{"id":16343,"date":"2022-04-05T10:50:37","date_gmt":"2022-04-05T05:20:37","guid":{"rendered":"https:\/\/ccssmathanswers.com\/?p=16343"},"modified":"2022-04-07T11:00:34","modified_gmt":"2022-04-07T05:30:34","slug":"big-ideas-math-answers-grade-5-chapter-9","status":"publish","type":"post","link":"https:\/\/bigideasmathanswers.com\/big-ideas-math-answers-grade-5-chapter-9\/","title":{"rendered":"Big Ideas Math Answers Grade 5 Chapter 9 Multiply Fractions"},"content":{"rendered":"<p>Are you in the search of <strong>Big Ideas Math Answers Grade 5 Chapter 9 Multiply Fractions<\/strong>? If yes, you are on the correct page. Check out the detailed explanation for all the problems available on Big Ideas Grade 5 Chapter 9 Multiply Fractions Math Answers. You can easily become a math expert by referring to the BIM Grade 5 Chapter 9 Math Answers. Download <a href=\"https:\/\/bigideasmathanswers.com\/big-ideas-math-answers-grade-5\/\">Big Ideas Math Book 5th Grade Answer Key<\/a> Chapter 9 Multiply Fractions now and start your preparation for the exam. You must prepare all the concepts and verify answers to test your preparation level.<\/p>\n<h2>Big Ideas 5th Grade Chapter 9 Multiply Fractions Math Book Answer Key<\/h2>\n<p>Every student must prepare each and every topic of ch 9 to score good marks in the exam. Also, take the math assignments and homework to get the perfect preparation. Prepare well by referring to our Big Ideas Math Book 5th Grade Answer Key Chapter 9 Multiply Fractions. <b><i>Download Big Ideas Math Answers Grade 5 Chapter 9 Multiply Fractions for free<\/i><\/b>. The below links have every topic problem along with explanations. So, check out every link and practice more where you lag.<\/p>\n<p><strong>Lesson: 1 Multiply Whole Numbers by Fractions<\/strong><\/p>\n<ul>\n<li><a href=\"#Lesson_9.1_Multiply_Whole_Numbers_by_Fractions\">Lesson 9.1 Multiply Whole Numbers by Fractions<\/a><\/li>\n<li><a href=\"#Multiply_Whole_Numbers_by_Fractions_Homework_&amp;_Practice_9.1\">Multiply Whole Numbers by Fractions Homework &amp; Practice 9.1<\/a><\/li>\n<\/ul>\n<p><strong>Lesson: 2 Use Models to Multiply Fractions by Whole Numbers<\/strong><\/p>\n<ul>\n<li><a href=\"#Lesson_9.2_Use_Models_to_Multiply_Fractions_by_Whole_Numbers\">Lesson 9.2 Use Models to Multiply Fractions by Whole Numbers<\/a><\/li>\n<li><a href=\"#Use_Models_to_Multiply_Fractions_by_Whole_Numbers_Homework_&amp;_Practice_9.2\">Use Models to Multiply Fractions by Whole Numbers Homework &amp; Practice 9.2<\/a><\/li>\n<\/ul>\n<p><strong>Lesson: 3 Multiply Fractions and Whole Numbers<\/strong><\/p>\n<ul>\n<li><a href=\"#Lesson_9.3_Multiply_Fractions_and_Whole_Numbers\">Lesson 9.3 Multiply Fractions and Whole Numbers<\/a><\/li>\n<li><a href=\"#Multiply_Fractions_and_Whole_Numbers_Homework_&amp;_Practice_9.3\">Multiply Fractions and Whole Numbers Homework &amp; Practice 9.3<\/a><\/li>\n<\/ul>\n<p><strong>Lesson: 4 Use Models to Multiply Fractions<\/strong><\/p>\n<ul>\n<li><a href=\"#Lesson_9.4_Use_Models_to_Multiply_Fractions\">Lesson 9.4 Use Models to Multiply Fractions<\/a><\/li>\n<li><a href=\"#Use_Models_to_Multiply_Fractions_Homework_&amp;_Practice_9.4\">Use Models to Multiply Fractions Homework &amp; Practice 9.4<\/a><\/li>\n<\/ul>\n<p><strong>Lesson: 5 Multiply Fractions<\/strong><\/p>\n<ul>\n<li><a href=\"#Lesson_9.5_Multiply_Fractions\">Lesson 9.5 Multiply Fractions<\/a><\/li>\n<li><a href=\"#Multiply_Fractions_Homework_&amp;_Practice_9.5\">Multiply Fractions Homework &amp; Practice 9.5<\/a><\/li>\n<\/ul>\n<p><strong>Lesson: 6 Find Areas of Rectangles<\/strong><\/p>\n<ul>\n<li><a href=\"#Lesson_9.6_Find_Areas_of_Rectangles\">Lesson 9.6 Find Areas of Rectangles<\/a><\/li>\n<li><a href=\"#Find_Areas_of_Rectangles_Homework_&amp;_Practice_9.6\">Find Areas of Rectangles Homework &amp; Practice 9.6<\/a><\/li>\n<\/ul>\n<p><strong>Lesson: 7 Multiply Mixed Numbers<\/strong><\/p>\n<ul>\n<li><a href=\"#Lesson_9.7_Multiply_Mixed_Numbers\">Lesson 9.7 Multiply Mixed Numbers<\/a><\/li>\n<li><a href=\"#Multiply_Mixed_Numbers_Homework_&amp;_Practice_9.7\">Multiply Mixed Numbers Homework &amp; Practice 9.7<\/a><\/li>\n<\/ul>\n<p><strong>Lesson: 8 Compare Factors and Products<\/strong><\/p>\n<ul>\n<li><a href=\"#Lesson_9.8_Compare_Factors_and_Products\">Lesson 9.8 Compare Factors and Products<\/a><\/li>\n<li><a href=\"#Compare_Factors_and_Products_Homework_&amp;_Practice_9.8\">Compare Factors and Products Homework &amp; Practice 9.8<\/a><\/li>\n<\/ul>\n<p><strong>Chapter: 9 &#8211; Multiply Fractions<\/strong><\/p>\n<ul>\n<li><a href=\"#Multiply_Fractions_Performance_Task\">Multiply Fractions Performance Task<\/a><\/li>\n<li><a href=\"#Multiply_Fractions_Activity\">Multiply Fractions Activity<\/a><\/li>\n<li><a href=\"#Multiply_Fractions_Chapter_Practice\">Multiply Fractions Chapter Practice<\/a><\/li>\n<\/ul>\n<h3><a id=\"Lesson_9.1_Multiply_Whole_Numbers_by_Fractions\"><\/a>Lesson 9.1 Multiply Whole Numbers by Fractions<\/h3>\n<p><strong>Explore and Grow<\/strong><\/p>\n<p>Write any proper fraction that is not a unit fraction. Draw a model to represent your fraction. Draw a model to find a multiple of your fraction?<br \/>\nAnswer:<br \/>\nThe proper fraction that is not a unit fraction is:\u00a0 \\(\\frac{5}{8}\\)<br \/>\nLet the proper fraction be multiplied by 5<br \/>\nSo,<br \/>\nWe have to find the value of 5 \u00d7 \\(\\frac{5}{8}\\)<br \/>\nNow,<br \/>\nWe know that,<br \/>\na = \\(\\frac{a}{1}\\)<br \/>\na \u00d7 \\(\\frac{a}{b}\\) = \\(\\frac{a \u00d7 a}{b \u00d7 1}\\)<br \/>\nSo,<br \/>\n5 \u00d7 \\(\\frac{5}{8}\\)<br \/>\n= \\(\\frac{5}{1}\\) \u00d7 \\(\\frac{5}{8}\\)<br \/>\n= \\(\\frac{5 \u00d7 5}{1 \u00d7 8}\\)<br \/>\n= \\(\\frac{25}{8}\\)<br \/>\nHence, from the above,<br \/>\nWe can conclude that the multiple of your proper fraction is: \\(\\frac{25}{8}\\)<\/p>\n<p><strong>Reasoning<\/strong><br \/>\nHow can you use a model to multiply a whole number by a fraction? Explain.<br \/>\nAnswer:<br \/>\nWe can multiply a whole number by a fraction using the properties of multiplication. They are:<br \/>\nA) a = \\(\\frac{a}{1}\\)<br \/>\nB) a \u00d7 \\(\\frac{a}{b}\\) = \\(\\frac{a \u00d7 a}{b \u00d7 1}\\)<br \/>\nHence, by using the above properties, we can multiply the whole number by a fraction.<\/p>\n<p><strong>Think and Grow: Multiply Whole Numbers by Fractions<\/strong><\/p>\n<p><strong>Example<\/strong><br \/>\nFind 3 \u00d7 \\(\\frac{2}{5}\\)<br \/>\n<img loading=\"lazy\" class=\"alignnone size-full wp-image-35581\" src=\"https:\/\/ccssmathanswers.com\/wp-content\/uploads\/2020\/12\/Big-Ideas-Math-Answers-Grade-5-Chapter-9.jpg\" alt=\"\" width=\"644\" height=\"448\" srcset=\"https:\/\/bigideasmathanswers.com\/wp-content\/uploads\/2020\/12\/Big-Ideas-Math-Answers-Grade-5-Chapter-9.jpg 644w, https:\/\/bigideasmathanswers.com\/wp-content\/uploads\/2020\/12\/Big-Ideas-Math-Answers-Grade-5-Chapter-9-300x209.jpg 300w\" sizes=\"(max-width: 644px) 100vw, 644px\" \/><\/p>\n<p><strong>Show and Grow<\/strong><\/p>\n<p><strong>Multiply.<\/strong><br \/>\nQuestion 1.<br \/>\n2 \u00d7 \\(\\frac{3}{4}\\) = ______<br \/>\nAnswer:<br \/>\n2 \u00d7 \\(\\frac{3}{4}\\) = \\(\\frac{6}{4}\\)<\/p>\n<p>Explanation:<br \/>\nThe given numbers are: 2 and \\(\\frac{3}{4}\\)<br \/>\nWe know that,<br \/>\na = \\(\\frac{a}{1}\\)<br \/>\na \u00d7 \\(\\frac{a}{b}\\) = \\(\\frac{a \u00d7 a}{b \u00d7 1}\\)<br \/>\nSo,<br \/>\n2 \u00d7 \\(\\frac{3}{4}\\)<br \/>\n= \\(\\frac{2}{1}\\) \u00d7 \\(\\frac{3}{4}\\)<br \/>\n= \\(\\frac{2 \u00d7 3}{1 \u00d7 4}\\)<br \/>\n= \\(\\frac{6}{4}\\)<br \/>\nHence,<br \/>\n2 \u00d7 \\(\\frac{3}{4}\\) = \\(\\frac{6}{4}\\)<\/p>\n<p>Question 2.<br \/>\n4 \u00d7 \\(\\frac{5}{8}\\) = ____<br \/>\nAnswer:<br \/>\n4 \u00d7 \\(\\frac{5}{8}\\) = \\(\\frac{20}{8}\\)<\/p>\n<p>Explanation:<br \/>\nThe given numbers are: 4 and \\(\\frac{5}{8}\\)<br \/>\nWe know that,<br \/>\na = \\(\\frac{a}{1}\\)<br \/>\na \u00d7 \\(\\frac{a}{b}\\) = \\(\\frac{a \u00d7 a}{b \u00d7 1}\\)<br \/>\nSo,<br \/>\n4 \u00d7 \\(\\frac{5}{8}\\)<br \/>\n= \\(\\frac{4}{1}\\) \u00d7 \\(\\frac{5}{8}\\)<br \/>\n= \\(\\frac{4 \u00d7 5}{1 \u00d7 8}\\)<br \/>\n= \\(\\frac{20}{8}\\)<br \/>\nHence,<br \/>\n4 \u00d7 \\(\\frac{5}{8}\\) = \\(\\frac{20}{8}\\)<\/p>\n<p><strong>Apply and Grow: Practice<\/strong><\/p>\n<p><strong>Multiply.<\/strong><br \/>\nQuestion 3.<br \/>\n5 \u00d7 \\(\\frac{7}{10}\\) = ______<br \/>\nAnswer:<br \/>\n5 \u00d7 \\(\\frac{7}{10}\\) = \\(\\frac{35}{10}\\)<\/p>\n<p>Explanation:<br \/>\nThe given numbers are: 5 and \\(\\frac{7}{10}\\)<br \/>\nWe know that,<br \/>\na = \\(\\frac{a}{1}\\)<br \/>\na \u00d7 \\(\\frac{a}{b}\\) = \\(\\frac{a \u00d7 a}{b \u00d7 1}\\)<br \/>\nSo,<br \/>\n5 \u00d7 \\(\\frac{7}{10}\\)<br \/>\n= \\(\\frac{5}{1}\\) \u00d7 \\(\\frac{7}{10}\\)<br \/>\n= \\(\\frac{5 \u00d7 7}{1 \u00d7 10}\\)<br \/>\n= \\(\\frac{35}{10}\\)<br \/>\nHence,<br \/>\n5 \u00d7 \\(\\frac{7}{10}\\) = \\(\\frac{35}{10}\\)<\/p>\n<p>Question 4.<br \/>\n8 \u00d7 \\(\\frac{2}{3}\\) = ______<br \/>\nAnswer:<br \/>\n8 \u00d7 \\(\\frac{2}{3}\\) = \\(\\frac{16}{3}\\)<\/p>\n<p>Explanation:<br \/>\nThe given numbers are: 8 and \\(\\frac{2}{3}\\)<br \/>\nWe know that,<br \/>\na = \\(\\frac{a}{1}\\)<br \/>\na \u00d7 \\(\\frac{a}{b}\\) = \\(\\frac{a \u00d7 a}{b \u00d7 1}\\)<br \/>\nSo,<br \/>\n8 \u00d7 \\(\\frac{2}{3}\\)<br \/>\n= \\(\\frac{8}{1}\\) \u00d7 \\(\\frac{2}{3}\\)<br \/>\n= \\(\\frac{8 \u00d7 2}{1 \u00d7 3}\\)<br \/>\n= \\(\\frac{16}{3}\\)<br \/>\nHence,<br \/>\n8 \u00d7 \\(\\frac{2}{3}\\) = \\(\\frac{16}{3}\\)<\/p>\n<p>Question 5.<br \/>\n7 \u00d7 \\(\\frac{5}{6}\\) = ______<br \/>\nAnswer:<br \/>\n7 \u00d7 \\(\\frac{5}{6}\\) = \\(\\frac{35}{6}\\)<\/p>\n<p>Explanation:<br \/>\nThe given numbers are: 7 and \\(\\frac{5}{6}\\)<br \/>\nWe know that,<br \/>\na = \\(\\frac{a}{1}\\)<br \/>\na \u00d7 \\(\\frac{a}{b}\\) = \\(\\frac{a \u00d7 a}{b \u00d7 1}\\)<br \/>\nSo,<br \/>\n7 \u00d7 \\(\\frac{5}{6}\\)<br \/>\n= \\(\\frac{7}{1}\\) \u00d7 \\(\\frac{5}{6}\\)<br \/>\n= \\(\\frac{7 \u00d7 5}{1 \u00d7 6}\\)<br \/>\n= \\(\\frac{35}{6}\\)<br \/>\nHence,<br \/>\n7 \u00d7 \\(\\frac{5}{6}\\) = \\(\\frac{35}{6}\\)<\/p>\n<p>Question 6.<br \/>\n9 \u00d7 \\(\\frac{1}{2}\\) = ______<br \/>\nAnswer:<br \/>\n9 \u00d7 \\(\\frac{1}{2}\\) = \\(\\frac{9}{2}\\)<\/p>\n<p>Explanation:<br \/>\nThe given numbers are: 9 and \\(\\frac{1}{2}\\)<br \/>\nWe know that,<br \/>\na = \\(\\frac{a}{1}\\)<br \/>\na \u00d7 \\(\\frac{a}{b}\\) = \\(\\frac{a \u00d7 a}{b \u00d7 1}\\)<br \/>\nSo,<br \/>\n9 \u00d7 \\(\\frac{1}{2}\\)<br \/>\n= \\(\\frac{9}{1}\\) \u00d7 \\(\\frac{1}{2}\\)<br \/>\n= \\(\\frac{9 \u00d7 1}{1 \u00d7 2}\\)<br \/>\n= \\(\\frac{9}{2}\\)<br \/>\nHence,<br \/>\n9 \u00d7 \\(\\frac{1}{2}\\) = \\(\\frac{9}{2}\\)<\/p>\n<p>Question 7.<br \/>\n6 \u00d7 \\(\\frac{3}{100}\\) = ______<br \/>\nAnswer:<br \/>\n6 \u00d7 \\(\\frac{3}{100}\\) = \\(\\frac{18}{100}\\)<\/p>\n<p>Explanation:<br \/>\nThe given numbers are: 6 and \\(\\frac{3}{100}\\)<br \/>\nWe know that,<br \/>\na = \\(\\frac{a}{1}\\)<br \/>\na \u00d7 \\(\\frac{a}{b}\\) = \\(\\frac{a \u00d7 a}{b \u00d7 1}\\)<br \/>\nSo,<br \/>\n6 \u00d7 \\(\\frac{3}{100}\\)<br \/>\n= \\(\\frac{6}{1}\\) \u00d7 \\(\\frac{3}{100}\\)<br \/>\n= \\(\\frac{6 \u00d7 3}{1 \u00d7 100}\\)<br \/>\n= \\(\\frac{18}{100}\\)<br \/>\nHence,<br \/>\n6 \u00d7 \\(\\frac{3}{100}\\) = \\(\\frac{18}{100}\\)<\/p>\n<p>Question 8.<br \/>\n15 \u00d7 \\(\\frac{4}{7}\\) = ______<br \/>\nAnswer:<br \/>\n15 \u00d7 \\(\\frac{4}{7}\\) = \\(\\frac{60}{7}\\)<\/p>\n<p>Explanation:<br \/>\nThe given numbers are: 15 and \\(\\frac{4}{7}\\)<br \/>\nWe know that,<br \/>\na = \\(\\frac{a}{1}\\)<br \/>\na \u00d7 \\(\\frac{a}{b}\\) = \\(\\frac{a \u00d7 a}{b \u00d7 1}\\)<br \/>\nSo,<br \/>\n15 \u00d7 \\(\\frac{4}{7}\\)<br \/>\n= \\(\\frac{15}{1}\\) \u00d7 \\(\\frac{4}{7}\\)<br \/>\n= \\(\\frac{15 \u00d7 4}{1 \u00d7 7}\\)<br \/>\n= \\(\\frac{60}{7}\\)<br \/>\nHence,<br \/>\n15 \u00d7 \\(\\frac{4}{7}\\) = \\(\\frac{60}{7}\\)<\/p>\n<p>Question 9.<br \/>\n10 \u00d7 \\(\\frac{5}{3}\\) = ______<br \/>\nAnswer:<br \/>\n10 \u00d7 \\(\\frac{5}{3}\\) = \\(\\frac{50}{3}\\)<\/p>\n<p>Explanation:<br \/>\nThe given numbers are: 10 and \\(\\frac{5}{3}\\)<br \/>\nWe know that,<br \/>\na = \\(\\frac{a}{1}\\)<br \/>\na \u00d7 \\(\\frac{a}{b}\\) = \\(\\frac{a \u00d7 a}{b \u00d7 1}\\)<br \/>\nSo,<br \/>\n10 \u00d7 \\(\\frac{5}{3}\\)<br \/>\n= \\(\\frac{10}{1}\\) \u00d7 \\(\\frac{5}{3}\\)<br \/>\n= \\(\\frac{10 \u00d7 5}{1 \u00d7 3}\\)<br \/>\n= \\(\\frac{50}{3}\\)<br \/>\nHence,<br \/>\n10 \u00d7 \\(\\frac{5}{3}\\) = \\(\\frac{50}{3}\\)<\/p>\n<p>Question 10.<br \/>\n4 \u00d7 \\(\\frac{5}{2}\\) = ______<br \/>\nAnswer:<br \/>\n4 \u00d7 \\(\\frac{5}{2}\\) = 10<\/p>\n<p>Explanation:<br \/>\nThe given numbers are: 4 and \\(\\frac{5}{2}\\)<br \/>\nWe know that,<br \/>\na = \\(\\frac{a}{1}\\)<br \/>\na \u00d7 \\(\\frac{a}{b}\\) = \\(\\frac{a \u00d7 a}{b \u00d7 1}\\)<br \/>\nSo,<br \/>\n4 \u00d7 \\(\\frac{5}{2}\\)<br \/>\n= \\(\\frac{4}{1}\\) \u00d7 \\(\\frac{5}{2}\\)<br \/>\n= \\(\\frac{4 \u00d7 5}{1 \u00d7 2}\\)<br \/>\n= \\(\\frac{20}{2}\\)<br \/>\n= 10<br \/>\nHence,<br \/>\n4 \u00d7 \\(\\frac{5}{2}\\) = 10<\/p>\n<p>Question 11.<br \/>\n3 \u00d7 \\(\\frac{11}{8}\\) = ______<br \/>\nAnswer:<br \/>\n3 \u00d7 \\(\\frac{11}{8}\\) = \\(\\frac{33}{8}\\)<\/p>\n<p>Explanation:<br \/>\nThe given numbers are: 3 and \\(\\frac{11}{8}\\)<br \/>\nWe know that,<br \/>\na = \\(\\frac{a}{1}\\)<br \/>\na \u00d7 \\(\\frac{a}{b}\\) = \\(\\frac{a \u00d7 a}{b \u00d7 1}\\)<br \/>\nSo,<br \/>\n3 \u00d7 \\(\\frac{11}{8}\\)<br \/>\n= \\(\\frac{3}{1}\\) \u00d7 \\(\\frac{11}{8}\\)<br \/>\n= \\(\\frac{11 \u00d7 3}{1 \u00d7 8}\\)<br \/>\n= \\(\\frac{33}{8}\\)<br \/>\nHence,<br \/>\n3 \u00d7 \\(\\frac{11}{8}\\) = \\(\\frac{33}{8}\\)<\/p>\n<p><strong>Find the unknown number.<\/strong><br \/>\nQuestion 12.<br \/>\n<img loading=\"lazy\" class=\"alignnone size-full wp-image-16345\" src=\"https:\/\/ccssmathanswers.com\/wp-content\/uploads\/2020\/12\/Big-Ideas-Math-Answer-Key-Grade-5-Chapter-9-Multiply-Fractions-9.1-2.png\" alt=\"Big Ideas Math Answer Key Grade 5 Chapter 9 Multiply Fractions 9.1 2\" width=\"114\" height=\"55\" \/><br \/>\nAnswer:<br \/>\nThe missing number is: 3<\/p>\n<p>Explanation:<br \/>\nThe given fractions are: \\(\\frac{3}{20}\\) and \\(\\frac{9}{20}\\)<br \/>\nLet the missing number be X<br \/>\nSo,<br \/>\nX \u00d7 \\(\\frac{3}{20}\\) = \\(\\frac{9}{20}\\)<br \/>\nWhen multiplication goes from left to right or from right to left, it will become the division<br \/>\nWhen division goes from left to right or from right to left, it will become multiplication.<br \/>\nSo,<br \/>\nX = \\(\\frac{9}{20}\\) \u00f7 \\(\\frac{3}{20}\\)<br \/>\nWe know that,<br \/>\n\\(\\frac{a}{b}\\) \u00f7 \\(\\frac{x}{y}\\) = \\(\\frac{a}{b}\\) \u00d7 \\(\\frac{y}{x}\\)<br \/>\nSo,<br \/>\n\\(\\frac{9}{20}\\) \u00f7 \\(\\frac{3}{20}\\)<br \/>\n= \\(\\frac{9}{20}\\) \u00d7 \\(\\frac{20}{3}\\)<br \/>\n= \\(\\frac{9 \u00d7 20}{20 \u00d7 3}\\)<br \/>\n= 3<br \/>\nHence,<br \/>\nThe missing number is: 3<\/p>\n<p>Question 13.<br \/>\n<img loading=\"lazy\" class=\"alignnone size-full wp-image-16346\" src=\"https:\/\/ccssmathanswers.com\/wp-content\/uploads\/2020\/12\/Big-Ideas-Math-Answer-Key-Grade-5-Chapter-9-Multiply-Fractions-9.1-3.png\" alt=\"Big Ideas Math Answer Key Grade 5 Chapter 9 Multiply Fractions 9.1 3\" width=\"110\" height=\"50\" \/><br \/>\nAnswer:<br \/>\nThe missing number is: 6<\/p>\n<p>Explanation:<br \/>\nThe given fractions are: \\(\\frac{4}{9}\\) and \\(\\frac{24}{9}\\)<br \/>\nLet the missing number be X<br \/>\nSo,<br \/>\nX \u00d7 \\(\\frac{4}{9}\\) = \\(\\frac{24}{9}\\)<br \/>\nWhen multiplication goes from left to right or from right to left, it will become the division<br \/>\nWhen division goes from left to right or from right to left, it will become multiplication.<br \/>\nSo,<br \/>\nX = \\(\\frac{24}{9}\\) \u00f7 \\(\\frac{4}{9}\\)<br \/>\nWe know that,<br \/>\n\\(\\frac{a}{b}\\) \u00f7 \\(\\frac{x}{y}\\) = \\(\\frac{a}{b}\\) \u00d7 \\(\\frac{y}{x}\\)<br \/>\nSo,<br \/>\n\\(\\frac{24}{9}\\) \u00f7 \\(\\frac{4}{9}\\)<br \/>\n= \\(\\frac{24}{9}\\) \u00d7 \\(\\frac{9}{4}\\)<br \/>\n= \\(\\frac{9 \u00d7 24}{9 \u00d7 4}\\)<br \/>\n= 6<br \/>\nHence,<br \/>\nThe missing number is: 6<\/p>\n<p>Question 14.<br \/>\n<img loading=\"lazy\" class=\"alignnone size-full wp-image-16347\" src=\"https:\/\/ccssmathanswers.com\/wp-content\/uploads\/2020\/12\/Big-Ideas-Math-Answer-Key-Grade-5-Chapter-9-Multiply-Fractions-9.1-4.png\" alt=\"Big Ideas Math Answer Key Grade 5 Chapter 9 Multiply Fractions 9.1 4\" width=\"119\" height=\"56\" \/><br \/>\nAnswer:<br \/>\nThe missing number is: 10<\/p>\n<p>Explanation:<br \/>\nThe given fractions are: \\(\\frac{5}{12}\\) and \\(\\frac{50}{12}\\)<br \/>\nLet the missing number be X<br \/>\nSo,<br \/>\nX \u00d7 \\(\\frac{5}{12}\\) = \\(\\frac{50}{12}\\)<br \/>\nWhen multiplication goes from left to right or from right to left, it will become the division<br \/>\nWhen division goes from left to right or from right to left, it will become multiplication.<br \/>\nSo,<br \/>\nX = \\(\\frac{50}{12}\\) \u00f7 \\(\\frac{5}{12}\\)<br \/>\nWe know that,<br \/>\n\\(\\frac{a}{b}\\) \u00f7 \\(\\frac{x}{y}\\) = \\(\\frac{a}{b}\\) \u00d7 \\(\\frac{y}{x}\\)<br \/>\nSo,<br \/>\n\\(\\frac{50}{12}\\) \u00f7 \\(\\frac{5}{12}\\)<br \/>\n= \\(\\frac{50}{12}\\) \u00d7 \\(\\frac{12}{5}\\)<br \/>\n= \\(\\frac{12 \u00d7 50}{12 \u00d7 5}\\)<br \/>\n= 10<br \/>\nHence,<br \/>\nThe missing number is: 10<\/p>\n<p>Question 15.<br \/>\nA recipe calls for \\(\\frac{3}{4}\\) cup of dried rice noodles. You make 44 batches of the recipe. How many cups of dried rice noodles do you use?<br \/>\n<img loading=\"lazy\" class=\"alignnone size-full wp-image-16348\" src=\"https:\/\/ccssmathanswers.com\/wp-content\/uploads\/2020\/12\/Big-Ideas-Math-Answer-Key-Grade-5-Chapter-9-Multiply-Fractions-9.1-5.png\" alt=\"Big Ideas Math Answer Key Grade 5 Chapter 9 Multiply Fractions 9.1 5\" width=\"176\" height=\"139\" \/><br \/>\nAnswer:<br \/>\nThe number of cups of dried rice noodles you used is: 33<\/p>\n<p>Explanation:<br \/>\nIt is given that a recipe calls for \\(\\frac{3}{4}\\) cup of dried rice noodles.<br \/>\nIt is also given that you make 44 batches of the recipe<br \/>\nSo,<br \/>\nThe number of cups of dried rice noodles you used = ( The number of batches of the recipe ) \u00d7 ( The number of dried rice noodles for each batch )<br \/>\n= 44 \u00d7 \\(\\frac{3}{4}\\)<br \/>\nNow,<br \/>\nWe know that,<br \/>\na = \\(\\frac{a}{1}\\)<br \/>\na \u00d7 \\(\\frac{a}{b}\\) = \\(\\frac{a \u00d7 a}{b \u00d7 1}\\)<br \/>\nSo,<br \/>\n44 \u00d7 \\(\\frac{3}{4}\\)<br \/>\n= \\(\\frac{44}{1}\\) \u00d7 \\(\\frac{3}{4}\\)<br \/>\n= \\(\\frac{44 \u00d7 3}{1 \u00d7 4}\\)<br \/>\n= \\(\\frac{33}{1}\\)<br \/>\n= 33<br \/>\nHence, from the above,<br \/>\nWe can conclude that the number of cups of dried noodles you used is: 33 cups<\/p>\n<p>Question 16.<br \/>\n<strong>YOU BE THE TEACHER<\/strong><br \/>\nYour 5 \u00d7 \\(\\frac{3}{5}\\) friend says that 5 is equal to \\(\\frac{3}{5}\\) + \\(\\frac{3}{5}\\) + \\(\\frac{3}{5}\\) + \\(\\frac{3}{5}\\) + \\(\\frac{3}{5}\\). Is your friend correct? Explain.<br \/>\nAnswer:<br \/>\nYes, your friend is correct.<\/p>\n<p>Explanation:<br \/>\nIt is given that your 5 \u00d7 \\(\\frac{3}{5}\\) friend says that 5 is equal to \\(\\frac{3}{5}\\) + \\(\\frac{3}{5}\\) + \\(\\frac{3}{5}\\) + \\(\\frac{3}{5}\\) + \\(\\frac{3}{5}\\).<br \/>\nNow,<br \/>\nWe know that,<br \/>\nn \u00d7 a = a + a + a + a + &#8230;&#8230;&#8230;&#8230;&#8230;.. + n times<br \/>\nWhere,<br \/>\n&#8216;n&#8217; is the multiple of a<br \/>\nHere,<br \/>\n&#8216;a&#8217; will be the whole number or the fraction<br \/>\nSo,<br \/>\nAccording to the above property,<br \/>\n5 \u00d7 \\(\\frac{3}{5}\\) = \\(\\frac{3}{5}\\) + \\(\\frac{3}{5}\\) + \\(\\frac{3}{5}\\) +\\(\\frac{3}{5}\\) + \\(\\frac{3}{5}\\)<br \/>\nHence, from the above,<br \/>\nWe can conclude that your friend is correct.<\/p>\n<p>Question 17.<br \/>\n<strong>Patterns<\/strong><br \/>\nDescribe and complete the pattern.<br \/>\n<img loading=\"lazy\" class=\"alignnone size-full wp-image-16349\" src=\"https:\/\/ccssmathanswers.com\/wp-content\/uploads\/2020\/12\/Big-Ideas-Math-Answer-Key-Grade-5-Chapter-9-Multiply-Fractions-9.1-6.png\" alt=\"Big Ideas Math Answer Key Grade 5 Chapter 9 Multiply Fractions 9.1 6\" width=\"187\" height=\"198\" \/><br \/>\nAnswer:<br \/>\nThe completed pattern is:<br \/>\n<img loading=\"lazy\" class=\"alignnone size-full wp-image-35610\" src=\"https:\/\/ccssmathanswers.com\/wp-content\/uploads\/2020\/12\/Big-Ideas-Math-Answers-Grade-5-Chapter-9-1.jpg\" alt=\"\" width=\"197\" height=\"197\" srcset=\"https:\/\/bigideasmathanswers.com\/wp-content\/uploads\/2020\/12\/Big-Ideas-Math-Answers-Grade-5-Chapter-9-1.jpg 197w, https:\/\/bigideasmathanswers.com\/wp-content\/uploads\/2020\/12\/Big-Ideas-Math-Answers-Grade-5-Chapter-9-1-150x150.jpg 150w\" sizes=\"(max-width: 197px) 100vw, 197px\" \/><br \/>\nFrom the above pattern,<br \/>\nWe can observe that<br \/>\nThe whole number is constant i.e., 9<br \/>\nThe fraction part is changing i.e., the numerator part is increasing by 1 till 4 and the denominator is constant<br \/>\nSo,<br \/>\nNow,<br \/>\n9 \u00d7 \\(\\frac{1}{4}\\)<br \/>\n= \\(\\frac{9}{1}\\) \u00d7 \\(\\frac{1}{4}\\)<br \/>\n= \\(\\frac{9 \u00d7 1}{1 \u00d7 4}\\)<br \/>\n= \\(\\frac{9}{4}\\)<br \/>\n9 \u00d7 \\(\\frac{2}{4}\\)<br \/>\n= \\(\\frac{9}{1}\\) \u00d7 \\(\\frac{2}{4}\\)<br \/>\n= \\(\\frac{9 \u00d7 2}{1 \u00d7 4}\\)<br \/>\n= \\(\\frac{18}{4}\\)<br \/>\nSo,<br \/>\nThe remaining two multiplication equations will also be solved in the same way.<\/p>\n<p><strong>Think and Grow: Modeling Real Life<\/strong><\/p>\n<p><strong>Example<\/strong><br \/>\nYour goal is to make a waterslide that is at least 10 meters long. You make the waterslide using 10 plastic mats that are each \\(\\frac{3}{2}\\) meters long. Do you reach your goal?<br \/>\n<img loading=\"lazy\" class=\"alignnone size-full wp-image-16350\" src=\"https:\/\/ccssmathanswers.com\/wp-content\/uploads\/2020\/12\/Big-Ideas-Math-Answer-Key-Grade-5-Chapter-9-Multiply-Fractions-9.1-7.png\" alt=\"Big Ideas Math Answer Key Grade 5 Chapter 9 Multiply Fractions 9.1 7\" width=\"216\" height=\"143\" \/><br \/>\nFind the length of the waterslide by multiplying the number of mats by the length of each mat.<br \/>\n<img loading=\"lazy\" class=\"alignnone size-full wp-image-35627\" src=\"https:\/\/ccssmathanswers.com\/wp-content\/uploads\/2020\/12\/Big-Ideas-Math-Answers-Grade-5-Chapter-9-2.jpg\" alt=\"\" width=\"415\" height=\"174\" srcset=\"https:\/\/bigideasmathanswers.com\/wp-content\/uploads\/2020\/12\/Big-Ideas-Math-Answers-Grade-5-Chapter-9-2.jpg 415w, https:\/\/bigideasmathanswers.com\/wp-content\/uploads\/2020\/12\/Big-Ideas-Math-Answers-Grade-5-Chapter-9-2-300x126.jpg 300w\" sizes=\"(max-width: 415px) 100vw, 415px\" \/><br \/>\nSo,<br \/>\nYou reached your goal.<\/p>\n<p><strong>Show and Grow<\/strong><\/p>\n<p>Question 18.<br \/>\nAn excavator is moving 4 piles of dirt that are the same size. Each pile requires \\(\\frac{3}{4}\\) hour to move. Can the excavator move all of the piles in 2 hours?<br \/>\nAnswer:<br \/>\nNo, the excavator can&#8217;t move all of the piles in 2 hours<\/p>\n<p>Explanation:<br \/>\nIt is given that an excavator is moving 4 piles of dirt that are of the same size and each pile requires \\(\\frac{3}{4}\\) hour to move.<br \/>\nSo,<br \/>\nWe know that,<br \/>\n1 hour = 60 minutes<br \/>\nSo,<br \/>\n\\(\\frac{3}{4}\\) of 1 hour = \\(\\frac{3}{4}\\) \u00d7 60<br \/>\n= \\(\\frac{3}{4}\\) \u00d7 \\(\\frac{60}{1}\\)<br \/>\n= \\(\\frac{3 \u00d7 60}{4 \u00d7 1}\\)<br \/>\n= 45 minutes<br \/>\nSo,<br \/>\nThe time is taken to move 4 piles of dirt = ( The time is taken to move each pile )\u00a0 \u00d7 ( The total number of piles )<br \/>\n= 45 \u00d7 4<br \/>\n=180 minutes<br \/>\nIt is given that you have to move the piles of dirt in 2 hours but the time taken is 4 hours.<br \/>\nHence, from the above,<br \/>\nWe can conclude that the excavator can&#8217;t move all the piles in 2 hours.<\/p>\n<p>Question 19.<br \/>\nYou walk dogs \\(\\frac{5}{4}\\) miles two times each day. How far do you walk the dogs in 1 week?<br \/>\n<img loading=\"lazy\" class=\"alignnone size-full wp-image-16352\" src=\"https:\/\/ccssmathanswers.com\/wp-content\/uploads\/2020\/12\/Big-Ideas-Math-Answer-Key-Grade-5-Chapter-9-Multiply-Fractions-9.1-9.png\" alt=\"Big Ideas Math Answer Key Grade 5 Chapter 9 Multiply Fractions 9.1 9\" width=\"183\" height=\"130\" \/><br \/>\nAnswer:<br \/>\nThe number of miles you walk the dogs in 1 week is: \\(\\frac{35}{2}\\)<\/p>\n<p>Explanation:<br \/>\nIt is given that you walk dogs \\(\\frac{5}{4}\\) miles two times each day<br \/>\nSo,<br \/>\nThe total number of miles you walk dogs in 1 day = 2 \u00d7 \\(\\frac{5}{4}\\)<br \/>\n= \\(\\frac{5}{4}\\) \u00d7 \\(\\frac{2}{1}\\)<br \/>\n= \\(\\frac{5 \u00d7 2}{4 \u00d7 1}\\)<br \/>\n= \\(\\frac{5}{2}\\) miles<br \/>\nWe know that,<br \/>\n1 week = 7 days<br \/>\nSo,<br \/>\nThe total number of miles you walk dogs in 1 week = ( The number of miles you walk dogs in 1 day ) \u00d7 7<br \/>\n= \\(\\frac{5}{2}\\) \u00d7 7<br \/>\n= \\(\\frac{5}{2}\\) \u00d7 \\(\\frac{7}{1}\\)<br \/>\n= \\(\\frac{5 \u00d7 7}{2 \u00d7 1}\\)<br \/>\n= \\(\\frac{35}{2}\\)<br \/>\nHence, from the above,<br \/>\nWe can conclude that the number of miles you walk dogs in 1 week is: \\(\\frac{35}{2}\\) miles<\/p>\n<p>Question 20.<br \/>\n<strong>DIG DEEPER<\/strong><br \/>\nYou have10 feet of string. You need \\(\\frac{5}{3}\\) feet of string to make 1 necklace. You make 5 necklaces. Do you have enough string to make another necklace? Explain.<br \/>\nAnswer:<br \/>\nYes, we have enough string to make another necklace<\/p>\n<p>Explanation:<br \/>\nIt is given that you have 10 feet of string and you need \\(\\frac{5}{3}\\) feet of string to make 1 necklace. and you make 5 necklaces.<br \/>\nSo,<br \/>\nThe length of the string required for 5 necklaces = ( The length of string required for 1 necklace ) \u00d7 ( The total number of necklaces )<br \/>\n= \\(\\frac{5}{3}\\) \u00d7 5<br \/>\n= \\(\\frac{5}{3}\\) \u00d7 \\(\\frac{5}{1}\\)<br \/>\n= \\(\\frac{5 \u00d7 5}{3 \u00d7 1}\\)<br \/>\n= \\(\\frac{25}{3}\\) feet<br \/>\nWe can write 10 feet as \\(\\frac{30}{3}\\) feet<br \/>\nSo,<br \/>\nWhen we compare the total length of the string and the length of the string to make 5 necklaces,<br \/>\nWe can observe that the length of the string to make 5 necklaces is less than the total length of the string.<br \/>\nHence, from the above,<br \/>\nWe can conclude that we have enough string to make another necklace.<\/p>\n<h3><a id=\"Multiply_Whole_Numbers_by_Fractions_Homework_&amp;_Practice_9.1\"><\/a>Multiply Whole Numbers by Fractions Homework &amp; Practice 9.1<\/h3>\n<p><strong>Multiply<\/strong><br \/>\nQuestion 1.<br \/>\n5 \u00d7 \\(\\frac{2}{3}\\) = ______<br \/>\nAnswer:<br \/>\n5 \u00d7 \\(\\frac{2}{3}\\) = \\(\\frac{10}{3}\\)<\/p>\n<p>Explanation:<br \/>\nThe given numbers are: 5 and \\(\\frac{2}{3}\\)<br \/>\nWe know that,<br \/>\na = \\(\\frac{a}{1}\\)<br \/>\na \u00d7 \\(\\frac{a}{b}\\) = \\(\\frac{a \u00d7 a}{b \u00d7 1}\\)<br \/>\nSo,<br \/>\n5 \u00d7 \\(\\frac{2}{3}\\)<br \/>\n= \\(\\frac{5}{1}\\) \u00d7 \\(\\frac{2}{3}\\)<br \/>\n= \\(\\frac{2 \u00d7 5}{1 \u00d7 3}\\)<br \/>\n= \\(\\frac{10}{3}\\)<br \/>\nHence,<br \/>\n5 \u00d7 \\(\\frac{2}{3}\\) = \\(\\frac{10}{3}\\)<\/p>\n<p>Question 2.<br \/>\n9 \u00d7 \\(\\frac{7}{8}\\) = ______<br \/>\nAnswer:<br \/>\n9 \u00d7 \\(\\frac{7}{8}\\) = \\(\\frac{63}{8}\\)<\/p>\n<p>Explanation:<br \/>\nThe given numbers are: 9 and \\(\\frac{7}{8}\\)<br \/>\nWe know that,<br \/>\na = \\(\\frac{a}{1}\\)<br \/>\na \u00d7 \\(\\frac{a}{b}\\) = \\(\\frac{a \u00d7 a}{b \u00d7 1}\\)<br \/>\nSo,<br \/>\n9 \u00d7 \\(\\frac{7}{8}\\)<br \/>\n= \\(\\frac{9}{1}\\) \u00d7 \\(\\frac{7}{8}\\)<br \/>\n= \\(\\frac{9 \u00d7 7}{1 \u00d7 8}\\)<br \/>\n= \\(\\frac{63}{8}\\)<br \/>\nHence,<br \/>\n9 \u00d7 \\(\\frac{7}{8}\\) = \\(\\frac{63}{8}\\)<\/p>\n<p>Question 3.<br \/>\n4 \u00d7 \\(\\frac{11}{12}\\) = ______<br \/>\nAnswer:<br \/>\n4 \u00d7 \\(\\frac{11}{12}\\) = \\(\\frac{44}{12}\\)<\/p>\n<p>Explanation:<br \/>\nThe given numbers are: 4 and \\(\\frac{11}{12}\\)<br \/>\nWe know that,<br \/>\na = \\(\\frac{a}{1}\\)<br \/>\na \u00d7 \\(\\frac{a}{b}\\) = \\(\\frac{a \u00d7 a}{b \u00d7 1}\\)<br \/>\nSo,<br \/>\n4 \u00d7 \\(\\frac{11}{12}\\)<br \/>\n= \\(\\frac{4}{1}\\) \u00d7 \\(\\frac{11}{12}\\)<br \/>\n= \\(\\frac{4 \u00d7 11}{1 \u00d7 12}\\)<br \/>\n= \\(\\frac{44}{12}\\)<br \/>\nHence,<br \/>\n4 \u00d7 \\(\\frac{11}{12}\\) = \\(\\frac{44}{12}\\)<\/p>\n<p>Question 4.<br \/>\n8 \u00d7 \\(\\frac{35}{100}\\) = ______<br \/>\nAnswer:<br \/>\n8 \u00d7 \\(\\frac{35}{100}\\) = \\(\\frac{280}{100}\\)<\/p>\n<p>Explanation:<br \/>\nThe given numbers are: 8 and \\(\\frac{35}{100}\\)<br \/>\nWe know that,<br \/>\na = \\(\\frac{a}{1}\\)<br \/>\na \u00d7 \\(\\frac{a}{b}\\) = \\(\\frac{a \u00d7 a}{b \u00d7 1}\\)<br \/>\nSo,<br \/>\n8 \u00d7 \\(\\frac{35}{100}\\)<br \/>\n= \\(\\frac{8}{1}\\) \u00d7 \\(\\frac{35}{100}\\)<br \/>\n= \\(\\frac{8 \u00d7 35}{1 \u00d7 100}\\)<br \/>\n= \\(\\frac{280}{100}\\)<br \/>\nHence,<br \/>\n8 \u00d7 \\(\\frac{35}{100}\\) = \\(\\frac{280}{100}\\)<\/p>\n<p>Question 5.<br \/>\n3 \u00d7 \\(\\frac{1}{2}\\) = ______<br \/>\nAnswer:<br \/>\n3 \u00d7 \\(\\frac{1}{2}\\) = \\(\\frac{3}{2}\\)<\/p>\n<p>Explanation:<br \/>\nThe given numbers are: 3 and \\(\\frac{1}{2}\\)<br \/>\nWe know that,<br \/>\na = \\(\\frac{a}{1}\\)<br \/>\na \u00d7 \\(\\frac{a}{b}\\) = \\(\\frac{a \u00d7 a}{b \u00d7 1}\\)<br \/>\nSo,<br \/>\n3 \u00d7 \\(\\frac{1}{2}\\)<br \/>\n= \\(\\frac{3}{1}\\) \u00d7 \\(\\frac{1}{2}\\)<br \/>\n= \\(\\frac{1 \u00d7 3}{1 \u00d7 2}\\)<br \/>\n= \\(\\frac{3}{2}\\)<br \/>\nHence,<br \/>\n3 \u00d7 \\(\\frac{1}{2}\\) = \\(\\frac{3}{2}\\)<\/p>\n<p>Question 6.<br \/>\n7 \u00d7 \\(\\frac{2}{5}\\) = ______<br \/>\nAnswer:<br \/>\n7 \u00d7 \\(\\frac{2}{5}\\) = \\(\\frac{14}{5}\\)<\/p>\n<p>Explanation:<br \/>\nThe given numbers are: 7 and \\(\\frac{2}{5}\\)<br \/>\nWe know that,<br \/>\na = \\(\\frac{a}{1}\\)<br \/>\na \u00d7 \\(\\frac{a}{b}\\) = \\(\\frac{a \u00d7 a}{b \u00d7 1}\\)<br \/>\nSo,<br \/>\n7 \u00d7 \\(\\frac{2}{5}\\)<br \/>\n= \\(\\frac{7}{1}\\) \u00d7 \\(\\frac{2}{5}\\)<br \/>\n= \\(\\frac{2 \u00d7 7}{1 \u00d7 5}\\)<br \/>\n= \\(\\frac{14}{5}\\)<br \/>\nHence,<br \/>\n7 \u00d7 \\(\\frac{2}{5}\\) = \\(\\frac{14}{5}\\)<\/p>\n<p>Question 7.<br \/>\n6 \u00d7 \\(\\frac{7}{4}\\) = ______<br \/>\nAnswer:<br \/>\n6 \u00d7 \\(\\frac{7}{4}\\) = \\(\\frac{42}{4}\\)<\/p>\n<p>Explanation:<br \/>\nThe given numbers are: 6 and \\(\\frac{7}{4}\\)<br \/>\nWe know that,<br \/>\na = \\(\\frac{a}{1}\\)<br \/>\na \u00d7 \\(\\frac{a}{b}\\) = \\(\\frac{a \u00d7 a}{b \u00d7 1}\\)<br \/>\nSo,<br \/>\n6 \u00d7 \\(\\frac{7}{4}\\)<br \/>\n= \\(\\frac{6}{1}\\) \u00d7 \\(\\frac{7}{4}\\)<br \/>\n= \\(\\frac{6 \u00d7 7}{1 \u00d7 4}\\)<br \/>\n= \\(\\frac{42}{4}\\)<br \/>\nHence,<br \/>\n6 \u00d7 \\(\\frac{7}{4}\\) = \\(\\frac{42}{4}\\)<\/p>\n<p>Question 8.<br \/>\n12 \u00d7 \\(\\frac{8}{7}\\) = ______<br \/>\nAnswer:<br \/>\n12 \u00d7 \\(\\frac{8}{7}\\) = \\(\\frac{96}{7}\\)<\/p>\n<p>Explanation:<br \/>\nThe given numbers are: 12 and \\(\\frac{8}{7}\\)<br \/>\nWe know that,<br \/>\na = \\(\\frac{a}{1}\\)<br \/>\na \u00d7 \\(\\frac{a}{b}\\) = \\(\\frac{a \u00d7 a}{b \u00d7 1}\\)<br \/>\nSo,<br \/>\n12 \u00d7 \\(\\frac{8}{7}\\)<br \/>\n= \\(\\frac{12}{1}\\) \u00d7 \\(\\frac{8}{7}\\)<br \/>\n= \\(\\frac{12 \u00d7 8}{1 \u00d7 7}\\)<br \/>\n= \\(\\frac{96}{7}\\)<br \/>\nHence,<br \/>\n12 \u00d7 \\(\\frac{8}{7}\\) = \\(\\frac{96}{7}\\)<\/p>\n<p>Question 9.<br \/>\n25 \u00d7 \\(\\frac{10}{9}\\) = ______<br \/>\nAnswer:<br \/>\n25 \u00d7 \\(\\frac{10}{9}\\) = \\(\\frac{250}{9}\\)<\/p>\n<p>Explanation:<br \/>\nThe given numbers are: 25 and \\(\\frac{10}{9}\\)<br \/>\nWe know that,<br \/>\na = \\(\\frac{a}{1}\\)<br \/>\na \u00d7 \\(\\frac{a}{b}\\) = \\(\\frac{a \u00d7 a}{b \u00d7 1}\\)<br \/>\nSo,<br \/>\n25 \u00d7 \\(\\frac{10}{9}\\)<br \/>\n= \\(\\frac{25}{1}\\) \u00d7 \\(\\frac{10}{9}\\)<br \/>\n= \\(\\frac{25 \u00d7 10}{1 \u00d7 9}\\)<br \/>\n= \\(\\frac{250}{9}\\)<br \/>\nHence,<br \/>\n25 \u00d7 \\(\\frac{10}{9}\\) = \\(\\frac{250}{9}\\)<\/p>\n<p><strong>Find the unknown number.<\/strong><br \/>\nQuestion 10.<br \/>\n<img loading=\"lazy\" class=\"alignnone size-full wp-image-16353\" src=\"https:\/\/ccssmathanswers.com\/wp-content\/uploads\/2020\/12\/Big-Ideas-Math-Answer-Key-Grade-5-Chapter-9-Multiply-Fractions-9.1-10.png\" alt=\"Big Ideas Math Answer Key Grade 5 Chapter 9 Multiply Fractions 9.1 10\" width=\"110\" height=\"56\" \/><br \/>\nAnswer:<br \/>\nThe missing number is: 5<\/p>\n<p>Explanation:<br \/>\nThe given fractions are: \\(\\frac{5}{7}\\) and \\(\\frac{25}{7}\\)<br \/>\nLet the missing number be X<br \/>\nSo,<br \/>\nX \u00d7 \\(\\frac{5}{7}\\) = \\(\\frac{25}{7}\\)<br \/>\nWhen multiplication goes from left to right or from right to left, it will become the division<br \/>\nWhen division goes from left to right or from right to left, it will become multiplication.<br \/>\nSo,<br \/>\nX = \\(\\frac{25}{7}\\) \u00f7 \\(\\frac{5}{7}\\)<br \/>\nWe know that,<br \/>\n\\(\\frac{a}{b}\\) \u00f7 \\(\\frac{x}{y}\\) = \\(\\frac{a}{b}\\) \u00d7 \\(\\frac{y}{x}\\)<br \/>\nSo,<br \/>\n\\(\\frac{25}{7}\\) \u00f7 \\(\\frac{5}{7}\\)<br \/>\n= \\(\\frac{25}{7}\\) \u00d7 \\(\\frac{7}{5}\\)<br \/>\n= \\(\\frac{7 \u00d7 25}{7 \u00d7 5}\\)<br \/>\n= 5<br \/>\nHence,<br \/>\nThe missing number is: 5<\/p>\n<p>Question 11.<br \/>\n<img loading=\"lazy\" class=\"alignnone size-full wp-image-16354\" src=\"https:\/\/ccssmathanswers.com\/wp-content\/uploads\/2020\/12\/Big-Ideas-Math-Answer-Key-Grade-5-Chapter-9-Multiply-Fractions-9.1-11.png\" alt=\"Big Ideas Math Answer Key Grade 5 Chapter 9 Multiply Fractions 9.1 11\" width=\"128\" height=\"65\" \/><br \/>\nAnswer:<br \/>\nThe missing number is: 7<\/p>\n<p>Explanation:<br \/>\nThe given fractions are: \\(\\frac{9}{10}\\) and \\(\\frac{63}{10}\\)<br \/>\nLet the missing number be X<br \/>\nSo,<br \/>\nX \u00d7 \\(\\frac{9}{10}\\) = \\(\\frac{63}{10}\\)<br \/>\nWhen multiplication goes from left to right or from right to left, it will become the division<br \/>\nWhen division goes from left to right or from right to left, it will become multiplication.<br \/>\nSo,<br \/>\nX = \\(\\frac{63}{10}\\) \u00f7 \\(\\frac{9}{10}\\)<br \/>\nWe know that,<br \/>\n\\(\\frac{a}{b}\\) \u00f7 \\(\\frac{x}{y}\\) = \\(\\frac{a}{b}\\) \u00d7 \\(\\frac{y}{x}\\)<br \/>\nSo,<br \/>\n\\(\\frac{63}{10}\\) \u00f7 \\(\\frac{9}{10}\\)<br \/>\n= \\(\\frac{63}{10}\\) \u00d7 \\(\\frac{10}{9}\\)<br \/>\n= \\(\\frac{63 \u00d7 10}{10 \u00d7 9}\\)<br \/>\n= 7<br \/>\nHence,<br \/>\nThe missing number is: 7<\/p>\n<p>Question 12.<br \/>\n<img loading=\"lazy\" class=\"alignnone size-full wp-image-16355\" src=\"https:\/\/ccssmathanswers.com\/wp-content\/uploads\/2020\/12\/Big-Ideas-Math-Answer-Key-Grade-5-Chapter-9-Multiply-Fractions-9.1-12.png\" alt=\"Big Ideas Math Answer Key Grade 5 Chapter 9 Multiply Fractions 9.1 12\" width=\"106\" height=\"55\" \/><br \/>\nAnswer:<br \/>\nThe missing number is: 9<\/p>\n<p>Explanation:<br \/>\nThe given fractions are: \\(\\frac{3}{5}\\) and \\(\\frac{27}{5}\\)<br \/>\nLet the missing number be X<br \/>\nSo,<br \/>\nX \u00d7 \\(\\frac{3}{5}\\) = \\(\\frac{27}{5}\\)<br \/>\nWhen multiplication goes from left to right or from right to left, it will become the division<br \/>\nWhen division goes from left to right or from right to left, it will become multiplication.<br \/>\nSo,<br \/>\nX = \\(\\frac{27}{5}\\) \u00f7 \\(\\frac{3}{5}\\)<br \/>\nWe know that,<br \/>\n\\(\\frac{a}{b}\\) \u00f7 \\(\\frac{x}{y}\\) = \\(\\frac{a}{b}\\) \u00d7 \\(\\frac{y}{x}\\)<br \/>\nSo,<br \/>\n\\(\\frac{27}{5}\\) \u00f7 \\(\\frac{3}{5}\\)<br \/>\n= \\(\\frac{27}{5}\\) \u00d7 \\(\\frac{5}{3}\\)<br \/>\n= \\(\\frac{5 \u00d7 27}{5 \u00d7 3}\\)<br \/>\n= 9<br \/>\nHence,<br \/>\nThe missing number is: 9<\/p>\n<p>Question 13.<br \/>\nYou make 5 servings of pancakes. You top each serving with \\(\\frac{1}{4}\\) cup of strawberries. How many cups of strawberries do you use?<br \/>\nAnswer:<br \/>\nThe number of cups of strawberries you used is: 20 cups<\/p>\n<p>Explanation:<br \/>\nIt is given that you make 5 servings of pancakes and you top each serving with \\(\\frac{1}{4}\\) cup of strawberries.<br \/>\nSo,<br \/>\nThe number of cups of strawberries = \\(\\frac{The number of servings of pancakes}{Each serving in pancake}\\)<br \/>\n= 5 \u00f7 \\(\\frac{1}{4}\\)<br \/>\n= \\(\\frac{5}{1}\\) \u00f7 \\(\\frac{1}{4}\\)<br \/>\n= \\(\\frac{5}{1}\\) \u00d7 \\(\\frac{4}{1}\\)<br \/>\n= \\(\\frac{5 \u00d7 4}{1 \u00d7 1}\\)<br \/>\n= 20 cups<br \/>\nhence, from the above,<br \/>\nWe can conclude that the number of cups of strawberries is: 20 cups<\/p>\n<p>Question 14.<br \/>\n<strong>Which One Doesn\u2019tBelong?<\/strong><br \/>\nWhich one does not belong with the other three?<br \/>\n4 \u00d7 \\(\\frac{3}{8}\\)<br \/>\n3 \u00d7 \\(\\frac{1}{8}\\)<br \/>\n\\(\\frac{3}{8}\\) + \\(\\frac{3}{8}\\) + \\(\\frac{3}{8}\\) + \\(\\frac{3}{8}\\)<br \/>\n1 + \\(\\frac{1}{2}\\)<br \/>\nAnswer:<br \/>\nLet the expresseons be named A., B., C., D.<br \/>\nSo,<br \/>\nA) 4 \u00d7 \\(\\frac{3}{8}\\)<br \/>\nB) 3 \u00d7 \\(\\frac{1}{8}\\)<br \/>\nC) \\(\\frac{3}{8}\\) + \\(\\frac{3}{8}\\) + \\(\\frac{3}{8}\\) + \\(\\frac{3}{8}\\)<br \/>\nD) 1 + \\(\\frac{1}{2}\\)<br \/>\nSo, from the above four expressions,<br \/>\nExpressions A), B), C) are in the normal form and C) is the expanded form of expression A)<br \/>\nHence, from the above,<br \/>\nWe can conclude that expression D) does not belong to the other three.<\/p>\n<p>Question 15.<br \/>\n<strong>Modeling Real Life<\/strong><br \/>\nYou complete \\(\\frac{5}{2}\\) inches of weaving each day for 5 days. The weaving needs to be at least 11 inches long. Is your weaving complete?<br \/>\n<img loading=\"lazy\" class=\"alignnone size-full wp-image-16356\" src=\"https:\/\/ccssmathanswers.com\/wp-content\/uploads\/2020\/12\/Big-Ideas-Math-Answer-Key-Grade-5-Chapter-9-Multiply-Fractions-9.1-13.png\" alt=\"Big Ideas Math Answer Key Grade 5 Chapter 9 Multiply Fractions 9.1 13\" width=\"132\" height=\"122\" \/><br \/>\nAnswer:<br \/>\nYes, your weaving is complete<\/p>\n<p>Explanation:<br \/>\nIt is given that you complete \\(\\frac{5}{2}\\) inches of weaving each day for 5 days.<br \/>\nSo,<br \/>\nThe total number of inches you completed in 5 days = ( The number of inches you weaved each day ) \u00d7 5<br \/>\n= \\(\\frac{5}{2}\\) \u00d7 5<br \/>\n= \\(\\frac{5}{2}\\) \u00d7 \\(\\frac{5}{1}\\)<br \/>\n= \\(\\frac{5 \u00d7 5}{2 \u00d7 1}\\)<br \/>\n= \\(\\frac{25}{2}\\)<br \/>\nIt is also given that the weaving needs to be at least 11 inches long.<br \/>\nSo,<br \/>\n11 inches can also be written as \\(\\frac{22}{2}\\)<br \/>\nSo,<br \/>\nWhen we compare the total number of inches needed for weaving and the total number of inches you weaved in 5 days, we can observe that<br \/>\nYou weaved more than the amount of the weaving.<br \/>\nHence, from the above,<br \/>\nWe can conclude that your weaving is completed.<\/p>\n<p>Question 16.<br \/>\n<strong>DIG DEEPER!<\/strong><br \/>\nYou spend \\(\\frac{7}{2}\\) hours playing drums each day for 2 days. Your friend spends \\(\\frac{5}{4}\\) hours playing drums each day for 6 days. Who spends more time playing drums? How much more?<br \/>\n<img loading=\"lazy\" class=\"alignnone size-full wp-image-16357\" src=\"https:\/\/ccssmathanswers.com\/wp-content\/uploads\/2020\/12\/Big-Ideas-Math-Answer-Key-Grade-5-Chapter-9-Multiply-Fractions-9.1-14.png\" alt=\"Big Ideas Math Answer Key Grade 5 Chapter 9 Multiply Fractions 9.1 14\" width=\"234\" height=\"149\" \/><br \/>\nAnswer:<br \/>\nYour friend spends more time playing drums than you<br \/>\nThe amount you played drums more than your friend is: \\(\\frac{1}{2}\\) hours<\/p>\n<p>Explanation:<br \/>\nIt is given that you spend \\(\\frac{7}{2}\\) hours each day playing drums for 2 days<br \/>\nSo,<br \/>\nThe time you played drums for 2 days = The time you played drums for each day \u00d7 2<br \/>\n= \\(\\frac{7}{2}\\) \u00d7 2<br \/>\n= \\(\\frac{7}{2}\\) \u00d7 \\(\\frac{2}{1}\\)<br \/>\n= \\(\\frac{7 \u00d7 2}{2 \u00d7 1}\\)<br \/>\n= \\(\\frac{14}{2}\\)<br \/>\n= \\(\\frac{28}{4}\\)<br \/>\n= 7 hours<br \/>\nIt is also given that Your friend spends \\(\\frac{5}{4}\\) hours playing drums each day for 6 days.<br \/>\nSo,<br \/>\nThe time your friend played drums for 6 days = The time your friend played drums for each day \u00d7 6<br \/>\n= \\(\\frac{5}{4}\\) \u00d7 6<br \/>\n= \\(\\frac{5}{4}\\) \u00d7 \\(\\frac{6}{1}\\)<br \/>\n= \\(\\frac{5 \u00d7 6}{4 \u00d7 1}\\)<br \/>\n= \\(\\frac{30}{4}\\) hours<br \/>\nNow,<br \/>\nWhen we compare the time played drums by you and your friends, your friend played more time than you<br \/>\nSo,<br \/>\nThe amount of time more your friend played than you = \\(\\frac{30}{4}\\) &#8211; \\(\\frac{28}{4}\\)<br \/>\n= \\(\\frac{30 &#8211; 28}{4}\\)<br \/>\n= \\(\\frac{2}{4}\\)<br \/>\n= \\(\\frac{1}{2}\\) hour<br \/>\nHence, from the above,<br \/>\nWe can conclude that<br \/>\nYour friend spends more time playing drums than you<br \/>\nThe amount you played drums more than your friend is: \\(\\frac{1}{2}\\) hours<\/p>\n<p><strong>Review &amp; Refresh<\/strong><\/p>\n<p><strong>Find the product.<\/strong><br \/>\nQuestion 17.<br \/>\n<img loading=\"lazy\" class=\"alignnone size-full wp-image-16358\" src=\"https:\/\/ccssmathanswers.com\/wp-content\/uploads\/2020\/12\/Big-Ideas-Math-Answer-Key-Grade-5-Chapter-9-Multiply-Fractions-9.1-15.png\" alt=\"Big Ideas Math Answer Key Grade 5 Chapter 9 Multiply Fractions 9.1 15\" width=\"64\" height=\"65\" \/><br \/>\nAnswer:<br \/>\n0.6 \u00d7 0.4 = 0.24<\/p>\n<p>Explanation:<br \/>\nThe given decimal numbers are: 0.6 and 0.4<br \/>\nthe representation of the decimal numbers in the fraction form is: \\(\\frac{6}{10}\\) and \\(\\frac{4}{10}\\)<br \/>\nNow,<br \/>\n\\(\\frac{6}{10}\\) \u00d7 \\(\\frac{4}{10}\\)<br \/>\n= \\(\\frac{6 \u00d7 4}{10 \u00d7 10}\\)<br \/>\n= \\(\\frac{24}{100}\\)<br \/>\nSo,<br \/>\nThe representation of \\(\\frac{24}{100}\\) in the decimal form is: 0.24<br \/>\nHence, 0.6 \u00d7 0.4 = 0.24<\/p>\n<p>Question 18.<br \/>\n<img loading=\"lazy\" class=\"alignnone size-full wp-image-16359\" src=\"https:\/\/ccssmathanswers.com\/wp-content\/uploads\/2020\/12\/Big-Ideas-Math-Answer-Key-Grade-5-Chapter-9-Multiply-Fractions-9.1-16.png\" alt=\"Big Ideas Math Answer Key Grade 5 Chapter 9 Multiply Fractions 9.1 16\" width=\"72\" height=\"62\" \/><br \/>\nAnswer:<br \/>\n2.37 \u00d7 1.9 = 4.503<\/p>\n<p>Explanation:<br \/>\nThe given decimal numbers are: 2.37 and 1.9<br \/>\nthe representation of the decimal numbers in the fraction form is: \\(\\frac{237}{100}\\) and \\(\\frac{19}{10}\\)<br \/>\nNow,<br \/>\n\\(\\frac{237}{100}\\) \u00d7 \\(\\frac{19}{10}\\)<br \/>\n= \\(\\frac{237 \u00d7 19}{100 \u00d7 10}\\)<br \/>\n= \\(\\frac{4,503}{1000}\\)<br \/>\nSo,<br \/>\nThe representation of \\(\\frac{4503}{1000}\\) in the decimal form is: 4.503<br \/>\nHence, 2.37 \u00d7 1.9 = 4.503<\/p>\n<p>Question 19.<br \/>\n<img loading=\"lazy\" class=\"alignnone size-full wp-image-16360\" src=\"https:\/\/ccssmathanswers.com\/wp-content\/uploads\/2020\/12\/Big-Ideas-Math-Answer-Key-Grade-5-Chapter-9-Multiply-Fractions-9.1-17.png\" alt=\"Big Ideas Math Answer Key Grade 5 Chapter 9 Multiply Fractions 9.1 17\" width=\"61\" height=\"64\" \/><br \/>\nAnswer:<br \/>\n52.8 \u00d7 0.75 = 39.6<\/p>\n<p>Explanation:<br \/>\nThe given decimal numbers are: 52.8 and 0.75<br \/>\nthe representation of the decimal numbers in the fraction form is: \\(\\frac{6}{10}\\) and \\(\\frac{4}{10}\\)<br \/>\nNow,<br \/>\n\\(\\frac{528}{10}\\) \u00d7 \\(\\frac{75}{100}\\)<br \/>\n= \\(\\frac{528 \u00d7 75}{10 \u00d7 100}\\)<br \/>\n= \\(\\frac{3960}{1000}\\)<br \/>\nSo,<br \/>\nThe representation of \\(\\frac{3960}{1000}\\) in the decimal form is: 39.6<br \/>\nHence, 52.8 \u00d7 0.75 = 39.6<\/p>\n<h3><a id=\"Lesson_9.2_Use_Models_to_Multiply_Fractions_by_Whole_Numbers\"><\/a>Lesson 9.2 Use Models to Multiply Fractions by Whole Numbers<\/h3>\n<p>You need to give water to \\(\\frac{2}{3}\\) of the dogs at a shelter. There are 12 dogs at the shelter. How many dogs need water? Draw a model to support your answer.<br \/>\nAnswer:<br \/>\nThe number of dogs that need water is: 8 dogs<\/p>\n<p>Explanation:<br \/>\nIt is given that you need to give water to \\(\\frac{2}{3}\\) of the dogs at a shelter and there are 12 dogs at the shelter<br \/>\nSo,<br \/>\nThe number of dogs that need water = ( The fraction of dogs that need water ) \u00d7 ( The total number of dogs )<br \/>\n= \\(\\frac{2}{3}\\) \u00d7 12<br \/>\nWe know that,<br \/>\n\\(\\frac{a}{b}\\) \u00d7 x = \\(\\frac{a}{b}\\) \u00d7 \\(\\frac{x}{1}\\)<br \/>\n= \\(\\frac{a \u00d7 x}{b \u00d7 1}\\)<br \/>\nSo,<br \/>\n\\(\\frac{2}{3}\\) \u00d7 12<br \/>\n= \\(\\frac{2}{3}\\) \u00d7 \\(\\frac{12}{1}\\)<br \/>\n= \\(\\frac{2 \u00d7 12}{3 \u00d7 1}\\)<br \/>\n= \\(\\frac{8}{1}\\)<br \/>\n= 8<br \/>\nHence, from the above,<br \/>\nWe can conclude that there are 8 dogs that need water<\/p>\n<p><strong>Reasoning<\/strong><br \/>\nHow can you use a model to multiply a fraction by a whole number? Explain.<br \/>\nAnswer:<br \/>\nWe can multiply a fraction by a whole number by using the following multiplication properties. They are:<br \/>\nA) \\(\\frac{a}{b}\\) \u00d7 x = \\(\\frac{a}{b}\\) \u00d7 \\(\\frac{x}{1}\\)<br \/>\nB) x = \\(\\frac{x}{1}\\)<\/p>\n<p><strong>Think and Grow: Multiply Fractions by Whole Numbers<\/strong><\/p>\n<p>You can use models to multiply a fraction by a whole number.<br \/>\n<strong>Example<\/strong><br \/>\nFind \\(\\frac{3}{4}\\) of 8.<br \/>\n<img loading=\"lazy\" class=\"alignnone size-full wp-image-36507\" src=\"https:\/\/ccssmathanswers.com\/wp-content\/uploads\/2020\/12\/Big-Ideas-Math-Answers-Grade-5-Chapter-9-3.jpg\" alt=\"\" width=\"671\" height=\"254\" srcset=\"https:\/\/bigideasmathanswers.com\/wp-content\/uploads\/2020\/12\/Big-Ideas-Math-Answers-Grade-5-Chapter-9-3.jpg 671w, https:\/\/bigideasmathanswers.com\/wp-content\/uploads\/2020\/12\/Big-Ideas-Math-Answers-Grade-5-Chapter-9-3-300x114.jpg 300w\" sizes=\"(max-width: 671px) 100vw, 671px\" \/><\/p>\n<p><strong>Example<\/strong><br \/>\nFind \\(\\frac{5}{8}\\) \u00d7 4.<br \/>\n<img loading=\"lazy\" class=\"alignnone size-full wp-image-36510\" src=\"https:\/\/ccssmathanswers.com\/wp-content\/uploads\/2020\/12\/Big-Ideas-Math-Answers-Grade-5-Chapter-9-4.jpg\" alt=\"\" width=\"741\" height=\"398\" srcset=\"https:\/\/bigideasmathanswers.com\/wp-content\/uploads\/2020\/12\/Big-Ideas-Math-Answers-Grade-5-Chapter-9-4.jpg 741w, https:\/\/bigideasmathanswers.com\/wp-content\/uploads\/2020\/12\/Big-Ideas-Math-Answers-Grade-5-Chapter-9-4-300x161.jpg 300w\" sizes=\"(max-width: 741px) 100vw, 741px\" \/><\/p>\n<p><strong>Show and Grow<\/strong><\/p>\n<p>Question 1.<br \/>\nFind \\(\\frac{2}{5}\\) of 10.<br \/>\nAnswer:<br \/>\n\\(\\frac{2}{5}\\) \u00d7 10 = 4<\/p>\n<p>Explanation:<br \/>\nThe given numbers are: \\(\\frac{2}{5}\\) and 10<br \/>\nWe know that,<br \/>\n\\(\\frac{a}{b}\\) \u00d7 x = \\(\\frac{a}{b}\\) \u00d7 \\(\\frac{x}{1}\\)<br \/>\n= \\(\\frac{a \u00d7 x}{b \u00d7 1}\\)<br \/>\nSo,<br \/>\n\\(\\frac{2}{5}\\) \u00d7 10 = \\(\\frac{2}{5}\\) \u00d7 \\(\\frac{10}{1}\\)<br \/>\n= \\(\\frac{2 \u00d7 10}{5 \u00d7 1}\\)<br \/>\n= \\(\\frac{4}{1}\\)<br \/>\n= 4<br \/>\nHence,<br \/>\n\\(\\frac{2}{5}\\) \u00d7 10 = 4<\/p>\n<p>Question 2.<br \/>\nFind \\(\\frac{7}{12}\\) \u00d7 6.<br \/>\nAnswer:<br \/>\n\\(\\frac{7}{12}\\) \u00d7 6 = \\(\\frac{7}{2}\\)<\/p>\n<p>Explanation:<br \/>\nThe given numbers are: \\(\\frac{7}{12}\\) and 6<br \/>\nWe know that,<br \/>\n\\(\\frac{a}{b}\\) \u00d7 x = \\(\\frac{a}{b}\\) \u00d7 \\(\\frac{x}{1}\\)<br \/>\n= \\(\\frac{a \u00d7 x}{b \u00d7 1}\\)<br \/>\nSo,<br \/>\n\\(\\frac{7}{12}\\) \u00d7 6 = \\(\\frac{7}{12}\\) \u00d7 \\(\\frac{6}{1}\\)<br \/>\n= \\(\\frac{7 \u00d7 6}{12 \u00d7 1}\\)<br \/>\n= \\(\\frac{7}{2}\\)<br \/>\nHence,<br \/>\n\\(\\frac{7}{12}\\) \u00d7 6 = \\(\\frac{7}{2}\\)<\/p>\n<p><strong>Apply and Grow: Practice<\/strong><\/p>\n<p><strong>Multiply. Use a model to help.<\/strong><br \/>\nQuestion 3.<br \/>\n\\(\\frac{5}{6}\\) of 12<br \/>\nAnswer:<br \/>\n\\(\\frac{5}{6}\\) \u00d7 12 = 10<\/p>\n<p>Explanation:<br \/>\nThe given numbers are: \\(\\frac{5}{6}\\) and 12<br \/>\nWe know that,<br \/>\n\\(\\frac{a}{b}\\) \u00d7 x = \\(\\frac{a}{b}\\) \u00d7 \\(\\frac{x}{1}\\)<br \/>\n= \\(\\frac{a \u00d7 x}{b \u00d7 1}\\)<br \/>\nSo,<br \/>\n\\(\\frac{5}{6}\\) \u00d7 12 = \\(\\frac{5}{6}\\) \u00d7 \\(\\frac{12}{1}\\)<br \/>\n= \\(\\frac{5 \u00d7 12}{6 \u00d7 1}\\)<br \/>\n= \\(\\frac{10}{1}\\)<br \/>\n= 10<br \/>\nHence,<br \/>\n\\(\\frac{5}{6}\\) \u00d7 12 = 10<\/p>\n<p>Question 4.<br \/>\n\\(\\frac{2}{3}\\) \u00d7 9<br \/>\nAnswer:<br \/>\n\\(\\frac{2}{3}\\) \u00d7 9 = 6<\/p>\n<p>Explanation:<br \/>\nThe given numbers are: \\(\\frac{2}{3}\\) and 9<br \/>\nWe know that,<br \/>\n\\(\\frac{a}{b}\\) \u00d7 x = \\(\\frac{a}{b}\\) \u00d7 \\(\\frac{x}{1}\\)<br \/>\n= \\(\\frac{a \u00d7 x}{b \u00d7 1}\\)<br \/>\nSo,<br \/>\n\\(\\frac{2}{3}\\) \u00d7 9 = \\(\\frac{2}{3}\\) \u00d7 \\(\\frac{9}{1}\\)<br \/>\n= \\(\\frac{2 \u00d7 9}{3 \u00d7 1}\\)<br \/>\n= \\(\\frac{6}{1}\\)<br \/>\n= 6<br \/>\nHence,<br \/>\n\\(\\frac{2}{3}\\) \u00d7 9 = 6<\/p>\n<p>Question 5.<br \/>\n\\(\\frac{1}{5}\\) \u00d7 10<br \/>\nAnswer:<br \/>\n\\(\\frac{1}{5}\\) \u00d7 10 = 2<\/p>\n<p>Explanation:<br \/>\nThe given numbers are: \\(\\frac{1}{5}\\) and 10<br \/>\nWe know that,<br \/>\n\\(\\frac{a}{b}\\) \u00d7 x = \\(\\frac{a}{b}\\) \u00d7 \\(\\frac{x}{1}\\)<br \/>\n= \\(\\frac{a \u00d7 x}{b \u00d7 1}\\)<br \/>\nSo,<br \/>\n\\(\\frac{1}{5}\\) \u00d7 10 = \\(\\frac{1}{5}\\) \u00d7 \\(\\frac{10}{1}\\)<br \/>\n= \\(\\frac{1 \u00d7 10}{5 \u00d7 1}\\)<br \/>\n= \\(\\frac{2}{1}\\)<br \/>\n= 2<br \/>\nHence,<br \/>\n\\(\\frac{1}{5}\\) \u00d7 10 = 2<\/p>\n<p>Question 6.<br \/>\n\\(\\frac{3}{5}\\) of 5<br \/>\nAnswer:<br \/>\n\\(\\frac{3}{5}\\) \u00d7 5 = 3<\/p>\n<p>Explanation:<br \/>\nThe given numbers are: \\(\\frac{3}{5}\\) and 5<br \/>\nWe know that,<br \/>\n\\(\\frac{a}{b}\\) \u00d7 x = \\(\\frac{a}{b}\\) \u00d7 \\(\\frac{x}{1}\\)<br \/>\n= \\(\\frac{a \u00d7 x}{b \u00d7 1}\\)<br \/>\nSo,<br \/>\n\\(\\frac{3}{5}\\) \u00d7 5 = \\(\\frac{3}{5}\\) \u00d7 \\(\\frac{5}{1}\\)<br \/>\n= \\(\\frac{3 \u00d7 5}{5 \u00d7 1}\\)<br \/>\n= \\(\\frac{3}{1}\\)<br \/>\n= 3<br \/>\nHence,<br \/>\n\\(\\frac{3}{5}\\) \u00d7 5 = 3<\/p>\n<p>Question 7.<br \/>\n\\(\\frac{1}{6}\\) of 3<br \/>\nAnswer:<br \/>\n\\(\\frac{1}{6}\\) \u00d7 3 = \\(\\frac{1}{2}\\)<\/p>\n<p>Explanation:<br \/>\nThe given numbers are: \\(\\frac{1}{6}\\) and 3<br \/>\nWe know that,<br \/>\n\\(\\frac{a}{b}\\) \u00d7 x = \\(\\frac{a}{b}\\) \u00d7 \\(\\frac{x}{1}\\)<br \/>\n= \\(\\frac{a \u00d7 x}{b \u00d7 1}\\)<br \/>\nSo,<br \/>\n\\(\\frac{1}{6}\\) \u00d7 3 = \\(\\frac{1}{6}\\) \u00d7 \\(\\frac{3}{1}\\)<br \/>\n= \\(\\frac{1 \u00d7 3}{6 \u00d7 1}\\)<br \/>\n= \\(\\frac{1}{2}\\)<br \/>\nHence,<br \/>\n\\(\\frac{1}{6}\\) \u00d7 3 = \\(\\frac{1}{2}\\)<\/p>\n<p>Question 8.<br \/>\n\\(\\frac{3}{8}\\) \u00d7 4<br \/>\nAnswer:<br \/>\n\\(\\frac{3}{8}\\) \u00d7 4 = \\(\\frac{3}{2}\\)<\/p>\n<p>Explanation:<br \/>\nThe given numbers are: \\(\\frac{3}{8}\\) and 4<br \/>\nWe know that,<br \/>\n\\(\\frac{a}{b}\\) \u00d7 x = \\(\\frac{a}{b}\\) \u00d7 \\(\\frac{x}{1}\\)<br \/>\n= \\(\\frac{a \u00d7 x}{b \u00d7 1}\\)<br \/>\nSo,<br \/>\n\\(\\frac{3}{8}\\) \u00d7 4 = \\(\\frac{3}{8}\\) \u00d7 \\(\\frac{4}{1}\\)<br \/>\n= \\(\\frac{3 \u00d7 4}{8 \u00d7 1}\\)<br \/>\n= \\(\\frac{3}{2}\\)<br \/>\nHence,<br \/>\n\\(\\frac{3}{8}\\) \u00d7 4 = \\(\\frac{3}{2}\\)<\/p>\n<p>Question 9.<br \/>\nYou have 25 beads. You use \\(\\frac{2}{5}\\) of the beads to make a bracelet. How many beads do you use?<br \/>\nAnswer:<br \/>\nThe number of beads you used is: 10 beads<\/p>\n<p>Explanation:<br \/>\nIt is given that you have 25 beads and you use \\(\\frac{2}{5}\\) of the beads to make a bracelet.<br \/>\nSo,<br \/>\nThe number of beads you used = ( The fraction of beads used to make 1 bracelet ) \u00d7 ( The total number of beads )<br \/>\n= \\(\\frac{2}{5}\\) \u00d7 25<br \/>\nWe know that,<br \/>\n\\(\\frac{a}{b}\\) \u00d7 x = \\(\\frac{a}{b}\\) \u00d7 \\(\\frac{x}{1}\\)<br \/>\n= \\(\\frac{a \u00d7 x}{b \u00d7 1}\\)<br \/>\nSo,<br \/>\n\\(\\frac{2}{5}\\) \u00d7 25 = \\(\\frac{2}{5}\\) \u00d7 \\(\\frac{25}{1}\\)<br \/>\n= \\(\\frac{2 \u00d7 25}{5 \u00d7 1}\\)<br \/>\n= \\(\\frac{10}{1}\\)<br \/>\n= 10 beads<br \/>\nHence, from the above,<br \/>\nWe can conclude that the number of beads you used to make bracelets are: 10 beads<\/p>\n<p>Question 10.<br \/>\n<strong>Writing<\/strong><br \/>\nWrite and solve a real-life problem for the expression.<br \/>\n\\(\\frac{3}{4}\\) \u00d7 20<br \/>\nAnswer:<br \/>\nSuppose there are 20 passengers in a bus and they occupied the place \\(\\frac{3}{4}\\) of the bus.<br \/>\nHence,<br \/>\nThe total number of seats in the bus = ( The fraction of the place occupied by the passengers ) \u00d7 ( The total number of passengers )<br \/>\n= \\(\\frac{3}{4}\\) \u00d7 20<br \/>\nNow,<br \/>\nWe know that,<br \/>\n\\(\\frac{a}{b}\\) \u00d7 x = \\(\\frac{a}{b}\\) \u00d7 \\(\\frac{x}{1}\\)<br \/>\n= \\(\\frac{a \u00d7 x}{b \u00d7 1}\\)<br \/>\nSo,<br \/>\n\\(\\frac{3}{4}\\) \u00d7 20 = \\(\\frac{3}{4}\\) \u00d7 \\(\\frac{20}{1}\\)<br \/>\n= \\(\\frac{3 \u00d7 20}{4 \u00d7 1}\\)<br \/>\n= \\(\\frac{15}{1}\\)<br \/>\n= 15 seats<br \/>\nHence, from the above,<br \/>\nWe can conclude that there are 15 seats in the bus.<\/p>\n<p>Question 11.<br \/>\n<strong>YOU BE THE TEACHER<\/strong><br \/>\nDescartes finds \\(\\frac{2}{3}\\) \u00d7 6. Is he correct? Explain.<br \/>\n<img loading=\"lazy\" class=\"alignnone size-full wp-image-16363\" src=\"https:\/\/ccssmathanswers.com\/wp-content\/uploads\/2020\/12\/Big-Ideas-Math-Answers-5th-Grade-Chapter-9-Multiply-Fractions-9.2-3.png\" alt=\"Big Ideas Math Answers 5th Grade Chapter 9 Multiply Fractions 9.2 3\" width=\"485\" height=\"218\" srcset=\"https:\/\/bigideasmathanswers.com\/wp-content\/uploads\/2020\/12\/Big-Ideas-Math-Answers-5th-Grade-Chapter-9-Multiply-Fractions-9.2-3.png 485w, https:\/\/bigideasmathanswers.com\/wp-content\/uploads\/2020\/12\/Big-Ideas-Math-Answers-5th-Grade-Chapter-9-Multiply-Fractions-9.2-3-300x135.png 300w\" sizes=\"(max-width: 485px) 100vw, 485px\" \/><br \/>\nAnswer:<br \/>\nNo, Descartes is not correct<\/p>\n<p>Explanation:<br \/>\nAccording to Descartes,<br \/>\nThe given numbers are: \\(\\frac{2}{3}\\) and 6<br \/>\nSo,<br \/>\nAccording to Descartes, 6 is divided into 3 equal parts<br \/>\nSo,<br \/>\n6 \u00f7 3 = 2 equal parts<br \/>\nSo,<br \/>\nAccording to Descartes, these 2 equal parts also divided into 2 parts.<br \/>\nSo,<br \/>\nThe total number of parts = 2 equal parts + 2 equal parts = 4 parts<br \/>\nSo,<br \/>\nThe product of \\(\\frac{2}{3}\\) and 6 is 4<br \/>\nNow,<br \/>\nWe know that,<br \/>\n\\(\\frac{a}{b}\\) \u00d7 x = \\(\\frac{a}{b}\\) \u00d7 \\(\\frac{x}{1}\\)<br \/>\n= \\(\\frac{a \u00d7 x}{b \u00d7 1}\\)<br \/>\nSo,<br \/>\n\\(\\frac{2}{3}\\) \u00d7 6 = \\(\\frac{2}{3}\\) \u00d7 \\(\\frac{6}{1}\\)<br \/>\n= \\(\\frac{6 \u00d7 2}{3 \u00d7 1}\\)<br \/>\n= \\(\\frac{4}{1}\\)<br \/>\n= 4<br \/>\nHence, from the above,<br \/>\nWe can conclude that Descartes is not correct.<\/p>\n<p><strong>Think and Grow: Modeling Real Life<\/strong><\/p>\n<p><strong>Example<\/strong><br \/>\nA recipe calls for 2 cups of rice. You only have \\(\\frac{3}{4}\\) of that amount. How much more rice do you need?<br \/>\n<img loading=\"lazy\" class=\"alignnone size-full wp-image-16364\" src=\"https:\/\/ccssmathanswers.com\/wp-content\/uploads\/2020\/12\/Big-Ideas-Math-Answers-5th-Grade-Chapter-9-Multiply-Fractions-9.2-4.png\" alt=\"Big Ideas Math Answers 5th Grade Chapter 9 Multiply Fractions 9.2 4\" width=\"157\" height=\"140\" \/><br \/>\nFind the number of cups of rice that you have by finding \\(\\frac{3}{4}\\) of 2.<br \/>\n<img loading=\"lazy\" class=\"alignnone size-full wp-image-16365\" src=\"https:\/\/ccssmathanswers.com\/wp-content\/uploads\/2020\/12\/Big-Ideas-Math-Answers-5th-Grade-Chapter-9-Multiply-Fractions-9.2-5.png\" alt=\"Big Ideas Math Answers 5th Grade Chapter 9 Multiply Fractions 9.2 5\" width=\"450\" height=\"252\" srcset=\"https:\/\/bigideasmathanswers.com\/wp-content\/uploads\/2020\/12\/Big-Ideas-Math-Answers-5th-Grade-Chapter-9-Multiply-Fractions-9.2-5.png 450w, https:\/\/bigideasmathanswers.com\/wp-content\/uploads\/2020\/12\/Big-Ideas-Math-Answers-5th-Grade-Chapter-9-Multiply-Fractions-9.2-5-300x168.png 300w\" sizes=\"(max-width: 450px) 100vw, 450px\" \/><br \/>\nSo,<br \/>\nYou have \\(\\frac{3}{2}\\) cups of rice.<br \/>\nSubtract the amount of rice you have from the amount of rice you need.<br \/>\n2 &#8211; \\(\\frac{3}{2}\\) = \\(\\frac{2}{1}\\) &#8211; \\(\\frac{3}{2}\\)<br \/>\n= \\(\\frac{(2 \u00d7 2) &#8211; 3}{2}\\)<br \/>\n= \\(\\frac{1}{2}\\)<br \/>\nSo,<br \/>\nyou need \\(\\frac{1}{2}\\) cup more of rice.<\/p>\n<p><strong>Show and Grow<\/strong><\/p>\n<p>Question 12.<br \/>\nYou have 12 tokens. You use \\(\\frac{3}{4}\\) of them to play a pinball game. How many tokens do you have left?<br \/>\nAnswer:<br \/>\nThe number of tokens you have left is: 3 tokens<\/p>\n<p>Explanation:<br \/>\nIt is given that you have 12 tokens and you use \\(\\frac{3}{4}\\) of them to play a pinball game.<br \/>\nSo,<br \/>\nThe number of tokens used to play a pinball game = ( The fraction of tokens used to play a pinball game ) \u00d7 ( The total number of tokens )<br \/>\n= \\(\\frac{3}{4}\\) \u00d7 12<br \/>\n= \\(\\frac{3}{4}\\) \u00d7 \\(\\frac{12}{1}\\)<br \/>\n= \\(\\frac{3 \u00d7 12}{4 \u00d7 1}\\)<br \/>\n= \\(\\frac{9}{1}\\)<br \/>\n= 9 tokens<br \/>\nSo,<br \/>\nThe number of tokens left = ( The total number of tokens ) &#8211; ( The number of tokens used to play the pinball )<br \/>\n= 12 &#8211; 9<br \/>\n= 3 tokens<br \/>\nHence, from the above,<br \/>\nWe can conclude that the number of tokens left are: 3 tokens<\/p>\n<p>Question 13.<br \/>\nA male lion sleeps \\(\\frac{5}{6}\\) \u00d7 6 hours of each day. How many hours does the lion sleep in 1 week?<br \/>\n<img loading=\"lazy\" class=\"alignnone size-full wp-image-16366\" src=\"https:\/\/ccssmathanswers.com\/wp-content\/uploads\/2020\/12\/Big-Ideas-Math-Answers-5th-Grade-Chapter-9-Multiply-Fractions-9.2-6.png\" alt=\"Big Ideas Math Answers 5th Grade Chapter 9 Multiply Fractions 9.2 6\" width=\"149\" height=\"113\" \/><br \/>\nAnswer:<br \/>\nThe number of hours the lion sleeps in 1 week is: 35 hours<\/p>\n<p>Explanation:<br \/>\nIt is given that a male lion sleeps \\(\\frac{5}{6}\\) \u00d7 6 hours of each day<br \/>\nSo,<br \/>\nThe number of hours the lion sleeps in 1 day = \\(\\frac{5}{6}\\) \u00d7 6 hours<br \/>\n= \\(\\frac{5}{6}\\) \u00d7 \\(\\frac{6}{1}\\)<br \/>\n= \\(\\frac{5 \u00d7 6}{6 \u00d7 1}\\)<br \/>\n= \\(\\frac{5}{1}\\)<br \/>\n= 5 hours<br \/>\nWe know that,<br \/>\n1 week = 7 days<br \/>\nSo,<br \/>\nThe total number of hours the lion sleeps in 1 week = ( The number of hours the lion sleeps in 1 day ) \u00d7 ( The number od fays in 1 week )<br \/>\n= 5 \u00d7 7<br \/>\n= 35 hours<br \/>\nHence, from the above,<br \/>\nWe can conclude that the lion sleeps for 35 hours in 1 week<\/p>\n<p>Question 14.<br \/>\n<strong>DIG DEEPER!<\/strong><br \/>\nIn a class of 20 students, \\(\\frac{1}{10}\\) of the students are 10 years old, \\(\\frac{4}{5}\\)of the students are 11 years old, and the rest are 12 years old. How many more 11-year-olds than 12-year-olds are in the class?<br \/>\nAnswer:<br \/>\nThe number of 11-year-olds more than 12-year-olds is: 14<\/p>\n<p>Explanation:<br \/>\nIt is given that in a class of 20 students, \\(\\frac{1}{10}\\) of the students are 10 years old, \\(\\frac{4}{5}\\)of the students are 11 years old, and the rest are 12 years old.<br \/>\nSo,<br \/>\nThe number of 10-year-olds = ( The fraction of 10-year-olds ) \u00d7 ( The total number of students )<br \/>\n= \\(\\frac{1}{10}\\) \u00d7 20<br \/>\n= \\(\\frac{1 \u00d7 20}{10 \u00d7 1}\\)<br \/>\n= 2 10-year-olds<br \/>\nThe number of 11-year-olds = ( The fraction of 11-year-olds ) \u00d7 ( The total number of students )<br \/>\n= \\(\\frac{4}{5}\\) \u00d7 20<br \/>\n= \\(\\frac{4}{5}\\) \u00d7 \\(\\frac{20}{1}\\)<br \/>\n= \\(\\frac{4 \u00d7 20}{5 \u00d7 1}\\)<br \/>\n= \\(\\frac{16}{1}\\)<br \/>\n= 16 11-year-olds<br \/>\nSo,<br \/>\nThe number of 12-year-olds = ( The total number of students ) &#8211; ( The number of 10-year-olds + The number of 11-year-olds )<br \/>\n= 20 &#8211; ( 16 + 2 )<br \/>\n= 2 12-year-olds<br \/>\nSo,<br \/>\nThe number of 11-year-olds more than 12-year-olds = ( The number of 11-year-olds ) &#8211; ( The numebr of 12-year-olds )<br \/>\n= 16 &#8211; 2<br \/>\n= 14 students<br \/>\nHence, from the above,<br \/>\nWe can conclude that there are 14 students who are 11-years-old more than 12-years-old.<\/p>\n<h3><a id=\"Use_Models_to_Multiply_Fractions_by_Whole_Numbers_Homework_&amp;_Practice_9.2\"><\/a>Use Models to Multiply Fractions by Whole Numbers Homework &amp; Practice 9.2<\/h3>\n<p><strong>Multiply. Use a model to help.<br \/>\n<\/strong>Question 1.<br \/>\n\\(\\frac{2}{3}\\) \u00d7 6<br \/>\nAnswer:<br \/>\n\\(\\frac{2}{3}\\) \u00d7 6 = 4<\/p>\n<p>Explanation:<br \/>\nThe given numbers are: \\(\\frac{2}{3}\\) and 6<br \/>\nWe know that,<br \/>\n\\(\\frac{a}{b}\\) \u00d7 x = \\(\\frac{a}{b}\\) \u00d7 \\(\\frac{x}{1}\\)<br \/>\n= \\(\\frac{a \u00d7 x}{b \u00d7 1}\\)<br \/>\nSo,<br \/>\n\\(\\frac{2}{3}\\) \u00d7 6 = \\(\\frac{2}{3}\\) \u00d7 \\(\\frac{6}{1}\\)<br \/>\n= \\(\\frac{2 \u00d7 6}{3 \u00d7 1}\\)<br \/>\n= \\(\\frac{4}{1}\\)<br \/>\n= 4<br \/>\nHence,<br \/>\n\\(\\frac{2}{3}\\) \u00d7 6 = 4<\/p>\n<p>Question 2.<br \/>\n\\(\\frac{3}{5}\\) of 10<br \/>\nAnswer:<br \/>\n\\(\\frac{3}{5}\\) \u00d7 10 = 6<\/p>\n<p>Explanation:<br \/>\nThe given numbers are: \\(\\frac{3}{5}\\) and 10<br \/>\nWe know that,<br \/>\n\\(\\frac{a}{b}\\) \u00d7 x = \\(\\frac{a}{b}\\) \u00d7 \\(\\frac{x}{1}\\)<br \/>\n= \\(\\frac{a \u00d7 x}{b \u00d7 1}\\)<br \/>\nSo,<br \/>\n\\(\\frac{3}{5}\\) \u00d7 10 = \\(\\frac{3}{5}\\) \u00d7 \\(\\frac{10}{1}\\)<br \/>\n= \\(\\frac{3 \u00d7 10}{5 \u00d7 1}\\)<br \/>\n= \\(\\frac{6}{1}\\)<br \/>\n= 6<br \/>\nHence,<br \/>\n\\(\\frac{3}{5}\\) \u00d7 10 = 6<\/p>\n<p>Question 3.<br \/>\n\\(\\frac{1}{2}\\) of 4<br \/>\nAnswer:<br \/>\n\\(\\frac{1}{2}\\) \u00d7 4 = 2<\/p>\n<p>Explanation:<br \/>\nThe given numbers are: \\(\\frac{1}{2}\\) and 4<br \/>\nWe know that,<br \/>\n\\(\\frac{a}{b}\\) \u00d7 x = \\(\\frac{a}{b}\\) \u00d7 \\(\\frac{x}{1}\\)<br \/>\n= \\(\\frac{a \u00d7 x}{b \u00d7 1}\\)<br \/>\nSo,<br \/>\n\\(\\frac{1}{2}\\) \u00d7 4 = \\(\\frac{1}{2}\\) \u00d7 \\(\\frac{4}{1}\\)<br \/>\n= \\(\\frac{1 \u00d7 4}{2 \u00d7 1}\\)<br \/>\n= \\(\\frac{2}{1}\\)<br \/>\n= 2<br \/>\nHence,<br \/>\n\\(\\frac{1}{2}\\) \u00d7 4 = 2<\/p>\n<p>Question 4.<br \/>\n\\(\\frac{1}{4}\\) \u00d7 12<br \/>\nAnswer:<br \/>\n\\(\\frac{1}{4}\\) \u00d7 12 = 3<\/p>\n<p>Explanation:<br \/>\nThe given numbers are: \\(\\frac{1}{4}\\) and 12<br \/>\nWe know that,<br \/>\n\\(\\frac{a}{b}\\) \u00d7 x = \\(\\frac{a}{b}\\) \u00d7 \\(\\frac{x}{1}\\)<br \/>\n= \\(\\frac{a \u00d7 x}{b \u00d7 1}\\)<br \/>\nSo,<br \/>\n\\(\\frac{1}{4}\\) \u00d7 12 = \\(\\frac{1}{4}\\) \u00d7 \\(\\frac{12}{1}\\)<br \/>\n= \\(\\frac{1 \u00d7 12}{4 \u00d7 1}\\)<br \/>\n= \\(\\frac{3}{1}\\)<br \/>\n= 3<br \/>\nHence,<br \/>\n\\(\\frac{1}{12}\\) \u00d7 4 = 3<\/p>\n<p>Question 5.<br \/>\n\\(\\frac{5}{6}\\) \u00d7 3<br \/>\nAnswer:<br \/>\n\\(\\frac{5}{6}\\) \u00d7 3 = \\(\\frac{5}{2}\\)<\/p>\n<p>Explanation:<br \/>\nThe given numbers are: \\(\\frac{5}{6}\\) and 3<br \/>\nWe know that,<br \/>\n\\(\\frac{a}{b}\\) \u00d7 x = \\(\\frac{a}{b}\\) \u00d7 \\(\\frac{x}{1}\\)<br \/>\n= \\(\\frac{a \u00d7 x}{b \u00d7 1}\\)<br \/>\nSo,<br \/>\n\\(\\frac{5}{6}\\) \u00d7 3 = \\(\\frac{5}{6}\\) \u00d7 \\(\\frac{3}{1}\\)<br \/>\n= \\(\\frac{5 \u00d7 3}{6 \u00d7 1}\\)<br \/>\n= \\(\\frac{5}{2}\\)<br \/>\nHence,<br \/>\n\\(\\frac{5}{6}\\) \u00d7 3 = \\(\\frac{5}{2}\\)<\/p>\n<p>Question 6.<br \/>\n\\(\\frac{3}{4}\\) of 2<br \/>\nAnswer:<br \/>\n\\(\\frac{3}{4}\\) \u00d7 2 = \\(\\frac{3}{2}\\)<\/p>\n<p>Explanation:<br \/>\nThe given numbers are: \\(\\frac{3}{4}\\) and 2<br \/>\nWe know that,<br \/>\n\\(\\frac{a}{b}\\) \u00d7 x = \\(\\frac{a}{b}\\) \u00d7 \\(\\frac{x}{1}\\)<br \/>\n= \\(\\frac{a \u00d7 x}{b \u00d7 1}\\)<br \/>\nSo,<br \/>\n\\(\\frac{3}{4}\\) \u00d7 2 = \\(\\frac{3}{4}\\) \u00d7 \\(\\frac{2}{1}\\)<br \/>\n= \\(\\frac{3 \u00d7 2}{4 \u00d7 1}\\)<br \/>\n= \\(\\frac{3}{2}\\)<br \/>\nHence,<br \/>\n\\(\\frac{3}{4}\\) \u00d7 2 = \\(\\frac{3}{2}\\)<\/p>\n<p>Question 7.<br \/>\nYou have 27 foam balls. You use \\(\\frac{1}{3}\\) of the balls for a model. How many balls do you use?<br \/>\n<img loading=\"lazy\" class=\"alignnone size-full wp-image-16367\" src=\"https:\/\/ccssmathanswers.com\/wp-content\/uploads\/2020\/12\/Big-Ideas-Math-Answers-5th-Grade-Chapter-9-Multiply-Fractions-9.2-7.png\" alt=\"Big Ideas Math Answers 5th Grade Chapter 9 Multiply Fractions 9.2 7\" width=\"210\" height=\"62\" \/><br \/>\nAnswer:<br \/>\nThe number of balls you used is: 9 balls<\/p>\n<p>Explanation:<br \/>\nIt is given that there are 27 foam balls and you use \\(\\frac{1}{3}\\) of the balls for a model.<br \/>\nSo,<br \/>\nThe number of balls you used = ( The fraction of balls you used ) \u00d7 ( The total number of balls )<br \/>\n= \\(\\frac{1}{3}\\) \u00d7 27<br \/>\nNow,<br \/>\nWe know that,<br \/>\n\\(\\frac{a}{b}\\) \u00d7 x = \\(\\frac{a}{b}\\) \u00d7 \\(\\frac{x}{1}\\)<br \/>\n= \\(\\frac{a \u00d7 x}{b \u00d7 1}\\)<br \/>\nSo,<br \/>\n\\(\\frac{1}{3}\\) \u00d7 27 = \\(\\frac{1}{3}\\) \u00d7 \\(\\frac{27}{1}\\)<br \/>\n= \\(\\frac{1 \u00d7 27}{3 \u00d7 1}\\)<br \/>\n= \\(\\frac{9}{1}\\)<br \/>\n= 9 balls<br \/>\nHence, from the above,<br \/>\nWe can conclude that the number of foam balls you used are: 27<\/p>\n<p>Question 8.<br \/>\nAn object that weighs 1 pound on Earth weighs about \\(\\frac{1}{15}\\) pound on Pluto. A man weighs 240 pounds on Earth. How many pounds does he weigh on Pluto?<br \/>\nAnswer:<br \/>\nThe number of pounds the man weigh in Pluto is: 16 pounds<\/p>\n<p>Explanation:<br \/>\nIt is given that an object that weighs 1 pound on Earth weighs about \\(\\frac{1}{15}\\) pound on Pluto.<br \/>\nIt is also given that a man weighs 240 pounds on Earth.<br \/>\nSo,<br \/>\nThe weight of a man on pluto = ( The fraction of weight of a man on pluto when compared to earth ) \u00d7 ( The weight of the man on earth )<br \/>\n= \\(\\frac{1}{15}\\) \u00d7 240<br \/>\nNow,<br \/>\nWe know that,<br \/>\n\\(\\frac{a}{b}\\) \u00d7 x = \\(\\frac{a}{b}\\) \u00d7 \\(\\frac{x}{1}\\)<br \/>\n= \\(\\frac{a \u00d7 x}{b \u00d7 1}\\)<br \/>\nSo,<br \/>\n\\(\\frac{1}{15}\\) \u00d7 240 = \\(\\frac{1}{15}\\) \u00d7 \\(\\frac{240}{1}\\)<br \/>\n= \\(\\frac{1 \u00d7 240}{15 \u00d7 1}\\)<br \/>\n= \\(\\frac{16}{1}\\)<br \/>\n= 16 pounds<br \/>\nHence, from the above,<br \/>\nWe can conclude that the weight of the man on pluto is: 16 pounds<\/p>\n<p>Question 9.<br \/>\n<strong>Structure<\/strong><br \/>\nWrite a multiplication equation represented by the model.<br \/>\n<img loading=\"lazy\" class=\"alignnone size-full wp-image-16368\" src=\"https:\/\/ccssmathanswers.com\/wp-content\/uploads\/2020\/12\/Big-Ideas-Math-Answers-5th-Grade-Chapter-9-Multiply-Fractions-9.2-8.png\" alt=\"Big Ideas Math Answers 5th Grade Chapter 9 Multiply Fractions 9.2 8\" width=\"297\" height=\"94\" \/><br \/>\nAnswer:<\/p>\n<p>Question 10.<br \/>\n<strong>DIG DEEPER!<\/strong><br \/>\nFind each missing number.<br \/>\n<img loading=\"lazy\" class=\"alignnone size-full wp-image-16369\" src=\"https:\/\/ccssmathanswers.com\/wp-content\/uploads\/2020\/12\/Big-Ideas-Math-Answers-5th-Grade-Chapter-9-Multiply-Fractions-9.2-9.png\" alt=\"Big Ideas Math Answers 5th Grade Chapter 9 Multiply Fractions 9.2 9\" width=\"274\" height=\"138\" \/><br \/>\nAnswer:<br \/>\nLet the expression be named A), B), C), and D)<br \/>\nSo,<br \/>\nThe missing number of A is: 12<br \/>\nThe missing number of B is: 6<br \/>\nThe missing number of C is: 2<br \/>\nThe missing number of D is: 5<\/p>\n<p>Explanation:<br \/>\nLet the expressions be named as A), B), C), and D)<br \/>\nSo,<br \/>\nA) The given fractions are: \\(\\frac{1}{3}\\) and 4<br \/>\nLet the missing number be X<br \/>\nSo,<br \/>\nX \u00d7 \\(\\frac{1}{3}\\) = 4<br \/>\nWhen multiplication goes from left to right or from right to left, it will become the division<br \/>\nWhen division goes from left to right or from right to left, it will become multiplication.<br \/>\nSo,<br \/>\nX = 4 \u00f7 \\(\\frac{1}{3}\\)<br \/>\nWe know that,<br \/>\n\\(\\frac{a}{b}\\) \u00f7 \\(\\frac{x}{y}\\) = \\(\\frac{a}{b}\\) \u00d7 \\(\\frac{y}{x}\\)<br \/>\nSo,<br \/>\n\\(\\frac{4}{1}\\) \u00f7 \\(\\frac{1}{3}\\)<br \/>\n= \\(\\frac{4}{1}\\) \u00d7 \\(\\frac{3}{1}\\)<br \/>\n= \\(\\frac{4 \u00d7 3}{1 \u00d7 1}\\)<br \/>\n= 12<br \/>\nHence, the missing number is 12<br \/>\nB) The given numbers are: \\(\\frac{2}{5}\\) and 15<br \/>\nWe know that,<br \/>\n\\(\\frac{a}{b}\\) \u00d7 x = \\(\\frac{a}{b}\\) \u00d7 \\(\\frac{x}{1}\\)<br \/>\n= \\(\\frac{a \u00d7 x}{b \u00d7 1}\\)<br \/>\nSo,<br \/>\n\\(\\frac{2}{5}\\) \u00d7 15 = \\(\\frac{2}{5}\\) \u00d7 \\(\\frac{15}{1}\\)<br \/>\n= \\(\\frac{2 \u00d7 15}{5 \u00d7 1}\\)<br \/>\n= \\(\\frac{6}{1}\\)<br \/>\n= 6<br \/>\nHence,<br \/>\n\\(\\frac{2}{5}\\) \u00d7 15 = 6<br \/>\nLike the above two expressions, the remaining two expressions can also be solved.<br \/>\nhence, from the above,<br \/>\nWe can conclude that<br \/>\nThe missing number of A is: 12<br \/>\nThe missing number of B is: 6<br \/>\nThe missing number of C is: 2<br \/>\nThe missing number of D is: 5<\/p>\n<p>Question 11.<br \/>\n<strong>Modeling Real Life<\/strong><br \/>\nYou have 28 craft sticks. You use \\(\\frac{4}{7}\\) of them for a project. How many craft sticks do you have left?<br \/>\nAnswer:<br \/>\nThe number of craft sticks you have left is: 12 craft sticks<\/p>\n<p>Explanation:<br \/>\nIt is given that you have 28 craft sticks and you used \\(\\frac{4}{7}\\) of them for a project.<br \/>\nSo,<br \/>\nThe number of craft sticks you used = ( The fraction of craft sticks you used ) \u00d7 ( The total number of craft sticks )<br \/>\n= \\(\\frac{4}{7}\\) \u00d7 28<br \/>\n= \\(\\frac{4}{7}\\) \u00d7 \\(\\frac{28}{1}\\)<br \/>\n= \\(\\frac{4 \u00d7 28}{7 \u00d7 1}\\)<br \/>\n= \\(\\frac{16}{1}\\)<br \/>\n= 16<br \/>\nSo,<br \/>\nThe number of craft sticks you left = ( The total number of craft sticks ) &#8211; ( The number of craft sticks you used )<br \/>\n= 28 &#8211; 16<br \/>\n= 12 craft sticks<br \/>\nHence, from the above,<br \/>\nWe can conclude that the number of craft sticks you left is: 12 craft sticks<\/p>\n<p>Question 12.<br \/>\n<strong>Modeling Real Life<\/strong><br \/>\nA mother otter spends \\(\\frac{1}{3}\\) of each day feeding her baby. How many hours does the mother otter spend feeding her baby in 1 week?<br \/>\n<img loading=\"lazy\" class=\"alignnone size-full wp-image-16370\" src=\"https:\/\/ccssmathanswers.com\/wp-content\/uploads\/2020\/12\/Big-Ideas-Math-Answers-5th-Grade-Chapter-9-Multiply-Fractions-9.2-10.png\" alt=\"Big Ideas Math Answers 5th Grade Chapter 9 Multiply Fractions 9.2 10\" width=\"279\" height=\"147\" \/><br \/>\nAnswer:<br \/>\nThe number of hours the mother otter spend feeding her baby in 1 week is: 56 hours<\/p>\n<p>Explanation:<br \/>\nIt is given that a mother otter spends \\(\\frac{1}{3}\\) of each day feeding her baby.<br \/>\nWe know that,<br \/>\n1 day = 24 hours<br \/>\nSo,<br \/>\nThe number of hours the mother otter spends feeding her baby in 1 day = ( The fraction of time the mother otter spends in feeding milk ) \u00d7 24<br \/>\n= \\(\\frac{1}{3}\\) \u00d7 24<br \/>\n= \\(\\frac{1}{3}\\) \u00d7 \\(\\frac{24}{1}\\)<br \/>\n= \\(\\frac{1 \u00d7 24}{3 \u00d7 1}\\)<br \/>\n= \\(\\frac{8}{1}\\)<br \/>\n= 8 hours<br \/>\nNow,<br \/>\nWe know that,<br \/>\n1 week = 7 days<br \/>\nSo,<br \/>\nThe number of hours the mother otter spends feeding her milk in 1 week = ( The number of hours the mother otter feeding her milk in 1 day ) \u00d7 7<br \/>\n= 8 \u00d7 7<br \/>\n= 56 hours<br \/>\nHence, from the above,<br \/>\nWe can conclude that the mother otter spends feeding her milk for 56 hours in 1 week<\/p>\n<p><strong>Review &amp; Refresh<\/strong><\/p>\n<p><strong>Estimate the quotient.<\/strong><br \/>\nQuestion 13.<br \/>\n5,692 \u00f7 5<br \/>\nAnswer:<br \/>\n5,692 \u00f7 5 =1,138 R 2<\/p>\n<p>Explanation:<br \/>\nBy using the partial quotients method,<br \/>\n5,692 \u00f7 5 = ( 5,000 + 600 + 90 ) \u00f7 5<br \/>\n= ( 5,000 \u00f7 5 ) + ( 600 \u00f7 5 ) + ( 90 \u00f7 5 )<br \/>\n= 1,000 + 120 + 18<br \/>\n= 1,138 R 2<br \/>\nHence, 5,692 \u00f7 5 = 1,138 R 2<\/p>\n<p>Question 14.<br \/>\n309 \u00f7 12<br \/>\nAnswer:<br \/>\n309 \u00f7 12 = 25 R 9<\/p>\n<p>Explanation:<br \/>\nBy using the partial quotients method,<br \/>\n309 \u00f7 12 = ( 240 + 60 ) \u00f7 12<br \/>\n= ( 240 \u00f7 12 ) + ( 60 \u00f7 12 )<br \/>\n= 20 + 5<br \/>\n= 25 R 9<br \/>\nHence, 309 \u00f7 12 = 25 R 2<\/p>\n<p>Question 15.<br \/>\n2,987 \u00f7 53<br \/>\nAnswer:<br \/>\n2,987 \u00f7 53 = 2,987 \u00f7 ( 50 + 3 )<br \/>\n= ( 2,985 \u00f7 50 ) + ( 2,985 \u00f7 3 )<br \/>\n= 995 R 2 + 59.7<br \/>\n= 1,054.7 R 2<\/p>\n<h3><a id=\"Lesson_9.3_Multiply_Fractions_and_Whole_Numbers\"><\/a>Lesson 9.3 Multiply Fractions and Whole Numbers<\/h3>\n<p><strong>Explore and Grow<\/strong><\/p>\n<p>Use models to help you complete the table. What do you notice about each expression and its product?<br \/>\n<img loading=\"lazy\" class=\"alignnone size-full wp-image-16371\" src=\"https:\/\/ccssmathanswers.com\/wp-content\/uploads\/2020\/12\/Big-Ideas-Math-Answers-Grade-5-Chapter-9-Multiply-Fractions-9.3-1.png\" alt=\"Big Ideas Math Answers Grade 5 Chapter 9 Multiply Fractions 9.3 1\" width=\"191\" height=\"305\" srcset=\"https:\/\/bigideasmathanswers.com\/wp-content\/uploads\/2020\/12\/Big-Ideas-Math-Answers-Grade-5-Chapter-9-Multiply-Fractions-9.3-1.png 191w, https:\/\/bigideasmathanswers.com\/wp-content\/uploads\/2020\/12\/Big-Ideas-Math-Answers-Grade-5-Chapter-9-Multiply-Fractions-9.3-1-188x300.png 188w\" sizes=\"(max-width: 191px) 100vw, 191px\" \/><br \/>\nAnswer:<br \/>\nThe completed table is:<br \/>\n<img loading=\"lazy\" class=\"alignnone size-full wp-image-36896\" src=\"https:\/\/ccssmathanswers.com\/wp-content\/uploads\/2020\/12\/Big-Ideas-Math-Answers-Grade-5-Chapter-9-5.jpg\" alt=\"\" width=\"193\" height=\"288\" \/><\/p>\n<p>From the completed table,<br \/>\nWe can observe the multiplication of the whole number and the fraction.<br \/>\nThe product of a whole number and a fraction may be a whole number or a fraction.<\/p>\n<p><strong>Construct Arguments<\/strong><br \/>\nExplain how to multiply fractions and whole numbers without using models.<br \/>\nAnswer:<br \/>\nWe can multiply the whole numbers and fractions by using the properties of the multiplication. They are:<br \/>\nA) \\(\\frac{a}{b}\\) \u00d7 p = \\(\\frac{a}{b}\\) \u00d7 \\(\\frac{p}{1}\\)<br \/>\n= \\(\\frac{a \u00d7 p}{ b \u00d7 1}\\)<br \/>\nB) p = \\(\\frac{p}{1}\\)<\/p>\n<p><strong>Think and Grow: Multiply Fractions and Whole Numbers<\/strong><\/p>\n<p><strong>Key Idea<\/strong><br \/>\nYou can find the product of a fraction and a whole number by multiplying the numerator and the whole number. Then write the result over the denominator.<br \/>\n<strong>Example<\/strong><br \/>\nFind 2 \u00d7 \\(\\frac{5}{6}\\).<br \/>\nMultiply the numerator and the whole number.<br \/>\n<img loading=\"lazy\" class=\"alignnone size-full wp-image-36898\" src=\"https:\/\/ccssmathanswers.com\/wp-content\/uploads\/2020\/12\/Big-Ideas-Math-Answers-Grade-5-Chapter-9-6.jpg\" alt=\"\" width=\"598\" height=\"154\" srcset=\"https:\/\/bigideasmathanswers.com\/wp-content\/uploads\/2020\/12\/Big-Ideas-Math-Answers-Grade-5-Chapter-9-6.jpg 598w, https:\/\/bigideasmathanswers.com\/wp-content\/uploads\/2020\/12\/Big-Ideas-Math-Answers-Grade-5-Chapter-9-6-300x77.jpg 300w\" sizes=\"(max-width: 598px) 100vw, 598px\" \/><\/p>\n<p><strong>Example<\/strong><br \/>\nFind \\(\\frac{5}{6}\\) \u00d7 2<br \/>\nMultiply the numerator and the whole number.<br \/>\n<img loading=\"lazy\" class=\"alignnone size-full wp-image-36899\" src=\"https:\/\/ccssmathanswers.com\/wp-content\/uploads\/2020\/12\/Big-Ideas-Math-Answers-Grade-5-Chapter-9-7.jpg\" alt=\"\" width=\"680\" height=\"235\" srcset=\"https:\/\/bigideasmathanswers.com\/wp-content\/uploads\/2020\/12\/Big-Ideas-Math-Answers-Grade-5-Chapter-9-7.jpg 680w, https:\/\/bigideasmathanswers.com\/wp-content\/uploads\/2020\/12\/Big-Ideas-Math-Answers-Grade-5-Chapter-9-7-300x104.jpg 300w\" sizes=\"(max-width: 680px) 100vw, 680px\" \/><\/p>\n<p><strong>Show and Grow<\/strong><\/p>\n<p><strong>Multiply.<\/strong><br \/>\nQuestion 1.<br \/>\n3 \u00d7 \\(\\frac{5}{8}\\) = _______<br \/>\nAnswer:<br \/>\n3 \u00d7 \\(\\frac{5}{8}\\) = \\(\\frac{15}{8}\\)<\/p>\n<p>Explanation:<br \/>\nThe given numbers are: 3 and \\(\\frac{5}{8}\\)<br \/>\nWe know that,<br \/>\n\\(\\frac{a}{b}\\) \u00d7 p = \\(\\frac{a}{b}\\) \u00d7 \\(\\frac{p}{1}\\)<br \/>\n= \\(\\frac{a \u00d7 p}{ b \u00d7 1}\\)<br \/>\np = \\(\\frac{p}{1}\\)<br \/>\nSo,<br \/>\n3 \u00d7 \\(\\frac{5}{8}\\) = \\(\\frac{3}{1}\\) \u00d7 \\(\\frac{5}{8}\\)<br \/>\n= \\(\\frac{5 \u00d7 3}{8 \u00d7 1}\\)<br \/>\n= \\(\\frac{15}{8}\\)<br \/>\nHence,<br \/>\n3 \u00d7 \\(\\frac{5}{8}\\) = \\(\\frac{15}{8}\\)<\/p>\n<p>Question 2.<br \/>\n6 \u00d7 \\(\\frac{4}{9}\\) = _______<br \/>\nAnswer:<br \/>\n6 \u00d7 \\(\\frac{4}{9}\\) = \\(\\frac{8}{3}\\)<\/p>\n<p>Explanation:<br \/>\nThe given numbers are: 6 and \\(\\frac{4}{9}\\)<br \/>\nWe know that,<br \/>\n\\(\\frac{a}{b}\\) \u00d7 p = \\(\\frac{a}{b}\\) \u00d7 \\(\\frac{p}{1}\\)<br \/>\n= \\(\\frac{a \u00d7 p}{ b \u00d7 1}\\)<br \/>\np = \\(\\frac{p}{1}\\)<br \/>\nSo,<br \/>\n6 \u00d7 \\(\\frac{4}{9}\\) = \\(\\frac{6}{1}\\) \u00d7 \\(\\frac{4}{9}\\)<br \/>\n= \\(\\frac{6 \u00d7 4}{9 \u00d7 1}\\)<br \/>\n= \\(\\frac{24}{9}\\)<br \/>\n= \\(\\frac{8}{3}\\)<br \/>\nHence,<br \/>\n6 \u00d7 \\(\\frac{4}{9}\\) = \\(\\frac{8}{3}\\)<\/p>\n<p>Question 3.<br \/>\n\\(\\frac{2}{5}\\) \u00d7 15 = _______<br \/>\nAnswer:<br \/>\n15 \u00d7 \\(\\frac{2}{5}\\) = 6<\/p>\n<p>Explanation:<br \/>\nThe given numbers are: 15 and \\(\\frac{2}{5}\\)<br \/>\nWe know that,<br \/>\n\\(\\frac{a}{b}\\) \u00d7 p = \\(\\frac{a}{b}\\) \u00d7 \\(\\frac{p}{1}\\)<br \/>\n= \\(\\frac{a \u00d7 p}{ b \u00d7 1}\\)<br \/>\np = \\(\\frac{p}{1}\\)<br \/>\nSo,<br \/>\n15\u00d7 \\(\\frac{2}{5}\\) = \\(\\frac{15}{1}\\) \u00d7 \\(\\frac{2}{5}\\)<br \/>\n= \\(\\frac{15 \u00d7 2}{5 \u00d7 1}\\)<br \/>\n= \\(\\frac{6}{1}\\)<br \/>\n= 6<br \/>\nHence,<br \/>\n15 \u00d7 \\(\\frac{2}{5}\\) = 6<\/p>\n<p><strong>Apply and Grow: Practice<\/strong><\/p>\n<p><strong>Multiply.<\/strong><br \/>\nQuestion 4.<br \/>\n\\(\\frac{3}{5}\\) \u00d7 2 = _______<br \/>\nAnswer:<br \/>\n2 \u00d7 \\(\\frac{3}{5}\\) = \\(\\frac{6}{5}\\)<\/p>\n<p>Explanation:<br \/>\nThe given numbers are: 2 and \\(\\frac{3}{5}\\)<br \/>\nWe know that,<br \/>\n\\(\\frac{a}{b}\\) \u00d7 p = \\(\\frac{a}{b}\\) \u00d7 \\(\\frac{p}{1}\\)<br \/>\n= \\(\\frac{a \u00d7 p}{ b \u00d7 1}\\)<br \/>\np = \\(\\frac{p}{1}\\)<br \/>\nSo,<br \/>\n2 \u00d7 \\(\\frac{3}{5}\\) = \\(\\frac{2}{1}\\) \u00d7 \\(\\frac{3}{5}\\)<br \/>\n= \\(\\frac{2 \u00d7 3}{5 \u00d7 1}\\)<br \/>\n= \\(\\frac{6}{5}\\)<br \/>\nHence,<br \/>\n2 \u00d7 \\(\\frac{3}{5}\\) = \\(\\frac{6}{5}\\)<\/p>\n<p>Question 5.<br \/>\n5 \u00d7 \\(\\frac{2}{9}\\) = _______<br \/>\nAnswer:<br \/>\n5 \u00d7 \\(\\frac{2}{9}\\) = \\(\\frac{10}{9}\\)<\/p>\n<p>Explanation:<br \/>\nThe given numbers are: 5 and \\(\\frac{2}{9}\\)<br \/>\nWe know that,<br \/>\n\\(\\frac{a}{b}\\) \u00d7 p = \\(\\frac{a}{b}\\) \u00d7 \\(\\frac{p}{1}\\)<br \/>\n= \\(\\frac{a \u00d7 p}{ b \u00d7 1}\\)<br \/>\np = \\(\\frac{p}{1}\\)<br \/>\nSo,<br \/>\n5 \u00d7 \\(\\frac{2}{9}\\) = \\(\\frac{5}{1}\\) \u00d7 \\(\\frac{2}{9}\\)<br \/>\n= \\(\\frac{5 \u00d7 2}{9 \u00d7 1}\\)<br \/>\n= \\(\\frac{10}{9}\\)<br \/>\nHence,<br \/>\n5 \u00d7 \\(\\frac{2}{9}\\) = \\(\\frac{10}{9}\\)<\/p>\n<p>Question 6.<br \/>\n\\(\\frac{5}{6}\\) \u00d7 4 = _______<br \/>\nAnswer:<br \/>\n4 \u00d7 \\(\\frac{5}{6}\\) = \\(\\frac{10}{3}\\)<\/p>\n<p>Explanation:<br \/>\nThe given numbers are: 4 and \\(\\frac{5}{6}\\)<br \/>\nWe know that,<br \/>\n\\(\\frac{a}{b}\\) \u00d7 p = \\(\\frac{a}{b}\\) \u00d7 \\(\\frac{p}{1}\\)<br \/>\n= \\(\\frac{a \u00d7 p}{ b \u00d7 1}\\)<br \/>\np = \\(\\frac{p}{1}\\)<br \/>\nSo,<br \/>\n4 \u00d7 \\(\\frac{5}{6}\\) = \\(\\frac{4}{1}\\) \u00d7 \\(\\frac{5}{6}\\)<br \/>\n= \\(\\frac{5 \u00d7 4}{6 \u00d7 1}\\)<br \/>\n= \\(\\frac{20}{6}\\)<br \/>\n= \\(\\frac{10}{3}\\)<br \/>\nHence,<br \/>\n4 \u00d7 \\(\\frac{5}{6}\\) = \\(\\frac{10}{3}\\)<\/p>\n<p>Question 7.<br \/>\n8 \u00d7 \\(\\frac{3}{10}\\) = _______<br \/>\nAnswer:<br \/>\n8 \u00d7 \\(\\frac{3}{10}\\) = \\(\\frac{12}{5}\\)<\/p>\n<p>Explanation:<br \/>\nThe given numbers are: 8 and \\(\\frac{3}{10}\\)<br \/>\nWe know that,<br \/>\n\\(\\frac{a}{b}\\) \u00d7 p = \\(\\frac{a}{b}\\) \u00d7 \\(\\frac{p}{1}\\)<br \/>\n= \\(\\frac{a \u00d7 p}{ b \u00d7 1}\\)<br \/>\np = \\(\\frac{p}{1}\\)<br \/>\nSo,<br \/>\n8 \u00d7 \\(\\frac{3}{10}\\) = \\(\\frac{8}{1}\\) \u00d7 \\(\\frac{3}{10}\\)<br \/>\n= \\(\\frac{8 \u00d7 3}{10 \u00d7 1}\\)<br \/>\n= \\(\\frac{24}{10}\\)<br \/>\n= \\(\\frac{12}{5}\\)<br \/>\nHence,<br \/>\n8 \u00d7 \\(\\frac{3}{10}\\) = \\(\\frac{12}{5}\\)<\/p>\n<p>Question 8.<br \/>\n\\(\\frac{1}{5}\\) \u00d7 7 = _______<br \/>\nAnswer:<br \/>\n7 \u00d7 \\(\\frac{1}{5}\\) = \\(\\frac{7}{5}\\)<\/p>\n<p>Explanation:<br \/>\nThe given numbers are: 7 and \\(\\frac{1}{5}\\)<br \/>\nWe know that,<br \/>\n\\(\\frac{a}{b}\\) \u00d7 p = \\(\\frac{a}{b}\\) \u00d7 \\(\\frac{p}{1}\\)<br \/>\n= \\(\\frac{a \u00d7 p}{ b \u00d7 1}\\)<br \/>\np = \\(\\frac{p}{1}\\)<br \/>\nSo,<br \/>\n7 \u00d7 \\(\\frac{1}{5}\\) = \\(\\frac{7}{1}\\) \u00d7 \\(\\frac{1}{5}\\)<br \/>\n= \\(\\frac{7 \u00d7 1}{5 \u00d7 1}\\)<br \/>\n= \\(\\frac{7}{5}\\)<br \/>\nHence,<br \/>\n7 \u00d7 \\(\\frac{1}{5}\\) = \\(\\frac{7}{5}\\)<\/p>\n<p>Question 9.<br \/>\n9 \u00d7 \\(\\frac{5}{12}\\) = _______<br \/>\nAnswer:<br \/>\n9 \u00d7 \\(\\frac{5}{12}\\) = \\(\\frac{15}{4}\\)<\/p>\n<p>Explanation:<br \/>\nThe given numbers are: 9 and \\(\\frac{5}{12}\\)<br \/>\nWe know that,<br \/>\n\\(\\frac{a}{b}\\) \u00d7 p = \\(\\frac{a}{b}\\) \u00d7 \\(\\frac{p}{1}\\)<br \/>\n= \\(\\frac{a \u00d7 p}{ b \u00d7 1}\\)<br \/>\np = \\(\\frac{p}{1}\\)<br \/>\nSo,<br \/>\n9 \u00d7 \\(\\frac{5}{12}\\) = \\(\\frac{9}{1}\\) \u00d7 \\(\\frac{5}{12}\\)<br \/>\n= \\(\\frac{9 \u00d7 5}{12 \u00d7 1}\\)<br \/>\n= \\(\\frac{45}{12}\\)<br \/>\n= \\(\\frac{15}{4}\\)<br \/>\nHence,<br \/>\n9 \u00d7 \\(\\frac{5}{12}\\) = \\(\\frac{15}{4}\\)<\/p>\n<p>Question 10.<br \/>\n15 \u00d7 \\(\\frac{5}{8}\\) = _______<br \/>\nAnswer:<br \/>\n15 \u00d7 \\(\\frac{5}{8}\\) = \\(\\frac{75}{8}\\)<\/p>\n<p>Explanation:<br \/>\nThe given numbers are: 15 and \\(\\frac{5}{8}\\)<br \/>\nWe know that,<br \/>\n\\(\\frac{a}{b}\\) \u00d7 p = \\(\\frac{a}{b}\\) \u00d7 \\(\\frac{p}{1}\\)<br \/>\n= \\(\\frac{a \u00d7 p}{ b \u00d7 1}\\)<br \/>\np = \\(\\frac{p}{1}\\)<br \/>\nSo,<br \/>\n15 \u00d7 \\(\\frac{5}{8}\\) = \\(\\frac{15}{1}\\) \u00d7 \\(\\frac{5}{8}\\)<br \/>\n= \\(\\frac{15 \u00d7 5}{8 \u00d7 1}\\)<br \/>\n= \\(\\frac{75}{8}\\)<br \/>\nHence,<br \/>\n15 \u00d7 \\(\\frac{5}{8}\\) = \\(\\frac{75}{8}\\)<\/p>\n<p>Question 11.<br \/>\n\\(\\frac{3}{4}\\) \u00d7 20 = _______<br \/>\nAnswer:<br \/>\n20 \u00d7 \\(\\frac{3}{4}\\) = 15<\/p>\n<p>Explanation:<br \/>\nThe given numbers are: 20 and \\(\\frac{3}{4}\\)<br \/>\nWe know that,<br \/>\n\\(\\frac{a}{b}\\) \u00d7 p = \\(\\frac{a}{b}\\) \u00d7 \\(\\frac{p}{1}\\)<br \/>\n= \\(\\frac{a \u00d7 p}{ b \u00d7 1}\\)<br \/>\np = \\(\\frac{p}{1}\\)<br \/>\nSo,<br \/>\n20 \u00d7 \\(\\frac{3}{4}\\) = \\(\\frac{20}{1}\\) \u00d7 \\(\\frac{3}{4}\\)<br \/>\n= \\(\\frac{20 \u00d7 3}{4 \u00d7 1}\\)<br \/>\n= \\(\\frac{60}{4}\\)<br \/>\n= \\(\\frac{15}{1}\\)<br \/>\n= 15<br \/>\nHence,<br \/>\n20 \u00d7 \\(\\frac{3}{4}\\) = 15<\/p>\n<p>Question 12.<br \/>\n\\(\\frac{7}{9}\\) \u00d7 5 = _______<br \/>\nAnswer:<br \/>\n5 \u00d7 \\(\\frac{7}{9}\\) = \\(\\frac{35}{9}\\)<\/p>\n<p>Explanation:<br \/>\nThe given numbers are: 5 and \\(\\frac{7}{9}\\)<br \/>\nWe know that,<br \/>\n\\(\\frac{a}{b}\\) \u00d7 p = \\(\\frac{a}{b}\\) \u00d7 \\(\\frac{p}{1}\\)<br \/>\n= \\(\\frac{a \u00d7 p}{ b \u00d7 1}\\)<br \/>\np = \\(\\frac{p}{1}\\)<br \/>\nSo,<br \/>\n5 \u00d7 \\(\\frac{7}{9}\\) = \\(\\frac{5}{1}\\) \u00d7 \\(\\frac{7}{9}\\)<br \/>\n= \\(\\frac{5 \u00d7 7}{9 \u00d7 1}\\)<br \/>\n= \\(\\frac{35}{9}\\)<br \/>\nHence,<br \/>\n5 \u00d7 \\(\\frac{7}{9}\\) = \\(\\frac{35}{9}\\)<\/p>\n<p>Question 13.<br \/>\nOne-tenth of the 50 states in the United States of America have a mockingbird as their state bird. How many states have a mockingbird as their state bird?<br \/>\n<img loading=\"lazy\" class=\"alignnone size-full wp-image-16374\" src=\"https:\/\/ccssmathanswers.com\/wp-content\/uploads\/2020\/12\/Big-Ideas-Math-Answers-Grade-5-Chapter-9-Multiply-Fractions-9.3-4.png\" alt=\"Big Ideas Math Answers Grade 5 Chapter 9 Multiply Fractions 9.3 4\" width=\"176\" height=\"130\" \/><br \/>\nAnswer:<br \/>\nThe number of states that have mockingbird as their state bird is: 5 states<\/p>\n<p>Explanation:<br \/>\nIt is given that one-tenth of the 50 states in the United States of America have a mockingbird as their state bird<br \/>\nSo,<br \/>\nThe number of states that have a mockingbird as their state bird = ( The fraction of the states that have a mockingbird as their state bird ) \u00d7 ( The total number of states in the United States of America )<br \/>\n= \\(\\frac{1}{10}\\) \u00d7 50<br \/>\nNow,<br \/>\nWe know that,<br \/>\n\\(\\frac{a}{b}\\) \u00d7 p = \\(\\frac{a}{b}\\) \u00d7 \\(\\frac{p}{1}\\)<br \/>\n= \\(\\frac{a \u00d7 p}{ b \u00d7 1}\\)<br \/>\np = \\(\\frac{p}{1}\\)<br \/>\nSo,<br \/>\n50 \u00d7 \\(\\frac{1}{10}\\) = \\(\\frac{50}{1}\\) \u00d7 \\(\\frac{1}{10}\\)<br \/>\n= \\(\\frac{50 \u00d7 1}{10 \u00d7 1}\\)<br \/>\n= \\(\\frac{50}{10}\\)<br \/>\n= \\(\\frac{5}{1}\\)<br \/>\n= 5 states<br \/>\nHence, from the above,<br \/>\nWe can conclude that there are 5 states that have mockingbird as their state bird<\/p>\n<p>Question 14.<br \/>\n<strong>Writing<\/strong><br \/>\nExplain why 9 \u00d7 \\(\\frac{2}{3}\\) is equivalent to \\(\\frac{2}{3}\\) \u00d7 9.<br \/>\nAnswer:<br \/>\nBy using the Commutative property of multiplication,<br \/>\na \u00d7 b = b \u00d7 a<br \/>\nSo,<br \/>\nBy using the above property,<br \/>\nIn 9 \u00d7 \\(\\frac{2}{3}\\),<br \/>\n&#8216;a&#8217; is: 9<br \/>\n&#8216;b&#8217; is: \\(\\frac{2}{3}\\)<br \/>\nHence, from the above,<br \/>\nWe can conclude that\u00a0 9 \u00d7 &#8220;\\(\\frac{2}{3}\\)&#8221; is equivalent to &#8220;\\(\\frac{2}{3}\\) \u00d7 9&#8243; by using the Commutative property of multiplication.<\/p>\n<p>Question 15.<br \/>\n<strong>Reasoning<\/strong><br \/>\nWithout calculating, determine which product is greater. Explain.<br \/>\n\\(\\frac{1}{8}\\) \u00d7 24<br \/>\n\\(\\frac{7}{8}\\) \u00d7 24<br \/>\nAnswer:<br \/>\nThe product of &#8220;\\(\\frac{7}{8}\\) \u00d7 24&#8243; is greater than &#8220;\\(\\frac{1}{8}\\) \u00d7 24&#8243;<\/p>\n<p>Explanation:<br \/>\nThe given products are: \\(\\frac{1}{8}\\) \u00d7 24 and \\(\\frac{7}{8}\\) \u00d7 24<br \/>\nWe know that,<br \/>\n\\(\\frac{a}{b}\\) \u00d7 p = \\(\\frac{a}{b}\\) \u00d7 \\(\\frac{p}{1}\\)<br \/>\n= \\(\\frac{a \u00d7 p}{ b \u00d7 1}\\)<br \/>\np = \\(\\frac{p}{1}\\)<br \/>\nSo, from the above fractions,<br \/>\nWe can observe that except numerator, the denominator and the whole number is all the same.<br \/>\nSo,<br \/>\nTo find which product is greater, we just have to compare the numerators of the two fractions without calculating the value of the product.<br \/>\nIn the comparison of the numerators,<br \/>\nWe can observe that,<br \/>\n1 &lt; 7<br \/>\nSo,<br \/>\nFirst fraction numerator &lt; Second fraction numerator<br \/>\nHence, from the above,<br \/>\nWe can conclude that the product of &#8220;\\(\\frac{7}{8}\\) \u00d7 24&#8243; is greater than &#8220;\\(\\frac{1}{8}\\) \u00d7 24&#8243;<\/p>\n<p><strong>Think and Grow: Modeling Real Life<\/strong><\/p>\n<p><strong>Example<\/strong><br \/>\nNewton buys 27 songs. Two-thirds of them are classical songs. Descartes buys 16 songs. Seven-eighths of them are classical songs. Who buys more classical songs? How many more?<br \/>\n<img loading=\"lazy\" class=\"alignnone size-full wp-image-16375\" src=\"https:\/\/ccssmathanswers.com\/wp-content\/uploads\/2020\/12\/Big-Ideas-Math-Answers-Grade-5-Chapter-9-Multiply-Fractions-9.3-5.png\" alt=\"Big Ideas Math Answers Grade 5 Chapter 9 Multiply Fractions 9.3 5\" width=\"174\" height=\"178\" \/><br \/>\nMultiply \\(\\frac{2}{3}\\) by 27 to find the number of classical songs Newton buys. Multiply \\(\\frac{7}{8}\\) by 16 to find the number Descartes buys.<br \/>\n<img loading=\"lazy\" class=\"alignnone size-full wp-image-36900\" src=\"https:\/\/ccssmathanswers.com\/wp-content\/uploads\/2020\/12\/Big-Ideas-Math-Answers-Grade-5-Chapter-9-8.jpg\" alt=\"\" width=\"529\" height=\"132\" srcset=\"https:\/\/bigideasmathanswers.com\/wp-content\/uploads\/2020\/12\/Big-Ideas-Math-Answers-Grade-5-Chapter-9-8.jpg 529w, https:\/\/bigideasmathanswers.com\/wp-content\/uploads\/2020\/12\/Big-Ideas-Math-Answers-Grade-5-Chapter-9-8-300x75.jpg 300w\" sizes=\"(max-width: 529px) 100vw, 529px\" \/><br \/>\nSo, Newton buys more classical songs.<br \/>\nSubtract the products to find how many more.<br \/>\n18 &#8211; 14 = 4<br \/>\nHence,<br \/>\nNewton buys 4 more classical songs than Descartes.<\/p>\n<p><strong>Show and Grow<\/strong><\/p>\n<p>Question 16.<br \/>\nYou take 48 pictures on a walking tour. Five-twelfths of them is of buildings. Your friend takes 45 pictures. Six-fifteenths of them are of buildings. Who takes more pictures of buildings? How many more?<br \/>\nAnswer:<br \/>\nYou take more pictures<br \/>\nYou take 2 pictures more than your friend<\/p>\n<p>Explanation:<br \/>\nIt is given that you take 48 pictures on a walking tour and five-twelfths if them is of buildings.<br \/>\nSo,<br \/>\nThe number of buildings taken by you = ( The total number of pictures taken by you ) \u00d7 ( The fraction of pictures that is of buildings )<br \/>\n= 48 \u00d7 \\(\\frac{5}{12}\\)<br \/>\n= \\(\\frac{48}{1}\\) \u00d7 \\(\\frac{5}{12}\\)<br \/>\n= \\(\\frac{48 \u00d7 5}{1 \u00d7 12}\\)<br \/>\n= 20 pictures<br \/>\nIt is also given that your friend taken 45 pictures and six-fifteenth of them is buildings<br \/>\nSo,<br \/>\nThe number of buildings taken by your friend = ( The total number of pictures taken by your friend ) \u00d7 ( The fraction of pictures that is of buildings )<br \/>\n= 45 \u00d7 \\(\\frac{6}{15}\\)<br \/>\n= \\(\\frac{45}{1}\\) \u00d7 \\(\\frac{6}{15}\\)<br \/>\n= \\(\\frac{45 \u00d7 6}{1 \u00d7 15}\\)<br \/>\n= 18 pictures<br \/>\nSo,<br \/>\nIn the comparison of the pictures of buildings,<br \/>\nYou take more pictures than your friend.<br \/>\nNow,<br \/>\nThe number of pictures more taken by you than your friend = ( The number of pictures taken by you ) &#8211; ( The number of pictures taken by your friend )<br \/>\n= 20 &#8211; 18<br \/>\n= 2 pictures<br \/>\nHence, from the above,<br \/>\nWe can conclude that<br \/>\nYou take more pictures<br \/>\nYou take 2 pictures more than your friend<\/p>\n<p>Question 17.<br \/>\nYou have 72 rocks in your rock collection. Five-eighths of them are sedimentary, one-sixth of them are igneous, and the rest are metamorphic. How many of your rocks are metamorphic?<br \/>\nAnswer:<br \/>\nThe number of rocks that are metamorphic is: 15 metamorphous rocks<\/p>\n<p>Explanation:<br \/>\nIt is given that you have 72 rocks in your rock collection and five-eighths of them are sedimentary, one-sixth of them are igneous, and the rest are metamorphic.<br \/>\nSo,<br \/>\nThe number of rocks that are sedimentary = ( The total number of rocks ) \u00d7 ( The fraction of rocks that are sedimentary )<br \/>\n= 72 \u00d7 \\(\\frac{5}{8}\\)<br \/>\n= \\(\\frac{72}{1}\\) \u00d7 \\(\\frac{5}{8}\\)<br \/>\n= \\(\\frac{72 \u00d7 5}{1 \u00d7 8}\\)<br \/>\n= 45 sedimentary rocks<br \/>\nThe number of rocks that are igneous = ( The total number of rocks ) \u00d7 ( The fraction of rocks that are igneous )<br \/>\n= 72 \u00d7 \\(\\frac{1}{6}\\)<br \/>\n= \\(\\frac{72}{1}\\) \u00d7 \\(\\frac{1}{6}\\)<br \/>\n= \\(\\frac{72 \u00d7 1}{1 \u00d7 6}\\)<br \/>\n= 12 igneous rocks<br \/>\nSo,<br \/>\nThe number of metamorphous rocks = ( The total number of rocks ) &#8211; ( The number of sedimentary rocks + The number of igneous rocks)<br \/>\n= 72 &#8211; ( 45 + 12 )<br \/>\n= 15 metamorphous rocks<br \/>\nHence, from the above,<br \/>\nWe can conclude that there are 15 metamorphous rocks<\/p>\n<p>Question 18.<br \/>\n<strong>DIG DEEPER!<\/strong><br \/>\nEach day, you spend \\(\\frac{3}{4}\\) hour reading and \\(\\frac{1}{2}\\) hour writing in a journal. How many total hours do you spend reading and writing in 1 week? Describe two ways to solve the problem.<br \/>\n<img loading=\"lazy\" class=\"alignnone size-full wp-image-16377\" src=\"https:\/\/ccssmathanswers.com\/wp-content\/uploads\/2020\/12\/Big-Ideas-Math-Answers-Grade-5-Chapter-9-Multiply-Fractions-9.3-7.png\" alt=\"Big Ideas Math Answers Grade 5 Chapter 9 Multiply Fractions 9.3 7\" width=\"176\" height=\"141\" \/><br \/>\nAnswer:<br \/>\nThe number of hours you spend on reading and writing in 1 week is:<\/p>\n<p>Explanation:<br \/>\nIt is given that, each day you spent \\(\\frac{3}{4}\\) hour reading and \\(\\frac{1}{2}\\) hour writing in a journal.<br \/>\nSo,<br \/>\nThe number of hours you spent on reading and writing a journal in 1 day = ( The number of hours spent on reading ) + ( The number of hours spent on writing )<br \/>\n= \\(\\frac{3}{4}\\) + \\(\\frac{1}{2}\\)<br \/>\nMultiply \\(\\frac{1}{2}\\) with \\(\\frac{2}{2}\\)<br \/>\nSo,<br \/>\n\\(\\frac{3}{4}\\) + \\(\\frac{2}{4}\\)<br \/>\n= \\(\\frac{3 + 2}{4}\\)<br \/>\n= \\(\\frac{5}{4}\\) hours<br \/>\nWe know that,<br \/>\n1 day = 24 hours<br \/>\n1 week = 7 days<br \/>\nSo,<br \/>\n1 week = 7 \u00d7 24 hours<br \/>\nSo,<br \/>\nThe number of hours you spent on reading and writing in 1 week = ( The number of hours you spent on reading and writing in 1 day ) \u00d7 ( The number of hours in 1 week )<br \/>\n= \\(\\frac{5}{4}\\) \u00d7 7 \u00d7 24<br \/>\n= \\(\\frac{5}{4}\\) \u00d7 \\(\\frac{7}{1}\\) \u00d7 \\(\\frac{24}{1}\\)<br \/>\n= \\(\\frac{5 \u00d7 7 \u00d7 24}{4 \u00d7 1}\\)<br \/>\n= 5 \u00d7 7 \u00d7 6<br \/>\n= 210 hours<br \/>\nHence, from the above,<br \/>\nWe can conclude that the number of hours you spent on reading and writing a journal in 1 week is: 210 hours<\/p>\n<h3><a id=\"Multiply_Fractions_and_Whole_Numbers_Homework_&amp;_Practice_9.3\"><\/a>Multiply Fractions and Whole Numbers Homework &amp; Practice 9.3<\/h3>\n<p><strong>Multiply.<\/strong><br \/>\nQuestion 1.<br \/>\n\\(\\frac{5}{6}\\) \u00d7 3 = _______<br \/>\nAnswer:<br \/>\n3 \u00d7 \\(\\frac{5}{6}\\) = \\(\\frac{5}{2}\\)<\/p>\n<p>Explanation:<br \/>\nThe given numbers are: 3 and \\(\\frac{5}{6}\\)<br \/>\nWe know that,<br \/>\n\\(\\frac{a}{b}\\) \u00d7 p = \\(\\frac{a}{b}\\) \u00d7 \\(\\frac{p}{1}\\)<br \/>\n= \\(\\frac{a \u00d7 p}{ b \u00d7 1}\\)<br \/>\np = \\(\\frac{p}{1}\\)<br \/>\nSo,<br \/>\n3 \u00d7 \\(\\frac{5}{6}\\) = \\(\\frac{3}{1}\\) \u00d7 \\(\\frac{5}{6}\\)<br \/>\n= \\(\\frac{3 \u00d7 5}{6 \u00d7 1}\\)<br \/>\n= \\(\\frac{5}{6}\\)<br \/>\n= \\(\\frac{5}{2}\\)<br \/>\nHence,<br \/>\n3 \u00d7 \\(\\frac{5}{6}\\) = \\(\\frac{5}{2}\\)<\/p>\n<p>Question 2.<br \/>\n\\(\\frac{2}{3}\\) \u00d7 6 = _______<br \/>\nAnswer:<br \/>\n6 \u00d7 \\(\\frac{2}{3}\\) = 4<\/p>\n<p>Explanation:<br \/>\nThe given numbers are: 6 and \\(\\frac{2}{3}\\)<br \/>\nWe know that,<br \/>\n\\(\\frac{a}{b}\\) \u00d7 p = \\(\\frac{a}{b}\\) \u00d7 \\(\\frac{p}{1}\\)<br \/>\n= \\(\\frac{a \u00d7 p}{ b \u00d7 1}\\)<br \/>\np = \\(\\frac{p}{1}\\)<br \/>\nSo,<br \/>\n6 \u00d7 \\(\\frac{2}{3}\\) = \\(\\frac{6}{1}\\) \u00d7 \\(\\frac{2}{3}\\)<br \/>\n= \\(\\frac{6 \u00d7 2}{3 \u00d7 1}\\)<br \/>\n= \\(\\frac{12}{3}\\)<br \/>\n= \\(\\frac{4}{1}\\)<br \/>\n= 4<br \/>\nHence,<br \/>\n6 \u00d7 \\(\\frac{2}{3}\\) = 4<\/p>\n<p>Question 3.<br \/>\n7 \u00d7 \\(\\frac{1}{8}\\) = _______<br \/>\nAnswer:<br \/>\n7 \u00d7 \\(\\frac{1}{8}\\) = \\(\\frac{7}{8}\\)<\/p>\n<p>Explanation:<br \/>\nThe given numbers are: 7 and \\(\\frac{1}{8}\\)<br \/>\nWe know that,<br \/>\n\\(\\frac{a}{b}\\) \u00d7 p = \\(\\frac{a}{b}\\) \u00d7 \\(\\frac{p}{1}\\)<br \/>\n= \\(\\frac{a \u00d7 p}{ b \u00d7 1}\\)<br \/>\np = \\(\\frac{p}{1}\\)<br \/>\nSo,<br \/>\n7 \u00d7 \\(\\frac{1}{8}\\) = \\(\\frac{7}{1}\\) \u00d7 \\(\\frac{1}{8}\\)<br \/>\n= \\(\\frac{7 \u00d7 1}{8 \u00d7 1}\\)<br \/>\n= \\(\\frac{7}{8}\\)<br \/>\nHence,<br \/>\n7 \u00d7 \\(\\frac{1}{8}\\) = \\(\\frac{7}{8}\\)<\/p>\n<p>Question 4.<br \/>\n2 \u00d7 \\(\\frac{1}{2}\\) = _______<br \/>\nAnswer:<br \/>\n2 \u00d7 \\(\\frac{1}{2}\\) = 1<\/p>\n<p>Explanation:<br \/>\nThe given numbers are: 2 and \\(\\frac{1}{2}\\)<br \/>\nWe know that,<br \/>\n\\(\\frac{a}{b}\\) \u00d7 p = \\(\\frac{a}{b}\\) \u00d7 \\(\\frac{p}{1}\\)<br \/>\n= \\(\\frac{a \u00d7 p}{ b \u00d7 1}\\)<br \/>\np = \\(\\frac{p}{1}\\)<br \/>\nSo,<br \/>\n2 \u00d7 \\(\\frac{1}{2}\\) = \\(\\frac{2}{1}\\) \u00d7 \\(\\frac{1}{2}\\)<br \/>\n= \\(\\frac{2 \u00d7 1}{2 \u00d7 1}\\)<br \/>\n= \\(\\frac{2}{2}\\)<br \/>\n= 1<br \/>\nHence,<br \/>\n2 \u00d7 \\(\\frac{1}{2}\\) = 1<\/p>\n<p>Question 5.<br \/>\n\\(\\frac{4}{5}\\) \u00d7 9 = _______<br \/>\nAnswer:<br \/>\n9 \u00d7 \\(\\frac{4}{5}\\) = \\(\\frac{36}{5}\\)<\/p>\n<p>Explanation:<br \/>\nThe given numbers are: 9 and \\(\\frac{4}{5}\\)<br \/>\nWe know that,<br \/>\n\\(\\frac{a}{b}\\) \u00d7 p = \\(\\frac{a}{b}\\) \u00d7 \\(\\frac{p}{1}\\)<br \/>\n= \\(\\frac{a \u00d7 p}{ b \u00d7 1}\\)<br \/>\np = \\(\\frac{p}{1}\\)<br \/>\nSo,<br \/>\n9 \u00d7 \\(\\frac{4}{5}\\) = \\(\\frac{9}{1}\\) \u00d7 \\(\\frac{4}{5}\\)<br \/>\n= \\(\\frac{9 \u00d7 4}{5 \u00d7 1}\\)<br \/>\n= \\(\\frac{36}{5}\\)<br \/>\nHence,<br \/>\n9 \u00d7 \\(\\frac{4}{5}\\) = \\(\\frac{36}{5}\\)<\/p>\n<p>Question 6.<br \/>\n4 \u00d7 \\(\\frac{5}{12}\\) = _______<br \/>\nAnswer:<br \/>\n4 \u00d7 \\(\\frac{5}{12}\\) = \\(\\frac{5}{3}\\)<\/p>\n<p>Explanation:<br \/>\nThe given numbers are: 4 and \\(\\frac{5}{12}\\)<br \/>\nWe know that,<br \/>\n\\(\\frac{a}{b}\\) \u00d7 p = \\(\\frac{a}{b}\\) \u00d7 \\(\\frac{p}{1}\\)<br \/>\n= \\(\\frac{a \u00d7 p}{ b \u00d7 1}\\)<br \/>\np = \\(\\frac{p}{1}\\)<br \/>\nSo,<br \/>\n4 \u00d7 \\(\\frac{5}{12}\\) = \\(\\frac{4}{1}\\) \u00d7 \\(\\frac{5}{12}\\)<br \/>\n= \\(\\frac{4 \u00d7 5}{12 \u00d7 1}\\)<br \/>\n= \\(\\frac{20}{12}\\)<br \/>\n= \\(\\frac{5}{3}\\)<br \/>\nHence,<br \/>\n4 \u00d7 \\(\\frac{5}{12}\\) = \\(\\frac{5}{3}\\)<\/p>\n<p>Question 7.<br \/>\n\\(\\frac{1}{4}\\) \u00d7 24 = _______<br \/>\nAnswer:<br \/>\n24 \u00d7 \\(\\frac{1}{24}\\) = 6<\/p>\n<p>Explanation:<br \/>\nThe given numbers are: 24 and \\(\\frac{1}{4}\\)<br \/>\nWe know that,<br \/>\n\\(\\frac{a}{b}\\) \u00d7 p = \\(\\frac{a}{b}\\) \u00d7 \\(\\frac{p}{1}\\)<br \/>\n= \\(\\frac{a \u00d7 p}{ b \u00d7 1}\\)<br \/>\np = \\(\\frac{p}{1}\\)<br \/>\nSo,<br \/>\n24 \u00d7 \\(\\frac{1}{4}\\) = \\(\\frac{24}{1}\\) \u00d7 \\(\\frac{1}{4}\\)<br \/>\n= \\(\\frac{24 \u00d7 1}{4 \u00d7 1}\\)<br \/>\n= \\(\\frac{24}{4}\\)<br \/>\n= 6<br \/>\nHence,<br \/>\n24 \u00d7 \\(\\frac{1}{4}\\) = 6<\/p>\n<p>Question 8.<br \/>\n16 \u00d7 \\(\\frac{3}{8}\\) = _______<br \/>\nAnswer:<br \/>\n16 \u00d7 \\(\\frac{3}{8}\\) = 6<\/p>\n<p>Explanation:<br \/>\nThe given numbers are: 16 and \\(\\frac{3}{8}\\)<br \/>\nWe know that,<br \/>\n\\(\\frac{a}{b}\\) \u00d7 p = \\(\\frac{a}{b}\\) \u00d7 \\(\\frac{p}{1}\\)<br \/>\n= \\(\\frac{a \u00d7 p}{ b \u00d7 1}\\)<br \/>\np = \\(\\frac{p}{1}\\)<br \/>\nSo,<br \/>\n16 \u00d7 \\(\\frac{3}{8}\\) = \\(\\frac{16}{1}\\) \u00d7 \\(\\frac{3}{8}\\)<br \/>\n= \\(\\frac{16 \u00d7 3}{8 \u00d7 1}\\)<br \/>\n= \\(\\frac{48}{8}\\)<br \/>\n= 6<br \/>\nHence,<br \/>\n16 \u00d7 \\(\\frac{3}{8}\\) = 6<\/p>\n<p>Question 9.<br \/>\n\\(\\frac{7}{10}\\) \u00d7 25 = _______<br \/>\nAnswer:<br \/>\n25 \u00d7 \\(\\frac{7}{10}\\) = \\(\\frac{35}{2}\\)<\/p>\n<p>Explanation:<br \/>\nThe given numbers are: 25 and \\(\\frac{7}{10}\\)<br \/>\nWe know that,<br \/>\n\\(\\frac{a}{b}\\) \u00d7 p = \\(\\frac{a}{b}\\) \u00d7 \\(\\frac{p}{1}\\)<br \/>\n= \\(\\frac{a \u00d7 p}{ b \u00d7 1}\\)<br \/>\np = \\(\\frac{p}{1}\\)<br \/>\nSo,<br \/>\n25 \u00d7 \\(\\frac{7}{10}\\) = \\(\\frac{25}{1}\\) \u00d7 \\(\\frac{7}{10}\\)<br \/>\n= \\(\\frac{7 \u00d7 25}{10 \u00d7 1}\\)<br \/>\n= \\(\\frac{175}{10}\\)<br \/>\n= \\(\\frac{35}{2}\\)<br \/>\nHence,<br \/>\n25 \u00d7 \\(\\frac{7}{10}\\) = \\(\\frac{35}{2}\\)<\/p>\n<p>Question 10.<br \/>\nYou spend \\(\\frac{3}{4}\\) hour jumping rope every week for 8 weeks. How many hours do you jump rope altogether?<br \/>\n<img loading=\"lazy\" class=\"alignnone size-full wp-image-16378\" src=\"https:\/\/ccssmathanswers.com\/wp-content\/uploads\/2020\/12\/Big-Ideas-Math-Answers-Grade-5-Chapter-9-Multiply-Fractions-9.3-8.png\" alt=\"Big Ideas Math Answers Grade 5 Chapter 9 Multiply Fractions 9.3 8\" width=\"163\" height=\"171\" \/><br \/>\nAnswer:<br \/>\nThe number of hours you jump rope altogether in 8 weeks is: 6 hours<\/p>\n<p>Explanation:<br \/>\nIt is given that you spent \\(\\frac{3}{4}\\) hour jumping rope every week for 8 weeks.<br \/>\nSo,<br \/>\nThe number of hours you spent jumping rope in 8 weeks = ( The number of hours you jump rope in 1 week ) \u00d7 ( The total number of weeks )<br \/>\n= \\(\\frac{3}{4}\\) \u00d7 8<br \/>\n= \\(\\frac{3}{4}\\) \u00d7\u00a0\\(\\frac{8}{1}\\)<br \/>\n= \\(\\frac{3 \u00d7 8}{4 \u00d7 1}\\)<br \/>\n= 6 hours<br \/>\nhence, from the above,<br \/>\nWe can conclude that you spent 6 hours on jumping rope in 8 weeks.<\/p>\n<p>Question 11.<br \/>\n<strong>Logic<\/strong><br \/>\nYour friend finds 25 items that are either insects or flowers. She says that \\(\\frac{1}{6}\\) of the items are insects. Can this be true? Explain.<br \/>\nAnswer:<br \/>\nNo, this is not true<\/p>\n<p>Explanation:<br \/>\nIt is given that your friend finds 25 items that are either insects or flowers and she says that \\(\\frac{1}{6}\\) of the items are insects.<br \/>\nBut,<br \/>\nThe number of either insects or flowers will always be a whole number.<br \/>\nBut, from the given information,<br \/>\n25 will not be divided by \\(\\frac{1}{6}\\)<br \/>\nSo,<br \/>\nThe statement &#8220;\\(\\frac{1}{6}\\) of the items are insects&#8221; is false.<\/p>\n<p>Question 12.<br \/>\n<strong>Open-Ended<\/strong><br \/>\nWrite two different pairs of fractions that could represent the insects and flowers your friend finds in Exercise 11.<br \/>\nAnswer:<br \/>\nThe different pairs of fractions that could represent the insects and flowers are:<br \/>\n\\(\\frac{1}{5}\\) and \\(\\frac{1}{25}\\)<\/p>\n<p>Explanation:<br \/>\nThese different pairs of fractions have to divide 25<br \/>\nSo,<br \/>\nWe have to take the fractions the multiples of 5 i.e., 5 and 25<br \/>\nHence, from the above,<br \/>\nWe can conclude that<br \/>\nThe different pairs of fractions that could represent the insects and flowers are:<br \/>\n\\(\\frac{1}{5}\\) and \\(\\frac{1}{25}\\)<\/p>\n<p>Question 13.<br \/>\n<strong>Modeling Real Life<\/strong><br \/>\nNewton bakes 56 treats. Five-eighths of them contains peanut butter. Descartes bakes 120 treats. Five-sixths of them contain peanut butter. Who bakes more peanut butter treats? How many more?<br \/>\n<img loading=\"lazy\" class=\"alignnone size-full wp-image-16379\" src=\"https:\/\/ccssmathanswers.com\/wp-content\/uploads\/2020\/12\/Big-Ideas-Math-Answers-Grade-5-Chapter-9-Multiply-Fractions-9.3-9.png\" alt=\"Big Ideas Math Answers Grade 5 Chapter 9 Multiply Fractions 9.3 9\" width=\"143\" height=\"140\" \/><br \/>\nAnswer:<br \/>\nDescartes bakes more peanut butter treats<br \/>\nThe number of peanut butter treats Descartes made more than Descartes is: 65<\/p>\n<p>Explanation:<br \/>\nIt is given that Newton bakes 56 treats and five-eights of them contains peanut butter<br \/>\nSo,<br \/>\nThe number of peanut butter treats made by Newton = \\(\\frac{5}{8}\\) \u00d7 56<br \/>\n= \\(\\frac{5}{8}\\) \u00d7 \\(\\frac{56}{1}\\)<br \/>\n= \\(\\frac{5 \u00d7 56}{8 \u00d7 1}\\)<br \/>\n= 35 peanut butter treats<br \/>\nIt is also given that Descartes bakes 120 treats and five-sixths of them contain peanut butter<br \/>\nSo,<br \/>\nthe number of peanut butter treats made by Descartes = \\(\\frac{5}{6}\\) \u00d7 120<br \/>\n= \\(\\frac{5}{6}\\) \u00d7 \\(\\frac{120}{1}\\)<br \/>\n= \\(\\frac{5 \u00d7 120}{6 \u00d7 1}\\)<br \/>\n= 100 peanut butter treats<br \/>\nSo,<br \/>\nIn the comparison of peanut butter treats,<br \/>\nDescartes bakes more<br \/>\nNow,<br \/>\nThe number of peanut butter treats baked by Descartes more than Newton = 100 &#8211; 35<br \/>\n= 65 peanut butter treats<br \/>\nHence, from the above,<br \/>\nWe can conclude that<br \/>\nDescartes bakes more peanut butter treats<br \/>\nThe number of peanut butter treats Descartes made more than Descartes is: 65<\/p>\n<p>Question 14.<br \/>\n<strong>Modeling Real Life<\/strong><br \/>\nYour class conducts an egg-dropping experiment with 60 eggs. Three-fifths of the eggs break open, one-sixth of the eggs crack, and the rest do not break at all. How many of the eggs do not crack or break open?<br \/>\nAnswer:<br \/>\nThe number of eggs that do not break is:<\/p>\n<p>Explanation:<br \/>\nIt is given that your class conducts an egg-dropping experiment with 60 eggs and three-fifths of the eggs break open, one-sixth of the eggs crack and the rest do not break.<br \/>\nSo,<br \/>\nThe number of eggs that break open = 60 \u00d7 \\(\\frac{3}{5}\\)<br \/>\n= \\(\\frac{60}{1}\\) \u00d7 \\(\\frac{3}{5}\\)<br \/>\n= 36<br \/>\nThe number of eggs that cracked = 60 \u00d7 \\(\\frac{1}{6}\\)<br \/>\n= \\(\\frac{60}{1}\\) \u00d7 \\(\\frac{1}{6}\\)<br \/>\n= 10<br \/>\nSo,<br \/>\nThe number of eggs that do not breaked = ( The total number of eggs ) &#8211; ( The number of eggs that break open + The number of eggs that cracked )<br \/>\n= 60 &#8211; ( 36 + 10 )<br \/>\n= 16<br \/>\nHence, from the above,<br \/>\nWe can conclude that the number of eggs that do not break is: 16 eggs<\/p>\n<p><strong>Review &amp; Refresh<\/strong><\/p>\n<p><strong>Add.<\/strong><br \/>\nQuestion 15.<br \/>\n5\\(\\frac{5}{8}\\) + 6\\(\\frac{3}{4}\\) = _______<br \/>\nAnswer:<br \/>\n5\\(\\frac{5}{8}\\) + 6\\(\\frac{3}{4}\\) = \\(\\frac{99}{8}\\)<\/p>\n<p>Explanation:<br \/>\nThe give mixed fractions are: 6\\(\\frac{3}{4}\\) and 5\\(\\frac{5}{8}\\)<br \/>\nThe representation of mixed fractions in the improper form is: \\(\\frac{45}{8}\\) and \\(\\frac{27}{4}\\)<br \/>\nIn addition,<br \/>\nWe have to make the denominators equal.<br \/>\nSo,<br \/>\nMultiply \\(\\frac{27}{4}\\) with \\(\\frac{2}{2}\\)<br \/>\nSo,<br \/>\n\\(\\frac{45}{8}\\) + \\(\\frac{54}{8}\\) = \\(\\frac{45 + 54}{8}\\)<br \/>\n= \\(\\frac{99}{8}\\)<br \/>\nHence,<br \/>\n5\\(\\frac{5}{8}\\) + 6\\(\\frac{3}{4}\\) = \\(\\frac{99}{8}\\)<\/p>\n<p>Question 16.<br \/>\n1\\(\\frac{5}{6}\\) + 8\\(\\frac{1}{12}\\) = ________<br \/>\nAnswer:<br \/>\n1\\(\\frac{5}{6}\\) + 8\\(\\frac{1}{12}\\) = \\(\\frac{119}{12}\\)<\/p>\n<p>Explanation:<br \/>\nThe give mixed fractions are: 1\\(\\frac{5}{6}\\) and 8\\(\\frac{1}{12}\\)<br \/>\nThe representation of mixed fractions in the improper form is: \\(\\frac{11}{6}\\) and \\(\\frac{97}{12}\\)<br \/>\nIn addition,<br \/>\nWe have to make the denominators equal.<br \/>\nSo,<br \/>\nMultiply \\(\\frac{11}{6}\\) with \\(\\frac{2}{2}\\)<br \/>\nSo,<br \/>\n\\(\\frac{97}{12}\\) + \\(\\frac{22}{12}\\) = \\(\\frac{97 + 22}{12}\\)<br \/>\n= \\(\\frac{119}{12}\\)<br \/>\nHence,<br \/>\n1\\(\\frac{5}{6}\\) + 8\\(\\frac{1}{12}\\) = \\(\\frac{119}{12}\\)<\/p>\n<p>Question 17.<br \/>\n3\\(\\frac{1}{2}\\) + \\(\\frac{3}{5}\\) + 2\\(\\frac{7}{10}\\) = _______<br \/>\nAnswer:<br \/>\n3\\(\\frac{1}{2}\\) + 2\\(\\frac{7}{10}\\) + \\(\\frac{3}{5}\\) \u00a0= \\(\\frac{68}{10}\\)<\/p>\n<p>Explanation:<br \/>\nThe give mixed fractions are: 3\\(\\frac{1}{2}\\), \\(\\frac{3}{5}\\) and 2\\(\\frac{7}{10}\\)<br \/>\nThe representation of mixed fractions in the improper form is: \\(\\frac{7}{2}\\) and \\(\\frac{27}{10}\\)<br \/>\nIn addition,<br \/>\nWe have to make the denominators equal.<br \/>\nSo,<br \/>\nMultiply \\(\\frac{7}{2}\\) with \\(\\frac{5}{5}\\)<br \/>\nMultiply \\(\\frac{3}{5}\\) with \\(\\frac{2}{2}\\)<br \/>\nSo,<br \/>\n\\(\\frac{27}{10}\\) + \\(\\frac{35}{10}\\) + \\(\\frac{6}{10}\\) \u00a0= \\(\\frac{27 + 35 + 6}{10}\\)<br \/>\n= \\(\\frac{68}{10}\\)<br \/>\nHence,<br \/>\n3\\(\\frac{1}{2}\\) + 2\\(\\frac{7}{10}\\) + \\(\\frac{3}{5}\\) \u00a0= \\(\\frac{68}{10}\\)<\/p>\n<h3><a id=\"Lesson_9.4_Use_Models_to_Multiply_Fractions\"><\/a>Lesson 9.4 Use Models to Multiply Fractions<\/h3>\n<p><strong>Explore and Grow<\/strong><\/p>\n<p>Fold a sheet of paper in half. Shade \\(\\frac{1}{4}\\) of either half. What fraction of the entire sheet of paper did you shade? Draw a model to support your answer.<br \/>\nAnswer:<br \/>\nThe fraction of the entire sheet of paper you shaded is: \\(\\frac{1}{8}\\)<\/p>\n<p>Explanation:<br \/>\nTake a full sheet of paper and fold in half<br \/>\nSo,<br \/>\nThe number of parts of full sheet of paper = \\(\\frac{1}{2}\\)<br \/>\nNow,<br \/>\nShade \\(\\frac{1}{4}\\) of the half of the paper<br \/>\nSo,,<br \/>\nThe fraction of the paper you shaded = \\(\\frac{1}{4}\\) \u00d7 \\(\\frac{1}{2}\\)<br \/>\nWe know that,<br \/>\n\\(\\frac{a}{b}\\) \u00d7 \\(\\frac{p}{q}\\) = \\(\\frac{a \u00d7 p}{b \u00d7 q}\\)<br \/>\na = \\(\\frac{a}{1}\\)<br \/>\nSo,<br \/>\n\\(\\frac{1}{4}\\) \u00d7 \\(\\frac{1}{2}\\)<br \/>\n= \\(\\frac{1 \u00d7 1}{4 \u00d7 2}\\)<br \/>\n= \\(\\frac{1}{8}\\)<br \/>\nHence, from the above,<br \/>\nWe can conclude that the \\(\\frac{1}{8}\\) part of the full sheet is shaded<\/p>\n<p><strong>Reasoning<\/strong><br \/>\nWhat multiplication expression does your model represent? Explain your reasoning.<br \/>\nAnswer:<br \/>\nThe multiplication expression your model represents is: \\(\\frac{1}{8}\\)<br \/>\nWe can obtain the multiplication expression by using the following multiplication properties. They are:<br \/>\nA) \\(\\frac{a}{b}\\) \u00d7 \\(\\frac{p}{q}\\) = \\(\\frac{a \u00d7 p}{b \u00d7 q}\\)<br \/>\nB) a = \\(\\frac{a}{1}\\)<\/p>\n<p><strong>Think and Grow: Use Models to Multiply Fractions<\/strong><\/p>\n<p>You can use models to multiply a fraction by a fraction.<br \/>\nExample<br \/>\nFind \\(\\frac{1}{2}\\) \u00d7 \\(\\frac{1}{3}\\).<br \/>\n<img loading=\"lazy\" class=\"alignnone size-full wp-image-37571\" src=\"https:\/\/ccssmathanswers.com\/wp-content\/uploads\/2020\/12\/Big-Ideas-Math-Answers-Grade-5-Chapter-9-9.jpg\" alt=\"\" width=\"643\" height=\"491\" srcset=\"https:\/\/bigideasmathanswers.com\/wp-content\/uploads\/2020\/12\/Big-Ideas-Math-Answers-Grade-5-Chapter-9-9.jpg 643w, https:\/\/bigideasmathanswers.com\/wp-content\/uploads\/2020\/12\/Big-Ideas-Math-Answers-Grade-5-Chapter-9-9-300x229.jpg 300w\" sizes=\"(max-width: 643px) 100vw, 643px\" \/><br \/>\n<strong>Show and Grow<\/strong><\/p>\n<p><strong>Multiply. Use a model to help.<\/strong><br \/>\nQuestion 1.<br \/>\n\\(\\frac{1}{3}\\) \u00d7 \\(\\frac{1}{4}\\) = _______<br \/>\nAnswer:<br \/>\n\\(\\frac{1}{3}\\) \u00d7 \\(\\frac{1}{4}\\) = \\(\\frac{1}{12}\\)<\/p>\n<p>Explanation:<br \/>\nThe given fractions are: \\(\\frac{1}{4}\\) and \\(\\frac{1}{3}\\)<br \/>\nWe know that,<br \/>\n\\(\\frac{a}{b}\\) \u00d7 \\(\\frac{p}{q}\\) = \\(\\frac{a \u00d7 p}{b \u00d7 q}\\)<br \/>\na = \\(\\frac{a}{1}\\)<br \/>\nSo,<br \/>\n\\(\\frac{1}{4}\\) \u00d7 \\(\\frac{1}{3}\\)<br \/>\n= \\(\\frac{1 \u00d7 1}{4 \u00d7 3}\\)<br \/>\n= \\(\\frac{1}{12}\\)<br \/>\nHence,<br \/>\n\\(\\frac{1}{4}\\) \u00d7 \\(\\frac{1}{3}\\) = \\(\\frac{1}{12}\\)<\/p>\n<p>Question 2.<br \/>\n\\(\\frac{2}{3}\\) \u00d7 \\(\\frac{1}{2}\\) = _______<br \/>\nAnswer:<br \/>\n\\(\\frac{2}{3}\\) \u00d7 \\(\\frac{1}{2}\\) = \\(\\frac{1}{3}\\)<\/p>\n<p>Explanation:<br \/>\nThe given fractions are: \\(\\frac{2}{3}\\) and \\(\\frac{1}{2}\\)<br \/>\nWe know that,<br \/>\n\\(\\frac{a}{b}\\) \u00d7 \\(\\frac{p}{q}\\) = \\(\\frac{a \u00d7 p}{b \u00d7 q}\\)<br \/>\na = \\(\\frac{a}{1}\\)<br \/>\nSo,<br \/>\n\\(\\frac{1}{2}\\) \u00d7 \\(\\frac{2}{3}\\)<br \/>\n= \\(\\frac{1 \u00d7 2}{2 \u00d7 3}\\)<br \/>\n= \\(\\frac{1}{3}\\)<br \/>\nHence,<br \/>\n\\(\\frac{1}{2}\\) \u00d7 \\(\\frac{2}{3}\\) = \\(\\frac{1}{3}\\)<\/p>\n<p><strong>Apply and Grow: Practice<\/strong><\/p>\n<p><strong>Multiply. Use a model to help.<\/strong><br \/>\nQuestion 3.<br \/>\n\\(\\frac{1}{2}\\) \u00d7 \\(\\frac{1}{6}\\) = _______<br \/>\nAnswer:<br \/>\n\\(\\frac{1}{2}\\) \u00d7 \\(\\frac{1}{6}\\) = \\(\\frac{1}{12}\\)<\/p>\n<p>Explanation:<br \/>\nThe given fractions are: \\(\\frac{1}{2}\\) and \\(\\frac{1}{6}\\)<br \/>\nWe know that,<br \/>\n\\(\\frac{a}{b}\\) \u00d7 \\(\\frac{p}{q}\\) = \\(\\frac{a \u00d7 p}{b \u00d7 q}\\)<br \/>\na = \\(\\frac{a}{1}\\)<br \/>\nSo,<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,<br \/>\n\\(\\frac{1}{2}\\) \u00d7 \\(\\frac{1}{6}\\) = \\(\\frac{1}{12}\\)<\/p>\n<p>Question 4.<br \/>\n\\(\\frac{1}{5}\\) \u00d7 \\(\\frac{1}{8}\\) = _______<br \/>\nAnswer:<br \/>\n\\(\\frac{1}{5}\\) \u00d7 \\(\\frac{1}{8}\\) = \\(\\frac{1}{40}\\)<\/p>\n<p>Explanation:<br \/>\nThe given fractions are: \\(\\frac{1}{5}\\) and \\(\\frac{1}{8}\\)<br \/>\nWe know that,<br \/>\n\\(\\frac{a}{b}\\) \u00d7 \\(\\frac{p}{q}\\) = \\(\\frac{a \u00d7 p}{b \u00d7 q}\\)<br \/>\na = \\(\\frac{a}{1}\\)<br \/>\nSo,<br \/>\n\\(\\frac{1}{5}\\) \u00d7 \\(\\frac{1}{8}\\)<br \/>\n= \\(\\frac{1 \u00d7 1}{5 \u00d7 8}\\)<br \/>\n= \\(\\frac{1}{40}\\)<br \/>\nHence,<br \/>\n\\(\\frac{1}{5}\\) \u00d7 \\(\\frac{1}{8}\\) = \\(\\frac{1}{40}\\)<\/p>\n<p>Question 5.<br \/>\n\\(\\frac{1}{4}\\) \u00d7 \\(\\frac{1}{6}\\) = _______<br \/>\nAnswer:<br \/>\n\\(\\frac{1}{4}\\) \u00d7 \\(\\frac{1}{6}\\) = \\(\\frac{1}{24}\\)<\/p>\n<p>Explanation:<br \/>\nThe given fractions are: \\(\\frac{1}{4}\\) and \\(\\frac{1}{6}\\)<br \/>\nWe know that,<br \/>\n\\(\\frac{a}{b}\\) \u00d7 \\(\\frac{p}{q}\\) = \\(\\frac{a \u00d7 p}{b \u00d7 q}\\)<br \/>\na = \\(\\frac{a}{1}\\)<br \/>\nSo,<br \/>\n\\(\\frac{1}{4}\\) \u00d7 \\(\\frac{1}{6}\\)<br \/>\n= \\(\\frac{1 \u00d7 1}{4 \u00d7 6}\\)<br \/>\n= \\(\\frac{1}{24}\\)<br \/>\nHence,<br \/>\n\\(\\frac{1}{4}\\) \u00d7 \\(\\frac{1}{6}\\) = \\(\\frac{1}{24}\\)<\/p>\n<p>Question 6.<br \/>\n\\(\\frac{2}{3}\\) \u00d7 \\(\\frac{1}{3}\\) = _______<br \/>\nAnswer:<br \/>\n\\(\\frac{2}{3}\\) \u00d7 \\(\\frac{1}{3}\\) = \\(\\frac{2}{9}\\)<\/p>\n<p>Explanation:<br \/>\nThe given fractions are: \\(\\frac{2}{3}\\) and \\(\\frac{1}{3}\\)<br \/>\nWe know that,<br \/>\n\\(\\frac{a}{b}\\) \u00d7 \\(\\frac{p}{q}\\) = \\(\\frac{a \u00d7 p}{b \u00d7 q}\\)<br \/>\na = \\(\\frac{a}{1}\\)<br \/>\nSo,<br \/>\n\\(\\frac{2}{3}\\) \u00d7 \\(\\frac{1}{3}\\)<br \/>\n= \\(\\frac{2 \u00d7 1}{3 \u00d7 3}\\)<br \/>\n= \\(\\frac{2}{9}\\)<br \/>\nHence,<br \/>\n\\(\\frac{2}{3}\\) \u00d7 \\(\\frac{1}{3}\\) = \\(\\frac{2}{9}\\)<\/p>\n<p><strong>Write a multiplication equation represented by the model.<\/strong><br \/>\nQuestion 7.<br \/>\n<img loading=\"lazy\" class=\"alignnone size-full wp-image-16381\" src=\"https:\/\/ccssmathanswers.com\/wp-content\/uploads\/2020\/12\/Big-Ideas-Math-Solutions-Grade-5-Chapter-9-Multiply-Fractions-9.4-2.png\" alt=\"Big Ideas Math Solutions Grade 5 Chapter 9 Multiply Fractions 9.4 2\" width=\"208\" height=\"68\" \/><br \/>\nAnswer:<br \/>\nThe multiplication equation represented by the model is:<br \/>\n\\(\\frac{1}{2}\\) \u00d7 \\(\\frac{1}{8}\\)<\/p>\n<p>Explanation:<br \/>\nThe given model is:<br \/>\n<img loading=\"lazy\" class=\"alignnone size-full wp-image-16381\" src=\"https:\/\/ccssmathanswers.com\/wp-content\/uploads\/2020\/12\/Big-Ideas-Math-Solutions-Grade-5-Chapter-9-Multiply-Fractions-9.4-2.png\" alt=\"Big Ideas Math Solutions Grade 5 Chapter 9 Multiply Fractions 9.4 2\" width=\"208\" height=\"68\" \/><br \/>\nFrom the above model,<br \/>\nThe number of rows is: 2<br \/>\nThe number of columns is: 8<br \/>\nSo,<br \/>\nThe value of 1 row = \\(\\frac{1}{2}\\)<br \/>\nThe value of 1 column = \\(\\frac{1}{8}\\)<br \/>\nSo,<br \/>\nRows \u00d7 Columns = \\(\\frac{1}{8}\\) \u00d7 \\(\\frac{1}{2}\\)<br \/>\nHence, from the above,<br \/>\nWe can conclude that the multiplication equation represented by the above model is:<br \/>\n\\(\\frac{1}{8}\\) \u00d7 \\(\\frac{1}{2}\\)<\/p>\n<p>Question 8.<br \/>\n<img loading=\"lazy\" class=\"alignnone size-full wp-image-16382\" src=\"https:\/\/ccssmathanswers.com\/wp-content\/uploads\/2020\/12\/Big-Ideas-Math-Solutions-Grade-5-Chapter-9-Multiply-Fractions-9.4-3.png\" alt=\"Big Ideas Math Solutions Grade 5 Chapter 9 Multiply Fractions 9.4 3\" width=\"134\" height=\"105\" \/><br \/>\nAnswer:<br \/>\nThe multiplication equation represented by the model is:<br \/>\n\\(\\frac{1}{4}\\) \u00d7 \\(\\frac{1}{5}\\)<\/p>\n<p>Explanation:<br \/>\nThe given model is:<br \/>\n<img loading=\"lazy\" class=\"alignnone size-full wp-image-16382\" src=\"https:\/\/ccssmathanswers.com\/wp-content\/uploads\/2020\/12\/Big-Ideas-Math-Solutions-Grade-5-Chapter-9-Multiply-Fractions-9.4-3.png\" alt=\"Big Ideas Math Solutions Grade 5 Chapter 9 Multiply Fractions 9.4 3\" width=\"134\" height=\"105\" \/><br \/>\nFrom the above model,<br \/>\nThe number of rows is: 4<br \/>\nThe number of columns is: 5<br \/>\nSo,<br \/>\nThe value of 1 row = \\(\\frac{1}{4}\\)<br \/>\nThe value of 1 column = \\(\\frac{1}{5}\\)<br \/>\nSo,<br \/>\nRows \u00d7 Columns = \\(\\frac{1}{4}\\) \u00d7 \\(\\frac{1}{5}\\)<br \/>\nHence, from the above,<br \/>\nWe can conclude that the multiplication equation represented by the above model is:<br \/>\n\\(\\frac{1}{4}\\) \u00d7 \\(\\frac{1}{5}\\)<\/p>\n<p>Question 9.<br \/>\nOne-fifth of the students in your school have tried skating. Of those students, \\(\\frac{1}{7}\\) have tried ice skating. What fraction of students in your school have tried ice skating?<br \/>\nAnswer:<br \/>\nThe fraction of students that have tried ice skating is: \\(\\frac{1}{35}\\)<\/p>\n<p>Explanation:<br \/>\nIt is given that one-fifth of the students in your school have tried skating and of these students, \\(\\frac{1}{7}\\) have tried ice skating<br \/>\nSo,<br \/>\nThe fraction of students that have tried ice skating = ( The fraction of students that have tried skating ) \u00d7 ( The fraction of students that tried ice skating out of the total students )<br \/>\n= \\(\\frac{1}{5}\\) \u00d7 \\(\\frac{1}{7}\\)<br \/>\nWe know that,<br \/>\n\\(\\frac{a}{b}\\) \u00d7 \\(\\frac{p}{q}\\) = \\(\\frac{a \u00d7 p}{b \u00d7 q}\\)<br \/>\na = \\(\\frac{a}{1}\\)<br \/>\nSo,<br \/>\n\\(\\frac{1}{5}\\) \u00d7 \\(\\frac{1}{7}\\)<br \/>\n= \\(\\frac{1 \u00d7 1}{5 \u00d7 7}\\)<br \/>\n= \\(\\frac{1}{35}\\)<br \/>\nHence, from the above,<br \/>\nWe can conclude that \\(\\frac{1}{35}\\) of the total students tried ice skating.<\/p>\n<p>Question 10.<br \/>\n<strong>DIG DEEPER!<\/strong><br \/>\nAre both Newton and Descartes correct? Explain.<br \/>\n<img loading=\"lazy\" class=\"alignnone size-full wp-image-16383\" src=\"https:\/\/ccssmathanswers.com\/wp-content\/uploads\/2020\/12\/Big-Ideas-Math-Solutions-Grade-5-Chapter-9-Multiply-Fractions-9.4-4.png\" alt=\"Big Ideas Math Solutions Grade 5 Chapter 9 Multiply Fractions 9.4 4\" width=\"552\" height=\"230\" srcset=\"https:\/\/bigideasmathanswers.com\/wp-content\/uploads\/2020\/12\/Big-Ideas-Math-Solutions-Grade-5-Chapter-9-Multiply-Fractions-9.4-4.png 552w, https:\/\/bigideasmathanswers.com\/wp-content\/uploads\/2020\/12\/Big-Ideas-Math-Solutions-Grade-5-Chapter-9-Multiply-Fractions-9.4-4-300x125.png 300w\" sizes=\"(max-width: 552px) 100vw, 552px\" \/><br \/>\nAnswer: Yes, both Newton and Descartes are correct.<\/p>\n<p>Explanation:<br \/>\nThe given models of Newton and Descartes are:<br \/>\n<img loading=\"lazy\" class=\"alignnone size-full wp-image-16383\" src=\"https:\/\/ccssmathanswers.com\/wp-content\/uploads\/2020\/12\/Big-Ideas-Math-Solutions-Grade-5-Chapter-9-Multiply-Fractions-9.4-4.png\" alt=\"Big Ideas Math Solutions Grade 5 Chapter 9 Multiply Fractions 9.4 4\" width=\"552\" height=\"230\" srcset=\"https:\/\/bigideasmathanswers.com\/wp-content\/uploads\/2020\/12\/Big-Ideas-Math-Solutions-Grade-5-Chapter-9-Multiply-Fractions-9.4-4.png 552w, https:\/\/bigideasmathanswers.com\/wp-content\/uploads\/2020\/12\/Big-Ideas-Math-Solutions-Grade-5-Chapter-9-Multiply-Fractions-9.4-4-300x125.png 300w\" sizes=\"(max-width: 552px) 100vw, 552px\" \/><br \/>\nFrom the model of Newton,<br \/>\nThe number of rows is: 3<br \/>\nThe number of columns is: 5<br \/>\nFrom the model of Descartes,<br \/>\nThe number of rows is: 5<br \/>\nThe number of columns is: 3<br \/>\nFrom the above models,<br \/>\nWe can observe that the Descartes model is obtained by reversing the rows and columns of Newton i.e., the rows of Newton&#8217;s model become the columns of Descartes&#8217;s model and the columns of Newton&#8217;s model becomes the rows of Descartes&#8217; model.<br \/>\nSo,<br \/>\nThe multiplication equation represented by Newton is:<br \/>\n\\(\\frac{1}{3}\\) \u00d7 \\(\\frac{1}{5}\\)<br \/>\nThe multiplication equation represented by Descartes is:<br \/>\n\\(\\frac{1}{5}\\) \u00d7 \\(\\frac{1}{3}\\)<br \/>\nHence, from the above,<br \/>\nWe can conclude that Newton and Descartes are correct<\/p>\n<p><strong>Think and Grow: Modeling Real Life<\/strong><\/p>\n<p><strong>Example<\/strong><br \/>\nA recipe calls for \\(\\frac{3}{4}\\) teaspoon of cinnamon. You4want to halve the recipe. What fraction of a teaspoon of cinnamon do you need?<br \/>\n<img loading=\"lazy\" class=\"alignnone size-full wp-image-16384\" src=\"https:\/\/ccssmathanswers.com\/wp-content\/uploads\/2020\/12\/Big-Ideas-Math-Solutions-Grade-5-Chapter-9-Multiply-Fractions-9.4-5.png\" alt=\"Big Ideas Math Solutions Grade 5 Chapter 9 Multiply Fractions 9.4 5\" width=\"245\" height=\"99\" \/><br \/>\nBecause you want to halve the recipe, multiply \\(\\frac{1}{2}\\) by \\(\\frac{3}{4}\\) to find how many teaspoons of cinnamon you need.<br \/>\n<img loading=\"lazy\" class=\"alignnone size-full wp-image-37621\" src=\"https:\/\/ccssmathanswers.com\/wp-content\/uploads\/2020\/12\/Big-Ideas-Math-Answers-Grade-5-Chapter-9-10.jpg\" alt=\"\" width=\"669\" height=\"195\" srcset=\"https:\/\/bigideasmathanswers.com\/wp-content\/uploads\/2020\/12\/Big-Ideas-Math-Answers-Grade-5-Chapter-9-10.jpg 669w, https:\/\/bigideasmathanswers.com\/wp-content\/uploads\/2020\/12\/Big-Ideas-Math-Answers-Grade-5-Chapter-9-10-300x87.jpg 300w\" sizes=\"(max-width: 669px) 100vw, 669px\" \/><br \/>\nSo,<br \/>\nYou need \\(\\frac{3}{8}\\) teaspoon of cinnamon.<\/p>\n<p><strong>Show and Grow<\/strong><\/p>\n<p>Question 11.<br \/>\nThe mass of mango is \\(\\frac{2}{5}\\) kilogram. The mass of guava is \\(\\frac{1}{4}\\) as much as the mango. What is the mass of the guava?<br \/>\n<img loading=\"lazy\" class=\"alignnone size-full wp-image-16386\" src=\"https:\/\/ccssmathanswers.com\/wp-content\/uploads\/2020\/12\/Big-Ideas-Math-Solutions-Grade-5-Chapter-9-Multiply-Fractions-9.4-7.png\" alt=\"Big Ideas Math Solutions Grade 5 Chapter 9 Multiply Fractions 9.4 7\" width=\"132\" height=\"97\" \/><br \/>\nAnswer:<br \/>\nThe mass of guava is: \\(\\frac{1}{10}\\) kilograms<\/p>\n<p>Explanation:<br \/>\nIt is given that the mass of mango is \\(\\frac{2}{5}\\) kilogram and the mass of guava is \\(\\frac{1}{4}\\) as much as the mango.<br \/>\nSo,<br \/>\nThe mass of guava = ( The mass of mango ) \u00d7 ( The fraction of mass of guava in the mass of mango )<br \/>\n= \\(\\frac{2}{5}\\) \u00d7 \\(\\frac{1}{4}\\)<br \/>\n= \\(\\frac{1 \u00d7 2}{4 \u00d7 5}\\)<br \/>\n= \\(\\frac{2}{20}\\)<br \/>\n= \\(\\frac{1}{10}\\) kilograms<br \/>\nHnce, from the above,<br \/>\nWe can conclude that the mass of guava is: \\(\\frac{1}{10}\\) kilogram<\/p>\n<p>Question 12.<br \/>\nA giant panda spends \\(\\frac{2}{3}\\) of 1-day eating and foraging. It spends \\(\\frac{3}{4}\\) of that time for eating bamboo. What fraction of 1 day does the panda spend eating bamboo?<br \/>\nAnswer:<br \/>\nThe fraction of 1 day the panda spent on eating bamboo is: \\(\\frac{1}{2}\\)<\/p>\n<p>Explanation:<br \/>\nIt is given that a giant panda spends \\(\\frac{2}{3}\\) of 1-day eating and foraging and it spends \\(\\frac{3}{4}\\) of that time for eating bamboo.<br \/>\nSo,<br \/>\nThe fraction of 1 day the panda spent on eating bamboo = ( The fraction of time the panda spent on eating ) \u00d7 ( The fraction of time the panda spent time on eating bamboo out of the total time )<br \/>\n= \\(\\frac{2}{3}\\) \u00d7 \\(\\frac{3}{4}\\)<br \/>\n= \\(\\frac{3 \u00d7 2}{4 \u00d7 3}\\)<br \/>\n= \\(\\frac{6}{12}\\)<br \/>\n= \\(\\frac{1}{2}\\) hour<br \/>\nHence, from the above,<br \/>\nWe can conclude that the time spent by the panda on eating bamboo is: \\(\\frac{1}{2}\\) hour<\/p>\n<p>Question 13.<br \/>\n<strong>DIG DEEPER!<\/strong><br \/>\nYou have a half-gallon carton of milk that you use only for cereal. You use the same amount each day for 5 days. There is \\(\\frac{3}{8}\\) of the carton left. How many cups of milk do you use each day? Explain.<br \/>\nAnswer:<\/p>\n<h3><a id=\"Use_Models_to_Multiply_Fractions_Homework_&amp;_Practice_9.4\"><\/a>Use Models to Multiply Fractions Homework &amp; Practice 9.4<\/h3>\n<p><strong>Multiply. Use a model to help.<\/strong><br \/>\nQuestion 1.<br \/>\n\\(\\frac{1}{3}\\) \u00d7 \\(\\frac{1}{7}\\) = _______<br \/>\nAnswer:<br \/>\n\\(\\frac{1}{3}\\) \u00d7 \\(\\frac{1}{7}\\) = \\(\\frac{1}{21}\\)<\/p>\n<p>Explanation:<br \/>\nThe given fractions are: \\(\\frac{1}{7}\\) and \\(\\frac{1}{3}\\)<br \/>\nWe know that,<br \/>\n\\(\\frac{a}{b}\\) \u00d7 \\(\\frac{p}{q}\\) = \\(\\frac{a \u00d7 p}{b \u00d7 q}\\)<br \/>\na = \\(\\frac{a}{1}\\)<br \/>\nSo,<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}\\) \u00d7 \\(\\frac{1}{3}\\) = \\(\\frac{1}{21}\\)<\/p>\n<p>Question 2.<br \/>\n\\(\\frac{1}{2}\\) \u00d7 \\(\\frac{1}{9}\\) = _______<br \/>\nAnswer:<br \/>\n\\(\\frac{1}{2}\\) \u00d7 \\(\\frac{1}{9}\\) = \\(\\frac{1}{18}\\)<\/p>\n<p>Explanation:<br \/>\nThe given fractions are: \\(\\frac{1}{2}\\) and \\(\\frac{1}{9}\\)<br \/>\nWe know that,<br \/>\n\\(\\frac{a}{b}\\) \u00d7 \\(\\frac{p}{q}\\) = \\(\\frac{a \u00d7 p}{b \u00d7 q}\\)<br \/>\na = \\(\\frac{a}{1}\\)<br \/>\nSo,<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}\\) \u00d7 \\(\\frac{1}{9}\\) = \\(\\frac{1}{18}\\)<\/p>\n<p>Question 3.<br \/>\n\\(\\frac{2}{5}\\) \u00d7 \\(\\frac{1}{6}\\) = _______<br \/>\nAnswer:<br \/>\n\\(\\frac{2}{5}\\) \u00d7 \\(\\frac{1}{6}\\) = \\(\\frac{1}{15}\\)<\/p>\n<p>Explanation:<br \/>\nThe given fractions are: \\(\\frac{2}{5}\\) and \\(\\frac{1}{6}\\)<br \/>\nWe know that,<br \/>\n\\(\\frac{a}{b}\\) \u00d7 \\(\\frac{p}{q}\\) = \\(\\frac{a \u00d7 p}{b \u00d7 q}\\)<br \/>\na = \\(\\frac{a}{1}\\)<br \/>\nSo,<br \/>\n\\(\\frac{2}{5}\\) \u00d7 \\(\\frac{1}{6}\\)<br \/>\n= \\(\\frac{2 \u00d7 1}{5 \u00d7 6}\\)<br \/>\n= \\(\\frac{1}{15}\\)<br \/>\nHence,<br \/>\n\\(\\frac{2}{5}\\) \u00d7 \\(\\frac{1}{6}\\) = \\(\\frac{1}{15}\\)<\/p>\n<p>Question 4.<br \/>\n\\(\\frac{3}{4}\\) \u00d7 \\(\\frac{2}{7}\\) = _______<br \/>\nAnswer:<br \/>\n\\(\\frac{3}{4}\\) \u00d7 \\(\\frac{2}{7}\\) = \\(\\frac{3}{14}\\)<\/p>\n<p>Explanation:<br \/>\nThe given fractions are: \\(\\frac{3}{4}\\) and \\(\\frac{2}{7}\\)<br \/>\nWe know that,<br \/>\n\\(\\frac{a}{b}\\) \u00d7 \\(\\frac{p}{q}\\) = \\(\\frac{a \u00d7 p}{b \u00d7 q}\\)<br \/>\na = \\(\\frac{a}{1}\\)<br \/>\nSo,<br \/>\n\\(\\frac{3}{4}\\) \u00d7 \\(\\frac{2}{7}\\)<br \/>\n= \\(\\frac{3 \u00d7 2}{4 \u00d7 7}\\)<br \/>\n= \\(\\frac{3}{14}\\)<br \/>\nHence,<br \/>\n\\(\\frac{3}{4}\\) \u00d7 \\(\\frac{2}{7}\\) = \\(\\frac{3}{14}\\)<\/p>\n<p><strong>Write a multiplication equation represented by the model.<\/strong><br \/>\nQuestion 5.<br \/>\n<img loading=\"lazy\" class=\"alignnone size-full wp-image-16387\" src=\"https:\/\/ccssmathanswers.com\/wp-content\/uploads\/2020\/12\/Big-Ideas-Math-Solutions-Grade-5-Chapter-9-Multiply-Fractions-9.4-8.png\" alt=\"Big Ideas Math Solutions Grade 5 Chapter 9 Multiply Fractions 9.4 8\" width=\"144\" height=\"67\" \/><br \/>\nAnswer:<br \/>\nThe multiplication equation represented by the model is:<br \/>\n\\(\\frac{1}{2}\\) \u00d7 \\(\\frac{1}{5}\\)<\/p>\n<p>Explanation:<br \/>\nThe given model is:<br \/>\n<img loading=\"lazy\" class=\"alignnone size-full wp-image-16387\" src=\"https:\/\/ccssmathanswers.com\/wp-content\/uploads\/2020\/12\/Big-Ideas-Math-Solutions-Grade-5-Chapter-9-Multiply-Fractions-9.4-8.png\" alt=\"Big Ideas Math Solutions Grade 5 Chapter 9 Multiply Fractions 9.4 8\" width=\"144\" height=\"67\" \/><br \/>\nFrom the above model,<br \/>\nThe number of rows is: 2<br \/>\nThe number of columns is: 5<br \/>\nSo,<br \/>\nThe value of 1 row = \\(\\frac{1}{2}\\)<br \/>\nThe value of 1 column = \\(\\frac{1}{5}\\)<br \/>\nSo,<br \/>\nRows \u00d7 Columns = \\(\\frac{1}{2}\\) \u00d7 \\(\\frac{1}{5}\\)<br \/>\nHence, from the above,<br \/>\nWe can conclude that the multiplication equation represented by the above model is:<br \/>\n\\(\\frac{1}{2}\\) \u00d7 \\(\\frac{1}{5}\\)<\/p>\n<p>Question 6.<br \/>\n<img loading=\"lazy\" class=\"alignnone size-full wp-image-16388\" src=\"https:\/\/ccssmathanswers.com\/wp-content\/uploads\/2020\/12\/Big-Ideas-Math-Solutions-Grade-5-Chapter-9-Multiply-Fractions-9.4-9.png\" alt=\"Big Ideas Math Solutions Grade 5 Chapter 9 Multiply Fractions 9.4 9\" width=\"165\" height=\"86\" \/><br \/>\nAnswer:<br \/>\nThe multiplication equation represented by the model is:<br \/>\n\\(\\frac{1}{3}\\) \u00d7 \\(\\frac{1}{6}\\)<\/p>\n<p>Explanation:<br \/>\nThe given model is:<br \/>\n<img loading=\"lazy\" class=\"alignnone size-full wp-image-16388\" src=\"https:\/\/ccssmathanswers.com\/wp-content\/uploads\/2020\/12\/Big-Ideas-Math-Solutions-Grade-5-Chapter-9-Multiply-Fractions-9.4-9.png\" alt=\"Big Ideas Math Solutions Grade 5 Chapter 9 Multiply Fractions 9.4 9\" width=\"165\" height=\"86\" \/><br \/>\nFrom the above model,<br \/>\nThe number of rows is: 3<br \/>\nThe number of columns is: 6<br \/>\nSo,<br \/>\nThe value of 1 row = \\(\\frac{1}{3}\\)<br \/>\nThe value of 1 column = \\(\\frac{1}{6}\\)<br \/>\nSo,<br \/>\nRows \u00d7 Columns = \\(\\frac{1}{3}\\) \u00d7 \\(\\frac{1}{6}\\)<br \/>\nHence, from the above,<br \/>\nWe can conclude that the multiplication equation represented by the above model is:<br \/>\n\\(\\frac{1}{3}\\) \u00d7 \\(\\frac{1}{6}\\)<\/p>\n<p>Question 7.<br \/>\nOne-sixth of the animals at a zoo are birds. Of the birds, \\(\\frac{1}{3}\\) are female. What fraction of the animals at the zoo are female birds?<br \/>\nAnswer:<br \/>\nThe fraction of the animals at the zoo that is female birds is: \\(\\frac{1}{18}\\)<\/p>\n<p>Explanation:<br \/>\nIt is given that one-sixth of the animals at the zoo are birds and of the birds, \\(\\frac{1}{3}\\) is female.<br \/>\nSo,<br \/>\nThe fraction of the animals at the zoo are female birds = ( The fraction of animals in the zoo that is birds ) \u00d7 ( The fraction of the animals in the zoo that is female birds )<br \/>\n= \\(\\frac{1}{3}\\) \u00d7 \\(\\frac{1}{6}\\)<br \/>\n\\(\\frac{1 \u00d7 1}{3 \u00d7 6}\\)<br \/>\n= \\(\\frac{1}{18}\\)<br \/>\nHence, from the above,<br \/>\nWe can conclude that the number of animals that are female birds at the zoo is: \\(\\frac{1}{18}\\)<\/p>\n<p>Question 8.<br \/>\n<strong>Writing<\/strong><br \/>\nWrite and solve a real-life problem for the expression.<br \/>\n\\(\\frac{2}{3}\\) \u00d7 \\(\\frac{3}{7}\\)<br \/>\nAnswer:<br \/>\nSuppose in a school, there are boys ad girls.<br \/>\nIn school, \\(\\frac{2}{3}\\) of the boys and \\(\\frac{3}{7}\\) of the girls passed the PET test<br \/>\nSo,<br \/>\nThe fraction of the students that passed the PET test out of the total number of students = ( The fraction of the boys that passed the PET test ) \u00d7 ( The fraction of the girls that passed the PET test )<br \/>\n= \\(\\frac{2}{3}\\) \u00d7 \\(\\frac{3}{7}\\)<br \/>\n= \\(\\frac{3 \u00d7 2}{7 \u00d7 3}\\)<br \/>\n= \\(\\frac{6}{21}\\)<br \/>\n= \\(\\frac{2}{7}\\)<br \/>\nHence, from the above,<br \/>\nWe can conclude that the number of students who passed the PET test is: \\(\\frac{2}{7}\\)<\/p>\n<p>Question 9.<br \/>\n<strong>Modeling Real Life<\/strong><br \/>\nA Gouldian \ufb01nch is \\(\\frac{1}{2}\\) the length of the sun conure. How long is the Gouldian \ufb01nch?<br \/>\n<img loading=\"lazy\" class=\"alignnone size-full wp-image-16389\" src=\"https:\/\/ccssmathanswers.com\/wp-content\/uploads\/2020\/12\/Big-Ideas-Math-Solutions-Grade-5-Chapter-9-Multiply-Fractions-9.4-10.png\" alt=\"Big Ideas Math Solutions Grade 5 Chapter 9 Multiply Fractions 9.4 10\" width=\"290\" height=\"186\" \/><br \/>\nAnswer:<br \/>\nThe length of Gouldian finch is: \\(\\frac{11}{24}\\) feet<\/p>\n<p>Explanation:<br \/>\nIt is given that a Gouldian finch is \\(\\frac{1}{2}\\) the length of the sun conure.<br \/>\nFrom the given figure,<br \/>\nThe length of the sun conure = \\(\\frac{11}{12}\\) feet<br \/>\nSo,<br \/>\nThe length of Gouldian finch = ( The length of Sun Conure ) \u00f7 2<br \/>\n= \\(\\frac{11}{12}\\) \u00f7 2<br \/>\n= \\(\\frac{11}{12}\\) \u00f7 \\(\\frac{2}{1}\\)<br \/>\n= \\(\\frac{11}{12}\\) \u00d7 \\(\\frac{1}{2}\\)<br \/>\n= \\(\\frac{11 \u00d7 1}{12 \u00d7 2}\\)<br \/>\n= \\(\\frac{11}{24}\\) feet<br \/>\nHence, from the above,<br \/>\nWe can conclude that the length of the Gouldian finch is: \\(\\frac{11}{24}\\) feet<\/p>\n<p>Question 10.<br \/>\n<strong>DIG DEEPER!<\/strong><br \/>\nA recipe calls for \\(\\frac{2}{3}\\) cup of chopped walnuts. You chop 4 walnuts and get \\(\\frac{1}{4}\\) of the amount you need. How much more of a cup of chopped walnuts do you need? All of your walnuts are the same size. How many more walnuts should you chop? Explain.<br \/>\nAnswer:<br \/>\nThe cup of chopped walnuts more you need is: \\(\\frac{1}{3}\\)<br \/>\nThe number of walnuts you should chop is: 6<\/p>\n<p>Explanation:<br \/>\nIt is given that a recipe calls for \\(\\frac{2}{3}\\) cup of chopped walnuts.<br \/>\nIt is also given that you chop 4 walnuts and get \\(\\frac{1}{4}\\) of the amount you need.<br \/>\nSo,<br \/>\nThe cup more of chopped walnuts you need = 1- ( The cup of chopped walnuts you need for recipe )<br \/>\n= 1 &#8211; \\(\\frac{2}{3}\\)<br \/>\n= \\(\\frac{3}{3}\\) &#8211; \\(\\frac{2}{3}\\)<br \/>\n= \\(\\frac{3 &#8211; 2}{3}\\)<br \/>\n= \\(\\frac{1}{3}\\) more cup<br \/>\nNow,<br \/>\nThe number of walnuts you need more = ( The number of walnuts you needed to get \\(\\frac{1}{4}\\) of cup of chopped walnuts ) \u00f7 ( The amount of chopped walnuts you need for recipe )<br \/>\n= 4 \u00f7 \\(\\frac{2}{3}\\)<br \/>\n= \\(\\frac{4}{1}\\) \u00f7 \\(\\frac{2}{3}\\)<br \/>\n= \\(\\frac{4}{1}\\) \u00d7 \\(\\frac{3}{2}\\)<br \/>\n= \\(\\frac{4 \u00d7 3}{1 \u00d7 2}\\)<br \/>\n= \\(\\frac{12}{2}\\)<br \/>\n= 6<br \/>\nHence, from the above,<br \/>\nWe can conclude that<br \/>\nThe cup of chopped walnuts more you need is: \\(\\frac{1}{3}\\)<br \/>\nThe number of walnuts you should chop is: 6<\/p>\n<p><strong>Review &amp; Refresh<\/strong><\/p>\n<p><strong>Subtract.<\/strong><br \/>\nQuestion 11.<br \/>\n5 &#8211; 1\\(\\frac{3}{4}\\) = ______<br \/>\nAnswer:<br \/>\n5 &#8211; 1\\(\\frac{3}{4}\\) = \\(\\frac{13}{4}\\)<\/p>\n<p>Explanation:<br \/>\nThe given numbers are: 5 and 1\\(\\frac{3}{4}\\)<br \/>\nThe representation of 1\\(\\frac{3}{4}\\) in the improper fraction form is: \\(\\frac{7}{4}\\)<br \/>\nSo,<br \/>\n5 &#8211; \\(\\frac{7}{4}\\) = \\(\\frac{20}{4}\\) &#8211; \\(\\frac{7}{4}\\)<br \/>\n= \\(\\frac{20 &#8211; 7}{4}\\)<br \/>\n= \\(\\frac{13}{4}\\)<br \/>\nHence,<br \/>\n5 &#8211; 1\\(\\frac{3}{4}\\) = \\(\\frac{13}{4}\\)<\/p>\n<p>Question 12.<br \/>\n13\\(\\frac{1}{4}\\) &#8211; 7\\(\\frac{5}{8}\\) = ________<br \/>\nAnswer:<br \/>\n13\\(\\frac{1}{4}\\) &#8211; 7\\(\\frac{5}{8}\\) = \\(\\frac{45}{8}\\)<\/p>\n<p>Explanation:<br \/>\nThe given mixed fractions are: 13\\(\\frac{1}{4}\\) and 7\\(\\frac{5}{8}\\)<br \/>\nThe representation of 13\\(\\frac{1}{4}\\) in the improper fraction form is: \\(\\frac{53}{4}\\)<br \/>\nThe representation of 13\\(\\frac{1}{4}\\) in the improper fraction form is: \\(\\frac{61}{8}\\)<br \/>\nTo subtract the fractions, we have to make the denominators equal.<br \/>\nSo,<br \/>\nMultiply \\(\\frac{53}{4}\\) by \\(\\frac{2}{2}\\)<br \/>\nSo,<br \/>\n\\(\\frac{53}{4}\\) = \\(\\frac{106}{8}\\)<br \/>\nSo,<br \/>\n\\(\\frac{106}{8}\\) &#8211; \\(\\frac{61}{8}\\)<br \/>\n= \\(\\frac{106 &#8211; 61}{8}\\)<br \/>\n= \\(\\frac{45}{8}\\)<br \/>\nHence,<br \/>\n13\\(\\frac{1}{4}\\) &#8211; 13\\(\\frac{1}{4}\\) = \\(\\frac{45}{8}\\)<\/p>\n<p>Question 13.<br \/>\n12\\(\\frac{7}{10}\\) &#8211; 5\\(\\frac{3}{10}\\) &#8211; 1\\(\\frac{1}{5}\\) = ________<br \/>\nAnswer:<br \/>\n12\\(\\frac{7}{10}\\) &#8211; 5\\(\\frac{3}{10}\\) &#8211; 1\\(\\frac{1}{5}\\) = \\(\\frac{62}{10}\\)<\/p>\n<p>Explanation:<br \/>\nThe given mixed fractions are: 12\\(\\frac{7}{10}\\), 5\\(\\frac{3}{10}\\) and 1\\(\\frac{1}{5}\\)<br \/>\nThe representation of 12\\(\\frac{7}{10}\\) in the improper fraction form is: \\(\\frac{127}{10}\\)<br \/>\nThe representation of 5\\(\\frac{3}{10}\\) in the improper fraction form is: \\(\\frac{53}{10}\\)<br \/>\nThe representation of 1\\(\\frac{1}{5}\\) in the improper fraction form is: \\(\\frac{6}{5}\\)<br \/>\nTo subtract the fractions, we have to make the denominators equal.<br \/>\nSo,<br \/>\nMultiply \\(\\frac{6}{5}\\) by \\(\\frac{2}{2}\\)<br \/>\nSo,<br \/>\n\\(\\frac{6}{5}\\) = \\(\\frac{12}{10}\\)<br \/>\nSo,<br \/>\n\\(\\frac{127}{10}\\) &#8211; \\(\\frac{53}{10}\\) &#8211; \\(\\frac{12}{10}\\)<br \/>\n= \\(\\frac{127 &#8211; 53 &#8211; 12}{8}\\)<br \/>\n= \\(\\frac{62}{10}\\)<br \/>\nHence,<br \/>\n12\\(\\frac{7}{10}\\) &#8211; 5\\(\\frac{3}{10}\\) &#8211; 1\\(\\frac{1}{5}\\) = \\(\\frac{62}{10}\\)<\/p>\n<h3><a id=\"Lesson_9.5_Multiply_Fractions\"><\/a>Lesson 9.5 Multiply Fractions<\/h3>\n<p><strong>Explore and Grow<\/strong><\/p>\n<p>Use models to help you complete the table. What do you notice about each expression and its product?<br \/>\n<img loading=\"lazy\" class=\"alignnone size-full wp-image-16390\" src=\"https:\/\/ccssmathanswers.com\/wp-content\/uploads\/2020\/12\/Big-Ideas-Math-Answer-Key-Grade-5-Chapter-9-Multiply-Fractions-9.5-1.png\" alt=\"Big Ideas Math Answer Key Grade 5 Chapter 9 Multiply Fractions 9.5 1\" width=\"184\" height=\"300\" \/><br \/>\nAnswer:<br \/>\nThe completed table is:<br \/>\n<img loading=\"lazy\" class=\"alignnone size-full wp-image-38027\" src=\"https:\/\/ccssmathanswers.com\/wp-content\/uploads\/2020\/12\/Big-Ideas-Math-Answers-Grade-5-Chapter-9-11.jpg\" alt=\"\" width=\"203\" height=\"288\" \/><br \/>\nFrom the given table,<br \/>\nWe can observe the product of fractions is also a product.<\/p>\n<p><strong>Construct Arguments<\/strong><br \/>\nExplain how to multiply two fractions without using a model.<br \/>\nAnswer:<br \/>\nWe can multiply the fractions by using the properties of multiplication. They are:<br \/>\nA) \\(\\frac{a}{b}\\) \u00d7 \\(\\frac{p}{q}\\)<br \/>\n= \\(\\frac{a \u00d7 p}{b \u00d7 q}\\)<br \/>\nB) a = \\(\\frac{a}{1}\\)<\/p>\n<p><strong>Think and Grow: Multiply Fractions<\/strong><\/p>\n<p><strong>Key Idea<\/strong><br \/>\nYou can find the product of a fraction and a fraction by multiplying the numerators and multiplying the denominators.<br \/>\n<strong>Example<\/strong><br \/>\nFind \\(\\frac{1}{2}\\) \u00d7 \\(\\frac{3}{2}\\).<br \/>\nMultiply the numerators and multiply the denominators.<br \/>\n<img loading=\"lazy\" class=\"alignnone size-full wp-image-38028\" src=\"https:\/\/ccssmathanswers.com\/wp-content\/uploads\/2020\/12\/Big-Ideas-Math-Answers-Grade-5-Chapter-9-12.jpg\" alt=\"\" width=\"665\" height=\"134\" srcset=\"https:\/\/bigideasmathanswers.com\/wp-content\/uploads\/2020\/12\/Big-Ideas-Math-Answers-Grade-5-Chapter-9-12.jpg 665w, https:\/\/bigideasmathanswers.com\/wp-content\/uploads\/2020\/12\/Big-Ideas-Math-Answers-Grade-5-Chapter-9-12-300x60.jpg 300w\" sizes=\"(max-width: 665px) 100vw, 665px\" \/><\/p>\n<p><strong>Example<\/strong><br \/>\nFind \\(\\frac{5}{6}\\) \u00d7 \\(\\frac{3}{5}\\).<br \/>\nMultiply the numerators and multiply the denominators.<br \/>\n<img loading=\"lazy\" class=\"alignnone size-full wp-image-38029\" src=\"https:\/\/ccssmathanswers.com\/wp-content\/uploads\/2020\/12\/Big-Ideas-Math-Answers-Grade-5-Chapter-9-13.jpg\" alt=\"\" width=\"645\" height=\"233\" srcset=\"https:\/\/bigideasmathanswers.com\/wp-content\/uploads\/2020\/12\/Big-Ideas-Math-Answers-Grade-5-Chapter-9-13.jpg 645w, https:\/\/bigideasmathanswers.com\/wp-content\/uploads\/2020\/12\/Big-Ideas-Math-Answers-Grade-5-Chapter-9-13-300x108.jpg 300w\" sizes=\"(max-width: 645px) 100vw, 645px\" \/><\/p>\n<p><strong>Show and Grow<\/strong><\/p>\n<p><strong>Multiply.<\/strong><br \/>\nQuestion 1.<br \/>\n\\(\\frac{1}{2}\\) \u00d7 \\(\\frac{4}{3}\\) = _______<br \/>\nAnswer:<br \/>\n\\(\\frac{1}{2}\\) \u00d7 \\(\\frac{4}{3}\\) = \\(\\frac{2}{3}\\)<\/p>\n<p>Explanation:<br \/>\nThe given fractions are: \\(\\frac{1}{2}\\) and \\(\\frac{4}{3}\\)<br \/>\nWe know that,<br \/>\n\\(\\frac{a}{b}\\) \u00d7 \\(\\frac{p}{q}\\)<br \/>\n= \\(\\frac{a \u00d7 p}{b \u00d7 q}\\)<br \/>\na = \\(\\frac{a}{1}\\)<br \/>\nSo,<br \/>\n\\(\\frac{1}{2}\\) \u00d7 \\(\\frac{4}{3}\\)<br \/>\n= \\(\\frac{1 \u00d7 4}{2 \u00d7 3}\\)<br \/>\n= \\(\\frac{4}{6}\\)<br \/>\n= \\(\\frac{2}{3}\\)<br \/>\nHence,<br \/>\n\\(\\frac{1}{2}\\) \u00d7 \\(\\frac{4}{3}\\) = \\(\\frac{2}{3}\\)<\/p>\n<p>Question 2.<br \/>\n\\(\\frac{2}{5}\\) \u00d7 \\(\\frac{2}{3}\\) = _______<br \/>\nAnswer:<br \/>\n\\(\\frac{2}{5}\\) \u00d7 \\(\\frac{2}{3}\\) = \\(\\frac{4}{15}\\)<\/p>\n<p>Explanation:<br \/>\nThe given fractions are: \\(\\frac{2}{5}\\) and \\(\\frac{2}{3}\\)<br \/>\nWe know that,<br \/>\n\\(\\frac{a}{b}\\) \u00d7 \\(\\frac{p}{q}\\)<br \/>\n= \\(\\frac{a \u00d7 p}{b \u00d7 q}\\)<br \/>\na = \\(\\frac{a}{1}\\)<br \/>\nSo,<br \/>\n\\(\\frac{2}{5}\\) \u00d7 \\(\\frac{2}{3}\\)<br \/>\n= \\(\\frac{2 \u00d7 2}{5 \u00d7 3}\\)<br \/>\n= \\(\\frac{4}{15}\\)<br \/>\nHence,<br \/>\n\\(\\frac{2}{5}\\) \u00d7 \\(\\frac{2}{3}\\) = \\(\\frac{4}{15}\\)<\/p>\n<p>Question 3.<br \/>\n\\(\\frac{3}{4}\\) \u00d7 \\(\\frac{5}{8}\\) = _______<br \/>\nAnswer:<br \/>\n\\(\\frac{3}{4}\\) \u00d7 \\(\\frac{5}{8}\\) = \\(\\frac{15}{32}\\)<\/p>\n<p>Explanation:<br \/>\nThe given fractions are: \\(\\frac{3}{4}\\) and \\(\\frac{5}{8}\\)<br \/>\nWe know that,<br \/>\n\\(\\frac{a}{b}\\) \u00d7 \\(\\frac{p}{q}\\)<br \/>\n= \\(\\frac{a \u00d7 p}{b \u00d7 q}\\)<br \/>\na = \\(\\frac{a}{1}\\)<br \/>\nSo,<br \/>\n\\(\\frac{3}{4}\\) \u00d7 \\(\\frac{5}{8}\\)<br \/>\n= \\(\\frac{3 \u00d7 5}{4 \u00d7 8}\\)<br \/>\n= \\(\\frac{15}{32}\\)<br \/>\nHence,<br \/>\n\\(\\frac{3}{4}\\) \u00d7 \\(\\frac{5}{8}\\) = \\(\\frac{15}{32}\\)<\/p>\n<p><strong>Apply and Grow: Practice<\/strong><\/p>\n<p><strong>Multiply.<\/strong><br \/>\nQuestion 4.<br \/>\n\\(\\frac{1}{4}\\) \u00d7 \\(\\frac{1}{4}\\) = _______<br \/>\nAnswer:<br \/>\n\\(\\frac{1}{4}\\) \u00d7 \\(\\frac{1}{4}\\) = \\(\\frac{1}{16}\\)<\/p>\n<p>Explanation:<br \/>\nThe given fractions are: \\(\\frac{1}{4}\\) and \\(\\frac{1}{4}\\)<br \/>\nWe know that,<br \/>\n\\(\\frac{a}{b}\\) \u00d7 \\(\\frac{p}{q}\\)<br \/>\n= \\(\\frac{a \u00d7 p}{b \u00d7 q}\\)<br \/>\na = \\(\\frac{a}{1}\\)<br \/>\nSo,<br \/>\n\\(\\frac{1}{4}\\) \u00d7 \\(\\frac{1}{4}\\)<br \/>\n= \\(\\frac{1 \u00d7 1}{4 \u00d7 4}\\)<br \/>\n= \\(\\frac{1}{16}\\)<br \/>\nHence,<br \/>\n\\(\\frac{1}{4}\\) \u00d7 \\(\\frac{1}{4}\\) = \\(\\frac{1}{16}\\)<\/p>\n<p>Question 5.<br \/>\n\\(\\frac{5}{6}\\) \u00d7 \\(\\frac{7}{10}\\) = _______<br \/>\nAnswer:<br \/>\n\\(\\frac{5}{6}\\) \u00d7 \\(\\frac{7}{10}\\) = \\(\\frac{7}{12}\\)<\/p>\n<p>Explanation:<br \/>\nThe given fractions are: \\(\\frac{5}{6}\\) and \\(\\frac{7}{10}\\)<br \/>\nWe know that,<br \/>\n\\(\\frac{a}{b}\\) \u00d7 \\(\\frac{p}{q}\\)<br \/>\n= \\(\\frac{a \u00d7 p}{b \u00d7 q}\\)<br \/>\na = \\(\\frac{a}{1}\\)<br \/>\nSo,<br \/>\n\\(\\frac{5}{6}\\) \u00d7 \\(\\frac{7}{10}\\)<br \/>\n= \\(\\frac{5 \u00d7 7}{6 \u00d7 10}\\)<br \/>\n= \\(\\frac{35}{60}\\)<br \/>\n= \\(\\frac{7}{12}\\)<br \/>\nHence,<br \/>\n\\(\\frac{5}{6}\\) \u00d7 \\(\\frac{7}{10}\\) = \\(\\frac{7}{12}\\)<\/p>\n<p>Question 6.<br \/>\n\\(\\frac{6}{9}\\) \u00d7 \\(\\frac{8}{2}\\) = _______<br \/>\nAnswer:<br \/>\n\\(\\frac{6}{9}\\) \u00d7 \\(\\frac{8}{2}\\) = \\(\\frac{8}{3}\\)<\/p>\n<p>Explanation:<br \/>\nThe given fractions are: \\(\\frac{6}{9}\\) and \\(\\frac{8}{2}\\)<br \/>\nWe know that,<br \/>\n\\(\\frac{a}{b}\\) \u00d7 \\(\\frac{p}{q}\\)<br \/>\n= \\(\\frac{a \u00d7 p}{b \u00d7 q}\\)<br \/>\na = \\(\\frac{a}{1}\\)<br \/>\nSo,<br \/>\n\\(\\frac{6}{9}\\) \u00d7 \\(\\frac{8}{2}\\)<br \/>\n= \\(\\frac{6 \u00d7 8}{2 \u00d7 9}\\)<br \/>\n= \\(\\frac{48}{18}\\)<br \/>\n= \\(\\frac{8}{3}\\)<br \/>\nHence,<br \/>\n\\(\\frac{6}{9}\\) \u00d7 \\(\\frac{8}{2}\\) = \\(\\frac{8}{3}\\)<\/p>\n<p>Question 7.<br \/>\n\\(\\frac{21}{100}\\) \u00d7 \\(\\frac{3}{5}\\) = _______<br \/>\nAnswer:<br \/>\n\\(\\frac{21}{100}\\) \u00d7 \\(\\frac{3}{5}\\) = \\(\\frac{63}{500}\\)<\/p>\n<p>Explanation:<br \/>\nThe given fractions are: \\(\\frac{21}{100}\\) and \\(\\frac{3}{5}\\)<br \/>\nWe know that,<br \/>\n\\(\\frac{a}{b}\\) \u00d7 \\(\\frac{p}{q}\\)<br \/>\n= \\(\\frac{a \u00d7 p}{b \u00d7 q}\\)<br \/>\na = \\(\\frac{a}{1}\\)<br \/>\nSo,<br \/>\n\\(\\frac{21}{100}\\) \u00d7 \\(\\frac{3}{5}\\)<br \/>\n= \\(\\frac{21 \u00d7 3}{100 \u00d7 5}\\)<br \/>\n= \\(\\frac{63}{500}\\)<br \/>\nHence,<br \/>\n\\(\\frac{21}{100}\\) \u00d7 \\(\\frac{3}{5}\\) = \\(\\frac{63}{500}\\)<\/p>\n<p>Question 8.<br \/>\n\\(\\frac{1}{12}\\) \u00d7 \\(\\frac{9}{4}\\) = _______<br \/>\nAnswer:<br \/>\n\\(\\frac{1}{12}\\) \u00d7 \\(\\frac{9}{4}\\) = \\(\\frac{3}{16}\\)<\/p>\n<p>Explanation:<br \/>\nThe given fractions are: \\(\\frac{1}{12}\\) and \\(\\frac{9}{4}\\)<br \/>\nWe know that,<br \/>\n\\(\\frac{a}{b}\\) \u00d7 \\(\\frac{p}{q}\\)<br \/>\n= \\(\\frac{a \u00d7 p}{b \u00d7 q}\\)<br \/>\na = \\(\\frac{a}{1}\\)<br \/>\nSo,<br \/>\n\\(\\frac{1}{12}\\) \u00d7 \\(\\frac{9}{4}\\)<br \/>\n= \\(\\frac{1 \u00d7 9}{12 \u00d7 4}\\)<br \/>\n= \\(\\frac{9}{48}\\)<br \/>\n= \\(\\frac{3}{16}\\)<br \/>\nHence,<br \/>\n\\(\\frac{1}{12}\\) \u00d7 \\(\\frac{9}{4}\\) = \\(\\frac{3}{16}\\)<\/p>\n<p>Question 9.<br \/>\n\\(\\frac{4}{7}\\) \u00d7 \\(\\frac{8}{8}\\) = _______<br \/>\nAnswer:<br \/>\n\\(\\frac{4}{7}\\) \u00d7 \\(\\frac{8}{8}\\) = \\(\\frac{4}{7}\\)<\/p>\n<p>Explanation:<br \/>\nThe given fractions are: \\(\\frac{4}{7}\\) and \\(\\frac{8}{8}\\)<br \/>\nWe know that,<br \/>\n\\(\\frac{a}{b}\\) \u00d7 \\(\\frac{p}{q}\\)<br \/>\n= \\(\\frac{a \u00d7 p}{b \u00d7 q}\\)<br \/>\na = \\(\\frac{a}{1}\\)<br \/>\nSo,<br \/>\n\\(\\frac{4}{7}\\) \u00d7 \\(\\frac{8}{8}\\)<br \/>\n= \\(\\frac{8 \u00d7 4}{7 \u00d7 8}\\)<br \/>\n= \\(\\frac{4}{7}\\)<br \/>\nHence,<br \/>\n\\(\\frac{4}{7}\\) \u00d7 \\(\\frac{8}{8}\\) = \\(\\frac{4}{7}\\)<\/p>\n<p><strong>Evaluate<\/strong><br \/>\nQuestion 10.<br \/>\n\\(\\left(\\frac{1}{2} \\times \\frac{7}{8}\\right)\\) \u00d7 2 = _______<br \/>\nAnswer:<br \/>\n\\(\\left(\\frac{1}{2} \\times \\frac{7}{8}\\right)\\) \u00d7 2 = \\(\\frac{7}{8}\\)<\/p>\n<p>Explanation:<br \/>\nThe given fractions are: \\(\\frac{7}{8}\\) and \\(\\frac{1}{2}\\)<\/p>\n<p>We know that,<br \/>\n\\(\\frac{a}{b}\\) \u00d7 \\(\\frac{p}{q}\\)<br \/>\n= \\(\\frac{a \u00d7 p}{b \u00d7 q}\\)<br \/>\na = \\(\\frac{a}{1}\\)<br \/>\nSo,<br \/>\n( \\(\\frac{1}{2}\\) \u00d7 \\(\\frac{7}{8}\\)\u00a0 ) \u00d7 2<br \/>\n= ( \\(\\frac{1 \u00d7 7}{2 \u00d7 8}\\) ) \u00d7 \\(\\frac{2}{1}\\)<br \/>\n= \\(\\frac{7}{16}\\) \u00d7 \\(\\frac{2}{1}\\)<br \/>\n= \\(\\frac{7 \u00d7 2}{16 \u00d7 1}\\)<br \/>\n= \\(\\frac{7}{8}\\)<br \/>\nHence,<br \/>\n\\(\\frac{4}{7}\\) \u00d7 \\(\\frac{8}{8}\\) = \\(\\frac{4}{7}\\)<\/p>\n<p>Question 11.<br \/>\n\\(\\left(\\frac{7}{6}-\\frac{5}{6}\\right)\\) \u00d7 \\(\\frac{2}{3}\\) = _______<br \/>\nAnswer:<br \/>\n\\(\\left(\\frac{7}{6}-\\frac{5}{6}\\right)\\) \u00d7 \\(\\frac{2}{3}\\) = \\(\\frac{2}{9}\\)<\/p>\n<p>Explanation:<br \/>\nThe given fractions are: \\(\\frac{7}{6}\\) , \\(\\frac{5}{6}\\), and \\(\\frac{2}{3}\\)<br \/>\nWe know that,<br \/>\n\\(\\frac{a}{b}\\) \u00d7 \\(\\frac{p}{q}\\)<br \/>\n= \\(\\frac{a \u00d7 p}{b \u00d7 q}\\)<br \/>\na = \\(\\frac{a}{1}\\)<br \/>\nSo,<br \/>\n( \\(\\frac{7}{6}\\) &#8211; \\(\\frac{5}{6}\\)\u00a0 ) \u00d7 \\(\\frac{2}{3}\\)<br \/>\n= ( \\(\\frac{7 &#8211; 5}{6}\\) ) \u00d7 \\(\\frac{2}{3}\\)<br \/>\n= \\(\\frac{2}{6}\\) \u00d7 \\(\\frac{2}{3}\\)<br \/>\n= \\(\\frac{2 \u00d7 2}{6 \u00d7 3}\\)<br \/>\n= \\(\\frac{4}{18}\\)<br \/>\n= \\(\\frac{2}{9}\\)<br \/>\nHence,<br \/>\n\\(\\left(\\frac{7}{6}-\\frac{5}{6}\\right)\\) \u00d7 \\(\\frac{2}{3}\\) = \\(\\frac{2}{9}\\)<\/p>\n<p>Question 12.<br \/>\n\\(\\frac{9}{10}\\) \u00d7 \\(\\left(\\frac{4}{9}+\\frac{1}{3}\\right)\\) = _________<br \/>\nAnswer:<br \/>\n\\(\\frac{9}{10}\\) \u00d7 \\(\\left(\\frac{4}{9}+\\frac{1}{3}\\right)\\) = \\(\\frac{7}{10}\\)<\/p>\n<p>Explanation:<br \/>\nThe given fractions are: \\(\\frac{9}{10}\\), \\(\\frac{4}{9}\\) and \\(\\frac{1}{3}\\)<br \/>\nWe know that,<br \/>\n\\(\\frac{a}{b}\\) \u00d7 \\(\\frac{p}{q}\\)<br \/>\n= \\(\\frac{a \u00d7 p}{b \u00d7 q}\\)<br \/>\na = \\(\\frac{a}{1}\\)<br \/>\nSo,<br \/>\n\\(\\frac{9}{10}\\) \u00d7 ( \\(\\frac{4}{9}\\) + \\(\\frac{1}{3}\\)\u00a0 )<br \/>\n= ( \\(\\frac{4 + 3}{9}\\) ) \u00d7 \\(\\frac{9}{10}\\)<br \/>\n= \\(\\frac{7}{9}\\) \u00d7 \\(\\frac{9}{10}\\)<br \/>\n= \\(\\frac{7 \u00d7 9}{9 \u00d7 10}\\)<br \/>\n= \\(\\frac{7}{10}\\)<br \/>\nHence,<br \/>\n\\(\\frac{9}{10}\\) \u00d7 \\(\\left(\\frac{4}{9}+\\frac{1}{3}\\right)\\) = \\(\\frac{7}{10}\\)<\/p>\n<p>Question 13.<br \/>\nAt a school, \\(\\frac{3}{4}\\) of the students play a sport. Of the students that play a sport, \\(\\frac{1}{5}\\) play baseball. What fraction of the students at the school play baseball?<br \/>\n<img loading=\"lazy\" class=\"alignnone size-full wp-image-16394\" src=\"https:\/\/ccssmathanswers.com\/wp-content\/uploads\/2020\/12\/Big-Ideas-Math-Answer-Key-Grade-5-Chapter-9-Multiply-Fractions-9.5-4.png\" alt=\"Big Ideas Math Answer Key Grade 5 Chapter 9 Multiply Fractions 9.5 4\" width=\"201\" height=\"140\" \/><br \/>\nAnswer:<br \/>\nThe fraction of the students at the school that play baseball is: \\(\\frac{3}{20}\\)<\/p>\n<p>Explanation:<br \/>\nIt is given that at a school, \\(\\frac{3}{4}\\) of the students play a sport and of the students that play a sport, \\(\\frac{1}{5}\\) play baseball.<br \/>\nSo,<br \/>\nThe fraction of the students at the school that play baseall = ( The fraction of the students that play a sport ) \u00d7 ( The fraction of the students that play baseball out of thetotal number of students )<br \/>\n= \\(\\frac{3}{4}\\) \u00d7 \\(\\frac{1}{5}\\)<br \/>\n= \\(\\frac{3 \u00d7 1}{4 \u00d7 5}\\)<br \/>\n= \\(\\frac{3}{20}\\)<br \/>\nHence, from the above,<br \/>\nWe can conclude that the fraction of the students that play baseball is: \\(\\frac{3}{20}\\)<\/p>\n<p>Question 14.<br \/>\n<strong>Reasoning<\/strong><br \/>\nDescartes says he can find the product of a whole number and a fraction the same way he finds the product of two fractions. Explain why his reasoning makes sense.<br \/>\nAnswer:<br \/>\nThe product of a whole number and a fraction follows the same procedure as that of the product of the two fractions because of the following properties of multiplication:<br \/>\nA) \\(\\frac{a}{b}\\) \u00d7 \\(\\frac{p}{q}\\)<br \/>\n= \\(\\frac{a \u00d7 p}{b \u00d7 q}\\)<br \/>\nB) a= \\(\\frac{a}{1}\\)<br \/>\nHence, from the above two properties of multiplication,<br \/>\nWe can conclude that the reasoning of Descartes makes sense<\/p>\n<p>Question 15.<br \/>\n<strong>Writing<\/strong><br \/>\nExplain how multiplying fractions is different than adding and subtracting fractions.<br \/>\nAnswer:<br \/>\nIn the multiplication of the fractions, we multiply numerators and denominators.<br \/>\nExample:<br \/>\n\\(\\frac{a}{b}\\) \u00d7 \\(\\frac{p}{q}\\)<br \/>\n= \\(\\frac{a \u00d7 p}{b \u00d7 q}\\)<br \/>\nIn addition of the fractions, we add only numerators making the denominators equal<br \/>\nExample:<br \/>\n\\(\\frac{a}{b}\\) + \\(\\frac{p}{b}\\)<br \/>\n= \\(\\frac{a + p}{b}\\)<br \/>\nIn subtraction of the fractions, we subtract only numerators making the denominators equal<br \/>\nExample:<br \/>\n\\(\\frac{a}{b}\\) &#8211; \\(\\frac{p}{b}\\)<br \/>\n= \\(\\frac{a &#8211; p}{b}\\)<\/p>\n<p><strong>Think and Grow: Modeling Real Life<\/strong><\/p>\n<p><strong>Example<\/strong><br \/>\nA tourist is walking from the Empire State Building to Times Square. She is \\(\\frac{2}{3}\\) of the way there. What fraction of a mile does she have left to walk?<br \/>\n<img loading=\"lazy\" class=\"alignnone size-full wp-image-16395\" src=\"https:\/\/ccssmathanswers.com\/wp-content\/uploads\/2020\/12\/Big-Ideas-Math-Answer-Key-Grade-5-Chapter-9-Multiply-Fractions-9.5-5.png\" alt=\"Big Ideas Math Answer Key Grade 5 Chapter 9 Multiply Fractions 9.5 5\" width=\"269\" height=\"226\" \/><br \/>\nFind the distance she has walked. Because she has walked \\(\\frac{2}{3}\\) of \\(\\frac{3}{4}\\) mile, multiply \\(\\frac{2}{3}\\) by \\(\\frac{3}{4}\\).<br \/>\n<img loading=\"lazy\" class=\"alignnone size-full wp-image-38229\" src=\"https:\/\/ccssmathanswers.com\/wp-content\/uploads\/2020\/12\/Big-Ideas-Math-Answers-Grade-5-Chapter-9-14.jpg\" alt=\"\" width=\"643\" height=\"274\" srcset=\"https:\/\/bigideasmathanswers.com\/wp-content\/uploads\/2020\/12\/Big-Ideas-Math-Answers-Grade-5-Chapter-9-14.jpg 643w, https:\/\/bigideasmathanswers.com\/wp-content\/uploads\/2020\/12\/Big-Ideas-Math-Answers-Grade-5-Chapter-9-14-300x128.jpg 300w\" sizes=\"(max-width: 643px) 100vw, 643px\" \/><\/p>\n<p><strong>Show and Grow<\/strong><\/p>\n<p>Question 16.<br \/>\nAt a zoo, \\(\\frac{3}{5}\\) of the animals are mammals. Of the mammals, \\(\\frac{5}{12}\\) are primates.What fraction of the animals at the zoo are not primates?<br \/>\n<img loading=\"lazy\" class=\"alignnone size-full wp-image-16397\" src=\"https:\/\/ccssmathanswers.com\/wp-content\/uploads\/2020\/12\/Big-Ideas-Math-Answer-Key-Grade-5-Chapter-9-Multiply-Fractions-9.5-7.png\" alt=\"Big Ideas Math Answer Key Grade 5 Chapter 9 Multiply Fractions 9.5 7\" width=\"71\" height=\"122\" \/><br \/>\nAnswer:<br \/>\nThe fractions of the animals at the zoo that are not primates is: \\(\\frac{3}{4}\\)<\/p>\n<p>Explanation:<br \/>\nIt is given that at the zoo, \\(\\frac{3}{5}\\) of the animals are mammals and of the animals, \\(\\frac{5}{12}\\) are primates<br \/>\nSo,<br \/>\nThe fraction of the animals that are primates =( The fraction of the animals that are primates ) \u00d7 ( The fraction of the animals that are primates )<br \/>\n= \\(\\frac{3}{5}\\) \u00d7 \\(\\frac{5}{12}\\)<br \/>\n= \\(\\frac{3 \u00d7 5}{5 \u00d7 12}\\)<br \/>\n= \\(\\frac{15}{60}\\)<br \/>\n= \\(\\frac{1}{4}\\)<br \/>\nNow,<br \/>\nLet the total number of animals that are mammals =1<br \/>\nSo,<br \/>\nThe fraction of the animals that are not primates = ( The total number of mammals ) &#8211; ( The fraction of the animals that are primates )<br \/>\n= 1 &#8211; \\(\\frac{1}{4}\\)<br \/>\n= \\(\\frac{4}{4}\\) &#8211; \\(\\frac{1}{4}\\)<br \/>\n= \\(\\frac{4 &#8211; 1}{4}\\)<br \/>\n= \\(\\frac{3}{4}\\)<br \/>\nHence, from the above,<br \/>\nWe can conclude that the fraction of the animals that are not primates is: \\(\\frac{3}{4}\\)<\/p>\n<p>Question 17.<br \/>\nYou have an album of 216 trading cards. One page contains \\(\\frac{1}{24}\\) of the cards. On that page, \\(\\frac{2}{3}\\) of the cards are epic. You only have one page with any epic cards. How many epic cards do you have?<br \/>\nAnswer:<br \/>\nThe number of epic cards is: 6 epic cards<\/p>\n<p>Explanation:<br \/>\nIt is given that you have an album of 216 trading cards<br \/>\nIt is also given that one page contains \\(\\frac{1}{24}\\) of the cards. On that page, \\(\\frac{2}{3}\\) of the cards are epic.<br \/>\nSo,<br \/>\nThe fraction of the epic cards = ( The total number of cards on that page ) \u00d7 ( The fraction of the epic cards that is on that page )<br \/>\n= \\(\\frac{1}{24}\\) \u00d7 \\(\\frac{2}{3}\\)<br \/>\n= \\(\\frac{2 \u00d7 1}{3 \u00d7 24}\\)<br \/>\n= \\(\\frac{1}{36}\\)<br \/>\nSo,<br \/>\nThe number of epic cards = ( The total number of cards ) \u00d7 ( The fraction of the epic cards )<br \/>\n= 216 \u00d7 \\(\\frac{1}{36}\\)<br \/>\n= \\(\\frac{216}{1}\\) \u00d7 \\(\\frac{}{36}\\)<br \/>\n= \\(\\frac{216}{36}\\)<br \/>\n= 6 epic cards<br \/>\nHence, from the above,<br \/>\nWe can conclude that there are 6 epic cards<\/p>\n<p>Question 18.<br \/>\n<strong>DIG DEEPER!<\/strong><br \/>\nIn a class, \\(\\frac{2}{5}\\) of the students play basketball and \\(\\frac{7}{10}\\) play soccer.Of the students who play basketball, \\(\\frac{2}{3}\\) also play soccer. There are 30 students in the class. How many students play soccer but do not play basketball?<br \/>\nAnswer:<br \/>\nThe number of students that play soccer but do not play basketball is: 4 students<\/p>\n<p>Explanation:<br \/>\nIt is given that in a class, \\(\\frac{2}{5}\\) of the students play basketball and \\(\\frac{7}{10}\\) play soccer.Of the students who play basketball, \\(\\frac{2}{3}\\) also play soccer.<br \/>\nSo,<br \/>\nThe number of students who play basketball and soccer = ( The number of students who play basketball ) \u00d7 ( The number of students playing soccer who are also playing basketball )<br \/>\n= \\(\\frac{2}{5}\\) \u00d7 \\(\\frac{2}{3}\\)<br \/>\n= \\(\\frac{4}{15}\\)<br \/>\nNow,<br \/>\nThe number of students who only play soccer but not basketball = ( The number of students who play soccer only ) &#8211; ( The number of students who play both basketball and soccer )<br \/>\n= \\(\\frac{2}{5}\\) &#8211; \\(\\frac{4}{15}\\)<br \/>\nIn subtraction, the denominators must be equal.<br \/>\nSo,<br \/>\nMultiply \\(\\frac{2}{5}\\) by \\(\\frac{3}{3}\\)<br \/>\nSo,<br \/>\n\\(\\frac{6}{15}\\) &#8211; \\(\\frac{4}{15}\\)<br \/>\n= \\(\\frac{4}{15}\\)<br \/>\nIt is also given that the total number of students are: 30<br \/>\nSo,<br \/>\nThe number of students who play soccer only = ( The fraction of the students who play soccer only ) \u00d7 ( The total number of students )<br \/>\n= \\(\\frac{2}{15}\\) \u00d7 30<br \/>\n= \\(\\frac{2}{15}\\) \u00d7 \\(\\frac{30}{1}\\)<br \/>\n= 4 students<br \/>\nHence, from the above,<br \/>\nWe can conclude that there are 4 students who play soccer only.<\/p>\n<h3><a id=\"Multiply_Fractions_Homework_&amp;_Practice_9.5\"><\/a>Multiply Fractions Homework &amp; Practice 9.5<\/h3>\n<p><strong>Multiply.<\/strong><br \/>\n\\(\\frac{1}{4}\\) \u00d7 \\(\\frac{1}{5}\\) = _______<br \/>\nAnswer:<br \/>\n\\(\\frac{1}{4}\\) \u00d7 \\(\\frac{1}{5}\\) = \\(\\frac{1}{20}\\)<\/p>\n<p>Explanation:<br \/>\nThe given fractions are: \\(\\frac{1}{4}\\) and \\(\\frac{1}{5}\\)<br \/>\nWe know that,<br \/>\n\\(\\frac{a}{b}\\) \u00d7 \\(\\frac{p}{q}\\)<br \/>\n= \\(\\frac{a \u00d7 p}{b \u00d7 q}\\)<br \/>\na = \\(\\frac{a}{1}\\)<br \/>\nSo,<br \/>\n\\(\\frac{1}{4}\\) \u00d7 \\(\\frac{1}{5}\\)<br \/>\n= \\(\\frac{1 \u00d7 1}{4 \u00d7 5}\\)<br \/>\n= \\(\\frac{1}{20}\\)<br \/>\nHence,<br \/>\n\\(\\frac{1}{4}\\) \u00d7 \\(\\frac{1}{5}\\) = \\(\\frac{1}{20}\\)<\/p>\n<p>Question 2.<br \/>\n\\(\\frac{2}{7}\\) \u00d7 \\(\\frac{1}{2}\\) = _______<br \/>\nAnswer:<br \/>\n\\(\\frac{1}{2}\\) \u00d7 \\(\\frac{2}{7}\\) = \\(\\frac{1}{7}\\)<\/p>\n<p>Explanation:<br \/>\nThe given fractions are: \\(\\frac{1}{2}\\) and \\(\\frac{2}{7}\\)<br \/>\nWe know that,<br \/>\n\\(\\frac{a}{b}\\) \u00d7 \\(\\frac{p}{q}\\)<br \/>\n= \\(\\frac{a \u00d7 p}{b \u00d7 q}\\)<br \/>\na = \\(\\frac{a}{1}\\)<br \/>\nSo,<br \/>\n\\(\\frac{1}{2}\\) \u00d7 \\(\\frac{2}{7}\\)<br \/>\n= \\(\\frac{1 \u00d7 2}{2 \u00d7 7}\\)<br \/>\n= \\(\\frac{2}{14}\\)<br \/>\n= \\(\\frac{1}{7}\\)<br \/>\nHence,<br \/>\n\\(\\frac{1}{2}\\) \u00d7 \\(\\frac{2}{7}\\) = \\(\\frac{1}{7}\\)<\/p>\n<p>Question 3.<br \/>\n\\(\\frac{9}{10}\\) \u00d7 \\(\\frac{2}{3}\\) = _______<br \/>\nAnswer:<br \/>\n\\(\\frac{9}{10}\\) \u00d7 \\(\\frac{2}{3}\\) = \\(\\frac{3}{5}\\)<\/p>\n<p>Explanation:<br \/>\nThe given fractions are: \\(\\frac{9}{10}\\) and \\(\\frac{2}{3}\\)<br \/>\nWe know that,<br \/>\n\\(\\frac{a}{b}\\) \u00d7 \\(\\frac{p}{q}\\)<br \/>\n= \\(\\frac{a \u00d7 p}{b \u00d7 q}\\)<br \/>\na = \\(\\frac{a}{1}\\)<br \/>\nSo,<br \/>\n\\(\\frac{9}{10}\\) \u00d7 \\(\\frac{2}{3}\\)<br \/>\n= \\(\\frac{9 \u00d7 2}{10 \u00d7 3}\\)<br \/>\n= \\(\\frac{18}{30}\\)<br \/>\n= \\(\\frac{3}{5}\\)<br \/>\nHence,<br \/>\n\\(\\frac{9}{10}\\) \u00d7 \\(\\frac{2}{3}\\) = \\(\\frac{3}{5}\\)<\/p>\n<p>Question 4.<br \/>\n\\(\\frac{5}{8}\\) \u00d7 \\(\\frac{5}{6}\\) = _______<br \/>\nAnswer:<br \/>\n\\(\\frac{5}{8}\\) \u00d7 \\(\\frac{5}{6}\\) = \\(\\frac{25}{48}\\)<\/p>\n<p>Explanation:<br \/>\nThe given fractions are: \\(\\frac{5}{8}\\) and \\(\\frac{5}{6}\\)<br \/>\nWe know that,<br \/>\n\\(\\frac{a}{b}\\) \u00d7 \\(\\frac{p}{q}\\)<br \/>\n= \\(\\frac{a \u00d7 p}{b \u00d7 q}\\)<br \/>\na = \\(\\frac{a}{1}\\)<br \/>\nSo,<br \/>\n\\(\\frac{5}{8}\\) \u00d7 \\(\\frac{5}{6}\\)<br \/>\n= \\(\\frac{5 \u00d7 5}{8 \u00d7 6}\\)<br \/>\n= \\(\\frac{25}{48}\\)<br \/>\nHence,<br \/>\n\\(\\frac{5}{8}\\) \u00d7 \\(\\frac{5}{6}\\) = \\(\\frac{25}{48}\\)<\/p>\n<p>Question 5.<br \/>\n\\(\\frac{9}{7}\\) \u00d7 \\(\\frac{3}{4}\\) = _______<br \/>\nAnswer:<br \/>\n\\(\\frac{9}{7}\\) \u00d7 \\(\\frac{3}{4}\\) = \\(\\frac{27}{28}\\)<\/p>\n<p>Explanation:<br \/>\nThe given fractions are: \\(\\frac{9}{7}\\) and \\(\\frac{3}{4}\\)<br \/>\nWe know that,<br \/>\n\\(\\frac{a}{b}\\) \u00d7 \\(\\frac{p}{q}\\)<br \/>\n= \\(\\frac{a \u00d7 p}{b \u00d7 q}\\)<br \/>\na = \\(\\frac{a}{1}\\)<br \/>\nSo,<br \/>\n\\(\\frac{9}{7}\\) \u00d7 \\(\\frac{3}{4}\\)<br \/>\n= \\(\\frac{9 \u00d7 3}{7 \u00d7 4}\\)<br \/>\n= \\(\\frac{27}{28}\\)<br \/>\nHence,<br \/>\n\\(\\frac{9}{7}\\) \u00d7 \\(\\frac{3}{4}\\) = \\(\\frac{27}{28}\\)<\/p>\n<p>Question 6.<br \/>\n\\(\\frac{11}{100}\\) \u00d7 \\(\\frac{2}{5}\\) = _______<br \/>\nAnswer:<br \/>\n\\(\\frac{11}{100}\\) \u00d7 \\(\\frac{2}{5}\\) = \\(\\frac{11}{250}\\)<\/p>\n<p>Explanation:<br \/>\nThe given fractions are: \\(\\frac{11}{100}\\) and \\(\\frac{2}{5}\\)<br \/>\nWe know that,<br \/>\n\\(\\frac{a}{b}\\) \u00d7 \\(\\frac{p}{q}\\)<br \/>\n= \\(\\frac{a \u00d7 p}{b \u00d7 q}\\)<br \/>\na = \\(\\frac{a}{1}\\)<br \/>\nSo,<br \/>\n\\(\\frac{11}{100}\\) \u00d7 \\(\\frac{2}{5}\\)<br \/>\n= \\(\\frac{11 \u00d7 2}{100 \u00d7 5}\\)<br \/>\n= \\(\\frac{22}{500}\\)<br \/>\n= \\(\\frac{11}{250}\\)<br \/>\nHence,<br \/>\n\\(\\frac{11}{100}\\) \u00d7 \\(\\frac{2}{5}\\) = \\(\\frac{11}{250}\\)<\/p>\n<p>Question 7.<br \/>\n\\(\\frac{7}{20}\\) \u00d7 \\(\\frac{6}{2}\\) = _______<br \/>\nAnswer:<br \/>\n\\(\\frac{7}{20}\\) \u00d7 \\(\\frac{6}{2}\\) = \\(\\frac{21}{20}\\)<\/p>\n<p>Explanation:<br \/>\nThe given fractions are: \\(\\frac{7}{20}\\) and \\(\\frac{6}{2}\\)<br \/>\nWe know that,<br \/>\n\\(\\frac{a}{b}\\) \u00d7 \\(\\frac{p}{q}\\)<br \/>\n= \\(\\frac{a \u00d7 p}{b \u00d7 q}\\)<br \/>\na = \\(\\frac{a}{1}\\)<br \/>\nSo,<br \/>\n\\(\\frac{7}{20}\\) \u00d7 \\(\\frac{6}{2}\\)<br \/>\n= \\(\\frac{7 \u00d7 6}{20 \u00d7 2}\\)<br \/>\n= \\(\\frac{42}{40}\\)<br \/>\n= \\(\\frac{21}{20}\\)<br \/>\nHence,<br \/>\n\\(\\frac{7}{20}\\) \u00d7 \\(\\frac{6}{2}\\) = \\(\\frac{21}{20}\\)<\/p>\n<p>Question 8.<br \/>\n\\(\\frac{15}{16}\\) \u00d7 \\(\\frac{1}{3}\\) = _______<br \/>\nAnswer:<br \/>\n\\(\\frac{15}{16}\\) \u00d7 \\(\\frac{1}{3}\\) = \\(\\frac{5}{16}\\)<\/p>\n<p>Explanation:<br \/>\nThe given fractions are: \\(\\frac{15}{16}\\) and \\(\\frac{1}{3}\\)<br \/>\nWe know that,<br \/>\n\\(\\frac{a}{b}\\) \u00d7 \\(\\frac{p}{q}\\)<br \/>\n= \\(\\frac{a \u00d7 p}{b \u00d7 q}\\)<br \/>\na = \\(\\frac{a}{1}\\)<br \/>\nSo,<br \/>\n\\(\\frac{15}{16}\\) \u00d7 \\(\\frac{1}{3}\\)<br \/>\n= \\(\\frac{15 \u00d7 1}{16 \u00d7 3}\\)<br \/>\n= \\(\\frac{15}{48}\\)<br \/>\n= \\(\\frac{5}{16}\\)<br \/>\nHence,<br \/>\n\\(\\frac{15}{16}\\) \u00d7 \\(\\frac{1}{3}\\) = \\(\\frac{5}{16}\\)<\/p>\n<p>Question 9.<br \/>\n\\(\\frac{5}{12}\\) \u00d7 \\(\\frac{3}{10}\\) = _______<br \/>\nAnswer:<br \/>\n\\(\\frac{5}{12}\\) \u00d7 \\(\\frac{3}{10}\\) = \\(\\frac{1}{8}\\)<\/p>\n<p>Explanation:<br \/>\nThe given fractions are: \\(\\frac{5}{12}\\) and \\(\\frac{3}{10}\\)<br \/>\nWe know that,<br \/>\n\\(\\frac{a}{b}\\) \u00d7 \\(\\frac{p}{q}\\)<br \/>\n= \\(\\frac{a \u00d7 p}{b \u00d7 q}\\)<br \/>\na = \\(\\frac{a}{1}\\)<br \/>\nSo,<br \/>\n\\(\\frac{5}{12}\\) \u00d7 \\(\\frac{3}{10}\\)<br \/>\n= \\(\\frac{5 \u00d7 3}{12 \u00d7 10}\\)<br \/>\n= \\(\\frac{15}{120}\\)<br \/>\n= \\(\\frac{1}{8}\\)<br \/>\nHence,<br \/>\n\\(\\frac{5}{12}\\) \u00d7 \\(\\frac{3}{10}\\) = \\(\\frac{1}{8}\\)<\/p>\n<p><strong>Evaluate.<\/strong><br \/>\nQuestion 10.<br \/>\n3 \u00d7 \\(\\frac{3}{10}\\) = _______<br \/>\nAnswer:<br \/>\n3 \u00d7\u00a0 \\(\\frac{3}{10}\\) = \\(\\frac{9}{10}\\)<\/p>\n<p>Explanation:<br \/>\nThe given numbers are: 3 and \\(\\frac{3}{10}\\)<br \/>\nWe know that,<br \/>\n\\(\\frac{a}{b}\\) \u00d7 \\(\\frac{p}{q}\\)<br \/>\n= \\(\\frac{a \u00d7 p}{b \u00d7 q}\\)<br \/>\na = \\(\\frac{a}{1}\\)<br \/>\nSo,<br \/>\n3 \u00d7 \\(\\frac{3}{10}\\)<br \/>\n= \\(\\frac{3}{1}\\) \u00d7 \\(\\frac{3}{10}\\)<br \/>\n= \\(\\frac{3 \u00d7 3}{10 \u00d7 1}\\)<br \/>\n= \\(\\frac{9}{10}\\)<br \/>\nHence,<br \/>\n3 \u00d7 \\(\\frac{3}{10}\\) = \\(\\frac{9}{10}\\)<\/p>\n<p>Question 11.<br \/>\n\\(\\left(\\frac{1}{3}+\\frac{1}{3}\\right)\\) \u00d7 \\(\\frac{4}{5}\\) = _______<br \/>\nAnswer:<br \/>\n\\(\\left(\\frac{1}{3}+\\frac{1}{3}\\right)\\) \u00d7 \\(\\frac{4}{5}\\) = \\(\\frac{8}{15}\\)<\/p>\n<p>Explanation:<br \/>\nThe given fractions are: \\(\\frac{1}{3}\\), \\(\\frac{1}{3}\\) and \\(\\frac{4}{5}\\)<\/p>\n<p>We know that,<br \/>\n\\(\\frac{a}{b}\\) \u00d7 \\(\\frac{p}{q}\\)<br \/>\n= \\(\\frac{a \u00d7 p}{b \u00d7 q}\\)<br \/>\na = \\(\\frac{a}{1}\\)<br \/>\nSo,<br \/>\n( \\(\\frac{1}{3}\\) + \\(\\frac{1}{3}\\)\u00a0 ) \u00d7 \\(\\frac{4}{5}\\)<br \/>\n= ( \\(\\frac{1 + 1}{3}\\) ) \u00d7 \\(\\frac{4}{5}\\)<br \/>\n= \\(\\frac{2}{3}\\) \u00d7 \\(\\frac{4}{5}\\)<br \/>\n= \\(\\frac{4 \u00d7 2}{3 \u00d7 5}\\)<br \/>\n= \\(\\frac{8}{15}\\)<br \/>\nHence,<br \/>\n\\(\\left(\\frac{1}{3}+\\frac{1}{3}\\right)\\) \u00d7 \\(\\frac{4}{5}\\) = \\(\\frac{8}{15}\\)<\/p>\n<p>Question 12.<br \/>\n\\(\\frac{6}{7}\\) \u00d7 \\(\\left(\\frac{3}{4}-\\frac{5}{12}\\right)\\) = _______<br \/>\nAnswer:<br \/>\n\\(\\frac{6}{7}\\) \u00d7 \\(\\left(\\frac{3}{4}-\\frac{5}{12}\\right)\\) = \\(\\frac{2}{7}\\)<\/p>\n<p>Explanation:<br \/>\nThe given fractions are: \\(\\frac{6}{7}\\), \\(\\frac{3}{4}\\) and \\(\\frac{5}{12}\\)<\/p>\n<p>We know that,<br \/>\n\\(\\frac{a}{b}\\) \u00d7 \\(\\frac{p}{q}\\)<br \/>\n= \\(\\frac{a \u00d7 p}{b \u00d7 q}\\)<br \/>\na = \\(\\frac{a}{1}\\)<br \/>\nSo,<br \/>\n( \\(\\frac{3}{4}\\) &#8211; \\(\\frac{5}{12}\\)\u00a0 ) \u00d7 \\(\\frac{6}{7}\\)<br \/>\n= ( \\(\\frac{9}{12}\\) &#8211; \\(\\frac{5}{12}\\) \u00a0) \u00d7 \\(\\frac{6}{7}\\)<br \/>\n= \\(\\frac{4}{12}\\) \u00d7 \\(\\frac{6}{7}\\)<br \/>\n= \\(\\frac{4 \u00d7 6}{12 \u00d7 7}\\)<br \/>\n= \\(\\frac{2}{7}\\)<br \/>\nHence,<br \/>\n\\(\\frac{6}{7}\\) \u00d7 \\(\\left(\\frac{3}{4}-\\frac{5}{12}\\right)\\) = \\(\\frac{2}{7}\\)<\/p>\n<p>Question 13.<br \/>\nA pancake recipe calls for \\(\\frac{1}{3}\\) cup of water. You want to halve the recipe. What fraction of a cup of water do you need?<br \/>\nAnswer:<br \/>\nThe fraction of a cup of water you need is: \\(\\frac{1}{6}\\)<\/p>\n<p>Explanation:<br \/>\nIt is given that a pancake recipe calls for \\(\\frac{1}{3}\\) cup of water and you want to halve the recipe.<br \/>\nSo,<br \/>\nThe fraction of a cup of water you need for half of the recipe = ( The cup of water you need for a recipe ) \u00d7 \\(\\frac{1}{2}\\)<br \/>\n= \\(\\frac{1}{3}\\) \u00d7 \\(\\frac{1}{2}\\)<br \/>\n= \\(\\frac{1 \u00d7 1}{3 \u00d7 2}\\)<br \/>\n= \\(\\frac{1}{6}\\)<br \/>\nHence, from the above,<br \/>\nWe can conclude that the fraction of water you need for half of the recipe is: \\(\\frac{1}{6}\\)<\/p>\n<p>Question 14.<br \/>\n<strong>Number Sense<\/strong><br \/>\nWhich is greater, \\(\\frac{3}{4}\\) \u00d7 \\(\\frac{1}{5}\\) or \\(\\frac{3}{4}\\) \u00d7 \\(\\frac{1}{8}\\)? Explain.<br \/>\nAnswer:<br \/>\n\\(\\frac{3}{4}\\) \u00d7 \\(\\frac{1}{5}\\)&#8221; is greater than &#8220;\\(\\frac{3}{4}\\) \u00d7 \\(\\frac{1}{8}\\)<\/p>\n<p>Explanation:<br \/>\nThe given fractions are: \\(\\frac{3}{4}\\), \\(\\frac{1}{5}\\) and \\(\\frac{1}{8}\\)<br \/>\nNow,<br \/>\n\\(\\frac{3}{4}\\) \u00d7 \\(\\frac{1}{5}\\)<br \/>\n= \\(\\frac{3 \u00d7 1}{4 \u00d7 5}\\)<br \/>\n= \\(\\frac{3}{20}\\)<br \/>\nNow,<br \/>\n\\(\\frac{3}{4}\\) \u00d7 \\(\\frac{1}{8}\\)<br \/>\n= \\(\\frac{3 \u00d7 1}{4 \u00d7 8}\\)<br \/>\n= \\(\\frac{3}{32}\\)<br \/>\nSo,<br \/>\nFor the comparison of the products, equate the numerators.<br \/>\nMultiply \\(\\frac{3}{20}\\) by \\(\\frac{32}{32}\\)<br \/>\nMultiply \\(\\frac{3}{32}\\) by \\(\\frac{20}{20}\\)<br \/>\nSo,<br \/>\n\\(\\frac{3}{20}\\) = \\(\\frac{96}{640}\\)<br \/>\n\\(\\frac{3}{32}\\) = \\(\\frac{60}{640}\\)<br \/>\nSo,<br \/>\nBy comparison of the products,<br \/>\nWe can observe that<br \/>\n96 &gt; 60<br \/>\nHence, from the above,<br \/>\nWe can conclude that &#8220;\\(\\frac{3}{4}\\) \u00d7 \\(\\frac{1}{5}\\)&#8221; is greater than &#8220;\\(\\frac{3}{4}\\) \u00d7 \\(\\frac{1}{8}\\)&#8221;<\/p>\n<p>Question 15.<br \/>\n<strong>Reasoning<\/strong><br \/>\nIs \\(\\frac{17}{24}\\) \u00d7 \\(\\frac{7}{8}\\) equal to \\(\\frac{17}{8}\\) \u00d7 \\(\\frac{7}{24}\\)? Explain.<br \/>\nAnswer:<br \/>\n\\(\\frac{17}{24}\\) \u00d7 \\(\\frac{7}{8}\\) is equal to \\(\\frac{17}{8}\\) \u00d7 \\(\\frac{7}{24}\\)<\/p>\n<p>Explanation:<br \/>\nBy the commutative property of multiplication,<br \/>\na \u00d7 b = b \u00d7 a<br \/>\nSo,<br \/>\nBy the above property of multiplication,<br \/>\nWe can interchange the numbers<br \/>\nHence, from the above,<br \/>\nWe can conclude that \\(\\frac{17}{24}\\) \u00d7 \\(\\frac{7}{8}\\) is equal to \\(\\frac{17}{8}\\) \u00d7 \\(\\frac{7}{24}\\)<\/p>\n<p>Question 16.<br \/>\n<strong>Number Sense<\/strong><br \/>\nIn which equations does k = \\(\\frac{5}{6}\\)?<br \/>\n<img loading=\"lazy\" class=\"alignnone size-full wp-image-16398\" src=\"https:\/\/ccssmathanswers.com\/wp-content\/uploads\/2020\/12\/Big-Ideas-Math-Answer-Key-Grade-5-Chapter-9-Multiply-Fractions-9.5-8.png\" alt=\"Big Ideas Math Answer Key Grade 5 Chapter 9 Multiply Fractions 9.5 8\" width=\"262\" height=\"142\" \/><br \/>\nAnswer:<br \/>\nLet the multiplication equations be represented A), B), C) and D)<br \/>\nThe given expressions are:<br \/>\n<img loading=\"lazy\" class=\"alignnone size-full wp-image-16398\" src=\"https:\/\/ccssmathanswers.com\/wp-content\/uploads\/2020\/12\/Big-Ideas-Math-Answer-Key-Grade-5-Chapter-9-Multiply-Fractions-9.5-8.png\" alt=\"Big Ideas Math Answer Key Grade 5 Chapter 9 Multiply Fractions 9.5 8\" width=\"262\" height=\"142\" \/><br \/>\nSo,<br \/>\nThe product of the given expressions are:<br \/>\nA) \\(\\frac{1}{2}\\) \u00d7 \\(\\frac{5}{3}\\) = \\(\\frac{5}{6}\\)<br \/>\nB) \\(\\frac{1}{10}\\) \u00d7 k = \\(\\frac{1}{12}\\)<br \/>\nC) \\(\\frac{1}{3}\\) \u00d7 k = \\(\\frac{2}{9}\\)<br \/>\nD) \\(\\frac{5}{4}\\) \u00d7 \\(\\frac{2}{3}\\) = k<br \/>\nHence, from the above expressions,<br \/>\nWe can conclude that equation A) fits the value of k perfectly.<\/p>\n<p>Question 17.<br \/>\n<strong>Modeling Real Life<\/strong><br \/>\nAt a town hall meeting, \\(\\frac{37}{50}\\) of the members are present. Of those who are present, \\(\\frac{1}{2}\\) vote in favor of a new park. What fraction of the members do not vote in favor of the new park?<br \/>\nAnswer:<br \/>\nThe fraction of the members that do not vote in favor of the new park is: \\(\\frac{13}{50}\\)<\/p>\n<p>Explanation:<br \/>\nIt is given that at a town hall meeting, \\(\\frac{37}{50}\\) of the members are present. Of those who are present, \\(\\frac{1}{2}\\) vote in favor of a new park.<br \/>\nSo,<br \/>\nThe fraction of the members that do not vote in favor of the new park = ( The total number of members at the town hall meeting ) &#8211; ( The fraction of the members that vote in the favor of a new park )<br \/>\n= 1 &#8211; \\(\\frac{37}{50}\\)<br \/>\n= \\(\\frac{50}{50}\\) &#8211; \\(\\frac{37}{50}\\)<br \/>\n= \\(\\frac{50 &#8211; 37}{50}\\)<br \/>\n= \\(\\frac{13}{50}\\)<br \/>\nHence, from the above,<br \/>\nWe can conclude that the number of members that do not vote in the favor of a new park is: \\(\\frac{13}{50}\\)<\/p>\n<p>Question 18.<br \/>\n<strong>Modeling Real Life<\/strong><br \/>\nThere are 50 U.S. states. Seven twenty-fifths of the states share a land border with Canada or Mexico.Of those states, \\(\\frac{2}{7}\\) share a border with Mexico. How many states share a border with Canada?<br \/>\nAnswer:<br \/>\nThe number of states that share a border with Canada is: 4 states<\/p>\n<p>Explanation:<br \/>\nIt is given that there are 50 U.S. states. Seven twenty-fifths of the states share a land border with Canada or Mexico and of those states, \\(\\frac{2}{7}\\) share a border with Mexico.<br \/>\nSo,<br \/>\nThe number of states that share a border with Canada or Mexico = \\(\\frac{7}{25}\\) \u00d7 50<br \/>\n= \\(\\frac{7}{25}\\) \u00d7 \\(\\frac{50}{1}\\)<br \/>\n= 14 states<br \/>\nSo,<br \/>\nThe number of states that share a border with Canada = \\(\\frac{2}{7}\\) \u00d7 14<br \/>\n= \\(\\frac{2}{7}\\) \u00d7 \\(\\frac{14}{1}\\)<br \/>\n= 4 states<br \/>\nHence, from the above,<br \/>\nWe can conclude that there are 4 states that share a border with Canada<\/p>\n<p><strong>Review &amp; Refresh<\/strong><\/p>\n<p><strong>Evaluate. Check whether your answer is reasonable.<\/strong><br \/>\nQuestion 19.<br \/>\n15.67 + 4 + 6.5 = _____<br \/>\nAnswer:<br \/>\n15.67 + 4 + 6.5 = 26.17<\/p>\n<p>Explanation:<br \/>\nThe given numbers are: 15.67, 4, and 6.5<br \/>\nThe representation of the numbers in the fraction form is: \\(\\frac{1567}{100}\\), \\(\\frac{65}{10}\\) and 4<br \/>\nAs the highest number in the denominator is 100, make all the denominators hundred<br \/>\nSo,<br \/>\nThe representation of 4 with 100 in the denominator is: \\(\\frac{400}{100}\\)<br \/>\nThe representation of 6.5 with 100 in the denominator is: \\(\\frac{650}{100}\\)<br \/>\nSo,<br \/>\n\\(\\frac{1567}{100}\\) + \\(\\frac{400}{100}\\) + \\(\\frac{650}{100}\\)<br \/>\n= \\(\\frac{\u00a0 1567 + 400 + 650 }{100}\\)<br \/>\n= \\(\\frac{2,617}{100}\\)<br \/>\n= 26.17<br \/>\nHence, 15.67 + 4 + 6.5 = 26.17<\/p>\n<p>Question 20.<br \/>\n20.7 &#8211; 9.54 + 25.81 = _______<br \/>\nAnswer:<br \/>\n20.7 &#8211; 9.54 + 25.81 = 36.97<\/p>\n<p>Explanation:<br \/>\nThe given numbers are: 20.7, 9.54, and 25.81<br \/>\nThe representation of the numbers in the fraction form is: \\(\\frac{2581}{100}\\), \\(\\frac{207}{10}\\) and \\(\\frac{954}{100}\\)<br \/>\nAs the highest number in the denominator is 100, make all the denominators hundred<br \/>\nSo,<br \/>\nThe representation of 20.7 with 100 in the denominator is: \\(\\frac{2070}{100}\\)<br \/>\nSo,<br \/>\n\\(\\frac{2581}{100}\\) + \\(\\frac{2070}{100}\\) &#8211; \\(\\frac{954}{100}\\)<br \/>\n= \\(\\frac{\u00a0 2581 + 2070 &#8211; 954 }{100}\\)<br \/>\n= \\(\\frac{3,697}{100}\\)<br \/>\n= 36.97<br \/>\nHence, 20.7 &#8211; 9.54 + 25.81 = 36.97<\/p>\n<h3><a id=\"Lesson_9.6_Find_Areas_of_Rectangles\"><\/a>Lesson 9.6 Find Areas of Rectangles<\/h3>\n<p><strong>Explore and Grow<\/strong><\/p>\n<p>Draw and cut out a rectangle that has any two of the side lengths below.<br \/>\n\\(\\frac{1}{2}\\) ft<br \/>\n\\(\\frac{1}{3}\\) ft<br \/>\n\\(\\frac{1}{4}\\) ft<br \/>\nUse several copies of your rectangle to create a unit square. What is the area (in square feet) of each small rectangle? Explain your reasoning.<br \/>\nAnswer:<br \/>\nLet there are two small rectangles with the following lengths:<br \/>\n\\(\\frac{1}{2}\\) ft and \\(\\frac{1}{3}\\) ft<br \/>\n\\(\\frac{1}{2}\\) ft and \\(\\frac{1}{4}\\) ft<br \/>\nSo,<br \/>\nThe area of the unit square with lengths \\(\\frac{1}{2}\\) ft and \\(\\frac{1}{3}\\) ft is:<br \/>\n\\(\\frac{1}{2}\\) ft \u00d7 \\(\\frac{1}{3}\\) ft<br \/>\n= \\(\\frac{1 \u00d7 1}{2 \u00d7 3}\\) ft<br \/>\n= \\(\\frac{1}{6}\\) ft<br \/>\nThe area of the unit square with lengths \\(\\frac{1}{2}\\) ft and \\(\\frac{1}{4}\\) ft is:<br \/>\n\\(\\frac{1}{2}\\) ft \u00d7 \\(\\frac{1}{4}\\) ft<br \/>\n= \\(\\frac{1 \u00d7 1}{2 \u00d7 4}\\) ft<br \/>\n= \\(\\frac{1}{8}\\) ft<br \/>\nHence, from the above,<br \/>\nWe can conclude that the areas ofthe smaller rectngles with unit lengths is: \\(\\frac{1}{6}\\) ft and \\(\\frac{1}{8}\\) ft<\/p>\n<p><strong>Reasoning<\/strong><br \/>\nHow can you use a rectangle with unit fraction side lengths to find the area of the rectangle below? Explain your reasoning.<br \/>\n<img loading=\"lazy\" class=\"alignnone size-full wp-image-16399\" src=\"https:\/\/ccssmathanswers.com\/wp-content\/uploads\/2020\/12\/Big-Ideas-Math-Answers-5th-Grade-Chapter-9-Multiply-Fractions-9.6-1.png\" alt=\"Big Ideas Math Answers 5th Grade Chapter 9 Multiply Fractions 9.6 1\" width=\"206\" height=\"149\" \/><br \/>\nAnswer:<br \/>\nThe given rectangle is:<br \/>\n<img loading=\"lazy\" class=\"alignnone size-full wp-image-16399\" src=\"https:\/\/ccssmathanswers.com\/wp-content\/uploads\/2020\/12\/Big-Ideas-Math-Answers-5th-Grade-Chapter-9-Multiply-Fractions-9.6-1.png\" alt=\"Big Ideas Math Answers 5th Grade Chapter 9 Multiply Fractions 9.6 1\" width=\"206\" height=\"149\" \/><br \/>\nTo find the area of the rectangle by the unit fractions, multiply the values of the length and the breadth<br \/>\nSo,<br \/>\n\\(\\frac{3}{4}\\) \u00d7 \\(\\frac{3}{2}\\)<br \/>\n= 3\u00a0 (\\(\\frac{1}{4}\\) ) \u00d7 3 ( \\(\\frac{1}{2}\\) )<br \/>\n= 9 ( \\(\\frac{1}{4}\\) \u00d7 \\(\\frac{1}{2}\\) )<br \/>\n= 9 \u00d7 \\(\\frac{1 \u00d7 1}{4 \u00d7 2}\\)<br \/>\n= \\(\\frac{9}{1}\\) \u00d7 \\(\\frac{1}{8}\\)<br \/>\n= \\(\\frac{9}{8}\\)<br \/>\nThe unit fractions are the fractions that contain the value 1 in the numerator.<br \/>\nHere,<br \/>\n\\(\\frac{1}{4}\\) and \\(\\frac{1}{2}\\) are the unit fractions<\/p>\n<p><strong>Think and Grow: Find Areas of Rectangles<\/strong><\/p>\n<p>One way to \ufb01nd the area of a rectangle with fractional side lengths is to fill it with smaller rectangles.<br \/>\n<img loading=\"lazy\" class=\"alignnone size-full wp-image-16400\" src=\"https:\/\/ccssmathanswers.com\/wp-content\/uploads\/2020\/12\/Big-Ideas-Math-Answers-5th-Grade-Chapter-9-Multiply-Fractions-9.6-2.png\" alt=\"Big Ideas Math Answers 5th Grade Chapter 9 Multiply Fractions 9.6 2\" width=\"191\" height=\"137\" \/><br \/>\n<strong>Example<\/strong><br \/>\nFind the area of the rectangle.<br \/>\n<img loading=\"lazy\" class=\"alignnone size-full wp-image-39243\" src=\"https:\/\/ccssmathanswers.com\/wp-content\/uploads\/2020\/12\/Big-Ideas-Math-Answers-Grade-5-Chapter-9-15.jpg\" alt=\"\" width=\"708\" height=\"587\" srcset=\"https:\/\/bigideasmathanswers.com\/wp-content\/uploads\/2020\/12\/Big-Ideas-Math-Answers-Grade-5-Chapter-9-15.jpg 708w, https:\/\/bigideasmathanswers.com\/wp-content\/uploads\/2020\/12\/Big-Ideas-Math-Answers-Grade-5-Chapter-9-15-300x249.jpg 300w\" sizes=\"(max-width: 708px) 100vw, 708px\" \/><\/p>\n<p><strong>Show and Grow<\/strong><\/p>\n<p>Question 1.<br \/>\nFind the area of the shaded region.<br \/>\n<img loading=\"lazy\" class=\"alignnone size-full wp-image-16402\" src=\"https:\/\/ccssmathanswers.com\/wp-content\/uploads\/2020\/12\/Big-Ideas-Math-Answers-5th-Grade-Chapter-9-Multiply-Fractions-9.6-4.png\" alt=\"Big Ideas Math Answers 5th Grade Chapter 9 Multiply Fractions 9.6 4\" width=\"159\" height=\"160\" srcset=\"https:\/\/bigideasmathanswers.com\/wp-content\/uploads\/2020\/12\/Big-Ideas-Math-Answers-5th-Grade-Chapter-9-Multiply-Fractions-9.6-4.png 159w, https:\/\/bigideasmathanswers.com\/wp-content\/uploads\/2020\/12\/Big-Ideas-Math-Answers-5th-Grade-Chapter-9-Multiply-Fractions-9.6-4-150x150.png 150w\" sizes=\"(max-width: 159px) 100vw, 159px\" \/><br \/>\nAnswer:<br \/>\nThe area of the shaded region is: \\(\\frac{3}{12}\\)<\/p>\n<p>Explanation:<br \/>\nThe given figure is:<br \/>\n<img loading=\"lazy\" class=\"alignnone size-full wp-image-16402\" src=\"https:\/\/ccssmathanswers.com\/wp-content\/uploads\/2020\/12\/Big-Ideas-Math-Answers-5th-Grade-Chapter-9-Multiply-Fractions-9.6-4.png\" alt=\"Big Ideas Math Answers 5th Grade Chapter 9 Multiply Fractions 9.6 4\" width=\"159\" height=\"160\" srcset=\"https:\/\/bigideasmathanswers.com\/wp-content\/uploads\/2020\/12\/Big-Ideas-Math-Answers-5th-Grade-Chapter-9-Multiply-Fractions-9.6-4.png 159w, https:\/\/bigideasmathanswers.com\/wp-content\/uploads\/2020\/12\/Big-Ideas-Math-Answers-5th-Grade-Chapter-9-Multiply-Fractions-9.6-4-150x150.png 150w\" sizes=\"(max-width: 159px) 100vw, 159px\" \/><br \/>\nFrom the given figure,<br \/>\nThe area of the shaded region = \\(\\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 area of the shaded region is: \\(\\frac{3}{12}\\)<\/p>\n<p><strong>Apply and Grow: Practice<\/strong><\/p>\n<p><strong>Find the area of the shaded region.<\/strong><br \/>\nQuestion 2.<br \/>\n<img loading=\"lazy\" class=\"alignnone size-full wp-image-16403\" src=\"https:\/\/ccssmathanswers.com\/wp-content\/uploads\/2020\/12\/Big-Ideas-Math-Answers-5th-Grade-Chapter-9-Multiply-Fractions-9.6-5.png\" alt=\"Big Ideas Math Answers 5th Grade Chapter 9 Multiply Fractions 9.6 5\" width=\"187\" height=\"172\" \/><br \/>\nAnswer:<br \/>\nThe area of the shaded region is: \\(\\frac{2}{12}\\)<\/p>\n<p>Explanation:<br \/>\nThe given figure is:<br \/>\n<img loading=\"lazy\" class=\"alignnone size-full wp-image-16403\" src=\"https:\/\/ccssmathanswers.com\/wp-content\/uploads\/2020\/12\/Big-Ideas-Math-Answers-5th-Grade-Chapter-9-Multiply-Fractions-9.6-5.png\" alt=\"Big Ideas Math Answers 5th Grade Chapter 9 Multiply Fractions 9.6 5\" width=\"187\" height=\"172\" \/><br \/>\nFrom the given figure,<br \/>\nThe area of the shaded region = \\(\\frac{2}{4}\\) \u00d7 \\(\\frac{1}{3}\\)<br \/>\n= \\(\\frac{2 \u00d7 1}{4 \u00d7 3}\\)<br \/>\n= \\(\\frac{2}{12}\\)<br \/>\nHence, from the above,<br \/>\nWe can conclude that the area of the shaded region is: \\(\\frac{2}{12}\\)<\/p>\n<p>Question 3.<br \/>\n<img loading=\"lazy\" class=\"alignnone size-full wp-image-16404\" src=\"https:\/\/ccssmathanswers.com\/wp-content\/uploads\/2020\/12\/Big-Ideas-Math-Answers-5th-Grade-Chapter-9-Multiply-Fractions-9.6-6.png\" alt=\"Big Ideas Math Answers 5th Grade Chapter 9 Multiply Fractions 9.6 6\" width=\"180\" height=\"178\" \/><br \/>\nAnswer:<br \/>\nThe area of the shaded region is: \\(\\frac{3}{16}\\)<\/p>\n<p>Explanation:<br \/>\nThe given figure is:<br \/>\n<img loading=\"lazy\" class=\"alignnone size-full wp-image-16404\" src=\"https:\/\/ccssmathanswers.com\/wp-content\/uploads\/2020\/12\/Big-Ideas-Math-Answers-5th-Grade-Chapter-9-Multiply-Fractions-9.6-6.png\" alt=\"Big Ideas Math Answers 5th Grade Chapter 9 Multiply Fractions 9.6 6\" width=\"180\" height=\"178\" \/><br \/>\nFrom the given figure,<br \/>\nThe area of the shaded region = \\(\\frac{3}{4}\\) \u00d7 \\(\\frac{1}{4}\\)<br \/>\n= \\(\\frac{3 \u00d7 1}{4 \u00d7 4}\\)<br \/>\n= \\(\\frac{3}{16}\\)<br \/>\nHence, from the above,<br \/>\nWe can conclude that the area of the shaded region is: \\(\\frac{3}{16}\\)<\/p>\n<p><strong>Use rectangles with unit fraction side lengths to \ufb01nd the area of the rectangle.<\/strong><br \/>\nQuestion 4.<br \/>\n<img loading=\"lazy\" class=\"alignnone size-full wp-image-16405\" src=\"https:\/\/ccssmathanswers.com\/wp-content\/uploads\/2020\/12\/Big-Ideas-Math-Answers-5th-Grade-Chapter-9-Multiply-Fractions-9.6-7.png\" alt=\"Big Ideas Math Answers 5th Grade Chapter 9 Multiply Fractions 9.6 7\" width=\"187\" height=\"94\" \/><br \/>\nAnswer:<br \/>\nThe area of the rectangle is: \\(\\frac{6}{10}\\)<\/p>\n<p>Explanation:<br \/>\nThe given figure is:<br \/>\n<img loading=\"lazy\" class=\"alignnone size-full wp-image-16405\" src=\"https:\/\/ccssmathanswers.com\/wp-content\/uploads\/2020\/12\/Big-Ideas-Math-Answers-5th-Grade-Chapter-9-Multiply-Fractions-9.6-7.png\" alt=\"Big Ideas Math Answers 5th Grade Chapter 9 Multiply Fractions 9.6 7\" width=\"187\" height=\"94\" \/><br \/>\nFrom the given figure,<br \/>\nThe area of the rectangle = \\(\\frac{3}{2}\\) \u00d7 \\(\\frac{2}{5}\\)<br \/>\n= \\(\\frac{3 \u00d7 2}{2 \u00d7 5}\\)<br \/>\n= \\(\\frac{6}{10}\\)<br \/>\nHence, from the above,<br \/>\nWe can conclude that the area of the shaded region is: \\(\\frac{6}{10}\\)<\/p>\n<p>Question 5.<br \/>\n<img loading=\"lazy\" class=\"alignnone size-full wp-image-16406\" src=\"https:\/\/ccssmathanswers.com\/wp-content\/uploads\/2020\/12\/Big-Ideas-Math-Answers-5th-Grade-Chapter-9-Multiply-Fractions-9.6-8.png\" alt=\"Big Ideas Math Answers 5th Grade Chapter 9 Multiply Fractions 9.6 8\" width=\"122\" height=\"150\" \/><br \/>\nAnswer:<br \/>\nThe area of the rectangle is: \\(\\frac{10}{18}\\)<\/p>\n<p>Explanation:<br \/>\nThe given figure is:<br \/>\n<img loading=\"lazy\" class=\"alignnone size-full wp-image-16406\" src=\"https:\/\/ccssmathanswers.com\/wp-content\/uploads\/2020\/12\/Big-Ideas-Math-Answers-5th-Grade-Chapter-9-Multiply-Fractions-9.6-8.png\" alt=\"Big Ideas Math Answers 5th Grade Chapter 9 Multiply Fractions 9.6 8\" width=\"122\" height=\"150\" \/><br \/>\nFrom the given figure,<br \/>\nThe area of the rectangle = \\(\\frac{5}{6}\\) \u00d7 \\(\\frac{2}{3}\\)<br \/>\n= \\(\\frac{5 \u00d7 2}{6 \u00d7 3}\\)<br \/>\n= \\(\\frac{10}{18}\\)<br \/>\nHence, from the above,<br \/>\nWe can conclude that the area of the shaded region is: \\(\\frac{10}{18}\\)<\/p>\n<p>Question 6.<br \/>\nFind the area of a rectangle with side lengths of \\(\\frac{5}{8}\\) and \\(\\frac{4}{3}\\)?<br \/>\nAnswer:<br \/>\nThe area of a rectangle is: \\(\\frac{20}{24}\\)<\/p>\n<p>Explanation:<br \/>\nThe given side lengths of a rectangle are: \\(\\frac{5}{8}\\) and \\(\\frac{4}{3}\\)<br \/>\nSo,<br \/>\nThe area of the rectangle = \\(\\frac{5}{8}\\) \u00d7 \\(\\frac{4}{3}\\)<br \/>\n= \\(\\frac{5 \u00d7 4}{8 \u00d7 3}\\)<br \/>\n= \\(\\frac{20}{24}\\)<br \/>\nHence, from the above,<br \/>\nWe can conclude that the area of the rectangle is: \\(\\frac{20}{24}\\)<\/p>\n<p>Question 7.<br \/>\nFind the area of a rectangle with side lengths of \\(\\frac{7}{9}\\) and \\(\\frac{1}{2}\\)?<br \/>\nAnswer:<br \/>\nThe area of a rectangle is: \\(\\frac{7}{18}\\)<\/p>\n<p>Explanation:<br \/>\nThe given side lengths of a rectangle are: \\(\\frac{7}{9}\\) and \\(\\frac{1}{2}\\)<br \/>\nSo,<br \/>\nThe area of the rectangle = \\(\\frac{7}{9}\\) \u00d7 \\(\\frac{1}{2}\\)<br \/>\n= \\(\\frac{7 \u00d7 1}{9 \u00d7 2}\\)<br \/>\n= \\(\\frac{7}{18}\\)<br \/>\nHence, from the above,<br \/>\nWe can conclude that the area of the rectangle is: \\(\\frac{7}{18}\\)<\/p>\n<p>Question 8.<br \/>\n<strong>Reasoning<\/strong><br \/>\nCan you find the area of a rectangle with fractional side lengths the same way you find the area of a rectangle with whole-number side lengths? Explain.<br \/>\nAnswer:<br \/>\nYes, we can find the area of a rectangle with fractional side lengths the same way you find the area of a rectangle with whole-number side lengths.<br \/>\nExample:<br \/>\nLet the fractional side lengths be: \\(\\frac{1}{5}\\) and \\(\\frac{1}{9}\\)<br \/>\nLet the whole number side lengths be: 3 and 4<br \/>\nSo,<br \/>\nThe area of the rectangle with the fractional side lengths = \\(\\frac{1}{5}\\) \u00d7 \\(\\frac{1}{9}\\)<br \/>\n= \\(\\frac{1 \u00d7 1}{9 \u00d7 5}\\)<br \/>\n= \\(\\frac{1}{45}\\)<br \/>\nThe area of the rectangle with the whole number side lengths = 3 \u00d7 4<br \/>\n= \\(\\frac{3}{1}\\) \u00d7 \\(\\frac{4}{1}\\)<br \/>\n= \\(\\frac{3 \u00d7 4}{1 \u00d7 1}\\)<br \/>\n= \\(\\frac{12}{1}\\)<br \/>\n= 12<br \/>\nHence, from the above,<br \/>\nWe can conclude that we can find the area of a rectangle with fractional side lengths the same way you find the area of a rectangle with whole-number side lengths.<\/p>\n<p>Question 9.<br \/>\n<strong>YOU BE THE TEACHER<\/strong><br \/>\nOur friend says she can find the area of a square given only one fractional side length. Is your friend correct? Explain.<br \/>\nAnswer:<br \/>\nYes, she can find the area of a square by only one fractional side length<\/p>\n<p>Explanation:<br \/>\nLet the unit fractional side length of the square be: \\(\\frac{1}{2}\\)<br \/>\nWe know that,<br \/>\nThe length of all the sides in a square are equal.<br \/>\nSo,<br \/>\nBy using this property, we can find the area of the square by taking the fractional unit side length of 1 side as the same for all the sides<br \/>\nSo,<br \/>\nThe area of the square = \\(\\frac{1}{2}\\) \u00d7 \\(\\frac{1}{2}\\)<br \/>\n= \\(\\frac{1 \u00d7 1}{2 \u00d7 2}\\)<br \/>\n= \\(\\frac{1}{4}\\)<br \/>\nHence, from the above,<br \/>\nWe can conclude that she can find the area of a square by only one fractional side length<\/p>\n<p><strong>Think and Grow: Modeling Real Life<\/strong><\/p>\n<p><strong>Example<\/strong><br \/>\nA zoo needs an outdoor enclosure with an area of at least \\(\\frac{3}{10}\\) square kilometer10for a camel. Is the rectangular enclosure shown large enough for a camel?<br \/>\n<img loading=\"lazy\" class=\"alignnone size-full wp-image-16407\" src=\"https:\/\/ccssmathanswers.com\/wp-content\/uploads\/2020\/12\/Big-Ideas-Math-Answers-5th-Grade-Chapter-9-Multiply-Fractions-9.6-9.png\" alt=\"Big Ideas Math Answers 5th Grade Chapter 9 Multiply Fractions 9.6 9\" width=\"270\" height=\"135\" \/><br \/>\nFind the area of the enclosure by multiplying the length and the width.<br \/>\n<img loading=\"lazy\" class=\"alignnone size-full wp-image-39253\" src=\"https:\/\/ccssmathanswers.com\/wp-content\/uploads\/2020\/12\/Big-Ideas-Math-Answers-Grade-5-Chapter-9-16.jpg\" alt=\"\" width=\"559\" height=\"287\" srcset=\"https:\/\/bigideasmathanswers.com\/wp-content\/uploads\/2020\/12\/Big-Ideas-Math-Answers-Grade-5-Chapter-9-16.jpg 559w, https:\/\/bigideasmathanswers.com\/wp-content\/uploads\/2020\/12\/Big-Ideas-Math-Answers-Grade-5-Chapter-9-16-300x154.jpg 300w\" sizes=\"(max-width: 559px) 100vw, 559px\" \/><br \/>\nSo, the enclosure is large enough for a camel.<\/p>\n<p><strong>Show and Grow<\/strong><\/p>\n<p>Question 10.<br \/>\nThe area of a square dog kennel is 4 square yards. Will the square mat fit in the kennel?<br \/>\n<img loading=\"lazy\" class=\"alignnone size-full wp-image-16409\" src=\"https:\/\/ccssmathanswers.com\/wp-content\/uploads\/2020\/12\/Big-Ideas-Math-Answers-5th-Grade-Chapter-9-Multiply-Fractions-9.6-11.png\" alt=\"Big Ideas Math Answers 5th Grade Chapter 9 Multiply Fractions 9.6 11\" width=\"146\" height=\"115\" \/><br \/>\nAnswer:<br \/>\nYes, the square mat will fit in the kennel<\/p>\n<p>Explanation:<br \/>\nIt is given that the area of a square dog kennel is 4 square yards and the side of the square mat is \\(\\frac{5}{3}\\) yd<br \/>\nWe know that,<br \/>\nThe length of all the sides in a square are equal.<br \/>\nSo,<br \/>\nBy using this property,<br \/>\nThe area of the square mat = \\(\\frac{5}{3}\\) \u00d7 \\(\\frac{5}{3}\\)<br \/>\n= \\(\\frac{5 \u00d7 5}{3 \u00d7 3}\\)<br \/>\n= \\(\\frac{25}{9}\\) yd<br \/>\nNow,<br \/>\nThe area of a square dog kennel can be written as: \\(\\frac{36}{9}\\) yd<br \/>\nSo,<br \/>\nWhen we compare the 2 areas,<br \/>\nWe can get 25 &lt; 36<br \/>\nHence, from the above,<br \/>\nWe can conclude that the square mat will fit in the kennel<\/p>\n<p>Question 11.<br \/>\n<strong>DIG DEEPER!<\/strong><br \/>\nThe side lengths of each chalk art square are \\(\\frac{11}{4}\\) meters. The side lengths of the square zone around each chalk square are an additional \\(\\frac{3}{4}\\) meter. How many square meters of concrete is used to create the chalk walk shown?<br \/>\n<img loading=\"lazy\" class=\"alignnone size-full wp-image-16410\" src=\"https:\/\/ccssmathanswers.com\/wp-content\/uploads\/2020\/12\/Big-Ideas-Math-Answers-5th-Grade-Chapter-9-Multiply-Fractions-9.6-12.png\" alt=\"Big Ideas Math Answers 5th Grade Chapter 9 Multiply Fractions 9.6 12\" width=\"292\" height=\"158\" \/><br \/>\nAnswer:<br \/>\nThe amount of the concrete used to create the chalk walk is: \\(\\frac{196}{16}\\) square meters<\/p>\n<p>Explanation:<br \/>\nIt is given that the side lengths of each chalk art square are \\(\\frac{11}{4}\\) meters. The side lengths of the square zone around each chalk square are an additional \\(\\frac{3}{4}\\) meter.<br \/>\nSo,<br \/>\nThe total side length of the chalk walk = \\(\\frac{11}{4}\\) + \\(\\frac{3}{4}\\)<br \/>\n= \\(\\frac{11 + 3}{4}\\)<br \/>\n= \\(\\frac{14}{4}\\) meters<br \/>\nWe know that,<br \/>\nThe length of all sides in the square are equal.<br \/>\nSo,<br \/>\nBy using this property,<br \/>\nThe amount of concrete used for the chalk walk = \\(\\frac{14}{4}\\) \u00d7 \\(\\frac{14}{4}\\)<br \/>\n= \\(\\frac{14 \u00d7 14}{4 \u00d7 4}\\)<br \/>\n= \\(\\frac{196}{16}\\) square meters<br \/>\nHence, from the above,<br \/>\nWe can conclude that the amount of the concrete used to create the chalk walk is: \\(\\frac{196}{16}\\) square meters<\/p>\n<h3><a id=\"Find_Areas_of_Rectangles_Homework_&amp;_Practice_9.6\"><\/a>Find Areas of Rectangles Homework &amp; Practice 9.6<\/h3>\n<p><strong>Find the area of the shaded region.<\/strong><br \/>\nQuestion 1.<br \/>\n<img loading=\"lazy\" class=\"alignnone size-full wp-image-16411\" src=\"https:\/\/ccssmathanswers.com\/wp-content\/uploads\/2020\/12\/Big-Ideas-Math-Answers-5th-Grade-Chapter-9-Multiply-Fractions-9.6-13.png\" alt=\"Big Ideas Math Answers 5th Grade Chapter 9 Multiply Fractions 9.6 13\" width=\"157\" height=\"169\" \/><br \/>\nAnswer:<br \/>\nThe area of the shaded region is: \\(\\frac{1}{12}\\)<\/p>\n<p>Explanation:<br \/>\nThe given figure is:<br \/>\n<img loading=\"lazy\" class=\"alignnone size-full wp-image-16411\" src=\"https:\/\/ccssmathanswers.com\/wp-content\/uploads\/2020\/12\/Big-Ideas-Math-Answers-5th-Grade-Chapter-9-Multiply-Fractions-9.6-13.png\" alt=\"Big Ideas Math Answers 5th Grade Chapter 9 Multiply Fractions 9.6 13\" width=\"157\" height=\"169\" \/><br \/>\nFrom the given figure,<br \/>\nThe area of the shaded region = \\(\\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 the area of the shaded region is: \\(\\frac{1}{12}\\)<\/p>\n<p>Question 2.<br \/>\n<img loading=\"lazy\" class=\"alignnone size-full wp-image-16412\" src=\"https:\/\/ccssmathanswers.com\/wp-content\/uploads\/2020\/12\/Big-Ideas-Math-Answers-5th-Grade-Chapter-9-Multiply-Fractions-9.6-14.png\" alt=\"Big Ideas Math Answers 5th Grade Chapter 9 Multiply Fractions 9.6 14\" width=\"162\" height=\"158\" \/><br \/>\nAnswer:<br \/>\nThe area of the shaded region is: \\(\\frac{8}{25}\\)<\/p>\n<p>Explanation:<br \/>\nThe given figure is:<br \/>\n<img loading=\"lazy\" class=\"alignnone size-full wp-image-16412\" src=\"https:\/\/ccssmathanswers.com\/wp-content\/uploads\/2020\/12\/Big-Ideas-Math-Answers-5th-Grade-Chapter-9-Multiply-Fractions-9.6-14.png\" alt=\"Big Ideas Math Answers 5th Grade Chapter 9 Multiply Fractions 9.6 14\" width=\"162\" height=\"158\" \/><br \/>\nFrom the given figure,<br \/>\nThe area of the shaded region = \\(\\frac{2}{5}\\) \u00d7 \\(\\frac{4}{5}\\)<br \/>\n= \\(\\frac{2 \u00d7 4}{5 \u00d7 5}\\)<br \/>\n= \\(\\frac{8}{25}\\)<br \/>\nHence, from the above,<br \/>\nWe can conclude that the area of the shaded region is: \\(\\frac{8}{25}\\)<\/p>\n<p><strong>Use rectangles with unit fraction side lengths to find the area of the rectangle.<\/strong><br \/>\nQuestion 3.<br \/>\n<img loading=\"lazy\" class=\"alignnone size-full wp-image-16413\" src=\"https:\/\/ccssmathanswers.com\/wp-content\/uploads\/2020\/12\/Big-Ideas-Math-Answers-5th-Grade-Chapter-9-Multiply-Fractions-9.6-15.png\" alt=\"Big Ideas Math Answers 5th Grade Chapter 9 Multiply Fractions 9.6 15\" width=\"55\" height=\"132\" \/><br \/>\nAnswer:<br \/>\nThe area of the rectangle is: \\(\\frac{2}{24}\\)<\/p>\n<p>Explanation:<br \/>\nThe given figure is:<br \/>\n<img loading=\"lazy\" class=\"alignnone size-full wp-image-16413\" src=\"https:\/\/ccssmathanswers.com\/wp-content\/uploads\/2020\/12\/Big-Ideas-Math-Answers-5th-Grade-Chapter-9-Multiply-Fractions-9.6-15.png\" alt=\"Big Ideas Math Answers 5th Grade Chapter 9 Multiply Fractions 9.6 15\" width=\"55\" height=\"132\" \/><br \/>\nFrom the given figure,<br \/>\nThe area of the rectangle = \\(\\frac{2}{3}\\) \u00d7 \\(\\frac{1}{8}\\)<br \/>\n= \\(\\frac{1 \u00d7 2}{3 \u00d7 8}\\)<br \/>\n= \\(\\frac{2}{24}\\)<br \/>\nHence, from the above,<br \/>\nWe can conclude that the area of the shaded region is: \\(\\frac{2}{24}\\)<\/p>\n<p>Question 4.<br \/>\n<img loading=\"lazy\" class=\"alignnone size-full wp-image-16414\" src=\"https:\/\/ccssmathanswers.com\/wp-content\/uploads\/2020\/12\/Big-Ideas-Math-Answers-5th-Grade-Chapter-9-Multiply-Fractions-9.6-16.png\" alt=\"Big Ideas Math Answers 5th Grade Chapter 9 Multiply Fractions 9.6 16\" width=\"121\" height=\"146\" \/><br \/>\nAnswer:<br \/>\nThe area of the rectangle is: \\(\\frac{35}{90}\\)<\/p>\n<p>Explanation:<br \/>\nThe given figure is:<br \/>\n<img loading=\"lazy\" class=\"alignnone size-full wp-image-16414\" src=\"https:\/\/ccssmathanswers.com\/wp-content\/uploads\/2020\/12\/Big-Ideas-Math-Answers-5th-Grade-Chapter-9-Multiply-Fractions-9.6-16.png\" alt=\"Big Ideas Math Answers 5th Grade Chapter 9 Multiply Fractions 9.6 16\" width=\"121\" height=\"146\" \/><br \/>\nFrom the given figure,<br \/>\nThe area of the rectangle = \\(\\frac{7}{10}\\) \u00d7 \\(\\frac{5}{9}\\)<br \/>\n= \\(\\frac{7 \u00d7 5}{10 \u00d7 9}\\)<br \/>\n= \\(\\frac{35}{90}\\)<br \/>\nHence, from the above,<br \/>\nWe can conclude that the area of the shaded region is: \\(\\frac{35}{90}\\)<\/p>\n<p>Question 5.<br \/>\nFind the area of a rectangle with a side length of \\(\\frac{3}{4}\\) and \\(\\frac{5}{12}\\).<br \/>\nAnswer:<br \/>\nThe area of a rectangle is: \\(\\frac{15}{48}\\)<\/p>\n<p>Explanation:<br \/>\nThe given side lengths of a rectangle are: \\(\\frac{5}{12}\\) and \\(\\frac{3}{4}\\)<br \/>\nSo,<br \/>\nThe area of the rectangle = \\(\\frac{5}{12}\\) \u00d7 \\(\\frac{3}{4}\\)<br \/>\n= \\(\\frac{5 \u00d7 3}{12 \u00d7 4}\\)<br \/>\n= \\(\\frac{15}{48}\\)<br \/>\nHence, from the above,<br \/>\nWe can conclude that the area of the rectangle is: \\(\\frac{15}{48}\\)<\/p>\n<p>Question 6.<br \/>\nFind the area of a square with side lengths of \\(\\frac{9}{16}\\)<br \/>\nAnswer:<br \/>\nThe area of a square is: \\(\\frac{81}{256}\\)<\/p>\n<p>Explanation:<br \/>\nWe know that,<br \/>\nThe length of all the sides of the square is equal.<br \/>\nSo,<br \/>\nThe given side lengths of a square are: \\(\\frac{9}{16}\\) and \\(\\frac{9}{16}\\)<br \/>\nSo,<br \/>\nThe area of the square = \\(\\frac{9}{16}\\) \u00d7 \\(\\frac{9}{16}\\)<br \/>\n= \\(\\frac{9 \u00d7 9}{16 \u00d7 16}\\)<br \/>\n= \\(\\frac{81}{256}\\)<br \/>\nHence, from the above,<br \/>\nWe can conclude that the area of the rectangle is: \\(\\frac{81}{256}\\)<\/p>\n<p>Question 7.<br \/>\n<strong>Open-Ended<\/strong><br \/>\nThe area of a rectangle is \\(\\frac{16}{24}\\). What are the possible side lengths of the rectangle?<br \/>\nAnswer:<br \/>\nThe possible side lengths for the given area of a rectangle are:<br \/>\nA) \\(\\frac{4}{2}\\) and \\(\\frac{4}{12}\\)<br \/>\nB) \\(\\frac{1}{3}\\) and \\(\\frac{4}{8}\\)<\/p>\n<p>Explanation:<br \/>\nThe given area of a rectangle is: \\(\\frac{16}{24}\\)<br \/>\nSo,<br \/>\nTo find the possible side lengths of a rectangle, find the factors for the numerator and denominator of \\(\\frac{16}{24}\\)<br \/>\nSo,<br \/>\nThe factors of 16 are: 1, 2, 4, 8, 16<br \/>\nThe factors of 24 are: 1, 2, 3, 4, 6, 8, 12, 24<br \/>\nSo,<br \/>\nThe possible side lengths of a rectangle are:<br \/>\nA) \\(\\frac{4}{2}\\) and \\(\\frac{4}{12}\\)<br \/>\nB) \\(\\frac{1}{3}\\) and \\(\\frac{4}{8}\\)<br \/>\nThere are so many possible side lengths of a rectangle like above<br \/>\nHence, from the above,<br \/>\nWe can conclude that the possible side lengths of a rectangle are:<br \/>\nA) \\(\\frac{4}{2}\\) and \\(\\frac{4}{12}\\)<br \/>\nB) \\(\\frac{1}{3}\\) and \\(\\frac{4}{8}\\)<\/p>\n<p>Question 8.<br \/>\n<strong>Structure<\/strong><br \/>\nWrite an expression that represents the area of the shaded rectangle.<br \/>\n<img loading=\"lazy\" class=\"alignnone size-full wp-image-16415\" src=\"https:\/\/ccssmathanswers.com\/wp-content\/uploads\/2020\/12\/Big-Ideas-Math-Answers-5th-Grade-Chapter-9-Multiply-Fractions-9.6-17.png\" alt=\"Big Ideas Math Answers 5th Grade Chapter 9 Multiply Fractions 9.6 17\" width=\"135\" height=\"125\" \/><br \/>\nAnswer:<br \/>\nThe expression that represents the area of the shaded region is: \\(\\frac{1}{3}\\) \u00d7 \\(\\frac{1}{3}\\)<\/p>\n<p>Explanation:<br \/>\nThe given shaded rectangle is:<br \/>\n<img loading=\"lazy\" class=\"alignnone size-full wp-image-16415\" src=\"https:\/\/ccssmathanswers.com\/wp-content\/uploads\/2020\/12\/Big-Ideas-Math-Answers-5th-Grade-Chapter-9-Multiply-Fractions-9.6-17.png\" alt=\"Big Ideas Math Answers 5th Grade Chapter 9 Multiply Fractions 9.6 17\" width=\"135\" height=\"125\" \/><br \/>\nFrom the given shaded rectangle,<br \/>\nThe number of shaded columns is: 3<br \/>\nThe number of shaded rows is: 3<br \/>\nThe total number of rows is: 1<br \/>\nThe total number of columns are: 1<br \/>\nSo,<br \/>\nThe expression representing the shaded region = \\(\\frac{The total number of rows}{The number of shaded rows}\\) \u00d7 \\(\\frac{The total number of rows}{The number of shaded rows}\\)<br \/>\n= \\(\\frac{1}{3}\\) \u00d7 \\(\\frac{1}{3}\\)<br \/>\nHence, from the above,<br \/>\nWe can conclude that the expression representing the shaded region of a rectangle is: \\(\\frac{1}{3}\\) \u00d7 \\(\\frac{1}{3}\\)<\/p>\n<p>Question 9.<br \/>\n<strong>Modeling Real Life<\/strong><br \/>\nThe area of a square table is 9 square feet. Will the board game fit on the table?<br \/>\n<img loading=\"lazy\" class=\"alignnone size-full wp-image-16416\" src=\"https:\/\/ccssmathanswers.com\/wp-content\/uploads\/2020\/12\/Big-Ideas-Math-Answers-5th-Grade-Chapter-9-Multiply-Fractions-9.6-18.png\" alt=\"Big Ideas Math Answers 5th Grade Chapter 9 Multiply Fractions 9.6 18\" width=\"180\" height=\"126\" \/><br \/>\nAnswer:<br \/>\nYes, the board game fit on the table<\/p>\n<p>Explanation:<br \/>\nThe given area of a square table is 9 square feet<br \/>\nSo,<br \/>\nThe representation of the area of the square table in the fraction form is: \\(\\frac{36}{4}\\)<br \/>\nNow,<br \/>\nThe given board game is:<br \/>\n<img loading=\"lazy\" class=\"alignnone size-full wp-image-16416\" src=\"https:\/\/ccssmathanswers.com\/wp-content\/uploads\/2020\/12\/Big-Ideas-Math-Answers-5th-Grade-Chapter-9-Multiply-Fractions-9.6-18.png\" alt=\"Big Ideas Math Answers 5th Grade Chapter 9 Multiply Fractions 9.6 18\" width=\"180\" height=\"126\" \/><br \/>\nThe area of the board game can find out by multiplying its side lengths<br \/>\nSo,<br \/>\nThe area of the board game = \\(\\frac{3}{2}\\) \u00d7 \\(\\frac{5}{2}\\)<br \/>\n= \\(\\frac{3 \u00d7 5}{2 \u00d7 2}\\)<br \/>\n= \\(\\frac{15}{4}\\)<br \/>\nSo,<br \/>\nCompare the area of the square table and the area of the board game,<br \/>\nWe get<br \/>\nArea of the square table &gt; Area of the board game<br \/>\nHence, from the above,<br \/>\nWe can conclude that the board game fit on the table<\/p>\n<p><strong>Review &amp; Refresh<\/strong><\/p>\n<p><strong>Divide. Then check your answer.<\/strong><br \/>\nQuestion 10.<br \/>\n365 \u00f7 14 = _______<br \/>\nAnswer:<br \/>\n365 \u00f7 14 = 26 R 1<\/p>\n<p>Explanation:<br \/>\nBy using the partial quotients method,<br \/>\n365 \u00f7 14 = ( 280 \u00f7 84 ) \u00f7 14<br \/>\n= ( 280 \u00f7 14 ) + ( 84 \u00f7 14 )<br \/>\n= 20 + 6<br \/>\n= 26 R 1<br \/>\nHence, 365 \u00f7 14 = 26 R 1<\/p>\n<p>Question 11.<br \/>\n282 \u00f7 27 = ______<br \/>\nAnswer:<br \/>\n282 \u00f7 27 = 10 R 12<\/p>\n<p>Explanation:<br \/>\nBy using the partial quotients method,<br \/>\n282 \u00f7 27 = 270 \u00f7 27<br \/>\n= 10 R 12<br \/>\nHence, 270 \u00f7 27 = 10 R 12<\/p>\n<p>Question 12.<br \/>\n601 \u00f7 72 = _____<br \/>\nAnswer:<br \/>\n601 \u00f7 72 = 8 R 25<\/p>\n<p>Explanation:<br \/>\nBy using the partial quotients method,<br \/>\n601 \u00f7 72 = 576 \u00f7 72<br \/>\n= 8 R 25<br \/>\nHence, 601 \u00f7 72 = 8 R 25<\/p>\n<h3><a id=\"Lesson_9.7_Multiply_Mixed_Numbers\"><\/a>Lesson 9.7 Multiply Mixed Numbers<\/h3>\n<p><strong>Explore and Grow<\/strong><\/p>\n<p>Find the area of the rectangle. Explain how you found your answer.<br \/>\n<img loading=\"lazy\" class=\"alignnone size-full wp-image-16417\" src=\"https:\/\/ccssmathanswers.com\/wp-content\/uploads\/2020\/12\/Big-Ideas-Math-Answers-Grade-5-Chapter-9-Multiply-Fractions-9.7-1.png\" alt=\"Big Ideas Math Answers Grade 5 Chapter 9 Multiply Fractions 9.7 1\" width=\"230\" height=\"178\" \/><br \/>\nAnswer:<br \/>\nThe area of the rectangle is: \\(\\frac{35}{4}\\)<\/p>\n<p>Explanation:<br \/>\nThe given rectangle is:<br \/>\n<img loading=\"lazy\" class=\"alignnone size-full wp-image-16417\" src=\"https:\/\/ccssmathanswers.com\/wp-content\/uploads\/2020\/12\/Big-Ideas-Math-Answers-Grade-5-Chapter-9-Multiply-Fractions-9.7-1.png\" alt=\"Big Ideas Math Answers Grade 5 Chapter 9 Multiply Fractions 9.7 1\" width=\"230\" height=\"178\" \/><br \/>\nFrom the above rectangle,<br \/>\nThe side lengths are: 2\\(\\frac{1}{2}\\) and 3\\(\\frac{1}{2}\\)<br \/>\nThe representation of the side lengths in the improper form is: \\(\\frac{5}{2}\\) and \\(\\frac{7}{2}\\)<br \/>\nSo,<br \/>\nThe area of rectangle = \\(\\frac{5}{2}\\) \u00d7 \\(\\frac{7}{2}\\)<br \/>\n= \\(\\frac{5 \u00d7 7}{2 \u00d7 2}\\)<br \/>\n= \\(\\frac{35}{4}\\)<br \/>\nHence,<br \/>\n2\\(\\frac{1}{2}\\) \u00d7 3\\(\\frac{1}{2}\\) = \\(\\frac{35}{4}\\)<\/p>\n<p><strong>Structure<\/strong><br \/>\nFind the area using a different method. Explain how you found your answer.<br \/>\nAnswer:<br \/>\nThe given mixed fractions of a rectangle are: 2\\(\\frac{1}{2}\\) and 3\\(\\frac{1}{2}\\)<br \/>\nTo convert a mixed fraction into an improper fraction, we have to add the whole number part and the fractional part in the mixed fraction.<br \/>\nSo,<br \/>\n2\\(\\frac{1}{2}\\) = 2 + \\(\\frac{1}{2}\\)<br \/>\n= \\(\\frac{4}{2}\\) + \\(\\frac{1}{2}\\)<br \/>\n= \\(\\frac{5}{2}\\)<br \/>\n3\\(\\frac{1}{2}\\) = 3 + \\(\\frac{1}{2}\\)<br \/>\n= \\(\\frac{6}{2}\\) + \\(\\frac{1}{2}\\)<br \/>\n= \\(\\frac{7}{2}\\)<br \/>\nSo,<br \/>\n\\(\\frac{5}{2}\\) \u00d7 \\(\\frac{7}{2}\\) = \\(\\frac{35}{4}\\)<\/p>\n<p><strong>Think and Grow: Multiply Mixed Numbers<\/strong><\/p>\n<p>You can use a model to find the product of two mixed numbers. You can also write the mixed numbers as improper fractions and then multiply.<br \/>\n<strong>Example<\/strong><br \/>\nFind 1\\(\\frac{1}{2}\\) \u00d7 2\\(\\frac{3}{4}\\).<br \/>\nOne Way: Use an area model.<br \/>\nStep 1: Write each mixed number as a sum.<br \/>\n1\\(\\frac{1}{2}\\) = 1 + \\(\\frac{1}{2}\\) 2\\(\\frac{3}{4}\\) = 2 + \\(\\frac{3}{4}\\)<br \/>\nStep 2: Draw an area model that represents the product of the sums.<br \/>\nStep 3: Find the sum of the areas of the sections.<br \/>\n<img loading=\"lazy\" class=\"alignnone size-full wp-image-39798\" src=\"https:\/\/ccssmathanswers.com\/wp-content\/uploads\/2020\/12\/Big-Ideas-Math-Answers-Grade-5-Chapter-9-17.jpg\" alt=\"\" width=\"622\" height=\"202\" srcset=\"https:\/\/bigideasmathanswers.com\/wp-content\/uploads\/2020\/12\/Big-Ideas-Math-Answers-Grade-5-Chapter-9-17.jpg 622w, https:\/\/bigideasmathanswers.com\/wp-content\/uploads\/2020\/12\/Big-Ideas-Math-Answers-Grade-5-Chapter-9-17-300x97.jpg 300w\" sizes=\"(max-width: 622px) 100vw, 622px\" \/><\/p>\n<p>Another Way: Write each mixed number as an improper fraction, then multiply.<br \/>\n<img loading=\"lazy\" class=\"alignnone size-full wp-image-39799\" src=\"https:\/\/ccssmathanswers.com\/wp-content\/uploads\/2020\/12\/Big-Ideas-Math-Answers-Grade-5-Chapter-9-18.jpg\" alt=\"\" width=\"684\" height=\"246\" srcset=\"https:\/\/bigideasmathanswers.com\/wp-content\/uploads\/2020\/12\/Big-Ideas-Math-Answers-Grade-5-Chapter-9-18.jpg 684w, https:\/\/bigideasmathanswers.com\/wp-content\/uploads\/2020\/12\/Big-Ideas-Math-Answers-Grade-5-Chapter-9-18-300x108.jpg 300w\" sizes=\"(max-width: 684px) 100vw, 684px\" \/><\/p>\n<p><strong>Show and Grow<\/strong><\/p>\n<p><strong>Multiply.<\/strong><br \/>\nQuestion 1.<br \/>\n2\\(\\frac{1}{2}\\) \u00d7 1\\(\\frac{1}{2}\\) = ________<br \/>\nAnswer:<br \/>\n2\\(\\frac{1}{2}\\) \u00d7 1\\(\\frac{1}{2}\\) = \\(\\frac{15}{4}\\)<\/p>\n<p>Explanation:<br \/>\nThe given fractions are: 2\\(\\frac{1}{2}\\) and 1\\(\\frac{1}{2}\\)<br \/>\nThe representation of the fractions in the improper form is: \\(\\frac{5}{2}\\) and \\(\\frac{3}{2}\\)<br \/>\nSo,<br \/>\n\\(\\frac{5}{2}\\) \u00d7 \\(\\frac{3}{2}\\)<br \/>\n= \\(\\frac{5 \u00d7 3}{2 \u00d7 2}\\)<br \/>\n= \\(\\frac{15}{4}\\)<br \/>\nHence,<br \/>\n2\\(\\frac{1}{2}\\) \u00d7 1\\(\\frac{1}{2}\\) = \\(\\frac{15}{4}\\)<\/p>\n<p>Question 2.<br \/>\n3\\(\\frac{1}{4}\\) \u00d7 2\\(\\frac{2}{3}\\) = ______<br \/>\nAnswer:<br \/>\n3\\(\\frac{1}{4}\\) \u00d7 2\\(\\frac{2}{3}\\) = \\(\\frac{104}{12}\\)<\/p>\n<p>Explanation:<br \/>\nThe given fractions are: 3\\(\\frac{1}{4}\\) and 2\\(\\frac{2}{3}\\)<br \/>\nThe representation of the fractions in the improper form is: \\(\\frac{13}{4}\\) and \\(\\frac{8}{3}\\)<br \/>\nSo,<br \/>\n\\(\\frac{13}{4}\\) \u00d7 \\(\\frac{8}{3}\\)<br \/>\n= \\(\\frac{13 \u00d7 8}{4 \u00d7 3}\\)<br \/>\n= \\(\\frac{104}{12}\\)<br \/>\nHence,<br \/>\n3\\(\\frac{1}{4}\\) \u00d7 2\\(\\frac{2}{3}\\) = \\(\\frac{104}{12}\\)<\/p>\n<p><strong>Apply and Grow: Practice<\/strong><\/p>\n<p><strong>Multiply.<\/strong><br \/>\nQuestion 3.<br \/>\n1\\(\\frac{3}{4}\\) \u00d7 2\\(\\frac{1}{6}\\) = ______<br \/>\nAnswer:<br \/>\n1\\(\\frac{3}{4}\\) \u00d7 2\\(\\frac{1}{6}\\) = \\(\\frac{91}{24}\\)<\/p>\n<p>Explanation:<br \/>\nThe given fractions are: 1\\(\\frac{3}{4}\\) and 2\\(\\frac{1}{6}\\)<br \/>\nThe representation of the fractions in the improper form is: \\(\\frac{7}{4}\\) and \\(\\frac{13}{6}\\)<br \/>\nSo,<br \/>\n\\(\\frac{7}{4}\\) \u00d7 \\(\\frac{13}{6}\\)<br \/>\n= \\(\\frac{13 \u00d7 7}{4 \u00d7 6}\\)<br \/>\n= \\(\\frac{91}{24}\\)<br \/>\nHence,<br \/>\n1\\(\\frac{3}{4}\\) \u00d7 2\\(\\frac{1}{6}\\) = \\(\\frac{91}{24}\\)<\/p>\n<p>Question 4.<br \/>\n4\\(\\frac{1}{3}\\) \u00d7 1\\(\\frac{5}{6}\\) = ______<br \/>\nAnswer:<br \/>\n4\\(\\frac{1}{3}\\) \u00d7 1\\(\\frac{5}{6}\\) = \\(\\frac{143}{18}\\)<\/p>\n<p>Explanation:<br \/>\nThe given fractions are: 4\\(\\frac{1}{3}\\) and 1\\(\\frac{5}{6}\\)<br \/>\nThe representation of the fractions in the improper form is: \\(\\frac{13}{3}\\) and \\(\\frac{11}{6}\\)<br \/>\nSo,<br \/>\n\\(\\frac{13}{3}\\) \u00d7 \\(\\frac{11}{6}\\)<br \/>\n= \\(\\frac{13 \u00d7 11}{6 \u00d7 3}\\)<br \/>\n= \\(\\frac{143}{18}\\)<br \/>\nHence,<br \/>\n4\\(\\frac{1}{3}\\) \u00d7 1\\(\\frac{5}{6}\\) = \\(\\frac{143}{18}\\)<\/p>\n<p>Question 5.<br \/>\n3\\(\\frac{2}{5}\\) \u00d7 1\\(\\frac{9}{10}\\) = ______<br \/>\nAnswer:<br \/>\n3\\(\\frac{2}{5}\\) \u00d7 1\\(\\frac{9}{10}\\) = \\(\\frac{323}{50}\\)<\/p>\n<p>Explanation:<br \/>\nThe given fractions are: 3\\(\\frac{2}{5}\\) and 1\\(\\frac{9}{10}\\)<br \/>\nThe representation of the fractions in the improper form is: \\(\\frac{17}{5}\\) and \\(\\frac{19}{10}\\)<br \/>\nSo,<br \/>\n\\(\\frac{17}{5}\\) \u00d7 \\(\\frac{19}{10}\\)<br \/>\n= \\(\\frac{17 \u00d7 19}{5 \u00d7 10}\\)<br \/>\n= \\(\\frac{323}{50}\\)<br \/>\nHence,<br \/>\n3\\(\\frac{2}{5}\\) \u00d7 1\\(\\frac{9}{10}\\) = \\(\\frac{323}{50}\\)<\/p>\n<p>Question 6.<br \/>\n2\\(\\frac{3}{8}\\) \u00d7 3\\(\\frac{1}{2}\\) = ______<br \/>\nAnswer:<br \/>\n2\\(\\frac{3}{8}\\) \u00d7 3\\(\\frac{1}{2}\\) = \\(\\frac{133}{16}\\)<\/p>\n<p>Explanation:<br \/>\nThe given fractions are: 2\\(\\frac{3}{8}\\) and 3\\(\\frac{1}{2}\\)<br \/>\nThe representation of the fractions in the improper form is: \\(\\frac{19}{8}\\) and \\(\\frac{7}{2}\\)<br \/>\nSo,<br \/>\n\\(\\frac{19}{8}\\) \u00d7 \\(\\frac{7}{2}\\)<br \/>\n= \\(\\frac{19 \u00d7 7}{8 \u00d7 2}\\)<br \/>\n= \\(\\frac{133}{16}\\)<br \/>\nHence,<br \/>\n2\\(\\frac{3}{8}\\) \u00d7 3\\(\\frac{1}{2}\\) = \\(\\frac{133}{16}\\)<\/p>\n<p><strong>Evaluate.<\/strong><br \/>\nQuestion 7.<br \/>\n5\\(\\frac{1}{4}\\) \u00d7 \\(\\frac{2}{5}\\) \u00d7 6\\(\\frac{1}{12}\\) = _________<br \/>\nAnswer:<br \/>\n5\\(\\frac{1}{4}\\) \u00d7 \\(\\frac{2}{5}\\) \u00d7 6\\(\\frac{1}{12}\\) = \\(\\frac{3,066}{240}\\)<\/p>\n<p>Explanation:<br \/>\nThe given fractions are: 5\\(\\frac{1}{4}\\), \\(\\frac{2}{5}\\) and 6\\(\\frac{1}{12}\\)<br \/>\nThe representation of the fractions in the improper form is: \\(\\frac{21}{4}\\) and \\(\\frac{73}{12}\\)<br \/>\nSo,<br \/>\n\\(\\frac{21}{4}\\) \u00d7 \\(\\frac{73}{12}\\) \u00d7 \\(\\frac{2}{5}\\)<br \/>\n= \\(\\frac{21 \u00d7 73 \u00d7 2}{4 \u00d7 12 \u00d7 5}\\)<br \/>\n= \\(\\frac{3,066}{240}\\)<br \/>\nHence,<br \/>\n5\\(\\frac{1}{4}\\) \u00d7 \\(\\frac{2}{5}\\) \u00d7 6\\(\\frac{1}{12}\\) = \\(\\frac{3,066}{240}\\)<\/p>\n<p>Question 8.<br \/>\n3\\(\\frac{2}{3}\\) \u00d7 (10\\(\\frac{7}{8}\\) &#8211; 2\\(\\frac{1}{4}\\)) = _________<br \/>\nAnswer:<br \/>\n3\\(\\frac{2}{3}\\) \u00d7 (10\\(\\frac{7}{8}\\) &#8211; 2\\(\\frac{1}{4}\\)) = \\(\\frac{759}{24}\\)<\/p>\n<p>Explanation:<br \/>\nThe given fractions are: 3\\(\\frac{2}{3}\\), 10\\(\\frac{7}{8}\\) and 2\\(\\frac{1}{4}\\)<br \/>\nThe representation of the fractions in the improper form is: \\(\\frac{11}{3}\\), \\(\\frac{87}{8}\\) \u00a0and \\(\\frac{9}{4}\\)<br \/>\nSo,<br \/>\n3\\(\\frac{2}{3}\\) \u00d7 (10\\(\\frac{7}{8}\\) &#8211; 2\\(\\frac{1}{4}\\))<br \/>\n= \\(\\frac{11}{3}\\) \u00d7 ( \\(\\frac{87}{8}\\) &#8211; \\(\\frac{9}{4}\\) )<br \/>\n= \\(\\frac{11}{3}\\) \u00d7 ( \\(\\frac{87 &#8211; 18}{8}\\) )<br \/>\n= \\(\\frac{11}{3}\\) \u00d7 \\(\\frac{69}{8}\\)<br \/>\n= \\(\\frac{11 \u00d7 69}{8 \u00d7 3}\\)<br \/>\n= \\(\\frac{759}{24}\\)<br \/>\nHence,<br \/>\n3\\(\\frac{2}{3}\\) \u00d7 (10\\(\\frac{7}{8}\\) &#8211; 2\\(\\frac{1}{4}\\)) = \\(\\frac{759}{24}\\)<\/p>\n<p>Question 9.<br \/>\n<strong>YOU BE THE TEACHER<\/strong><br \/>\nYour friend uses the model to find 4\\(\\frac{1}{2}\\) \u00d7 3\\(\\frac{2}{3}\\). Is your friend correct? Explain.<br \/>\n<img loading=\"lazy\" class=\"alignnone size-full wp-image-16420\" src=\"https:\/\/ccssmathanswers.com\/wp-content\/uploads\/2020\/12\/Big-Ideas-Math-Answers-Grade-5-Chapter-9-Multiply-Fractions-9.7-4.png\" alt=\"Big Ideas Math Answers Grade 5 Chapter 9 Multiply Fractions 9.7 4\" width=\"276\" height=\"137\" \/><br \/>\nAnswer:<br \/>\nNo, your friend is not correct<\/p>\n<p>Explanation:<br \/>\nThe given fractions are: 4\\(\\frac{1}{2}\\) and 3\\(\\frac{2}{3}\\)<br \/>\nThe representation of the side lengths in the improper form is: \\(\\frac{9}{2}\\) and \\(\\frac{11}{3}\\)<br \/>\nSo,<br \/>\nThe area of rectangle = \\(\\frac{9}{2}\\) \u00d7 \\(\\frac{11}{3}\\)<br \/>\n= \\(\\frac{9 \u00d7 11}{3 \u00d7 2}\\)<br \/>\n= \\(\\frac{99}{6}\\)<br \/>\n= \\(\\frac{33}{2}\\)<br \/>\n= 15\\(\\frac{3}{2}\\)<br \/>\nBut according to your friend,<br \/>\n4\\(\\frac{1}{2}\\) \u00d7 3\\(\\frac{2}{3}\\) = 12\\(\\frac{1}{2}\\)<br \/>\nHence, from the above,<br \/>\nWe can conclude that your friend is not correct.<\/p>\n<p>Question 10.<br \/>\n<strong>Logic<\/strong><br \/>\nFind the missing numbers.<br \/>\n<img loading=\"lazy\" class=\"alignnone size-full wp-image-16421\" src=\"https:\/\/ccssmathanswers.com\/wp-content\/uploads\/2020\/12\/Big-Ideas-Math-Answers-Grade-5-Chapter-9-Multiply-Fractions-9.7-5.png\" alt=\"Big Ideas Math Answers Grade 5 Chapter 9 Multiply Fractions 9.7 5\" width=\"154\" height=\"69\" \/><br \/>\nAnswer:<br \/>\nThe missing numbers are: 1 and \\(\\frac{8}{5}\\)<\/p>\n<p>Explanation:<br \/>\nAccording to the separation method,<br \/>\nTo convert the mixed number into the improper fraction, we can add whole numbers and the fractions separately<br \/>\nNow,<br \/>\nLet the missing numbers be p and q<br \/>\nSo,<br \/>\np + 5 = 6<br \/>\nSo,<br \/>\np = 6 &#8211; 5 = 1<br \/>\nNow,<br \/>\n\\(\\frac{1}{4}\\) + \\(\\frac{1}{q}\\) = \\(\\frac{7}{8}\\)<br \/>\nSo,<br \/>\n\\(\\frac{1}{q}\\) = \\(\\frac{7}{8}\\) &#8211; \\(\\frac{1}{4}\\)<br \/>\n= \\(\\frac{7}{8}\\) &#8211; \\(\\frac{2}{8}\\)<br \/>\n= \\(\\frac{7 &#8211; 2}{8}\\)<br \/>\n= \\(\\frac{5}{8}\\)<br \/>\nSo,<br \/>\nq= \\(\\frac{8}{5}\\)<br \/>\nHence, from the above,<br \/>\nWe can conclude that the missing numbers are: 1 and \\(\\frac{8}{5}\\)<\/p>\n<p><strong>Think and Grow: Modeling Real Life<\/strong><\/p>\n<p><strong>Example<\/strong><br \/>\nA construction crew is paving 15 miles of a highway. The crew paves 4\\(\\frac{2}{10}\\) miles each month. Does the crew finish paving the highway in 3\\(\\frac{1}{2}\\) months?<br \/>\n<img loading=\"lazy\" class=\"alignnone size-full wp-image-16422\" src=\"https:\/\/ccssmathanswers.com\/wp-content\/uploads\/2020\/12\/Big-Ideas-Math-Answers-Grade-5-Chapter-9-Multiply-Fractions-9.7-6.png\" alt=\"Big Ideas Math Answers Grade 5 Chapter 9 Multiply Fractions 9.7 6\" width=\"170\" height=\"119\" \/><br \/>\nFind the length of the highway the crew paves by multiplying the number of months by the number of miles they pave each month. Write each mixed number as an improper fraction, then multiply.<br \/>\n<img loading=\"lazy\" class=\"alignnone size-full wp-image-39847\" src=\"https:\/\/ccssmathanswers.com\/wp-content\/uploads\/2020\/12\/Big-Ideas-Math-Answers-Grade-5-Chapter-9-19.jpg\" alt=\"\" width=\"575\" height=\"197\" srcset=\"https:\/\/bigideasmathanswers.com\/wp-content\/uploads\/2020\/12\/Big-Ideas-Math-Answers-Grade-5-Chapter-9-19.jpg 575w, https:\/\/bigideasmathanswers.com\/wp-content\/uploads\/2020\/12\/Big-Ideas-Math-Answers-Grade-5-Chapter-9-19-300x103.jpg 300w\" sizes=\"(max-width: 575px) 100vw, 575px\" \/><br \/>\nCompare the length the crew paves to the amount that needs to be paved.<br \/>\nThe Crew can finish paving the highway in 3\\(\\frac{1}{2}\\) months.<\/p>\n<p><strong>Show and Grow<\/strong><\/p>\n<p>Question 11.<br \/>\nYou have 3 cups of strawberries. You want to make 1\\(\\frac{1}{2}\\) batches of the recipe. Do you have enough strawberries?<br \/>\n<img loading=\"lazy\" class=\"alignnone size-full wp-image-16424\" src=\"https:\/\/ccssmathanswers.com\/wp-content\/uploads\/2020\/12\/Big-Ideas-Math-Answers-Grade-5-Chapter-9-Multiply-Fractions-9.7-8.png\" alt=\"Big Ideas Math Answers Grade 5 Chapter 9 Multiply Fractions 9.7 8\" width=\"198\" height=\"146\" \/><br \/>\nAnswer:<br \/>\nYes, you have enough strawberries<\/p>\n<p>Explanation:<br \/>\nThe given recipe for a strawberry smoothie is:<br \/>\n<img loading=\"lazy\" class=\"alignnone size-full wp-image-16424\" src=\"https:\/\/ccssmathanswers.com\/wp-content\/uploads\/2020\/12\/Big-Ideas-Math-Answers-Grade-5-Chapter-9-Multiply-Fractions-9.7-8.png\" alt=\"Big Ideas Math Answers Grade 5 Chapter 9 Multiply Fractions 9.7 8\" width=\"198\" height=\"146\" \/><br \/>\nIt is given that you want to make 1\\(\\frac{1}{2}\\) batches of the recipe<br \/>\nFrom the table,<br \/>\nThe number of cups of strawberry is: 1\\(\\frac{3}{4}\\)<br \/>\nNow,<br \/>\nThe representation of 1\\(\\frac{1}{2}\\) in the iproper fraction is: \\(\\frac{3}{2}\\)<br \/>\nThe representation of 1\\(\\frac{3}{4}\\) in the mixed form is: \\(\\frac{7}{4}\\)<br \/>\nSo,<br \/>\nThe number of strawberries for the recipe = \\(\\frac{3}{2}\\) \u00d7 \\(\\frac{7}{4}\\)<br \/>\n= \\(\\frac{3 \u00d7 7}{4 \u00d7 2}\\)<br \/>\n= \\(\\frac{21}{8}\\)<br \/>\nIt is also given that you have 3 cups of strawberries<br \/>\nSo,<br \/>\nWe can write 3 in the fraction form and as the multiples of 8 is: \\(\\frac{24}{8}\\)<br \/>\nSo,<br \/>\nWhen we compare the number of cups we obtained and given,<br \/>\nWe can say that we have enough strawberries to make the recipe<br \/>\nHence, from the above,<br \/>\nWe can conclude that we have enough strawberries<\/p>\n<p>Question 12.<br \/>\nOn Monday,you roller-skate 6\\(\\frac{1}{4}\\) miles. On Tuesday, you skate 1\\(\\frac{2}{5}\\) times as far as you did on Monday. How many total miles do you roller-skate on Monday and Tuesday combined?<br \/>\nAnswer:<br \/>\nThe number of miles you do roller-skate on Monday and Tuesday combined is: 15 miles<\/p>\n<p>Explanation:<br \/>\nIt is given that on Monday,you roller-skate 6\\(\\frac{1}{4}\\) miles. On Tuesday, you skate 1\\(\\frac{2}{5}\\) times as far as you did on Monday.<br \/>\nSo,<br \/>\nThe number of miles you do roller-skate on Tuesday = ( The number of miles you do roller-skate on Monday ) \u00d7 1\\(\\frac{2}{5}\\)<br \/>\n= 6\\(\\frac{1}{4}\\) \u00d7 1\\(\\frac{2}{5}\\)<br \/>\n= \\(\\frac{25}{4}\\) \u00d7 \\(\\frac{7}{5}\\)<br \/>\n= \\(\\frac{25 \u00d7 7}{5 \u00d7 4}\\)<br \/>\n= \\(\\frac{175}{20}\\)<br \/>\nNow,<br \/>\nThe number of miles you do roller-skate on Monday and Tuesday combined = 6\\(\\frac{1}{4}\\) + \\(\\frac{175}{20}\\)<br \/>\n= \\(\\frac{25}{4}\\) + \\(\\frac{175}{20}\\)<br \/>\n= \\(\\frac{125}{20}\\) + \\(\\frac{175}{20}\\)<br \/>\n= \\(\\frac{175 + 125}{20}\\)<br \/>\n= \\(\\frac{300}{20}\\)<br \/>\n= 15 miles<br \/>\nHence, from the above,<br \/>\nWe can conclude that the number of miles you do roller- skate on Monday and Tuesday combined is: 15 miles<\/p>\n<p>Question 13.<br \/>\n<strong>DIG DEEPER!<\/strong><br \/>\nAn artist paints a rectangular mural. The mural is 4\\(\\frac{1}{3}\\) feet wide. The length is 2\\(\\frac{1}{4}\\) times the width. What is the area of the mural?<br \/>\nAnswer:<br \/>\nThe area of the mural is: \\(\\frac{117}{12}\\) square feet<\/p>\n<p>Explanation:<br \/>\nIt is given that an artist paints a rectangular mural. The mural is 4\\(\\frac{1}{3}\\) feet wide. The length is 2\\(\\frac{1}{4}\\) times the width.<br \/>\nSo,<br \/>\nThe area of the mural = ( The width of the mural ) \u00d7 ( The length of the mural )<br \/>\n= 4\\(\\frac{1}{3}\\) \u00d7 2\\(\\frac{1}{4}\\)<br \/>\n= \\(\\frac{13}{3}\\) \u00d7 \\(\\frac{9}{4}\\)<br \/>\n= \\(\\frac{13 \u00d7 9}{4 \u00d7 3}\\)<br \/>\n= \\(\\frac{117}{12}\\)<br \/>\nHence, from the above,<br \/>\nWe can conclude that the area of the mural is: \\(\\frac{117}{12}\\) square feet<\/p>\n<h3><a id=\"Multiply_Mixed_Numbers_Homework_&amp;_Practice_9.7\"><\/a>Multiply Mixed Numbers Homework &amp; Practice 9.7<\/h3>\n<p><strong>Multiply.<\/strong><br \/>\nQuestion 1.<br \/>\n1\\(\\frac{1}{2}\\) \u00d7 1\\(\\frac{1}{8}\\) = ______<br \/>\nAnswer:<br \/>\n1\\(\\frac{1}{2}\\) \u00d7 1\\(\\frac{1}{8}\\) = \\(\\frac{18}{16}\\)<\/p>\n<p>Explanation:<br \/>\nThe given fractions are: 1\\(\\frac{1}{2}\\) and 1\\(\\frac{1}{8}\\)<br \/>\nThe representation of the fractions in the improper form is: \\(\\frac{3}{2}\\) and \\(\\frac{9}{8}\\)<br \/>\nSo,<br \/>\n\\(\\frac{9}{8}\\) \u00d7 \\(\\frac{3}{2}\\)<br \/>\n= \\(\\frac{9 \u00d7 3}{8 \u00d7 2}\\)<br \/>\n= \\(\\frac{18}{16}\\)<br \/>\nHence,<br \/>\n1\\(\\frac{1}{2}\\) \u00d7 1\\(\\frac{1}{8}\\) = \\(\\frac{18}{16}\\)<\/p>\n<p>Question 2.<br \/>\n1\\(\\frac{5}{6}\\) \u00d7 2\\(\\frac{1}{4}\\) = ______<br \/>\nAnswer:<br \/>\n1\\(\\frac{5}{6}\\) \u00d7 2\\(\\frac{1}{4}\\) = \\(\\frac{99}{24}\\)<\/p>\n<p>Explanation:<br \/>\nThe given fractions are: 1\\(\\frac{5}{6}\\) and 2\\(\\frac{1}{4}\\)<br \/>\nThe representation of the fractions in the improper form is: \\(\\frac{11}{6}\\) and \\(\\frac{9}{4}\\)<br \/>\nSo,<br \/>\n\\(\\frac{9}{4}\\) \u00d7 \\(\\frac{11}{6}\\)<br \/>\n= \\(\\frac{9 \u00d7 11}{4 \u00d7 6}\\)<br \/>\n= \\(\\frac{99}{24}\\)<br \/>\nHence,<br \/>\n1\\(\\frac{5}{6}\\) \u00d7 2\\(\\frac{1}{4}\\) = \\(\\frac{99}{24}\\)<\/p>\n<p><strong style=\"font-size: 16px;\">Evaluate.<\/strong><\/p>\n<p>Question 3.<br \/>\n2\\(\\frac{3}{8}\\) \u00d7 2\\(\\frac{3}{4}\\) = ______<br \/>\nAnswer:<br \/>\n2\\(\\frac{3}{8}\\) \u00d7 2\\(\\frac{3}{4}\\) = \\(\\frac{209}{32}\\)<\/p>\n<p>Explanation:<br \/>\nThe given fractions are: 2\\(\\frac{3}{8}\\) and 2\\(\\frac{3}{4}\\)<br \/>\nThe representation of the fractions in the improper form is: \\(\\frac{19}{8}\\) and \\(\\frac{11}{4}\\)<br \/>\nSo,<br \/>\n\\(\\frac{19}{8}\\) \u00d7 \\(\\frac{11}{4}\\)<br \/>\n= \\(\\frac{19 \u00d7 11}{4 \u00d7 8}\\)<br \/>\n= \\(\\frac{209}{32}\\)<br \/>\nHence,<br \/>\n2\\(\\frac{3}{8}\\) \u00d7 2\\(\\frac{3}{4}\\) = \\(\\frac{209}{32}\\)<\/p>\n<p>Question 4.<br \/>\n4\\(\\frac{1}{6}\\) \u00d7 3\\(\\frac{2}{7}\\) = ______<br \/>\nAnswer:<br \/>\n4\\(\\frac{1}{6}\\) \u00d7 3\\(\\frac{2}{7}\\) = \\(\\frac{575}{42}\\)<\/p>\n<p>Explanation:<br \/>\nThe given fractions are: 4\\(\\frac{1}{6}\\) and 3\\(\\frac{2}{7}\\)<br \/>\nThe representation of the fractions in the improper form is: \\(\\frac{25}{6}\\) and \\(\\frac{23}{7}\\)<br \/>\nSo,<br \/>\n\\(\\frac{23}{7}\\) \u00d7 \\(\\frac{25}{6}\\)<br \/>\n= \\(\\frac{23 \u00d7 25}{7 \u00d7 6}\\)<br \/>\n= \\(\\frac{575}{42}\\)<br \/>\nHence,<br \/>\n4\\(\\frac{1}{6}\\) \u00d7 3\\(\\frac{2}{7}\\) = \\(\\frac{575}{42}\\)<\/p>\n<p>Question 5.<br \/>\n2\\(\\frac{1}{3}\\) \u00d7 3\\(\\frac{9}{10}\\) \u00d7 5\\(\\frac{1}{5}\\) = ______<br \/>\nAnswer:<br \/>\n2\\(\\frac{1}{3}\\)\u00d7 3\\(\\frac{9}{10}\\) \u00d75\\(\\frac{1}{5}\\) = \\(\\frac{7,098}{150}\\)<\/p>\n<p>Explanation:<br \/>\nThe given fractions are: 2\\(\\frac{1}{3}\\), 3\\(\\frac{9}{10}\\) and 5\\(\\frac{1}{5}\\)<br \/>\nThe representation of the fractions in the improper form is: \\(\\frac{7}{3}\\), \\(\\frac{39}{10}\\) \u00a0and \\(\\frac{26}{5}\\)<br \/>\nSo,<br \/>\n\\(\\frac{7}{3}\\) \u00d7 \\(\\frac{39}{10}\\) \u00d7\\(\\frac{26}{5}\\)<br \/>\n= \\(\\frac{7 \u00d7 39 \u00d7 26}{3 \u00d7 10 \u00d7 5}\\)<br \/>\n= \\(\\frac{7,098}{150}\\)<br \/>\nHence,<br \/>\n2\\(\\frac{1}{3}\\)\u00d7 3\\(\\frac{9}{10}\\) \u00d75\\(\\frac{1}{5}\\) = \\(\\frac{7,098}{150}\\)<\/p>\n<p>Question 6.<br \/>\n(1\\(\\frac{7}{8}\\) + 4\\(\\frac{4}{5}\\)) \u00d7 2\\(\\frac{1}{12}\\) = _______<br \/>\nAnswer:<br \/>\n(1\\(\\frac{7}{8}\\) + 4\\(\\frac{4}{5}\\)) \u00d7 2\\(\\frac{1}{12}\\) = \\(\\frac{6,675}{480}\\)<\/p>\n<p>Explanation:<br \/>\nThe given fractions are: 1\\(\\frac{7}{8}\\), 4\\(\\frac{4}{5}\\) and 2\\(\\frac{1}{12}\\)<br \/>\nThe representation of the fractions in the improper form is: \\(\\frac{15}{8}\\), \\(\\frac{24}{5}\\) and \\(\\frac{25}{12}\\)<br \/>\nSo,<br \/>\n(1\\(\\frac{7}{8}\\) + 4\\(\\frac{4}{5}\\)) \u00d7 \\(\\frac{25}{12}\\)<br \/>\n= ( \\(\\frac{15}{8}\\) + \\(\\frac{24}{5}\\) ) \u00d7 \\(\\frac{25}{12}\\)<br \/>\n= ( \\(\\frac{75}{40}\\) + \\(\\frac{192}{40}\\) ) \u00d7 \\(\\frac{25}{12}\\)<br \/>\n= \\(\\frac{75 + 192}{40}\\) \u00d7 \\(\\frac{25}{12}\\)<br \/>\n= \\(\\frac{267}{40}\\) \u00d7 \\(\\frac{25}{12}\\)<br \/>\n= \\(\\frac{267 \u00d7 25}{40\u00d7 12 }\\)<br \/>\n= \\(\\frac{6,675}{480}\\)<br \/>\nHence,<br \/>\n(1\\(\\frac{7}{8}\\) + 4\\(\\frac{4}{5}\\)) \u00d7 2\\(\\frac{1}{12}\\) = \\(\\frac{6,675}{480}\\)<\/p>\n<p>Question 7.<br \/>\n<strong>Structure<\/strong><br \/>\nFind the missing numbers.<br \/>\n<img loading=\"lazy\" class=\"alignnone size-full wp-image-16425\" src=\"https:\/\/ccssmathanswers.com\/wp-content\/uploads\/2020\/12\/Big-Ideas-Math-Answers-Grade-5-Chapter-9-Multiply-Fractions-9.7-9.png\" alt=\"Big Ideas Math Answers Grade 5 Chapter 9 Multiply Fractions 9.7 9\" width=\"189\" height=\"139\" \/><br \/>\nAnswer:<br \/>\nThe missing numbers are: 5 and \\(\\frac{3}{10}\\)<\/p>\n<p>Explanation:<br \/>\nLet the missing numbers be p and q<br \/>\nBy using the partial products method,<br \/>\n( p \u00d7 4 ) + ( p \u00d7 \\(\\frac{1}{7}\\) ) = 20 + \\(\\frac{5}{7}\\)<br \/>\np \u00d7 ( 4 + \\(\\frac{1}{7}\\) ) = 20 + \\(\\frac{5}{7}\\)<br \/>\np \u00d7 \\(\\frac{29}{7}\\) = \\(\\frac{145}{7}\\)<br \/>\nSo,<br \/>\np = \\(\\frac{145}{7}\\) \u00f7 \\(\\frac{29}{7}\\)<br \/>\n= \\(\\frac{145}{7}\\) \u00d7 \\(\\frac{7}{29}\\)<br \/>\n= \\(\\frac{145 \u00d7 7}{7 \u00d7 29}\\)<br \/>\n= 5<br \/>\nNow,<br \/>\n(q \u00d7 4 ) + ( q \u00d7 \\(\\frac{1}{7}\\) ) = \\(\\frac{12}{10}\\) + \\(\\frac{3}{70}\\)<br \/>\nq \u00d7 ( 4 + \\(\\frac{1}{7}\\) ) = \\(\\frac{12}{10}\\) + \\(\\frac{3}{70}\\)<br \/>\nq \u00d7 \\(\\frac{29}{7}\\) = \\(\\frac{84 + 3}{70}\\)<br \/>\nq \u00d7 \\(\\frac{29}{7}\\) = \\(\\frac{87}{70}\\)<br \/>\nSo,<br \/>\nq = \\(\\frac{87}{70}\\) \u00f7 \\(\\frac{29}{7}\\)<br \/>\n= \\(\\frac{87}{70}\\) \u00d7 \\(\\frac{7}{29}\\)<br \/>\n= \\(\\frac{87 \u00d7 7}{70 \u00d7 29}\\)<br \/>\n= \\(\\frac{3}{10}\\)<br \/>\nHence, from the above,<br \/>\nWe can conclude that the missing numbers are: 5 and \\(\\frac{3}{10}\\)<\/p>\n<p>Question 8.<br \/>\n<strong>YOU BE THE TEACHER<\/strong><br \/>\nYour friend finds 1\\(\\frac{11}{12}\\) \u00d7 2\\(\\frac{3}{8}\\) . Is your friend correct? Explain.<br \/>\n<img loading=\"lazy\" class=\"alignnone size-full wp-image-16426\" src=\"https:\/\/ccssmathanswers.com\/wp-content\/uploads\/2020\/12\/Big-Ideas-Math-Answers-Grade-5-Chapter-9-Multiply-Fractions-9.7-10.png\" alt=\"Big Ideas Math Answers Grade 5 Chapter 9 Multiply Fractions 9.7 10\" width=\"278\" height=\"65\" \/><br \/>\nAnswer:<br \/>\nYes your friend is correct<\/p>\n<p>Explanation:<br \/>\nThe given mixed numbers are: 1\\(\\frac{11}{12}\\) and 2\\(\\frac{3}{8}\\)<br \/>\nThe representation of the mixed numbers in the fraction form is: \\(\\frac{23}{12}\\) and \\(\\frac{19}{8}\\)<br \/>\nSo,<br \/>\n\\(\\frac{23}{12}\\) \u00d7 \\(\\frac{19}{8}\\)<br \/>\n= \\(\\frac{23 \u00d7 19}{8 \u00d7 12}\\)<br \/>\n= \\(\\frac{437}{96}\\)<br \/>\n= 4\\(\\frac{53}{96}\\)<br \/>\nHence, from the above,<br \/>\nWe can conclude that your friend is correct<\/p>\n<p>Question 9.<br \/>\n<strong>Modeling Real Life<\/strong><br \/>\nYour friend earns 7\\(\\frac{1}{2}\\) dollars each hour. Will she earn enough money to buy a $35 toy after working 4\\(\\frac{3}{4}\\) hours?<br \/>\nAnswer:<br \/>\nshe can&#8217;t earn enough money to buy $35 toy after working 4\\(\\frac{3}{4}\\) hours<\/p>\n<p>Explanation:<br \/>\nIt is given that your friend earns 7\\(\\frac{1}{2}\\) dollars each hour.<br \/>\nIt is given that will she earn enough money to buy a $35 toy after working 4\\(\\frac{3}{4}\\) hours<br \/>\nSo,<br \/>\nThe number of dollars she can earn = 7\\(\\frac{1}{2}\\) \u00d7 4\\(\\frac{3}{4}\\)<br \/>\n= \\(\\frac{15}{2}\\) \u00d7 \\(\\frac{19}{4}\\)<br \/>\n= \\(\\frac{15 \u00d7 19}{4 \u00d7 2}\\)<br \/>\n= \\(\\frac{285}{8}\\)<br \/>\nNow,<br \/>\nThe representation of $35 as the multiple of 8 is: \\(\\frac{280}{8}\\)<br \/>\nSo,<br \/>\nBy comparing the given money with he money she earned,<br \/>\nWe can say that she can&#8217;t buy the toy.<br \/>\nHence, from the above,<br \/>\nWe can conclude that she can&#8217;t earn enough money to buy a $35 toy after working 4\\(\\frac{3}{4}\\) hours<\/p>\n<p>Question 10.<br \/>\n<strong>Modeling Real Life<\/strong><br \/>\nOne class collects 8\\(\\frac{1}{4}\\) pounds of recyclable materials. Another class collects 1\\(\\frac{1}{2}\\) times as many pounds as the first class. How many pounds of recyclable materials do the two classes collect altogether?<br \/>\nAnswer:<br \/>\nThe number of pounds of recyclable materials the two classes collects together is: \\(\\frac{231}{8}\\) pounds<\/p>\n<p>Explanation:<br \/>\nIt is given that one class collects 8\\(\\frac{1}{4}\\) pounds of recyclable materials. Another class collects 1\\(\\frac{1}{2}\\) times as many pounds as the first class.<br \/>\nSo,<br \/>\nThe number of pounds of recyclable materials collected by another class = 8\\(\\frac{1}{4}\\) \u00d7 1\\(\\frac{1}{2}\\)<br \/>\n= \\(\\frac{33}{4}\\) \u00d7 \\(\\frac{3}{2}\\)<br \/>\n= \\(\\frac{99}{8}\\) pounds<br \/>\nSo,<br \/>\nThe number of pouds of recyclable materials collected by two classes together = 8\\(\\frac{1}{4}\\) + \\(\\frac{99}{8}\\)<br \/>\n= \\(\\frac{33}{4}\\) + \\(\\frac{99}{8}\\)<br \/>\n= \\(\\frac{132 + 99}{8}\\)<br \/>\n= \\(\\frac{231}{8}\\) pounds<br \/>\nHence, from the above,<br \/>\nWe can conclude that the number of pounds of recyclable materials the two classes collects together is: \\(\\frac{231}{8}\\) pounds<\/p>\n<p><strong>Review &amp; Refresh<\/strong><\/p>\n<p><strong>Find the product.<\/strong><br \/>\nQuestion 11.<br \/>\n6 \u00d7 5.7 = ______<br \/>\nAnswer:<br \/>\n6 \u00d7 5.7 = 34.2<\/p>\n<p>Explanation:<br \/>\nBy using the partial products method,<br \/>\n6 \u00d7 5.7 = 6 \u00d7 ( 5 + 0.7 )<br \/>\n= ( 6 \u00d7 5 ) + ( 6 \u00d7 0.7 )<br \/>\n= 30 + 4.2<br \/>\n= 34.2<br \/>\nHence, 6 \u00d7 5.7 = 34.2<\/p>\n<p>Question 12.<br \/>\n0.84 \u00d7 9 = ______<br \/>\nAnswer:<br \/>\n0.84 \u00d7 9 = 73.17<\/p>\n<p>Explanation:<br \/>\nBy using the partial quotients method,<br \/>\n0.84 \u00d7 9 = ( 0.81 + 0.03 ) \u00d7 9<br \/>\n= ( 0.81 \u00d7 9 ) + ( 0.03 \u00d7 9 )<br \/>\n= 72.9 + 0.27<br \/>\n= 73.17<br \/>\nHence, 0.84 \u00d7 9 = 73.17<\/p>\n<h3><a id=\"Lesson_9.8_Compare_Factors_and_Products\"><\/a>Lesson 9.8 Compare Factors and Products<\/h3>\n<p><strong>Explore and Grow<\/strong><\/p>\n<p>Without calculating, order the rectangles by area from least to greatest. Explain your reasoning.<br \/>\n<img loading=\"lazy\" class=\"alignnone size-full wp-image-16427\" src=\"https:\/\/ccssmathanswers.com\/wp-content\/uploads\/2020\/12\/Big-Ideas-Math-Solutions-Grade-5-Chapter-9-Multiply-Fractions-9.8-1.png\" alt=\"Big Ideas Math Solutions Grade 5 Chapter 9 Multiply Fractions 9.8 1\" width=\"517\" height=\"473\" srcset=\"https:\/\/bigideasmathanswers.com\/wp-content\/uploads\/2020\/12\/Big-Ideas-Math-Solutions-Grade-5-Chapter-9-Multiply-Fractions-9.8-1.png 517w, https:\/\/bigideasmathanswers.com\/wp-content\/uploads\/2020\/12\/Big-Ideas-Math-Solutions-Grade-5-Chapter-9-Multiply-Fractions-9.8-1-300x274.png 300w\" sizes=\"(max-width: 517px) 100vw, 517px\" \/><br \/>\nAnswer:<br \/>\nLet the given rectangles be named A), B), C), and D)<br \/>\nSo,<br \/>\nThe side lengths of A are: 1 and 1\\(\\frac{1}{2}\\)<br \/>\nThe side lengths of B are: 1\\(\\frac{1}{3}\\) and \\(\\frac{11}{12}\\)<br \/>\nThe side lengths of C are: \\(\\frac{3}{2}\\) and \\(\\frac{11}{12}\\)<br \/>\nThe side lengths of D are: \\(\\frac{11}{10}\\) and \\(\\frac{3}{2}\\)<br \/>\nNow,<br \/>\nThe area of A is: \\(\\frac{1}{2}\\)<br \/>\nThe area of B is: \\(\\frac{44}{36}\\)<br \/>\nThe area of C is: \\(\\frac{33}{24}\\)<br \/>\nThe area of D is: \\(\\frac{33}{20}\\)<br \/>\nFor comparison make the denominators of the areas of the four rectangles equal.<br \/>\nSo,<br \/>\nThe area of A is: \\(\\frac{18}{36}\\)<br \/>\nThe area of B is: \\(\\frac{44}{36}\\)<br \/>\nSo, by comparing these 2 areas,<br \/>\nWe can say that B is greater<br \/>\nNow,<br \/>\nThe area of C is: \\(\\frac{165}{120}\\)<br \/>\nThe area of D is: \\(\\frac{198}{120}\\)<br \/>\nSo, by comparing these 2 areas,<br \/>\nWe can say that D is greater<br \/>\nHence, from the above,<br \/>\nWe can conclude that the order of rectangles by areas from the greatest to the least is: B &gt; D&gt; A &gt; C<\/p>\n<p><strong>Construct Arguments<\/strong><br \/>\nExplain your strategy to your partner. Compare your strategies.<br \/>\nAnswer:<br \/>\nThe strategy you followed is:<br \/>\nA) Write the side lengths of the rectangles<br \/>\nB) Find the areas of the four rectangles<br \/>\nC) Make the denominators of all the four areas of rectangles equal<br \/>\nD) Compare the numerators of all the four areas of the four rectangles<\/p>\n<p><strong>Think and Grow: Compare Factors and Products<\/strong><\/p>\n<p><strong>Key Idea<\/strong><br \/>\nWhen you multiply a number by a fraction greater than 1, the product is greater than the number. When you multiply a number by a fraction less than 1, the product is less than the number.<br \/>\n<strong>Example<\/strong><br \/>\nWithout calculating, tell whether the product 3\\(\\frac{1}{8}\\) \u00d7 \\(\\frac{5}{6}\\) is less than, greater than, or equal to or each of its factors.<br \/>\n<img loading=\"lazy\" class=\"alignnone size-full wp-image-39988\" src=\"https:\/\/ccssmathanswers.com\/wp-content\/uploads\/2020\/12\/Big-Ideas-Math-Answers-Grade-5-Chapter-9-20.jpg\" alt=\"\" width=\"691\" height=\"337\" srcset=\"https:\/\/bigideasmathanswers.com\/wp-content\/uploads\/2020\/12\/Big-Ideas-Math-Answers-Grade-5-Chapter-9-20.jpg 691w, https:\/\/bigideasmathanswers.com\/wp-content\/uploads\/2020\/12\/Big-Ideas-Math-Answers-Grade-5-Chapter-9-20-300x146.jpg 300w\" sizes=\"(max-width: 691px) 100vw, 691px\" \/><\/p>\n<p><strong>Show and Grow<\/strong><\/p>\n<p><strong>Without calculating, tell whether the product is less than, greater than, or equal to each of its factors.<\/strong><br \/>\nQuestion 1.<br \/>\n8 \u00d7 \\(\\frac{3}{10}\\)<br \/>\nAnswer:<br \/>\nThe value of 8 \u00d7 \\(\\frac{3}{10}\\) is less than 8<\/p>\n<p>Explanation:<br \/>\nThe given numbers are: 8 and \\(\\frac{3}{10}\\)<br \/>\nWe know that,<br \/>\nWhen you multiply a number by a fraction greater than 1, the product is greater than the number. When you multiply a number by a fraction less than 1, the product is less than the number.<br \/>\nSo,<br \/>\n\\(\\frac{3}{10}\\) is less than 1<br \/>\nSo,<br \/>\n8 \u00d7 \\(\\frac{3}{10}\\) is less than 8<br \/>\nHence, from the above,<br \/>\nWe can conclude that the value of 8 \u00d7 \\(\\frac{3}{10}\\) is less than 8<\/p>\n<p>Question 2.<br \/>\n\\(\\frac{4}{4}\\) \u00d7 5\\(\\frac{2}{3}\\)<br \/>\nAnswer:<br \/>\nThe value of \\(\\frac{4}{4}\\) \u00d7 5\\(\\frac{2}{3}\\) is greater than \\(\\frac{4}{4}\\)<\/p>\n<p>Explanation:<br \/>\nThe given fractions are: \\(\\frac{4}{4}\\) and 5\\(\\frac{2}{3}\\)<br \/>\nWe know that,<br \/>\nWhen you multiply a number by a fraction greater than 1, the product is greater than the number. When you multiply a number by a fraction less than 1, the product is less than the number.<br \/>\nWe know that,<br \/>\n\\(\\frac{4}{4}\\) is 1<br \/>\nNow,<br \/>\nThe representation of 5\\(\\frac{2}{3}\\) in the improper fraction form is: \\(\\frac{17}{3}\\)<br \/>\nSo,<br \/>\n\\(\\frac{17}{3}\\) is greater than 1<br \/>\nSo,<br \/>\n\\(\\frac{4}{4}\\) \u00d7 5\\(\\frac{2}{3}\\) is greater than 1<br \/>\nHence, from the above,<br \/>\nWe can conclude that the value of \\(\\frac{4}{4}\\) \u00d7 5\\(\\frac{2}{3}\\) is greater than \\(\\frac{4}{4}\\)<\/p>\n<p>Question 3.<br \/>\n\\(\\frac{4}{3}\\) \u00d7 \\(\\frac{1}{6}\\)<br \/>\nAnswer:<br \/>\nThe value of \\(\\frac{4}{3}\\) \u00d7 \\(\\frac{1}{6}\\) is greater than \\(\\frac{1}{6}\\) or less than \\(\\frac{4}{3}\\)<\/p>\n<p>Explanation:<br \/>\nThe given fractions are: \\(\\frac{4}{3}\\) and \\(\\frac{1}{6}\\)<br \/>\nWe know that,<br \/>\nWhen you multiply a number by a fraction greater than 1, the product is greater than the number. When you multiply a number by a fraction less than 1, the product is less than the number.<br \/>\nNow,<br \/>\n\\(\\frac{4}{3}\\) is greater than 1<br \/>\n\\(\\frac{1}{6}\\) is less than 1<br \/>\nSo,<br \/>\n\\(\\frac{4}{3}\\) \u00d7 \\(\\frac{1}{6}\\) is less than \\(\\frac{4}{3}\\)<br \/>\nHence, from the above,<br \/>\nWe can conclude that the value of \\(\\frac{4}{3}\\) \u00d7 \\(\\frac{1}{6}\\) is greater than \\(\\frac{1}{6}\\) or less than \\(\\frac{4}{3}\\)<\/p>\n<p><strong>Apply and Grow<\/strong><\/p>\n<p><strong>Without calculating, tell whether the product is less than, greater than, or equal to each of its factors.<\/strong><br \/>\nQuestion 4.<br \/>\n\\(\\frac{1}{4}\\) \u00d7 \\(\\frac{1}{12}\\)<br \/>\nAnswer:<br \/>\nThe value of \\(\\frac{1}{4}\\) \u00d7 \\(\\frac{1}{12}\\) is less than 1<\/p>\n<p>Explanation:<br \/>\nThe given fractions are: latex]\\frac{1}{4}[\/latex] and \\(\\frac{1}{12}\\)<br \/>\nWe know that,<br \/>\nWhen you multiply a number by a fraction greater than 1, the product is greater than the number. When you multiply a number by a fraction less than 1, the product is less than the number.<br \/>\nSo,<br \/>\n\\(\\frac{1}{4}\\) is less than 1<br \/>\n\\(\\frac{1}{12}\\) is less than 1<br \/>\nSo,<br \/>\n\\(\\frac{1}{4}\\) \u00d7 \\(\\frac{1}{12}\\) is less than 1<br \/>\nHence, from the above,<br \/>\nWe can conclude that the value of \\(\\frac{1}{4}\\) \u00d7 \\(\\frac{1}{12}\\) is less than 1<\/p>\n<p>Question 5.<br \/>\n3\\(\\frac{4}{5}\\) \u00d7 6\\(\\frac{7}{8}\\)<br \/>\nAnswer:<br \/>\nThe value of 3\\(\\frac{4}{5}\\) \u00d7 6\\(\\frac{7}{8}\\) is greater than 1<\/p>\n<p>Explanation:<br \/>\nThe given fractions are: 3\\(\\frac{4}{5}\\) and 6\\(\\frac{7}{8}\\)<br \/>\nThe representation of 3\\(\\frac{4}{5}\\) and 6\\(\\frac{7}{8}\\) in the improper fractions form is: \\(\\frac{19}{5}\\) and \\(\\frac{55}{8}\\)<br \/>\nWe know that,<br \/>\nWhen you multiply a number by a fraction greater than 1, the product is greater than the number. When you multiply a number by a fraction less than 1, the product is less than the number.<br \/>\nSo,<br \/>\n\\(\\frac{19}{5}\\) is greater than 1<br \/>\n\\(\\frac{55}{8}\\) is greater than 1<br \/>\nSo,<br \/>\n3\\(\\frac{4}{5}\\) \u00d7 6\\(\\frac{7}{8}\\) is greater than 1<br \/>\nHence, from the above,<br \/>\nWe can conclude that the value of 3\\(\\frac{4}{5}\\) \u00d7 6\\(\\frac{7}{8}\\) is greater than 1<\/p>\n<p>Question 6.<br \/>\n\\(\\frac{1}{6}\\) \u00d7 \\(\\frac{10}{10}\\)<br \/>\nAnswer:<br \/>\nThe value of \\(\\frac{1}{6}\\) \u00d7 \\(\\frac{10}{10}\\) is less than 1<\/p>\n<p>Explanation:<br \/>\nThe given fractions are: \\(\\frac{1}{6}\\) and \\(\\frac{10}{10}\\)<br \/>\nWe know that,<br \/>\nWhen you multiply a number by a fraction greater than 1, the product is greater than the number. When you multiply a number by a fraction less than 1, the product is less than the number.<br \/>\nWe know that,<br \/>\n\\(\\frac{10}{10}\\) is 1<br \/>\nSo,<br \/>\n\\(\\frac{1}{6}\\) is less than 1<br \/>\nSo,<br \/>\n\\(\\frac{1}{6}\\) \u00d7 \\(\\frac{10}{10}\\) is less than 1<br \/>\nHence, from the above,<br \/>\nWe can conclude that the value of \\(\\frac{1}{6}\\) \u00d7 \\(\\frac{10}{10}\\) is less than 1<\/p>\n<p>Question 7.<br \/>\n\\(\\frac{2}{3}\\) \u00d7 5<br \/>\nAnswer:<br \/>\nThe value of \\(\\frac{2}{3}\\) \u00d7 5 is less than 5<\/p>\n<p>Explanation:<br \/>\nThe given fractions are: \\(\\frac{2}{3}\\) and 5<br \/>\nWe know that,<br \/>\nWhen you multiply a number by a fraction greater than 1, the product is greater than the number. When you multiply a number by a fraction less than 1, the product is less than the number.<br \/>\nSo,<br \/>\n\\(\\frac{2}{3}\\) is less than 1<br \/>\nSo,<br \/>\n\\(\\frac{2}{3}\\) \u00d7 5 is less than 5<br \/>\nHence, from the above,<br \/>\nWe can conclude that the value of \\(\\frac{2}{3}\\) \u00d7 5 is less than 5<\/p>\n<p>Question 8.<br \/>\n\\(\\frac{7}{10}\\) \u00d7 4\\(\\frac{8}{9}\\)<br \/>\nAnswer:<br \/>\nThe value of \\(\\frac{7}{10}\\) \u00d7 4\\(\\frac{8}{9}\\) is greater than 1<\/p>\n<p>Explanation:<br \/>\nThe given fractions are: \\(\\frac{7}{10}\\) and 4\\(\\frac{8}{9}\\)<br \/>\nThe representation of 4\\(\\frac{8}{9}\\) in the improper fraction form is: \\(\\frac{44}{9}\\)<br \/>\nWe know that,<br \/>\nWhen you multiply a number by a fraction greater than 1, the product is greater than the number. When you multiply a number by a fraction less than 1, the product is less than the number.<br \/>\nSo,<br \/>\n\\(\\frac{7}{10}\\) is less than 1<br \/>\n\\(\\frac{44}{9}\\) is greater than 1<br \/>\nSo,<br \/>\n\\(\\frac{7}{10}\\) \u00d7 4\\(\\frac{8}{9}\\) is greater than 1<br \/>\nHence, from the above,<br \/>\nWe can conclude that the value of \\(\\frac{7}{10}\\) \u00d7 4\\(\\frac{8}{9}\\) is greater than 1<\/p>\n<p>Question 9.<br \/>\n\\(\\frac{9}{2}\\) \u00d7 1\\(\\frac{3}{4}\\)<br \/>\nAnswer:<br \/>\nThe value of \\(\\frac{9}{2}\\) \u00d7 1\\(\\frac{3}{4}\\) is greater than 1<\/p>\n<p>Explanation:<br \/>\nThe given fractions are: \\(\\frac{9}{2}\\) \u00d7 1\\(\\frac{3}{4}\\)<br \/>\nThe representation of 1\\(\\frac{3}{4}\\) in the improper fraction form is: \\(\\frac{7}{4}\\)<br \/>\nWe know that,<br \/>\nWhen you multiply a number by a fraction greater than 1, the product is greater than the number. When you multiply a number by a fraction less than 1, the product is less than the number.<br \/>\nSo,<br \/>\n\\(\\frac{9}{2}\\) is greater than 1<br \/>\n\\(\\frac{7}{4}\\) is greater than 1<br \/>\nSo,<br \/>\n\\(\\frac{9}{2}\\) \u00d7 1\\(\\frac{3}{4}\\) is greater than 1<br \/>\nHence, from the above,<br \/>\nWe can conclude that the value of \\(\\frac{9}{2}\\) \u00d7 1\\(\\frac{3}{4}\\) is greater than 1<\/p>\n<p><strong>Without calculating, order the products from least to greatest.<\/strong><br \/>\nQuestion 10.<br \/>\n<img loading=\"lazy\" class=\"alignnone size-full wp-image-16429\" src=\"https:\/\/ccssmathanswers.com\/wp-content\/uploads\/2020\/12\/Big-Ideas-Math-Solutions-Grade-5-Chapter-9-Multiply-Fractions-9.8-3.png\" alt=\"Big Ideas Math Solutions Grade 5 Chapter 9 Multiply Fractions 9.8 3\" width=\"252\" height=\"54\" \/><br \/>\nAnswer:<br \/>\nThe order of products from the least to the greatest is:<br \/>\n\\(\\frac{5}{6}\\) \u00d7 \\(\\frac{1}{3}\\) &lt; \\(\\frac{5}{6}\\) \u00d7 \\(\\frac{7}{7}\\) &lt; \\(\\frac{5}{6}\\) \u00d7 1\\(\\frac{8}{9}\\)<\/p>\n<p>Explanation:<br \/>\nThe given products are:<br \/>\nA) \\(\\frac{5}{6}\\) \u00d7 \\(\\frac{1}{3}\\)<br \/>\nB) \\(\\frac{5}{6}\\) \u00d7 \\(\\frac{7}{7}\\)<br \/>\nC) \\(\\frac{5}{6}\\) \u00d7 1\\(\\frac{8}{9}\\)<br \/>\nSo,<br \/>\nIn A),<br \/>\n\\(\\frac{5}{6}\\) and \\(\\frac{1}{3}\\) are less than 1<br \/>\nSo,<br \/>\n\\(\\frac{5}{6}\\) \u00d7 \\(\\frac{1}{3}\\) is less than 1<br \/>\nIn B),<br \/>\n\\(\\frac{5}{6}\\) is less than 1<br \/>\n\\(\\frac{7}{7}\\) is 1<br \/>\nSo,<br \/>\n\\(\\frac{5}{6}\\) \u00d7 \\(\\frac{7}{7}\\) is less than 1<br \/>\nIn C),<br \/>\n\\(\\frac{5}{6}\\) is less than1<br \/>\nThe representation of\u00a0 1\\(\\frac{8}{9}\\) in the improper fraction form is: \\(\\frac{17}{9}\\)<br \/>\nSo,<br \/>\n\\(\\frac{17}{9}\\) is greater than 1<br \/>\nSo,<br \/>\n\\(\\frac{5}{6}\\) \u00d7 1\\(\\frac{8}{9}\\) is greater than 1<br \/>\nHence, from the above,<br \/>\nWe can conclude that the order of the products from the least to the greatest is:<br \/>\n\\(\\frac{5}{6}\\) \u00d7 \\(\\frac{1}{3}\\) &lt; \\(\\frac{5}{6}\\) \u00d7 \\(\\frac{7}{7}\\) &lt; \\(\\frac{5}{6}\\) \u00d7 1\\(\\frac{8}{9}\\)<\/p>\n<p>Question 11.<br \/>\n<img loading=\"lazy\" class=\"alignnone size-full wp-image-16430\" src=\"https:\/\/ccssmathanswers.com\/wp-content\/uploads\/2020\/12\/Big-Ideas-Math-Solutions-Grade-5-Chapter-9-Multiply-Fractions-9.8-4.png\" alt=\"Big Ideas Math Solutions Grade 5 Chapter 9 Multiply Fractions 9.8 4\" width=\"268\" height=\"53\" \/><br \/>\nAnswer:<br \/>\nThe order of products from the least to the greatest is:<br \/>\n\\(\\frac{1}{6}\\) \u00d7 \\(\\frac{1}{4}\\) &lt; \\(\\frac{1}{10}\\) \u00d7 \\(\\frac{1}{4}\\) &lt; 5\\(\\frac{7}{10}\\) \u00d7 \\(\\frac{1}{4}\\)<\/p>\n<p>Explanation:<br \/>\nThe given products are:<br \/>\nA) \\(\\frac{1}{6}\\) \u00d7 \\(\\frac{1}{4}\\)<br \/>\nB) \\(\\frac{1}{10}\\) \u00d7 \\(\\frac{1}{4}\\)<br \/>\nC) \\(\\frac{1}{4}\\) \u00d7 5\\(\\frac{7}{10}\\)<br \/>\nSo,<br \/>\nIn A),<br \/>\n\\(\\frac{1}{6}\\) and \\(\\frac{1}{4}\\) are less than 1<br \/>\nSo,<br \/>\n\\(\\frac{1}{6}\\) \u00d7 \\(\\frac{1}{4}\\) is less than 1<br \/>\nIn B),<br \/>\n\\(\\frac{1}{10}\\) is less than 1<br \/>\n\\(\\frac{1}{4}\\) is less than 1<br \/>\nSo,<br \/>\n\\(\\frac{1}{10}\\) \u00d7 \\(\\frac{1}{4}\\) is less than 1<br \/>\nIn C),<br \/>\n\\(\\frac{1}{4}\\) is less than1<br \/>\nThe representation of\u00a0 5\\(\\frac{7}{10}\\) in the improper fraction form is: \\(\\frac{57}{10}\\)<br \/>\nSo,<br \/>\n\\(\\frac{57}{10}\\) is greater than 1<br \/>\nSo,<br \/>\n\\(\\frac{1}{4}\\) \u00d7 5\\(\\frac{7}{10}\\) is greater than 1<br \/>\nHence, from the above,<br \/>\nWe can conclude that the order of the products from the least to the greatest is:<br \/>\n\\(\\frac{1}{6}\\) \u00d7 \\(\\frac{1}{4}\\) &lt; \\(\\frac{1}{10}\\) \u00d7 \\(\\frac{1}{4}\\) &lt; 5\\(\\frac{7}{10}\\) \u00d7 \\(\\frac{1}{4}\\)<\/p>\n<p>Question 12.<br \/>\n<strong>YOU BE THE TEACHER<\/strong><br \/>\nYour friend says that \\(\\frac{1}{2}\\) \u00d7 8 is half as much as 8. Is your friend correct? Explain.<br \/>\nAnswer:<br \/>\nYes, your friend is correct<\/p>\n<p>Explanation:<br \/>\nThe given numbers are: \\(\\frac{1}{2}\\) and 8<br \/>\nSo,<br \/>\n\\(\\frac{1}{2}\\) \u00d7 8 = \\(\\frac{1}{2}\\) \u00d7 \\(\\frac{8}{1}\\)<br \/>\n= \\(\\frac{1 \u00d7 8}{2 \u00d7 1}\\)<br \/>\n= 4<br \/>\nIt is also given that according to your friend,<br \/>\n\\(\\frac{1}{2}\\) \u00d7 8 is half as much as 8.<br \/>\nSo,<br \/>\n8 \u00f7 2 = 4<br \/>\nHence, from the above,<br \/>\nWe can conclude that your friend is correct.<\/p>\n<p>Question 13.<br \/>\n<strong>DIG DEEPER!<\/strong><br \/>\nWithout calculating, tell whether the product is less than, greater than, or equal to 3\\(\\frac{3}{4}\\). Explain.<br \/>\n\\(\\left(\\frac{1}{2} \\times 3 \\frac{3}{4}\\right)\\) \u00d7 \\(\\frac{2}{7}\\)<br \/>\nAnswer:<br \/>\n\\(\\left(\\frac{1}{2} \\times 3 \\frac{3}{4}\\right)\\) \u00d7 \\(\\frac{2}{7}\\) is less than\u00a0 3\\(\\frac{3}{4}\\)<\/p>\n<p>Explanation:<br \/>\nThe representation of 3\\(\\frac{3}{4}\\) in the improper fraction form is: \\(\\frac{15}{4}\\)<br \/>\nNow,<br \/>\n\\(\\left(\\frac{1}{2} \\times 3 \\frac{3}{4}\\right)\\) \u00d7 \\(\\frac{2}{7}\\)<br \/>\n= ( \\(\\frac{1}{2}\\) \u00d7 \\(\\frac{15}{4}\\) ) \u00d7 \\(\\frac{2}{7}\\)<br \/>\n= \\(\\frac{15}{8}\\) \u00d7 \\(\\frac{2}{7}\\)<br \/>\n= \\(\\frac{2 \u00d7 15}{7 \u00d7 8}\\)<br \/>\n= \\(\\frac{30}{56}\\)<br \/>\n= \\(\\frac{15}{28}\\)<br \/>\nNow,<br \/>\n\\(\\frac{15}{4}\\) is multiplied by \\(\\frac{7}{7}\\)<br \/>\nSo,<br \/>\n\\(\\frac{15}{4}\\) = \\(\\frac{105}{28}\\)<br \/>\nSo,<br \/>\nWhen we compare \\(\\frac{105}{28}\\) and \\(\\frac{15}{28}\\)<br \/>\nWe will get \\(\\frac{105}{28}\\) is greater<br \/>\nHence, from the above,<br \/>\nWe can conclude that \\(\\left(\\frac{1}{2} \\times 3 \\frac{3}{4}\\right)\\) \u00d7 \\(\\frac{2}{7}\\) is less than\u00a0 3\\(\\frac{3}{4}\\)<\/p>\n<p><strong>Think and Grow: Modeling Real Life<\/strong><\/p>\n<p><strong>Example<\/strong><br \/>\nMen\u2019s shot put competitions use a shot with a mass of 7\\(\\frac{1}{4}\\) kilograms. The mass of a bowling ball is \\(\\frac{7}{8}\\) as much as the mass of the shot. Is the mass of the bowling ball less than, greater than, or equal to the mass of the shot?<br \/>\n<img loading=\"lazy\" class=\"alignnone size-full wp-image-16431\" src=\"https:\/\/ccssmathanswers.com\/wp-content\/uploads\/2020\/12\/Big-Ideas-Math-Solutions-Grade-5-Chapter-9-Multiply-Fractions-9.8-5.png\" alt=\"Big Ideas Math Solutions Grade 5 Chapter 9 Multiply Fractions 9.8 5\" width=\"183\" height=\"184\" srcset=\"https:\/\/bigideasmathanswers.com\/wp-content\/uploads\/2020\/12\/Big-Ideas-Math-Solutions-Grade-5-Chapter-9-Multiply-Fractions-9.8-5.png 183w, https:\/\/bigideasmathanswers.com\/wp-content\/uploads\/2020\/12\/Big-Ideas-Math-Solutions-Grade-5-Chapter-9-Multiply-Fractions-9.8-5-150x150.png 150w\" sizes=\"(max-width: 183px) 100vw, 183px\" \/><br \/>\nWrite an expression to represent the mass of the bowling ball.<br \/>\n<img loading=\"lazy\" class=\"alignnone size-full wp-image-40151\" src=\"https:\/\/ccssmathanswers.com\/wp-content\/uploads\/2020\/12\/Big-Ideas-Math-Answers-Grade-5-Chapter-9-21.jpg\" alt=\"\" width=\"660\" height=\"222\" srcset=\"https:\/\/bigideasmathanswers.com\/wp-content\/uploads\/2020\/12\/Big-Ideas-Math-Answers-Grade-5-Chapter-9-21.jpg 660w, https:\/\/bigideasmathanswers.com\/wp-content\/uploads\/2020\/12\/Big-Ideas-Math-Answers-Grade-5-Chapter-9-21-300x101.jpg 300w\" sizes=\"(max-width: 660px) 100vw, 660px\" \/><br \/>\nSo, the mass of the bowling ball is greater than the mass of the shot.<\/p>\n<p><strong>Show and Grow<\/strong><\/p>\n<p>Question 14.<br \/>\nYou practice playing the keyboard for 3\\(\\frac{1}{2}\\) hours. Your friend practices playing the keyboard for \\(\\frac{5}{4}\\) as many hours as you. Does your friend practice for fewer hours, more hours, or the same number of hours as you?<br \/>\nAnswer:<br \/>\nYou practice more hours than your friend<\/p>\n<p>Explanation:<br \/>\nIt is given that you practice playing the keyboard for 3\\(\\frac{1}{2}\\) hours. Your friend practices playing the keyboard for \\(\\frac{5}{4}\\) as many hours as you.<br \/>\nSo,<br \/>\nNow,<br \/>\nThe representation of 3\\(\\frac{1}{2}\\) in the improper fraction form is: \\(\\frac{7}{2}\\)<br \/>\nSo,<br \/>\nThe number of hours you practice playing the keyboard is: \\(\\frac{7}{2}\\) hours<br \/>\nThe number of hours your friend practice playing the keyboard is: \\(\\frac{5}{4}\\) hours<br \/>\nSo,<br \/>\nFor comparison, make the denominators equal.<br \/>\nSo,<br \/>\nMultiply \\(\\frac{7}{2}\\) with \\(\\frac{2}{2}\\)<br \/>\nSo,<br \/>\n\\(\\frac{7}{2}\\) = \\(\\frac{14}{4}\\)<br \/>\nBy comparing the timings ,<br \/>\nWe can say that<br \/>\n\\(\\frac{14}{4}\\) &gt; \\(\\frac{5}{4}\\)<br \/>\nHence, from the above,<br \/>\nWe can conclude that you practice more hours than your friend<\/p>\n<p>Question 15.<br \/>\nThe original price of a telescope is $99. The sale price is \\(\\frac{4}{5}\\) of the original price. An astrologist buys the telescope at its sale price and uses a half-off-coupon. What fraction of the original price does the astrologist pay for the telescope?<br \/>\nAnswer:<br \/>\nThe fraction of the original price the astrologist pays for the telescope is: \\(\\frac{4}{10}\\)<\/p>\n<p>Explanation:<br \/>\nIt is given that the original price of a telescope is $99. The sale price is \\(\\frac{4}{5}\\) of the original price. and an astrologist buys the telescope at its sale price and uses a half-off-coupon.<br \/>\nSo,<br \/>\nThe cost of the telescope that an astrologist bought = ( The \\(\\frac{4}{5}\\)th of the original price ) \u00d7 ( Half-off -coupon on the \\(\\frac{4}{5}\\)th of the original price )<br \/>\n= \\(\\frac{4}{5}\\) \u00d7 \\(\\frac{1}{2}\\)<br \/>\n= \\(\\frac{4 \u00d7 1}{5 \u00d7 2}\\)<br \/>\n= \\(\\frac{4}{10}\\)<br \/>\nHence, from the above,<br \/>\nWe can conclude that the fraction of the original price the astrologist pays for the telescope is: \\(\\frac{4}{10}\\)<\/p>\n<p>Question 16.<br \/>\nThe Abraj Al-Bait Clock Tower is \\(\\frac{6}{10}\\) kilometer tall. Zifeng Tower is \\(\\frac{3}{4}\\) as tall as the clock tower. Is Zifeng Tower shorter than, taller than, or the same height as the Abraj Al-Bait Clock Tower? What is the height of each tower in meters?<br \/>\n<img loading=\"lazy\" class=\"alignnone size-full wp-image-16433\" src=\"https:\/\/ccssmathanswers.com\/wp-content\/uploads\/2020\/12\/Big-Ideas-Math-Solutions-Grade-5-Chapter-9-Multiply-Fractions-9.8-7.png\" alt=\"Big Ideas Math Solutions Grade 5 Chapter 9 Multiply Fractions 9.8 7\" width=\"140\" height=\"181\" \/><br \/>\nAnswer:<br \/>\nThe Abraj al-Bait Clock tower is taller than the Zifeng tower<br \/>\nThe height of Abraj al-Bait Clock tower is: \\(\\frac{24}{40}\\)<br \/>\nThe height of Zifeng tower is: \\(\\frac{18}{40}\\)<\/p>\n<p>Explanation:<br \/>\nIt is given that the Abraj Al-Bait Clock Tower is \\(\\frac{6}{10}\\) kilometer tall and Zifeng Tower is \\(\\frac{3}{4}\\) as tall as the clock tower.<br \/>\nSo,<br \/>\nThe height of Abraj al-Bait Clock tower is: \\(\\frac{6}{10}\\) kilometer<br \/>\nNow,<br \/>\nThe height of Zifeng tower is = \\(\\frac{6}{10}\\) \u00d7 \\(\\frac{3}{4}\\)<br \/>\n= \\(\\frac{6 \u00d7 3}{10 \u00d7 4}\\)<br \/>\n= \\(\\frac{18}{40}\\)<br \/>\nNow, for comparison, make the denomonators of both the towers equal.<br \/>\nSo,<br \/>\n\\(\\frac{6}{10}\\) is multiplied by \\(\\frac{4}{4}\\)<br \/>\nSo,<br \/>\n\\(\\frac{6}{10}\\) = \\(\\frac{24}{40}\\)<br \/>\nBy comparing the heights of the two towers,<br \/>\nWe can say that<br \/>\n\\(\\frac{24}{40}\\) &gt; \\(\\frac{18}{40}\\)<br \/>\nHence, from the above,<br \/>\nWe can conclude that<br \/>\nThe Abraj al-Bait Clock tower is taller than the Zifeng tower<br \/>\nThe height of Abraj al-Bait Clock tower is: \\(\\frac{24}{40}\\)<br \/>\nThe height of Zifeng tower is: \\(\\frac{18}{40}\\)<\/p>\n<h3><a id=\"Compare_Factors_and_Products_Homework_&amp;_Practice_9.8\"><\/a>Compare Factors and Products Homework &amp; Practice 9.8<\/h3>\n<p><strong>Without calculating, tell whether the product is less than, greater than, or equal to each of its factors.<\/strong><br \/>\nQuestion 1.<br \/>\n1\\(\\frac{3}{4}\\) \u00d7 6<br \/>\nAnswer:<br \/>\nThe value of 1\\(\\frac{3}{4}\\) \u00d7 6 is greater than 6<\/p>\n<p>Explanation:<br \/>\nThe given numbers are: 1\\(\\frac{3}{4}\\) and 6<br \/>\nThe representation of 1\\(\\frac{3}{4}\\) in the improper fraction form is: \\(\\frac{7}{4}\\)<br \/>\nWe know that,<br \/>\nWhen you multiply a number by a fraction greater than 1, the product is greater than the number. When you multiply a number by a fraction less than 1, the product is less than the number.<br \/>\nSo,<br \/>\n\\(\\frac{7}{4}\\) is greater than 1<br \/>\nSo,<br \/>\n1\\(\\frac{3}{4}\\) \u00d7 6 is greater than 6<br \/>\nHence, from the above,<br \/>\nWe can conclude that the value of 1\\(\\frac{3}{4}\\) \u00d7 6 is greater than 6<\/p>\n<p>Question 2.<br \/>\n\\(\\frac{5}{12}\\) \u00d7 \\(\\frac{1}{6}\\)<br \/>\nAnswer:<br \/>\nThe value of \\(\\frac{5}{12}\\) \u00d7 \\(\\frac{1}{6}\\) is less than 1<\/p>\n<p>Explanation;<br \/>\nThe given fractions are: \\(\\frac{5}{12}\\) and \\(\\frac{1}{6}\\)<br \/>\nWe know that,<br \/>\nWhen you multiply a number by a fraction greater than 1, the product is greater than the number. When you multiply a number by a fraction less than 1, the product is less than the number.<br \/>\nSo,<br \/>\n\\(\\frac{5}{12}\\) is less than 1<br \/>\n\\(\\frac{1}{6}\\) is less than 1<br \/>\nSo,<br \/>\n\\(\\frac{5}{12}\\) \u00d7 \\(\\frac{1}{6}\\) is less than 1<br \/>\nHence, from the above,<br \/>\nWe can conclude that the value of \\(\\frac{5}{12}\\) \u00d7 \\(\\frac{1}{6}\\) is less than 1<\/p>\n<p>Question 3.<br \/>\n\\(\\frac{2}{7}\\) \u00d7 \\(\\frac{5}{5}\\)<br \/>\nAnswer:<br \/>\nThe value of \\(\\frac{2}{7}\\) \u00d7 \\(\\frac{5}{5}\\) is less than 1<\/p>\n<p>Explanation:<br \/>\nThe given fractions are: \\(\\frac{2}{7}\\) and \\(\\frac{5}{5}\\)<br \/>\nWe know that,<br \/>\nWhen you multiply a number by a fraction greater than 1, the product is greater than the number. When you multiply a number by a fraction less than 1, the product is less than the number.<br \/>\nSo,<br \/>\n\\(\\frac{2}{7}\\) is less than 1<br \/>\nWe know that<br \/>\n\\(\\frac{5}{5}\\) is 1<br \/>\nSo,<br \/>\n\\(\\frac{2}{7}\\) \u00d7 \\(\\frac{5}{5}\\) is less than 1<br \/>\nHence, from the above,<br \/>\nWe can conclude that the value of \\(\\frac{2}{7}\\) \u00d7 \\(\\frac{5}{5}\\) is less than 1<\/p>\n<p>Question 4.<br \/>\n3\\(\\frac{4}{5}\\) \u00d7 2\\(\\frac{9}{10}\\)<br \/>\nAnswer:<br \/>\nThe value of 3\\(\\frac{4}{5}\\) \u00d7 2\\(\\frac{9}{10}\\) is greater than 1<\/p>\n<p>Explanation:<br \/>\nthe given mixed fractions are: 3\\(\\frac{4}{5}\\) and 2\\(\\frac{9}{10}\\)<br \/>\nWe know that,<br \/>\nWhen you multiply a number by a fraction greater than 1, the product is greater than the number. When you multiply a number by a fraction less than 1, the product is less than the number.<br \/>\nSo,<br \/>\nThe representation of the mixed numbers in the fraction form is: \\(\\frac{19}{5}\\) and \\(\\frac{29}{10}\\)<br \/>\nSo,<br \/>\n\\(\\frac{19}{5}\\) is greater than 1<br \/>\n\\(\\frac{29}{10}\\) is greater than<br \/>\nSo,<br \/>\n3\\(\\frac{4}{5}\\) \u00d7 2\\(\\frac{9}{10}\\) is greater than 1<br \/>\nHence, from the above,<br \/>\nWe can conclude that the value of 3\\(\\frac{4}{5}\\) \u00d7 2\\(\\frac{9}{10}\\) is greater than 1<\/p>\n<p>Question 5.<br \/>\n8 \u00d7 \\(\\frac{2}{3}\\)<br \/>\nAnswer:<br \/>\nThe value of\u00a0 8 is greater than \\(\\frac{2}{3}\\)<\/p>\n<p>Explanation:<br \/>\nThe given numbers are: 8 and \\(\\frac{2}{3}\\)<br \/>\nWe know that,<br \/>\nWhen you multiply a number by a fraction greater than 1, the product is greater than the number. When you multiply a number by a fraction less than 1, the product is less than the number.<br \/>\nSo,<br \/>\n\\(\\frac{2}{3}\\) is less than 1<br \/>\nSo,<br \/>\n8 is greater than \\(\\frac{2}{3}\\)<br \/>\nHence, from the above,<br \/>\nWe can conclude that the value of 8 is greater than \\(\\frac{2}{3}\\)<\/p>\n<p>Question 6.<br \/>\n1\\(\\frac{7}{8}\\) \u00d7 \\(\\frac{1}{4}\\)<br \/>\nAnswer:<br \/>\nThe value of 1\\(\\frac{7}{8}\\) \u00d7 \\(\\frac{1}{4}\\) is less than 1<\/p>\n<p>Explanation:<br \/>\nThe given fractions are: 1\\(\\frac{7}{8}\\) and \\(\\frac{1}{4}\\)<br \/>\nThe representation of 1\\(\\frac{7}{8}\\) in the fraction form is: \\(\\frac{15}{8}\\)<br \/>\nWe know that,<br \/>\nWhen you multiply a number by a fraction greater than 1, the product is greater than the number. When you multiply a number by a fraction less than 1, the product is less than the number.<br \/>\nSo,<br \/>\n\\(\\frac{15}{8}\\) is greater than 1<br \/>\n\\(\\frac{1}{4}\\) is less than 1<br \/>\nSo,<br \/>\n1\\(\\frac{7}{8}\\) \u00d7 \\(\\frac{1}{4}\\) is less than 1<br \/>\nHence, from the above,<br \/>\nWe can conclude that the value of 1\\(\\frac{7}{8}\\) \u00d7 \\(\\frac{1}{4}\\) is less than 1<\/p>\n<p><strong>Without calculating, order the products from least to greatest.<\/strong><br \/>\nQuestion 7.<br \/>\n<img loading=\"lazy\" class=\"alignnone size-full wp-image-16434\" src=\"https:\/\/ccssmathanswers.com\/wp-content\/uploads\/2020\/12\/Big-Ideas-Math-Solutions-Grade-5-Chapter-9-Multiply-Fractions-9.8-8.png\" alt=\"Big Ideas Math Solutions Grade 5 Chapter 9 Multiply Fractions 9.8 8\" width=\"256\" height=\"54\" \/><br \/>\nAnswer:<br \/>\nThe order of products from the least to the greatest is:<br \/>\n\\(\\frac{1}{3}\\) \u00d7 \\(\\frac{4}{5}\\) &lt; \\(\\frac{1}{3}\\) \u00d7 \\(\\frac{6}{6}\\) &lt; 8\\(\\frac{2}{9}\\) \u00d7 \\(\\frac{1}{3}\\)<\/p>\n<p>Explanation:<br \/>\nThe given products are:<br \/>\nA) \\(\\frac{1}{3}\\) \u00d7 \\(\\frac{4}{5}\\)<br \/>\nB) \\(\\frac{1}{3}\\) \u00d7 \\(\\frac{6}{6}\\)<br \/>\nC) 8\\(\\frac{2}{9}\\) \u00d7 \\(\\frac{1}{3}\\)<br \/>\nSo,<br \/>\nIn A),<br \/>\n\\(\\frac{1}{3}\\) and \\(\\frac{4}{5}\\) are less than 1<br \/>\nSo,<br \/>\n\\(\\frac{1}{3}\\) \u00d7 \\(\\frac{4}{5}\\) is less than 1<br \/>\nIn B),<br \/>\n\\(\\frac{1}{3}\\) is less than 1<br \/>\n\\(\\frac{6}{6}\\) is 1<br \/>\nSo,<br \/>\n\\(\\frac{1}{3}\\) \u00d7 \\(\\frac{6}{6}\\) is less than 1<br \/>\nIn C),<br \/>\n\\(\\frac{1}{3}\\) is less than1<br \/>\nThe representation of\u00a0 8\\(\\frac{2}{9}\\) in the improper fraction form is: \\(\\frac{74}{9}\\)<br \/>\nSo,<br \/>\n\\(\\frac{74}{9}\\) is greater than 1<br \/>\nSo,<br \/>\n\\(\\frac{1}{3}\\) \u00d7 8\\(\\frac{2}{9}\\) is greater than 1<br \/>\nHence, from the above,<br \/>\nWe can conclude that the order of the products from the least to the greatest is:<br \/>\n\\(\\frac{1}{3}\\) \u00d7 \\(\\frac{4}{5}\\) &lt; \\(\\frac{1}{3}\\) \u00d7 \\(\\frac{6}{6}\\) &lt; 8\\(\\frac{2}{9}\\) \u00d7 \\(\\frac{1}{3}\\)<\/p>\n<p>Question 8.<br \/>\n<img loading=\"lazy\" class=\"alignnone size-full wp-image-16435\" src=\"https:\/\/ccssmathanswers.com\/wp-content\/uploads\/2020\/12\/Big-Ideas-Math-Solutions-Grade-5-Chapter-9-Multiply-Fractions-9.8-9.png\" alt=\"Big Ideas Math Solutions Grade 5 Chapter 9 Multiply Fractions 9.8 9\" width=\"247\" height=\"57\" \/><br \/>\nAnswer:<br \/>\nThe order of products from the least to the greatest is:<br \/>\n\\(\\frac{1}{12}\\) \u00d7 \\(\\frac{3}{5}\\) &lt; 4 \u00d7 \\(\\frac{3}{5}\\) &lt; 2\\(\\frac{1}{2}\\) \u00d7 \\(\\frac{3}{5}\\)<\/p>\n<p>Explanation:<br \/>\nThe given products are:<br \/>\nA) \\(\\frac{1}{12}\\) \u00d7 \\(\\frac{3}{5}\\)<br \/>\nB) 4 \u00d7 \\(\\frac{3}{5}\\)<br \/>\nC) 2\\(\\frac{1}{2}\\) \u00d7 \\(\\frac{3}{5}\\)<br \/>\nSo,<br \/>\nIn A),<br \/>\n\\(\\frac{1}{12}\\) and \\(\\frac{3}{5}\\) are less than 1<br \/>\nSo,<br \/>\n\\(\\frac{1}{12}\\) \u00d7 \\(\\frac{3}{5}\\) is less than 1<br \/>\nIn B),<br \/>\n\\(\\frac{3}{5}\\) is less than 1<br \/>\nSo,<br \/>\n4 \u00d7 \\(\\frac{3}{5}\\) is less than 4<br \/>\nIn C),<br \/>\n\\(\\frac{3}{5}\\) is less than1<br \/>\nThe representation of\u00a0 2\\(\\frac{1}{2}\\) in the improper fraction form is: \\(\\frac{5}{2}\\)<br \/>\nSo,<br \/>\n\\(\\frac{5}{2}\\) is greater than 1<br \/>\nSo,<br \/>\n\\(\\frac{3}{5}\\) \u00d7 2\\(\\frac{1}{2}\\) is greater than 1<br \/>\nHence, from the above,<br \/>\nWe can conclude that the order of the products from the least to the greatest is:<br \/>\n\\(\\frac{1}{12}\\) \u00d7 \\(\\frac{3}{5}\\) &lt; 4 \u00d7 \\(\\frac{3}{5}\\) &lt; 2\\(\\frac{1}{2}\\) \u00d7 \\(\\frac{3}{5}\\)<\/p>\n<p>Question 9.<br \/>\n<strong>Logic<\/strong><br \/>\nWithout calculating, use &gt;, &lt;, or = to make the statement true. Explain.<br \/>\n<img loading=\"lazy\" class=\"alignnone size-full wp-image-16436\" src=\"https:\/\/ccssmathanswers.com\/wp-content\/uploads\/2020\/12\/Big-Ideas-Math-Solutions-Grade-5-Chapter-9-Multiply-Fractions-9.8-10.png\" alt=\"Big Ideas Math Solutions Grade 5 Chapter 9 Multiply Fractions 9.8 10\" width=\"144\" height=\"66\" \/><br \/>\nAnswer:<br \/>\nThe value of 3\\(\\frac{1}{3}\\) \u00d7 \\(\\frac{1}{6}\\) is less than 3\\(\\frac{1}{2}\\)<\/p>\n<p>Explanation:<br \/>\nThe given fractions are: 3\\(\\frac{1}{3}\\), \\(\\frac{1}{6}\\) and 3\\(\\frac{1}{2}\\)<br \/>\nThe representations of the 3\\(\\frac{1}{3}\\) and\u00a0 3\\(\\frac{1}{2}\\)\u00a0\u00a0in the fraction form is: \\(\\frac{7}{2}\\) and \\(\\frac{10}{3}\\)<br \/>\nSo,<br \/>\n3\\(\\frac{1}{3}\\) \u00d7 \\(\\frac{1}{6}\\)<br \/>\n= \\(\\frac{10}{3}\\)\u00a0 \u00d7 \\(\\frac{1}{6}\\)<br \/>\n= \\(\\frac{10}{18}\\)<br \/>\nTo compare the fractions, equate the denominators<br \/>\nSo,<br \/>\nMultiply \\(\\frac{7}{2}\\) by \\(\\frac{9}{9}\\)<br \/>\n= \\(\\frac{63}{18}\\)<br \/>\nSo,<br \/>\nBy comparison,<br \/>\nWe can say that<br \/>\n\\(\\frac{10}{18}\\) &lt; \\(\\frac{63}{18}\\)<br \/>\nHence, from the above,<br \/>\nWe can conclude that the value of 3\\(\\frac{1}{3}\\) \u00d7 \\(\\frac{1}{6}\\) is less than 3\\(\\frac{1}{2}\\)<\/p>\n<p>Question 10.<br \/>\n<strong>Logic<\/strong><br \/>\nWithout calculating, determine which number makes the statement true.<br \/>\n<img loading=\"lazy\" class=\"alignnone size-full wp-image-16438\" src=\"https:\/\/ccssmathanswers.com\/wp-content\/uploads\/2020\/12\/Big-Ideas-Math-Solutions-Grade-5-Chapter-9-Multiply-Fractions-9.8-11.png\" alt=\"Big Ideas Math Solutions Grade 5 Chapter 9 Multiply Fractions 9.8 11\" width=\"273\" height=\"119\" \/><br \/>\nAnswer:<br \/>\nLet the missing number be x.<br \/>\nThe options for x are given as:<br \/>\nA) 1 B) \\(\\frac{1}{2}\\) and C) 1\\(\\frac{4}{5}\\)<br \/>\nSo,<br \/>\nFrom the given three fractions,<br \/>\nThe value of x is: 1\\(\\frac{4}{5}\\)<\/p>\n<p>Explanation:<br \/>\nThe given multiplication equation is:<br \/>\nx \u00d7 1\\(\\frac{7}{8}\\) is greater than 1\\(\\frac{7}{8}\\)<br \/>\nSo,<br \/>\nTo find the value of x, there are 3 options. They are:<br \/>\nA) 1 B) \\(\\frac{1}{2}\\) and C) 1\\(\\frac{4}{5}\\)<br \/>\nNow,<br \/>\nLet x = 1\\(\\frac{4}{5}\\)<br \/>\nSo,<br \/>\n1\\(\\frac{4}{5}\\) \u00d7 1\\(\\frac{7}{8}\\)<br \/>\n= \\(\\frac{9}{5}\\) \u00d7 \\(\\frac{15}{8}\\)<br \/>\n= \\(\\frac{27}{8}\\)<br \/>\nSo, by comparison,<br \/>\nWe will get,<br \/>\n\\(\\frac{27}{8}\\) is greater than \\(\\frac{15}{8}\\)<br \/>\nHence, from the above,<br \/>\nWe can conclude that the missing number is: 1\\(\\frac{4}{5}\\)<\/p>\n<p>Question 11.<br \/>\n<strong>Reasoning<\/strong><br \/>\nWhy does multiplying by a fraction greater than one result in a product greater than the original number?<br \/>\nAnswer:<br \/>\nIn the given fraction, if the numerator is greater than the denominator, then the given fraction is greater than 1<br \/>\nSo,<br \/>\nWhen the whole number is multiplied by the fraction which is greater than 1, the result in a product will be greater than the original number i.e, the whole number<\/p>\n<p>Question 12.<br \/>\n<strong>Modeling Real Life<\/strong><br \/>\nYou snowboard 1\\(\\frac{7}{8}\\) miles. Your friend snowboards 3\\(\\frac{2}{3}\\) times as far as you. Does your friend snowboard fewer miles, more miles, or the same number of miles as you?<br \/>\nAnswer:<br \/>\nThe number of miles you snowboarded is less than your friend<\/p>\n<p>Explanation:<br \/>\nIt is given that you snowboard 1\\(\\frac{7}{8}\\) miles. Your friend snowboards 3\\(\\frac{2}{3}\\) times as far as you.<br \/>\nSo,<br \/>\nThe number of miles you snowboard is: 1\\(\\frac{7}{8}\\) miles<br \/>\nSo,<br \/>\nThe number of miles your friend snowboard is = 1\\(\\frac{7}{8}\\) \u00d7 3\\(\\frac{2}{3}\\)<br \/>\n= \\(\\frac{15}{8}\\) \u00d7 \\(\\frac{11}{3}\\)<br \/>\n= \\(\\frac{15 \u00d7 11}{3 \u00d7 8}\\)<br \/>\n= \\(\\frac{165}{24}\\) miles<br \/>\nSo,<br \/>\nFor comparison we have to make the denominators equal.<br \/>\nSo,<br \/>\nMultiply \\(\\frac{15}{8}\\) by \\(\\frac{3}{3}\\)<br \/>\nSo,<br \/>\n\\(\\frac{15}{8}\\) = \\(\\frac{45}{24}\\)<br \/>\nSo,<br \/>\nBy comparing, we will get<br \/>\n\\(\\frac{45}{24}\\) is less than \\(\\frac{165}{24}\\) miles<br \/>\nHence, from the above,<br \/>\nWe can conclude that the number of miles you snowboarded is less than your friend<\/p>\n<p>Question 13.<br \/>\n<strong>Modeling Real Life<\/strong><br \/>\nA pet owner has three dogs. The youngest dog weighs \\(\\frac{1}{4}\\) as much as the second oldest dog. The oldest dog weighs 1\\(\\frac{1}{4}\\) as much as the second oldest. The second oldest weighs 20 pounds. Which dog weighs the most? the least?<br \/>\n<img loading=\"lazy\" class=\"alignnone size-full wp-image-16439\" src=\"https:\/\/ccssmathanswers.com\/wp-content\/uploads\/2020\/12\/Big-Ideas-Math-Solutions-Grade-5-Chapter-9-Multiply-Fractions-9.8-12.png\" alt=\"Big Ideas Math Solutions Grade 5 Chapter 9 Multiply Fractions 9.8 12\" width=\"199\" height=\"185\" \/><\/p>\n<p>Answer:<br \/>\nThe dog that weighs the most is: The oldest dog<br \/>\nThe dog that weighs the least is: The youngest dog<\/p>\n<p>Explanation:<br \/>\nIt is given that a pet owner has three dogs. The youngest dog weighs \\(\\frac{1}{4}\\) as much as the second oldest dog. The oldest dog weighs 1\\(\\frac{1}{4}\\) as much as the second oldest. The second oldest weighs 20 pounds.<br \/>\nSo,<br \/>\nThe weight of the second oldest dog is: 20 pounds<br \/>\nNow,<br \/>\nThe weight of the oldest dog = 1\\(\\frac{1}{4}\\) \u00d7 ( The weight of the oldest second dog )<br \/>\n= 1\\(\\frac{1}{4}\\) \u00d7 20<br \/>\n= \\(\\frac{5}{4}\\) \u00d7 20<br \/>\n= \\(\\frac{5 \u00d7 20}{4 \u00d7 1}\\)<br \/>\n= 25 pounds<br \/>\nNow,<br \/>\nThe weight of the youngest dog = \\(\\frac{1}{4}\\) \u00d7 ( The weight of the second oldest dog )<br \/>\n= \\(\\frac{1}{4}\\) \u00d7 20<br \/>\n= \\(\\frac{1 \u00d7 20}{4}\\)<br \/>\n= 5 pounds<br \/>\nHence, from the above,<br \/>\nWe can conclude that<br \/>\nThe dog that weighs the most is: The oldest dog<br \/>\nThe dog that weighs the least is: The youngest dog<\/p>\n<p><strong>Review &amp; Refresh<\/strong><\/p>\n<p><strong>Compare.<\/strong><br \/>\nQuestion 14.<br \/>\n<img loading=\"lazy\" class=\"alignnone size-full wp-image-16440\" src=\"https:\/\/ccssmathanswers.com\/wp-content\/uploads\/2020\/12\/Big-Ideas-Math-Solutions-Grade-5-Chapter-9-Multiply-Fractions-9.8-13.png\" alt=\"Big Ideas Math Solutions Grade 5 Chapter 9 Multiply Fractions 9.8 13\" width=\"117\" height=\"43\" \/><br \/>\nAnswer:<br \/>\n40.5 is greater than 40.13<\/p>\n<p>Explanation:<br \/>\nThe given decimal numbers are: 40.5 and 40.13<br \/>\nFor comparison, compare the place value of the given digits<br \/>\nIf there are more than 2 digits after the decimal, first compare the tenths position and after that only compare the hundredths position<br \/>\nIf we can get the result in the tenths position only, then there is no need for further comparison<br \/>\nHence, from the above,<br \/>\nWe can conclude that 40.5 is greater than 40.13<\/p>\n<p>Question 15.<br \/>\n<img loading=\"lazy\" class=\"alignnone size-full wp-image-16441\" src=\"https:\/\/ccssmathanswers.com\/wp-content\/uploads\/2020\/12\/Big-Ideas-Math-Solutions-Grade-5-Chapter-9-Multiply-Fractions-9.8-14.png\" alt=\"Big Ideas Math Solutions Grade 5 Chapter 9 Multiply Fractions 9.8 14\" width=\"126\" height=\"46\" \/><br \/>\nAnswer:<br \/>\n13.90 is equal to 13.9<\/p>\n<p>Explanation:<br \/>\nThe given decimal numbers are: 13.90 and 13.9<br \/>\nFor comparison, compare the place value of the given digits<br \/>\nIf there are more than 2 digits after the decimal, first compare the tenths position and after that only compare the hundredths position<br \/>\nIf we can get the result in the tenths position only, then there is no need for further comparison<br \/>\nHence, from the above,<br \/>\nWe can conclude that 13.90 is equal to 13.9<\/p>\n<p>Question 16.<br \/>\n<img loading=\"lazy\" class=\"alignnone size-full wp-image-16442\" src=\"https:\/\/ccssmathanswers.com\/wp-content\/uploads\/2020\/12\/Big-Ideas-Math-Solutions-Grade-5-Chapter-9-Multiply-Fractions-9.8-15.png\" alt=\"Big Ideas Math Solutions Grade 5 Chapter 9 Multiply Fractions 9.8 15\" width=\"140\" height=\"41\" \/><br \/>\nAnswer:<br \/>\n32.006 is less than 32.06<\/p>\n<p>Explanation:<br \/>\nThe given decimal numbers are: 32.006 and 32.06<br \/>\nFor comparison, compare the place value of the given digits<br \/>\nIf there are more than 2 digits after the decimal, first compare the tenths position and after that only compare the hundredths position<br \/>\nIf we can get the result in the tenths position only, then there is no need for further comparison<br \/>\nHence, from the above,<br \/>\nWe can conclude that 32.006 is less than 32.06<\/p>\n<h3><a id=\"Multiply_Fractions_Performance_Task\"><\/a>Multiply Fractions Performance Task<\/h3>\n<p>Question 1.<br \/>\nYou see a rock formation at a national park. The formation has layers that formed millions of years ago when particles settled in the water and became rock. You make a model of the rock formation using \\(\\frac{3}{16}\\) -inch foam sheets.<br \/>\n<img loading=\"lazy\" class=\"alignnone size-full wp-image-16443\" src=\"https:\/\/ccssmathanswers.com\/wp-content\/uploads\/2020\/12\/Big-Ideas-Math-Answer-Key-Grade-5-Chapter-9-Multiply-Fractions-1.png\" alt=\"Big Ideas Math Answer Key Grade 5 Chapter 9 Multiply Fractions 1\" width=\"381\" height=\"274\" srcset=\"https:\/\/bigideasmathanswers.com\/wp-content\/uploads\/2020\/12\/Big-Ideas-Math-Answer-Key-Grade-5-Chapter-9-Multiply-Fractions-1.png 381w, https:\/\/bigideasmathanswers.com\/wp-content\/uploads\/2020\/12\/Big-Ideas-Math-Answer-Key-Grade-5-Chapter-9-Multiply-Fractions-1-300x216.png 300w\" sizes=\"(max-width: 381px) 100vw, 381px\" \/><br \/>\na. The three types of sedimentary rocks are limestone, sandstone, and shale. Use the number of foam sheets to find the height of each sedimentary rock layer.<br \/>\nAnswer:<br \/>\nThe height of limestone is: \\(\\frac{9}{4}\\) inches<br \/>\nThe height of sandstone is: \\(\\frac{3}{2}\\) inches<br \/>\nThe height of shale is: \\(\\frac{15}{4}\\) inches<\/p>\n<p>Explanation:<br \/>\nIt is given that the height of each foam sheet is: \\(\\frac{3}{16}\\) -inches<br \/>\n<img loading=\"lazy\" class=\"alignnone size-full wp-image-16443\" src=\"https:\/\/ccssmathanswers.com\/wp-content\/uploads\/2020\/12\/Big-Ideas-Math-Answer-Key-Grade-5-Chapter-9-Multiply-Fractions-1.png\" alt=\"Big Ideas Math Answer Key Grade 5 Chapter 9 Multiply Fractions 1\" width=\"381\" height=\"274\" srcset=\"https:\/\/bigideasmathanswers.com\/wp-content\/uploads\/2020\/12\/Big-Ideas-Math-Answer-Key-Grade-5-Chapter-9-Multiply-Fractions-1.png 381w, https:\/\/bigideasmathanswers.com\/wp-content\/uploads\/2020\/12\/Big-Ideas-Math-Answer-Key-Grade-5-Chapter-9-Multiply-Fractions-1-300x216.png 300w\" sizes=\"(max-width: 381px) 100vw, 381px\" \/><br \/>\nFrom the table,<br \/>\nThe number of foam sheets for Limestone is: 12<br \/>\nThe number of foam sheets for sandstone is: 8<br \/>\nThe number of foam sheets for shale is: 20<br \/>\nSo,<br \/>\nThe height of limestone is: ( The height of each foam sheet ) \u00d7 ( The total number of foam sheets )<br \/>\n= \\(\\frac{3}{16}\\) \u00d7 12<br \/>\n= \\(\\frac{3}{16}\\) \u00d7 \\(\\frac{12}{1}\\)<br \/>\n= \\(\\frac{9}{4}\\) inches<br \/>\nThe height of sandstone is: ( The height of each foam sheet ) \u00d7 ( The total number of foam sheets )<br \/>\n= \\(\\frac{3}{16}\\) \u00d7 8<br \/>\n= \\(\\frac{3}{16}\\) \u00d7 \\(\\frac{8}{1}\\)<br \/>\n= \\(\\frac{3}{2}\\) inches<br \/>\nThe height of shale is: ( The height of each foam sheet ) \u00d7 ( The total number of foam sheets )<br \/>\n= \\(\\frac{3}{16}\\) \u00d7 20<br \/>\n= \\(\\frac{3}{16}\\) \u00d7 \\(\\frac{20}{1}\\)<br \/>\n= \\(\\frac{15}{4}\\) inches<br \/>\nHence, from the above,<br \/>\nWe can conclude that<br \/>\nThe height of limestone is: \\(\\frac{9}{4}\\) inches<br \/>\nThe height of sandstone is: \\(\\frac{3}{2}\\) inches<br \/>\nThe height of shale is: \\(\\frac{15}{4}\\) inches<\/p>\n<p>b. What is the combined height of the sedimentary rock layers?<br \/>\nAnswer:<br \/>\nThe combined height of the sedimentary layers is: \\(\\frac{15}{2}\\) inches<\/p>\n<p>Explanation:<br \/>\nThe combined height of the sedimentary rock layers = The height of limestone + The height of sandstone + The height of the shale<br \/>\n= \\(\\frac{9}{4}\\) + \\(\\frac{3}{2}\\) + \\(\\frac{15}{4}\\)<br \/>\n= \\(\\frac{24}{4}\\) + \\(\\frac{3}{2}\\)<br \/>\n= \\(\\frac{12}{2}\\) + \\(\\frac{3}{2}\\)<br \/>\n= \\(\\frac{15}{2}\\) inches<br \/>\nHence, from the above,<br \/>\nWe can conclude that the combined height of the sedimentary layers is: \\(\\frac{15}{2}\\) inches<\/p>\n<p>c. Will you use more foam sheets for the granite layers of the shale layers? Explain.<br \/>\nAnswer:<br \/>\nWe use\u00a0 more foam sheets for the granite layers<\/p>\n<p>Explanation:<br \/>\nFrom the above,<br \/>\nThe height of the shale layers is: \\(\\frac{15}{4}\\) inches<br \/>\nFrom the table,<br \/>\nThe height of the granite layers is: 3 inches<br \/>\nWhen we compare the two values,<br \/>\nWe can observe that the height of shale layers is greater than the granite layers<br \/>\nHence, from the above,<br \/>\nWe can conclude that we will use more foam sheets for granite layers<\/p>\n<p>d. The height of the topsoil layer is 1\\(\\frac{1}{4}\\) times the height of the sandstone layer. How many foam sheets do you use in the topsoil layer?<br \/>\nAnswer:<br \/>\nThe height of the topsoil layer is: \\(\\frac{15}{8}\\) inches<\/p>\n<p>Explanation:<br \/>\nFrom the above,<br \/>\nThe height of the sandstone layer is: \\(\\frac{3}{2}\\) inches<br \/>\nSo,<br \/>\nThe height of topsoil layer = 1\\(\\frac{1}{4}\\) \u00d7 \\(\\frac{3}{2}\\)<br \/>\n= \\(\\frac{5}{4}\\) \u00d7 \\(\\frac{3}{2}\\)<br \/>\n= \\(\\frac{15}{8}\\) inches<br \/>\nHence, from the above,<br \/>\nWe can conclude that the height of the topsoil layer is: \\(\\frac{15}{8}\\) inches<\/p>\n<p>e. On your model, 1 inch represents 40 feet. What is the actual height of the rock formation?<br \/>\nAnswer:<br \/>\nThe actual height of the rock formation is: 495 feet<\/p>\n<p>Explanation:<br \/>\nFrom the above,<br \/>\nThe height of the sedimentary layers is: \\(\\frac{15}{2}\\) inches<br \/>\nThe height of the topsoil layer is: \\(\\frac{15}{8}\\) inches<br \/>\nThe height of the granite layer is: 3 inches<br \/>\nSo,<br \/>\nThe combined height of the rock formation = \\(\\frac{15}{2}\\) + \\(\\frac{15}{8}\\) + 3<br \/>\n= \\(\\frac{99}{8}\\) inches<br \/>\nBut, it is given that,<br \/>\n1 inch = 40 feet<br \/>\nSo,<br \/>\nThe combined height of the rock formation in feet = \\(\\frac{99}{8}\\) inches \u00d7 40<br \/>\n= 495 feet<br \/>\nHence, from the above,<br \/>\nWe can conclude that the height of the rock formation in feet is: 495 feet<\/p>\n<p>f. Why do you think the rock formation has layers?<br \/>\nAnswer:<br \/>\nThe rock formation has layers because of the tectonic plates.<\/p>\n<h3><a id=\"Multiply_Fractions_Activity\"><\/a>Multiply Fractions Activity<\/h3>\n<p><strong>Fraction Connection: Multiplication<\/strong><br \/>\n<strong>Directions:<\/strong><br \/>\n1. Players take turns rolling three dice.<br \/>\n2. On your turn, evaluate the expression indicated by your roll and cover the answer.<br \/>\n3. The first player to get four in a row, horizontally, vertically, or diagonally, wins?<br \/>\n<img loading=\"lazy\" class=\"alignnone size-full wp-image-16444\" src=\"https:\/\/ccssmathanswers.com\/wp-content\/uploads\/2020\/12\/Big-Ideas-Math-Answer-Key-Grade-5-Chapter-9-Multiply-Fractions-2.png\" alt=\"Big Ideas Math Answer Key Grade 5 Chapter 9 Multiply Fractions 2\" width=\"323\" height=\"428\" srcset=\"https:\/\/bigideasmathanswers.com\/wp-content\/uploads\/2020\/12\/Big-Ideas-Math-Answer-Key-Grade-5-Chapter-9-Multiply-Fractions-2.png 323w, https:\/\/bigideasmathanswers.com\/wp-content\/uploads\/2020\/12\/Big-Ideas-Math-Answer-Key-Grade-5-Chapter-9-Multiply-Fractions-2-226x300.png 226w\" sizes=\"(max-width: 323px) 100vw, 323px\" \/><br \/>\n<img loading=\"lazy\" class=\"alignnone size-full wp-image-16445\" src=\"https:\/\/ccssmathanswers.com\/wp-content\/uploads\/2020\/12\/Big-Ideas-Math-Answer-Key-Grade-5-Chapter-9-Multiply-Fractions-3.png\" alt=\"Big Ideas Math Answer Key Grade 5 Chapter 9 Multiply Fractions 3\" width=\"568\" height=\"434\" srcset=\"https:\/\/bigideasmathanswers.com\/wp-content\/uploads\/2020\/12\/Big-Ideas-Math-Answer-Key-Grade-5-Chapter-9-Multiply-Fractions-3.png 568w, https:\/\/bigideasmathanswers.com\/wp-content\/uploads\/2020\/12\/Big-Ideas-Math-Answer-Key-Grade-5-Chapter-9-Multiply-Fractions-3-300x229.png 300w\" sizes=\"(max-width: 568px) 100vw, 568px\" \/><\/p>\n<h3><a id=\"Multiply_Fractions_Chapter_Practice\"><\/a>Multiply Fractions Chapter Practice<\/h3>\n<p><strong>9.1 Multiply Whole Numbers by Fractions<\/strong><\/p>\n<p><strong>Multiply.<\/strong><br \/>\nQuestion 1.<br \/>\n5 \u00d7 \\(\\frac{1}{2}\\) = _______<br \/>\nAnswer:<br \/>\n5 \u00d7 \\(\\frac{1}{2}\\) = \\(\\frac{5}{2}\\)<\/p>\n<p>Explanation:<br \/>\nThe given numbers are: 5 and \\(\\frac{1}{2}\\)<br \/>\nSo,<br \/>\n5 \u00d7 \\(\\frac{1}{2}\\)<br \/>\n= \\(\\frac{5}{1}\\) \u00d7 \\(\\frac{1}{2}\\)<br \/>\n= \\(\\frac{5 \u00d7 1}{1 \u00d7 2}\\)<br \/>\n= \\(\\frac{5}{2}\\)<br \/>\nHence,<br \/>\n5 \u00d7 \\(\\frac{1}{2}\\) = \\(\\frac{5}{2}\\)<\/p>\n<p>Question 2.<br \/>\n2 \u00d7 \\(\\frac{7}{10}\\) = _______<br \/>\nAnswer:<br \/>\n2 \u00d7 \\(\\frac{7}{10}\\) = \\(\\frac{14}{10}\\)<\/p>\n<p>Explanation:<br \/>\nThe given numbers are: 2 and \\(\\frac{7}{10}\\)<br \/>\nSo,<br \/>\n2 \u00d7 \\(\\frac{7}{10}\\)<br \/>\n= \\(\\frac{2}{1}\\) \u00d7 \\(\\frac{7}{10}\\)<br \/>\n= \\(\\frac{2 \u00d7 7}{1 \u00d7 10}\\)<br \/>\n= \\(\\frac{14}{10}\\)<br \/>\nHence,<br \/>\n2 \u00d7 \\(\\frac{7}{10}\\) = \\(\\frac{14}{10}\\)<\/p>\n<p>Question 3.<br \/>\n9 \u00d7 \\(\\frac{5}{8}\\) = _______<br \/>\nAnswer:<br \/>\n9 \u00d7 \\(\\frac{5}{8}\\) = \\(\\frac{45}{8}\\)<\/p>\n<p>Explanation:<br \/>\nThe given numbers are: 9 and \\(\\frac{5}{8}\\)<br \/>\nSo,<br \/>\n9 \u00d7 \\(\\frac{5}{8}\\)<br \/>\n= \\(\\frac{9}{1}\\) \u00d7 \\(\\frac{5}{8}\\)<br \/>\n= \\(\\frac{5 \u00d7 9}{1 \u00d7 8}\\)<br \/>\n= \\(\\frac{45}{8}\\)<br \/>\nHence,<br \/>\n9 \u00d7 \\(\\frac{5}{8}\\) = \\(\\frac{45}{8}\\)<\/p>\n<p>Question 4.<br \/>\n6 \u00d7 \\(\\frac{71}{100}\\) = _______<br \/>\nAnswer:<br \/>\n6 \u00d7 \\(\\frac{71}{100}\\) = \\(\\frac{426}{100}\\)<\/p>\n<p>Explanation:<br \/>\nThe given numbers are: 6 and \\(\\frac{71}{100}\\)<br \/>\nSo,<br \/>\n6 \u00d7 \\(\\frac{71}{100}\\)<br \/>\n= \\(\\frac{6}{1}\\) \u00d7 \\(\\frac{71}{100}\\)<br \/>\n= \\(\\frac{6 \u00d7 71}{1 \u00d7 100}\\)<br \/>\n= \\(\\frac{426}{100}\\)<br \/>\nHence,<br \/>\n6 \u00d7 \\(\\frac{71}{100}\\) = \\(\\frac{426}{100}\\)<\/p>\n<p>Question 5.<br \/>\n4 \u00d7 \\(\\frac{8}{5}\\) = _______<br \/>\nAnswer:<br \/>\n4 \u00d7 \\(\\frac{8}{5}\\) = \\(\\frac{32}{5}\\)<\/p>\n<p>Explanation:<br \/>\nThe given numbers are: 4 and \\(\\frac{8}{5}\\)<br \/>\nSo,<br \/>\n4 \u00d7 \\(\\frac{8}{5}\\)<br \/>\n= \\(\\frac{4}{1}\\) \u00d7 \\(\\frac{8}{5}\\)<br \/>\n= \\(\\frac{4 \u00d7 8}{1 \u00d7 5}\\)<br \/>\n= \\(\\frac{32}{5}\\)<br \/>\nHence,<br \/>\n4 \u00d7 \\(\\frac{8}{5}\\) = \\(\\frac{32}{5}\\)<\/p>\n<p>Question 6.<br \/>\n7 \u00d7 \\(\\frac{5}{3}\\) = _______<br \/>\nAnswer:<br \/>\n7 \u00d7 \\(\\frac{5}{3}\\) = \\(\\frac{35}{3}\\)<\/p>\n<p>Explanation:<br \/>\nThe given numbers are: 7 and \\(\\frac{5}{3}\\)<br \/>\nSo,<br \/>\n7 \u00d7 \\(\\frac{5}{3}\\)<br \/>\n= \\(\\frac{7}{1}\\) \u00d7 \\(\\frac{5}{3}\\)<br \/>\n= \\(\\frac{5 \u00d7 7}{1 \u00d7 3}\\)<br \/>\n= \\(\\frac{35}{3}\\)<br \/>\nHence,<br \/>\n7 \u00d7 \\(\\frac{5}{3}\\) = \\(\\frac{35}{3}\\)<\/p>\n<p><strong>9.2 Use Models to Multiply Fractions by Whole Numbers<\/strong><\/p>\n<p><strong>Multiply. Use a model to help.<\/strong><br \/>\nQuestion 7.<br \/>\n\\(\\frac{2}{5}\\) of 20<br \/>\nAnswer:<br \/>\n20 \u00d7 \\(\\frac{2}{5}\\) = 8<\/p>\n<p>Explanation:<br \/>\nThe given numbers are: 20 and \\(\\frac{2}{5}\\)<br \/>\nSo,<br \/>\n20 \u00d7 \\(\\frac{2}{5}\\)<br \/>\n= \\(\\frac{20}{1}\\) \u00d7 \\(\\frac{2}{5}\\)<br \/>\n= \\(\\frac{20 \u00d7 2}{1 \u00d7 5}\\)<br \/>\n= \\(\\frac{8}{1}\\)<br \/>\n= 8<br \/>\nHence,<br \/>\n20 \u00d7 \\(\\frac{2}{5}\\) = 8<\/p>\n<p>Question 8.<br \/>\n\\(\\frac{1}{6}\\) \u00d7 12<br \/>\nAnswer:<br \/>\n12 \u00d7 \\(\\frac{1}{6}\\) = 2<\/p>\n<p>Explanation:<br \/>\nThe given numbers are: 12 and \\(\\frac{1}{6}\\)<br \/>\nSo,<br \/>\n12 \u00d7 \\(\\frac{1}{6}\\)<br \/>\n= \\(\\frac{12}{1}\\) \u00d7 \\(\\frac{1}{6}\\)<br \/>\n= \\(\\frac{12 \u00d7 1}{1 \u00d7 6}\\)<br \/>\n= \\(\\frac{2}{1}\\)<br \/>\n= 2<br \/>\nHence,<br \/>\n12 \u00d7 \\(\\frac{1}{6}\\) = 2<\/p>\n<p>Question 9.<br \/>\n\\(\\frac{1}{3}\\) \u00d7 6<br \/>\nAnswer:<br \/>\n6 \u00d7 \\(\\frac{1}{3}\\) = 2<\/p>\n<p>Explanation:<br \/>\nThe given numbers are: 6 and \\(\\frac{1}{3}\\)<br \/>\nSo,<br \/>\n6 \u00d7 \\(\\frac{1}{3}\\)<br \/>\n= \\(\\frac{6}{1}\\) \u00d7 \\(\\frac{1}{3}\\)<br \/>\n= \\(\\frac{6 \u00d7 1}{1 \u00d7 3}\\)<br \/>\n= \\(\\frac{2}{1}\\)<br \/>\n= 2<br \/>\nHence,<br \/>\n6 \u00d7 \\(\\frac{1}{3}\\) = 2<\/p>\n<p>Question 10.<br \/>\n\\(\\frac{5}{16}\\) of 8<br \/>\nAnswer:<br \/>\n8 \u00d7 \\(\\frac{5}{16}\\) = \\(\\frac{5}{2}\\)<\/p>\n<p>Explanation:<br \/>\nThe given numbers are: 8 and \\(\\frac{5}{16}\\)<br \/>\nSo,<br \/>\n8 \u00d7 \\(\\frac{5}{16}\\)<br \/>\n= \\(\\frac{8}{1}\\) \u00d7 \\(\\frac{5}{16}\\)<br \/>\n= \\(\\frac{5 \u00d7 8}{1 \u00d7 16}\\)<br \/>\n= \\(\\frac{5}{2}\\)<br \/>\nHence,<br \/>\n8 \u00d7 \\(\\frac{5}{16}\\) = \\(\\frac{5}{2}\\)<\/p>\n<p>Question 11.<br \/>\n<strong>Modeling Real Life<\/strong><br \/>\nYou have 24 apples. You use \\(\\frac{1}{4}\\) of them to make a single serving of applesauce. How many apples do you not use?<br \/>\n<img loading=\"lazy\" class=\"alignnone size-full wp-image-16446\" src=\"https:\/\/ccssmathanswers.com\/wp-content\/uploads\/2020\/12\/Big-Ideas-Math-Answer-Key-Grade-5-Chapter-9-Multiply-Fractions-chp-11.png\" alt=\"Big Ideas Math Answer Key Grade 5 Chapter 9 Multiply Fractions chp 11\" width=\"204\" height=\"143\" \/><br \/>\nAnswer:<br \/>\nThe number of apples you do not use is: 18 apples<\/p>\n<p>Explanation:<br \/>\nIt is given that you have 24 apples and you use \\(\\frac{1}{4}\\) of them to make a single serving of applesauce.<br \/>\nSo,<br \/>\nThe number of apples you used = ( The total number of apples ) \u00d7 ( The fraction of apples you used to make a single serving of applesauce )<br \/>\n= 24 \u00d7 \\(\\frac{1}{4}\\)<br \/>\n= \\(\\frac{24}{1}\\) \u00d7 \\(\\frac{1}{4}\\)<br \/>\n= \\(\\frac{6}{1}\\)<br \/>\n= 6 apples<br \/>\nNow,<br \/>\nThe number of apples that do not use = ( The total number of apples ) &#8211; ( The number of apples you used )<br \/>\n= 24 &#8211; 6<br \/>\n= 18 apples<br \/>\nHence, from the above,<br \/>\nWe can conclude that the number of apples that do not use is: 18 apples<\/p>\n<p><strong>9.3 Multiply Fractions and Whole Numbers<\/strong><\/p>\n<p><strong>Multiply.<\/strong><br \/>\nQuestion 12.<br \/>\n\\(\\frac{3}{5}\\) \u00d7 15 = _______<br \/>\nAnswer:<br \/>\n15 \u00d7 \\(\\frac{3}{5}\\) = 9<\/p>\n<p>Explanation:<br \/>\nThe given numbers are: 15 and \\(\\frac{3}{5}\\)<br \/>\nSo,<br \/>\n15 \u00d7 \\(\\frac{3}{5}\\)<br \/>\n= \\(\\frac{15}{1}\\) \u00d7 \\(\\frac{3}{5}\\)<br \/>\n= \\(\\frac{15 \u00d7 3}{1 \u00d7 5}\\)<br \/>\n= \\(\\frac{9}{1}\\)<br \/>\n= 9<br \/>\nHence,<br \/>\n15 \u00d7 \\(\\frac{3}{5}\\) = 9<\/p>\n<p>Question 13.<br \/>\n\\(\\frac{9}{10}\\) \u00d7 30 = _______<br \/>\nAnswer:<br \/>\n30 \u00d7 \\(\\frac{9}{10}\\) = 27<\/p>\n<p>Explanation:<br \/>\nThe given numbers are: 30 and \\(\\frac{9}{10}\\)<br \/>\nSo,<br \/>\n30 \u00d7 \\(\\frac{9}{10}\\)<br \/>\n= \\(\\frac{30}{1}\\) \u00d7 \\(\\frac{9}{10}\\)<br \/>\n= \\(\\frac{30 \u00d7 9}{1 \u00d7 10}\\)<br \/>\n= \\(\\frac{27}{1}\\)<br \/>\n= 27<br \/>\nHence,<br \/>\n30 \u00d7 \\(\\frac{9}{10}\\) = 27<\/p>\n<p>Question 14.<br \/>\n48 \u00d7 \\(\\frac{3}{4}\\) = _______<br \/>\nAnswer:<br \/>\n48 \u00d7 \\(\\frac{3}{4}\\) = 36<\/p>\n<p>Explanation:<br \/>\nThe given numbers are: 48 and \\(\\frac{3}{4}\\)<br \/>\nSo,<br \/>\n48 \u00d7 \\(\\frac{3}{4}\\)<br \/>\n= \\(\\frac{48}{1}\\) \u00d7 \\(\\frac{3}{4}\\)<br \/>\n= \\(\\frac{48 \u00d7 3}{1 \u00d7 4}\\)<br \/>\n= \\(\\frac{36}{1}\\)<br \/>\n= 36<br \/>\nHence,<br \/>\n48 \u00d7 \\(\\frac{3}{4}\\) = 36<\/p>\n<p>Question 15.<br \/>\n11 \u00d7 \\(\\frac{5}{9}\\) = _______<br \/>\nAnswer:<br \/>\n11 \u00d7 \\(\\frac{5}{9}\\) = \\(\\frac{55}{9}\\)<\/p>\n<p>Explanation:<br \/>\nThe given numbers are: 11 and \\(\\frac{5}{9}\\)<br \/>\nSo,<br \/>\n11 \u00d7 \\(\\frac{5}{9}\\)<br \/>\n= \\(\\frac{11}{1}\\) \u00d7 \\(\\frac{5}{9}\\)<br \/>\n= \\(\\frac{5 \u00d7 11}{1 \u00d7 9}\\)<br \/>\n= \\(\\frac{55}{9}\\)<br \/>\nHence,<br \/>\n11 \u00d7 \\(\\frac{5}{9}\\) = \\(\\frac{55}{9}\\)<\/p>\n<p>Question 16.<br \/>\n\\(\\frac{1}{6}\\) \u00d7 19 = _______<br \/>\nAnswer:<br \/>\n19 \u00d7 \\(\\frac{1}{6}\\) = \\(\\frac{19}{6}\\)<\/p>\n<p>Explanation:<br \/>\nThe given numbers are: 19 and \\(\\frac{1}{6}\\)<br \/>\nSo,<br \/>\n19 \u00d7 \\(\\frac{1}{6}\\)<br \/>\n= \\(\\frac{19}{1}\\) \u00d7 \\(\\frac{1}{6}\\)<br \/>\n= \\(\\frac{19 \u00d7 1}{1 \u00d7 6}\\)<br \/>\n= \\(\\frac{19}{6}\\)<br \/>\nHence,<br \/>\n19 \u00d7 \\(\\frac{1}{6}\\) = \\(\\frac{19}{6}\\)<\/p>\n<p>Question 17.<br \/>\n7 \u00d7 \\(\\frac{13}{50}\\) = _______<br \/>\nAnswer:<br \/>\n7 \u00d7 \\(\\frac{13}{50}\\) = \\(\\frac{91}{50}\\)<\/p>\n<p>Explanation:<br \/>\nThe given numbers are: 7 and \\(\\frac{13}{50}\\)<br \/>\nSo,<br \/>\n7 \u00d7 \\(\\frac{13}{50}\\)<br \/>\n= \\(\\frac{7}{1}\\) \u00d7 \\(\\frac{13}{50}\\)<br \/>\n= \\(\\frac{7 \u00d7 13}{1 \u00d7 50}\\)<br \/>\n= \\(\\frac{91}{50}\\)<br \/>\nHence,<br \/>\n7 \u00d7 \\(\\frac{13}{50}\\) = \\(\\frac{91}{50}\\)<\/p>\n<p><strong>9.4 Use Models to Multiply Fractions<\/strong><\/p>\n<p><strong>Multiply. Use a model to help.<\/strong><br \/>\nQuestion 18.<br \/>\n\\(\\frac{1}{2}\\) \u00d7 \\(\\frac{1}{10}\\) = _______<br \/>\nAnswer:<br \/>\n\\(\\frac{1}{2}\\) \u00d7 \\(\\frac{1}{10}\\) = \\(\\frac{1}{20}\\)<\/p>\n<p>Explanation:<br \/>\nThe given numbers are: \\(\\frac{1}{2}\\) and \\(\\frac{1}{10}\\)<br \/>\nSo,<br \/>\n\\(\\frac{1}{2}\\) \u00d7 \\(\\frac{1}{10}\\)<br \/>\n= \\(\\frac{1 \u00d7 1}{2 \u00d7 10}\\)<br \/>\n= \\(\\frac{1}{20}\\)<br \/>\nHence,<br \/>\n\\(\\frac{1}{2}\\) \u00d7 \\(\\frac{1}{10}\\) = \\(\\frac{1}{20}\\)<\/p>\n<p>Question 19.<br \/>\n\\(\\frac{1}{5}\\) \u00d7 \\(\\frac{1}{9}\\) = _______<br \/>\nAnswer:<br \/>\n\\(\\frac{1}{5}\\) \u00d7 \\(\\frac{1}{9}\\) = \\(\\frac{1}{45}\\)<\/p>\n<p>Explanation:<br \/>\nThe given numbers are: \\(\\frac{1}{5}\\) and \\(\\frac{1}{9}\\)<br \/>\nSo,<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}\\) \u00d7 \\(\\frac{1}{9}\\) = \\(\\frac{1}{45}\\)<\/p>\n<p>Question 20.<br \/>\n\\(\\frac{1}{6}\\) \u00d7 \\(\\frac{1}{7}\\) = _______<br \/>\nAnswer:<br \/>\n\\(\\frac{1}{6}\\) \u00d7 \\(\\frac{1}{7}\\) = \\(\\frac{1}{42}\\)<\/p>\n<p>Explanation:<br \/>\nThe given numbers are: \\(\\frac{1}{6}\\) and \\(\\frac{1}{7}\\)<br \/>\nSo,<br \/>\n\\(\\frac{1}{6}\\) \u00d7 \\(\\frac{1}{7}\\)<br \/>\n= \\(\\frac{1 \u00d7 1}{6 \u00d7 7}\\)<br \/>\n= \\(\\frac{1}{42}\\)<br \/>\nHence,<br \/>\n\\(\\frac{1}{6}\\) \u00d7 \\(\\frac{1}{7}\\) = \\(\\frac{1}{42}\\)<\/p>\n<p>Question 21.<br \/>\n\\(\\frac{1}{3}\\) \u00d7 \\(\\frac{1}{8}\\) = _______<br \/>\nAnswer:<br \/>\n\\(\\frac{1}{3}\\) \u00d7 \\(\\frac{1}{8}\\) = \\(\\frac{1}{24}\\)<\/p>\n<p>Explanation:<br \/>\nThe given numbers are: \\(\\frac{1}{3}\\) and \\(\\frac{1}{8}\\)<br \/>\nSo,<br \/>\n\\(\\frac{1}{3}\\) \u00d7 \\(\\frac{1}{8}\\)<br \/>\n= \\(\\frac{1 \u00d7 1}{3 \u00d7 8}\\)<br \/>\n= \\(\\frac{1}{24}\\)<br \/>\nHence,<br \/>\n\\(\\frac{1}{3}\\) \u00d7 \\(\\frac{1}{8}\\) = \\(\\frac{1}{24}\\)<\/p>\n<p>Question 22.<br \/>\n\\(\\frac{2}{5}\\) \u00d7 \\(\\frac{1}{3}\\) = _______<br \/>\nAnswer:<br \/>\n\\(\\frac{2}{5}\\) \u00d7 \\(\\frac{1}{3}\\) = \\(\\frac{2}{15}\\)<\/p>\n<p>Explanation:<br \/>\nThe given numbers are: \\(\\frac{2}{5}\\) and \\(\\frac{1}{3}\\)<br \/>\nSo,<br \/>\n\\(\\frac{2}{5}\\) \u00d7 \\(\\frac{1}{3}\\)<br \/>\n= \\(\\frac{2 \u00d7 1}{5 \u00d7 3}\\)<br \/>\n= \\(\\frac{2}{15}\\)<br \/>\nHence,<br \/>\n\\(\\frac{2}{5}\\) \u00d7 \\(\\frac{1}{3}\\) = \\(\\frac{2}{15}\\)<\/p>\n<p>Question 23.<br \/>\n\\(\\frac{2}{3}\\) \u00d7 \\(\\frac{3}{5}\\) = _______<br \/>\nAnswer:<br \/>\n\\(\\frac{2}{3}\\) \u00d7 \\(\\frac{3}{5}\\) = \\(\\frac{2}{5}\\)<\/p>\n<p>Explanation:<br \/>\nThe given numbers are: \\(\\frac{2}{3}\\) and \\(\\frac{3}{5}\\)<br \/>\nSo,<br \/>\n\\(\\frac{2}{3}\\) \u00d7 \\(\\frac{3}{5}\\)<br \/>\n= \\(\\frac{2 \u00d7 3}{3 \u00d7 5}\\)<br \/>\n= \\(\\frac{2}{5}\\)<br \/>\nHence,<br \/>\n\\(\\frac{2}{3}\\) \u00d7 \\(\\frac{3}{5}\\) = \\(\\frac{2}{5}\\)<\/p>\n<p><strong>9.5 Multiply Fractions<\/strong><\/p>\n<p><strong>Evaluate.<\/strong><br \/>\nQuestion 24.<br \/>\n\\(\\frac{1}{3}\\) \u00d7 \\(\\frac{1}{8}\\) = _______<br \/>\nAnswer:<br \/>\n\\(\\frac{1}{3}\\) \u00d7 \\(\\frac{1}{8}\\) = \\(\\frac{1}{24}\\)<\/p>\n<p>Explanation:<br \/>\nThe given numbers are: \\(\\frac{1}{3}\\) and \\(\\frac{1}{8}\\)<br \/>\nSo,<br \/>\n\\(\\frac{1}{3}\\) \u00d7 \\(\\frac{1}{8}\\)<br \/>\n= \\(\\frac{1 \u00d7 1}{3 \u00d7 8}\\)<br \/>\n= \\(\\frac{1}{24}\\)<br \/>\nHence,<br \/>\n\\(\\frac{1}{3}\\) \u00d7 \\(\\frac{1}{8}\\) = \\(\\frac{1}{24}\\)<\/p>\n<p>Question 25.<br \/>\n\\(\\frac{5}{6}\\) \u00d7 \\(\\frac{1}{4}\\) = _______<br \/>\nAnswer:<br \/>\n\\(\\frac{5}{6}\\) \u00d7 \\(\\frac{1}{4}\\) = \\(\\frac{5}{24}\\)<\/p>\n<p>Explanation:<br \/>\nThe given numbers are: \\(\\frac{5}{6}\\) and \\(\\frac{1}{4}\\)<br \/>\nSo,<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,<br \/>\n\\(\\frac{5}{6}\\) \u00d7 \\(\\frac{1}{4}\\) = \\(\\frac{5}{24}\\)<\/p>\n<p>Question 26.<br \/>\n\\(\\frac{7}{2}\\) \u00d7 \\(\\frac{2}{5}\\) = _______<br \/>\nAnswer:<br \/>\n\\(\\frac{7}{2}\\) \u00d7 \\(\\frac{2}{5}\\) = \\(\\frac{7}{5}\\)<\/p>\n<p>Explanation:<br \/>\nThe given numbers are: \\(\\frac{7}{2}\\) and \\(\\frac{2}{5}\\)<br \/>\nSo,<br \/>\n\\(\\frac{7}{2}\\) \u00d7 \\(\\frac{2}{5}\\)<br \/>\n= \\(\\frac{7 \u00d7 2}{2 \u00d7 5}\\)<br \/>\n= \\(\\frac{7}{5}\\)<br \/>\nHence,<br \/>\n\\(\\frac{7}{2}\\) \u00d7 \\(\\frac{2}{5}\\) = \\(\\frac{7}{5}\\)<\/p>\n<p>Question 27.<br \/>\n\\(\\frac{9}{10}\\) \u00d7 \\(\\frac{3}{7}\\) = _______<br \/>\nAnswer:<br \/>\n\\(\\frac{9}{10}\\) \u00d7 \\(\\frac{3}{7}\\) = \\(\\frac{27}{70}\\)<\/p>\n<p>Explanation:<br \/>\nThe given numbers are: \\(\\frac{9}{10}\\) and \\(\\frac{3}{7}\\)<br \/>\nSo,<br \/>\n\\(\\frac{9}{10}\\) \u00d7 \\(\\frac{3}{7}\\)<br \/>\n= \\(\\frac{9 \u00d7 3}{7 \u00d7 10}\\)<br \/>\n= \\(\\frac{27}{70}\\)<br \/>\nHence,<br \/>\n\\(\\frac{9}{10}\\) \u00d7 \\(\\frac{3}{7}\\) = \\(\\frac{27}{70}\\)<\/p>\n<p>Question 28.<br \/>\n\\(\\frac{4}{5}\\) \u00d7 \\(\\frac{13}{100}\\) = _______<br \/>\nAnswer:<br \/>\n\\(\\frac{4}{5}\\) \u00d7 \\(\\frac{13}{100}\\) = \\(\\frac{52}{500}\\)<\/p>\n<p>Explanation:<br \/>\nThe given numbers are: \\(\\frac{4}{5}\\) and \\(\\frac{13}{100}\\)<br \/>\nSo,<br \/>\n\\(\\frac{4}{5}\\) \u00d7 \\(\\frac{13}{100}\\)<br \/>\n= \\(\\frac{4 \u00d7 13}{5 \u00d7 100}\\)<br \/>\n= \\(\\frac{52}{500}\\)<br \/>\nHence,<br \/>\n\\(\\frac{4}{5}\\) \u00d7 \\(\\frac{13}{100}\\) = \\(\\frac{52}{500}\\)<\/p>\n<p>Question 29.<br \/>\n\\(\\frac{11}{25}\\) \u00d7 \\(\\frac{3}{4}\\) = _______<br \/>\nAnswer:<br \/>\n\\(\\frac{11}{25}\\) \u00d7 \\(\\frac{3}{4}\\) = \\(\\frac{33}{100}\\)<\/p>\n<p>Explanation:<br \/>\nThe given numbers are: \\(\\frac{11}{25}\\) and \\(\\frac{3}{4}\\)<br \/>\nSo,<br \/>\n\\(\\frac{11}{25}\\) \u00d7 \\(\\frac{3}{4}\\)<br \/>\n= \\(\\frac{11 \u00d7 3}{25 \u00d7 4}\\)<br \/>\n= \\(\\frac{33}{100}\\)<br \/>\nHence,<br \/>\n\\(\\frac{11}{25}\\) \u00d7 \\(\\frac{3}{4}\\) = \\(\\frac{33}{100}\\)<\/p>\n<p>Question 30.<br \/>\n9 \u00d7 \\(\\left(\\frac{2}{9} \\times \\frac{1}{2}\\right)\\) = _______<br \/>\nAnswer:<br \/>\n9 \u00d7 ( \\(\\frac{1}{2}\\) \u00d7 \\(\\frac{2}{9}\\) ) = 1<\/p>\n<p>Explanation:<br \/>\nThe given numbers are: 9, \\(\\frac{1}{2}\\) and \\(\\frac{2}{9}\\)<br \/>\nSo,<br \/>\n9 \u00d7 (\\(\\frac{1}{2}\\) \u00d7 \\(\\frac{2}{9}\\) )<br \/>\n= 9 \u00d7 (\\(\\frac{1 \u00d7 2}{2 \u00d7 9}\\) )<br \/>\n=\u00a0 9 \u00d7 \\(\\frac{1}{9}\\)<br \/>\n= 1<br \/>\nHence,<br \/>\n9 \u00d7 ( \\(\\frac{1}{2}\\) \u00d7 \\(\\frac{2}{9}\\) ) = 1<\/p>\n<p>Question 31.<br \/>\n\\(\\left(\\frac{1}{10}+\\frac{7}{10}\\right)\\) \u00d7 \\(\\frac{3}{4}\\) = _______<br \/>\nAnswer:<br \/>\n\\(\\left(\\frac{1}{10}+\\frac{7}{10}\\right)\\) \u00d7 \\(\\frac{3}{4}\\) = \\(\\frac{3}{5}\\)<\/p>\n<p>Explanation:<br \/>\nThe given fractions are: \\(\\frac{1}{10}\\), \\(\\frac{7}{10}\\) and \\(\\frac{3}{4}\\)<br \/>\nSo,<br \/>\n\\(\\frac{3}{4}\\) \u00d7 (\\(\\frac{1}{10}\\) + \\(\\frac{7}{10}\\) )<br \/>\n= \\(\\frac{3}{4}\\) \u00d7 (\\(\\frac{7 \u00d7 1}{10}\\) )<br \/>\n=\u00a0 \\(\\frac{3}{4}\\) \u00d7 \\(\\frac{8}{10}\\)<br \/>\n= \\(\\frac{3 \u00d7 8}{4 \u00d7 10}\\)<br \/>\n= \\(\\frac{24}{40}\\)<br \/>\n= \\(\\frac{3}{5}\\)<br \/>\nHence,<br \/>\n\\(\\left(\\frac{1}{10}+\\frac{7}{10}\\right)\\) \u00d7 \\(\\frac{3}{4}\\) = \\(\\frac{3}{5}\\)<\/p>\n<p>Question 32.<br \/>\n\\(\\frac{4}{7}\\) \u00d7 \\(\\left(\\frac{5}{8}-\\frac{1}{4}\\right)\\) = _______<br \/>\nAnswer:<br \/>\n\\(\\frac{4}{7}\\) \u00d7 \\(\\left(\\frac{5}{8}-\\frac{1}{4}\\right)\\) = \\(\\frac{3}{14}\\)<\/p>\n<p>Explanation:<br \/>\nThe given fractions are: \\(\\frac{4}{7}\\), \\(\\frac{5}{8}\\) and \\(\\frac{1}{4}\\)<br \/>\nSo,<br \/>\n\\(\\frac{4}{7}\\) \u00d7 (\\(\\frac{5}{8}\\) &#8211; \\(\\frac{1}{4}\\) )<br \/>\n= \\(\\frac{4}{7}\\) \u00d7 (\\(\\frac{5 &#8211; 2}{8}\\) )<br \/>\n=\u00a0 \\(\\frac{4}{7}\\) \u00d7 \\(\\frac{3}{8}\\)<br \/>\n= \\(\\frac{3 \u00d7 4}{7 \u00d7 8}\\)<br \/>\n= \\(\\frac{12}{56}\\)<br \/>\n= \\(\\frac{3}{14}\\)<br \/>\nHence,<br \/>\n\\(\\frac{4}{7}\\) \u00d7 \\(\\left(\\frac{5}{8}-\\frac{1}{4}\\right)\\) = \\(\\frac{3}{14}\\)<\/p>\n<p><strong>9.6 Find Areas of Rectangles<\/strong><\/p>\n<p><strong>Use rectangles with unit fraction side lengths to find the area of the rectangle.<\/strong><br \/>\nQuestion 33.<br \/>\n<img loading=\"lazy\" class=\"alignnone size-full wp-image-16447\" src=\"https:\/\/ccssmathanswers.com\/wp-content\/uploads\/2020\/12\/Big-Ideas-Math-Answer-Key-Grade-5-Chapter-9-Multiply-Fractions-chp-33.png\" alt=\"Big Ideas Math Answer Key Grade 5 Chapter 9 Multiply Fractions chp 33\" width=\"169\" height=\"115\" \/><br \/>\nAnswer:<br \/>\nThe area of the rectangle is: \\(\\frac{1}{4}\\)<\/p>\n<p>Explanation:<br \/>\nThe given figure is:<br \/>\n<img loading=\"lazy\" class=\"alignnone size-full wp-image-16447\" src=\"https:\/\/ccssmathanswers.com\/wp-content\/uploads\/2020\/12\/Big-Ideas-Math-Answer-Key-Grade-5-Chapter-9-Multiply-Fractions-chp-33.png\" alt=\"Big Ideas Math Answer Key Grade 5 Chapter 9 Multiply Fractions chp 33\" width=\"169\" height=\"115\" \/><br \/>\nFrom the given figure,<br \/>\nThe side lengths of the rectangle are: \\(\\frac{3}{8}\\) and \\(\\frac{2}{3}\\)<br \/>\nSo,<br \/>\nThe area of the rectangle = \\(\\frac{3}{8}\\) \u00d7 \\(\\frac{2}{3}\\)<br \/>\n= \\(\\frac{2 \u00d7 3}{3 \u00d7 8}\\)<br \/>\n= \\(\\frac{1}{4}\\)<br \/>\nHence, from the above,<br \/>\nWe can conclude that the area of the rectangle is: \\(\\frac{1}{4}\\)<\/p>\n<p>Question 34.<br \/>\n<img loading=\"lazy\" class=\"alignnone size-full wp-image-16448\" src=\"https:\/\/ccssmathanswers.com\/wp-content\/uploads\/2020\/12\/Big-Ideas-Math-Answer-Key-Grade-5-Chapter-9-Multiply-Fractions-chp-34.png\" alt=\"Big Ideas Math Answer Key Grade 5 Chapter 9 Multiply Fractions chp 34\" width=\"102\" height=\"171\" \/><br \/>\nAnswer:<br \/>\nThe area of the rectangle is: \\(\\frac{35}{48}\\)<\/p>\n<p>Explanation:<br \/>\nThe given figure is:<br \/>\n<img loading=\"lazy\" class=\"alignnone size-full wp-image-16448\" src=\"https:\/\/ccssmathanswers.com\/wp-content\/uploads\/2020\/12\/Big-Ideas-Math-Answer-Key-Grade-5-Chapter-9-Multiply-Fractions-chp-34.png\" alt=\"Big Ideas Math Answer Key Grade 5 Chapter 9 Multiply Fractions chp 34\" width=\"102\" height=\"171\" \/><br \/>\nFrom the given figure,<br \/>\nThe side lengths of the rectangle are: \\(\\frac{7}{12}\\) and \\(\\frac{5}{4}\\)<br \/>\nSo,<br \/>\nThe area of the rectangle = \\(\\frac{7}{12}\\) \u00d7 \\(\\frac{5}{4}\\)<br \/>\n= \\(\\frac{7 \u00d7 5}{12 \u00d7 4}\\)<br \/>\n= \\(\\frac{35}{48}\\)<br \/>\nHence, from the above,<br \/>\nWe can conclude that the area of the rectangle is: \\(\\frac{35}{48}\\)<\/p>\n<p>Question 35.<br \/>\nFind the area of a rectangle with side lengths of \\(\\frac{2}{9}\\) and \\(\\frac{1}{10}\\).<br \/>\nAnswer:<br \/>\nThe area of the rectangle is: \\(\\frac{1}{45}\\)<\/p>\n<p>Explanation:<br \/>\nThe given side lengths of a rectangle are: \\(\\frac{2}{9}\\) and \\(\\frac{1}{10}\\)<br \/>\nSo,<br \/>\nThe area of the rectangle = \\(\\frac{2}{9}\\) \u00d7 \\(\\frac{1}{10}\\)<br \/>\n= \\(\\frac{2 \u00d7 1}{10 \u00d7 9}\\)<br \/>\n= \\(\\frac{1}{45}\\)<br \/>\nHence, from the above,<br \/>\nWe can conclude that the area of the rectangle is: \\(\\frac{1}{45}\\)<\/p>\n<p>Question 36.<br \/>\nFind the area of a with a side length of \\(\\frac{3}{4}\\).<br \/>\nAnswer:<br \/>\nThe area of the square is: \\(\\frac{9}{16}\\)<\/p>\n<p>Explanation:<br \/>\nThe given side length of a square is: \\(\\frac{3}{4}\\)<br \/>\nWe know that,<br \/>\nThe length of all sides of a square are equal<br \/>\nSo,<br \/>\nthe area of the square = \\(\\frac{3}{4}\\) \u00d7 \\(\\frac{3}{4}\\)<br \/>\n= \\(\\frac{3 \u00d7 3}{4 \u00d7 4}\\)<br \/>\n= \\(\\frac{9}{16}\\)<br \/>\nHence, from the above,<br \/>\nWe can conclude that the area of the square is: \\(\\frac{9}{16}\\)<\/p>\n<p><strong>9.7 Multiply Mixed Numbers<\/strong><\/p>\n<p><strong>Multiply.<\/strong><br \/>\nQuestion 37.<br \/>\n1\\(\\frac{1}{4}\\) \u00d7 2\\(\\frac{1}{4}\\) = _______<br \/>\nAnswer:<br \/>\n1\\(\\frac{1}{4}\\) \u00d7 2\\(\\frac{1}{4}\\) =\\(\\frac{45}{16}\\)<\/p>\n<p>Explanation:<br \/>\nThe given mixed fractions are: 1\\(\\frac{1}{4}\\) and 2\\(\\frac{1}{4}\\)<br \/>\nThe representation of 1\\(\\frac{1}{4}\\) and 2\\(\\frac{1}{4}\\) in the improper fraction form is: \\(\\frac{5}{4}\\) and \\(\\frac{9}{4}\\)<br \/>\nSo,<br \/>\n\\(\\frac{5}{4}\\) \u00d7 \\(\\frac{9}{4}\\)<br \/>\n= \\(\\frac{5 \u00d7 9}{4 \u00d7 4}\\)<br \/>\n= \\(\\frac{45}{16}\\)<br \/>\nHence,<br \/>\n1\\(\\frac{1}{4}\\) \u00d7 2\\(\\frac{1}{4}\\) =\\(\\frac{45}{16}\\)<\/p>\n<p>Question 38.<br \/>\n3\\(\\frac{4}{5}\\) \u00d7 1\\(\\frac{1}{2}\\) = _______<br \/>\nAnswer:<br \/>\n3\\(\\frac{4}{5}\\) \u00d7 1\\(\\frac{1}{2}\\) = \\(\\frac{57}{10}\\)<\/p>\n<p>Explanation:<br \/>\nThe given mixed fractions are: 3\\(\\frac{4}{5}\\) and 1\\(\\frac{1}{2}\\)<br \/>\nThe representation of 3\\(\\frac{4}{5}\\) and 1\\(\\frac{1}{2}\\) in the improper fraction form is: \\(\\frac{19}{5}\\)\u00a0 and \\(\\frac{3}{2}\\)<br \/>\nSo,<br \/>\n\\(\\frac{19}{5}\\) \u00d7 \\(\\frac{3}{2}\\)<br \/>\n= \\(\\frac{19 \u00d7 3}{5 \u00d7 2}\\)<br \/>\n= \\(\\frac{57}{10}\\)<br \/>\nHence,<br \/>\n3\\(\\frac{4}{5}\\) \u00d7 1\\(\\frac{1}{2}\\) = \\(\\frac{57}{10}\\)<\/p>\n<p>Question 39.<br \/>\n5\\(\\frac{1}{3}\\) \u00d7 4\\(\\frac{7}{8}\\) = _______<br \/>\nAnswer:<br \/>\n5\\(\\frac{1}{3}\\) \u00d7 4\\(\\frac{7}{8}\\) = \\(\\frac{624}{24}\\)<\/p>\n<p>Explanation:<br \/>\nThe given mixed fractions are: 5\\(\\frac{1}{3}\\) and 4\\(\\frac{7}{8}\\)<br \/>\nThe representation of 5\\(\\frac{1}{3}\\) and 4\\(\\frac{7}{8}\\) in the improper fraction form is: \\(\\frac{16}{3}\\)\u00a0 and \\(\\frac{39}{8}\\)<br \/>\nSo,<br \/>\n\\(\\frac{16}{3}\\) \u00d7 \\(\\frac{39}{8}\\)<br \/>\n= \\(\\frac{39 \u00d7 16}{3 \u00d7 8}\\)<br \/>\n= \\(\\frac{624}{24}\\)<br \/>\nHence,<br \/>\n5\\(\\frac{1}{3}\\) \u00d7 4\\(\\frac{7}{8}\\) = \\(\\frac{624}{24}\\)<\/p>\n<p>Question 40.<br \/>\n4\\(\\frac{5}{6}\\) \u00d7 2\\(\\frac{9}{10}\\) \u00d7 \\(\\frac{1}{8}\\) = _______<br \/>\nAnswer:<br \/>\n4\\(\\frac{5}{6}\\) \u00d7 2\\(\\frac{9}{10}\\) \u00d7 \\(\\frac{1}{8}\\) = \\(\\frac{841}{480}\\)<\/p>\n<p>Explanation:<br \/>\nThe given mixed fractions are: 4\\(\\frac{5}{6}\\), 2\\(\\frac{9}{10}\\) and \\(\\frac{1}{8}\\)<br \/>\nThe representation of 4\\(\\frac{5}{6}\\) and 2\\(\\frac{9}{10}\\) in the improper fraction form is: \\(\\frac{29}{6}\\) and \\(\\frac{29}{10}\\)<br \/>\nSo,<br \/>\n\\(\\frac{29}{6}\\) \u00d7 \\(\\frac{29}{10}\\)\u00a0 \u00d7 \\(\\frac{1}{8}\\)<br \/>\n= \\(\\frac{29 \u00d7 29 \u00d7 1}{8 \u00d7 10 \u00d7 6}\\)<br \/>\n= \\(\\frac{841}{480}\\)<br \/>\nHence,<br \/>\n4\\(\\frac{5}{6}\\) \u00d7 2\\(\\frac{9}{10}\\) \u00d7 \\(\\frac{1}{8}\\) = \\(\\frac{841}{480}\\)<\/p>\n<p>Question 41.<br \/>\n<strong>Logic<\/strong><br \/>\nFind the missing numbers.<br \/>\n<img loading=\"lazy\" class=\"alignnone size-full wp-image-16449\" src=\"https:\/\/ccssmathanswers.com\/wp-content\/uploads\/2020\/12\/Big-Ideas-Math-Answer-Key-Grade-5-Chapter-9-Multiply-Fractions-chp-41.png\" alt=\"Big Ideas Math Answer Key Grade 5 Chapter 9 Multiply Fractions chp 41\" width=\"159\" height=\"77\" \/><br \/>\nAnswer:<br \/>\nThe missing numbers are: 2 and 11<\/p>\n<p>Explanation:<br \/>\nLet the missing numbers be: p and q<br \/>\nSo,<br \/>\n4\\(\\frac{1}{p}\\) \u00d7 2\\(\\frac{1}{5}\\) = 9\\(\\frac{q}{10}\\)<br \/>\nSo,<br \/>\nTo solve the mixed numbers, we can separate the whole numbers and the fraction numbers<br \/>\nSo,<br \/>\n\\(\\frac{1}{p}\\) \u00d7 2\\(\\frac{1}{5}\\) = \\(\\frac{q}{10}\\)<br \/>\n\\(\\frac{1}{p}\\) \u00d7 \\(\\frac{11}{5}\\) = \\(\\frac{q}{10}\\)<br \/>\n\\(\\frac{1 \u00d7 11}{p \u00d7 5}\\) = \\(\\frac{q}{10}\\)<br \/>\n\\(\\frac{11}{5p}\\) = \\(\\frac{q}{10}\\)<br \/>\nBy comparing LHS and RHS<br \/>\nq = 11 and p = 2<br \/>\nHence, from the above,<br \/>\nWe can conclude that the missing numbers are: 2 and 11<\/p>\n<p><strong>9.8 Compare Factors and Products<\/strong><\/p>\n<p><strong>Without calculating, tell whether the product is less than, greater than, or equal to each of its factors.<\/strong><br \/>\nQuestion 42.<br \/>\n1\\(\\frac{1}{2}\\) \u00d7 3<br \/>\nAnswer:<br \/>\nThe value of 1\\(\\frac{1}{2}\\) \u00d7 3 is greater than 3<\/p>\n<p>Explanation:<br \/>\nThe given numbers are: 3 and 1\\(\\frac{1}{2}\\)<br \/>\nThe representation of 1\\(\\frac{1}{2}\\) in the mixed form is: \\(\\frac{3}{2}\\)<br \/>\nSo,<br \/>\n\\(\\frac{3}{2}\\) is greater than 1<br \/>\nSo,<br \/>\n\\(\\frac{3}{2}\\) \u00d7 3 is greater than 3<br \/>\nHence, from the above,<br \/>\nWe can conclude that the value of 1\\(\\frac{1}{2}\\) \u00d7 3 is greater than 3<\/p>\n<p>Question 43.<br \/>\n\\(\\frac{1}{8}\\) \u00d7 \\(\\frac{1}{6}\\)<br \/>\nAnswer:<br \/>\nThe value of \\(\\frac{1}{8}\\) \u00d7 \\(\\frac{1}{6}\\) is less than 1<\/p>\n<p>Explanation:<br \/>\nThe given numbers are: \\(\\frac{1}{8}\\) and \\(\\frac{1}{6}\\)<br \/>\nSo,<br \/>\n\\(\\frac{1}{8}\\) is less than 1<br \/>\n\\(\\frac{1}{6}\\) is less than 1<br \/>\nSo,<br \/>\n\\(\\frac{1}{8}\\) \u00d7 \\(\\frac{1}{6}\\) is less than 1<br \/>\nHence, from the above,<br \/>\nWe can conclude that the value of \\(\\frac{1}{8}\\) \u00d7 \\(\\frac{1}{6}\\) is less than 1<\/p>\n<p>Question 44.<br \/>\n\\(\\frac{5}{5}\\) \u00d7 2\\(\\frac{4}{7}\\)<br \/>\nAnswer:<br \/>\nThe value of \\(\\frac{5}{5}\\) \u00d7 2\\(\\frac{4}{7}\\) is greater than 1<\/p>\n<p>Explanation:<br \/>\nThe given numbers are: \\(\\frac{5}{5}\\) and 2\\(\\frac{4}{7}\\)<br \/>\nThe representation of 2\\(\\frac{4}{7}\\) in the improper fraction form is: \\(\\frac{18}{7}\\)<br \/>\nSo,<br \/>\n\\(\\frac{18}{7}\\) is greater than 1<br \/>\n\\(\\frac{5}{5}\\) is 1<br \/>\nSo,<br \/>\n\\(\\frac{5}{5}\\) \u00d7 2\\(\\frac{4}{7}\\) is greater than 1<br \/>\nHence, from the above,<br \/>\nWe can conclude that the value of \\(\\frac{5}{5}\\) \u00d7 2\\(\\frac{4}{7}\\) is greater than 1<\/p>\n<p>Question 45.<br \/>\n\\(\\frac{3}{4}\\) \u00d7 2\\(\\frac{11}{12}\\)<br \/>\nAnswer:<br \/>\nThe value of \\(\\frac{3}{4}\\) \u00d7 2\\(\\frac{11}{12}\\) is greater than 1<\/p>\n<p>Explanation:<br \/>\nThe given numbers are: \\(\\frac{3}{4}\\) and 2\\(\\frac{11}{12}\\)<br \/>\nThe representation of 2\\(\\frac{11}{12}\\) in the improper fraction form is: \\(\\frac{35}{12}\\)<br \/>\nSo,<br \/>\n\\(\\frac{35}{12}\\) is greater than 1<br \/>\n\\(\\frac{3}{4}\\) is less than 1<br \/>\nSo,<br \/>\n\\(\\frac{3}{4}\\) \u00d7 2\\(\\frac{11}{12}\\) is greater than 1<br \/>\nHence, from the above,<br \/>\nWe can conclude that the value of \\(\\frac{3}{4}\\) \u00d7 2\\(\\frac{11}{12}\\) is greater than 1<\/p>\n<p>Question 46.<br \/>\n3\\(\\frac{1}{9}\\) \u00d7 2\\(\\frac{7}{8}\\)<br \/>\nAnswer:<br \/>\nThe value of 3\\(\\frac{1}{9}\\) \u00d7 2\\(\\frac{7}{8}\\) is greater than 1<\/p>\n<p>Explanation:<br \/>\nThe given mixed fractions are: 3\\(\\frac{1}{9}\\) and 2\\(\\frac{7}{8}\\)<br \/>\nThe representation of 3\\(\\frac{1}{9}\\) and 2\\(\\frac{7}{8}\\) in the improper fractions form is: \\(\\frac{28}{9}\\) and \\(\\frac{23}{8}\\)<br \/>\nSo,<br \/>\n\\(\\frac{28}{9}\\) is greater than 1<br \/>\n\\(\\frac{23}{8}\\) is greater than 1<br \/>\nSo,<br \/>\n3\\(\\frac{1}{9}\\) \u00d7 2\\(\\frac{7}{8}\\) is greater than 1<br \/>\nHence, from the above,<br \/>\nWe can conclude that the value of 3\\(\\frac{1}{9}\\) \u00d7 2\\(\\frac{7}{8}\\) is greater than 1<\/p>\n<p>Question 47.<br \/>\n\\(\\frac{9}{8}\\) \u00d7 \\(\\frac{5}{2}\\)<br \/>\nAnswer:<br \/>\nThe value of \\(\\frac{9}{8}\\) \u00d7 \\(\\frac{5}{2}\\) is greater than 1<\/p>\n<p>Explanation:<br \/>\nThe given fractions are: \\(\\frac{9}{8}\\) and \\(\\frac{5}{2}\\)<br \/>\nSo,<br \/>\n\\(\\frac{9}{8}\\) is greater than 1<br \/>\nSo,<br \/>\n\\(\\frac{9}{8}\\) \u00d7 \\(\\frac{5}{2}\\) is greater than 1<br \/>\nHence, from the above,<br \/>\nWe can conclude that the value of \\(\\frac{9}{8}\\) \u00d7 \\(\\frac{5}{2}\\) is greater than 1<\/p>\n<p><em>Conclusion:<\/em><\/p>\n<p>Hope the information provided in the above answer key is beneficial for all the students of grade 5. Follow our Big Ideas Math Answers and make your learning fun and interesting.<\/p>\n","protected":false},"excerpt":{"rendered":"<p>Are you in the search of Big Ideas Math Answers Grade 5 Chapter 9 Multiply Fractions? If yes, you are on the correct page. Check out the detailed explanation for all the problems available on Big Ideas Grade 5 Chapter 9 Multiply Fractions Math Answers. You can easily become a math expert by referring to &#8230; <a title=\"Big Ideas Math Answers Grade 5 Chapter 9 Multiply Fractions\" class=\"read-more\" href=\"https:\/\/bigideasmathanswers.com\/big-ideas-math-answers-grade-5-chapter-9\/\" aria-label=\"More on Big Ideas Math Answers Grade 5 Chapter 9 Multiply Fractions\">Read more<\/a><\/p>\n","protected":false},"author":7,"featured_media":89682,"comment_status":"open","ping_status":"open","sticky":false,"template":"","format":"standard","meta":{"spay_email":""},"categories":[4],"tags":[],"jetpack_featured_media_url":"https:\/\/bigideasmathanswers.com\/wp-content\/uploads\/2020\/12\/Big-Ideas-Math-Answers-Grade-5-Chapter-9-Multiply-Fractions.png","_links":{"self":[{"href":"https:\/\/bigideasmathanswers.com\/wp-json\/wp\/v2\/posts\/16343"}],"collection":[{"href":"https:\/\/bigideasmathanswers.com\/wp-json\/wp\/v2\/posts"}],"about":[{"href":"https:\/\/bigideasmathanswers.com\/wp-json\/wp\/v2\/types\/post"}],"author":[{"embeddable":true,"href":"https:\/\/bigideasmathanswers.com\/wp-json\/wp\/v2\/users\/7"}],"replies":[{"embeddable":true,"href":"https:\/\/bigideasmathanswers.com\/wp-json\/wp\/v2\/comments?post=16343"}],"version-history":[{"count":1,"href":"https:\/\/bigideasmathanswers.com\/wp-json\/wp\/v2\/posts\/16343\/revisions"}],"predecessor-version":[{"id":90252,"href":"https:\/\/bigideasmathanswers.com\/wp-json\/wp\/v2\/posts\/16343\/revisions\/90252"}],"wp:featuredmedia":[{"embeddable":true,"href":"https:\/\/bigideasmathanswers.com\/wp-json\/wp\/v2\/media\/89682"}],"wp:attachment":[{"href":"https:\/\/bigideasmathanswers.com\/wp-json\/wp\/v2\/media?parent=16343"}],"wp:term":[{"taxonomy":"category","embeddable":true,"href":"https:\/\/bigideasmathanswers.com\/wp-json\/wp\/v2\/categories?post=16343"},{"taxonomy":"post_tag","embeddable":true,"href":"https:\/\/bigideasmathanswers.com\/wp-json\/wp\/v2\/tags?post=16343"}],"curies":[{"name":"wp","href":"https:\/\/api.w.org\/{rel}","templated":true}]}}