrac{1}{2}[\/latex]<\/li>\n<li>[latex]3\\dfrac{3}{4}[\/latex]<\/li>\n<\/ol>\n<p><strong>Answers to Exercise 7<\/strong><\/p>\n<ol class=\"twocolumn\" type=\"a\">\n<li>Two and one eighth<\/li>\n<li>Four and three fourths (or four and three quarters)<\/li>\n<li>One and one half<\/li>\n<li>Three and three fourths (or three and three quarters)<\/li>\n<\/ol>\n<\/div>\n<\/div>\n<h1>Topic B: Self-Test<\/h1>\n<p><strong>Mark\u00a0 \u00a0 \u00a0 \u00a0\/12\u00a0 \u00a0 \u00a0 \u00a0 \u00a0 \u00a0 \u00a0 \u00a0 \u00a0 Aim\u00a0 \u00a0 \u00a0 \u00a0 9\/12<\/strong><\/p>\n<ol type=\"A\">\n<li>Write the improper fraction and the mixed number that describe the shaded part of the drawings in each question (4 marks).\n<ol type=\"a\">\n<li><img loading=\"lazy\" decoding=\"async\" class=\"alignnone wp-image-96\" src=\"https:\/\/pressbooks.bccampus.ca\/wp-content\/uploads\/sites\/2383\/2025\/01\/4-1-3-circles.jpg\" alt=\"4 circles each divided into 3 parts. Three circles are fully shaded. One circle has one part shaded.\" width=\"300\" height=\"47\" srcset=\"https:\/\/pressbooks.bccampus.ca\/math025\/wp-content\/uploads\/sites\/2383\/2025\/01\/4-1-3-circles.jpg 600w, https:\/\/pressbooks.bccampus.ca\/math025\/wp-content\/uploads\/sites\/2383\/2025\/01\/4-1-3-circles-300x47.jpg 300w, https:\/\/pressbooks.bccampus.ca\/math025\/wp-content\/uploads\/sites\/2383\/2025\/01\/4-1-3-circles-65x10.jpg 65w, https:\/\/pressbooks.bccampus.ca\/math025\/wp-content\/uploads\/sites\/2383\/2025\/01\/4-1-3-circles-225x35.jpg 225w, https:\/\/pressbooks.bccampus.ca\/math025\/wp-content\/uploads\/sites\/2383\/2025\/01\/4-1-3-circles-350x55.jpg 350w\" sizes=\"auto, (max-width: 300px) 100vw, 300px\" \/><\/li>\n<li><img loading=\"lazy\" decoding=\"async\" class=\"alignnone wp-image-97\" src=\"https:\/\/pressbooks.bccampus.ca\/wp-content\/uploads\/sites\/2383\/2025\/01\/2-3-4-banner.jpg\" alt=\"Two shapes each divided into four parts. The first shape is fully shaded. The second shape has three parts shaded.\" width=\"168\" height=\"47\" srcset=\"https:\/\/pressbooks.bccampus.ca\/math025\/wp-content\/uploads\/sites\/2383\/2025\/01\/2-3-4-banner.jpg 357w, https:\/\/pressbooks.bccampus.ca\/math025\/wp-content\/uploads\/sites\/2383\/2025\/01\/2-3-4-banner-300x84.jpg 300w, https:\/\/pressbooks.bccampus.ca\/math025\/wp-content\/uploads\/sites\/2383\/2025\/01\/2-3-4-banner-65x18.jpg 65w, https:\/\/pressbooks.bccampus.ca\/math025\/wp-content\/uploads\/sites\/2383\/2025\/01\/2-3-4-banner-225x63.jpg 225w, https:\/\/pressbooks.bccampus.ca\/math025\/wp-content\/uploads\/sites\/2383\/2025\/01\/2-3-4-banner-350x98.jpg 350w\" sizes=\"auto, (max-width: 168px) 100vw, 168px\" \/><\/li>\n<\/ol>\n<\/li>\n<li>Rename each improper fraction as an equivalent mixed number or whole number (4 marks).\n<ol class=\"twocolumn\" type=\"a\">\n<li>[latex]\\dfrac{9}{4}=[\/latex]<\/li>\n<li>[latex]\\dfrac{12}{3}=[\/latex]<\/li>\n<li>[latex]\\dfrac{5}{3}=[\/latex]<\/li>\n<li>[latex]\\dfrac{7}{2}=[\/latex]<\/li>\n<\/ol>\n<\/li>\n<li>Rename as improper fractions (4 marks).\n<ol class=\"twocolumn\" type=\"a\">\n<li>[latex]3\\dfrac{1}{2}=[\/latex]<\/li>\n<li>[latex]4\\dfrac{3}{8}=[\/latex]<\/li>\n<li>[latex]1\\dfrac{7}{8}=[\/latex]<\/li>\n<li>[latex]2\\dfrac{5}{6}=[\/latex]<\/li>\n<\/ol>\n<\/li>\n<\/ol>\n<h2>Answers to Topic B Self-Test<\/h2>\n<ol type=\"A\">\n<li>Write the improper fraction and the mixed number that describe the shaded part of the drawings in each question.\n<ol type=\"a\">\n<li>[latex]\\dfrac{10}{3} = 3\\dfrac{1}{3}[\/latex]<\/li>\n<li>[latex]\\dfrac{7}{4} = 1\\dfrac{3}{4}[\/latex]<\/li>\n<\/ol>\n<\/li>\n<li>Rename each improper fraction as an equivalent mixed number or whole number.\n<ol class=\"twocolumn\" type=\"a\">\n<li>[latex]2\\dfrac{1}{4}[\/latex]<\/li>\n<li>[latex]4[\/latex]<\/li>\n<li>[latex]1\\dfrac{2}{3}[\/latex]<\/li>\n<li>[latex]3\\dfrac{1}{2}[\/latex]<\/li>\n<\/ol>\n<\/li>\n<li>Rename as improper fractions.\n<ol class=\"twocolumn\" type=\"a\">\n<li>[latex]\\dfrac{7}{2}[\/latex]<\/li>\n<li>[latex]\\dfrac{35}{8}[\/latex]<\/li>\n<li>[latex]\\dfrac{15}{8}[\/latex]<\/li>\n<li>[latex]\\dfrac{17}{6}[\/latex]<\/li>\n<\/ol>\n<\/li>\n<\/ol>\n<div class=\"glossary\"><span class=\"screen-reader-text\" id=\"definition\">definition<\/span><template id=\"term_98_282\"><div class=\"glossary__definition\" role=\"dialog\" data-id=\"term_98_282\"><div tabindex=\"-1\"><p>A common fraction with a value less than one.<\/p>\n<\/div><button><span aria-hidden=\"true\">&times;<\/span><span class=\"screen-reader-text\">Close definition<\/span><\/button><\/div><\/template><template id=\"term_98_285\"><div class=\"glossary__definition\" role=\"dialog\" data-id=\"term_98_285\"><div tabindex=\"-1\"><p>A common fraction with a value equal to or more than one.<\/p>\n<\/div><button><span aria-hidden=\"true\">&times;<\/span><span class=\"screen-reader-text\">Close definition<\/span><\/button><\/div><\/template><template id=\"term_98_286\"><div class=\"glossary__definition\" role=\"dialog\" data-id=\"term_98_286\"><div tabindex=\"-1\"><p>A whole number and a common fraction. 1 3\/4<\/p>\n<\/div><button><span aria-hidden=\"true\">&times;<\/span><span class=\"screen-reader-text\">Close definition<\/span><\/button><\/div><\/template><template id=\"term_98_265\"><div class=\"glossary__definition\" role=\"dialog\" data-id=\"term_98_265\"><div tabindex=\"-1\"><p>The amount left when a divisor does not divide evenly into the dividend. The remainder must be less than the divisor.<\/p>\n<\/div><button><span aria-hidden=\"true\">&times;<\/span><span class=\"screen-reader-text\">Close definition<\/span><\/button><\/div><\/template><template id=\"term_98_272\"><div class=\"glossary__definition\" role=\"dialog\" data-id=\"term_98_272\"><div tabindex=\"-1\"><p>The amount altogether.<\/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":999,"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-98","chapter","type-chapter","status-publish","hentry"],"part":23,"_links":{"self":[{"href":"https:\/\/pressbooks.bccampus.ca\/math025\/wp-json\/pressbooks\/v2\/chapters\/98","targetHints":{"allow":["GET"]}}],"collection":[{"href":"https:\/\/pressbooks.bccampus.ca\/math025\/wp-json\/pressbooks\/v2\/chapters"}],"about":[{"href":"https:\/\/pressbooks.bccampus.ca\/math025\/wp-json\/wp\/v2\/types\/chapter"}],"author":[{"embeddable":true,"href":"https:\/\/pressbooks.bccampus.ca\/math025\/wp-json\/wp\/v2\/users\/999"}],"version-history":[{"count":6,"href":"https:\/\/pressbooks.bccampus.ca\/math025\/wp-json\/pressbooks\/v2\/chapters\/98\/revisions"}],"predecessor-version":[{"id":303,"href":"https:\/\/pressbooks.bccampus.ca\/math025\/wp-json\/pressbooks\/v2\/chapters\/98\/revisions\/303"}],"part":[{"href":"https:\/\/pressbooks.bccampus.ca\/math025\/wp-json\/pressbooks\/v2\/parts\/23"}],"metadata":[{"href":"https:\/\/pressbooks.bccampus.ca\/math025\/wp-json\/pressbooks\/v2\/chapters\/98\/metadata\/"}],"wp:attachment":[{"href":"https:\/\/pressbooks.bccampus.ca\/math025\/wp-json\/wp\/v2\/media?parent=98"}],"wp:term":[{"taxonomy":"chapter-type","embeddable":true,"href":"https:\/\/pressbooks.bccampus.ca\/math025\/wp-json\/pressbooks\/v2\/chapter-type?post=98"},{"taxonomy":"contributor","embeddable":true,"href":"https:\/\/pressbooks.bccampus.ca\/math025\/wp-json\/wp\/v2\/contributor?post=98"},{"taxonomy":"license","embeddable":true,"href":"https:\/\/pressbooks.bccampus.ca\/math025\/wp-json\/wp\/v2\/license?post=98"}],"curies":[{"name":"wp","href":"https:\/\/api.w.org\/{rel}","templated":true}]}}