{"id":15149,"date":"2022-04-04T10:10:43","date_gmt":"2022-04-04T04:40:43","guid":{"rendered":"https:\/\/ccssmathanswers.com\/?p=15149"},"modified":"2022-04-07T11:06:32","modified_gmt":"2022-04-07T05:36:32","slug":"big-ideas-math-answers-grade-5-chapter-10","status":"publish","type":"post","link":"https:\/\/bigideasmathanswers.com\/big-ideas-math-answers-grade-5-chapter-10\/","title":{"rendered":"Big Ideas Math Answers Grade 5 Chapter 10 Divide Fractions"},"content":{"rendered":"<p><strong>Big Ideas Math Answers Grade 5 Chapter 10 Divide Fractions PDF<\/strong> is included here. We have given the solutions to all the questions in Big Ideas Math Answers Grade 5 Chapter 10 Divide Fractions in pdf format. Either you can learn BIM Grade 5 Chapter 10 Divide Fractions Answers online or offline using pdf. <a href=\"https:\/\/bigideasmathanswers.com\/big-ideas-math-answers-grade-5\/\">Big Ideas Math Answers Grade 5<\/a> Chapter 10 Divide Fractions Answer Key helps the students to enhance their knowledge. Also, it is the best source to get in-depth knowledge on the concept. Find out the real-time examples on Big Ideas Grade 5 Chapter 10 Divide Fractions Math Answers for better practice.<\/p>\n<h2>Big Ideas Grade 5 Chapter 10 Divide Fractions Math Book Answer Key<\/h2>\n<p>All the quick methods and tips are helpful for the students to save their time. Therefore, get the Big Ideas Math Answers Grade 5 Chapter 10 Divide Fractions and make use of it to have quick learning. Check answers for every question of every topic. The following sections have quick links where they have each topic with problems. Get the complete grip on the fractions by referring to our <strong><em>Big Ideas Grade 5 Math Answers Chapter 10 Divide Fractions.<\/em><\/strong><\/p>\n<p><strong>Lesson: 1 Interpret Fractions as Division<\/strong><\/p>\n<ul>\n<li><a href=\"#Lesson_10.1_Interpret_Fractions_as_Division\">Lesson 10.1 Interpret Fractions as Division<\/a><\/li>\n<li><a href=\"#Interpret_Fractions_as_Division_Homework_&amp;_Practice_10.1\">Interpret Fractions as Division Homework &amp; Practice 10.1<\/a><\/li>\n<\/ul>\n<p><strong>Lesson: 2 Mixed Numbers as Quotients<\/strong><\/p>\n<ul>\n<li><a href=\"#Lesson_10.2_Mixed_Numbers_as_Quotients\">Lesson 10.2 Mixed Numbers as Quotients<\/a><\/li>\n<li><a href=\"#Mixed_Numbers_as_Quotients_Homework_&amp;_Practice_10.2\">Mixed Numbers as Quotients Homework &amp; Practice 10.2<\/a><\/li>\n<\/ul>\n<p><strong>Lesson: 3 Divide Whole Numbers by Unit Fractions<\/strong><\/p>\n<ul>\n<li><a href=\"#Lesson_10.3_Divide_Whole_Numbers_by_Unit_Fractions\">Lesson 10.3 Divide Whole Numbers by Unit Fractions<\/a><\/li>\n<li><a href=\"#Divide_Whole_Numbers_by_Unit_Fractions_Homework_&amp;_Practice_10.3\">Divide Whole Numbers by Unit Fractions Homework &amp; Practice 10.3<\/a><\/li>\n<\/ul>\n<p><strong>Lesson: 4 Divide Unit Fractions by Whole Numbers<\/strong><\/p>\n<ul>\n<li><a href=\"#Lesson_10.4_Divide_Unit_Fractions_by_Whole_Numbers\">Lesson 10.4 Divide Unit Fractions by Whole Numbers<\/a><\/li>\n<li><a href=\"#Divide_Unit_Fractions_by_Whole_Numbers_Homework_&amp;_Practice_10.4\">Divide Unit Fractions by Whole Numbers Homework &amp; Practice 10.4<\/a><\/li>\n<\/ul>\n<p><strong>Lesson: 5 Problem Solving: Fraction Division<\/strong><\/p>\n<ul>\n<li><a href=\"#Lesson_10.5_Problem_Solving:_Fraction_Division\">Lesson 10.5 Problem Solving: Fraction Division<\/a><\/li>\n<li><a href=\"#Problem_Solving:_Fraction_Division_Homework_&amp;\u00a0_10.5\">Problem Solving: Fraction Division Homework &amp;\u00a0 10.5<\/a><\/li>\n<\/ul>\n<p><strong>Chapter: 10 &#8211; Divide Fractions<\/strong><\/p>\n<ul>\n<li><a href=\"#Divide_Fractions_Performance_Task_10\">Divide Fractions Performance Task 10<\/a><\/li>\n<li><a href=\"#Divide_Fractions_Activity\">Divide Fractions Activity<\/a><\/li>\n<li><a href=\"#Divide_Fractions_Chapter_Practice_10\">Divide Fractions Chapter Practice 10<\/a><\/li>\n<\/ul>\n<h3><a id=\"Lesson_10.1_Interpret_Fractions_as_Division\"><\/a>Lesson 10.1 Interpret Fractions as Division<\/h3>\n<p><strong>Explore and Grow`<\/strong><\/p>\n<p>You share 4 sheets of construction paper equally among 8 people. Write a division expression that represents the situation. What fraction of a sheet of paper does each person get? Use a model to support your answer?<br \/>\nAnswer:<br \/>\nThe division expression that represents the fraction of a sheet of paper does each person get is:<br \/>\n4 \u00f7 8 = \\(\\frac{1}{2}\\)<\/p>\n<p>Explanation:<br \/>\nIt is given that you have 4 sheets of construction paper equally among 8 people.<br \/>\nHence,<br \/>\nThe division expression that represents the fraction of a sheet of paper is:<br \/>\n( The number of sheets of construction paper ) \u00f7 ( The number of people )<br \/>\n= 4 \u00f7 8<br \/>\n= \\(\\frac{1}{2}\\)<br \/>\nHence, from the above,<br \/>\nWe can conclude that the fraction of a sheet of paper does each person get is: \\(\\frac{1}{2}\\)<\/p>\n<p><strong>Structure<\/strong><br \/>\nHow can you check your answer using multiplication?<br \/>\nAnswer: We can check the answer by using the partial products method or by using the simplification method.<\/p>\n<p><strong>Think and Grow: Divide Whole Numbers<br \/>\n<\/strong>You can use models to divide whole numbers that have a fraction as the quotient.<br \/>\nAnswer:\u00a0 <img loading=\"lazy\" class=\"alignnone size-full wp-image-33766\" src=\"https:\/\/ccssmathanswers.com\/wp-content\/uploads\/2020\/12\/Big-Ideas-Math-Answers-Grade-5-Chapter-10.jpg\" alt=\"\" width=\"458\" height=\"284\" srcset=\"https:\/\/bigideasmathanswers.com\/wp-content\/uploads\/2020\/12\/Big-Ideas-Math-Answers-Grade-5-Chapter-10.jpg 458w, https:\/\/bigideasmathanswers.com\/wp-content\/uploads\/2020\/12\/Big-Ideas-Math-Answers-Grade-5-Chapter-10-300x186.jpg 300w\" sizes=\"(max-width: 458px) 100vw, 458px\" \/><br \/>\nFrom the above model,<br \/>\nThe number of colored parts is: 4<br \/>\nThe total number of parts are: 8<br \/>\nSo,<br \/>\nThe fraction of the colored part out of the total number of parts = 4 \u00f7 8<br \/>\n= \\(\\frac{4}{8}\\) = \\(\\frac{1}{2}\\)<br \/>\nIn \\(\\frac{1}{2}\\),<br \/>\n1 represents the quotient<br \/>\n2 represents the remainder<br \/>\n<strong>Example<\/strong><br \/>\nFind 2 \u00f7 3.<br \/>\n<strong>One Way:<\/strong> Use a tape diagram. Show 2 wholes. Divide each whole into 3 equal parts.<br \/>\n<img loading=\"lazy\" class=\"alignnone size-full wp-image-33768\" src=\"https:\/\/ccssmathanswers.com\/wp-content\/uploads\/2020\/12\/Big-Ideas-Math-Answers-Grade-5-Chapter-10-1.jpg\" alt=\"\" width=\"649\" height=\"287\" srcset=\"https:\/\/bigideasmathanswers.com\/wp-content\/uploads\/2020\/12\/Big-Ideas-Math-Answers-Grade-5-Chapter-10-1.jpg 649w, https:\/\/bigideasmathanswers.com\/wp-content\/uploads\/2020\/12\/Big-Ideas-Math-Answers-Grade-5-Chapter-10-1-300x133.jpg 300w\" sizes=\"(max-width: 649px) 100vw, 649px\" \/><br \/>\n<strong>Another Way:<\/strong> Use an area model. Show 2 wholes. Divide each whole into 3 equal parts. Then separate the parts into 3 equal groups.<br \/>\n<img loading=\"lazy\" class=\"alignnone size-full wp-image-33770\" src=\"https:\/\/ccssmathanswers.com\/wp-content\/uploads\/2020\/12\/Big-Ideas-Math-Answers-Grade-5-Chapter-10-2.jpg\" alt=\"\" width=\"629\" height=\"157\" srcset=\"https:\/\/bigideasmathanswers.com\/wp-content\/uploads\/2020\/12\/Big-Ideas-Math-Answers-Grade-5-Chapter-10-2.jpg 629w, https:\/\/bigideasmathanswers.com\/wp-content\/uploads\/2020\/12\/Big-Ideas-Math-Answers-Grade-5-Chapter-10-2-300x75.jpg 300w\" sizes=\"(max-width: 629px) 100vw, 629px\" \/><\/p>\n<p><strong>Show and Grow<\/strong><\/p>\n<p>Divide. Use a model to help<\/p>\n<p>Question 1.<br \/>\n2 \u00f7 4 =0.5<br \/>\nAnswer: <img loading=\"lazy\" class=\"alignnone size-full wp-image-33772\" src=\"https:\/\/ccssmathanswers.com\/wp-content\/uploads\/2020\/12\/Big-Ideas-Math-Answers-Grade-5-Chapter-10-3.jpg\" alt=\"\" width=\"458\" height=\"284\" srcset=\"https:\/\/bigideasmathanswers.com\/wp-content\/uploads\/2020\/12\/Big-Ideas-Math-Answers-Grade-5-Chapter-10-3.jpg 458w, https:\/\/bigideasmathanswers.com\/wp-content\/uploads\/2020\/12\/Big-Ideas-Math-Answers-Grade-5-Chapter-10-3-300x186.jpg 300w\" sizes=\"(max-width: 458px) 100vw, 458px\" \/><br \/>\nFrom the above model,<br \/>\nThe number of colored parts is: 2<br \/>\nThe number of total parts is: 4<br \/>\nSo,<br \/>\nThe fraction of the colored parts out of the total number of parts = 2 \u00f7 4<br \/>\n= \\(\\frac{2}{4}\\)<br \/>\n= \\(\\frac{1}{2}\\)<br \/>\nSo,<br \/>\nThe fraction of the colored parts out of the total number of parts in the decimal form is: 0.5<\/p>\n<p>Question 2.<br \/>\n1 \u00f7 3 = 0.33<br \/>\nAnswer: <img loading=\"lazy\" class=\"alignnone size-full wp-image-33775\" src=\"https:\/\/ccssmathanswers.com\/wp-content\/uploads\/2020\/12\/Big-Ideas-Math-Answers-Grade-5-Chapter-10-4.jpg\" alt=\"\" width=\"458\" height=\"284\" srcset=\"https:\/\/bigideasmathanswers.com\/wp-content\/uploads\/2020\/12\/Big-Ideas-Math-Answers-Grade-5-Chapter-10-4.jpg 458w, https:\/\/bigideasmathanswers.com\/wp-content\/uploads\/2020\/12\/Big-Ideas-Math-Answers-Grade-5-Chapter-10-4-300x186.jpg 300w\" sizes=\"(max-width: 458px) 100vw, 458px\" \/><\/p>\n<p>From the above model,<br \/>\nThe number of colored parts is: 1<br \/>\nThe number of total parts is: 3<br \/>\nSo,<br \/>\nThe fraction of the colored parts out of the total number of parts = 1 \u00f7 3<br \/>\n= \\(\\frac{1}{3}\\)<br \/>\nSo,<br \/>\nThe fraction of the colored parts out of the total number of parts in the decimal form is: 0.33<\/p>\n<p><strong>Apply and Grow: Practice<\/strong><\/p>\n<p>Divide. Use a model to help.<\/p>\n<p>Question 3.<br \/>\n1 \u00f7 8 =0.018<br \/>\nAnswer: <img loading=\"lazy\" class=\"alignnone size-full wp-image-33783\" src=\"https:\/\/ccssmathanswers.com\/wp-content\/uploads\/2020\/12\/Big-Ideas-Math-Answers-Grade-5-Chapter-10-5.jpg\" alt=\"\" width=\"458\" height=\"284\" srcset=\"https:\/\/bigideasmathanswers.com\/wp-content\/uploads\/2020\/12\/Big-Ideas-Math-Answers-Grade-5-Chapter-10-5.jpg 458w, https:\/\/bigideasmathanswers.com\/wp-content\/uploads\/2020\/12\/Big-Ideas-Math-Answers-Grade-5-Chapter-10-5-300x186.jpg 300w\" sizes=\"(max-width: 458px) 100vw, 458px\" \/><br \/>\nFrom the above model,<br \/>\nThe number of colored parts is: 1<br \/>\nThe number of total parts is: 8<br \/>\nSo,<br \/>\nThe fraction of the colored parts out of the total number of parts = 1 \u00f7 8<br \/>\n= \\(\\frac{1}{8}\\)<br \/>\nSo,<br \/>\nThe fraction of the colored parts out of the total number of parts in the decimal form is: 0.018<\/p>\n<p>Question 4.<br \/>\n1 \u00f7 4 =0.25<br \/>\nAnswer: <img loading=\"lazy\" class=\"alignnone size-full wp-image-33787\" src=\"https:\/\/ccssmathanswers.com\/wp-content\/uploads\/2020\/12\/Big-Ideas-Math-Answers-Grade-5-Chapter-10-6.jpg\" alt=\"\" width=\"458\" height=\"284\" srcset=\"https:\/\/bigideasmathanswers.com\/wp-content\/uploads\/2020\/12\/Big-Ideas-Math-Answers-Grade-5-Chapter-10-6.jpg 458w, https:\/\/bigideasmathanswers.com\/wp-content\/uploads\/2020\/12\/Big-Ideas-Math-Answers-Grade-5-Chapter-10-6-300x186.jpg 300w\" sizes=\"(max-width: 458px) 100vw, 458px\" \/><br \/>\nFrom the above model,<br \/>\nThe number of colored parts is: 1<br \/>\nThe number of total parts is: 4<br \/>\nSo,<br \/>\nThe fraction of the colored parts out of the total number of parts = 1 \u00f7 4<br \/>\n= \\(\\frac{1}{4}\\)<br \/>\nSo,<br \/>\nThe fraction of the colored parts out of the total number of parts in the decimal form is: 0.25<\/p>\n<p>Question 5.<br \/>\n2 \u00f7 6 =0.33<br \/>\nAnswer: <img loading=\"lazy\" class=\"alignnone size-full wp-image-33789\" src=\"https:\/\/ccssmathanswers.com\/wp-content\/uploads\/2020\/12\/Big-Ideas-Math-Answers-Grade-5-Chapter-10-7.jpg\" alt=\"\" width=\"458\" height=\"284\" srcset=\"https:\/\/bigideasmathanswers.com\/wp-content\/uploads\/2020\/12\/Big-Ideas-Math-Answers-Grade-5-Chapter-10-7.jpg 458w, https:\/\/bigideasmathanswers.com\/wp-content\/uploads\/2020\/12\/Big-Ideas-Math-Answers-Grade-5-Chapter-10-7-300x186.jpg 300w\" sizes=\"(max-width: 458px) 100vw, 458px\" \/><br \/>\nFrom the above model,<br \/>\nThe number of colored parts is: 2<br \/>\nThe number of total parts is: 6<br \/>\nSo,<br \/>\nThe fraction of the colored parts out of the total number of parts = 2 \u00f7 6<br \/>\n= \\(\\frac{2}{6}\\)<br \/>\n= \\(\\frac{1}{3}\\)<br \/>\nSo,<br \/>\nThe fraction of the colored parts out of the total number of parts in the decimal form is: 0.33<\/p>\n<p>Question 6.<br \/>\n2 \u00f7 5 = 0.4<br \/>\nAnswer: <img loading=\"lazy\" class=\"alignnone size-full wp-image-33793\" src=\"https:\/\/ccssmathanswers.com\/wp-content\/uploads\/2020\/12\/Big-Ideas-Math-Answers-Grade-5-Chapter-10-8.jpg\" alt=\"\" width=\"458\" height=\"284\" srcset=\"https:\/\/bigideasmathanswers.com\/wp-content\/uploads\/2020\/12\/Big-Ideas-Math-Answers-Grade-5-Chapter-10-8.jpg 458w, https:\/\/bigideasmathanswers.com\/wp-content\/uploads\/2020\/12\/Big-Ideas-Math-Answers-Grade-5-Chapter-10-8-300x186.jpg 300w\" sizes=\"(max-width: 458px) 100vw, 458px\" \/><br \/>\nFrom the above model,<br \/>\nThe number of colored parts is: 2<br \/>\nThe number of total parts is: 5<br \/>\nSo,<br \/>\nThe fraction of the colored parts out of the total number of parts = 2 \u00f7 5<br \/>\n= \\(\\frac{2}{5}\\)<br \/>\nSo,<br \/>\nThe fraction of the colored parts out of the total number of parts in the decimal form is: 0.4<\/p>\n<p>Question 7.<br \/>\n3 \u00f7 7 = 0.42<br \/>\nAnswer:\u00a0 <img loading=\"lazy\" class=\"alignnone size-full wp-image-33795\" src=\"https:\/\/ccssmathanswers.com\/wp-content\/uploads\/2020\/12\/Big-Ideas-Math-Answers-Grade-5-Chapter-10-9.jpg\" alt=\"\" width=\"458\" height=\"284\" srcset=\"https:\/\/bigideasmathanswers.com\/wp-content\/uploads\/2020\/12\/Big-Ideas-Math-Answers-Grade-5-Chapter-10-9.jpg 458w, https:\/\/bigideasmathanswers.com\/wp-content\/uploads\/2020\/12\/Big-Ideas-Math-Answers-Grade-5-Chapter-10-9-300x186.jpg 300w\" sizes=\"(max-width: 458px) 100vw, 458px\" \/><br \/>\nFrom the above model,<br \/>\nThe number of colored parts is: 3<br \/>\nThe number of total parts is: 7<br \/>\nSo,<br \/>\nThe fraction of the colored parts out of the total number of parts = 3 \u00f7 7<br \/>\n= \\(\\frac{3}{7}\\)<br \/>\nSo,<br \/>\nThe fraction of the colored parts out of the total number of parts in the decimal form is: 0.42<\/p>\n<p>Question 8.<br \/>\n5 \u00f7 6 = 0.83<br \/>\nAnswer: <img loading=\"lazy\" class=\"alignnone size-full wp-image-33796\" src=\"https:\/\/ccssmathanswers.com\/wp-content\/uploads\/2020\/12\/Big-Ideas-Math-Answers-Grade-5-Chapter-10-10.jpg\" alt=\"\" width=\"458\" height=\"284\" srcset=\"https:\/\/bigideasmathanswers.com\/wp-content\/uploads\/2020\/12\/Big-Ideas-Math-Answers-Grade-5-Chapter-10-10.jpg 458w, https:\/\/bigideasmathanswers.com\/wp-content\/uploads\/2020\/12\/Big-Ideas-Math-Answers-Grade-5-Chapter-10-10-300x186.jpg 300w\" sizes=\"(max-width: 458px) 100vw, 458px\" \/><br \/>\nFrom the above model,<br \/>\nThe number of colored parts is: 5<br \/>\nThe number of total parts is: 6<br \/>\nSo,<br \/>\nThe fraction of the colored parts out of the total number of parts = 5 \u00f7 6<br \/>\n= \\(\\frac{5}{6}\\)<br \/>\nSo,<br \/>\nThe fraction of the colored parts out of the total number of parts in the decimal form is: 0.83<\/p>\n<p>Question 9.<br \/>\nHow many 6s are in 1?<br \/>\nAnswer: There are six \\(\\frac{1}{6}\\)s in 1<\/p>\n<p>Explanation:<br \/>\nThe number of 6s in 1 can be obtained by dividing 1 into 6 equal parts.<br \/>\nSo,<br \/>\nThe figure obtained will be like;<br \/>\n<img loading=\"lazy\" class=\"alignnone size-full wp-image-33799\" src=\"https:\/\/ccssmathanswers.com\/wp-content\/uploads\/2020\/12\/Big-Ideas-Math-Answers-Grade-5-Chapter-10-11.jpg\" alt=\"\" width=\"458\" height=\"284\" srcset=\"https:\/\/bigideasmathanswers.com\/wp-content\/uploads\/2020\/12\/Big-Ideas-Math-Answers-Grade-5-Chapter-10-11.jpg 458w, https:\/\/bigideasmathanswers.com\/wp-content\/uploads\/2020\/12\/Big-Ideas-Math-Answers-Grade-5-Chapter-10-11-300x186.jpg 300w\" sizes=\"(max-width: 458px) 100vw, 458px\" \/><br \/>\nFrom the above model,<br \/>\nThe number of colored parts is: 1<br \/>\nThe number of total parts is: 6<br \/>\nSo,<br \/>\nThe fraction of the colored parts out of the total number of parts = 1 \u00f7 6<br \/>\n= \\(\\frac{1}{6}\\)<br \/>\nHence, from the above,<br \/>\nWe can conclude that there are six 6s in 1<\/p>\n<p>Question 10.<br \/>\nHow many 10s are in 9?<br \/>\nAnswer: There are 9 \\(\\frac{9}{10}\\)s in 9<\/p>\n<p>Explanation:<br \/>\nThe model for the number of 10s in 9 are:<br \/>\n<img loading=\"lazy\" class=\"alignnone size-full wp-image-33802\" src=\"https:\/\/ccssmathanswers.com\/wp-content\/uploads\/2020\/12\/Big-Ideas-Math-Answers-Grade-5-Chapter-10-13.jpg\" alt=\"\" width=\"458\" height=\"284\" srcset=\"https:\/\/bigideasmathanswers.com\/wp-content\/uploads\/2020\/12\/Big-Ideas-Math-Answers-Grade-5-Chapter-10-13.jpg 458w, https:\/\/bigideasmathanswers.com\/wp-content\/uploads\/2020\/12\/Big-Ideas-Math-Answers-Grade-5-Chapter-10-13-300x186.jpg 300w\" sizes=\"(max-width: 458px) 100vw, 458px\" \/><\/p>\n<p>From the above model,<br \/>\nThe number of colored parts is: 9<br \/>\nThe number of total parts is: 10<br \/>\nSo,<br \/>\nThe fraction of the colored parts out of the total number of parts = 9 \u00f7 10<br \/>\n= \\(\\frac{9}{10}\\)<br \/>\nHence, from the above,<br \/>\nWe can conclude that there are nine 9s in 10<\/p>\n<p>Question 11.<br \/>\n<strong>Number Sense<\/strong><br \/>\nFor which equations does k = 8?<br \/>\n<img loading=\"lazy\" class=\"alignnone size-full wp-image-15158\" src=\"https:\/\/ccssmathanswers.com\/wp-content\/uploads\/2020\/12\/Big-Ideas-Math-Answer-Key-Grade-5-Chapter-10-Divide-Fractions-3.png\" alt=\"Big Ideas Math Answer Key Grade 5 Chapter 10 Divide Fractions 3\" width=\"252\" height=\"108\" \/><br \/>\nAnswer: Let the equations named A), B), C), and D)<br \/>\nSo,<br \/>\nThe four equations are:<br \/>\n<img loading=\"lazy\" class=\"alignnone size-full wp-image-15158\" src=\"https:\/\/ccssmathanswers.com\/wp-content\/uploads\/2020\/12\/Big-Ideas-Math-Answer-Key-Grade-5-Chapter-10-Divide-Fractions-3.png\" alt=\"Big Ideas Math Answer Key Grade 5 Chapter 10 Divide Fractions 3\" width=\"252\" height=\"108\" \/><br \/>\nFrom the above equations,<br \/>\nThe value &#8216;k&#8217; must be in the numerator.<br \/>\nSo,<br \/>\nIn A), the value of the numerator is: 3<br \/>\nIn B), the value of the numerator is: k<br \/>\nIn C), the value of the numerator is: 2<br \/>\nIn D) the value of the numerator is: 8<br \/>\nSo,<br \/>\nFrom the above numerator values,<br \/>\nWe can say that &#8220;k=8&#8221; holds good for Equation B)<\/p>\n<p>Question 12.<br \/>\n<strong>Writing<\/strong><br \/>\nWrite and solve a real-life problem for 7 \u00f7 12.<br \/>\nAnswer: <img loading=\"lazy\" class=\"alignnone size-full wp-image-33807\" src=\"https:\/\/ccssmathanswers.com\/wp-content\/uploads\/2020\/12\/Big-Ideas-Math-Answers-Grade-5-Chapter-10-14.jpg\" alt=\"\" width=\"458\" height=\"284\" srcset=\"https:\/\/bigideasmathanswers.com\/wp-content\/uploads\/2020\/12\/Big-Ideas-Math-Answers-Grade-5-Chapter-10-14.jpg 458w, https:\/\/bigideasmathanswers.com\/wp-content\/uploads\/2020\/12\/Big-Ideas-Math-Answers-Grade-5-Chapter-10-14-300x186.jpg 300w\" sizes=\"(max-width: 458px) 100vw, 458px\" \/><br \/>\nFrom the above model,<br \/>\nThe number of colored parts is: 7<br \/>\nThe number of total parts is: 12<br \/>\nSo,<br \/>\nThe fraction of the colored parts out of the total number of parts = 7 \u00f7 12<br \/>\n= \\(\\frac{7}{12}\\)<br \/>\nHence,<br \/>\nThe fraction of the colored parts out of the total number of parts in the decimal form is: 0.58<\/p>\n<p><strong>Think and Grow: Modeling Real Life<\/strong><\/p>\n<p><strong>Example<\/strong><br \/>\nThree fruit bars are shared equally among 4 friends. What fraction of a fruit bar does each friend get?<br \/>\n<img loading=\"lazy\" class=\"alignnone size-full wp-image-15159\" src=\"https:\/\/ccssmathanswers.com\/wp-content\/uploads\/2020\/12\/Big-Ideas-Math-Answer-Key-Grade-5-Chapter-10-Divide-Fractions-4.png\" alt=\"Big Ideas Math Answer Key Grade 5 Chapter 10 Divide Fractions 4\" width=\"179\" height=\"110\" \/><br \/>\nDivide 3 by 4 to \ufb01nd what fraction of a fruit bar each friend gets.<br \/>\nUse an area model to \ufb01nd 3 \u00f7 4. Show 3 whole fruit bars. Divide each fruit bar into 4 equal parts. Then separate the parts into 4 equal groups.<br \/>\n<img loading=\"lazy\" class=\"alignnone size-full wp-image-33810\" src=\"https:\/\/ccssmathanswers.com\/wp-content\/uploads\/2020\/12\/Big-Ideas-Math-Answers-Grade-5-Chapter-10-15.jpg\" alt=\"\" width=\"695\" height=\"336\" srcset=\"https:\/\/bigideasmathanswers.com\/wp-content\/uploads\/2020\/12\/Big-Ideas-Math-Answers-Grade-5-Chapter-10-15.jpg 695w, https:\/\/bigideasmathanswers.com\/wp-content\/uploads\/2020\/12\/Big-Ideas-Math-Answers-Grade-5-Chapter-10-15-300x145.jpg 300w\" sizes=\"(max-width: 695px) 100vw, 695px\" \/><\/p>\n<p><strong>Show and Grow<\/strong><\/p>\n<p>Question 13.<br \/>\nYou cut a 5-foot streamer into 6 pieces of equal size. What is the length of each piece in feet? in inches?<br \/>\nAnswer: The length of each piece in feet is: \\(\\frac{5}{6}\\)<\/p>\n<p>Explanation:<br \/>\nIt is given that you cut a 5-foot streamer into 6 equal pieces of equal size.<br \/>\nSo,<br \/>\nThe model representing the 6 equal pieces of the 5-foot streamer is:<br \/>\n<img loading=\"lazy\" class=\"alignnone size-full wp-image-33813\" src=\"https:\/\/ccssmathanswers.com\/wp-content\/uploads\/2020\/12\/Big-Ideas-Math-Answers-Grade-5-Chapter-10-16.jpg\" alt=\"\" width=\"458\" height=\"344\" srcset=\"https:\/\/bigideasmathanswers.com\/wp-content\/uploads\/2020\/12\/Big-Ideas-Math-Answers-Grade-5-Chapter-10-16.jpg 458w, https:\/\/bigideasmathanswers.com\/wp-content\/uploads\/2020\/12\/Big-Ideas-Math-Answers-Grade-5-Chapter-10-16-300x225.jpg 300w\" sizes=\"(max-width: 458px) 100vw, 458px\" \/><br \/>\nFrom the above model,<br \/>\nWe can see that each part in the model represents \\(\\frac{5}{6}\\) of each part.<br \/>\nHence, from the above,<br \/>\nWe can conclude that the length of each piece of a 5-foot streamer in feet is: \\(\\frac{5}{6}\\)<\/p>\n<p>Question 14.<br \/>\nFour circular lemon slices are shared equally among 8 glasses of water. What fraction of a lemon slice does each glass get?<br \/>\n<img loading=\"lazy\" class=\"alignnone size-full wp-image-15161\" src=\"https:\/\/ccssmathanswers.com\/wp-content\/uploads\/2020\/12\/Big-Ideas-Math-Answer-Key-Grade-5-Chapter-10-Divide-Fractions-7.png\" alt=\"Big Ideas Math Answer Key Grade 5 Chapter 10 Divide Fractions 7\" width=\"88\" height=\"81\" \/><br \/>\nAnswer: The fraction of a lemon slice does each glass get is: \\(\\frac{1}{2}\\)<\/p>\n<p>Explanation:<br \/>\nIt is given that the four circular lemon slices are shared equally among 8 glasses of water.<br \/>\nSo,<br \/>\nThe model representing the portion that each glass get is:<br \/>\n<img loading=\"lazy\" class=\"alignnone size-full wp-image-33815\" src=\"https:\/\/ccssmathanswers.com\/wp-content\/uploads\/2020\/12\/Big-Ideas-Math-Answers-Grade-5-Chapter-10-17.jpg\" alt=\"\" width=\"458\" height=\"344\" srcset=\"https:\/\/bigideasmathanswers.com\/wp-content\/uploads\/2020\/12\/Big-Ideas-Math-Answers-Grade-5-Chapter-10-17.jpg 458w, https:\/\/bigideasmathanswers.com\/wp-content\/uploads\/2020\/12\/Big-Ideas-Math-Answers-Grade-5-Chapter-10-17-300x225.jpg 300w\" sizes=\"(max-width: 458px) 100vw, 458px\" \/><br \/>\nFrom the above model,<br \/>\nWe can say that each part represents \\(\\frac{1}{2}\\) part<br \/>\nHence, from the above,<br \/>\nWe can conclude that the portion of a lemon slice does glass get is: \\(\\frac{1}{2}\\)<\/p>\n<p>Question 15.<br \/>\nYou cut a 5-foot streamer into 6 pieces of equal size. What is the length of each piece in feet? in inches?<br \/>\nAnswer: The length of each piece in feet is: \\(\\frac{5}{6}\\)<\/p>\n<p>Explanation:<br \/>\nIt is given that you cut a 5-foot streamer into 6 equal pieces of equal size.<br \/>\nSo,<br \/>\nThe model representing the 6 equal pieces of the 5-foot streamer is:<br \/>\n<img loading=\"lazy\" class=\"alignnone size-full wp-image-33813\" src=\"https:\/\/ccssmathanswers.com\/wp-content\/uploads\/2020\/12\/Big-Ideas-Math-Answers-Grade-5-Chapter-10-16.jpg\" alt=\"\" width=\"458\" height=\"344\" srcset=\"https:\/\/bigideasmathanswers.com\/wp-content\/uploads\/2020\/12\/Big-Ideas-Math-Answers-Grade-5-Chapter-10-16.jpg 458w, https:\/\/bigideasmathanswers.com\/wp-content\/uploads\/2020\/12\/Big-Ideas-Math-Answers-Grade-5-Chapter-10-16-300x225.jpg 300w\" sizes=\"(max-width: 458px) 100vw, 458px\" \/><br \/>\nFrom the above model,<br \/>\nWe can see that each part in the model represents \\(\\frac{5}{6}\\) of each part.<br \/>\nHence, from the above,<br \/>\nWe can conclude that the length of each piece of a 5-foot streamer in feet is: \\(\\frac{5}{6}\\)<\/p>\n<p>Question 16.<br \/>\n<strong>DIG DEEPER!<\/strong><br \/>\nA fruit drink is made using \\(\\frac{7}{4}\\) quarts of orange juice and \\(\\frac{5}{4}\\) quarts of pineapple juice. The drink is shared equally among 12 guests. What fraction of a quart does each guest get?<br \/>\nAnswer: The fraction of a quart does each guest get is: \\(\\frac{1}{4}\\)<\/p>\n<p>Explanation:<br \/>\nIt is given that a fruit drink is made using \\(\\frac{7}{4}\\) quarts of orange juice and \\(\\frac{5}{4}\\) quarts of pineapple juice.<br \/>\nSo,<br \/>\nThe total amount of fruit juice= \\(\\frac{7}{4}\\) + \\(\\frac{5}{4}\\)<br \/>\n= \\(\\frac{ 7 + 5}{4}\\)<br \/>\n= \\(\\frac{12}{4}\\)<br \/>\nIt is also given that the drink is shared equally among 12 guests<br \/>\nSo,<br \/>\nThe fraction of a quart does each gust get = \\(\\frac{12}{4}\\) \u00f7 12<br \/>\n= \\(\\frac{12}{4}\\) \u00f7 \\(\\frac{12}{1}\\)<br \/>\n= \\(\\frac{12}{4}\\) \u00d7 \\(\\frac{1}{12}\\)<br \/>\n= \\(\\frac{1}{4}\\)<br \/>\nHence, from the above,<br \/>\nWe can conclude that the fraction of a quart does each person get is: \\(\\frac{1}{4}\\)<\/p>\n<h3><a id=\"Interpret_Fractions_as_Division_Homework_&amp;_Practice_10.1\"><\/a>Interpret Fractions as Division Homework &amp; Practice 10.1<\/h3>\n<p>Divide. Use a model to help.<\/p>\n<p>Question 1.<br \/>\n1 \u00f7 6 =0.16<br \/>\nAnswer:<\/p>\n<p><img loading=\"lazy\" class=\"alignnone size-full wp-image-34142\" src=\"https:\/\/ccssmathanswers.com\/wp-content\/uploads\/2020\/12\/Big-Ideas-Math-Answers-Grade-5-Chapter-10-18.jpg\" alt=\"\" width=\"458\" height=\"284\" srcset=\"https:\/\/bigideasmathanswers.com\/wp-content\/uploads\/2020\/12\/Big-Ideas-Math-Answers-Grade-5-Chapter-10-18.jpg 458w, https:\/\/bigideasmathanswers.com\/wp-content\/uploads\/2020\/12\/Big-Ideas-Math-Answers-Grade-5-Chapter-10-18-300x186.jpg 300w\" sizes=\"(max-width: 458px) 100vw, 458px\" \/><br \/>\nFrom the above model,<br \/>\nThe number of colored parts is: 1<br \/>\nThe number of total parts is: 6<br \/>\nSo,<br \/>\nThe fraction of the colored parts out of the total number of parts = 1 \u00f7 6<br \/>\n= \\(\\frac{1}{6}\\)<br \/>\nSo,<br \/>\nThe fraction of the colored parts out of the total number of parts in the decimal form is: 0.16<\/p>\n<p>Question 2.<br \/>\n1 \u00f7 7 =0.14<br \/>\nAnswer: <img loading=\"lazy\" class=\"alignnone size-full wp-image-34143\" src=\"https:\/\/ccssmathanswers.com\/wp-content\/uploads\/2020\/12\/Big-Ideas-Math-Answers-Grade-5-Chapter-10-19.jpg\" alt=\"\" width=\"458\" height=\"284\" srcset=\"https:\/\/bigideasmathanswers.com\/wp-content\/uploads\/2020\/12\/Big-Ideas-Math-Answers-Grade-5-Chapter-10-19.jpg 458w, https:\/\/bigideasmathanswers.com\/wp-content\/uploads\/2020\/12\/Big-Ideas-Math-Answers-Grade-5-Chapter-10-19-300x186.jpg 300w\" sizes=\"(max-width: 458px) 100vw, 458px\" \/><br \/>\nFrom the above model,<br \/>\nThe number of colored parts is: 1<br \/>\nThe number of total parts is: 7<br \/>\nSo,<br \/>\nThe fraction of the colored parts out of the total number of parts = 1 \u00f7 7<br \/>\n= \\(\\frac{1}{7}\\)<br \/>\nSo,<br \/>\nThe fraction of the colored parts out of the total number of parts in the decimal form is: 0.14<\/p>\n<p>Question 3.<br \/>\n1 \u00f7 5 = 0.20<br \/>\nAnswer: <img loading=\"lazy\" class=\"alignnone size-full wp-image-34144\" src=\"https:\/\/ccssmathanswers.com\/wp-content\/uploads\/2020\/12\/Big-Ideas-Math-Answers-Grade-5-Chapter-10-20.jpg\" alt=\"\" width=\"458\" height=\"284\" srcset=\"https:\/\/bigideasmathanswers.com\/wp-content\/uploads\/2020\/12\/Big-Ideas-Math-Answers-Grade-5-Chapter-10-20.jpg 458w, https:\/\/bigideasmathanswers.com\/wp-content\/uploads\/2020\/12\/Big-Ideas-Math-Answers-Grade-5-Chapter-10-20-300x186.jpg 300w\" sizes=\"(max-width: 458px) 100vw, 458px\" \/><br \/>\nFrom the above model,<br \/>\nThe number of colored parts is: 1<br \/>\nThe number of total parts is: 5<br \/>\nSo,<br \/>\nThe fraction of the colored parts out of the total number of parts = 1 \u00f7 5<br \/>\n= \\(\\frac{1}{5}\\)<br \/>\nSo,<br \/>\nThe fraction of the colored parts out of the total number of parts in the decimal form is: 0.20<\/p>\n<p>Question 4.<br \/>\n3 \u00f7 4 = 0.75<br \/>\nAnswer: <img loading=\"lazy\" class=\"alignnone size-full wp-image-34145\" src=\"https:\/\/ccssmathanswers.com\/wp-content\/uploads\/2020\/12\/Big-Ideas-Math-Answers-Grade-5-Chapter-10-21.jpg\" alt=\"\" width=\"458\" height=\"284\" srcset=\"https:\/\/bigideasmathanswers.com\/wp-content\/uploads\/2020\/12\/Big-Ideas-Math-Answers-Grade-5-Chapter-10-21.jpg 458w, https:\/\/bigideasmathanswers.com\/wp-content\/uploads\/2020\/12\/Big-Ideas-Math-Answers-Grade-5-Chapter-10-21-300x186.jpg 300w\" sizes=\"(max-width: 458px) 100vw, 458px\" \/><br \/>\nFrom the above model,<br \/>\nThe number of colored parts is: 3<br \/>\nThe number of total parts is: 4<br \/>\nSo,<br \/>\nThe fraction of the colored parts out of the total number of parts = 3 \u00f7 4<br \/>\n= \\(\\frac{3}{4}\\)<br \/>\nSo,<br \/>\nThe fraction of the colored parts out of the total number of parts in the decimal form is: 0.75<\/p>\n<p>Question 5.<br \/>\n6 \u00f7 7 = 0.85<br \/>\nAnswer: <img loading=\"lazy\" class=\"alignnone size-full wp-image-34146\" src=\"https:\/\/ccssmathanswers.com\/wp-content\/uploads\/2020\/12\/Big-Ideas-Math-Answers-Grade-5-Chapter-10-22.jpg\" alt=\"\" width=\"458\" height=\"284\" srcset=\"https:\/\/bigideasmathanswers.com\/wp-content\/uploads\/2020\/12\/Big-Ideas-Math-Answers-Grade-5-Chapter-10-22.jpg 458w, https:\/\/bigideasmathanswers.com\/wp-content\/uploads\/2020\/12\/Big-Ideas-Math-Answers-Grade-5-Chapter-10-22-300x186.jpg 300w\" sizes=\"(max-width: 458px) 100vw, 458px\" \/><br \/>\nFrom the above model,<br \/>\nThe number of colored parts is: 6<br \/>\nThe number of total parts is: 7<br \/>\nSo,<br \/>\nThe fraction of the colored parts out of the total number of parts = 6 \u00f7 7<br \/>\n= \\(\\frac{6}{7}\\)<br \/>\nSo,<br \/>\nThe fraction of the colored parts out of the total number of parts in the decimal form is: 0.85<\/p>\n<p>Question 6.<br \/>\n5 \u00f7 9 = 0.55<br \/>\nAnswer: <img loading=\"lazy\" class=\"alignnone size-full wp-image-34147\" src=\"https:\/\/ccssmathanswers.com\/wp-content\/uploads\/2020\/12\/Big-Ideas-Math-Answers-Grade-5-Chapter-10-23.jpg\" alt=\"\" width=\"458\" height=\"284\" srcset=\"https:\/\/bigideasmathanswers.com\/wp-content\/uploads\/2020\/12\/Big-Ideas-Math-Answers-Grade-5-Chapter-10-23.jpg 458w, https:\/\/bigideasmathanswers.com\/wp-content\/uploads\/2020\/12\/Big-Ideas-Math-Answers-Grade-5-Chapter-10-23-300x186.jpg 300w\" sizes=\"(max-width: 458px) 100vw, 458px\" \/><br \/>\nFrom the above model,<br \/>\nThe number of colored parts is: 5<br \/>\nThe number of total parts is: 9<br \/>\nSo,<br \/>\nThe fraction of the colored parts out of the total number of parts = 5 \u00f7 9<br \/>\n= \\(\\frac{5}{9}\\)<br \/>\nSo,<br \/>\nThe fraction of the colored parts out of the total number of parts in the decimal form is: 0.55<\/p>\n<p>Question 7.<br \/>\n<strong>YOU BE THE TEACHER<\/strong><br \/>\nYour friend says \\(\\frac{5}{12}\\) is equivalent to 12 \u00f7 5. Is your friend correct? Explain.<br \/>\nAnswer: No, your friend s not correct.<\/p>\n<p>Explanation:<br \/>\nThe given fraction is: \\(\\frac{5}{12}\\)<br \/>\nFrom the given fraction,<br \/>\nThe numerator is: 5<br \/>\nThe denominator is: 12<br \/>\nWe can write a fraction in the following form:<br \/>\nFraction = \\(\\frac{Numerator}{Denominator}\\)<br \/>\nSo,<br \/>\n\\(\\frac{5}{12}\\) is equivalent to 5 \u00f7 12<br \/>\nBut, according to your friend,<br \/>\n\\(\\frac{5}{12}\\) is equivalent to 12 \u00f7 5<br \/>\nHence, from the above,<br \/>\nwe can conclude that your friend is not correct.<\/p>\n<p>Question 8.<br \/>\n<strong>Writing<\/strong><br \/>\nExplain how fractions and division are related.<\/p>\n<p>Question 9.<br \/>\n<strong>Structure<\/strong><br \/>\nWrite a division equation represented by the model.<br \/>\n<img loading=\"lazy\" class=\"alignnone size-full wp-image-15162\" src=\"https:\/\/ccssmathanswers.com\/wp-content\/uploads\/2020\/12\/Big-Ideas-Math-Answer-Key-Grade-5-Chapter-10-Divide-Fractions-8.png\" alt=\"Big Ideas Math Answer Key Grade 5 Chapter 10 Divide Fractions 8\" width=\"445\" height=\"57\" srcset=\"https:\/\/bigideasmathanswers.com\/wp-content\/uploads\/2020\/12\/Big-Ideas-Math-Answer-Key-Grade-5-Chapter-10-Divide-Fractions-8.png 445w, https:\/\/bigideasmathanswers.com\/wp-content\/uploads\/2020\/12\/Big-Ideas-Math-Answer-Key-Grade-5-Chapter-10-Divide-Fractions-8-300x38.png 300w\" sizes=\"(max-width: 445px) 100vw, 445px\" \/><br \/>\nAnswer:<br \/>\nThe division equation represented by the model is: 1 \u00f7 4<\/p>\n<p>Explanation:<br \/>\nThe given model is:<br \/>\n<img loading=\"lazy\" class=\"alignnone size-full wp-image-15162\" src=\"https:\/\/ccssmathanswers.com\/wp-content\/uploads\/2020\/12\/Big-Ideas-Math-Answer-Key-Grade-5-Chapter-10-Divide-Fractions-8.png\" alt=\"Big Ideas Math Answer Key Grade 5 Chapter 10 Divide Fractions 8\" width=\"445\" height=\"57\" srcset=\"https:\/\/bigideasmathanswers.com\/wp-content\/uploads\/2020\/12\/Big-Ideas-Math-Answer-Key-Grade-5-Chapter-10-Divide-Fractions-8.png 445w, https:\/\/bigideasmathanswers.com\/wp-content\/uploads\/2020\/12\/Big-Ideas-Math-Answer-Key-Grade-5-Chapter-10-Divide-Fractions-8-300x38.png 300w\" sizes=\"(max-width: 445px) 100vw, 445px\" \/><br \/>\nFrom the given model,<br \/>\nThe number of shaded parts is: 1<br \/>\nThe total number of parts are: 4<br \/>\nSo,<br \/>\nThe division equation can be represented as:<br \/>\nDivision equation = (The number of shaded parts) \u00f7 ( The total number of parts )<br \/>\n= 1 \u00f7 4<br \/>\n= \\(\\frac{1}{4}\\)<\/p>\n<p>Question 10.<br \/>\n<strong>Number Sense<\/strong><br \/>\nEight friends share multiple vegetable pizzas, and each gets \\(\\frac{3}{8}\\) of a pizza. How many pizzas do they share?<br \/>\nAnswer: The total number of pizzas the eight friends shared are: 3 pizzas<\/p>\n<p>Explanation:<br \/>\nIt is given that the eight friends share multiple vegetable pizzas and each gets \\(\\frac{3}{8}\\) of a pizza.<br \/>\nSo,<br \/>\nThe total number of pizzas shared by the eight friends = \\(\\frac{3}{8}\\) \u00d7 8<br \/>\n= \\(\\frac{3}{8}\\) \u00d7 \\(\\frac{8}{1}\\)<br \/>\n= \\(\\frac{3 \u00d7 8}{8 \u00d7 1}\\)<br \/>\n= \\(\\frac{3}{1}\\)<br \/>\n= 3<br \/>\nHence, from the above,<br \/>\nWe can conclude that the total number of pizzas shared by the eight friends is: 3 pizzas<\/p>\n<p>Question 11.<br \/>\n<strong>Modeling Real Life<\/strong><br \/>\nSeven friends each run an equal part of a 5-kilometer relay race. What fraction of a kilometer does each friend complete?<br \/>\nAnswer: The fraction of a kilometer does each friend complete is: \\(\\frac{5}{7}\\) kilometer<\/p>\n<p>Explanation:<br \/>\nIt is given that there are seven friends each run an equal part of a 5-kilometer relay race.<br \/>\nSo,<br \/>\nThe fraction that each friend run = \\(\\frac{The total distance} {The number of friends}\\)<br \/>\n= \\(\\frac{5}{7}\\)<br \/>\nHence, from the above,<br \/>\nWe can conclude that the fraction of a kilometer does each friend complete is: \\(\\frac{5}{7}\\) kilometer<\/p>\n<p>Question 12.<br \/>\n<strong>Modeling Real Life<\/strong><br \/>\nA group of friends equally share 3 bags of pretzels. Each friend gets \\(\\frac{3}{5}\\) of a bag of pretzels. How many friends are in the group?<br \/>\nAnswer: The total number of friends in the group are: 5<\/p>\n<p>Explanation:<br \/>\nIt is given that a group of friends equally share 3 bags of pretzels and each friend gets \\(\\frac{3}{5}\\) of a bag of pretzels.<br \/>\nSo,<br \/>\nThe total number of friends = \\(\\frac{The total number of bags}{The amount each friend gets}\\)<br \/>\n= \\(\\frac{3}{1}\\) \u00d7 \\(\\frac{5}{3}\\)<br \/>\n= \\(\\frac{5}{1}\\)<br \/>\n= 5<br \/>\nHence, from the above,<br \/>\nWe can conclude that the total number of friends are: 5<\/p>\n<p><strong>Review &amp; Refresh<\/strong><\/p>\n<p>Multiply.<\/p>\n<p>Question 13.<br \/>\n<img loading=\"lazy\" class=\"alignnone size-full wp-image-15163\" src=\"https:\/\/ccssmathanswers.com\/wp-content\/uploads\/2020\/12\/Big-Ideas-Math-Answer-Key-Grade-5-Chapter-10-Divide-Fractions-9.png\" alt=\"Big Ideas Math Answer Key Grade 5 Chapter 10 Divide Fractions 9\" width=\"117\" height=\"48\" \/><br \/>\nAnswer: 9 \u00d7 \\(\\frac{2}{3}\\) = 6<\/p>\n<p>Explanation:<br \/>\nThe given fractions are: \\(\\frac{9}{1}\\) and \\(\\frac{2}{3}\\)<br \/>\nSo,<br \/>\n\\(\\frac{9}{1}\\) \u00d7 \\(\\frac{2}{3}\\)<br \/>\n= \\(\\frac{9 \u00d7 2}{1 \u00d7 3}\\)<br \/>\n= \\(\\frac{6}{1}\\)<br \/>\n= 6<br \/>\nHence,<br \/>\n9 \u00d7 \\(\\frac{2}{3}\\) = 6<\/p>\n<p>Question 14.<br \/>\n<img loading=\"lazy\" class=\"alignnone size-full wp-image-15164\" src=\"https:\/\/ccssmathanswers.com\/wp-content\/uploads\/2020\/12\/Big-Ideas-Math-Answer-Key-Grade-5-Chapter-10-Divide-Fractions-10.png\" alt=\"Big Ideas Math Answer Key Grade 5 Chapter 10 Divide Fractions 10\" width=\"123\" height=\"56\" \/><br \/>\nAnswer: 5 \u00d7 \\(\\frac{7}{10}\\) = \\(\\frac{7}{2}\\)<\/p>\n<p>Explanation:<br \/>\nThe given fractions are: \\(\\frac{5}{1}\\) and \\(\\frac{7}{10}\\)<br \/>\nSo,<br \/>\n\\(\\frac{5}{1}\\) \u00d7 \\(\\frac{7}{10}\\)<br \/>\n= \\(\\frac{5 \u00d7 7}{1 \u00d7 10}\\)<br \/>\n= \\(\\frac{7}{2}\\)<br \/>\nHence,<br \/>\n5 \u00d7 \\(\\frac{7}{10}\\) = \\(\\frac{7}{2}\\)<\/p>\n<p>Question 15.<br \/>\n<img loading=\"lazy\" class=\"alignnone size-full wp-image-15165\" src=\"https:\/\/ccssmathanswers.com\/wp-content\/uploads\/2020\/12\/Big-Ideas-Math-Answer-Key-Grade-5-Chapter-10-Divide-Fractions-11.png\" alt=\"Big Ideas Math Answer Key Grade 5 Chapter 10 Divide Fractions 11\" width=\"128\" height=\"64\" \/><br \/>\nAnswer: 3 \u00d7 \\(\\frac{5}{12}\\) = \\(\\frac{5}{4}\\)<\/p>\n<p>Explanation:<br \/>\nThe given fractions are: \\(\\frac{3}{1}\\) and \\(\\frac{5}{12}\\)<br \/>\nSo,<br \/>\n\\(\\frac{3}{1}\\) \u00d7 \\(\\frac{5}{12}\\)<br \/>\n= \\(\\frac{3 \u00d7 5}{1 \u00d7 12}\\)<br \/>\n= \\(\\frac{5}{4}\\)<br \/>\nHence,<br \/>\n3 \u00d7 \\(\\frac{5}{12}\\) = \\(\\frac{5}{4}\\)<\/p>\n<h3><a id=\"Lesson_10.2_Mixed_Numbers_as_Quotients\"><\/a>Lesson 10.2 Mixed Numbers as Quotients<\/h3>\n<p><strong>Explore and Grow<\/strong><\/p>\n<p>You share 6 sheets of construction paper equally among 4 people. Write a division expression that represents the situation. How much paper does each person get? Use a model to support your answer.<br \/>\nAnswer:<br \/>\nThe division expression representing the situation is: 6 \u00f7 4<\/p>\n<p>Explanation:<br \/>\nIt s given that you have shared 6 sheets of construction paper equally among 4 people<br \/>\nSo,<br \/>\nThe division equation representing the sharing of construction papers is: 6 \u00f7 4<br \/>\nNow,<br \/>\n6 \u00f7 4 = \\(\\frac{6}{4}\\)<br \/>\nSo,<br \/>\nThe above equation represents that 4 is divided into 6 parts.<br \/>\nSo,<br \/>\nThe model representing the situation is:<br \/>\n<img loading=\"lazy\" class=\"alignnone size-full wp-image-34255\" src=\"https:\/\/ccssmathanswers.com\/wp-content\/uploads\/2020\/12\/Big-Ideas-Math-Answers-Grade-5-Chapter-10-24.jpg\" alt=\"\" width=\"458\" height=\"313\" srcset=\"https:\/\/bigideasmathanswers.com\/wp-content\/uploads\/2020\/12\/Big-Ideas-Math-Answers-Grade-5-Chapter-10-24.jpg 458w, https:\/\/bigideasmathanswers.com\/wp-content\/uploads\/2020\/12\/Big-Ideas-Math-Answers-Grade-5-Chapter-10-24-300x205.jpg 300w\" sizes=\"(max-width: 458px) 100vw, 458px\" \/><br \/>\nFrom the above model,<br \/>\nWe can say that the amount of does each person get is: 1\\(\\frac{1}{2}\\) or 1.5 or \\(\\frac{3}{2}\\)<\/p>\n<p><strong>Precision<\/strong><br \/>\nDoes each person get less than or more than 1 sheet of paper? Use the dividend and divisor to explain why your answer makes sense.<br \/>\nAnswer:<br \/>\nFrom the above problem,<br \/>\nWe can say that each person gets more than 1 paper.<br \/>\nSo,<br \/>\nThe division equation of the above problem is: 6 \u00f7 4<br \/>\nThe equivalent form of 6 \u00f7 4 is: \\(\\frac{6}{4}\\)<br \/>\nNow,<br \/>\nThe simplest form of \\(\\frac{6}{4}\\) is: \\(\\frac{3}{2}\\) ( The simplest form is the division of the numerator and the denominator with the common multiple if we can divide)<br \/>\nThe mixed form of \\(\\frac{3}{2}\\) is: 1\\(\\frac{1}{2}\\)<\/p>\n<p><strong>Think and Grow: Divide Whole Numbers<\/strong><\/p>\n<p>You can use models to divide whole numbers that have a mixed number as the quotient.<br \/>\n<strong>Example<\/strong><br \/>\nFind 3 \u00f7 2.<br \/>\n<strong>One Way:<\/strong><br \/>\nUse a tape diagram. Show 3 wholes. Divide each whole into 2 equal parts.<br \/>\n<img loading=\"lazy\" class=\"alignnone size-full wp-image-34258\" src=\"https:\/\/ccssmathanswers.com\/wp-content\/uploads\/2020\/12\/Big-Ideas-Math-Answers-Grade-5-Chapter-10-25.jpg\" alt=\"\" width=\"649\" height=\"251\" srcset=\"https:\/\/bigideasmathanswers.com\/wp-content\/uploads\/2020\/12\/Big-Ideas-Math-Answers-Grade-5-Chapter-10-25.jpg 649w, https:\/\/bigideasmathanswers.com\/wp-content\/uploads\/2020\/12\/Big-Ideas-Math-Answers-Grade-5-Chapter-10-25-300x116.jpg 300w\" sizes=\"(max-width: 649px) 100vw, 649px\" \/><br \/>\n<strong>Another Way:<\/strong> Use an area model. Show 3 wholes. Divide each whole into 2 equal parts. Then separate the parts into 2 equal groups.<br \/>\n<img loading=\"lazy\" class=\"alignnone size-full wp-image-34259\" src=\"https:\/\/ccssmathanswers.com\/wp-content\/uploads\/2020\/12\/Big-Ideas-Math-Answers-Grade-5-Chapter-10-26.jpg\" alt=\"\" width=\"594\" height=\"207\" srcset=\"https:\/\/bigideasmathanswers.com\/wp-content\/uploads\/2020\/12\/Big-Ideas-Math-Answers-Grade-5-Chapter-10-26.jpg 594w, https:\/\/bigideasmathanswers.com\/wp-content\/uploads\/2020\/12\/Big-Ideas-Math-Answers-Grade-5-Chapter-10-26-300x105.jpg 300w\" sizes=\"(max-width: 594px) 100vw, 594px\" \/><\/p>\n<p><strong>Show and Grow<\/strong><\/p>\n<p>Divide. Use a model to help<\/p>\n<p>Question 1.<br \/>\n5 \u00f7 3 = ___<br \/>\nAnswer: 5 \u00f7 3 = 1\\(\\frac{2}{3}\\)<\/p>\n<p>Explanation;<br \/>\nThe given division equation is: 5 \u00f7 3<br \/>\nThe model representing the division equation is:<br \/>\n<img loading=\"lazy\" class=\"alignnone size-full wp-image-34260\" src=\"https:\/\/ccssmathanswers.com\/wp-content\/uploads\/2020\/12\/Big-Ideas-Math-Answers-Grade-5-Chapter-10-27.jpg\" alt=\"\" width=\"458\" height=\"313\" srcset=\"https:\/\/bigideasmathanswers.com\/wp-content\/uploads\/2020\/12\/Big-Ideas-Math-Answers-Grade-5-Chapter-10-27.jpg 458w, https:\/\/bigideasmathanswers.com\/wp-content\/uploads\/2020\/12\/Big-Ideas-Math-Answers-Grade-5-Chapter-10-27-300x205.jpg 300w\" sizes=\"(max-width: 458px) 100vw, 458px\" \/><br \/>\nFrom the above model,<br \/>\n5 \u00f7 3 = 3 \u00f7 3<br \/>\n= 1 R 2<br \/>\nHence,<br \/>\nWe can say that each part is divided into 1\\(\\frac{2}{3}\\) or \\(\\frac{5}{3}\\)<\/p>\n<p>Question 2.<br \/>\n7 \u00f7 2 = ___<\/p>\n<p>Answer: 7 \u00f7 2 = 3\\(\\frac{1}{2}\\)<\/p>\n<p>Explanation;<br \/>\nThe given division equation is: 7 \u00f7 2<br \/>\nThe model representing the division equation is:<br \/>\n<img loading=\"lazy\" class=\"alignnone size-full wp-image-34261\" src=\"https:\/\/ccssmathanswers.com\/wp-content\/uploads\/2020\/12\/Big-Ideas-Math-Answers-Grade-5-Chapter-10-28.jpg\" alt=\"\" width=\"458\" height=\"313\" srcset=\"https:\/\/bigideasmathanswers.com\/wp-content\/uploads\/2020\/12\/Big-Ideas-Math-Answers-Grade-5-Chapter-10-28.jpg 458w, https:\/\/bigideasmathanswers.com\/wp-content\/uploads\/2020\/12\/Big-Ideas-Math-Answers-Grade-5-Chapter-10-28-300x205.jpg 300w\" sizes=\"(max-width: 458px) 100vw, 458px\" \/><br \/>\nFrom the above model,<br \/>\n7 \u00f7 2 = 6 \u00f7 2<br \/>\n= 3 R 1<br \/>\nHence,<br \/>\nWe can say that each part is divided into 3\\(\\frac{1}{2}\\) or \\(\\frac{7}{2}\\) or 3.5<\/p>\n<p><strong>Apply and Grow: Practice<\/strong><\/p>\n<p>Divide. Use a model to help.<\/p>\n<p>Question 3.<br \/>\n12 \u00f7 7 = ___<\/p>\n<p>Answer: 12 \u00f7 7 = 1\\(\\frac{5}{7}\\)<\/p>\n<p>Explanation;<br \/>\nThe given division equation is: 12 \u00f7 7<br \/>\nThe model representing the division equation is:<br \/>\n<img loading=\"lazy\" class=\"alignnone size-full wp-image-34263\" src=\"https:\/\/ccssmathanswers.com\/wp-content\/uploads\/2020\/12\/Big-Ideas-Math-Answers-Grade-5-Chapter-10-30.jpg\" alt=\"\" width=\"458\" height=\"313\" srcset=\"https:\/\/bigideasmathanswers.com\/wp-content\/uploads\/2020\/12\/Big-Ideas-Math-Answers-Grade-5-Chapter-10-30.jpg 458w, https:\/\/bigideasmathanswers.com\/wp-content\/uploads\/2020\/12\/Big-Ideas-Math-Answers-Grade-5-Chapter-10-30-300x205.jpg 300w\" sizes=\"(max-width: 458px) 100vw, 458px\" \/><br \/>\nFrom the above model,<br \/>\n12 \u00f7 7 = 7 \u00f7 7<br \/>\n= 1 R 5<br \/>\nHence,<br \/>\nWe can say that each part is divided into 1\\(\\frac{5}{7}\\) or \\(\\frac{12}{7}\\)<\/p>\n<p>Question 4.<br \/>\n25 \u00f7 20 = ___<\/p>\n<p>Answer: 25 \u00f7 20 = 1\\(\\frac{5}{20}\\) = \\(\\frac{5}{4}\\)<\/p>\n<p>Explanation;<br \/>\nThe given division equation is: 25 \u00f7 20<br \/>\nThe model representing the division equation is:<br \/>\n<img loading=\"lazy\" class=\"alignnone size-full wp-image-34268\" src=\"https:\/\/ccssmathanswers.com\/wp-content\/uploads\/2020\/12\/Big-Ideas-Math-Answers-Grade-5-Chapter-10-33.jpg\" alt=\"\" width=\"458\" height=\"313\" srcset=\"https:\/\/bigideasmathanswers.com\/wp-content\/uploads\/2020\/12\/Big-Ideas-Math-Answers-Grade-5-Chapter-10-33.jpg 458w, https:\/\/bigideasmathanswers.com\/wp-content\/uploads\/2020\/12\/Big-Ideas-Math-Answers-Grade-5-Chapter-10-33-300x205.jpg 300w\" sizes=\"(max-width: 458px) 100vw, 458px\" \/><br \/>\nFrom the above model,<br \/>\n25 \u00f7 20 = 20 \u00f7 20<br \/>\n= 1 R 5<br \/>\nHence,<br \/>\nWe can say that each part is divided into 1\\(\\frac{5}{20}\\) or \\(\\frac{5}{4}\\)<\/p>\n<p>Question 5.<br \/>\n15 \u00f7 4 = ___<\/p>\n<p>Answer: 15 \u00f7 4 = 3\\(\\frac{3}{4}\\)<\/p>\n<p>Explanation;<br \/>\nThe given division equation is: 15 \u00f7 4<br \/>\nThe model representing the division equation is:<br \/>\n<img loading=\"lazy\" class=\"alignnone size-full wp-image-34264\" src=\"https:\/\/ccssmathanswers.com\/wp-content\/uploads\/2020\/12\/Big-Ideas-Math-Answers-Grade-5-Chapter-10-31.jpg\" alt=\"\" width=\"458\" height=\"313\" srcset=\"https:\/\/bigideasmathanswers.com\/wp-content\/uploads\/2020\/12\/Big-Ideas-Math-Answers-Grade-5-Chapter-10-31.jpg 458w, https:\/\/bigideasmathanswers.com\/wp-content\/uploads\/2020\/12\/Big-Ideas-Math-Answers-Grade-5-Chapter-10-31-300x205.jpg 300w\" sizes=\"(max-width: 458px) 100vw, 458px\" \/><br \/>\nFrom the above model,<br \/>\n15 \u00f7 4 = 12 \u00f7 4<br \/>\n= 3 R 3<br \/>\nHence,<br \/>\nWe can say that each part is divided into 3\\(\\frac{3}{4}\\) or \\(\\frac{15}{4}\\)<\/p>\n<p>Question 6.<br \/>\n13 \u00f7 6 = ___<\/p>\n<p>Answer: 13 \u00f7 6 = 2\\(\\frac{1}{6}\\)<\/p>\n<p>Explanation;<br \/>\nThe given division equation is: 13\u00f7 6<br \/>\nThe model representing the division equation is:<br \/>\n<img loading=\"lazy\" class=\"alignnone size-full wp-image-34265\" src=\"https:\/\/ccssmathanswers.com\/wp-content\/uploads\/2020\/12\/Big-Ideas-Math-Answers-Grade-5-Chapter-10-32.jpg\" alt=\"\" width=\"458\" height=\"313\" srcset=\"https:\/\/bigideasmathanswers.com\/wp-content\/uploads\/2020\/12\/Big-Ideas-Math-Answers-Grade-5-Chapter-10-32.jpg 458w, https:\/\/bigideasmathanswers.com\/wp-content\/uploads\/2020\/12\/Big-Ideas-Math-Answers-Grade-5-Chapter-10-32-300x205.jpg 300w\" sizes=\"(max-width: 458px) 100vw, 458px\" \/><br \/>\nFrom the above model,<br \/>\n13 \u00f7 6 = 12 \u00f7 6<br \/>\n= 2 R 1<br \/>\nHence,<br \/>\nWe can say that each part is divided into 2\\(\\frac{1}{6}\\) or \\(\\frac{13}{6}\\)<\/p>\n<p>Question 7.<br \/>\n16 \u00f7 8 = ___<\/p>\n<p>Answer: 16 \u00f7 8 = 2<\/p>\n<p>Explanation;<br \/>\nThe given division equation is: 16\u00f7 8<br \/>\nThe model representing the division equation is:<br \/>\n<img loading=\"lazy\" class=\"alignnone size-full wp-image-34271\" src=\"https:\/\/ccssmathanswers.com\/wp-content\/uploads\/2020\/12\/Big-Ideas-Math-Answers-Grade-5-Chapter-10-34.jpg\" alt=\"\" width=\"458\" height=\"313\" srcset=\"https:\/\/bigideasmathanswers.com\/wp-content\/uploads\/2020\/12\/Big-Ideas-Math-Answers-Grade-5-Chapter-10-34.jpg 458w, https:\/\/bigideasmathanswers.com\/wp-content\/uploads\/2020\/12\/Big-Ideas-Math-Answers-Grade-5-Chapter-10-34-300x205.jpg 300w\" sizes=\"(max-width: 458px) 100vw, 458px\" \/><br \/>\nFrom the above model,<br \/>\n16 \u00f7 8<br \/>\n= 2 R 0<br \/>\nHence,<br \/>\nWe can say that each part is divided into 2 equal parts<\/p>\n<p>Question 8.<br \/>\n92 \u00f7 50 = ___<\/p>\n<p>Answer: 92 \u00f7 50 = 1\\(\\frac{21}{25}\\)<\/p>\n<p>Explanation;<br \/>\nThe given division equation is: 92\u00f7 50<br \/>\nSo,<br \/>\n92 \u00f7 50 = 50 \u00f7 50<br \/>\n= 1 R 42<br \/>\nHence,<br \/>\nWe can say that each part is divided into 1\\(\\frac{42}{50}\\) or 1\\(\\frac{21}{25}\\)<\/p>\n<p>Question 9.<br \/>\nHow many 3s are in 7?<br \/>\nAnswer: The number of 3 in 7 are: \\(\\frac{7}{3}\\) or 2\\(\\frac{1}{3}\\)<\/p>\n<p>Explanation:<br \/>\nThe division equation is: 7 \u00f7 3<br \/>\nSo,<br \/>\nThe model for the given division equation is:<br \/>\n<img loading=\"lazy\" class=\"alignnone size-full wp-image-34314\" src=\"https:\/\/ccssmathanswers.com\/wp-content\/uploads\/2020\/12\/Big-Ideas-Math-Answers-Grade-5-Chapter-10-35.jpg\" alt=\"\" width=\"458\" height=\"313\" srcset=\"https:\/\/bigideasmathanswers.com\/wp-content\/uploads\/2020\/12\/Big-Ideas-Math-Answers-Grade-5-Chapter-10-35.jpg 458w, https:\/\/bigideasmathanswers.com\/wp-content\/uploads\/2020\/12\/Big-Ideas-Math-Answers-Grade-5-Chapter-10-35-300x205.jpg 300w\" sizes=\"(max-width: 458px) 100vw, 458px\" \/><br \/>\nFrom the above model,<br \/>\n7 \u00f7 3 = 6 \u00f7 3<br \/>\n= 2 R 1<br \/>\nHence, from the above,<br \/>\nWe can conclude that there are 2\\(\\frac{1}{3}\\) 3s in 7<\/p>\n<p>Question 10.<br \/>\nHow many 6s are in 21?<br \/>\nAnswer: The number of 6s in 21 are: \\(\\frac{21}{6}\\) or 3\\(\\frac{3}{6}\\)<\/p>\n<p>Explanation:<br \/>\nThe division equation is: 21 \u00f7 6<br \/>\nSo,<br \/>\nThe model for the given division equation is:<br \/>\n<img loading=\"lazy\" class=\"alignnone size-full wp-image-34316\" src=\"https:\/\/ccssmathanswers.com\/wp-content\/uploads\/2020\/12\/Big-Ideas-Math-Answers-Grade-5-Chapter-10-37.jpg\" alt=\"\" width=\"458\" height=\"313\" srcset=\"https:\/\/bigideasmathanswers.com\/wp-content\/uploads\/2020\/12\/Big-Ideas-Math-Answers-Grade-5-Chapter-10-37.jpg 458w, https:\/\/bigideasmathanswers.com\/wp-content\/uploads\/2020\/12\/Big-Ideas-Math-Answers-Grade-5-Chapter-10-37-300x205.jpg 300w\" sizes=\"(max-width: 458px) 100vw, 458px\" \/><br \/>\nFrom the above model,<br \/>\n21 \u00f7 6 = 18 \u00f7 6<br \/>\n= 3 R 3<br \/>\nHence, from the above,<br \/>\nWe can conclude that there are 3\\(\\frac{3}{6}\\) 3s in 21<\/p>\n<p>Question 11.<br \/>\n<strong>YOU BE THE TEACHER<\/strong><br \/>\nYour friend says that \\(\\frac{35}{6}\\) is equivalent to 35 \u00f7 6. Is your friend correct? Explain.<br \/>\nAnswer: Yes, your friend is correct<\/p>\n<p>Explanation:<br \/>\nIt is given that \\(\\frac{35}{6}\\)<br \/>\nWe know that,<br \/>\nThe decimal equation can be converted into a fraction as \\(\\frac{Numerator}{Denominator}\\)<br \/>\nSo,<br \/>\n\\(\\frac{35}{6}\\) = 35 \u00f7 6<br \/>\nHence, from the above,<br \/>\nWe can conclude that your friend is correct<\/p>\n<p>Question 12.<br \/>\n<strong>Writing<\/strong><br \/>\nWrite and solve a real-life problem for 24 \u00f7 5.<br \/>\nAnswer: 24 \u00f7 5 = 4\\(\\frac{4}{5}\\)<\/p>\n<p>Explanation;<br \/>\nThe given division equation is: 24\u00f7 5<br \/>\nThe model for the above division equation is:<br \/>\n<img loading=\"lazy\" class=\"alignnone size-full wp-image-34320\" src=\"https:\/\/ccssmathanswers.com\/wp-content\/uploads\/2020\/12\/Big-Ideas-Math-Answers-Grade-5-Chapter-10-38.jpg\" alt=\"\" width=\"458\" height=\"313\" srcset=\"https:\/\/bigideasmathanswers.com\/wp-content\/uploads\/2020\/12\/Big-Ideas-Math-Answers-Grade-5-Chapter-10-38.jpg 458w, https:\/\/bigideasmathanswers.com\/wp-content\/uploads\/2020\/12\/Big-Ideas-Math-Answers-Grade-5-Chapter-10-38-300x205.jpg 300w\" sizes=\"(max-width: 458px) 100vw, 458px\" \/><br \/>\nFrom the above model,<br \/>\n24 \u00f7 5 = 20 \u00f7 5<br \/>\n= 4 R 4<br \/>\nHence,<br \/>\nWe can say that each part is divided into 4\\(\\frac{4}{5}\\)<\/p>\n<p><strong>Think and Grow: Modeling Real Life<\/strong><\/p>\n<p><strong>Example<\/strong><br \/>\nYou share 7 bales of hay equally among 3 horse stalls. How many whole bales are in each stall? What fractional amount of a bale is in each stall?<br \/>\nDivide 7 by 3 to \ufb01nd how many bales of hay are in each stall. Use an area model to help.<br \/>\n<img loading=\"lazy\" class=\"alignnone size-full wp-image-34324\" src=\"https:\/\/ccssmathanswers.com\/wp-content\/uploads\/2020\/12\/Big-Ideas-Math-Answers-Grade-5-Chapter-10-39.jpg\" alt=\"\" width=\"690\" height=\"534\" srcset=\"https:\/\/bigideasmathanswers.com\/wp-content\/uploads\/2020\/12\/Big-Ideas-Math-Answers-Grade-5-Chapter-10-39.jpg 690w, https:\/\/bigideasmathanswers.com\/wp-content\/uploads\/2020\/12\/Big-Ideas-Math-Answers-Grade-5-Chapter-10-39-300x232.jpg 300w\" sizes=\"(max-width: 690px) 100vw, 690px\" \/><\/p>\n<p><strong>Show and Grow<\/strong><\/p>\n<p>Question 13.<br \/>\nSix muffins are shared equally among 4 friends. How many whole muffins does each friend get? What fractional amount of a muffin does each friend get?<br \/>\nAnswer: Each friend will get 1 muffin and 2 muffins are leftovers<br \/>\nThe fractional part of a muffin does each friend get is: \\(\\frac{1}{2}\\)<\/p>\n<p>Explanation:<br \/>\nIt is given that there are six muffins are shared equally among 4 friends.<br \/>\nSo,<br \/>\nThe number of muffins each friend get = 6 \u00f7 4<br \/>\n= 4 \u00f7 4<br \/>\n= 1 R 2<br \/>\nHence, from the above,<br \/>\nWe can conclude that each friend gets 1 muffin each and the fraction of each muffin get is: \\(\\frac{1}{2}\\)<\/p>\n<p>Question 14.<br \/>\nA cyclist bikes 44 miles in 5 days. She bikes the same distance each day. Does she bike more than 8\\(\\frac{1}{2}\\) miles each day? Explain.<br \/>\nAnswer: She bikes more than 8\\(\\frac{1}{2}\\) miles each day.<\/p>\n<p>Explanation:<br \/>\nIt is given that a cyclist bikes 44 miles in 5 days.<br \/>\nSo,<br \/>\nThe distance that she bikes each day = 44 \u00f7 5<br \/>\nSo,<br \/>\n44 \u00f7 5 = 40 \u00f7 5<br \/>\n= 8 R 4<br \/>\n= 8\\(\\frac{4}{5}\\) miles<br \/>\nBut, it is given that she bikes 8\\(\\frac{1}{2}\\) miles each day<br \/>\nHence, from the above,<br \/>\nWe can conclude that she bikes more than 8\\(\\frac{1}{2}\\) miles each day.<\/p>\n<p>Question 15.<br \/>\n<strong>DIG DEEPER!<\/strong><br \/>\nAt Table A, 4 students share 7 packs of clay equally. At Table B, 5 students share 8 packs of clay equally. At which table does each student get a greater amount of clay? Explain.<br \/>\n<img loading=\"lazy\" class=\"alignnone size-full wp-image-15169\" src=\"https:\/\/ccssmathanswers.com\/wp-content\/uploads\/2020\/12\/Big-Ideas-Math-Answer-Key-Grade-5-Chapter-10-Divide-Fractions-15.png\" alt=\"Big Ideas Math Answer Key Grade 5 Chapter 10 Divide Fractions 15\" width=\"137\" height=\"108\" \/><br \/>\nAnswer: At Table A, each student gets a greater amount of clay.<\/p>\n<p>Explanation:<br \/>\nIt is given that at Table A, 4 students share 7 packs of clay equally.<br \/>\nSo,<br \/>\nThe representation of clay at table A is: \\(\\frac{7}{4}\\)<br \/>\nIt is also given that at Table B, 5 students share 8 packs of clay equally.<br \/>\nSo,<br \/>\nThe representation of clay at table B is: \\(\\frac{8}{5}\\)<br \/>\nSo,<br \/>\nFor comparison, equate the denominators.<br \/>\nSo,<br \/>\nMultiply the first fraction at table A by \\(\\frac{5}{5}\\) and the fraction at table B by \\(\\frac{4}{4}\\)<br \/>\nSo,<br \/>\n\\(\\frac{7}{4}\\) \u00d7 \\(\\frac{5}{5}\\)<br \/>\n= \\(\\frac{35}{20}\\)<br \/>\nSo,<br \/>\n\\(\\frac{8}{5}\\) \u00d7 \\(\\frac{4}{4}\\)<br \/>\n= \\(\\frac{32}{20}\\)<br \/>\nHence, from the above,<br \/>\nWe can conclude that at table A, the students will get more amount of clay.<\/p>\n<h3><a id=\"Mixed_Numbers_as_Quotients_Homework_&amp;_Practice_10.2\"><\/a>Mixed Numbers as Quotients Homework &amp; Practice 10.2<\/h3>\n<p>Divide. Use a model to help.<\/p>\n<p>Question 1.<br \/>\n5 \u00f7 2 = ___<br \/>\nAnswer: 5 \u00f7 2 = 2\\(\\frac{1}{2}\\)<\/p>\n<p>Explanation;<br \/>\nThe given division equation is: 5 \u00f7 2<br \/>\nThe model representing the division equation is:<br \/>\n<img loading=\"lazy\" class=\"alignnone size-full wp-image-34570\" src=\"https:\/\/ccssmathanswers.com\/wp-content\/uploads\/2020\/12\/Big-Ideas-Math-Answers-Grade-5-Chapter-10-40.jpg\" alt=\"\" width=\"458\" height=\"313\" srcset=\"https:\/\/bigideasmathanswers.com\/wp-content\/uploads\/2020\/12\/Big-Ideas-Math-Answers-Grade-5-Chapter-10-40.jpg 458w, https:\/\/bigideasmathanswers.com\/wp-content\/uploads\/2020\/12\/Big-Ideas-Math-Answers-Grade-5-Chapter-10-40-300x205.jpg 300w\" sizes=\"(max-width: 458px) 100vw, 458px\" \/><br \/>\nFrom the above model,<br \/>\n5 \u00f7 2 = 4 \u00f7 2<br \/>\n= 2 R 1<br \/>\nHence,<br \/>\nWe can say that 5 \u00f7 2 = 2\\(\\frac{1}{2}\\) or 2.5 or \\(\\frac{5}{2}\\)<\/p>\n<p>Question 2.<br \/>\n10 \u00f7 7 = ___<br \/>\nAnswer: 10 \u00f7 7 = 1\\(\\frac{3}{7}\\) = \\(\\frac{10}{7}\\)<\/p>\n<p>Explanation;<br \/>\nThe given division equation is: 10 \u00f7 7<br \/>\nThe model representing the division equation is:<br \/>\n<img loading=\"lazy\" class=\"alignnone size-full wp-image-34571\" src=\"https:\/\/ccssmathanswers.com\/wp-content\/uploads\/2020\/12\/Big-Ideas-Math-Answers-Grade-5-Chapter-10-41.jpg\" alt=\"\" width=\"458\" height=\"313\" srcset=\"https:\/\/bigideasmathanswers.com\/wp-content\/uploads\/2020\/12\/Big-Ideas-Math-Answers-Grade-5-Chapter-10-41.jpg 458w, https:\/\/bigideasmathanswers.com\/wp-content\/uploads\/2020\/12\/Big-Ideas-Math-Answers-Grade-5-Chapter-10-41-300x205.jpg 300w\" sizes=\"(max-width: 458px) 100vw, 458px\" \/><br \/>\nFrom the above model,<br \/>\n10 \u00f7 7 = 7 \u00f7 7<br \/>\n= 1 R 3<br \/>\nHence,<br \/>\nWe can say that 10 \u00f7 7 = 1\\(\\frac{3}{7}\\) or \\(\\frac{10}{7}\\)<\/p>\n<p>Question 3.<br \/>\n3 \u00f7 9 = ___<br \/>\nAnswer: 3 \u00f7 9 = \\(\\frac{1}{3}\\)<\/p>\n<p>Explanation;<br \/>\nThe given division equation is: 3 \u00f7 9<br \/>\nThe model representing the division equation is:<br \/>\n<img loading=\"lazy\" class=\"alignnone size-full wp-image-34572\" src=\"https:\/\/ccssmathanswers.com\/wp-content\/uploads\/2020\/12\/Big-Ideas-Math-Answers-Grade-5-Chapter-10-42.jpg\" alt=\"\" width=\"458\" height=\"313\" srcset=\"https:\/\/bigideasmathanswers.com\/wp-content\/uploads\/2020\/12\/Big-Ideas-Math-Answers-Grade-5-Chapter-10-42.jpg 458w, https:\/\/bigideasmathanswers.com\/wp-content\/uploads\/2020\/12\/Big-Ideas-Math-Answers-Grade-5-Chapter-10-42-300x205.jpg 300w\" sizes=\"(max-width: 458px) 100vw, 458px\" \/><br \/>\nFrom the above model,<br \/>\n3 and 9 are the multiples of 3.<br \/>\nSo,<br \/>\n3 \u00f7 9 = \\(\\frac{1}{3}\\)<br \/>\nHence,<br \/>\nWe can say that 3 \u00f7 9 = \\(\\frac{1}{3}\\)<\/p>\n<p>Question 4.<br \/>\n11 \u00f7 4 = ___<br \/>\nAnswer: 11 \u00f7 4 = 2\\(\\frac{3}{4}\\)<\/p>\n<p>Explanation;<br \/>\nThe given division equation is: 11 \u00f7 4<br \/>\nThe model representing the division equation is:<br \/>\n<img loading=\"lazy\" class=\"alignnone size-full wp-image-34573\" src=\"https:\/\/ccssmathanswers.com\/wp-content\/uploads\/2020\/12\/Big-Ideas-Math-Answers-Grade-5-Chapter-10-43.jpg\" alt=\"\" width=\"458\" height=\"313\" srcset=\"https:\/\/bigideasmathanswers.com\/wp-content\/uploads\/2020\/12\/Big-Ideas-Math-Answers-Grade-5-Chapter-10-43.jpg 458w, https:\/\/bigideasmathanswers.com\/wp-content\/uploads\/2020\/12\/Big-Ideas-Math-Answers-Grade-5-Chapter-10-43-300x205.jpg 300w\" sizes=\"(max-width: 458px) 100vw, 458px\" \/><br \/>\nFrom the above model,<br \/>\n11 \u00f7 4 = 8 \u00f7 4<br \/>\n= 2 R 3<br \/>\nHence,<br \/>\nWe can say that 11 \u00f7 4 = \\(\\frac{11}{4}\\) or 2\\(\\frac{3}{4}\\)<\/p>\n<p>Question 5.<br \/>\n13 \u00f7 6 = ___<br \/>\nAnswer: 13 \u00f7 6 = 2\\(\\frac{1}{6}\\)<\/p>\n<p>Explanation;<br \/>\nThe given division equation is: 13 \u00f7 6<br \/>\nThe model representing the division equation is:<br \/>\n<img loading=\"lazy\" class=\"alignnone size-full wp-image-34574\" src=\"https:\/\/ccssmathanswers.com\/wp-content\/uploads\/2020\/12\/Big-Ideas-Math-Answers-Grade-5-Chapter-10-44.jpg\" alt=\"\" width=\"458\" height=\"313\" srcset=\"https:\/\/bigideasmathanswers.com\/wp-content\/uploads\/2020\/12\/Big-Ideas-Math-Answers-Grade-5-Chapter-10-44.jpg 458w, https:\/\/bigideasmathanswers.com\/wp-content\/uploads\/2020\/12\/Big-Ideas-Math-Answers-Grade-5-Chapter-10-44-300x205.jpg 300w\" sizes=\"(max-width: 458px) 100vw, 458px\" \/><br \/>\nFrom the above model,<br \/>\n13 \u00f7 6 = 12 \u00f7 6<br \/>\n= 2 R 1<br \/>\nHence,<br \/>\nWe can say that 13 \u00f7 6 = \\(\\frac{13}{6}\\) or 2\\(\\frac{1}{6}\\)<\/p>\n<p>Question 6.<br \/>\n45 \u00f7 8 = ___<br \/>\nAnswer: 45 \u00f7 8 = 5\\(\\frac{5}{8}\\)<\/p>\n<p>Explanation;<br \/>\nThe given division equation is: 45 \u00f7 8<br \/>\nThe model representing the division equation is:<br \/>\n<img loading=\"lazy\" class=\"alignnone size-full wp-image-34575\" src=\"https:\/\/ccssmathanswers.com\/wp-content\/uploads\/2020\/12\/Big-Ideas-Math-Answers-Grade-5-Chapter-10-45.jpg\" alt=\"\" width=\"458\" height=\"313\" srcset=\"https:\/\/bigideasmathanswers.com\/wp-content\/uploads\/2020\/12\/Big-Ideas-Math-Answers-Grade-5-Chapter-10-45.jpg 458w, https:\/\/bigideasmathanswers.com\/wp-content\/uploads\/2020\/12\/Big-Ideas-Math-Answers-Grade-5-Chapter-10-45-300x205.jpg 300w\" sizes=\"(max-width: 458px) 100vw, 458px\" \/><br \/>\nFrom the above model,<br \/>\n45 \u00f7 8 = 40 \u00f7 8<br \/>\n= 5 R 5<br \/>\nHence,<br \/>\nWe can say that 45 \u00f7 8 = \\(\\frac{45}{8}\\) or 5\\(\\frac{5}{8}\\)<\/p>\n<p>Question 7.<br \/>\n<strong>Number Sense<\/strong><br \/>\nBetween which two whole numbers is the quotient of 74 and 9?<br \/>\nAnswer: The quotient of 74 and 9 is between 8 and 9<\/p>\n<p>Explanation:<br \/>\nThe given two numbers are 7 and 9<br \/>\nSo,<br \/>\nBy using the partial quotients method,<br \/>\n74 \u00f7 9= 72 \u00f7 9<br \/>\n= 8 R 2<br \/>\nSo,<br \/>\n74 \u00f7 9 = \\(\\frac{74}{9}\\) or 8\\(\\frac{2}{9}\\) or 8.3<br \/>\nHence, from the above,<br \/>\nWe can conclude that the quotient of 74 and 9 is between 8 and 9<\/p>\n<p>Question 8.<br \/>\n<strong>Reasoning<\/strong><br \/>\nThree friends want to share 22 baseball cards. For this situation, why does the quotient 7 R1 make more sense than the quotient 7\\(\\frac{1}{3}\\)?<br \/>\nAnswer:<br \/>\nIt is given that three friends want to share 22 baseball cards.<br \/>\nSo,<br \/>\nWe have to find the number of baseball cards each friend possesses.<br \/>\nSo,<br \/>\nIt is sufficient to write the number of baseball cards possessed by each friend in the remainder form rather than the fraction form.<br \/>\nSo,<br \/>\nThe number of baseball cards possessed by each friend = \\(\\frac{The total number of baseball cards}{The number of friends}\\)<br \/>\n= 22 \u00f7 3<br \/>\n= 21 \u00f7 3<br \/>\n= 7 R 1<br \/>\nHence, from the above,<br \/>\nWe can conclude that the remainder form is sufficient to find the number of baseball cars possessed by each friend rather than the fraction form.<\/p>\n<p>Question 9.<br \/>\n<strong>DIG DEEPER!<\/strong><br \/>\nIs \\(\\frac{2}{5}\\) \u00d7 3 equivalent to 2 \u00d7 3 \u00f7 5? Explain.<br \/>\nAnswer: Yes, \\(\\frac{2}{5}\\) \u00d7 3 equivalent to 2 \u00d7 3 \u00f7 5<\/p>\n<p>Explanation:<br \/>\nThe given fraction and the number is: \\(\\frac{2}{5}\\) and 3<br \/>\nSo,<br \/>\n\\(\\frac{2}{5}\\) \u00d7 3 = \\(\\frac{2}{5}\\) \u00d7 \\(\\frac{3}{1}\\)<br \/>\n= \\(\\frac{2 \u00d7 3}{5}\\)<br \/>\n= 2 \u00d7 3 \u00f7 5<br \/>\nHence, from the above,<br \/>\nWe can conclude that \\(\\frac{2}{5}\\) \u00d7 3 equivalent to 2 \u00d7 3 \u00f7 5<\/p>\n<p>Question 10.<br \/>\n<strong>Modeling Real Life<\/strong><br \/>\nA bag of 4 balls weighs 6 pounds. Each ball weighs the same amount. What is the weight of each ball?<br \/>\nAnswer: The weight of each ball is: \\(\\frac{3}{2}\\) pounds or 1.5 pounds<\/p>\n<p>Explanation:<br \/>\nIt is given that a bag of 4 balls weighs 6 pounds<br \/>\nSo,<br \/>\nThe weight of each ball = \\(\\frac{The total weight of the balls}{The number of balls}\\)<br \/>\n= 6 \u00f7 4<br \/>\nSince 6 and 4 are the multiples of 2, divide the two numbers by 2<br \/>\nSo,<br \/>\n6 \u00f7 4 = 3 \u00f7 2<br \/>\nSo,<br \/>\n3 \u00f7 2 = 2 \u00f7 2<br \/>\n= 1 R 1<br \/>\n= 1\\(\\frac{1}{2}\\) pounds<br \/>\nHence, from the above,<br \/>\nWe can conclude that the weight of each ball is: 1\\(\\frac{1}{2}\\) pounds or 1.5 pounds<\/p>\n<p>Question 11.<br \/>\n<strong>Modeling Real Life<\/strong><br \/>\nZookeepers order 600 pounds of bamboo for the pandas. The bamboo lasts 7 days. How many whole pounds of bamboo do the pandas eat each day? What fractional amount of a pound do the pandas eat each day?<br \/>\n<img loading=\"lazy\" class=\"alignnone size-full wp-image-15170\" src=\"https:\/\/ccssmathanswers.com\/wp-content\/uploads\/2020\/12\/Big-Ideas-Math-Answer-Key-Grade-5-Chapter-10-Divide-Fractions-17.png\" alt=\"Big Ideas Math Answer Key Grade 5 Chapter 10 Divide Fractions 17\" width=\"185\" height=\"139\" \/><br \/>\nAnswer:<br \/>\nThe amount of bamboos the pandas eat each day is around 85 pounds<br \/>\nThe amount of bamboos the pandas eat each day in the fraction form is: 85\\(\\frac{5}{7}\\)<\/p>\n<p>Explanation:<br \/>\nIt is given that zookeepers order 600 pounds of bamboo for the pandas and the bamboos last 7 days for the pandas<br \/>\nSo,<br \/>\nThe number of bamboos the pandas eat each day = 600 \u00f7 7<br \/>\nSo,<br \/>\nBy using the partial quotients method,<br \/>\n600 \u00f7 7 = ( 560 + 35 ) \u00f7 7<br \/>\n= ( 560 \u00f7 7 ) + ( 35 \u00f7 7 )<br \/>\n= 80 + 5<br \/>\n= 85 R 5<br \/>\nHence, from the above,<br \/>\nWe can conclude that<br \/>\nThe amount of bamboos the pandas eat each day is around 85 pounds<br \/>\nThe amount of bamboos the pandas eat each day in the fraction form is: 85\\(\\frac{5}{7}\\)<\/p>\n<p>Question 12.<br \/>\n<strong>Modeling Real Life<\/strong><br \/>\nA plumber has 20 feet of piping. He cuts the piping into 6 equal pieces. Is each piece greater than, less than, or equal to 3\\(\\frac{1}{2}\\) feet?<br \/>\nAnswer: Each piece is less than 3\\(\\frac{1}{2}\\) feet<\/p>\n<p>Explanation:<br \/>\nIt is given that a plumber has 20 feet of piping and he cuts the piping into 6 equal pieces.<br \/>\nSo,<br \/>\nThe length of each piece = 20 \u00f7 6<br \/>\nBy using the partial quotients method,<br \/>\n20 \u00f7 6 = 18 \u00f7 6<br \/>\n= 3 R 2<br \/>\nSo,<br \/>\n20 \u00f7 6 = 3\\(\\frac{2}{6}\\)<br \/>\nNow,<br \/>\n3\\(\\frac{1}{2}\\) = \\(\\frac{7}{2}\\)<br \/>\n3\\(\\frac{2}{6}\\) = \\(\\frac{20}{6}\\)<br \/>\nFor comparison, we have to equate whether the denominators or the numerators.<br \/>\nSo,<br \/>\nMultiply 3\\(\\frac{1}{2}\\) with \\(\\frac{3}{3}\\)<br \/>\nSo,<br \/>\n3\\(\\frac{1}{2}\\) = \\(\\frac{21}{6}\\)<br \/>\nHence, from the above,<br \/>\nWe can conclude that each piece is less than 3\\(\\frac{1}{2}\\) feet<\/p>\n<p><strong>Review &amp; Refresh<\/strong><\/p>\n<p>Add.<\/p>\n<p>Question 13.<br \/>\n<img loading=\"lazy\" class=\"alignnone size-full wp-image-15171\" src=\"https:\/\/ccssmathanswers.com\/wp-content\/uploads\/2020\/12\/Big-Ideas-Math-Answer-Key-Grade-5-Chapter-10-Divide-Fractions-18.png\" alt=\"Big Ideas Math Answer Key Grade 5 Chapter 10 Divide Fractions 18\" width=\"115\" height=\"54\" \/><br \/>\nAnswer: \\(\\frac{2}{9}\\) + \\(\\frac{2}{3}\\) = \\(\\frac{8}{9}\\)<\/p>\n<p>Explanation:<br \/>\nThe two given fractions are: \\(\\frac{2}{9}\\) and \\(\\frac{2}{3}\\)<br \/>\nSo, in addition, we have to make either the numerators or the denominators equal<br \/>\nSo,<br \/>\nMultiply \\(\\frac{2}{3}\\)\u00a0 with \\(\\frac{3}{3}\\)<br \/>\nSo,<br \/>\n\\(\\frac{2}{3}\\)\u00a0 = \\(\\frac{6}{9}\\)<br \/>\nHence, from the above,<br \/>\nWe can conclude that \\(\\frac{2}{9}\\) + \\(\\frac{2}{3}\\) = \\(\\frac{8}{9}\\)<\/p>\n<p>Question 14.<br \/>\n<img loading=\"lazy\" class=\"alignnone size-full wp-image-15172\" src=\"https:\/\/ccssmathanswers.com\/wp-content\/uploads\/2020\/12\/Big-Ideas-Math-Answer-Key-Grade-5-Chapter-10-Divide-Fractions-19.png\" alt=\"Big Ideas Math Answer Key Grade 5 Chapter 10 Divide Fractions 19\" width=\"123\" height=\"57\" \/><br \/>\nAnswer: \\(\\frac{1}{10}\\) + \\(\\frac{3}{4}\\) = \\(\\frac{34}{40}\\)<\/p>\n<p>Explanation:<br \/>\nThe two given fractions are: \\(\\frac{1}{10}\\) and \\(\\frac{3}{4}\\)<br \/>\nSo, in addition, we have to make either the numerators or the denominators equal<br \/>\nSo,<br \/>\nMultiply \\(\\frac{1}{10}\\)\u00a0 with \\(\\frac{4}{4}\\)<br \/>\nMultiply \\(\\frac{3}{4}\\)\u00a0 with \\(\\frac{10}{10}\\)<br \/>\nSo,<br \/>\n\\(\\frac{1}{10}\\)\u00a0 = \\(\\frac{4}{40}\\)<br \/>\n\\(\\frac{3}{4}\\)\u00a0 = \\(\\frac{30}{40}\\)<br \/>\nHence, from the above,<br \/>\nWe can conclude that \\(\\frac{1}{10}\\) + \\(\\frac{3}{4}\\) = \\(\\frac{34}{40}\\)<\/p>\n<p>Question 15.<br \/>\n<img loading=\"lazy\" class=\"alignnone size-full wp-image-15173\" src=\"https:\/\/ccssmathanswers.com\/wp-content\/uploads\/2020\/12\/Big-Ideas-Math-Answer-Key-Grade-5-Chapter-10-Divide-Fractions-20.png\" alt=\"Big Ideas Math Answer Key Grade 5 Chapter 10 Divide Fractions 20\" width=\"151\" height=\"56\" \/><br \/>\nAnswer: \\(\\frac{3}{5}\\) + \\(\\frac{5}{6}\\) + \\(\\frac{1}{5}\\) = \\(\\frac{49}{30}\\)<\/p>\n<p>Explanation:<br \/>\nThe three given fractions are: \\(\\frac{3}{5}\\) , \\(\\frac{5}{6}\\) and \\(\\frac{1}{5}\\)<br \/>\nSo, in addition, we have to make either the numerators or the denominators equal<br \/>\nSo,<br \/>\nMultiply \\(\\frac{3}{5}\\)\u00a0 with \\(\\frac{6}{6}\\)<br \/>\nMultiply \\(\\frac{5}{6}\\)\u00a0 with \\(\\frac{5}{5}\\)<br \/>\nMultiply \\(\\frac{1}{5}\\)\u00a0 with \\(\\frac{6}{6}\\)<br \/>\nSo,<br \/>\n\\(\\frac{3}{5}\\)\u00a0 = \\(\\frac{18}{30}\\)<br \/>\n\\(\\frac{5}{6}\\)\u00a0 = \\(\\frac{25}{30}\\)<br \/>\n\\(\\frac{1}{5}\\)\u00a0 = \\(\\frac{6}{30}\\)<br \/>\nHence, from the above,<br \/>\nWe can conclude that \\(\\frac{3}{5}\\) + \\(\\frac{5}{6}\\) +\\(\\frac{1}{5}\\)\u00a0 = \\(\\frac{49}{30}\\)<\/p>\n<h3><a id=\"Lesson_10.3_Divide_Whole_Numbers_by_Unit_Fractions\"><\/a>Lesson 10.3 Divide Whole Numbers by Unit Fractions<\/h3>\n<p><strong>Explore and Grow<\/strong><\/p>\n<p>Write a real-life problem that can be represented by 6 \u00f7 \\(\\frac{1}{2}\\)?<br \/>\nAnswer:<br \/>\nSuppose, we have an apple and there are 6 children and we are giving each child half of the piece.<br \/>\nSo,<br \/>\nEach child receives 6 \u00f7 \\(\\frac{1}{2}\\) piece of the apple<\/p>\n<p>What is the solution to the problem? Use a model to support your answer?<br \/>\nAnswer:<br \/>\nThe above problem is the division of an apple among the six children<br \/>\nWe know that,<br \/>\na \u00f7 \\(\\frac{a}{b}\\) = a \u00d7 \\(\\frac{b}{a}\\)<br \/>\na= \\(\\frac{a}{1}\\)<br \/>\nSo,<br \/>\nThe amount each child receive from an apple = 6 \u00f7 \\(\\frac{1}{2}\\)<br \/>\n= 6 \u00d7 \\(\\frac{2}{1}\\)<br \/>\n= \\(\\frac{6}{1}\\) \u00d7 \\(\\frac{2}{1}\\)<br \/>\n= \\(\\frac{ 6 \u00d7 2}{1 \u00d7 1}\\)<br \/>\n= 12<\/p>\n<p><strong>Structure<\/strong><br \/>\nHow can you check your answer using multiplication?<br \/>\nAnswer:<br \/>\nWe can check the answer using multiplication by the two rules regarding division and multiplication. They are:<br \/>\nA) a \u00f7 \\(\\frac{a}{b}\\) = a \u00d7 \\(\\frac{b}{a}\\)<br \/>\nB) a= \\(\\frac{a}{1}\\)<\/p>\n<p><strong>Think and Grow: Divide Whole Numbers by Unit Fractions<\/strong><\/p>\n<p>You can use models to divide whole numbers by unit fractions.<br \/>\n<strong>Example<\/strong><br \/>\nFind 4 \u00f7 \\(\\frac{1}{3}\\)<br \/>\n<strong>One Way:<\/strong><br \/>\nUse a tape diagram to find how many \\(\\frac{1}{3}\\)s are in 4. There are 4 wholes.<br \/>\nDivide each whole into 3 equal parts. Each part is \\(\\frac{1}{3}\\).<br \/>\n<img loading=\"lazy\" class=\"alignnone size-full wp-image-15174\" src=\"https:\/\/ccssmathanswers.com\/wp-content\/uploads\/2020\/12\/Big-Ideas-Math-Answer-Key-Grade-5-Chapter-10-Divide-Fractions-21.png\" alt=\"Big Ideas Math Answer Key Grade 5 Chapter 10 Divide Fractions 21\" width=\"396\" height=\"119\" srcset=\"https:\/\/bigideasmathanswers.com\/wp-content\/uploads\/2020\/12\/Big-Ideas-Math-Answer-Key-Grade-5-Chapter-10-Divide-Fractions-21.png 396w, https:\/\/bigideasmathanswers.com\/wp-content\/uploads\/2020\/12\/Big-Ideas-Math-Answer-Key-Grade-5-Chapter-10-Divide-Fractions-21-300x90.png 300w\" sizes=\"(max-width: 396px) 100vw, 396px\" \/><br \/>\nBecause there are 3 one-thirds in 1 whole, there are<br \/>\n4 \u00d7 3 equal parts = 12 one-thirds in 4 wholes.<br \/>\n<img loading=\"lazy\" class=\"alignnone size-full wp-image-34579\" src=\"https:\/\/ccssmathanswers.com\/wp-content\/uploads\/2020\/12\/Big-Ideas-Math-Answers-Grade-5-Chapter-10-46.jpg\" alt=\"\" width=\"341\" height=\"240\" srcset=\"https:\/\/bigideasmathanswers.com\/wp-content\/uploads\/2020\/12\/Big-Ideas-Math-Answers-Grade-5-Chapter-10-46.jpg 341w, https:\/\/bigideasmathanswers.com\/wp-content\/uploads\/2020\/12\/Big-Ideas-Math-Answers-Grade-5-Chapter-10-46-300x211.jpg 300w\" sizes=\"(max-width: 341px) 100vw, 341px\" \/><br \/>\n<img loading=\"lazy\" class=\"alignnone size-full wp-image-34580\" src=\"https:\/\/ccssmathanswers.com\/wp-content\/uploads\/2020\/12\/Big-Ideas-Math-Answers-Grade-5-Chapter-10-47.jpg\" alt=\"\" width=\"539\" height=\"276\" srcset=\"https:\/\/bigideasmathanswers.com\/wp-content\/uploads\/2020\/12\/Big-Ideas-Math-Answers-Grade-5-Chapter-10-47.jpg 539w, https:\/\/bigideasmathanswers.com\/wp-content\/uploads\/2020\/12\/Big-Ideas-Math-Answers-Grade-5-Chapter-10-47-300x154.jpg 300w\" sizes=\"(max-width: 539px) 100vw, 539px\" \/><\/p>\n<p><strong>Show and Grow<\/strong><\/p>\n<p>Divide. Use a model to help<\/p>\n<p>Question 1.<br \/>\n<img loading=\"lazy\" class=\"alignnone size-full wp-image-15177\" src=\"https:\/\/ccssmathanswers.com\/wp-content\/uploads\/2020\/12\/Big-Ideas-Math-Answer-Key-Grade-5-Chapter-10-Divide-Fractions-23.png\" alt=\"Big Ideas Math Answer Key Grade 5 Chapter 10 Divide Fractions 23\" width=\"120\" height=\"56\" \/><br \/>\nAnswer: 3 \u00f7 \\(\\frac{1}{2}\\) = 6<\/p>\n<p>Explanation:<br \/>\nThe given numbers are: 3 and \\(\\frac{1}{2}\\)<br \/>\nWe know that,<br \/>\na \u00f7 \\(\\frac{a}{b}\\) = a \u00d7 \\(\\frac{b}{a}\\)<br \/>\na= \\(\\frac{a}{1}\\)<br \/>\nSo,<br \/>\n3 \u00f7 \\(\\frac{1}{2}\\)\u00a0 = 3 \u00d7 \\(\\frac{2}{1}\\)<br \/>\n= \\(\\frac{3}{1}\\) \u00d7 \\(\\frac{2}{1}\\)<br \/>\n= \\(\\frac{ 3 \u00d7 2}{1 \u00d7 1}\\)<br \/>\n= 6<br \/>\nHence,<br \/>\n3\u00f7 \\(\\frac{1}{2}\\) = 6<\/p>\n<p>Question 2.<br \/>\n<img loading=\"lazy\" class=\"alignnone size-full wp-image-15178\" src=\"https:\/\/ccssmathanswers.com\/wp-content\/uploads\/2020\/12\/Big-Ideas-Math-Answer-Key-Grade-5-Chapter-10-Divide-Fractions-24.png\" alt=\"Big Ideas Math Answer Key Grade 5 Chapter 10 Divide Fractions 24\" width=\"116\" height=\"56\" \/><br \/>\nAnswer: 2 \u00f7 \\(\\frac{1}{5}\\) = 10<\/p>\n<p>Explanation:<br \/>\nThe given numbers are: 2 and \\(\\frac{1}{5}\\)<br \/>\nWe know that,<br \/>\na \u00f7 \\(\\frac{a}{b}\\) = a \u00d7 \\(\\frac{b}{a}\\)<br \/>\na= \\(\\frac{a}{1}\\)<br \/>\nSo,<br \/>\n2 \u00f7 \\(\\frac{1}{5}\\)\u00a0 = 2 \u00d7 \\(\\frac{5}{1}\\)<br \/>\n= \\(\\frac{5}{1}\\) \u00d7 \\(\\frac{2}{1}\\)<br \/>\n= \\(\\frac{ 5 \u00d7 2}{1 \u00d7 1}\\)<br \/>\n= 10<br \/>\nHence,<br \/>\n2\u00f7 \\(\\frac{1}{5}\\) = 10<\/p>\n<p><strong>Apply and Grow: Practice<\/strong><\/p>\n<p>Divide. Use a model to help.<\/p>\n<p>Question 3.<\/p>\n<p><img loading=\"lazy\" class=\"alignnone size-full wp-image-15179\" src=\"https:\/\/ccssmathanswers.com\/wp-content\/uploads\/2020\/12\/Big-Ideas-Math-Answer-Key-Grade-5-Chapter-10-Divide-Fractions-25.png\" alt=\"Big Ideas Math Answer Key Grade 5 Chapter 10 Divide Fractions 25\" width=\"124\" height=\"60\" \/><br \/>\nAnswer: 1 \u00f7 \\(\\frac{1}{3}\\) = 3<\/p>\n<p>Explanation:<br \/>\nThe given numbers are: 1 and \\(\\frac{1}{3}\\)<br \/>\nWe know that,<br \/>\na \u00f7 \\(\\frac{a}{b}\\) = a \u00d7 \\(\\frac{b}{a}\\)<br \/>\na= \\(\\frac{a}{1}\\)<br \/>\nSo,<br \/>\n1 \u00f7 \\(\\frac{1}{3}\\)\u00a0 = 1 \u00d7 \\(\\frac{3}{1}\\)<br \/>\n= \\(\\frac{3}{1}\\) \u00d7 \\(\\frac{1}{1}\\)<br \/>\n= \\(\\frac{ 3 \u00d7 1}{1 \u00d7 1}\\)<br \/>\n= 3<br \/>\nHence,<br \/>\n1\u00f7 \\(\\frac{1}{3}\\) = 3<\/p>\n<p>Question 4.<br \/>\n<img loading=\"lazy\" class=\"alignnone size-full wp-image-15180\" src=\"https:\/\/ccssmathanswers.com\/wp-content\/uploads\/2020\/12\/Big-Ideas-Math-Answer-Key-Grade-5-Chapter-10-Divide-Fractions-26.png\" alt=\"Big Ideas Math Answer Key Grade 5 Chapter 10 Divide Fractions 26\" width=\"122\" height=\"59\" \/><br \/>\nAnswer: 3 \u00f7 \\(\\frac{1}{5}\\) = 15<\/p>\n<p>Explanation:<br \/>\nThe given numbers are: 3 and \\(\\frac{1}{5}\\)<br \/>\nWe know that,<br \/>\na \u00f7 \\(\\frac{a}{b}\\) = a \u00d7 \\(\\frac{b}{a}\\)<br \/>\na= \\(\\frac{a}{1}\\)<br \/>\nSo,<br \/>\n3 \u00f7 \\(\\frac{1}{5}\\)\u00a0 = 3 \u00d7 \\(\\frac{5}{1}\\)<br \/>\n= \\(\\frac{3}{1}\\) \u00d7 \\(\\frac{5}{1}\\)<br \/>\n= \\(\\frac{ 3 \u00d7 5}{1 \u00d7 1}\\)<br \/>\n= 15<br \/>\nHence,<br \/>\n3\u00f7 \\(\\frac{1}{5}\\) = 15<\/p>\n<p>Question 5.<br \/>\n<img loading=\"lazy\" class=\"alignnone size-full wp-image-15181\" src=\"https:\/\/ccssmathanswers.com\/wp-content\/uploads\/2020\/12\/Big-Ideas-Math-Answer-Key-Grade-5-Chapter-10-Divide-Fractions-27.png\" alt=\"Big Ideas Math Answer Key Grade 5 Chapter 10 Divide Fractions 27\" width=\"117\" height=\"56\" \/><br \/>\nAnswer: 5 \u00f7 \\(\\frac{1}{3}\\) = 15<\/p>\n<p>Explanation:<br \/>\nThe given numbers are: 5 and \\(\\frac{1}{3}\\)<br \/>\nWe know that,<br \/>\na \u00f7 \\(\\frac{a}{b}\\) = a \u00d7 \\(\\frac{b}{a}\\)<br \/>\na= \\(\\frac{a}{1}\\)<br \/>\nSo,<br \/>\n5 \u00f7 \\(\\frac{1}{3}\\)\u00a0 = 5 \u00d7 \\(\\frac{3}{1}\\)<br \/>\n= \\(\\frac{3}{1}\\) \u00d7 \\(\\frac{5}{1}\\)<br \/>\n= \\(\\frac{ 3 \u00d7 5}{1 \u00d7 1}\\)<br \/>\n= 15<br \/>\nHence,<br \/>\n5\u00f7 \\(\\frac{1}{3}\\) = 15<\/p>\n<p>Question 6.<br \/>\n<img loading=\"lazy\" class=\"alignnone size-full wp-image-15182\" src=\"https:\/\/ccssmathanswers.com\/wp-content\/uploads\/2020\/12\/Big-Ideas-Math-Answer-Key-Grade-5-Chapter-10-Divide-Fractions-28.png\" alt=\"Big Ideas Math Answer Key Grade 5 Chapter 10 Divide Fractions 28\" width=\"124\" height=\"60\" \/><br \/>\nAnswer: 4 \u00f7 \\(\\frac{1}{4}\\) = 16<\/p>\n<p>Explanation:<br \/>\nThe given numbers are: 4 and \\(\\frac{1}{4}\\)<br \/>\nWe know that,<br \/>\na \u00f7 \\(\\frac{a}{b}\\) = a \u00d7 \\(\\frac{b}{a}\\)<br \/>\na= \\(\\frac{a}{1}\\)<br \/>\nSo,<br \/>\n4 \u00f7 \\(\\frac{1}{4}\\)\u00a0 = 4 \u00d7 \\(\\frac{4}{1}\\)<br \/>\n= \\(\\frac{4}{1}\\) \u00d7 \\(\\frac{4}{1}\\)<br \/>\n= \\(\\frac{ 4 \u00d7 4}{1 \u00d7 1}\\)<br \/>\n= 16<br \/>\nHence,<br \/>\n4\u00f7 \\(\\frac{1}{4}\\) = 16<\/p>\n<p>Question 7.<br \/>\n<img loading=\"lazy\" class=\"alignnone size-full wp-image-15183\" src=\"https:\/\/ccssmathanswers.com\/wp-content\/uploads\/2020\/12\/Big-Ideas-Math-Answer-Key-Grade-5-Chapter-10-Divide-Fractions-29.png\" alt=\"Big Ideas Math Answer Key Grade 5 Chapter 10 Divide Fractions 29\" width=\"120\" height=\"72\" \/><br \/>\nAnswer: 7 \u00f7 \\(\\frac{1}{2}\\) = 14<\/p>\n<p>Explanation:<br \/>\nThe given numbers are: 7 and \\(\\frac{1}{2}\\)<br \/>\nWe know that,<br \/>\na \u00f7 \\(\\frac{a}{b}\\) = a \u00d7 \\(\\frac{b}{a}\\)<br \/>\na= \\(\\frac{a}{1}\\)<br \/>\nSo,<br \/>\n7 \u00f7 \\(\\frac{1}{2}\\)\u00a0 = 7 \u00d7 \\(\\frac{2}{1}\\)<br \/>\n= \\(\\frac{7}{1}\\) \u00d7 \\(\\frac{2}{1}\\)<br \/>\n= \\(\\frac{ 7 \u00d7 2}{1 \u00d7 1}\\)<br \/>\n= 14<br \/>\nHence,<br \/>\n7\u00f7 \\(\\frac{1}{2}\\) = 14<\/p>\n<p>Question 8.<br \/>\n<img loading=\"lazy\" class=\"alignnone size-full wp-image-15184\" src=\"https:\/\/ccssmathanswers.com\/wp-content\/uploads\/2020\/12\/Big-Ideas-Math-Answer-Key-Grade-5-Chapter-10-Divide-Fractions-30.png\" alt=\"Big Ideas Math Answer Key Grade 5 Chapter 10 Divide Fractions 30\" width=\"110\" height=\"56\" \/><br \/>\nAnswer: 2 \u00f7 \\(\\frac{1}{7}\\) = 14<\/p>\n<p>Explanation:<br \/>\nThe given numbers are: 2 and \\(\\frac{1}{7}\\)<br \/>\nWe know that,<br \/>\na \u00f7 \\(\\frac{a}{b}\\) = a \u00d7 \\(\\frac{b}{a}\\)<br \/>\na= \\(\\frac{a}{1}\\)<br \/>\nSo,<br \/>\n2 \u00f7 \\(\\frac{1}{7}\\)\u00a0 = 2 \u00d7 \\(\\frac{7}{1}\\)<br \/>\n= \\(\\frac{2}{1}\\) \u00d7 \\(\\frac{7}{1}\\)<br \/>\n= \\(\\frac{ 7 \u00d7 2}{1 \u00d7 1}\\)<br \/>\n= 14<br \/>\nHence,<br \/>\n2\u00f7 \\(\\frac{1}{7}\\) = 14<\/p>\n<p>Question 9.<br \/>\nHow many \\(\\frac{1}{4}\\)s are in 5?<br \/>\nAnswer: There are 20 \\(\\frac{1}{4}\\)s in 5<\/p>\n<p>Explanation:<br \/>\nWe know that,<br \/>\na \u00f7 \\(\\frac{a}{b}\\) = a \u00d7 \\(\\frac{b}{a}\\)<br \/>\na= \\(\\frac{a}{1}\\)<br \/>\nNow,<br \/>\nWe have to find the number of \\(\\frac{1}{4}\\)s in 5<br \/>\nSo,<br \/>\n5 \u00f7 \\(\\frac{1}{4}\\)\u00a0 = 5 \u00d7 \\(\\frac{4}{1}\\)<br \/>\n= \\(\\frac{5}{1}\\) \u00d7 \\(\\frac{4}{1}\\)<br \/>\n= \\(\\frac{ 5 \u00d7 4}{1 \u00d7 1}\\)<br \/>\n= 20<br \/>\nHence, from the above,<br \/>\nWe can conclude that there are 20 \\(\\frac{1}{4}\\)s in 5.<\/p>\n<p>Question 10.<br \/>\nHow many \\(\\frac{1}{6}\\)s are in 2?<br \/>\nAnswer: There are 12 \\(\\frac{1}{6}\\)s in 2<\/p>\n<p>Explanation:<br \/>\nWe know that,<br \/>\na \u00f7 \\(\\frac{a}{b}\\) = a \u00d7 \\(\\frac{b}{a}\\)<br \/>\na= \\(\\frac{a}{1}\\)<br \/>\nNow,<br \/>\nWe have to find the number of \\(\\frac{1}{6}\\)s in 2<br \/>\nSo,<br \/>\n2 \u00f7 \\(\\frac{1}{6}\\)\u00a0 = 2 \u00d7 \\(\\frac{6}{1}\\)<br \/>\n= \\(\\frac{2}{1}\\) \u00d7 \\(\\frac{6}{1}\\)<br \/>\n= \\(\\frac{ 2 \u00d7 6}{1 \u00d7 1}\\)<br \/>\n= 12<br \/>\nHence, from the above,<br \/>\nWe can conclude that there are 12 \\(\\frac{1}{6}\\)s in 2.<\/p>\n<p>Question 11.<br \/>\n<strong>YOU BE THE TEACHER<\/strong><br \/>\nNewton finds 6 \u00f7 \\(\\frac{1}{3}\\). Is he correct? Explain.<br \/>\n<img loading=\"lazy\" class=\"alignnone size-full wp-image-15185\" src=\"https:\/\/ccssmathanswers.com\/wp-content\/uploads\/2020\/12\/Big-Ideas-Math-Answer-Key-Grade-5-Chapter-10-Divide-Fractions-31.png\" alt=\"Big Ideas Math Answer Key Grade 5 Chapter 10 Divide Fractions 31\" width=\"292\" height=\"201\" \/><br \/>\nAnswer: No, Newton is not correct<\/p>\n<p>Explanation:<br \/>\nThe given division equation is: 6 \u00f7 \\(\\frac{1}{3}\\)<br \/>\nWe know that,<br \/>\na \u00f7 \\(\\frac{a}{b}\\) = a \u00d7 \\(\\frac{b}{a}\\)<br \/>\na= \\(\\frac{a}{1}\\)<br \/>\nSo,<br \/>\n6 \u00f7 \\(\\frac{1}{3}\\)\u00a0 = 6 \u00d7 \\(\\frac{3}{1}\\)<br \/>\n= \\(\\frac{6}{1}\\) \u00d7 \\(\\frac{3}{1}\\)<br \/>\n= \\(\\frac{ 3 \u00d7 6}{1 \u00d7 1}\\)<br \/>\n= 18<br \/>\nBut, according to Newton,<br \/>\n6 \u00f7 \\(\\frac{1}{3}\\) = 2<br \/>\nHence, from the above,<br \/>\nWe can conclude that Newton is not correct.<\/p>\n<p>Question 12.<br \/>\n<strong>Writing<\/strong><br \/>\nWrite and solve a real-life problem for 4 \u00f7 \\(\\frac{1}{2}\\).<br \/>\nAnswer:<br \/>\nSuppose we have 4 bags of wheat and we have to distribute the 4 bags by dividing each bag of wheat in half<br \/>\nSo,<br \/>\nEach person receives 4 \u00f7 \\(\\frac{1}{2}\\) bag of wheat<br \/>\nNow,<br \/>\nWe know that,<br \/>\na \u00f7 \\(\\frac{a}{b}\\) = a \u00d7 \\(\\frac{b}{a}\\)<br \/>\na= \\(\\frac{a}{1}\\)<br \/>\nSo,<br \/>\n4 \u00f7 \\(\\frac{1}{2}\\)\u00a0 = 4 \u00d7 \\(\\frac{2}{1}\\)<br \/>\n= \\(\\frac{4}{1}\\) \u00d7 \\(\\frac{2}{1}\\)<br \/>\n= \\(\\frac{ 4 \u00d7 2}{1 \u00d7 1}\\)<br \/>\n= 8<br \/>\nHence, from the above,<br \/>\nWe can conclude that there are 8 bags of wheat when divide the 4 bags of wheat in half.<\/p>\n<p><strong>Think and Grow: Modeling Real Life<\/strong><\/p>\n<p><strong>Example<\/strong><br \/>\nA chef makes 3 cups of salsa. A serving of salsa is \\(\\frac{1}{8}\\) cup. How many servings does the chef make?<br \/>\nTo find the number of servings, find the number of \\(\\frac{1}{8}\\) cups in 3 cups.<br \/>\nUse an area model to find 3 \u00f7 \\(\\frac{1}{8}\\). Divide each cup into 8 equal parts.<br \/>\n<img loading=\"lazy\" class=\"alignnone size-full wp-image-15187\" src=\"https:\/\/ccssmathanswers.com\/wp-content\/uploads\/2020\/12\/Big-Ideas-Math-Answer-Key-Grade-5-Chapter-10-Divide-Fractions-32.png\" alt=\"Big Ideas Math Answer Key Grade 5 Chapter 10 Divide Fractions 32\" width=\"136\" height=\"130\" \/><br \/>\n<img loading=\"lazy\" class=\"alignnone size-full wp-image-34581\" src=\"https:\/\/ccssmathanswers.com\/wp-content\/uploads\/2020\/12\/Big-Ideas-Math-Answers-Grade-5-Chapter-10-48.jpg\" alt=\"\" width=\"701\" height=\"289\" srcset=\"https:\/\/bigideasmathanswers.com\/wp-content\/uploads\/2020\/12\/Big-Ideas-Math-Answers-Grade-5-Chapter-10-48.jpg 701w, https:\/\/bigideasmathanswers.com\/wp-content\/uploads\/2020\/12\/Big-Ideas-Math-Answers-Grade-5-Chapter-10-48-300x124.jpg 300w\" sizes=\"(max-width: 701px) 100vw, 701px\" \/><\/p>\n<p><strong>Show and Grow<\/strong><\/p>\n<p>Question 13.<br \/>\nA litter of kittens weighs a total of 2 pounds. Each newborn kitten weighs \\(\\frac{1}{4}\\) pound. How many kittens are in the litter?<br \/>\nAnswer: The number of kittens in the litter are: 8 kittens<\/p>\n<p>Explanation:<br \/>\nIt is given that a litter of kittens weighs a total of 2 pounds and each newborn kitten weighs \\(\\frac{1}{4}\\) pound.<br \/>\nSo,<br \/>\nThe number of kittens in the litter = \\(\\frac{The total weight of litter}{The weight of each newborn kitten}\\)<br \/>\n= 2 \u00f7 \\(\\frac{1}{4}\\)<br \/>\nNow,<br \/>\nWe know that,<br \/>\na \u00f7 \\(\\frac{a}{b}\\) = a \u00d7 \\(\\frac{b}{a}\\)<br \/>\na= \\(\\frac{a}{1}\\)<br \/>\nSo,<br \/>\n2 \u00f7 \\(\\frac{1}{4}\\)\u00a0 = 2 \u00d7 \\(\\frac{4}{1}\\)<br \/>\n= \\(\\frac{4}{1}\\) \u00d7 \\(\\frac{2}{1}\\)<br \/>\n= \\(\\frac{ 4 \u00d7 2}{1 \u00d7 1}\\)<br \/>\n= 8<br \/>\nHence, from the above,<br \/>\nWe can conclude that the number of kittens in the litter are: 8 kittens<\/p>\n<p>Question 14.<br \/>\nYou put signs on a walking trail that is 7 miles long. You put a sign at the start and at the end of the trail. You also put a sign every \\(\\frac{1}{10}\\) mile. How many signs do you put on the trail?<br \/>\nAnswer: The total number of signs you put on the trail is: 72<\/p>\n<p>Explanation:<br \/>\nIt is given that you put signs on a walking trail that is 7 miles long and you put a sign at the start and at the end of the trail.<br \/>\nIt is also given that you put a sign every \\(\\frac{1}{10}\\) mile.<br \/>\nSo,<br \/>\nThe total number of signs you put on the trail = The sign at the start of the trail + The sign at the end of the trail + The total number of signs for \\(\\frac{1}{10}\\) mile<br \/>\nNow,<br \/>\nThe total number of signs for \\(\\frac{1}{10}\\) mile = 7 \u00f7 \\(\\frac{1}{10}\\)<br \/>\nWe know that,<br \/>\na \u00f7 \\(\\frac{a}{b}\\) = a \u00d7 \\(\\frac{b}{a}\\)<br \/>\na= \\(\\frac{a}{1}\\)<br \/>\nSo,<br \/>\n7 \u00f7 \\(\\frac{1}{10}\\)\u00a0 = 7 \u00d7 \\(\\frac{10}{1}\\)<br \/>\n= \\(\\frac{7}{1}\\) \u00d7 \\(\\frac{10}{1}\\)<br \/>\n= \\(\\frac{ 7 \u00d7 10}{1 \u00d7 1}\\)<br \/>\n= 70<br \/>\nSo,<br \/>\nThe total number of signs you put on the trail = 1 + 1 + 70<br \/>\n= 72<br \/>\nhence, from the above,<br \/>\nWe can conclude that there are 72 signs that you put on the trail<\/p>\n<p>Question 15.<br \/>\n<strong>DIG DEEPER!<\/strong><br \/>\nYou have 2 boards that are each 8 feet long. You cut \\(\\frac{1}{2}\\)&#8211; foot pieces to make square picture frames. How many picture frames can you make?<br \/>\nAnswer: The number of picture frames you can make is: 32<\/p>\n<p>Explanation:<br \/>\nIt is given that you have 2 boards that are each 8 feet long.<br \/>\nSo,<br \/>\nThe total length of 2 boards = 2 \u00d7 8 = 16 feet<br \/>\nIt is also given that you cut \\(\\frac{1}{2}\\)&#8211; foot pieces to make square picture frames.<br \/>\nSo,<br \/>\nThe total number of picture frames = \\(\\frac{The total length of 2 boards}{The length of each square frame}\\)<br \/>\n= 16 \u00f7 \\(\\frac{1}{2}\\)<br \/>\nWe know that,<br \/>\na \u00f7 \\(\\frac{a}{b}\\) = a \u00d7 \\(\\frac{b}{a}\\)<br \/>\na= \\(\\frac{a}{1}\\)<br \/>\nSo,<br \/>\n16 \u00f7 \\(\\frac{1}{2}\\)\u00a0 = 16 \u00d7 \\(\\frac{2}{1}\\)<br \/>\n= \\(\\frac{16}{1}\\) \u00d7 \\(\\frac{2}{1}\\)<br \/>\n= \\(\\frac{ 16 \u00d7 2}{1 \u00d7 1}\\)<br \/>\n= 32<br \/>\nHence, from the above,<br \/>\nWe can conclude that we can make 32 picture frames.<\/p>\n<h3><a id=\"Divide_Whole_Numbers_by_Unit_Fractions_Homework_&amp;_Practice_10.3\"><\/a>Divide Whole Numbers by Unit Fractions Homework &amp; Practice 10.3<\/h3>\n<p>Divide. Use a model to help.<\/p>\n<p>Question 1.<br \/>\n<img loading=\"lazy\" class=\"alignnone size-full wp-image-15188\" src=\"https:\/\/ccssmathanswers.com\/wp-content\/uploads\/2020\/12\/Big-Ideas-Math-Answer-Key-Grade-5-Chapter-10-Divide-Fractions-33.png\" alt=\"Big Ideas Math Answer Key Grade 5 Chapter 10 Divide Fractions 33\" width=\"118\" height=\"56\" data-wp-editing=\"1\" \/><br \/>\nAnswer: 1 \u00f7 \\(\\frac{1}{9}\\) = 9<\/p>\n<p>Explanation:<br \/>\nThe given numbers are: 1 and \\(\\frac{1}{9}\\)<br \/>\nWe know that,<br \/>\na \u00f7 \\(\\frac{a}{b}\\) = a \u00d7 \\(\\frac{b}{a}\\)<br \/>\na= \\(\\frac{a}{1}\\)<br \/>\nSo,<br \/>\n1 \u00f7 \\(\\frac{1}{9}\\)\u00a0 = 1 \u00d7 \\(\\frac{9}{1}\\)<br \/>\n= \\(\\frac{1}{1}\\) \u00d7 \\(\\frac{9}{1}\\)<br \/>\n= \\(\\frac{ 1 \u00d7 9}{1 \u00d7 1}\\)<br \/>\n= 9<br \/>\nHence,<br \/>\n1\u00f7 \\(\\frac{1}{9}\\) = 9<\/p>\n<p>Question 2.<br \/>\n<img loading=\"lazy\" class=\"alignnone size-full wp-image-15189\" src=\"https:\/\/ccssmathanswers.com\/wp-content\/uploads\/2020\/12\/Big-Ideas-Math-Answer-Key-Grade-5-Chapter-10-Divide-Fractions-34.png\" alt=\"Big Ideas Math Answer Key Grade 5 Chapter 10 Divide Fractions 34\" width=\"119\" height=\"61\" \/><br \/>\nAnswer: 2 \u00f7 \\(\\frac{1}{3}\\) = 6<\/p>\n<p>Explanation:<br \/>\nThe given numbers are: 2 and \\(\\frac{1}{3}\\)<br \/>\nWe know that,<br \/>\na \u00f7 \\(\\frac{a}{b}\\) = a \u00d7 \\(\\frac{b}{a}\\)<br \/>\na= \\(\\frac{a}{1}\\)<br \/>\nSo,<br \/>\n2 \u00f7 \\(\\frac{1}{3}\\)\u00a0 = 2 \u00d7 \\(\\frac{3}{1}\\)<br \/>\n= \\(\\frac{3}{1}\\) \u00d7 \\(\\frac{2}{1}\\)<br \/>\n= \\(\\frac{ 3 \u00d7 2}{1 \u00d7 1}\\)<br \/>\n= 6<br \/>\nHence,<br \/>\n2\u00f7 \\(\\frac{1}{3}\\) = 6<\/p>\n<p>Question 3.<br \/>\n<img loading=\"lazy\" class=\"alignnone size-full wp-image-15190\" src=\"https:\/\/ccssmathanswers.com\/wp-content\/uploads\/2020\/12\/Big-Ideas-Math-Answer-Key-Grade-5-Chapter-10-Divide-Fractions-35.png\" alt=\"Big Ideas Math Answer Key Grade 5 Chapter 10 Divide Fractions 35\" width=\"114\" height=\"56\" \/><br \/>\nAnswer: 5 \u00f7 \\(\\frac{1}{2}\\) = 10<\/p>\n<p>Explanation:<br \/>\nThe given numbers are: 5 and \\(\\frac{1}{2}\\)<br \/>\nWe know that,<br \/>\na \u00f7 \\(\\frac{a}{b}\\) = a \u00d7 \\(\\frac{b}{a}\\)<br \/>\na= \\(\\frac{a}{1}\\)<br \/>\nSo,<br \/>\n5 \u00f7 \\(\\frac{1}{2}\\)\u00a0 = 5 \u00d7 \\(\\frac{2}{1}\\)<br \/>\n= \\(\\frac{5}{1}\\) \u00d7 \\(\\frac{2}{1}\\)<br \/>\n= \\(\\frac{ 5 \u00d7 2}{1 \u00d7 1}\\)<br \/>\n= 10<br \/>\nHence,<br \/>\n5\u00f7 \\(\\frac{1}{2}\\) = 10<\/p>\n<p>Divide. Use a model to help.<\/p>\n<p>Question 4.<br \/>\n<img loading=\"lazy\" class=\"alignnone size-full wp-image-15191\" src=\"https:\/\/ccssmathanswers.com\/wp-content\/uploads\/2020\/12\/Big-Ideas-Math-Answer-Key-Grade-5-Chapter-10-Divide-Fractions-36.png\" alt=\"Big Ideas Math Answer Key Grade 5 Chapter 10 Divide Fractions 36\" width=\"119\" height=\"59\" \/><br \/>\nAnswer: 9 \u00f7 \\(\\frac{1}{4}\\) = 36<\/p>\n<p>Explanation:<br \/>\nThe given numbers are: 9 and \\(\\frac{1}{4}\\)<br \/>\nWe know that,<br \/>\na \u00f7 \\(\\frac{a}{b}\\) = a \u00d7 \\(\\frac{b}{a}\\)<br \/>\na= \\(\\frac{a}{1}\\)<br \/>\nSo,<br \/>\n9 \u00f7 \\(\\frac{1}{4}\\)\u00a0 = 9 \u00d7 \\(\\frac{4}{1}\\)<br \/>\n= \\(\\frac{9}{1}\\) \u00d7 \\(\\frac{4}{1}\\)<br \/>\n= \\(\\frac{ 9 \u00d7 4}{1 \u00d7 1}\\)<br \/>\n= 36<br \/>\nHence,<br \/>\n9\u00f7 \\(\\frac{1}{4}\\) = 36<\/p>\n<p>Question 5.<br \/>\n<img loading=\"lazy\" class=\"alignnone size-full wp-image-15192\" src=\"https:\/\/ccssmathanswers.com\/wp-content\/uploads\/2020\/12\/Big-Ideas-Math-Answer-Key-Grade-5-Chapter-10-Divide-Fractions-37.png\" alt=\"Big Ideas Math Answer Key Grade 5 Chapter 10 Divide Fractions 37\" width=\"112\" height=\"54\" \/><br \/>\nAnswer: 7 \u00f7 \\(\\frac{1}{3}\\) = 21<\/p>\n<p>Explanation:<br \/>\nThe given numbers are: 7 and \\(\\frac{1}{3}\\)<br \/>\nWe know that,<br \/>\na \u00f7 \\(\\frac{a}{b}\\) = a \u00d7 \\(\\frac{b}{a}\\)<br \/>\na= \\(\\frac{a}{1}\\)<br \/>\nSo,<br \/>\n7 \u00f7 \\(\\frac{1}{3}\\)\u00a0 = 7 \u00d7 \\(\\frac{3}{1}\\)<br \/>\n= \\(\\frac{3}{1}\\) \u00d7 \\(\\frac{7}{1}\\)<br \/>\n= \\(\\frac{ 3 \u00d7 7}{1 \u00d7 1}\\)<br \/>\n= 21<br \/>\nHence,<br \/>\n7\u00f7 \\(\\frac{1}{3}\\) = 21<\/p>\n<p>Question 6.<br \/>\n<img loading=\"lazy\" class=\"alignnone size-full wp-image-15194\" src=\"https:\/\/ccssmathanswers.com\/wp-content\/uploads\/2020\/12\/Big-Ideas-Math-Answer-Key-Grade-5-Chapter-10-Divide-Fractions-38.png\" alt=\"Big Ideas Math Answer Key Grade 5 Chapter 10 Divide Fractions 38\" width=\"119\" height=\"62\" \/><br \/>\nAnswer: 8 \u00f7 \\(\\frac{1}{5}\\) = 40<\/p>\n<p>Explanation:<br \/>\nThe given numbers are: 8 and \\(\\frac{1}{5}\\)<br \/>\nWe know that,<br \/>\na \u00f7 \\(\\frac{a}{b}\\) = a \u00d7 \\(\\frac{b}{a}\\)<br \/>\na= \\(\\frac{a}{1}\\)<br \/>\nSo,<br \/>\n8 \u00f7 \\(\\frac{1}{5}\\)\u00a0 = 8 \u00d7 \\(\\frac{5}{1}\\)<br \/>\n= \\(\\frac{8}{1}\\) \u00d7 \\(\\frac{5}{1}\\)<br \/>\n= \\(\\frac{ 8 \u00d7 5}{1 \u00d7 1}\\)<br \/>\n= 40<br \/>\nHence,<br \/>\n8\u00f7 \\(\\frac{1}{5}\\) = 40<\/p>\n<p>Question 7.<br \/>\n<strong>Number Sense<\/strong><br \/>\nExplain how you can check your answer for Exercise 6.<br \/>\nAnswer:<br \/>\nWe can check the answer for exercise 6 by using the below model:<br \/>\n<img loading=\"lazy\" class=\"alignnone size-full wp-image-34594\" src=\"https:\/\/ccssmathanswers.com\/wp-content\/uploads\/2020\/12\/Big-Ideas-Math-Answers-Grade-5-Chapter-10-49.jpg\" alt=\"\" width=\"458\" height=\"313\" srcset=\"https:\/\/bigideasmathanswers.com\/wp-content\/uploads\/2020\/12\/Big-Ideas-Math-Answers-Grade-5-Chapter-10-49.jpg 458w, https:\/\/bigideasmathanswers.com\/wp-content\/uploads\/2020\/12\/Big-Ideas-Math-Answers-Grade-5-Chapter-10-49-300x205.jpg 300w\" sizes=\"(max-width: 458px) 100vw, 458px\" \/><br \/>\nFrom the above model,<br \/>\nEach part represents \\(\\frac{8}{5}\\)<br \/>\nSo,<br \/>\nThe total value of the 5 parts is: \\(\\frac{40}{5}\\)<br \/>\nHence,<br \/>\nIn the above way, we can say that we check the answer<\/p>\n<p>Question 8.<br \/>\n<strong>YOU BE THE TEACHER<\/strong><br \/>\nDescartes finds 5 \u00f7 \\(\\frac{1}{4}\\). Is he correct? Explain.<br \/>\n<img loading=\"lazy\" class=\"alignnone size-full wp-image-15193\" src=\"https:\/\/ccssmathanswers.com\/wp-content\/uploads\/2020\/12\/Big-Ideas-Math-Answer-Key-Grade-5-Chapter-10-Divide-Fractions-38.1.png\" alt=\"Big Ideas Math Answer Key Grade 5 Chapter 10 Divide Fractions 38.1\" width=\"156\" height=\"59\" \/><br \/>\nAnswer: Yes, he is correct<\/p>\n<p>Explanation:<br \/>\nWe can write 5 as \\(\\frac{20}{4}\\) or \\(\\frac{5}{1}\\)<br \/>\nBut, we only take \\(\\frac{20}{4}\\) because the divided number given is 4<br \/>\nWe know that,<br \/>\na \u00f7 \\(\\frac{a}{b}\\) = a \u00d7 \\(\\frac{b}{a}\\)<br \/>\na= \\(\\frac{a}{1}\\)<br \/>\nSo,<br \/>\n\\(\\frac{20}{4}\\) \u00f7 \\(\\frac{1}{4}\\)<br \/>\n= \\(\\frac{20}{4}\\) \u00d7 \\(\\frac{4}{1}\\)<br \/>\n= \\(\\frac{ 20 \u00d7 4}{4 \u00d7 1}\\)<br \/>\n= 20<br \/>\nHence, from the above,<br \/>\nWe can conclude that Descartes is correct.<\/p>\n<p>Question 9.<br \/>\n<strong>Modeling Real Life<\/strong><br \/>\nYou need \\(\\frac{1}{2}\\) pound of clay to make a pinch pot. How many pinch pots can you make with 12 pounds of clay?<br \/>\n<img loading=\"lazy\" class=\"alignnone size-full wp-image-15195\" src=\"https:\/\/ccssmathanswers.com\/wp-content\/uploads\/2020\/12\/Big-Ideas-Math-Answer-Key-Grade-5-Chapter-10-Divide-Fractions-42.png\" alt=\"Big Ideas Math Answer Key Grade 5 Chapter 10 Divide Fractions 42\" width=\"162\" height=\"124\" \/><br \/>\nAnswer: You can make 24 pinch pots with 12 pounds of clay<\/p>\n<p>Explanation:<br \/>\nIt is given that you need \\(\\frac{1}{2}\\) pound of clay to make a pinch pot.<br \/>\nIt is also given that you have 12 pounds of clay<br \/>\nSo,<br \/>\nThe number of pinch pots you can make by using 12 pounds of clay = \\(\\frac{The total amount of clay}{The amount of clay used to make each pinch pot}\\)<br \/>\n= 12 \u00f7 \\(\\frac{1}{2}\\)<br \/>\nNow,<br \/>\nWe know that,<br \/>\na \u00f7 \\(\\frac{a}{b}\\) = a \u00d7 \\(\\frac{b}{a}\\)<br \/>\na= \\(\\frac{a}{1}\\)<br \/>\nSo,<br \/>\n12 \u00f7 \\(\\frac{1}{2}\\)<br \/>\n= \\(\\frac{12}{1}\\) \u00d7 \\(\\frac{2}{1}\\)<br \/>\n= \\(\\frac{ 12 \u00d7 2}{4 \u00d7 1}\\)<br \/>\n= 24<br \/>\nHence, from the above,<br \/>\nWe can conclude that we can make 24 pinch pots by using 12 pounds of clay.<\/p>\n<p>Question 10.<br \/>\n<strong>Modeling Real Life<\/strong><br \/>\nYour art teacher has 5 yards of yellow string and 4 yards of green string. She cuts both colors \\(\\frac{1}{3}\\)-yard pieces to hang of string into student artwork. How many pieces of student artwork can she hang?<br \/>\nAnswer: The number of pieces of student artwork she can hang is: 27<\/p>\n<p>Explanation:<br \/>\nIt is given that your art teacher has 5 yards of yellow string and 4 yards of green string.<br \/>\nSo,<br \/>\nThe total number of yards of string = 5 + 4 = 9 yards of string<br \/>\nIt is also given that she cuts both colors \\(\\frac{1}{3}\\)-yard pieces to hang of string into student artwork.<br \/>\nSo,<br \/>\nThe number of pieces of student artwork she can hang = \\(\\frac{The total number of yards of strings}{The length of each yard f string}\\)<br \/>\n= 9 \u00f7 \\(\\frac{1}{3}\\)<br \/>\nNow,<br \/>\nWe know that,<br \/>\na \u00f7 \\(\\frac{a}{b}\\) = a \u00d7 \\(\\frac{b}{a}\\)<br \/>\na= \\(\\frac{a}{1}\\)<br \/>\nSo,<br \/>\n9 \u00f7 \\(\\frac{1}{3}\\)<br \/>\n= \\(\\frac{9}{1}\\) \u00d7 \\(\\frac{3}{1}\\)<br \/>\n= \\(\\frac{ 9 \u00d7 3}{1 \u00d7 1}\\)<br \/>\n= 27<br \/>\nHence, from the above,<br \/>\nWe can conclude that there are 27 pieces of student artwork that she can hang.<\/p>\n<p><strong>Review &amp; Refresh<\/strong><\/p>\n<p>Question 11.<br \/>\n<img loading=\"lazy\" class=\"alignnone size-full wp-image-15196\" src=\"https:\/\/ccssmathanswers.com\/wp-content\/uploads\/2020\/12\/Big-Ideas-Math-Answer-Key-Grade-5-Chapter-10-Divide-Fractions-43.png\" alt=\"Big Ideas Math Answer Key Grade 5 Chapter 10 Divide Fractions 43\" width=\"123\" height=\"57\" \/><br \/>\nAnswer: \\(\\frac{2}{5}\\) \u00d7 \\(\\frac{3}{4}\\) = \\(\\frac{6}{20}\\)<\/p>\n<p>Explanation:<br \/>\nThe given fractions are: \\(\\frac{3}{4}\\) and \\(\\frac{2}{5}\\)<br \/>\nSo,<br \/>\n\\(\\frac{2}{5}\\) \u00d7 \\(\\frac{3}{4}\\)<br \/>\n= \\(\\frac{2 \u00d7 3}{5 \u00d7 4}\\)<br \/>\n= \\(\\frac{6}{20}\\)<br \/>\nHence,<br \/>\n\\(\\frac{2}{5}\\) \u00d7 \\(\\frac{3}{4}\\) = \\(\\frac{6}{20}\\)<\/p>\n<p>Question 12.<br \/>\n<img loading=\"lazy\" class=\"alignnone size-full wp-image-15197\" src=\"https:\/\/ccssmathanswers.com\/wp-content\/uploads\/2020\/12\/Big-Ideas-Math-Answer-Key-Grade-5-Chapter-10-Divide-Fractions-44.png\" alt=\"Big Ideas Math Answer Key Grade 5 Chapter 10 Divide Fractions 44\" width=\"121\" height=\"55\" \/><br \/>\nAnswer: \\(\\frac{1}{8}\\) \u00d7 \\(\\frac{5}{8}\\) = \\(\\frac{5}{64}\\)<\/p>\n<p>Explanation:<br \/>\nThe given fractions are: \\(\\frac{1}{8}\\) and \\(\\frac{5}{8}\\)<br \/>\nSo,<br \/>\n\\(\\frac{1}{8}\\) \u00d7 \\(\\frac{5}{8}\\)<br \/>\n= \\(\\frac{1 \u00d7 5}{8 \u00d7 8}\\)<br \/>\n= \\(\\frac{5}{64}\\)<br \/>\nHence,<br \/>\n\\(\\frac{1}{8}\\) \u00d7 \\(\\frac{5}{8}\\) = \\(\\frac{5}{64}\\)<\/p>\n<p>Question 13.<br \/>\n<img loading=\"lazy\" class=\"alignnone size-full wp-image-15198\" src=\"https:\/\/ccssmathanswers.com\/wp-content\/uploads\/2020\/12\/Big-Ideas-Math-Answer-Key-Grade-5-Chapter-10-Divide-Fractions-45.png\" alt=\"Big Ideas Math Answer Key Grade 5 Chapter 10 Divide Fractions 45\" width=\"117\" height=\"56\" \/><br \/>\nAnswer: \\(\\frac{4}{9}\\) \u00d7 \\(\\frac{2}{7}\\) = \\(\\frac{8}{63}\\)<\/p>\n<p>Explanation:<br \/>\nThe given fractions are: \\(\\frac{4}{9}\\) and \\(\\frac{2}{7}\\)<br \/>\nSo,<br \/>\n\\(\\frac{4}{9}\\) \u00d7 \\(\\frac{2}{7}\\)<br \/>\n= \\(\\frac{2 \u00d7 4}{7 \u00d7 9}\\)<br \/>\n= \\(\\frac{8}{63}\\)<br \/>\nHence,<br \/>\n\\(\\frac{4}{9}\\) \u00d7 \\(\\frac{2}{7}\\) = \\(\\frac{8}{63}\\)<\/p>\n<h3><a id=\"Lesson_10.4_Divide_Unit_Fractions_by_Whole_Numbers\"><\/a>Lesson 10.4 Divide Unit Fractions by Whole Numbers<\/h3>\n<p>Write a real-life problem that can be represented by \\(\\frac{1}{2}\\) \u00f7 3?<br \/>\nAnswer:<br \/>\nSuppose we have 3 people and those 3 people each has to share \\(\\frac{1}{2}\\) of the apple<\/p>\n<p>What is the solution to the problem? Use a model to support your answer?<br \/>\nAnswer:<br \/>\nThe above problem is: We have to share \\(\\frac{1}{2}\\) each for the 3 people<br \/>\nNow,<br \/>\nWe know that,<br \/>\n\\(\\frac{a}{b}\\) \u00f7 a\u00a0 = \\(\\frac{a}{b}\\) \u00d7 \\(\\frac{1}{a}\\)<br \/>\na= \\(\\frac{a}{1}\\)<br \/>\nSo,<br \/>\n\\(\\frac{1}{2}\\) \u00f7 3<br \/>\n= \\(\\frac{1}{2}\\) \u00d7 \\(\\frac{1}{3}\\)<br \/>\n= \\(\\frac{ 1 \u00d7 1}{2 \u00d7 3}\\)<br \/>\n= \\(\\frac{1}{6}\\)<br \/>\nHence,<br \/>\n\\(\\frac{1}{6}\\) is the solution to the above problem.<\/p>\n<p><strong>Precision<\/strong><br \/>\nIs the answer greater than or less than 1? Explain?<br \/>\nAnswer: The answer is less than 1<\/p>\n<p>Explanation:<br \/>\nThe answer for the problem is: \\(\\frac{1}{6}\\)<br \/>\nSo,<br \/>\nFor the comparison of \\(\\frac{1}{6}\\) with 1, we have to see whether the numerators or the denominators are equal or not<br \/>\nSo, in this case, the numerators are equal<br \/>\nSo, compare the denominators<br \/>\nSo,<br \/>\n1 &lt; 6<br \/>\nHence, from the above,<br \/>\nWe can conclude that \\(\\frac{1}{6}\\) is less than 1<\/p>\n<p><strong>Think and Grow: Divide Unit Fractions by Whole Numbers<\/strong><\/p>\n<p>You can use models to divide unit fractions by whole numbers.<br \/>\n<img loading=\"lazy\" class=\"alignnone size-full wp-image-34598\" src=\"https:\/\/ccssmathanswers.com\/wp-content\/uploads\/2020\/12\/Big-Ideas-Math-Answers-Grade-5-Chapter-10-50.jpg\" alt=\"\" width=\"646\" height=\"359\" srcset=\"https:\/\/bigideasmathanswers.com\/wp-content\/uploads\/2020\/12\/Big-Ideas-Math-Answers-Grade-5-Chapter-10-50.jpg 646w, https:\/\/bigideasmathanswers.com\/wp-content\/uploads\/2020\/12\/Big-Ideas-Math-Answers-Grade-5-Chapter-10-50-300x167.jpg 300w\" sizes=\"(max-width: 646px) 100vw, 646px\" \/><br \/>\n<img loading=\"lazy\" class=\"alignnone size-full wp-image-34599\" src=\"https:\/\/ccssmathanswers.com\/wp-content\/uploads\/2020\/12\/Big-Ideas-Math-Answers-Grade-5-Chapter-10-51.jpg\" alt=\"\" width=\"667\" height=\"305\" srcset=\"https:\/\/bigideasmathanswers.com\/wp-content\/uploads\/2020\/12\/Big-Ideas-Math-Answers-Grade-5-Chapter-10-51.jpg 667w, https:\/\/bigideasmathanswers.com\/wp-content\/uploads\/2020\/12\/Big-Ideas-Math-Answers-Grade-5-Chapter-10-51-300x137.jpg 300w\" sizes=\"(max-width: 667px) 100vw, 667px\" \/><\/p>\n<p><strong>Show and Grow<\/strong><\/p>\n<p>Divide. Use a model to help.<\/p>\n<p>Question 1.<br \/>\n<img loading=\"lazy\" class=\"alignnone size-full wp-image-15201\" src=\"https:\/\/ccssmathanswers.com\/wp-content\/uploads\/2020\/12\/Big-Ideas-Math-Answer-Key-Grade-5-Chapter-10-Divide-Fractions-48.png\" alt=\"Big Ideas Math Answer Key Grade 5 Chapter 10 Divide Fractions 48\" width=\"118\" height=\"56\" \/><br \/>\nAnswer: \\(\\frac{1}{4}\\) \u00f7 2 = \\(\\frac{1}{8}\\)<\/p>\n<p>Explanation:<br \/>\nThe given numbers are: \\(\\frac{1}{4}\\) and 2<br \/>\nWe know that,<br \/>\n\\(\\frac{a}{b}\\) \u00f7 a\u00a0 = \\(\\frac{a}{b}\\) \u00d7 \\(\\frac{1}{a}\\)<br \/>\na= \\(\\frac{a}{1}\\)<br \/>\nSo,<br \/>\n\\(\\frac{1}{4}\\) \u00f7 2<br \/>\n= \\(\\frac{1}{4}\\) \u00d7 \\(\\frac{1}{2}\\)<br \/>\n= \\(\\frac{ 1 \u00d7 1}{2 \u00d7 4}\\)<br \/>\n= \\(\\frac{1}{8}\\)<br \/>\nHence,<br \/>\n\\(\\frac{1}{4}\\) \u00f7 2 = \\(\\frac{1}{8}\\)<\/p>\n<p>Question 2.<br \/>\n<img loading=\"lazy\" class=\"alignnone size-full wp-image-15202\" src=\"https:\/\/ccssmathanswers.com\/wp-content\/uploads\/2020\/12\/Big-Ideas-Math-Answer-Key-Grade-5-Chapter-10-Divide-Fractions-49.png\" alt=\"Big Ideas Math Answer Key Grade 5 Chapter 10 Divide Fractions 49\" width=\"119\" height=\"54\" \/><br \/>\nAnswer: \\(\\frac{1}{2}\\) \u00f7 5 = \\(\\frac{1}{10}\\)<\/p>\n<p>Explanation:<br \/>\nThe given numbers are: \\(\\frac{1}{2}\\) and 5<br \/>\nWe know that,<br \/>\n\\(\\frac{a}{b}\\) \u00f7 a\u00a0 = \\(\\frac{a}{b}\\) \u00d7 \\(\\frac{1}{a}\\)<br \/>\na= \\(\\frac{a}{1}\\)<br \/>\nSo,<br \/>\n\\(\\frac{1}{2}\\) \u00f7 5<br \/>\n= \\(\\frac{1}{2}\\) \u00d7 \\(\\frac{1}{5}\\)<br \/>\n= \\(\\frac{ 1 \u00d7 1}{2 \u00d7 5}\\)<br \/>\n= \\(\\frac{1}{10}\\)<br \/>\nHence,<br \/>\n\\(\\frac{1}{2}\\) \u00f7 5 = \\(\\frac{1}{10}\\)<\/p>\n<p><strong>Apply and Grow: Practice<\/strong><\/p>\n<p>Divide. Use a model to help.<\/p>\n<p>Question 3.<br \/>\n<img loading=\"lazy\" class=\"alignnone size-full wp-image-15203\" src=\"https:\/\/ccssmathanswers.com\/wp-content\/uploads\/2020\/12\/Big-Ideas-Math-Answer-Key-Grade-5-Chapter-10-Divide-Fractions-50.png\" alt=\"Big Ideas Math Answer Key Grade 5 Chapter 10 Divide Fractions 50\" width=\"120\" height=\"63\" \/><br \/>\nAnswer: \\(\\frac{1}{5}\\) \u00f7 3 = \\(\\frac{1}{15}\\)<\/p>\n<p>Explanation:<br \/>\nThe given numbers are: \\(\\frac{1}{5}\\) and 3<br \/>\nWe know that,<br \/>\n\\(\\frac{a}{b}\\) \u00f7 a\u00a0 = \\(\\frac{a}{b}\\) \u00d7 \\(\\frac{1}{a}\\)<br \/>\na= \\(\\frac{a}{1}\\)<br \/>\nSo,<br \/>\n\\(\\frac{1}{5}\\) \u00f7 3<br \/>\n= \\(\\frac{1}{5}\\) \u00d7 \\(\\frac{1}{3}\\)<br \/>\n= \\(\\frac{ 1 \u00d7 1}{5 \u00d7 3}\\)<br \/>\n= \\(\\frac{1}{15}\\)<br \/>\nHence,<br \/>\n\\(\\frac{1}{5}\\) \u00f7 3 = \\(\\frac{1}{15}\\)<\/p>\n<p>Question 4.<br \/>\n<img loading=\"lazy\" class=\"alignnone size-full wp-image-15204\" src=\"https:\/\/ccssmathanswers.com\/wp-content\/uploads\/2020\/12\/Big-Ideas-Math-Answer-Key-Grade-5-Chapter-10-Divide-Fractions-51.png\" alt=\"Big Ideas Math Answer Key Grade 5 Chapter 10 Divide Fractions 51\" width=\"123\" height=\"62\" \/><br \/>\nAnswer: \\(\\frac{1}{6}\\) \u00f7 2 = \\(\\frac{1}{12}\\)<\/p>\n<p>Explanation:<br \/>\nThe given numbers are: \\(\\frac{1}{6}\\) and 2<br \/>\nWe know that,<br \/>\n\\(\\frac{a}{b}\\) \u00f7 a\u00a0 = \\(\\frac{a}{b}\\) \u00d7 \\(\\frac{1}{a}\\)<br \/>\na= \\(\\frac{a}{1}\\)<br \/>\nSo,<br \/>\n\\(\\frac{1}{6}\\) \u00f7 2<br \/>\n= \\(\\frac{1}{6}\\) \u00d7 \\(\\frac{1}{2}\\)<br \/>\n= \\(\\frac{ 1 \u00d7 1}{2 \u00d7 6}\\)<br \/>\n= \\(\\frac{1}{12}\\)<br \/>\nHence,<br \/>\n\\(\\frac{1}{6}\\) \u00f7 2 = \\(\\frac{1}{12}\\)<\/p>\n<p>Question 5.<br \/>\n<img loading=\"lazy\" class=\"alignnone size-full wp-image-15205\" src=\"https:\/\/ccssmathanswers.com\/wp-content\/uploads\/2020\/12\/Big-Ideas-Math-Answer-Key-Grade-5-Chapter-10-Divide-Fractions-52.png\" alt=\"Big Ideas Math Answer Key Grade 5 Chapter 10 Divide Fractions 52\" width=\"122\" height=\"61\" \/><br \/>\nAnswer: \\(\\frac{1}{3}\\) \u00f7 5 = \\(\\frac{1}{15}\\)<\/p>\n<p>Explanation:<br \/>\nThe given numbers are: \\(\\frac{1}{3}\\) and 5<br \/>\nWe know that,<br \/>\n\\(\\frac{a}{b}\\) \u00f7 a\u00a0 = \\(\\frac{a}{b}\\) \u00d7 \\(\\frac{1}{a}\\)<br \/>\na= \\(\\frac{a}{1}\\)<br \/>\nSo,<br \/>\n\\(\\frac{1}{3}\\) \u00f7 5<br \/>\n= \\(\\frac{1}{3}\\) \u00d7 \\(\\frac{1}{5}\\)<br \/>\n= \\(\\frac{ 1 \u00d7 1}{3 \u00d7 5}\\)<br \/>\n= \\(\\frac{1}{15}\\)<br \/>\nHence,<br \/>\n\\(\\frac{1}{3}\\) \u00f7 5 = \\(\\frac{1}{15}\\)<\/p>\n<p>Question 6.<br \/>\n<img loading=\"lazy\" class=\"alignnone size-full wp-image-15207\" src=\"https:\/\/ccssmathanswers.com\/wp-content\/uploads\/2020\/12\/Big-Ideas-Math-Answers-5th-Grade-Chapter-10-Divide-Fractions-53.png\" alt=\"Big Ideas Math Answers 5th Grade Chapter 10 Divide Fractions 53\" width=\"130\" height=\"55\" \/><br \/>\nAnswer: \\(\\frac{1}{5}\\) \u00f7 4 = \\(\\frac{1}{20}\\)<\/p>\n<p>Explanation:<br \/>\nThe given numbers are: \\(\\frac{1}{5}\\) and 4<br \/>\nWe know that,<br \/>\n\\(\\frac{a}{b}\\) \u00f7 a\u00a0 = \\(\\frac{a}{b}\\) \u00d7 \\(\\frac{1}{a}\\)<br \/>\na= \\(\\frac{a}{1}\\)<br \/>\nSo,<br \/>\n\\(\\frac{1}{5}\\) \u00f7 4<br \/>\n= \\(\\frac{1}{5}\\) \u00d7 \\(\\frac{1}{4}\\)<br \/>\n= \\(\\frac{ 1 \u00d7 1}{5 \u00d7 4}\\)<br \/>\n= \\(\\frac{1}{20}\\)<br \/>\nHence,<br \/>\n\\(\\frac{1}{5}\\) \u00f7 4 = \\(\\frac{1}{20}\\)<\/p>\n<p>Question 7.<br \/>\n<img loading=\"lazy\" class=\"alignnone size-full wp-image-15208\" src=\"https:\/\/ccssmathanswers.com\/wp-content\/uploads\/2020\/12\/Big-Ideas-Math-Answers-5th-Grade-Chapter-10-Divide-Fractions-54.png\" alt=\"Big Ideas Math Answers 5th Grade Chapter 10 Divide Fractions 54\" width=\"121\" height=\"57\" \/><br \/>\nAnswer: \\(\\frac{1}{3}\\) \u00f7 3 = \\(\\frac{1}{9}\\)<\/p>\n<p>Explanation:<br \/>\nThe given numbers are: \\(\\frac{1}{3}\\) and 3<br \/>\nWe know that,<br \/>\n\\(\\frac{a}{b}\\) \u00f7 a\u00a0 = \\(\\frac{a}{b}\\) \u00d7 \\(\\frac{1}{a}\\)<br \/>\na= \\(\\frac{a}{1}\\)<br \/>\nSo,<br \/>\n\\(\\frac{1}{3}\\) \u00f7 3<br \/>\n= \\(\\frac{1}{3}\\) \u00d7 \\(\\frac{1}{3}\\)<br \/>\n= \\(\\frac{ 1 \u00d7 1}{3 \u00d7 3}\\)<br \/>\n= \\(\\frac{1}{9}\\)<br \/>\nHence,<br \/>\n\\(\\frac{1}{3}\\) \u00f7 3 = \\(\\frac{1}{9}\\)<\/p>\n<p>Question 8.<br \/>\n<img loading=\"lazy\" class=\"alignnone size-full wp-image-15209\" src=\"https:\/\/ccssmathanswers.com\/wp-content\/uploads\/2020\/12\/Big-Ideas-Math-Answers-5th-Grade-Chapter-10-Divide-Fractions-55.png\" alt=\"Big Ideas Math Answers 5th Grade Chapter 10 Divide Fractions 55\" width=\"126\" height=\"59\" \/><br \/>\nAnswer: \\(\\frac{1}{8}\\) \u00f7 2 = \\(\\frac{1}{16}\\)<\/p>\n<p>Explanation:<br \/>\nThe given numbers are: \\(\\frac{1}{8}\\) and 2<br \/>\nWe know that,<br \/>\n\\(\\frac{a}{b}\\) \u00f7 a\u00a0 = \\(\\frac{a}{b}\\) \u00d7 \\(\\frac{1}{a}\\)<br \/>\na= \\(\\frac{a}{1}\\)<br \/>\nSo,<br \/>\n\\(\\frac{1}{8}\\) \u00f7 2<br \/>\n= \\(\\frac{1}{8}\\) \u00d7 \\(\\frac{1}{2}\\)<br \/>\n= \\(\\frac{ 1 \u00d7 1}{2 \u00d7 8}\\)<br \/>\n= \\(\\frac{1}{16}\\)<br \/>\nHence,<br \/>\n\\(\\frac{1}{8}\\) \u00f7 2 = \\(\\frac{1}{16}\\)<\/p>\n<p>Question 9.<br \/>\nHow many 6s are in \\(\\frac{1}{2}\\)?<br \/>\nAnswer: There are \\(\\frac{1}{12}\\) 6s in \\(\\frac{1}{2}\\)<\/p>\n<p>Explanation:<br \/>\nWe know that,<br \/>\n\\(\\frac{a}{b}\\) \u00f7 a\u00a0 = \\(\\frac{a}{b}\\) \u00d7 \\(\\frac{1}{a}\\)<br \/>\na= \\(\\frac{a}{1}\\)<br \/>\nNow,<br \/>\nWe have to find the number of 6s in \\(\\frac{1}{2}\\)<br \/>\nSo,<br \/>\n\\(\\frac{1}{2}\\) \u00f7 6<br \/>\n= \\(\\frac{1}{2}\\) \u00d7 \\(\\frac{1}{6}\\)<br \/>\n= \\(\\frac{ 1 \u00d7 1}{2 \u00d7 6}\\)<br \/>\n= \\(\\frac{1}{12}\\)<br \/>\nHence, from the above,<br \/>\nWe can conclude that there are \\(\\frac{1}{12}\\) 6s in \\(\\frac{1}{2}\\)<\/p>\n<p>Question 10.<br \/>\nHow many 2s are in \\(\\frac{1}{3}\\) ?<br \/>\nAnswer: There are \\(\\frac{1}{6}\\) 2s in \\(\\frac{1}{3}\\)<\/p>\n<p>Explanation:<br \/>\nWe know that,<br \/>\n\\(\\frac{a}{b}\\) \u00f7 a\u00a0 = \\(\\frac{a}{b}\\) \u00d7 \\(\\frac{1}{a}\\)<br \/>\na= \\(\\frac{a}{1}\\)<br \/>\nNow,<br \/>\nWe have to find the number of 2s in \\(\\frac{1}{3}\\)<br \/>\nSo,<br \/>\n\\(\\frac{1}{3}\\) \u00f7 2<br \/>\n= \\(\\frac{1}{3}\\) \u00d7 \\(\\frac{1}{2}\\)<br \/>\n= \\(\\frac{ 1 \u00d7 1}{2 \u00d7 3}\\)<br \/>\n= \\(\\frac{1}{6}\\)<br \/>\nHence, from the above,<br \/>\nWe can conclude that there are \\(\\frac{1}{6}\\) 2s in \\(\\frac{1}{2}\\)<\/p>\n<p>Question 11.<br \/>\n<strong>Writing<\/strong><br \/>\nWrite and solve a real-life problem for<br \/>\n<img loading=\"lazy\" class=\"alignnone size-full wp-image-15210\" src=\"https:\/\/ccssmathanswers.com\/wp-content\/uploads\/2020\/12\/Big-Ideas-Math-Answers-5th-Grade-Chapter-10-Divide-Fractions-56.png\" alt=\"Big Ideas Math Answers 5th Grade Chapter 10 Divide Fractions 56\" width=\"57\" height=\"45\" \/><br \/>\nAnswer:<br \/>\nSuppose a box has 7 chocolates. We have to divide these seven chocolates into further \\(\\frac{1}{2}\\) parts so that the chocolates can be distributed to more people<br \/>\nSo,<br \/>\nThe each part of chocolate we can get = \\(\\frac{1}{2}\\) \u00f7 7<br \/>\nNow,<br \/>\nWe know that,<br \/>\n\\(\\frac{a}{b}\\) \u00f7 a\u00a0 = \\(\\frac{a}{b}\\) \u00d7 \\(\\frac{1}{a}\\)<br \/>\na= \\(\\frac{a}{1}\\)<br \/>\nSo,<br \/>\n\\(\\frac{1}{2}\\) \u00f7 7<br \/>\n= \\(\\frac{1}{2}\\) \u00d7 \\(\\frac{1}{7}\\)<br \/>\n= \\(\\frac{ 1 \u00d7 1}{2 \u00d7 7}\\)<br \/>\n= \\(\\frac{1}{14}\\)<br \/>\nHence, from the above,<br \/>\nWe can conclude that we can get \\(\\frac{1}{14}\\) part of each chocolate.<\/p>\n<p>Question 12.<br \/>\nReasoning<br \/>\nComplete the statements.<br \/>\n<img loading=\"lazy\" class=\"alignnone size-full wp-image-34602\" src=\"https:\/\/ccssmathanswers.com\/wp-content\/uploads\/2020\/12\/Big-Ideas-Math-Answers-Grade-5-Chapter-10-52.jpg\" alt=\"\" width=\"253\" height=\"151\" \/><\/p>\n<p><strong>Think and Grow: Modeling Real Life<\/strong><\/p>\n<p>You melt \\(\\frac{1}{4}\\) quart of soap. You pour the soap into 4 of the same-sized molds. What fraction of a quart of soap does each mold hold?<br \/>\nYou are dividing \\(\\frac{1}{4}\\) quart into 4 equal parts, so you need to find \\(\\frac{1}{4}\\) \u00f7 4.<br \/>\n<img loading=\"lazy\" class=\"alignnone size-full wp-image-34603\" src=\"https:\/\/ccssmathanswers.com\/wp-content\/uploads\/2020\/12\/Big-Ideas-Math-Answers-Grade-5-Chapter-10-53.jpg\" alt=\"\" width=\"711\" height=\"311\" srcset=\"https:\/\/bigideasmathanswers.com\/wp-content\/uploads\/2020\/12\/Big-Ideas-Math-Answers-Grade-5-Chapter-10-53.jpg 711w, https:\/\/bigideasmathanswers.com\/wp-content\/uploads\/2020\/12\/Big-Ideas-Math-Answers-Grade-5-Chapter-10-53-300x131.jpg 300w\" sizes=\"(max-width: 711px) 100vw, 711px\" \/><\/p>\n<p><strong>Show and Grow<\/strong><\/p>\n<p>Question 13.<br \/>\nYou buy \\(\\frac{1}{2}\\) pound of grapes. You equally divide the grapes into 2 bags. What fraction of a pound of grapes do you put into each bag?<br \/>\nAnswer: The fraction of a pound of grapes you put into each bag is: \\(\\frac{1}{8}\\) pound<\/p>\n<p>Explanation:<br \/>\nIt is given that you buy \\(\\frac{1}{2}\\) pound of grapes.<br \/>\nIt is also given that you equally divide the grapes into 2 bags.<br \/>\nSo,<br \/>\nThe number of grapes in each bag = \\(\\frac{1}{2}\\) \u00f7 2<br \/>\nNow,<br \/>\nThe fraction of pound of grapes you put into each bag = \\(\\frac{The number of grapes in each bag}{2}\\)<br \/>\n=\u00a0 ( \\(\\frac{1}{2}\\) \u00f7 2 ) \u00f7 2<br \/>\nNow,<br \/>\nWe know that,<br \/>\n\\(\\frac{a}{b}\\) \u00f7 a\u00a0 = \\(\\frac{a}{b}\\) \u00d7 \\(\\frac{1}{a}\\)<br \/>\na= \\(\\frac{a}{1}\\)<br \/>\nSo,<br \/>\n( \\(\\frac{1}{2}\\) \u00f7 2 ) \u00f7 2<br \/>\n= ( \\(\\frac{1}{2}\\) \u00d7 \\(\\frac{1}{2}\\) ) \u00d7 \\(\\frac{1}{2}\\)<br \/>\n= \\(\\frac{ 1 \u00d7 1}{2 \u00d7 2}\\) \u00d7 \\(\\frac{1}{2}\\)<br \/>\n= \\(\\frac{1}{4}\\) \u00d7 \\(\\frac{1}{2}\\)<br \/>\n= \\(\\frac{ 1 \u00d7 1}{2 \u00d7 4}\\)<br \/>\n= \\(\\frac{1}{8}\\)<br \/>\nHence, from the above<br \/>\nWe can conclude that the fraction of pound of grapes in each bag is: \\(\\frac{1}{8}\\) pound<\/p>\n<p>Question 14.<br \/>\nYou have \\(\\frac{1}{8}\\) cup of red sand, \\(\\frac{1}{4}\\) cup of blue sand, and \\(\\frac{1}{2}\\) cup of white sand. You equally divide the sand into 3 containers. What fraction of a cup of sand do you pour into each container?<br \/>\nAnswer: The fraction of a cup of sand you pour into each container is: \\(\\frac{7}{24}\\)<\/p>\n<p>Explanation:<br \/>\nIt is given that you have \\(\\frac{1}{8}\\) cup of red sand, \\(\\frac{1}{4}\\) cup of blue sand, and \\(\\frac{1}{2}\\) cup of white sand.<br \/>\nSo,<br \/>\nThe total amount of sand = \\(\\frac{1}{8}\\) cup of red sand + \\(\\frac{1}{4}\\) cup of blue sand + \\(\\frac{1}{2}\\) cup of white sand<br \/>\nIn addition, we have to see either the numerators are equal or the denominators are equal.<br \/>\nIf the numerators are equal we have to ake the denominators also equal.<br \/>\nSo,<br \/>\n\\(\\frac{1}{4}\\) is multplied by \\(\\frac{2}{2}\\)<br \/>\n\\(\\frac{1}{2}\\) is multiplied by \\(\\frac{4}{4}\\)<br \/>\nSo,<br \/>\n\\(\\frac{1}{4}\\) = \\(\\frac{2}{8}\\)<br \/>\n\\(\\frac{1}{2}\\) = \\(\\frac{4}{8}\\)<br \/>\nSo,<br \/>\n\\(\\frac{1}{8}\\) + \\(\\frac{2}{8}\\) + \\(\\frac{4}{8}\\) = \\(\\frac{7}{8}\\)<br \/>\nIt is also given that all the sand is equally distributed into 3 containers<br \/>\nSo,<br \/>\nThe amount of sand in each container = \\(\\frac{7}{8}\\) \u00f7 3<br \/>\nNow,<br \/>\nWe know that,<br \/>\n\\(\\frac{a}{b}\\) \u00f7 a\u00a0 = \\(\\frac{a}{b}\\) \u00d7 \\(\\frac{1}{a}\\)<br \/>\na= \\(\\frac{a}{1}\\)<br \/>\nSo,<br \/>\n\\(\\frac{7}{8}\\) \u00f7 3<br \/>\n= \\(\\frac{7}{8}\\) \u00d7 \\(\\frac{1}{3}\\)<br \/>\n= \\(\\frac{ 7 \u00d7 1}{8 \u00d7 3}\\)<br \/>\n= \\(\\frac{7}{24}\\)<br \/>\nHence, from the above,<br \/>\nWe can conclude that the amount of sand in each container is: \\(\\frac{7}{24}\\) cup.<\/p>\n<p>Question 15.<br \/>\n<strong>DIG DEEPER!<\/strong><br \/>\nYou, your friend, and your cousin share \\(\\frac{1}{2}\\) of a vegetable pizza and \\(\\frac{1}{4}\\) of a cheese share pizza. The pizzas are the same size. What fraction of a pizza do you get in all?<br \/>\n<img loading=\"lazy\" class=\"alignnone size-full wp-image-15212\" src=\"https:\/\/ccssmathanswers.com\/wp-content\/uploads\/2020\/12\/Big-Ideas-Math-Answers-5th-Grade-Chapter-10-Divide-Fractions-58.png\" alt=\"Big Ideas Math Answers 5th Grade Chapter 10 Divide Fractions 58\" width=\"249\" height=\"126\" \/><\/p>\n<p>Divide. Use a model to help<br \/>\nAnswer: The fraction of a pizza you got is: \\(\\frac{3}{12}\\)<\/p>\n<p>Explanation:<br \/>\nIt is given that you, your friend, and your cousin share \\(\\frac{1}{2}\\) of a vegetable pizza and \\(\\frac{1}{4}\\) of a cheese share pizza.<br \/>\nSo,<br \/>\nThe total amount of pizza = \\(\\frac{1}{2}\\) of a vegetable pizza + \\(\\frac{1}{4}\\) of a cheese share pizza<br \/>\nIn addition, we have to see either the numerators are equal or the denominators are equal.<br \/>\nIf the numerators are equal we have to ake the denominators also equal.<br \/>\nSo,<br \/>\n\\(\\frac{1}{2}\\) is multplied by \\(\\frac{2}{2}\\)<br \/>\nSo,<br \/>\n\\(\\frac{1}{2}\\) = \\(\\frac{2}{4}\\)<br \/>\nSo,<br \/>\n\\(\\frac{2}{4}\\) + \\(\\frac{1}{4}\\) = \\(\\frac{3}{4}\\)<br \/>\nSo,<br \/>\nThe fraction of pizza each get = \\(\\frac{The total amount of pizza}{3}\\)<br \/>\n= \\(\\frac{3}{4}\\) \u00f7 3<br \/>\nNow,<br \/>\nWe know that,<br \/>\n\\(\\frac{a}{b}\\) \u00f7 a\u00a0 = \\(\\frac{a}{b}\\) \u00d7 \\(\\frac{1}{a}\\)<br \/>\na= \\(\\frac{a}{1}\\)<br \/>\nSo,<br \/>\n\\(\\frac{3}{4}\\) \u00f7 3<br \/>\n= \\(\\frac{3}{4}\\) \u00d7 \\(\\frac{1}{3}\\)<br \/>\n= \\(\\frac{ 3 \u00d7 1}{4 \u00d7 3}\\)<br \/>\n= \\(\\frac{3}{12}\\)<br \/>\nHence, from the above,<br \/>\nWe can conclude that the fraction of pizza each get is: \\(\\frac{3}{12}\\)<\/p>\n<h3><a id=\"Divide_Unit_Fractions_by_Whole_Numbers_Homework_&amp;_Practice_10.4\"><\/a>Divide Unit Fractions by Whole Numbers Homework &amp; Practice 10.4<\/h3>\n<p>Question 1.<br \/>\n<img loading=\"lazy\" class=\"alignnone size-full wp-image-15213\" src=\"https:\/\/ccssmathanswers.com\/wp-content\/uploads\/2020\/12\/Big-Ideas-Math-Answers-5th-Grade-Chapter-10-Divide-Fractions-59.png\" alt=\"Big Ideas Math Answers 5th Grade Chapter 10 Divide Fractions 59\" width=\"117\" height=\"55\" \/><br \/>\nAnswer: \\(\\frac{1}{3}\\) \u00f7 4 = \\(\\frac{1}{12}\\)<\/p>\n<p>Explanation:<br \/>\nThe given numbers are: \\(\\frac{1}{3}\\) and 4<br \/>\nWe know that,<br \/>\n\\(\\frac{a}{b}\\) \u00f7 a\u00a0 = \\(\\frac{a}{b}\\) \u00d7 \\(\\frac{1}{a}\\)<br \/>\na= \\(\\frac{a}{1}\\)<br \/>\nSo,<br \/>\n\\(\\frac{1}{3}\\) \u00f7 4<br \/>\n= \\(\\frac{1}{3}\\) \u00d7 \\(\\frac{1}{4}\\)<br \/>\n= \\(\\frac{ 1 \u00d7 1}{3 \u00d7 4}\\)<br \/>\n= \\(\\frac{1}{12}\\)<br \/>\nHence,<br \/>\n\\(\\frac{1}{3}\\) \u00f7 4 = \\(\\frac{1}{12}\\)<\/p>\n<p>Question 2.<br \/>\n<img loading=\"lazy\" class=\"alignnone size-full wp-image-15214\" src=\"https:\/\/ccssmathanswers.com\/wp-content\/uploads\/2020\/12\/Big-Ideas-Math-Answers-5th-Grade-Chapter-10-Divide-Fractions-60.png\" alt=\"Big Ideas Math Answers 5th Grade Chapter 10 Divide Fractions 60\" width=\"115\" height=\"50\" \/><br \/>\nAnswer: \\(\\frac{1}{6}\\) \u00f7 3 = \\(\\frac{1}{18}\\)<\/p>\n<p>Explanation:<br \/>\nThe given numbers are: \\(\\frac{1}{6}\\) and 3<br \/>\nWe know that,<br \/>\n\\(\\frac{a}{b}\\) \u00f7 a\u00a0 = \\(\\frac{a}{b}\\) \u00d7 \\(\\frac{1}{a}\\)<br \/>\na= \\(\\frac{a}{1}\\)<br \/>\nSo,<br \/>\n\\(\\frac{1}{6}\\) \u00f7 3<br \/>\n= \\(\\frac{1}{6}\\) \u00d7 \\(\\frac{1}{3}\\)<br \/>\n= \\(\\frac{ 1 \u00d7 1}{6 \u00d7 3}\\)<br \/>\n= \\(\\frac{1}{18}\\)<br \/>\nHence,<br \/>\n\\(\\frac{1}{6}\\) \u00f7 3 = \\(\\frac{1}{18}\\)<\/p>\n<p>Question 3.<br \/>\n<img loading=\"lazy\" class=\"alignnone size-full wp-image-15215\" src=\"https:\/\/ccssmathanswers.com\/wp-content\/uploads\/2020\/12\/Big-Ideas-Math-Answers-5th-Grade-Chapter-10-Divide-Fractions-61.png\" alt=\"Big Ideas Math Answers 5th Grade Chapter 10 Divide Fractions 61\" width=\"114\" height=\"66\" \/><br \/>\nAnswer: \\(\\frac{1}{4}\\) \u00f7 5 = \\(\\frac{1}{20}\\)<\/p>\n<p>Explanation:<br \/>\nThe given numbers are: \\(\\frac{1}{4}\\) and 5<br \/>\nWe know that,<br \/>\n\\(\\frac{a}{b}\\) \u00f7 a\u00a0 = \\(\\frac{a}{b}\\) \u00d7 \\(\\frac{1}{a}\\)<br \/>\na= \\(\\frac{a}{1}\\)<br \/>\nSo,<br \/>\n\\(\\frac{1}{4}\\) \u00f7 5<br \/>\n= \\(\\frac{1}{4}\\) \u00d7 \\(\\frac{1}{5}\\)<br \/>\n= \\(\\frac{ 1 \u00d7 1}{5 \u00d7 4}\\)<br \/>\n= \\(\\frac{1}{20}\\)<br \/>\nHence,<br \/>\n\\(\\frac{1}{4}\\) \u00f7 5 = \\(\\frac{1}{20}\\)<\/p>\n<p>Divide. Use a model to help.<\/p>\n<p>Question 4.<br \/>\n<img loading=\"lazy\" class=\"alignnone size-full wp-image-15216\" src=\"https:\/\/ccssmathanswers.com\/wp-content\/uploads\/2020\/12\/Big-Ideas-Math-Answers-5th-Grade-Chapter-10-Divide-Fractions-62.png\" alt=\"Big Ideas Math Answers 5th Grade Chapter 10 Divide Fractions 62\" width=\"123\" height=\"53\" \/><br \/>\nAnswer: \\(\\frac{1}{5}\\) \u00f7 9 = \\(\\frac{1}{45}\\)<\/p>\n<p>Explanation:<br \/>\nThe given numbers are: \\(\\frac{1}{5}\\) and 9<br \/>\nWe know that,<br \/>\n\\(\\frac{a}{b}\\) \u00f7 a\u00a0 = \\(\\frac{a}{b}\\) \u00d7 \\(\\frac{1}{a}\\)<br \/>\na= \\(\\frac{a}{1}\\)<br \/>\nSo,<br \/>\n\\(\\frac{1}{5}\\) \u00f7 9<br \/>\n= \\(\\frac{1}{5}\\) \u00d7 \\(\\frac{1}{9}\\)<br \/>\n= \\(\\frac{ 1 \u00d7 1}{5 \u00d7 9}\\)<br \/>\n= \\(\\frac{1}{45}\\)<br \/>\nHence,<br \/>\n\\(\\frac{1}{5}\\) \u00f7 9 = \\(\\frac{1}{45}\\)<\/p>\n<p>Question 5.<br \/>\n<img loading=\"lazy\" class=\"alignnone size-full wp-image-15217\" src=\"https:\/\/ccssmathanswers.com\/wp-content\/uploads\/2020\/12\/Big-Ideas-Math-Answers-5th-Grade-Chapter-10-Divide-Fractions-63.png\" alt=\"Big Ideas Math Answers 5th Grade Chapter 10 Divide Fractions 63\" width=\"130\" height=\"50\" \/><br \/>\nAnswer: \\(\\frac{1}{8}\\) \u00f7 6 = \\(\\frac{1}{48}\\)<\/p>\n<p>Explanation:<br \/>\nThe given numbers are: \\(\\frac{1}{8}\\) and 6<br \/>\nWe know that,<br \/>\n\\(\\frac{a}{b}\\) \u00f7 a\u00a0 = \\(\\frac{a}{b}\\) \u00d7 \\(\\frac{1}{a}\\)<br \/>\na= \\(\\frac{a}{1}\\)<br \/>\nSo,<br \/>\n\\(\\frac{1}{8}\\) \u00f7 6<br \/>\n= \\(\\frac{1}{8}\\) \u00d7 \\(\\frac{1}{6}\\)<br \/>\n= \\(\\frac{ 1 \u00d7 1}{8 \u00d7 6}\\)<br \/>\n= \\(\\frac{1}{48}\\)<br \/>\nHence,<br \/>\n\\(\\frac{1}{8}\\) \u00f7 6 = \\(\\frac{1}{48}\\)<\/p>\n<p>Question 6.<br \/>\n<img loading=\"lazy\" class=\"alignnone size-full wp-image-15218\" src=\"https:\/\/ccssmathanswers.com\/wp-content\/uploads\/2020\/12\/Big-Ideas-Math-Answers-5th-Grade-Chapter-10-Divide-Fractions-64.png\" alt=\"Big Ideas Math Answers 5th Grade Chapter 10 Divide Fractions 64\" width=\"119\" height=\"68\" \/><br \/>\nAnswer: \\(\\frac{1}{7}\\) \u00f7 4 = \\(\\frac{1}{28}\\)<\/p>\n<p>Explanation:<br \/>\nThe given numbers are: \\(\\frac{1}{7}\\) and 4<br \/>\nWe know that,<br \/>\n\\(\\frac{a}{b}\\) \u00f7 a\u00a0 = \\(\\frac{a}{b}\\) \u00d7 \\(\\frac{1}{a}\\)<br \/>\na= \\(\\frac{a}{1}\\)<br \/>\nSo,<br \/>\n\\(\\frac{1}{7}\\) \u00f7 4<br \/>\n= \\(\\frac{1}{7}\\) \u00d7 \\(\\frac{1}{4}\\)<br \/>\n= \\(\\frac{ 1 \u00d7 1}{7 \u00d7 4}\\)<br \/>\n= \\(\\frac{1}{28}\\)<br \/>\nHence,<br \/>\n\\(\\frac{1}{7}\\) \u00f7 4 = \\(\\frac{1}{28}\\)<\/p>\n<p>Question 7.<br \/>\n<strong>YOU BE THE TEACHER<\/strong><br \/>\nYour friend divides \\(\\frac{1}{3}\\) by 7 to get \\(\\frac{1}{21}\\). He checks his answer by multiplying \\(\\frac{1}{21}\\) \u00d7 \\(\\frac{1}{3}\\). Does your friend check his answer correctly? Explain.<br \/>\nAnswer: No, your friend does not check his answer correctly<\/p>\n<p>Explanation:<br \/>\nIt is given that your friend divides \\(\\frac{1}{3}\\) by 7 to get \\(\\frac{1}{21}\\).<br \/>\nWe know that,<br \/>\n\\(\\frac{a}{b}\\) \u00f7 a\u00a0 = \\(\\frac{a}{b}\\) \u00d7 \\(\\frac{1}{a}\\)<br \/>\na= \\(\\frac{a}{1}\\)<br \/>\nSo,<br \/>\n\\(\\frac{1}{3}\\) \u00f7 7<br \/>\n= \\(\\frac{1}{3}\\) \u00d7 \\(\\frac{1}{7}\\)<br \/>\n= \\(\\frac{ 1 \u00d7 1}{7 \u00d7 3}\\)<br \/>\n= \\(\\frac{1}{21}\\)<br \/>\nIt is also given that your friend checks his answer by multiplying \\(\\frac{1}{21}\\) \u00d7 \\(\\frac{1}{3}\\).<br \/>\nNow,<br \/>\n\\(\\frac{1}{21}\\) \u00d7 \\(\\frac{1}{3}\\)<br \/>\n= \\(\\frac{1 \u00d7 1}{21 \u00d7 3}\\)<br \/>\n= \\(\\frac{1}{63}\\)<br \/>\nBut, your friend wanted to check whether \\(\\frac{1}{21}\\) \u00d7 \\(\\frac{1}{3}\\) = \\(\\frac{1}{7}\\)<br \/>\nBut, the value becomes \\(\\frac{1}{63}\\)<br \/>\nHence, from the above,<br \/>\nWe can conclude that your friend does not check the answer correctly.<\/p>\n<p>Question 8.<br \/>\n<strong>Logic<\/strong><br \/>\nFind the missing numbers.<br \/>\n<img loading=\"lazy\" class=\"alignnone size-full wp-image-34642\" src=\"https:\/\/ccssmathanswers.com\/wp-content\/uploads\/2020\/12\/Big-Ideas-Math-Answers-Grade-5-Chapter-10-54.jpg\" alt=\"\" width=\"229\" height=\"66\" \/><\/p>\n<p>Question 9.<br \/>\n<strong>Modeling Real Life<\/strong><br \/>\nYou win tickets that you can exchange for prizes. You exchange \\(\\frac{1}{5}\\) of your tickets and then divide them equally among 3 prizes. What fraction of your tickets do you spend on each prize?<br \/>\nAnswer: The fraction of your tickets you spend on each prize is: \\(\\frac{1}{15}\\)<\/p>\n<p>Explanation:<br \/>\nIt is given that you win tickets that you can exchange for prizes.<br \/>\nIt is also given that you exchange \\(\\frac{1}{5}\\) of your tickets and then divide them equally among 3 prizes<br \/>\nSo,<br \/>\nThe fraction of the tickets spent on each prize = \\(\\frac{The value of Exchange}{The number of prizes}\\)<br \/>\n= \\(\\frac{1}{5}\\) \u00f7 3<br \/>\nNow,<br \/>\nWe know that,<br \/>\n\\(\\frac{a}{b}\\) \u00f7 a\u00a0 = \\(\\frac{a}{b}\\) \u00d7 \\(\\frac{1}{a}\\)<br \/>\na= \\(\\frac{a}{1}\\)<br \/>\nSo,<br \/>\n\\(\\frac{1}{5}\\) \u00f7 3<br \/>\n= \\(\\frac{1}{5}\\) \u00d7 \\(\\frac{1}{3}\\)<br \/>\n= \\(\\frac{ 1 \u00d7 1}{5 \u00d7 3}\\)<br \/>\n= \\(\\frac{1}{15}\\)<br \/>\nHence, from the above,<br \/>\nWe can conlude that the fraction of tickets you spend on each prize is: \\(\\frac{1}{15}\\)<\/p>\n<p>Question 10.<br \/>\n<strong>DIG DEEPER!<\/strong><br \/>\nYou have \\(\\frac{1}{8}\\) gallon of melted crayon wax. You pour the wax equally into 8 different molds to make new crayons. What fraction of a cup of melted wax is in each mold? Think: 1 gallon is 16 cups.<br \/>\n<img loading=\"lazy\" class=\"alignnone size-full wp-image-15220\" src=\"https:\/\/ccssmathanswers.com\/wp-content\/uploads\/2020\/12\/Big-Ideas-Math-Answers-5th-Grade-Chapter-10-Divide-Fractions-66.png\" alt=\"Big Ideas Math Answers 5th Grade Chapter 10 Divide Fractions 66\" width=\"253\" height=\"164\" \/><br \/>\nAnswer: The fraction of a cup of melted wax in each mold is: \\(\\frac{1}{4}\\)<\/p>\n<p>Explanation:<br \/>\nIt is given that you have \\(\\frac{1}{8}\\) gallon of melted crayon wax.<br \/>\nIt is also given that you pour the wax equally into 8 different molds to make new crayons.<br \/>\nSo,<br \/>\nThe fraction of melted crayon wax in each mold in gallons = \\(\\frac{The total amount of melted crayon wax }{The number of molds}\\)<br \/>\n= \\(\\frac{1}{8}\\) \u00f7 8<br \/>\nNow,<br \/>\nWe know that,<br \/>\n\\(\\frac{a}{b}\\) \u00f7 a\u00a0 = \\(\\frac{a}{b}\\) \u00d7 \\(\\frac{1}{a}\\)<br \/>\na= \\(\\frac{a}{1}\\)<br \/>\nSo,<br \/>\n\\(\\frac{1}{8}\\) \u00f7 8<br \/>\n= \\(\\frac{1}{8}\\) \u00d7 \\(\\frac{1}{8}\\)<br \/>\n= \\(\\frac{ 1 \u00d7 1}{8 \u00d7 8}\\)<br \/>\n= \\(\\frac{1}{64}\\) gallons<br \/>\nBut, it is given that<br \/>\n1 gallon = 16 cups<br \/>\nSo,<br \/>\nThe total number of cups that the melted crayon wax contained = \\(\\frac{1}{64}\\) \u00d7 \\(\\frac{16}{1}\\)<br \/>\n= \\(\\frac{1 \u00d7 16 }{64 \u00d7 1}\\)<br \/>\n= \\(\\frac{1}{4}\\)<br \/>\nHence, from the above,<br \/>\nWe can conclude that there are \\(\\frac{1}{4}\\) cups of melted crayon wax in each mold.<\/p>\n<p><strong>Review &amp; Refresh<\/strong><\/p>\n<p>Question 11.<br \/>\n0.9 \u00f7 0.1 = ___<br \/>\nAnswer: 0.9 \u00f7 0.1 = 9<\/p>\n<p>Explanation:<br \/>\nThe given decimal numbers are: 0.9 and 0.1<br \/>\nThe representation of the decimal numbers in the fraction form is: \\(\\frac{9}{10}\\) and \\(\\frac{1}{10}\\)<br \/>\nNow,<br \/>\nWe know that,<br \/>\na \u00f7 \\(\\frac{a}{b}\\) = a \u00d7 \\(\\frac{b}{a}\\)<br \/>\na= \\(\\frac{a}{1}\\)<br \/>\nSo,<br \/>\n\\(\\frac{9}{10}\\) \u00f7 \\(\\frac{1}{10}\\)\u00a0 = \\(\\frac{9}{10}\\) \u00d7 \\(\\frac{10}{1}\\)<br \/>\n= \\(\\frac{ 9 \u00d7 10}{10 \u00d7 1}\\)<br \/>\n= 9<br \/>\nHence, 0.9 \u00f7 0.1 = 9<\/p>\n<p>Question 12.<br \/>\n38.6 \u00f7 100 = ___<\/p>\n<p>Answer: 38.6 \u00f7 100 = 0.386<\/p>\n<p>Explanation:<br \/>\nThe given numbers are: 38.6 and 100<br \/>\nThe representation of the numbers in the fraction form is: \\(\\frac{386}{10}\\) and \\(\\frac{100}{1}\\)<br \/>\nNow,<br \/>\nWe know that,<br \/>\na \u00f7 \\(\\frac{a}{b}\\) = a \u00d7 \\(\\frac{b}{a}\\)<br \/>\na= \\(\\frac{a}{1}\\)<br \/>\nSo,<br \/>\n\\(\\frac{386}{10}\\) \u00f7 \\(\\frac{100}{1}\\)\u00a0 = \\(\\frac{386}{10}\\) \u00d7 \\(\\frac{1}{100}\\)<br \/>\n= \\(\\frac{ 386 \u00d7 1}{100 \u00d7 10}\\)<br \/>\n= \\(\\frac{386}{1000}\\)<br \/>\n= 0.386<br \/>\nHence, 38.6 \u00f7 100 = 0.386<\/p>\n<p>Question 13.<br \/>\n2.57 \u00f7 0.01 = ___<br \/>\nAnswer: 2.57 \u00f7 0.01 = 257<\/p>\n<p>Explanation:<br \/>\nThe given decimal numbers are: 2.57 and 0.01<br \/>\nThe representation of the decimal numbers in the fraction form is: \\(\\frac{257}{100}\\) and \\(\\frac{1}{100}\\)<br \/>\nNow,<br \/>\nWe know that,<br \/>\na \u00f7 \\(\\frac{a}{b}\\) = a \u00d7 \\(\\frac{b}{a}\\)<br \/>\na= \\(\\frac{a}{1}\\)<br \/>\nSo,<br \/>\n\\(\\frac{257}{100}\\) \u00f7 \\(\\frac{1}{100}\\)\u00a0 = \\(\\frac{257}{100}\\) \u00d7 \\(\\frac{100}{1}\\)<br \/>\n= \\(\\frac{ 257 \u00d7 100}{100 \u00d7 1}\\)<br \/>\n= 257<br \/>\nHence, 2.57 \u00f7 0.01 = 257<\/p>\n<h3><a id=\"Lesson_10.5_Problem_Solving:_Fraction_Division\"><\/a>Lesson 10.5 Problem Solving: Fraction Division<\/h3>\n<p><strong>Explore and Grow<\/strong><\/p>\n<p>You want to make a \\(\\frac{1}{3}\\) batch of the recipe. How you can use division to find the amount of each ingredient you need?<br \/>\nAnswer:<br \/>\nIt is given that you want to make a \\(\\frac{1}{3}\\) batch of the recipe.<br \/>\nSo,<br \/>\nFrom \\(\\frac{1}{3}\\),<br \/>\n1 represents a batch of the recipe<br \/>\n3 represents the total number of ingredients in a batch<br \/>\nSo,<br \/>\nThe amount of each ingredient you need = \\(\\frac{The amount of the batch of the recipe }{The total number of ingredients}\\)<br \/>\n= \\(\\frac{1}{3}\\) \u00f7 3<br \/>\nNow,<br \/>\nWe know that,<br \/>\n\\(\\frac{a}{b}\\) \u00f7 a\u00a0 = \\(\\frac{a}{b}\\) \u00d7 \\(\\frac{1}{a}\\)<br \/>\na= \\(\\frac{a}{1}\\)<br \/>\nSo,<br \/>\n\\(\\frac{1}{3}\\) \u00f7 3<br \/>\n= \\(\\frac{1}{3}\\) \u00d7 \\(\\frac{1}{3}\\)<br \/>\n= \\(\\frac{ 1 \u00d7 1}{3 \u00d7 3}\\)<br \/>\n= \\(\\frac{1}{9}\\)<br \/>\nHence, from the above,<br \/>\nWe can conclude that the amount of each ingredient you need is: \\(\\frac{1}{9}\\)<\/p>\n<p><strong>Reasoning<\/strong><br \/>\nWithout calculating, explain how you can tell whether you need more than or less than 1 tablespoon of olive oil?<br \/>\nAnswer: You need less than 1 tablespoon of olive oil<\/p>\n<p>Explanation:<br \/>\nFrom the above problem,<br \/>\nThe amount of each ingredient is: \\(\\frac{1}{9}\\)<br \/>\nSince the amount of each ingredient is less than 1, you need less than 1 tablespoon of olive oil<\/p>\n<p><strong>Think and Grow: Problem Solving: Fraction Division<\/strong><\/p>\n<p><strong>Example<\/strong><br \/>\nYou have 4 cups of yellow paint and 3 cups of blue paint. How many batches of green paint can you make?<br \/>\n<img loading=\"lazy\" class=\"alignnone size-full wp-image-15221\" src=\"https:\/\/ccssmathanswers.com\/wp-content\/uploads\/2020\/12\/Big-Ideas-Math-Answers-5th-Grade-Chapter-10-Divide-Fractions-67.png\" alt=\"Big Ideas Math Answers 5th Grade Chapter 10 Divide Fractions 67\" width=\"204\" height=\"108\" \/><\/p>\n<p><strong>Understand the Problem<\/strong><\/p>\n<p>What do you know?<\/p>\n<ul>\n<li>You have 4 cups of yellow paint and 3 cups of blue paint.<\/li>\n<li>One batch of green paint is made of \\(\\frac{1}{2}\\) cup of yellow and \\(\\frac{1}{3}\\) cup of blue.<\/li>\n<\/ul>\n<p>What do you need to find?<\/p>\n<ul>\n<li>You need to find how many batches of green paint you can make.<\/li>\n<\/ul>\n<p><strong>Make a Plan<\/strong><br \/>\nHow will you solve?<\/p>\n<ul>\n<li>Find how many batches are possible from yellow, and how many from blue.<\/li>\n<li>Choose the lesser number of batches.<\/li>\n<\/ul>\n<p><strong>Solve<\/strong><br \/>\n<img loading=\"lazy\" class=\"alignnone size-full wp-image-34650\" src=\"https:\/\/ccssmathanswers.com\/wp-content\/uploads\/2020\/12\/Big-Ideas-Math-Answers-Grade-5-Chapter-10-55.jpg\" alt=\"\" width=\"595\" height=\"305\" srcset=\"https:\/\/bigideasmathanswers.com\/wp-content\/uploads\/2020\/12\/Big-Ideas-Math-Answers-Grade-5-Chapter-10-55.jpg 595w, https:\/\/bigideasmathanswers.com\/wp-content\/uploads\/2020\/12\/Big-Ideas-Math-Answers-Grade-5-Chapter-10-55-300x154.jpg 300w\" sizes=\"(max-width: 595px) 100vw, 595px\" \/><br \/>\nSo, you can make 8 batches of green paint.<\/p>\n<p><strong>Show and Grow<\/strong><\/p>\n<p>Question 1.<br \/>\nIn the example, explain why you choose the fewer number of batches.<br \/>\nAnswer: In the above example, the yellow paint has the less number of batches as the amount of each batch of yellow paint-filled is more than the batch of green paint<br \/>\nHence,<br \/>\nWe choose the fewer number of batches of yellow paint<\/p>\n<p><strong>Apply and Grow: Practice<\/strong><\/p>\n<p>Understand the problem. What do you know? What do you need to find? Explain.<\/p>\n<p>Question 2.<br \/>\nA landowner donates 3 acres of land to a city. The mayor of the city uses 1 acre of the land for a playground and the rest of the land for community garden plots. Each garden plot is \\(\\frac{1}{3}\\) acre. How many plots are there?<br \/>\nUnderstand the problem. Then make a plan. How will you solve it? Explain?<br \/>\nAnswer: The number of plots in the community is: 6<\/p>\n<p>Explanation:<br \/>\nIt is given that a landowner donates 3 acres of land to a city and the mayor of the city uses 1 acre of the land for a playground and the rest of the land for community garden plots.<br \/>\nSo,<br \/>\nThe portion of the land used for community garden plots is: 2 acres<br \/>\nIt is also given that each garden plot is \\(\\frac{1}{3}\\) acre.<br \/>\nSo,<br \/>\nThe number of plots = \\(\\frac{The portion of the land used for community garden plots}{The area of each garden plot}\\)<br \/>\n= 2 \u00f7 \\(\\frac{1}{3}\\)<br \/>\n= 2 \u00d7 \\(\\frac{3}{1}\\)<br \/>\n= \\(\\frac{2}{1}\\) \u00d7 \\(\\frac{3}{1}\\)<br \/>\n= 6<br \/>\nHence, from the above,<br \/>\nWe can conclude that there are 6 plots<\/p>\n<p>Question 3.<br \/>\nA craftsman uses \\(\\frac{3}{4}\\) gallon of paint to paint 4 identical dressers. He uses the same amount of paint on each dresser. How much paint does he use to paint 7 of the same dressers?<br \/>\n<img loading=\"lazy\" class=\"alignnone size-full wp-image-15223\" src=\"https:\/\/ccssmathanswers.com\/wp-content\/uploads\/2020\/12\/Big-Ideas-Math-Answers-5th-Grade-Chapter-10-Divide-Fractions-69.png\" alt=\"Big Ideas Math Answers 5th Grade Chapter 10 Divide Fractions 69\" width=\"96\" height=\"129\" \/><br \/>\nAnswer: The paint used by the craftsman to paint 7 of the same dressers is: \\(\\frac{21}{16}\\)<\/p>\n<p>Explanation:<br \/>\nIt is given that a craftsman uses \\(\\frac{3}{4}\\) gallon of paint to paint 4 identical dressers.<br \/>\nSo,<br \/>\nThe paint used to paint each dresser = \\(\\frac{3}{4}\\) \u00f7 4<br \/>\n= \\(\\frac{3}{4}\\) \u00d7 \\(\\frac{1}{4}\\)<br \/>\n= \\(\\frac{3}{16}\\) gallon<br \/>\nSo,<br \/>\nThe amount of paint used to paint the 7 identical dressers = \\(\\frac{The paint used to paint each dresser}{1}\\) \u00d7 7<br \/>\n= \\(\\frac{3}{16}\\) \u00d7 \\(\\frac{7}{1}\\)<br \/>\n= \\(\\frac{3 \u00d7 7}{16 \u00d7 1}\\)<br \/>\n= \\(\\frac{21}{16}\\) gallon<br \/>\nHence, from the above,<br \/>\nWe can conclude that the paint used to paint 7 identical dressers is: \\(\\frac{21}{16}\\) gallon<\/p>\n<p>Question 4.<br \/>\nAn airplane travels 125 miles in \\(\\frac{1}{4}\\) hour. It travels the same number of miles each hour. How many miles does the plane travel in 5 hours?<br \/>\nAnswer: The number of miles the plane travel in 5 hours is: 2,500 miles<\/p>\n<p>Explanation:<br \/>\nIt is given that an airplane travels 125 miles in \\(\\frac{1}{4}\\) hour<br \/>\nSo,<br \/>\nThe number of miles traveled by plane in 1 hour = 125 \u00f7 \\(\\frac{1}{4}\\)<br \/>\n= 125 \u00d7 \\(\\frac{4}{1}\\)<br \/>\n= 125 \u00d7 4<br \/>\n= 500 miles<br \/>\nSo,<br \/>\nThe number of miles traveled by plane in 5 hours = ( The number of miles traveled by plane in 1 hour ) \u00d7 5<br \/>\n= 500 \u00d7 5<br \/>\n= 2,500 miles<br \/>\nHence, from the above,<br \/>\nWe can conclude that the number of miles traveled by plane in 5 hours is: 2,500 miles<\/p>\n<p>Question 5.<br \/>\nYou make bows for gifts using \\(\\frac{2}{3}\\) yard of ribbon for each bow. You have 4 feet of red ribbon and 5 feet of green ribbon. How many bows can you make?<br \/>\nAnswer: The number of bows you can make is: 2 bows<\/p>\n<p>Explanation:<br \/>\nIt is given that you make bows for gifts using \\(\\frac{2}{3}\\) yard of ribbon for each bow.<br \/>\nIt is also given that you have 4 feet of red ribbon and 5 feet of green ribbon<br \/>\nSo,<br \/>\nThe total length of ribbon = 5 + 4 = 9 feet<br \/>\nwe know that,<br \/>\n1 foot = \\(\\frac{1}{3}\\) yards<br \/>\nSo,<br \/>\n9 feet = 9 \u00d7 \\(\\frac{1}{3}\\) yards<br \/>\n= \\(\\frac{9}{1}\\) yards \u00d7 \\(\\frac{1}{3}\\) yards<br \/>\n= 3 yards<br \/>\nSo,<br \/>\nThe number of bows you can make = \\(\\frac{2}{3}\\) yards \u00d7 3<br \/>\n= 2 bows<br \/>\nHence, from the above,<br \/>\nWe can conclude that the number of bows we can make is: 2<\/p>\n<p>Question 6.<br \/>\nA landscaper buys 1 gallon of plant fertilizer. He uses \\(\\frac{1}{5}\\) of the fertilizer, and then divides the rest into 3 smaller bottles. How many gallons does he put into each bottle?<br \/>\nAnswer: The number of gallons he put into each bottle is: \\(\\frac{4}{15}\\)<\/p>\n<p>Explanation:<br \/>\nIt is given that a landscaper buys 1 gallon of plant fertilizer and he uses \\(\\frac{1}{5}\\) of the fertilizer<br \/>\nSo,<br \/>\nThe remaining amount of the fertilizer = 1 &#8211; \\(\\frac{1}{5}\\)<br \/>\n= \\(\\frac{4}{5}\\) gallons<br \/>\nIt is also given that he divided the remaining amount of fertilizer into 3 smaller bottles.<br \/>\nSo,<br \/>\nThe amount of fertilizer put into each bottle = \\(\\frac{The remaining amount of the fertilizer}{The total number of bottles}\\)<br \/>\n= \\(\\frac{4}{5}\\) \u00f7 3<br \/>\n= \\(\\frac{4}{5}\\) \u00d7 \\(\\frac{1}{3}\\)<br \/>\n= \\(\\frac{4 \u00d7 1}{5 \u00d7 3}\\)<br \/>\n= \\(\\frac{4}{15}\\) gallons<br \/>\nhence, from the above,<br \/>\nWe can conclude that the amount of remaining fertilizer put into each bottle is: \\(\\frac{4}{15}\\) gallons<\/p>\n<p><strong>Think and Grow: Modeling Real Life<\/strong><\/p>\n<p><strong>Example<\/strong><br \/>\nA sponsor donates $0.10 to a charity for every \\(\\frac{1}{4}\\) kilometer of the triathlon an athlete completes. The athlete completes the entire triathlon. How much money does the sponsor donate?<br \/>\n<img loading=\"lazy\" class=\"alignnone size-full wp-image-15224\" src=\"https:\/\/ccssmathanswers.com\/wp-content\/uploads\/2020\/12\/Big-Ideas-Math-Answers-5th-Grade-Chapter-10-Divide-Fractions-70.png\" alt=\"Big Ideas Math Answers 5th Grade Chapter 10 Divide Fractions 70\" width=\"188\" height=\"161\" \/><br \/>\nThink: What do you know? What do you need to find? How will you solve?<br \/>\nWrite and solve an equation.<br \/>\nAdd 1.9, 90, and 21.1 to find how many kilometers the athlete completes.<br \/>\nDivide the sum by \\(\\frac{1}{4}\\) to find how many \\(\\frac{1}{4}\\) kilometers the athlete completes.<br \/>\nMultiply the quotient by $0.10 to find how much money the sponsor donates.<br \/>\n<img loading=\"lazy\" class=\"alignnone size-full wp-image-15225\" src=\"https:\/\/ccssmathanswers.com\/wp-content\/uploads\/2020\/12\/Big-Ideas-Math-Answers-5th-Grade-Chapter-10-Divide-Fractions-71.png\" alt=\"Big Ideas Math Answers 5th Grade Chapter 10 Divide Fractions 71\" width=\"593\" height=\"81\" srcset=\"https:\/\/bigideasmathanswers.com\/wp-content\/uploads\/2020\/12\/Big-Ideas-Math-Answers-5th-Grade-Chapter-10-Divide-Fractions-71.png 593w, https:\/\/bigideasmathanswers.com\/wp-content\/uploads\/2020\/12\/Big-Ideas-Math-Answers-5th-Grade-Chapter-10-Divide-Fractions-71-300x41.png 300w\" sizes=\"(max-width: 593px) 100vw, 593px\" \/><br \/>\nLet m represent the total amount of money donated.<br \/>\n<img loading=\"lazy\" class=\"alignnone size-full wp-image-34655\" src=\"https:\/\/ccssmathanswers.com\/wp-content\/uploads\/2020\/12\/Big-Ideas-Math-Answers-Grade-5-Chapter-10-56.jpg\" alt=\"\" width=\"585\" height=\"181\" srcset=\"https:\/\/bigideasmathanswers.com\/wp-content\/uploads\/2020\/12\/Big-Ideas-Math-Answers-Grade-5-Chapter-10-56.jpg 585w, https:\/\/bigideasmathanswers.com\/wp-content\/uploads\/2020\/12\/Big-Ideas-Math-Answers-Grade-5-Chapter-10-56-300x93.jpg 300w\" sizes=\"(max-width: 585px) 100vw, 585px\" \/><\/p>\n<p><strong>Show and Grow<\/strong><\/p>\n<p>Question 7.<br \/>\nYou earn $5 for every \\(\\frac{1}{2}\\) hour you do yard work. How much money do you earn in 1 week?<br \/>\n<img loading=\"lazy\" class=\"alignnone size-full wp-image-15227\" src=\"https:\/\/ccssmathanswers.com\/wp-content\/uploads\/2020\/12\/Big-Ideas-Math-Answers-5th-Grade-Chapter-10-Divide-Fractions-73.png\" alt=\"Big Ideas Math Answers 5th Grade Chapter 10 Divide Fractions 73\" width=\"267\" height=\"179\" \/><br \/>\nAnswer: The amount you earn in 1 week is: $700<\/p>\n<p>Explanation:<br \/>\nThe given table is:<br \/>\n<img loading=\"lazy\" class=\"alignnone size-full wp-image-15227\" src=\"https:\/\/ccssmathanswers.com\/wp-content\/uploads\/2020\/12\/Big-Ideas-Math-Answers-5th-Grade-Chapter-10-Divide-Fractions-73.png\" alt=\"Big Ideas Math Answers 5th Grade Chapter 10 Divide Fractions 73\" width=\"267\" height=\"179\" \/><br \/>\nFrom the above table,<br \/>\nThe total amount of time = 5\\(\\frac{1}{2}\\) + 3 + 1\\(\\frac{1}{2}\\)<br \/>\n= \\(\\frac{11}{2}\\) + 3 + \\(\\frac{3}{2}\\)<br \/>\n= \\(\\frac{11 + 3}{2}\\) + 3<br \/>\n= 7 + 3<br \/>\n= 10 hours<br \/>\nIt is given that you earn $5 for every \\(\\frac{1}{2}\\) hour you do yard work<br \/>\nSo,<br \/>\nThe amount earned in 10 hours in a day = 10 \u00f7\\(\\frac{1}{2}\\) \u00d7 5 ( Since we have the time in hours but the money earned is given in half an hour basis )<br \/>\n= 20 \u00d7 5<br \/>\n= $100<br \/>\nWe know that 1 week = 7 days<br \/>\nSo,<br \/>\nThe amount earned in 1 week = 100 \u00d7 7 = $700<br \/>\nhence, from the above,<br \/>\nWe can conclude that we can earn $700 in a week<\/p>\n<h3><a id=\"Problem_Solving:_Fraction_Division_Homework_&amp;\u00a0_10.5\"><\/a>Problem Solving: Fraction Division Homework &amp;\u00a0 10.5<\/h3>\n<p>Understand the problem. Then make a plan. How will you solve? Explain.<\/p>\n<p>Question 1.<br \/>\nA train travels 75 miles in \\(\\frac{1}{2}\\) hour. How many miles does the train travel in 8 hours?<br \/>\nAnswer: The number of miles the train travel in\u00a0 hours is: 1,200 miles<\/p>\n<p>Explanation:<br \/>\nIt is given that a train travels 75 miles in \\(\\frac{1}{2}\\) hour.<br \/>\nSo,<br \/>\nThe number of miles the train travel in 1 hour = 75 \u00f7 \\(\\frac{1}{2}\\)<br \/>\n= 75 \u00d7 2<br \/>\n= 150 miles<br \/>\nSo,<br \/>\nThe number of miles the train travel in 8 hours = The number of miles traveled by train in 1 hour \u00d7 8<br \/>\n= 150 \u00d7 8<br \/>\n= 1,200 miles<br \/>\nHence, from the above,<br \/>\nWe can conclude that the train travels 1,200 miles in 8 hours.<\/p>\n<p>Question 2.<br \/>\nYou need \\(\\frac{2}{3}\\) yard of fabric to create a headband. You have 12 feet of blue fabric and 4 feet of yellow fabric. How many headbands can you make with all of the fabric?<br \/>\nAnswer: The number of headbands you can make with all of the fabric is: 8 headbands<\/p>\n<p>Explanation:<br \/>\nIt is given that you need \\(\\frac{2}{3}\\) yard of fabric to create a headband.<br \/>\nIt is also given that you have 12 feet of blue fabric and 4 feet of yellow fabric.<br \/>\nSo,<br \/>\nThe total length of the fabric = 12 + 4 = 16 feet<br \/>\nWe know that<br \/>\n1 foot = \\(\\frac{1}{3}\\) yards<br \/>\nSo,<br \/>\n16 feet = \\(\\frac{16}{3}\\) yards<br \/>\nSo,<br \/>\nThe number of headbands you can create with all the fabric = \\(\\frac{The total length of the fabric}{The length of each fabric}\\)<br \/>\n= \\(\\frac{16}{3}\\) \u00f7 \\(\\frac{2}{3}\\)<br \/>\n= \\(\\frac{16}{3}\\) \u00d7 \\(\\frac{3}{2}\\)<br \/>\n= \\(\\frac{16 \u00d7 3}{3 \u00d7 2}\\)<br \/>\n= 8 headbands<br \/>\nHence, from the above,<br \/>\nWe can conclude that we can create 8 headbands with all the fabric.<\/p>\n<p>Question 3.<br \/>\nAn art teacher has 8 gallons of paint. Her class uses \\(\\frac{3}{4}\\) of the paint. The teacher divides the rest of the paint into 4 bottles. How much paint is in each bottle?<br \/>\nAnswer: The amount of paint in each bottle is: \\(\\frac{1}{2}\\)<\/p>\n<p>Explanation:<br \/>\nIt is given that an art teacher has 8 gallons of paint and her class uses \\(\\frac{3}{4}\\) of the paint.<br \/>\nSo,<br \/>\nThe remaining amount of paint = \\(\\frac{1}{4}\\) \u00d7 8<br \/>\n= \\(\\frac{1}{4}\\) \u00d7 \\(\\frac{8}{1}\\)<br \/>\n=\\(\\frac{1 \u00d7 8}{4 \u00d7 1}\\)<br \/>\n= 2 gallons<br \/>\nIt is also given that the remaining amount of the paint divided into 4 bottles by the teacher<br \/>\nSo,<br \/>\nThe amount of paint present in each bottle = 2 \u00f7 4<br \/>\n= \\(\\frac{1}{2}\\) gallons<br \/>\nHence, from the above,<br \/>\nWe can conclude that the amout of paint present in each bottle is: \\(\\frac{1}{2}\\) gallons<\/p>\n<p>Question 4.<br \/>\nYou mix 3\\(\\frac{1}{4}\\) cups of frozen strawberries and 4\\(\\frac{1}{2}\\) cups of frozen blueberries in a bowl. A smoothie requires \\(\\frac{1}{2}\\) cup of your berry mix. How many smoothies can you make?<br \/>\nAnswer: The number of smoothies you can make is:<\/p>\n<p>Explanation:<br \/>\nIt is given that you mix 3\\(\\frac{1}{4}\\) cups of frozen strawberries and 4\\(\\frac{1}{2}\\) cups of frozen blueberries in a bowl.<br \/>\nSo,<br \/>\nThe amount of berry mix = 3\\(\\frac{1}{4}\\) cups of frozen strawberries + 4\\(\\frac{1}{2}\\) cups of frozen blueberries<br \/>\n= 3\\(\\frac{1}{4}\\) + 4\\(\\frac{1}{2}\\)<br \/>\n= \\(\\frac{13}{4}\\) + \\(\\frac{9}{2}\\)<br \/>\nIn addition, equate the denominators<br \/>\nSo,<br \/>\nMultiply \\(\\frac{9}{2}\\) with \\(\\frac{2}{2}\\)<br \/>\nSo,<br \/>\n\\(\\frac{9}{2}\\) = \\(\\frac{18}{4}\\)<br \/>\nSo,<br \/>\nThe amount of berry mix = \\(\\frac{13}{4}\\) + \\(\\frac{18}{4}\\)<br \/>\n= \\(\\frac{31}{4}\\)<br \/>\nNow,<br \/>\nIt is also given that the smoothie requires \\(\\frac{1}{2}\\) cup of your berry mix.<br \/>\nSo,<br \/>\nThe number of smoothies = \\(\\frac{31}{4}\\) \u00f7 \\(\\frac{1}{2}\\)<br \/>\n= \\(\\frac{31}{4}\\) \u00d7 \\(\\frac{2}{1}\\)<br \/>\n= \\(\\frac{31 \u00d7 2}{4 \u00d7 1}\\)<br \/>\n= \\(\\frac{31}{2}\\)<br \/>\nHence, from the above,<br \/>\nWe can conclude that the number of smoothies we can make are: \\(\\frac{31}{2}\\)<\/p>\n<p>Question 5.<br \/>\n<strong>Modeling Real Life<\/strong><br \/>\nA sponsor donates $0.10 for every \\(\\frac{1}{4}\\) dollar donated at the locations shown. How much money does the sponsor donate?<br \/>\n<img loading=\"lazy\" class=\"alignnone size-full wp-image-15228\" src=\"https:\/\/ccssmathanswers.com\/wp-content\/uploads\/2020\/12\/Big-Ideas-Math-Answers-5th-Grade-Chapter-10-Divide-Fractions-74.png\" alt=\"Big Ideas Math Answers 5th Grade Chapter 10 Divide Fractions 74\" width=\"279\" height=\"159\" \/><br \/>\nAnswer: The amount of money the sponsor donates is: $40.4<\/p>\n<p>Explanation:<br \/>\nThe given table is:<br \/>\n<img loading=\"lazy\" class=\"alignnone size-full wp-image-15228\" src=\"https:\/\/ccssmathanswers.com\/wp-content\/uploads\/2020\/12\/Big-Ideas-Math-Answers-5th-Grade-Chapter-10-Divide-Fractions-74.png\" alt=\"Big Ideas Math Answers 5th Grade Chapter 10 Divide Fractions 74\" width=\"279\" height=\"159\" \/><br \/>\nFrom the above table,<br \/>\nThe total amount of money collected = 25.25 + 12.50 + 63.25<br \/>\n= $101<br \/>\nIt is given that a\u00a0sponsor donates $0.10 for every \\(\\frac{1}{4}\\) dollar<br \/>\nSo,<br \/>\nthe total amount of donated = The total amount of money collected \u00f7 \\(\\frac{1}{4}\\) \u00d7 0.10<br \/>\n= 101 \u00f7 \\(\\frac{1}{4}\\) \u00d7 0.10<br \/>\n= 101 \u00d7 4 \u00d7 0.10<br \/>\n= 04 \u00d7 0.10<br \/>\n= $40.4<br \/>\nHence, from the above,<br \/>\nWe can conclude that the amount of money donated by a sponsor is: $40.4<\/p>\n<p>Question 6.<br \/>\n<strong>DIG DEEPER!<\/strong><br \/>\nA nurse earns $16 for every \\(\\frac{1}{2}\\) hour at work. How much money does she earn in 5 days?<br \/>\n<img loading=\"lazy\" class=\"alignnone size-full wp-image-15229\" src=\"https:\/\/ccssmathanswers.com\/wp-content\/uploads\/2020\/12\/Big-Ideas-Math-Answers-5th-Grade-Chapter-10-Divide-Fractions-75.png\" alt=\"Big Ideas Math Answers 5th Grade Chapter 10 Divide Fractions 75\" width=\"281\" height=\"193\" \/><br \/>\nAnswer: The money she earns in 5 days is: $1,280<\/p>\n<p>Explanation:<br \/>\nThe given table is:<br \/>\n<img loading=\"lazy\" class=\"alignnone size-full wp-image-15229\" src=\"https:\/\/ccssmathanswers.com\/wp-content\/uploads\/2020\/12\/Big-Ideas-Math-Answers-5th-Grade-Chapter-10-Divide-Fractions-75.png\" alt=\"Big Ideas Math Answers 5th Grade Chapter 10 Divide Fractions 75\" width=\"281\" height=\"193\" \/><br \/>\nFrom the above table,<br \/>\nThe total amount of time = 6\\(\\frac{3}{4}\\) + 1 + \\(\\frac{1}{4}\\)<br \/>\n= \\(\\frac{27}{4}\\) + 1 + \\(\\frac{1}{4}\\)<br \/>\n= \\(\\frac{27 + 1}{4}\\) + 1<br \/>\n= 7 + 1<br \/>\n= 8 hours<br \/>\nIt is given that a nurse earns $16 for every \\(\\frac{1}{2}\\) hour at work.<br \/>\nSo,<br \/>\nThe money she earned for 1 hour = 16 \u00f7 \\(\\frac{1}{2}\\)<br \/>\n= 16 \u00d7 2 = $32<br \/>\nSo,<br \/>\nThe money earned for 8 hours = The money earned in 1 hour \u00d7 8<br \/>\n= 32 \u00d7 8 = $256<br \/>\nSo,<br \/>\nThe money earned in 5 days = The money earned in 1 day \u00d7 5<br \/>\n= 256 \u00d7 5 = $1,280<br \/>\nhence, from the above,<br \/>\nwe can conclude that she can earn $1,280 in 5 days.<\/p>\n<p><strong>Review &amp; Refresh<\/strong><\/p>\n<p>Find the quotient. Then check your answer.<\/p>\n<p>Question 7.<br \/>\n<img loading=\"lazy\" class=\"alignnone size-full wp-image-15230\" src=\"https:\/\/ccssmathanswers.com\/wp-content\/uploads\/2020\/12\/Big-Ideas-Math-Answers-5th-Grade-Chapter-10-Divide-Fractions-76.png\" alt=\"Big Ideas Math Answers 5th Grade Chapter 10 Divide Fractions 76\" width=\"82\" height=\"42\" \/><br \/>\nAnswer:\u00a0 186 \u00f7 12 = 1 R 4<\/p>\n<p>Explanation:<br \/>\nLet 185.88 be rounded to 186<br \/>\nSo,<br \/>\nBy using the partial quotients method,<br \/>\n186 \u00f7 12 = ( 120 + 36 + 24 ) \u00f7 12<br \/>\n= ( 120 \u00f7 12 ) + ( 36 \u00f7 12 ) + ( 24 \u00f7 12 )<br \/>\n= 10 + 3 + 2<br \/>\n= 17 R 4<br \/>\nHence, 186 \u00f7 12 = 17 R 4<\/p>\n<p>Question 8.<br \/>\n<img loading=\"lazy\" class=\"alignnone size-full wp-image-15231\" src=\"https:\/\/ccssmathanswers.com\/wp-content\/uploads\/2020\/12\/Big-Ideas-Math-Answers-5th-Grade-Chapter-10-Divide-Fractions-77.png\" alt=\"Big Ideas Math Answers 5th Grade Chapter 10 Divide Fractions 77\" width=\"75\" height=\"46\" \/><br \/>\nAnswer: 74 \u00f7 24 = 3 R 2<\/p>\n<p>Explanation:<br \/>\nLet 74.4 be rounded to 74<br \/>\nSo,<br \/>\nBy using the partial quotients method,<br \/>\n74 \u00f7 24 = 72 \u00f7 24<br \/>\n= 3 R 2<br \/>\nHence, 74 \u00f7 24 = 3 R 2<\/p>\n<p>Question 9.<br \/>\n<img loading=\"lazy\" class=\"alignnone size-full wp-image-15232\" src=\"https:\/\/ccssmathanswers.com\/wp-content\/uploads\/2020\/12\/Big-Ideas-Math-Answers-5th-Grade-Chapter-10-Divide-Fractions-78.png\" alt=\"Big Ideas Math Answers 5th Grade Chapter 10 Divide Fractions 78\" width=\"79\" height=\"44\" \/><br \/>\nAnswer: 42 \u00f7 46 = 0.9<\/p>\n<p>Explanation:<br \/>\nLet 42.32 be rounded to 42<br \/>\nSo,<br \/>\nBy using the partial quotients method,<br \/>\n42 \u00f7 46 = 0.9<br \/>\nHence,<br \/>\n42 \u00f7 46 = 0.9<\/p>\n<h3><a id=\"Divide_Fractions_Performance_Task_10\"><\/a>Divide Fractions Performance Task 10<\/h3>\n<p>Your city has a robotics competition. Each team makes a robot that travels through a maze. The time each robot spends in the maze is used to \ufb01nd the team\u2019s score.<br \/>\n1. One-third of the students in your grade participate in the competition. The number of participating students is divided into 12 teams.<br \/>\n<img loading=\"lazy\" class=\"alignnone size-full wp-image-15233\" src=\"https:\/\/ccssmathanswers.com\/wp-content\/uploads\/2020\/12\/Big-Ideas-Math-Answers-5th-Grade-Chapter-10-Divide-Fractions-79.png\" alt=\"Big Ideas Math Answers 5th Grade Chapter 10 Divide Fractions 79\" width=\"216\" height=\"153\" \/><br \/>\na. What fraction of the total number of students in your grade is on each team?<br \/>\nAnswer: The fraction of the total number of students in your grade is: \\(\\frac{1}{36}\\)<\/p>\n<p>Explanation:<br \/>\nIt is given that there are \\(\\frac{1}{3}\\) of the students in your grade are participating in the competition.<br \/>\nIt is also given that the participating students are divided into 12 teams.<br \/>\nSo,<br \/>\nThe fraction of the total number of students in each team = \\(\\frac{The number of participating students}{Th total number of teams}\\)<br \/>\n= \\(\\frac{1}{3}\\) \u00f7 12<br \/>\n= \\(\\frac{1}{3}\\) \u00f7 \\(\\frac{12}{1}\\)<br \/>\n= \\(\\frac{1}{3}\\) \u00d7 \\(\\frac{1}{12}\\)<br \/>\n= \\(\\frac{1 \u00d7 1}{12 \u00d7 3}\\)<br \/>\n= \\(\\frac{1}{36}\\)<br \/>\nHence, from the above,<br \/>\nWe can conclude that the fraction of students that are in each team is: \\(\\frac{1}{36}\\)<\/p>\n<p>b. There are 3 students on each team. How many students are in your grade?<br \/>\nAnswer: The number of students in your grade is: 36<\/p>\n<p>Explanation:<br \/>\nIt is given that the number of students is divided into 12 teams<br \/>\nIt is also given that there are 3 students on each team<br \/>\nSo,<br \/>\nThe total number of students = The number of teams \u00d7 The number of students in each team<br \/>\n= 12 \u00d7 3 = 36 students<br \/>\nHence, from the above,<br \/>\nWe can conclude that there are 36 students in your grade<\/p>\n<p>Question 2.<br \/>\nThe maze for the competition is shown.<br \/>\na. Write the length of the maze in feet.<br \/>\n<img loading=\"lazy\" class=\"alignnone size-full wp-image-15234\" src=\"https:\/\/ccssmathanswers.com\/wp-content\/uploads\/2020\/12\/Big-Ideas-Math-Answers-5th-Grade-Chapter-10-Divide-Fractions-80.png\" alt=\"Big Ideas Math Answers 5th Grade Chapter 10 Divide Fractions 80\" width=\"503\" height=\"131\" srcset=\"https:\/\/bigideasmathanswers.com\/wp-content\/uploads\/2020\/12\/Big-Ideas-Math-Answers-5th-Grade-Chapter-10-Divide-Fractions-80.png 503w, https:\/\/bigideasmathanswers.com\/wp-content\/uploads\/2020\/12\/Big-Ideas-Math-Answers-5th-Grade-Chapter-10-Divide-Fractions-80-300x78.png 300w\" sizes=\"(max-width: 503px) 100vw, 503px\" \/><br \/>\nAnswer:<br \/>\nThe given maze for the competition is:<br \/>\n<img loading=\"lazy\" class=\"alignnone size-full wp-image-15234\" src=\"https:\/\/ccssmathanswers.com\/wp-content\/uploads\/2020\/12\/Big-Ideas-Math-Answers-5th-Grade-Chapter-10-Divide-Fractions-80.png\" alt=\"Big Ideas Math Answers 5th Grade Chapter 10 Divide Fractions 80\" width=\"503\" height=\"131\" srcset=\"https:\/\/bigideasmathanswers.com\/wp-content\/uploads\/2020\/12\/Big-Ideas-Math-Answers-5th-Grade-Chapter-10-Divide-Fractions-80.png 503w, https:\/\/bigideasmathanswers.com\/wp-content\/uploads\/2020\/12\/Big-Ideas-Math-Answers-5th-Grade-Chapter-10-Divide-Fractions-80-300x78.png 300w\" sizes=\"(max-width: 503px) 100vw, 503px\" \/><br \/>\nFrom the above maze,<br \/>\nThe total length of the maze is: 8 feet 6 inches<br \/>\nWe know that,<br \/>\n1 foot = 12 inches<br \/>\nHence,<br \/>\n1 inch = \\(\\frac{1}{12}\\) feet<br \/>\nSo,<br \/>\n6 inches = 6 \u00d7 \\(\\frac{1}{12}\\)<br \/>\n= \\(\\frac{1}{12}\\) \u00d7 \\(\\frac{6}{1}\\)<br \/>\n= \\(\\frac{1}{2}\\) feet<br \/>\nSo,<br \/>\nThe total length of the maze in feet = 8 feet + \\(\\frac{1}{2}\\) feet<br \/>\n= 8.5 feet or 8\\(\\frac{1}{2}\\) feet<\/p>\n<p>b. The length of the maze is divided into 6 equal sections. What is the length of each section of the maze?<br \/>\nAnswer: The length of each section of the maze is: \\(\\frac{17}{12}\\) feet<\/p>\n<p>Explanation:<br \/>\nFrom the above Exercise,<br \/>\nThe total length of the maze in feet is: 8.5 feet or 8\\(\\frac{1}{2}\\) feet<br \/>\nIt is given that the length of the maze is divided into 6 equal sections<br \/>\nSo,<br \/>\nThe length of each section of the maze = 8\\(\\frac{1}{2}\\) \u00f7 6<br \/>\n= 8\\(\\frac{1}{2}\\) \u00f7 \\(\\frac{6}{1}\\)<br \/>\n= 8\\(\\frac{1}{2}\\) \u00d7 \\(\\frac{1}{6}\\)<br \/>\n= \\(\\frac{17}{2}\\) \u00d7 \\(\\frac{1}{6}\\)<br \/>\n= \\(\\frac{17}{12}\\) feet<br \/>\nHence, from the above,<br \/>\nWe can conclude that the length of each section in a maze is: \\(\\frac{17}{12}\\) feet<\/p>\n<p>Question 3.<br \/>\nEach team has 200 seconds to complete the maze. The rules require judges to use the expression (200 &#8211; x) \u00f7 \\(\\frac{1}{5}\\), where x is the total number of seconds, to find a team\u2019s total score.<br \/>\na. Your robot completes the maze in 3 minutes 5 seconds. How many points does your team earn?<br \/>\nAnswer: The number of points your team earn is: 75 points<\/p>\n<p>Explanation:<br \/>\nIt is given that each team has 200 seconds to complete the maze and the rules require judges to use the expression (200 &#8211; x) \u00f7 \\(\\frac{1}{5}\\) where x is the total number of seconds<br \/>\nIt is also given that your robot completes the maze in 3 minutes 5 seconds<br \/>\nWe know that,<br \/>\n1 minute = 60 seconds<br \/>\nSo,<br \/>\nThe time taken by the robot to complete the maze in seconds = ( 3 \u00d7 60 ) + 5<br \/>\n= 185 seconds<br \/>\nSo,<br \/>\nx= 185<br \/>\nSo,<br \/>\n200 &#8211; x = 200 &#8211; 185 = 15<br \/>\nSo,<br \/>\nThe number of points the team earned = ( 200 &#8211; x ) \u00f7 \\(\\frac{1}{5}\\)<br \/>\n= 15 \u00f7 \\(\\frac{1}{5}\\)<br \/>\n= 15 \u00d7 5<br \/>\n= 75 points<br \/>\nHence, from the above,<br \/>\nWe can conclude that the number of points earned by the team is: 75 points<\/p>\n<p>b. Do you think the team with the most points or the fewest points wins? Use an example to justify your answer.<br \/>\nAnswer: The team with the most points wins the competition because<br \/>\nReason:<br \/>\nSuppose team A takes 2 minutes and team B takes 3 minutes to complete the competition<br \/>\nSo,<br \/>\nThe time is taken by team A in seconds = 120 seconds<br \/>\nSo,<br \/>\nx= 120<br \/>\nSo,<br \/>\n200 &#8211; x = 200 &#8211; 120 = 80<br \/>\nNow,<br \/>\nThe time is taken by team B in seconds = 180 seconds<br \/>\nSo,<br \/>\nx= 180<br \/>\nSo,<br \/>\n200 &#8211; x = 200 &#8211; 180 = 20<br \/>\nNow,<br \/>\nThe number of points earned by team A = 80 \u00f7 \\(\\frac{1}{5}\\)<br \/>\n= 400 points<br \/>\nThe number of points earned by team B = 20 \u00f7 \\(\\frac{1}{5}\\)<br \/>\n= 100 points<br \/>\nHence, from the above,<br \/>\nWe can conclude that the team with more points wins the competition<\/p>\n<h3><a id=\"Divide_Fractions_Activity\"><\/a>Divide Fractions Activity<\/h3>\n<p><strong>Fraction Connection: Division<\/strong><\/p>\n<p><strong>Directions:<\/strong><\/p>\n<ol>\n<li>Players take turns rolling three dice.<\/li>\n<li>On your turn, evaluate the expression indicated by your roll and cover the answer.<\/li>\n<li>The first player to get four in a row, horizontally, vertically, or diagonally, wins!<\/li>\n<\/ol>\n<p><img loading=\"lazy\" class=\"alignnone size-full wp-image-15235\" src=\"https:\/\/ccssmathanswers.com\/wp-content\/uploads\/2020\/12\/Big-Ideas-Math-Answers-5th-Grade-Chapter-10-Divide-Fractions-81.png\" alt=\"Big Ideas Math Answers 5th Grade Chapter 10 Divide Fractions 81\" width=\"351\" height=\"362\" srcset=\"https:\/\/bigideasmathanswers.com\/wp-content\/uploads\/2020\/12\/Big-Ideas-Math-Answers-5th-Grade-Chapter-10-Divide-Fractions-81.png 351w, https:\/\/bigideasmathanswers.com\/wp-content\/uploads\/2020\/12\/Big-Ideas-Math-Answers-5th-Grade-Chapter-10-Divide-Fractions-81-291x300.png 291w\" sizes=\"(max-width: 351px) 100vw, 351px\" \/><br \/>\n<img loading=\"lazy\" class=\"alignnone size-full wp-image-15236\" src=\"https:\/\/ccssmathanswers.com\/wp-content\/uploads\/2020\/12\/Big-Ideas-Math-Answers-5th-Grade-Chapter-10-Divide-Fractions-82.png\" alt=\"Big Ideas Math Answers 5th Grade Chapter 10 Divide Fractions 82\" width=\"696\" height=\"533\" srcset=\"https:\/\/bigideasmathanswers.com\/wp-content\/uploads\/2020\/12\/Big-Ideas-Math-Answers-5th-Grade-Chapter-10-Divide-Fractions-82.png 696w, https:\/\/bigideasmathanswers.com\/wp-content\/uploads\/2020\/12\/Big-Ideas-Math-Answers-5th-Grade-Chapter-10-Divide-Fractions-82-300x230.png 300w\" sizes=\"(max-width: 696px) 100vw, 696px\" \/><\/p>\n<h3><a id=\"Divide_Fractions_Chapter_Practice_10\"><\/a>Divide Fractions Chapter Practice 10<\/h3>\n<p><strong>10.1 Interpret Fractions as Division<\/strong><\/p>\n<p>Divide. Use a model to help.<\/p>\n<p>Question 1.<br \/>\n1 \u00f7 2 = ___<br \/>\nAnswer: 1 \u00f7 2 = \\(\\frac{1}{2}\\)<\/p>\n<p>Explanation:<br \/>\nWe know that,<br \/>\na \u00f7 b = \\(\\frac{a}{b}\\)<br \/>\nHence,<br \/>\n1 \u00f7 2 = \\(\\frac{1}{2}\\)<\/p>\n<p>Question 2.<br \/>\n3 \u00f7 10 = __<br \/>\nAnswer: 3 \u00f7 10 = \\(\\frac{3}{10}\\)<\/p>\n<p>Explanation:<br \/>\nWe know that,<br \/>\na \u00f7 b = \\(\\frac{a}{b}\\)<br \/>\nHence,<br \/>\n3 \u00f7 10 = \\(\\frac{3}{10}\\)<\/p>\n<p>Question 3.<br \/>\n4 \u00f7 7 = __<br \/>\nAnswer: 4 \u00f7 7 = \\(\\frac{4}{7}\\)<\/p>\n<p>Explanation:<br \/>\nWe know that,<br \/>\na \u00f7 b = \\(\\frac{a}{b}\\)<br \/>\nHence,<br \/>\n4 \u00f7 7 = \\(\\frac{4}{7}\\)<\/p>\n<p>Question 4.<br \/>\n11 \u00f7 15 = ___<br \/>\nAnswer: 11 \u00f7 15 = \\(\\frac{11}{15}\\)<\/p>\n<p>Explanation:<br \/>\nWe know that,<br \/>\na \u00f7 b = \\(\\frac{a}{b}\\)<br \/>\nHence,<br \/>\n11 \u00f7 15 = \\(\\frac{11}{15}\\)<\/p>\n<p>Question 5.<br \/>\n8 \u00f7 9 = ___<br \/>\nAnswer: 8 \u00f7 9 = \\(\\frac{8}{9}\\)<\/p>\n<p>Explanation:<br \/>\nWe know that,<br \/>\na \u00f7 b = \\(\\frac{a}{b}\\)<br \/>\nHence,<br \/>\n8 \u00f7 9 = \\(\\frac{8}{9}\\)<\/p>\n<p>Question 6.<br \/>\n13 \u00f7 20 = ___<br \/>\nAnswer: 13 \u00f7 20 = \\(\\frac{13}{20}\\)<\/p>\n<p>Explanation:<br \/>\nWe know that,<br \/>\na \u00f7 b = \\(\\frac{a}{b}\\)<br \/>\nHence,<br \/>\n13 \u00f7 20 = \\(\\frac{13}{20}\\)<\/p>\n<p>Question 7.<br \/>\n<strong>Modeling Real Life<\/strong><br \/>\nNine friends equally share 12 apples. What fraction of an apple does each friend get?<br \/>\nAnswer: The fraction of an apple each friend get is: \\(\\frac{9}{12}\\)<\/p>\n<p>Explanation:<br \/>\nIt is given that nine friends equally share 12 apples.<br \/>\nSo,<br \/>\nThe fraction of an apple each friend get = \\(\\frac{The number of friends}{The number of apples}\\)<br \/>\n= \\(\\frac{9}{12}\\)<br \/>\nHence, from the above,<br \/>\nWe can conclude that the fraction of an apple each friend get is: \\(\\frac{9}{12}\\)<\/p>\n<p><strong>10.2 Mixed Numbers as Quotients<\/strong><\/p>\n<p>Divide. Use a model to help<\/p>\n<p>Question 8.<br \/>\n8 \u00f7 3 = ___<\/p>\n<p>Answer: 8 \u00f7 3 = 2\\(\\frac{2}{3}\\)<\/p>\n<p>Explanation:<br \/>\nWe know that,<br \/>\na \u00f7 b = \\(\\frac{a}{b}\\)<br \/>\na\\(\\frac{b}{c}\\) = \\(\\frac{ac + b}{c}\\)<br \/>\n\\(\\frac{a}{b}\\) = Remainder\\(\\frac{Quotient}{Divisor}\\)<br \/>\nSo,<br \/>\n8 \u00f7 3 = \\(\\frac{8}{3}\\)<br \/>\nBy using the partial quotients method,<br \/>\n8 \u00f7 3 = 6 \u00f7 3<br \/>\n= 2 R 2<br \/>\nHence,<br \/>\n8 \u00f7 3 = 2\\(\\frac{2}{3}\\)<\/p>\n<p>Question 9.<br \/>\n6 \u00f7 5 = ___<br \/>\nAnswer: 6 \u00f7 5 = 1\\(\\frac{1}{5}\\)<\/p>\n<p>Explanation:<br \/>\nWe know that,<br \/>\na \u00f7 b = \\(\\frac{a}{b}\\)<br \/>\na\\(\\frac{b}{c}\\) = \\(\\frac{ac + b}{c}\\)<br \/>\n\\(\\frac{a}{b}\\) = Remainder\\(\\frac{Quotient}{Divisor}\\)<br \/>\nSo,<br \/>\n6 \u00f7 5 = \\(\\frac{6}{5}\\)<br \/>\nBy using the partial quotients method,<br \/>\n6 \u00f7 5 = 5 \u00f7 5<br \/>\n= 1 R 1<br \/>\nHence,<br \/>\n6 \u00f7 5 = 1\\(\\frac{1}{5}\\)<\/p>\n<p><span style=\"font-size: 16px;\">Question 10.<\/span><\/p>\n<p>10 \u00f7 4 = ___<br \/>\nAnswer: 10 \u00f7 4 = 2\\(\\frac{2}{4}\\)<\/p>\n<p>Explanation:<br \/>\nWe know that,<br \/>\na \u00f7 b = \\(\\frac{a}{b}\\)<br \/>\na\\(\\frac{b}{c}\\) = \\(\\frac{ac + b}{c}\\)<br \/>\n\\(\\frac{a}{b}\\) = Remainder\\(\\frac{Quotient}{Divisor}\\)<br \/>\nSo,<br \/>\n10 \u00f7 4 = \\(\\frac{10}{4}\\)<br \/>\nBy using the partial quotients method,<br \/>\n10 \u00f7 4 = 8 \u00f7 4<br \/>\n= 2 R 2<br \/>\nHence,<br \/>\n10 \u00f7 4 = 2\\(\\frac{2}{4}\\)<\/p>\n<p><span style=\"font-size: 16px;\">Question 11.<\/span><\/p>\n<p>20 \u00f7 11 = __<br \/>\nAnswer: 20 \u00f7 11 = 1\\(\\frac{9}{11}\\)<\/p>\n<p>Explanation:<br \/>\nWe know that,<br \/>\na \u00f7 b = \\(\\frac{a}{b}\\)<br \/>\na\\(\\frac{b}{c}\\) = \\(\\frac{ac + b}{c}\\)<br \/>\n\\(\\frac{a}{b}\\) = Remainder\\(\\frac{Quotient}{Divisor}\\)<br \/>\nSo,<br \/>\n20 \u00f7 11 = \\(\\frac{20}{11}\\)<br \/>\nBy using the partial quotients method,<br \/>\n20 \u00f7 11 = 11 \u00f7 11<br \/>\n= 1 R 9<br \/>\nHence,<br \/>\n20 \u00f7 11 = 1\\(\\frac{9}{11}\\)<\/p>\n<p><span style=\"font-size: 16px;\">Question 12.<\/span><\/p>\n<p>25 \u00f7 2 = ___<br \/>\nAnswer: 25 \u00f7 2 = 12\\(\\frac{1}{2}\\)<\/p>\n<p>Explanation:<br \/>\nWe know that,<br \/>\na \u00f7 b = \\(\\frac{a}{b}\\)<br \/>\na\\(\\frac{b}{c}\\) = \\(\\frac{ac + b}{c}\\)<br \/>\n\\(\\frac{a}{b}\\) = Remainder\\(\\frac{Quotient}{Divisor}\\)<br \/>\nSo,<br \/>\n25 \u00f7 2 = \\(\\frac{25}{2}\\)<br \/>\nBy using the partial quotients method,<br \/>\n25 \u00f7 2 = 24 \u00f7 2<br \/>\n= 12 R 1<br \/>\nHence,<br \/>\n25 \u00f7 2 = 12\\(\\frac{1}{2}\\)<\/p>\n<p><span style=\"font-size: 16px;\">Question 13.<\/span><\/p>\n<p>64 \u00f7 9 = ___<br \/>\nAnswer: 64 \u00f7 9 = 7\\(\\frac{1}{9}\\)<\/p>\n<p>Explanation:<br \/>\nWe know that,<br \/>\na \u00f7 b = \\(\\frac{a}{b}\\)<br \/>\na\\(\\frac{b}{c}\\) = \\(\\frac{ac + b}{c}\\)<br \/>\n\\(\\frac{a}{b}\\) = Remainder\\(\\frac{Quotient}{Divisor}\\)<br \/>\nSo,<br \/>\n64 \u00f7 9 = \\(\\frac{64}{9}\\)<br \/>\nBy using the partial quotients method,<br \/>\n64 \u00f7 9 = 63 \u00f7 9<br \/>\n= 7 R 1<br \/>\nHence,<br \/>\n64 \u00f7 9 = 7\\(\\frac{1}{9}\\)<\/p>\n<p><strong style=\"font-size: 16px;\">10.3 Divide Whole Numbers by Unit Fractions<\/strong><\/p>\n<p>Divide. Use a model to help.<\/p>\n<p>Question 14.<br \/>\n<img loading=\"lazy\" class=\"alignnone size-full wp-image-15238\" src=\"https:\/\/ccssmathanswers.com\/wp-content\/uploads\/2020\/12\/Big-Ideas-Math-Answers-Grade-5-Chapter-10-Divide-Fractions-83.png\" alt=\"Big Ideas Math Answers Grade 5 Chapter 10 Divide Fractions 83\" width=\"116\" height=\"57\" \/><br \/>\nAnswer: 4 \u00f7 \\(\\frac{1}{2}\\) = 8<\/p>\n<p>Explanation:<br \/>\nThe given numbers are: 4 and \\(\\frac{1}{2}\\)<br \/>\nWe know that,<br \/>\na \u00f7 \\(\\frac{a}{b}\\) = a \u00d7 \\(\\frac{b}{a}\\)<br \/>\na= \\(\\frac{a}{1}\\)<br \/>\nSo,<br \/>\n4 \u00f7 \\(\\frac{1}{2}\\)\u00a0 = 4 \u00d7 \\(\\frac{2}{1}\\)<br \/>\n= \\(\\frac{4}{1}\\) \u00d7 \\(\\frac{2}{1}\\)<br \/>\n= \\(\\frac{ 2 \u00d7 4}{1 \u00d7 1}\\)<br \/>\n= 8<br \/>\nHence,<br \/>\n4\u00f7 \\(\\frac{1}{2}\\) = 8<\/p>\n<p>Question 15.<br \/>\n<img loading=\"lazy\" class=\"alignnone size-full wp-image-15239\" src=\"https:\/\/ccssmathanswers.com\/wp-content\/uploads\/2020\/12\/Big-Ideas-Math-Answers-Grade-5-Chapter-10-Divide-Fractions-84.png\" alt=\"Big Ideas Math Answers Grade 5 Chapter 10 Divide Fractions 84\" width=\"118\" height=\"65\" \/><br \/>\nAnswer: 6 \u00f7 \\(\\frac{1}{5}\\) = 30<\/p>\n<p>Explanation:<br \/>\nThe given numbers are: 6 and \\(\\frac{1}{5}\\)<br \/>\nWe know that,<br \/>\na \u00f7 \\(\\frac{a}{b}\\) = a \u00d7 \\(\\frac{b}{a}\\)<br \/>\na= \\(\\frac{a}{1}\\)<br \/>\nSo,<br \/>\n6 \u00f7 \\(\\frac{1}{5}\\)\u00a0 = 6 \u00d7 \\(\\frac{5}{1}\\)<br \/>\n= \\(\\frac{6}{1}\\) \u00d7 \\(\\frac{5}{1}\\)<br \/>\n= \\(\\frac{ 6 \u00d7 5}{1 \u00d7 1}\\)<br \/>\n= 30<br \/>\nHence,<br \/>\n6\u00f7 \\(\\frac{1}{5}\\) = 30<\/p>\n<p>Question 16.<br \/>\n<img loading=\"lazy\" class=\"alignnone size-full wp-image-15240\" src=\"https:\/\/ccssmathanswers.com\/wp-content\/uploads\/2020\/12\/Big-Ideas-Math-Answers-Grade-5-Chapter-10-Divide-Fractions-85.png\" alt=\"Big Ideas Math Answers Grade 5 Chapter 10 Divide Fractions 85\" width=\"126\" height=\"69\" \/><br \/>\nAnswer: 7 \u00f7 \\(\\frac{1}{4}\\) = 28<\/p>\n<p>Explanation:<br \/>\nThe given numbers are: 7 and \\(\\frac{1}{4}\\)<br \/>\nWe know that,<br \/>\na \u00f7 \\(\\frac{a}{b}\\) = a \u00d7 \\(\\frac{b}{a}\\)<br \/>\na= \\(\\frac{a}{1}\\)<br \/>\nSo,<br \/>\n7 \u00f7 \\(\\frac{1}{4}\\)\u00a0 = 7 \u00d7 \\(\\frac{4}{1}\\)<br \/>\n= \\(\\frac{7}{1}\\) \u00d7 \\(\\frac{4}{1}\\)<br \/>\n= \\(\\frac{ 7 \u00d7 4}{1 \u00d7 1}\\)<br \/>\n= 28<br \/>\nHence,<br \/>\n7\u00f7 \\(\\frac{1}{4}\\) = 36<\/p>\n<p>Question 17.<br \/>\n<img loading=\"lazy\" class=\"alignnone size-full wp-image-15241\" src=\"https:\/\/ccssmathanswers.com\/wp-content\/uploads\/2020\/12\/Big-Ideas-Math-Answers-Grade-5-Chapter-10-Divide-Fractions-86.png\" alt=\"Big Ideas Math Answers Grade 5 Chapter 10 Divide Fractions 86\" width=\"118\" height=\"61\" \/><br \/>\nAnswer: 8 \u00f7 \\(\\frac{1}{3}\\) = 24<\/p>\n<p>Explanation:<br \/>\nThe given numbers are: 8 and \\(\\frac{1}{3}\\)<br \/>\nWe know that,<br \/>\na \u00f7 \\(\\frac{a}{b}\\) = a \u00d7 \\(\\frac{b}{a}\\)<br \/>\na= \\(\\frac{a}{1}\\)<br \/>\nSo,<br \/>\n8 \u00f7 \\(\\frac{1}{3}\\)\u00a0 = 8 \u00d7 \\(\\frac{3}{1}\\)<br \/>\n= \\(\\frac{8}{1}\\) \u00d7 \\(\\frac{3}{1}\\)<br \/>\n= \\(\\frac{ 8 \u00d7 3}{1 \u00d7 1}\\)<br \/>\n= 24<br \/>\nHence,<br \/>\n8\u00f7 \\(\\frac{1}{3}\\) = 24<\/p>\n<p>Question 18.<br \/>\n<img loading=\"lazy\" class=\"alignnone size-full wp-image-15242\" src=\"https:\/\/ccssmathanswers.com\/wp-content\/uploads\/2020\/12\/Big-Ideas-Math-Answers-Grade-5-Chapter-10-Divide-Fractions-87.png\" alt=\"Big Ideas Math Answers Grade 5 Chapter 10 Divide Fractions 87\" width=\"119\" height=\"61\" \/><br \/>\nAnswer: 9 \u00f7 \\(\\frac{1}{2}\\) = 18<\/p>\n<p>Explanation:<br \/>\nThe given numbers are: 9 and \\(\\frac{1}{2}\\)<br \/>\nWe know that,<br \/>\na \u00f7 \\(\\frac{a}{b}\\) = a \u00d7 \\(\\frac{b}{a}\\)<br \/>\na= \\(\\frac{a}{1}\\)<br \/>\nSo,<br \/>\n9 \u00f7 \\(\\frac{1}{2}\\)\u00a0 = 9 \u00d7 \\(\\frac{2}{1}\\)<br \/>\n= \\(\\frac{9}{1}\\) \u00d7 \\(\\frac{2}{1}\\)<br \/>\n= \\(\\frac{ 9 \u00d7 2}{1 \u00d7 1}\\)<br \/>\n= 18<br \/>\nHence,<br \/>\n9\u00f7 \\(\\frac{1}{2}\\) = 18<\/p>\n<p>Question 19.<br \/>\n<img loading=\"lazy\" class=\"alignnone size-full wp-image-15243\" src=\"https:\/\/ccssmathanswers.com\/wp-content\/uploads\/2020\/12\/Big-Ideas-Math-Answers-Grade-5-Chapter-10-Divide-Fractions-88.png\" alt=\"Big Ideas Math Answers Grade 5 Chapter 10 Divide Fractions 88\" width=\"124\" height=\"59\" \/><br \/>\nAnswer: 2 \u00f7 \\(\\frac{1}{10}\\) = 20<\/p>\n<p>Explanation:<br \/>\nThe given numbers are: 2 and \\(\\frac{1}{10}\\)<br \/>\nWe know that,<br \/>\na \u00f7 \\(\\frac{a}{b}\\) = a \u00d7 \\(\\frac{b}{a}\\)<br \/>\na= \\(\\frac{a}{1}\\)<br \/>\nSo,<br \/>\n2 \u00f7 \\(\\frac{1}{10}\\)\u00a0 = 2 \u00d7 \\(\\frac{10}{1}\\)<br \/>\n= \\(\\frac{2}{1}\\) \u00d7 \\(\\frac{10}{1}\\)<br \/>\n= \\(\\frac{ 2 \u00d7 10}{1 \u00d7 1}\\)<br \/>\n= 20<br \/>\nHence,<br \/>\n2\u00f7 \\(\\frac{1}{10}\\) = 20<\/p>\n<p><strong>10.4 Divide Unit Fractions by Whole Numbers<\/strong><\/p>\n<p>Divide. Use a model to help.<\/p>\n<p>Question 20.<br \/>\n<img loading=\"lazy\" class=\"alignnone size-full wp-image-15244\" src=\"https:\/\/ccssmathanswers.com\/wp-content\/uploads\/2020\/12\/Big-Ideas-Math-Answers-Grade-5-Chapter-10-Divide-Fractions-89.png\" alt=\"Big Ideas Math Answers Grade 5 Chapter 10 Divide Fractions 89\" width=\"126\" height=\"51\" \/><br \/>\nAnswer: \\(\\frac{1}{7}\\) \u00f7 2 = \\(\\frac{1}{14}\\)<\/p>\n<p>Explanation:<br \/>\nThe given numbers are: \\(\\frac{1}{7}\\) and 2<br \/>\nWe know that,<br \/>\n\\(\\frac{a}{b}\\) \u00f7 a\u00a0 = \\(\\frac{a}{b}\\) \u00d7 \\(\\frac{1}{a}\\)<br \/>\na= \\(\\frac{a}{1}\\)<br \/>\nSo,<br \/>\n\\(\\frac{1}{7}\\) \u00f7 2<br \/>\n= \\(\\frac{1}{7}\\) \u00d7 \\(\\frac{1}{2}\\)<br \/>\n= \\(\\frac{ 1 \u00d7 1}{7 \u00d7 2}\\)<br \/>\n= \\(\\frac{1}{14}\\)<br \/>\nHence,<br \/>\n\\(\\frac{1}{7}\\) \u00f7 2 = \\(\\frac{1}{14}\\)<\/p>\n<p>Question 21.<br \/>\n<img loading=\"lazy\" class=\"alignnone size-full wp-image-15245\" src=\"https:\/\/ccssmathanswers.com\/wp-content\/uploads\/2020\/12\/Big-Ideas-Math-Answers-Grade-5-Chapter-10-Divide-Fractions-90.png\" alt=\"Big Ideas Math Answers Grade 5 Chapter 10 Divide Fractions 90\" width=\"120\" height=\"61\" \/><br \/>\nAnswer: \\(\\frac{1}{2}\\) \u00f7 9 = \\(\\frac{1}{18}\\)<\/p>\n<p>Explanation:<br \/>\nThe given numbers are: \\(\\frac{1}{2}\\) and 9<br \/>\nWe know that,<br \/>\n\\(\\frac{a}{b}\\) \u00f7 a\u00a0 = \\(\\frac{a}{b}\\) \u00d7 \\(\\frac{1}{a}\\)<br \/>\na= \\(\\frac{a}{1}\\)<br \/>\nSo,<br \/>\n\\(\\frac{1}{2}\\) \u00f7 9<br \/>\n= \\(\\frac{1}{2}\\) \u00d7 \\(\\frac{1}{9}\\)<br \/>\n= \\(\\frac{ 1 \u00d7 1}{2 \u00d7 9}\\)<br \/>\n= \\(\\frac{1}{18}\\)<br \/>\nHence,<br \/>\n\\(\\frac{1}{2}\\) \u00f7 9 = \\(\\frac{1}{18}\\)<\/p>\n<p>Question 22.<br \/>\n<img loading=\"lazy\" class=\"alignnone size-full wp-image-15246\" src=\"https:\/\/ccssmathanswers.com\/wp-content\/uploads\/2020\/12\/Big-Ideas-Math-Solutions-Grade-5-Chapter-10-Divide-Fractions-91.png\" alt=\"Big Ideas Math Solutions Grade 5 Chapter 10 Divide Fractions 91\" width=\"121\" height=\"66\" \/><br \/>\nAnswer: \\(\\frac{1}{3}\\) \u00f7 7 = \\(\\frac{1}{21}\\)<\/p>\n<p>Explanation:<br \/>\nThe given numbers are: \\(\\frac{1}{3}\\) and 7<br \/>\nWe know that,<br \/>\n\\(\\frac{a}{b}\\) \u00f7 a\u00a0 = \\(\\frac{a}{b}\\) \u00d7 \\(\\frac{1}{a}\\)<br \/>\na= \\(\\frac{a}{1}\\)<br \/>\nSo,<br \/>\n\\(\\frac{1}{3}\\) \u00f7 7<br \/>\n= \\(\\frac{1}{3}\\) \u00d7 \\(\\frac{1}{7}\\)<br \/>\n= \\(\\frac{ 1 \u00d7 1}{7 \u00d7 3}\\)<br \/>\n= \\(\\frac{1}{21}\\)<br \/>\nHence,<br \/>\n\\(\\frac{1}{3}\\) \u00f7 7 = \\(\\frac{1}{21}\\)<\/p>\n<p>Question 23.<br \/>\n<img loading=\"lazy\" class=\"alignnone size-full wp-image-15247\" src=\"https:\/\/ccssmathanswers.com\/wp-content\/uploads\/2020\/12\/Big-Ideas-Math-Solutions-Grade-5-Chapter-10-Divide-Fractions-92.png\" alt=\"Big Ideas Math Solutions Grade 5 Chapter 10 Divide Fractions 92\" width=\"126\" height=\"63\" \/><br \/>\nAnswer: \\(\\frac{1}{6}\\) \u00f7 5 = \\(\\frac{1}{30}\\)<\/p>\n<p>Explanation:<br \/>\nThe given numbers are: \\(\\frac{1}{6}\\) and 5<br \/>\nWe know that,<br \/>\n\\(\\frac{a}{b}\\) \u00f7 a\u00a0 = \\(\\frac{a}{b}\\) \u00d7 \\(\\frac{1}{a}\\)<br \/>\na= \\(\\frac{a}{1}\\)<br \/>\nSo,<br \/>\n\\(\\frac{1}{6}\\) \u00f7 5<br \/>\n= \\(\\frac{1}{6}\\) \u00d7 \\(\\frac{1}{5}\\)<br \/>\n= \\(\\frac{ 1 \u00d7 1}{6 \u00d7 5}\\)<br \/>\n= \\(\\frac{1}{30}\\)<br \/>\nHence,<br \/>\n\\(\\frac{1}{6}\\) \u00f7 5 = \\(\\frac{1}{30}\\)<\/p>\n<p>Question 24.<br \/>\n<img loading=\"lazy\" class=\"alignnone size-full wp-image-15248\" src=\"https:\/\/ccssmathanswers.com\/wp-content\/uploads\/2020\/12\/Big-Ideas-Math-Solutions-Grade-5-Chapter-10-Divide-Fractions-93.png\" alt=\"Big Ideas Math Solutions Grade 5 Chapter 10 Divide Fractions 93\" width=\"115\" height=\"56\" \/><br \/>\nAnswer: \\(\\frac{1}{7}\\) \u00f7 3 = \\(\\frac{1}{21}\\)<\/p>\n<p>Explanation:<br \/>\nThe given numbers are: \\(\\frac{1}{7}\\) and 3<br \/>\nWe know that,<br \/>\n\\(\\frac{a}{b}\\) \u00f7 a\u00a0 = \\(\\frac{a}{b}\\) \u00d7 \\(\\frac{1}{a}\\)<br \/>\na= \\(\\frac{a}{1}\\)<br \/>\nSo,<br \/>\n\\(\\frac{1}{7}\\) \u00f7 3<br \/>\n= \\(\\frac{1}{7}\\) \u00d7 \\(\\frac{1}{3}\\)<br \/>\n= \\(\\frac{ 1 \u00d7 1}{7 \u00d7 3}\\)<br \/>\n= \\(\\frac{1}{21}\\)<br \/>\nHence,<br \/>\n\\(\\frac{1}{7}\\) \u00f7 3 = \\(\\frac{1}{21}\\)<\/p>\n<p>Question 25.<br \/>\n<img loading=\"lazy\" class=\"alignnone size-full wp-image-15249\" src=\"https:\/\/ccssmathanswers.com\/wp-content\/uploads\/2020\/12\/Big-Ideas-Math-Solutions-Grade-5-Chapter-10-Divide-Fractions-94.png\" alt=\"Big Ideas Math Solutions Grade 5 Chapter 10 Divide Fractions 94\" width=\"120\" height=\"64\" \/><\/p>\n<p>Answer: \\(\\frac{1}{8}\\) \u00f7 4 = \\(\\frac{1}{32}\\)<\/p>\n<p>Explanation:<br \/>\nThe given numbers are: \\(\\frac{1}{8}\\) and 4<br \/>\nWe know that,<br \/>\n\\(\\frac{a}{b}\\) \u00f7 a\u00a0 = \\(\\frac{a}{b}\\) \u00d7 \\(\\frac{1}{a}\\)<br \/>\na= \\(\\frac{a}{1}\\)<br \/>\nSo,<br \/>\n\\(\\frac{1}{8}\\) \u00f7 4<br \/>\n= \\(\\frac{1}{8}\\) \u00d7 \\(\\frac{1}{4}\\)<br \/>\n= \\(\\frac{ 1 \u00d7 1}{8 \u00d7 4}\\)<br \/>\n= \\(\\frac{1}{32}\\)<br \/>\nHence,<br \/>\n\\(\\frac{1}{8}\\) \u00f7 4 = \\(\\frac{1}{32}\\)<\/p>\n<p><strong>10.5 Problem Solving: Fraction Division<\/strong><\/p>\n<p>Question 26.<br \/>\nA mechanic buys 1 gallon of oil. She uses \\(\\frac{1}{6}\\) of the oil, and then divides the rest into 4 smaller bottles. How much does she put into each bottle?<br \/>\n<img loading=\"lazy\" class=\"alignnone size-full wp-image-15250\" src=\"https:\/\/ccssmathanswers.com\/wp-content\/uploads\/2020\/12\/Big-Ideas-Math-Solutions-Grade-5-Chapter-10-Divide-Fractions-95.png\" alt=\"Big Ideas Math Solutions Grade 5 Chapter 10 Divide Fractions 95\" width=\"119\" height=\"165\" \/><br \/>\nAnswer: The amount of oil she put into each bottle is: \\(\\frac{5}{24}\\)<\/p>\n<p>Explanation:<br \/>\nIt is given that a mechanic buys 1 gallon of oil and she uses \\(\\frac{1}{6}\\) of the oil<br \/>\nSo,<br \/>\nthe remaining part of the oil = 1 &#8211;\u00a0 \\(\\frac{1}{6}\\)<br \/>\n= \\(\\frac{5}{6}\\)<br \/>\nIt is also given that she divides the rest of the oil into 4 smaller bottles.<br \/>\nSo,<br \/>\nThe amount of oil in each bottle = \\(\\frac{The remaining part of the oil}{The number of bottles}\\)<br \/>\n= \\(\\frac{5}{6}\\) \u00f7 4<br \/>\n= \\(\\frac{5}{6}\\) \u00d7 \\(\\frac{1}{4}\\)<br \/>\n= \\(\\frac{5 \u00d7 1}{6 \u00d7 4}\\)<br \/>\n= \\(\\frac{5}{24}\\)<br \/>\nHence, from the above,<br \/>\nWe can conclude that the amount of oil in each bottle is: \\(\\frac{5}{24}\\)<\/p>\n<p><em>Conclusion:<\/em><\/p>\n<p>Make use of the quick links and try to solve the problems in a simple manner. Redefine your true self with the BIM Answer Key for Grade 5 curated by subject experts. Test your knowledge by solving the questions which are given at the end of the chapter.<\/p>\n","protected":false},"excerpt":{"rendered":"<p>Big Ideas Math Answers Grade 5 Chapter 10 Divide Fractions PDF is included here. We have given the solutions to all the questions in Big Ideas Math Answers Grade 5 Chapter 10 Divide Fractions in pdf format. Either you can learn BIM Grade 5 Chapter 10 Divide Fractions Answers online or offline using pdf. 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