{"id":12974,"date":"2023-01-03T10:53:26","date_gmt":"2023-01-03T05:23:26","guid":{"rendered":"https:\/\/ccssanswers.com\/?p=12974"},"modified":"2023-01-04T12:01:55","modified_gmt":"2023-01-04T06:31:55","slug":"big-ideas-math-answers-grade-4-chapter-9","status":"publish","type":"post","link":"https:\/\/ccssanswers.com\/big-ideas-math-answers-grade-4-chapter-9\/","title":{"rendered":"Big Ideas Math Answers Grade 4 Chapter 9 Multiply Whole Numbers and Fractions"},"content":{"rendered":"<p>Download Big Ideas Math Answers Grade 4 Chapter 9 Multiply Whole Numbers and Fractions for free of cost. We are here to help you to overcome the difficulties in maths. Enhance your math skills by practicing the problems from our <a href=\"https:\/\/ccssanswers.com\/big-ideas-math-answers-grade-4\/\" target=\"_blank\" rel=\"noopener\">Big Ideas Math Answers Grade 4<\/a> Chapter 9 Multiply Whole Numbers and Fractions. Test yourself by solving the problems given in the performance task and chapter practice.<\/p>\n<h2>Big Ideas Math Book 4th Grade Answer Key Chapter 9 Multiply Whole Numbers and Fractions<\/h2>\n<p>The topics covered in Multiply Whole Numbers and Fractions are Understand Multiples of Unit Fractions, Fraction Operations, Understand Multiples of Fractions, Understand Multiples of Fractions, and so on. We have provided solutions as per the topics provided in the chapter. So go through the BIM Grade 4 Chapter 9 Solution Key topicwise and start preparing now.<\/p>\n<p><strong>Lesson: 1 Understand Multiples of Unit Fractions<\/strong><\/p>\n<ul>\n<li><a href=\"#Lesson_9.1_Understand_Multiples_of_Unit_Fractions\">Lesson 9.1 Understand Multiples of Unit Fractions<\/a><\/li>\n<li><a href=\"#Understand Multiples_of_Unit_Fractions_Homework_&amp;_practice_9.1\">Understand Multiples of Unit Fractions Homework &amp; practice 9.1<\/a><\/li>\n<\/ul>\n<p><strong>Lesson: 2 Understand Multiples of Fractions<\/strong><\/p>\n<ul>\n<li><a href=\"#Lesson_9.2_Understand_Multiples_of_Fractions\">Lesson 9.2 Understand Multiples of Fractions<\/a><\/li>\n<li><a href=\"#Understand_Multiples_of_Fractions_Homework_&amp;_Practice_9.2\">Understand Multiples of Fractions Homework &amp; Practice 9.2<\/a><\/li>\n<\/ul>\n<p><strong>Lesson: 3 Multiply Whole Numbers and Fractions<\/strong><\/p>\n<ul>\n<li><a href=\"#Lesson_9.3_Multiply_Whole_Numbers_and_Fractions\">Lesson 9.3 Multiply Whole Numbers and Fractions<\/a><\/li>\n<li><a href=\"#Multiply_Whole_Numbers_and_Fractions_Homework_&amp;_practice_9.3\">Multiply Whole Numbers and Fractions Homework &amp; practice 9.3<\/a><\/li>\n<\/ul>\n<p><strong>Lesson: 4 Multiply Whole Numbers and Mixed Numbers<\/strong><\/p>\n<ul>\n<li><a href=\"#Lesson_9.4_Multiply_Whole_Numbers_and_Mixed_Numbers\">Lesson 9.4 Multiply Whole Numbers and Mixed Numbers<\/a><\/li>\n<li><a href=\"#Multiply_Whole_Numbers_and_Mixed_Numbers_Homework_&amp;_Practice_9.4\">Multiply Whole Numbers and Mixed Numbers Homework &amp; Practice 9.4<\/a><\/li>\n<\/ul>\n<p><strong>Lesson: 5 Problem Solving: Fraction Operations<\/strong><\/p>\n<ul>\n<li><a href=\"#Lesson_9.5_Problem_Solving:_Fraction_Operations\">Lesson 9.5 Problem Solving: Fraction Operations<\/a><\/li>\n<li><a href=\"#Problem_Solving:_Fraction_Operations_Homework_&amp;_Practice_9.5\">Problem Solving: Fraction Operations Homework &amp; Practice 9.5<\/a><\/li>\n<\/ul>\n<p><strong>Performance Task<\/strong><\/p>\n<ul>\n<li><a href=\"#Multiply_Whole_Numbers_and_Fractions_Performance_Task\">Multiply Whole Numbers and Fractions Performance Task<\/a><\/li>\n<li><a href=\"#Multiply_Whole_Numbers_and_Fractions_Activity\">Multiply Whole Numbers and Fractions Activity<\/a><\/li>\n<li><a href=\"#Multiply_Whole_Numbers_and_Fractions_Chapter_Practice\">Multiply Whole Numbers and Fractions Chapter Practice<\/a><\/li>\n<\/ul>\n<h3><a id=\"Lesson_9.1_Understand_Multiples_of_Unit_Fractions\"><\/a>Lesson 9.1 Understand Multiples of Unit Fractions<\/h3>\n<p><strong>Explore and Grow<\/strong><\/p>\n<p>Draw a model of any fraction using unit fractions. Then write an addition equation to represent your model.<br \/>\n<strong>Reasoning<\/strong><br \/>\nHow can you rewrite the equation using multiplication? Explain.<br \/>\nAnswer:<br \/>\nLet us take the fraction as \\(\\frac{3}{5}\\) we draw a model using fractions as below<br \/>\n<img decoding=\"async\" loading=\"lazy\" class=\"alignnone wp-image-20960 size-full\" src=\"https:\/\/ccssanswers.com\/wp-content\/uploads\/2020\/12\/9-Multiply-Whole-Numbers-and-Fractions-1-1.bmp\" alt=\"\" width=\"354\" height=\"207\" srcset=\"https:\/\/ccssanswers.com\/wp-content\/uploads\/2020\/12\/9-Multiply-Whole-Numbers-and-Fractions-1-1.bmp 354w, https:\/\/ccssanswers.com\/wp-content\/uploads\/2020\/12\/9-Multiply-Whole-Numbers-and-Fractions-1-1-300x175.jpg 300w\" sizes=\"(max-width: 354px) 100vw, 354px\" \/><img decoding=\"async\" loading=\"lazy\" class=\"alignnone wp-image-23743 size-full\" src=\"https:\/\/ccssanswers.com\/wp-content\/uploads\/2020\/12\/9-Multiply-Whole-Numbers-and-Fractions-2-2.bmp\" alt=\"\" width=\"672\" height=\"307\" srcset=\"https:\/\/ccssanswers.com\/wp-content\/uploads\/2020\/12\/9-Multiply-Whole-Numbers-and-Fractions-2-2.bmp 672w, https:\/\/ccssanswers.com\/wp-content\/uploads\/2020\/12\/9-Multiply-Whole-Numbers-and-Fractions-2-2-300x137.jpg 300w\" sizes=\"(max-width: 672px) 100vw, 672px\" \/><br \/>\nAddition equation to represent \\(\\frac{3}{5}\\)\u00a0 model is \\(\\frac{3}{5}\\) = \\(\\frac{1}{5}\\) +<br \/>\n\\(\\frac{1}{5}\\) +\\(\\frac{1}{5}\\) to rewrite the equation using multiplication,<br \/>\nWe write the equation as \\(\\frac{3}{5}\\) = \\(\\frac{1}{5}\\) +\\(\\frac{1}{5}\\) +<br \/>\n\\(\\frac{1}{5}\\) = 3 X \\(\\frac{1}{5}\\) as the fraction \\(\\frac{3}{5}\\)<br \/>\nrepresents 3 parts that are each \\(\\frac{1}{5}\\) of the whole.<\/p>\n<p><strong>Think and Grow: Multiples of Unit Fractions<\/strong><\/p>\n<p>Any fraction can be written as a multiple of a unit fraction with a like denominator.<br \/>\n<strong>Example<\/strong><br \/>\nWrite \\(\\frac{5}{8}\\) as a multiple of a unit fraction.<br \/>\nThe fraction \\(\\frac{5}{8}\\) represents 5 parts that are each \\(\\frac{1}{8}\\) of the whole.<br \/>\n<img decoding=\"async\" loading=\"lazy\" class=\"alignnone size-full wp-image-13054\" src=\"https:\/\/ccssanswers.com\/wp-content\/uploads\/2020\/12\/Big-Ideas-Math-Answers-Grade-4-Chapter-9-Multiply-Whole-Numbers-and-Fractions-500.png\" alt=\"Big Ideas Math Answers Grade 4 Chapter 9 Multiply Whole Numbers and Fractions 500\" width=\"633\" height=\"412\" srcset=\"https:\/\/ccssanswers.com\/wp-content\/uploads\/2020\/12\/Big-Ideas-Math-Answers-Grade-4-Chapter-9-Multiply-Whole-Numbers-and-Fractions-500.png 633w, https:\/\/ccssanswers.com\/wp-content\/uploads\/2020\/12\/Big-Ideas-Math-Answers-Grade-4-Chapter-9-Multiply-Whole-Numbers-and-Fractions-500-300x195.png 300w\" sizes=\"(max-width: 633px) 100vw, 633px\" \/><br \/>\nAnswer:<br \/>\n<img decoding=\"async\" loading=\"lazy\" class=\"alignnone wp-image-21021 size-full\" src=\"https:\/\/ccssanswers.com\/wp-content\/uploads\/2020\/12\/9-Multiply-Whole-Numbers-and-Fractions-3-2.bmp\" alt=\"\" width=\"661\" height=\"363\" srcset=\"https:\/\/ccssanswers.com\/wp-content\/uploads\/2020\/12\/9-Multiply-Whole-Numbers-and-Fractions-3-2.bmp 661w, https:\/\/ccssanswers.com\/wp-content\/uploads\/2020\/12\/9-Multiply-Whole-Numbers-and-Fractions-3-2-300x165.jpg 300w\" sizes=\"(max-width: 661px) 100vw, 661px\" \/><\/p>\n<p><strong>Show and Grow<\/strong><\/p>\n<p>Write the fraction as a multiple of a unit fraction.<\/p>\n<p>Question 1.<br \/>\n<img decoding=\"async\" loading=\"lazy\" class=\"alignnone size-full wp-image-13033\" src=\"https:\/\/ccssanswers.com\/wp-content\/uploads\/2020\/12\/Big-Ideas-Math-Answers-Grade-4-Chapter-9-Multiply-Whole-Numbers-and-Fractions-1.png\" alt=\"Big Ideas Math Answers Grade 4 Chapter 9 Multiply Whole Numbers and Fractions 1\" width=\"140\" height=\"122\" \/><br \/>\nAnswer:<br \/>\n\\(\\frac{2}{3}\\) = \\(\\frac{1}{3}\\) +\\(\\frac{1}{3}\\)<br \/>\n=\u00a0 2 X \\(\\frac{1}{3}\\).<\/p>\n<p>Explanation:<br \/>\nWe write \\(\\frac{2}{3}\\) in addition equation as \\(\\frac{2}{3}\\) =\\(\\frac{1}{3}\\) +<br \/>\n\\(\\frac{1}{3}\\) and multiplication as fraction \\(\\frac{2}{3}\\) represents 2 parts that are each<br \/>\n\\(\\frac{1}{3}\\) of the whole, \\(\\frac{2}{3}\\) =2 X \\(\\frac{1}{3}\\).<\/p>\n<p>Question 2.<br \/>\n<img decoding=\"async\" loading=\"lazy\" class=\"alignnone size-full wp-image-13056\" src=\"https:\/\/ccssanswers.com\/wp-content\/uploads\/2020\/12\/Big-Ideas-Math-Solutions-Grade-4-Chapter-9-Multiply-Whole-Numbers-and-Fractions-2.png\" alt=\"Big Ideas Math Solutions Grade 4 Chapter 9 Multiply Whole Numbers and Fractions 2\" width=\"199\" height=\"130\" \/><br \/>\nAnswer:<br \/>\n\\(\\frac{4}{8}\\) = \\(\\frac{1}{8}\\) +\\(\\frac{1}{8}\\) + \\(\\frac{1}{8}\\) +<br \/>\n\\(\\frac{1}{8}\\) = 4 X \\(\\frac{1}{8}\\).<br \/>\nExplanation:<br \/>\nWe write \\(\\frac{4}{8}\\) in addition equation as \\(\\frac{4}{8}\\) = \\(\\frac{1}{8}\\) +<br \/>\n\\(\\frac{1}{8}\\)\u00a0 + \\(\\frac{1}{8}\\) +\\(\\frac{1}{8}\\) and multiplication as<br \/>\nfraction \\(\\frac{4}{8}\\) represents 4 parts that are each \\(\\frac{1}{8}\\) of the whole,<br \/>\n\\(\\frac{4}{8}\\) =4 X \\(\\frac{1}{8}\\).<\/p>\n<p>Question 3.<br \/>\n\\(\\frac{6}{5}\\)<br \/>\nAnswer:<br \/>\n\\(\\frac{6}{5}\\) = \\(\\frac{1}{5}\\)+\\(\\frac{1}{5}\\) +\\(\\frac{1}{5}\\)+<br \/>\n\\(\\frac{1}{5}\\)+\\(\\frac{1}{5}\\)+\\(\\frac{1}{5}\\) = 6 X \\(\\frac{1}{5}\\).<\/p>\n<p>Explanation:<br \/>\nWe write \\(\\frac{6}{5}\\) in addition equation as \\(\\frac{6}{5}\\)= \\(\\frac{1}{5}\\)+<br \/>\n\\(\\frac{1}{5}\\) +\\(\\frac{1}{5}\\)+\\(\\frac{1}{5}\\)+\\(\\frac{1}{5}\\)+<br \/>\n\\(\\frac{1}{5}\\) and multiplication as fraction \\(\\frac{6}{5}\\) represents 6 parts<br \/>\nthat are \\(\\frac{1}{5}\\) of the whole \\(\\frac{6}{5}\\) = 6 X \\(\\frac{1}{5}\\).<\/p>\n<p>Question 4.<br \/>\n\\(\\frac{7}{100}\\)<br \/>\nAnswer:<br \/>\n\\(\\frac{7}{100}\\) = \\(\\frac{1}{100}\\) + \\(\\frac{1}{100}\\) + \\(\\frac{1}{100}\\) +<br \/>\n\\(\\frac{1}{100}\\)+ \\(\\frac{1}{100}\\)+ \\(\\frac{1}{100}\\)+ \\(\\frac{1}{100}\\)<br \/>\n= 7 X \\(\\frac{1}{100}\\).<\/p>\n<p>Explanation:<br \/>\nWe write \\(\\frac{7}{100}\\) in addition equation as \\(\\frac{7}{100}\\)= \\(\\frac{1}{100}\\) +<br \/>\n\\(\\frac{1}{100}\\) + \\(\\frac{1}{100}\\) + \\(\\frac{1}{100}\\)+ \\(\\frac{1}{100}\\)+<br \/>\n\\(\\frac{1}{100}\\)+ \\(\\frac{1}{100}\\) and multiplication as fraction \\(\\frac{7}{100}\\) represents<br \/>\n7 parts that are \\(\\frac{1}{100}\\) of the whole, \\(\\frac{7}{100}\\)= 7 X \\(\\frac{1}{100}\\).<\/p>\n<p><strong>Apply and Grow: Practice<\/strong><\/p>\n<p>Write the fraction as a multiple of a unit fraction.<\/p>\n<p>Question 5.<br \/>\n\\(\\frac{2}{6}\\)<br \/>\nAnswer:<br \/>\n\\(\\frac{2}{6}\\) = \\(\\frac{1}{6}\\) + \\(\\frac{1}{6}\\)<br \/>\n= 2 X \\(\\frac{1}{6}\\).<\/p>\n<p>Explanation:<br \/>\nWe write \\(\\frac{2}{6}\\) in addition equation as \\(\\frac{2}{6}\\)= \\(\\frac{1}{6}\\) +<br \/>\n\\(\\frac{1}{6}\\) and multiplication as fraction \\(\\frac{2}{6}\\) represents 2 parts that are<br \/>\n\\(\\frac{1}{6}\\) of the whole,\\(\\frac{2}{6}\\) = 2 X \\(\\frac{1}{6}\\).<\/p>\n<p>Question 6.<br \/>\n\\(\\frac{6}{8}\\)<br \/>\nAnswer:<br \/>\n\\(\\frac{6}{8}\\) = \\(\\frac{1}{8}\\) + \\(\\frac{1}{8}\\) + \\(\\frac{1}{8}\\)+<br \/>\n\\(\\frac{1}{8}\\)+ \\(\\frac{1}{8}\\)+ \\(\\frac{1}{8}\\) = 6 X \\(\\frac{1}{8}\\).<\/p>\n<p>Explanation:<br \/>\nWe write \\(\\frac{6}{8}\\) in addition equation as \\(\\frac{6}{8}\\) = \\(\\frac{1}{8}\\) +<br \/>\n\\(\\frac{1}{8}\\) + \\(\\frac{1}{8}\\)+ \\(\\frac{1}{8}\\)+ \\(\\frac{1}{8}\\)+<br \/>\n\\(\\frac{1}{8}\\) and multiplication as fraction \\(\\frac{6}{8}\\) represents 6 parts that are<br \/>\n\\(\\frac{1}{8}\\) of the whole, \\(\\frac{6}{8}\\) =6 X \\(\\frac{1}{8}\\).<\/p>\n<p>Question 7.<br \/>\n\\(\\frac{5}{4}\\)<br \/>\nAnswer:<br \/>\n\\(\\frac{5}{4}\\) = \\(\\frac{1}{4}\\) + \\(\\frac{1}{4}\\) +\\(\\frac{1}{4}\\) +<br \/>\n\\(\\frac{1}{4}\\) +\\(\\frac{1}{4}\\) = 5 X \\(\\frac{1}{4}\\).<\/p>\n<p>Explanation:<br \/>\nWe write \\(\\frac{5}{4}\\) in addition equation as \\(\\frac{5}{4}\\)=\\(\\frac{1}{4}\\) +<br \/>\n\\(\\frac{1}{4}\\) +\\(\\frac{1}{4}\\) +\\(\\frac{1}{4}\\) + \\(\\frac{1}{4}\\)<br \/>\nand multiplication as fraction \\(\\frac{5}{4}\\) represents 5 parts that are \\(\\frac{1}{4}\\)<br \/>\nof the whole, \\(\\frac{5}{4}\\) = 5 X \\(\\frac{1}{4}\\).<\/p>\n<p>Question 8.<br \/>\n\\(\\frac{3}{12}\\)<br \/>\nAnswer:<br \/>\n\\(\\frac{3}{12}\\)= \\(\\frac{1}{12}\\) + \\(\\frac{1}{12}\\) +<span style=\"font-size: 16px;\">\\(\\frac{1}{12}\\) <\/span>=<br \/>\n<span style=\"font-size: 16px;\">3 X \\(\\frac{1}{12}\\)<\/span><\/p>\n<p>Explanation :<br \/>\nWe write \\(\\frac{3}{12}\\) in addition equation as \\(\\frac{3}{12}\\)= \\(\\frac{1}{12}\\) +<br \/>\n\\(\\frac{1}{12}\\) + \\(\\frac{1}{12}\\) and multiplication as fraction \\(\\frac{3}{12}\\)<br \/>\nrepresents 3 parts that are \\(\\frac{1}{12}\\) of the whole, \\(\\frac{3}{12}\\) =<br \/>\n3 X \\(\\frac{1}{12}\\).<\/p>\n<p><span style=\"font-size: 16px;\">Question 9.<br \/>\n<\/span>\\(\\frac{8}{100}\\)<br \/>\nAnswer:<br \/>\n\\(\\frac{8}{100}\\) = \\(\\frac{1}{100}\\) + \\(\\frac{1}{100}\\)+\\(\\frac{1}{100}\\)+<br \/>\n\\(\\frac{1}{100}\\)+\\(\\frac{1}{100}\\)+\\(\\frac{1}{100}\\)+\\(\\frac{1}{100}\\)+<br \/>\n\\(\\frac{1}{100}\\) = 8 X \\(\\frac{1}{100}\\).<\/p>\n<p>Explanation :<br \/>\nWe write \\(\\frac{8}{100}\\) in addition equation as \\(\\frac{8}{100}\\) =<br \/>\n\\(\\frac{1}{100}\\) + \\(\\frac{1}{100}\\)+\\(\\frac{1}{100}\\)+<br \/>\n\\(\\frac{1}{100}\\)+\\(\\frac{1}{100}\\)+ \\(\\frac{1}{100}\\)+<br \/>\n\\(\\frac{1}{100}\\)+\\(\\frac{1}{100}\\) and multiplication as fraction<br \/>\n\\(\\frac{8}{100}\\) represents 8 parts that are \\(\\frac{1}{100}\\) of the whole,<br \/>\n\\(\\frac{8}{100}\\)= 8 X \\(\\frac{1}{100}\\).<\/p>\n<p>Question 10.<br \/>\n\\(\\frac{7}{10}\\)<br \/>\nAnswer:<br \/>\n\\(\\frac{7}{10}\\) = \\(\\frac{1}{10}\\) +\\(\\frac{1}{10}\\) +\\(\\frac{1}{10}\\) +<br \/>\n\\(\\frac{1}{10}\\) +\\(\\frac{1}{10}\\) +\\(\\frac{1}{10}\\) +\\(\\frac{1}{10}\\)<br \/>\n= 7 X \\(\\frac{1}{10}\\).<\/p>\n<p>Explanation:<br \/>\nWe write \\(\\frac{7}{10}\\) in addition equation as \\(\\frac{7}{10}\\) = \\(\\frac{1}{10}\\) +<br \/>\n\\(\\frac{1}{10}\\) +\\(\\frac{1}{10}\\) +\\(\\frac{1}{10}\\) +\\(\\frac{1}{10}\\) +<br \/>\n\\(\\frac{1}{10}\\) +\\(\\frac{1}{10}\\) and multiplication as fraction \\(\\frac{7}{10}\\)<br \/>\nrepresents 7 parts that are \\(\\frac{1}{10}\\) of the whole,\\(\\frac{7}{10}\\) = 7 X \\(\\frac{1}{10}\\).<\/p>\n<p>Question 11.<br \/>\n<strong>Structure<\/strong><br \/>\nWhen a fraction is written as a multiple of a unit fraction, what is the relationship between the numerator of the<br \/>\nfraction and the number that is multiplied by the unit fraction?<br \/>\nAnswer:<br \/>\nWhen a fraction is written as a multiple of a unit fraction, the relationship between the numerator of the fraction<br \/>\nand the number that is multiplied by the unit fraction, is the whole number times the unit fraction.<\/p>\n<p>Explanation : We know that the numerator of a unit fraction is always one. So When a fraction is<br \/>\nwritten as a multiple of a unit fraction the number will be always the whole number (whole number of times the unit fraction)<br \/>\nand is multiplied by unit fraction. For example \\(\\frac{3}{8}\\) we write it as 3 X \\(\\frac{1}{8}\\)<br \/>\nhere it is 3 and this 3 is multiplied by unit fraction.<\/p>\n<p><strong>DIG DEEPER!<\/strong><br \/>\nWrite the mixed number as a multiple of a unit fraction.<\/p>\n<p>Question 12.<br \/>\n1\\(\\frac{1}{8}\\)<br \/>\nAnswer:<br \/>\n1\\(\\frac{1}{8}\\) = \\(\\frac{9}{8}\\) = \\(\\frac{1}{8}\\)+\\(\\frac{1}{8}\\)+<br \/>\n\\(\\frac{1}{8}\\)+\\(\\frac{1}{8}\\)+\\(\\frac{1}{8}\\)+\\(\\frac{1}{8}\\)+<br \/>\n\\(\\frac{1}{8}\\)+\\(\\frac{1}{8}\\)+\\(\\frac{1}{8}\\)= 9 X \\(\\frac{1}{8}\\) .<\/p>\n<p>Explanation:<br \/>\nFirst we convert a mixed number to an improper fraction, It is to multiply the bottom number 8 by the<br \/>\n&#8220;regular&#8221; number 1, add in the top number 1, and then put this on top of the original bottom number as 9 by 8.<br \/>\n1\\(\\frac{1}{8}\\) = 1+\\(\\frac{1}{8}\\) = \\(\\frac{9}{8}\\)<br \/>\nWe write \\(\\frac{9}{8}\\) in addition equation as \\(\\frac{9}{8}\\)= \\(\\frac{1}{8}\\)+<br \/>\n\\(\\frac{1}{8}\\)+\\(\\frac{1}{8}\\)+\\(\\frac{1}{8}\\)+\\(\\frac{1}{8}\\)+<br \/>\n\\(\\frac{1}{8}\\)+\\(\\frac{1}{8}\\)+\\(\\frac{1}{8}\\) +\\(\\frac{1}{8}\\)<br \/>\nand multiplication as fraction \\(\\frac{9}{8}\\) represents 9 parts that are \\(\\frac{1}{10}\\)<br \/>\nof the whole, \\(\\frac{9}{8}\\) = 9 X \\(\\frac{1}{8}\\).<\/p>\n<p>Question 13.<br \/>\n3\\(\\frac{4}{5}\\)<br \/>\nAnswer:<br \/>\n3\\(\\frac{4}{5}\\) = \\(\\frac{19}{5}\\)=\\(\\frac{1}{5}\\)+\\(\\frac{1}{5}\\)+<br \/>\n\\(\\frac{1}{5}\\) +\\(\\frac{1}{5}\\)+\\(\\frac{1}{5}\\)+\\(\\frac{1}{5}\\)+<br \/>\n\\(\\frac{1}{5}\\)+\\(\\frac{1}{5}\\)+\\(\\frac{1}{5}\\)+\\(\\frac{1}{5}\\)+<br \/>\n\\(\\frac{1}{5}\\)+\\(\\frac{1}{5}\\)+\\(\\frac{1}{5}\\)+\\(\\frac{1}{5}\\)+<br \/>\n\\(\\frac{1}{5}\\)+\\(\\frac{1}{5}\\)+\\(\\frac{1}{5}\\)+\\(\\frac{1}{5}\\)+<br \/>\n\\(\\frac{1}{5}\\)= 19 X \\(\\frac{1}{5}\\).<\/p>\n<p>Explanation:<br \/>\nFirst we convert a mixed number to an improper fraction, It is to multiply the bottom number 5 by the &#8220;regular&#8221;<br \/>\nnumber 3, add in the top number 4, and then put this on top of the original bottom number as 19 by 5.<br \/>\n3\\(\\frac{4}{5}\\)=3+\\(\\frac{4}{5}\\) = \\(\\frac{19}{5}\\)<br \/>\nWe write \\(\\frac{19}{5}\\) in addition equation as \\(\\frac{19}{5}\\) = \\(\\frac{1}{5}\\)+<br \/>\n\\(\\frac{1}{5}\\)+\\(\\frac{1}{5}\\) +\\(\\frac{1}{5}\\)+\\(\\frac{1}{5}\\)+<br \/>\n\\(\\frac{1}{5}\\)+\\(\\frac{1}{5}\\)+\\(\\frac{1}{5}\\)+\\(\\frac{1}{5}\\)+<br \/>\n\\(\\frac{1}{5}\\)+\\(\\frac{1}{5}\\)+\\(\\frac{1}{5}\\)+\\(\\frac{1}{5}\\)+<br \/>\n\\(\\frac{1}{5}\\)+\\(\\frac{1}{5}\\)+\\(\\frac{1}{5}\\)+\\(\\frac{1}{5}\\)+<br \/>\n\\(\\frac{1}{5}\\)+\\(\\frac{1}{5}\\) and multiplication as fraction \\(\\frac{19}{5}\\)<br \/>\nrepresents 19 parts that are \\(\\frac{1}{5}\\) of the whole,\\(\\frac{19}{5}\\)= 19 X \\(\\frac{1}{5}\\).<\/p>\n<p>Question 13.<\/p>\n<p><strong>Think and Grow: Modeling Real Life<\/strong><\/p>\n<p><strong>Example<\/strong><br \/>\nA juice stand worker uses \\(\\frac{1}{2}\\) of an orange to garnish each drink.<br \/>\nThe worker has \\(\\frac{7}{12}\\) of an orange left. How many more drinks can the worker garnish?<br \/>\nWrite the fraction of orange left as a multiple of \\(\\frac{1}{12}\\).<br \/>\n<img decoding=\"async\" loading=\"lazy\" class=\"alignnone size-full wp-image-13057\" src=\"https:\/\/ccssanswers.com\/wp-content\/uploads\/2020\/12\/Big-Ideas-Math-Solutions-Grade-4-Chapter-9-Multiply-Whole-Numbers-and-Fractions-3.png\" alt=\"Big Ideas Math Solutions Grade 4 Chapter 9 Multiply Whole Numbers and Fractions 3\" width=\"111\" height=\"203\" \/><br \/>\n<img decoding=\"async\" loading=\"lazy\" class=\"alignnone size-full wp-image-13055\" src=\"https:\/\/ccssanswers.com\/wp-content\/uploads\/2020\/12\/Big-Ideas-Math-Answers-Grade-4-Chapter-9-Multiply-Whole-Numbers-and-Fractions-501.png\" alt=\"Big Ideas Math Answers Grade 4 Chapter 9 Multiply Whole Numbers and Fractions 501\" width=\"578\" height=\"121\" srcset=\"https:\/\/ccssanswers.com\/wp-content\/uploads\/2020\/12\/Big-Ideas-Math-Answers-Grade-4-Chapter-9-Multiply-Whole-Numbers-and-Fractions-501.png 578w, https:\/\/ccssanswers.com\/wp-content\/uploads\/2020\/12\/Big-Ideas-Math-Answers-Grade-4-Chapter-9-Multiply-Whole-Numbers-and-Fractions-501-300x63.png 300w\" sizes=\"(max-width: 578px) 100vw, 578px\" \/><br \/>\nAnswer:<br \/>\nThe worker can garnish \\(\\frac{1}{12}\\) more drinks,<br \/>\n\\(\\frac{7}{12}\\) minus \\(\\frac{1}{2}\\) means \\(\\frac{7}{12}\\) &#8211; \\(\\frac{1}{2}\\)<br \/>\n= \\(\\frac{1}{12}\\), Orange left is 7 X \\(\\frac{1}{12}\\).<br \/>\n<img decoding=\"async\" loading=\"lazy\" class=\"alignnone wp-image-21639 size-full\" src=\"https:\/\/ccssanswers.com\/wp-content\/uploads\/2020\/12\/9-Multiply-Whole-Numbers-and-Fractions-6-1.bmp\" alt=\"\" width=\"660\" height=\"239\" srcset=\"https:\/\/ccssanswers.com\/wp-content\/uploads\/2020\/12\/9-Multiply-Whole-Numbers-and-Fractions-6-1.bmp 660w, https:\/\/ccssanswers.com\/wp-content\/uploads\/2020\/12\/9-Multiply-Whole-Numbers-and-Fractions-6-1-300x109.jpg 300w\" sizes=\"(max-width: 660px) 100vw, 660px\" \/><\/p>\n<p>Explanation:<br \/>\nGiven a juice stand worker uses \\(\\frac{1}{2}\\) of an orange to garnish each drink.<br \/>\nThe worker has \\(\\frac{7}{12}\\) of an orange left. So the worker can garnish more \\(\\frac{7}{12}\\)<br \/>\nminus \\(\\frac{1}{2}\\) means \\(\\frac{7}{12}\\) &#8211; \\(\\frac{1}{2}\\) = \\(\\frac{1}{12}\\),<br \/>\nGiven \\(\\frac{7}{12}\\) of an orange is left , to write orange left as a multiple of \\(\\frac{1}{12}\\)<br \/>\nwe have orange left as \\(\\frac{7}{12}\\) so write it as 7 parts that are \\(\\frac{1}{12}\\) of the whole,<br \/>\n\\(\\frac{7}{12}\\)= 7 X \\(\\frac{1}{12}\\).<\/p>\n<p><strong>Show and Grow<\/strong><\/p>\n<p>Question 14.<br \/>\nA piece of rope is \\(\\frac{8}{5}\\) meters long. You cut the rope into \\(\\frac{1}{5}\\) meter long pieces.<br \/>\nHow many pieces do you cut?<br \/>\nAnswer:<br \/>\n8 pieces I have cut.<\/p>\n<p>Explanation:<br \/>\nGiven a piece of rope is \\(\\frac{8}{5}\\) meters long and it has been cut into \\(\\frac{1}{5}\\)<br \/>\nmeter long pieces, therefore pieces of rope cut is \\(\\frac{8}{5}\\) divided by \\(\\frac{1}{5}\\)<br \/>\n= \\(\\frac{8}{5}\\) X latex]\\frac{5}{1}[\/latex] = 8.<\/p>\n<p>Question 15.<br \/>\nA restaurant serves \\(\\frac{4}{10}\\) of a meatloaf to 4 customers. Each customer receives<br \/>\nthe same amount of meatloaf. What fraction of the meatloaf does each customer receive?<br \/>\nAnswer:<br \/>\nThe fraction of the meatloaf each customer receives is \\(\\frac{1}{10}\\)<\/p>\n<p>Explanation:<br \/>\nGiven a restaurant serves \\(\\frac{4}{10}\\) of a meatloaf to 4 customers and each customer receives the same<br \/>\namount of meatloaf so fraction of the meatloaf each customer receives is\u00a0 \\(\\frac{4}{10}\\)\u00a0 divided by 4 =<br \/>\n\\(\\frac{4}{10}\\) x \\(\\frac{1}{4}\\) = \\(\\frac{1}{10}\\).<\/p>\n<p>Question 16.<br \/>\nYou use 3\\(\\frac{3}{4}\\) pounds of trail mix to make treat bags. You put \\(\\frac{1}{4}\\)<br \/>\npound of trail mix into each bag. How many treat bags do you make?<br \/>\n<img decoding=\"async\" loading=\"lazy\" class=\"alignnone size-full wp-image-13058\" src=\"https:\/\/ccssanswers.com\/wp-content\/uploads\/2020\/12\/Big-Ideas-Math-Solutions-Grade-4-Chapter-9-Multiply-Whole-Numbers-and-Fractions-4.png\" alt=\"Big Ideas Math Solutions Grade 4 Chapter 9 Multiply Whole Numbers and Fractions 4\" width=\"232\" height=\"127\" \/><br \/>\nAnswer:<br \/>\nTotal number of treat bags made are 15<\/p>\n<p>Explanation:<br \/>\nI use 3\\(\\frac{3}{4}\\) pounds of trail mix to make treat bags, We convert a mixed number to an<br \/>\nimproper fraction,It is to multiply the bottom number 4 by the &#8220;regular&#8221; number 3, add in the top number 3,<br \/>\nand then put this on top of the original bottom number as 15 by 4, it becomes \\(\\frac{15}{4}\\),Each bag i kept<br \/>\n\\(\\frac{1}{4}\\) pound of trail mix so total number of treat bags required to make are \\(\\frac{15}{4}\\)<br \/>\ndivided by \\(\\frac{1}{4}\\)=\\(\\frac{15}{4}\\) X \\(\\frac{4}{1}\\)=15 treat bags.<\/p>\n<p>Question 17.<br \/>\n<strong>DIG DEEPER!<\/strong><br \/>\nYou walk from home to school and then back home again each day for 5 days. Altogether, you walk \\(\\frac{10}{8}\\) miles. What is the distance from your home to school? Explain.<br \/>\nAnswer:<br \/>\nThe distance from home to school is \\(\\frac{1}{8}\\) miles<\/p>\n<p>Explanation:<br \/>\nTotal number of miles walked is \\(\\frac{10}{8}\\) in 5 days that to from home to school and<br \/>\nthen back home again means it is twice a day , Let us take X as the distance from home to school is,<br \/>\nGiven 2X x 5=\\(\\frac{10}{8}\\) miles, X = Then each day number of miles walked is\u00a0 \\(\\frac{10}{8}\\)<br \/>\ndivided by 10 which is\u00a0 equal to\u00a0 \\(\\frac{10}{8}\\) x \\(\\frac{1}{10}\\) =\\(\\frac{1}{8}\\),<br \/>\nTherefore X = \\(\\frac{1}{8}\\) miles.<\/p>\n<h3><a id=\"Understand Multiples_of_Unit_Fractions_Homework_&amp;_practice_9.1\"><\/a>Understand Multiples of Unit Fractions Homework &amp; practice 9.1<\/h3>\n<p>Write the fraction as a multiple of a unit fraction.<\/p>\n<p>Question 1.<br \/>\n<img decoding=\"async\" loading=\"lazy\" class=\"alignnone size-full wp-image-13059\" src=\"https:\/\/ccssanswers.com\/wp-content\/uploads\/2020\/12\/Big-Ideas-Math-Solutions-Grade-4-Chapter-9-Multiply-Whole-Numbers-and-Fractions-5.png\" alt=\"Big Ideas Math Solutions Grade 4 Chapter 9 Multiply Whole Numbers and Fractions 5\" width=\"145\" height=\"117\" \/><br \/>\nAnswer:<br \/>\n\\(\\frac{2}{12}\\)= \\(\\frac{1}{12}\\)+\\(\\frac{1}{12}\\) = 2 X \\(\\frac{1}{12}\\)<\/p>\n<p>Explanation:<br \/>\nWe write \\(\\frac{2}{12}\\) in addition equation as \\(\\frac{2}{12}\\)= \\(\\frac{1}{12}\\) +<br \/>\n\\(\\frac{1}{12}\\) and multiplication as fraction \\(\\frac{2}{12}\\) represents 2 parts that are<br \/>\n\\(\\frac{1}{12}\\) of the whole, \\(\\frac{2}{12}\\)= 2 X \\(\\frac{1}{12}\\).<\/p>\n<p>Question 2.<br \/>\n<img decoding=\"async\" loading=\"lazy\" class=\"alignnone size-full wp-image-13060\" src=\"https:\/\/ccssanswers.com\/wp-content\/uploads\/2020\/12\/Big-Ideas-Math-Solutions-Grade-4-Chapter-9-Multiply-Whole-Numbers-and-Fractions-6.png\" alt=\"Big Ideas Math Solutions Grade 4 Chapter 9 Multiply Whole Numbers and Fractions 6\" width=\"255\" height=\"120\" \/><br \/>\nAnswer:<br \/>\n\\(\\frac{5}{100}\\)= \\(\\frac{1}{100}\\)+\\(\\frac{1}{100}\\)+\\(\\frac{1}{100}\\)+<br \/>\n\\(\\frac{1}{100}\\)+\\(\\frac{1}{100}\\) = 5 X \\(\\frac{1}{100}\\).<\/p>\n<p>Explanation:<br \/>\nWe write \\(\\frac{5}{100}\\) in addition equation as \\(\\frac{5}{100}\\)= \\(\\frac{1}{100}\\)+<br \/>\n\\(\\frac{1}{100}\\)+\\(\\frac{1}{100}\\)+\\(\\frac{1}{100}\\)+\\(\\frac{1}{100}\\)<br \/>\nand multiplication as fraction \\(\\frac{5}{100}\\) represents 5 parts that are \\(\\frac{1}{100}\\) of the whole, \\(\\frac{5}{100}\\) = 5 X \\(\\frac{1}{100}\\).<\/p>\n<p>Question 3.<br \/>\n\\(\\frac{3}{6}\\)<br \/>\nAnswer:<br \/>\n\\(\\frac{3}{6}\\)=\\(\\frac{1}{6}\\)+\\(\\frac{1}{6}\\)+\\(\\frac{1}{6}\\)<br \/>\n= 3 X \\(\\frac{1}{6}\\).<\/p>\n<p>Explanation:<br \/>\nWe write \\(\\frac{3}{6}\\) in addition equation as \\(\\frac{3}{6}\\)=\\(\\frac{1}{6}\\)+<br \/>\n\\(\\frac{1}{6}\\)+\\(\\frac{1}{6}\\) and multiplication as fraction \\(\\frac{3}{6}\\)<br \/>\nrepresents 3 parts that are \\(\\frac{1}{6}\\) of the whole,\\(\\frac{3}{6}\\) = 3 X \\(\\frac{1}{6}\\).<\/p>\n<p>Question 4.<br \/>\n\\(\\frac{7}{10}\\)<br \/>\nAnswer:<br \/>\n\\(\\frac{7}{10}\\) =\\(\\frac{1}{10}\\)+\\(\\frac{1}{10}\\)+\\(\\frac{1}{10}\\)+<br \/>\n\\(\\frac{1}{10}\\)+\\(\\frac{1}{10}\\)+\\(\\frac{1}{10}\\)+\\(\\frac{1}{10}\\)<br \/>\n= 7 X \\(\\frac{1}{10}\\)<\/p>\n<p>Explanation:<br \/>\nWe write \\(\\frac{7}{10}\\) in addition equation as \\(\\frac{7}{10}\\)= \\(\\frac{1}{10}\\)+<br \/>\n\\(\\frac{1}{10}\\)+\\(\\frac{1}{10}\\)+\\(\\frac{1}{10}\\)+\\(\\frac{1}{10}\\)+<br \/>\n\\(\\frac{1}{10}\\)+\\(\\frac{1}{10}\\) and multiplication as \\(\\frac{7}{10}\\) represents<br \/>\n7 parts that are \\(\\frac{1}{10}\\) of the whole,\\(\\frac{7}{10}\\) = 7 X \\(\\frac{1}{10}\\).<\/p>\n<p>Question 5.<br \/>\n\\(\\frac{4}{5}\\)<br \/>\nAnswer:<br \/>\n\\(\\frac{4}{5}\\) = \\(\\frac{1}{5}\\)+\\(\\frac{1}{5}\\)+<br \/>\n\\(\\frac{1}{5}\\)+\\(\\frac{1}{5}\\) = 4 X \\(\\frac{1}{5}\\).<\/p>\n<p>Explanation:<br \/>\nWe write \\(\\frac{4}{5}\\) in addition equation as \\(\\frac{4}{5}\\)=\\(\\frac{1}{5}\\)+<br \/>\n\\(\\frac{1}{5}\\)+\\(\\frac{1}{5}\\)+\\(\\frac{1}{5}\\) and multiplication as \\(\\frac{4}{5}\\)<br \/>\nrepresents 4 parts that are \\(\\frac{1}{5}\\) of the whole,\\(\\frac{4}{5}\\)= 4 X \\(\\frac{1}{5}\\).<\/p>\n<p>Question 6.<br \/>\n\\(\\frac{9}{2}\\)<br \/>\nAnswer:<br \/>\n\\(\\frac{9}{2}\\) = \\(\\frac{1}{2}\\)+\\(\\frac{1}{2}\\)+\\(\\frac{1}{2}\\)+<br \/>\n\\(\\frac{1}{2}\\)+\\(\\frac{1}{2}\\)+\\(\\frac{1}{2}\\)+\\(\\frac{1}{2}\\)+<br \/>\n\\(\\frac{1}{2}\\)+\\(\\frac{1}{2}\\) = 9 X \\(\\frac{1}{2}\\).<\/p>\n<p>Explanation:<br \/>\nWe write \\(\\frac{9}{2}\\) in addition equation as \\(\\frac{9}{2}\\) = \\(\\frac{1}{2}\\)+<br \/>\n\\(\\frac{1}{2}\\)+\\(\\frac{1}{2}\\)+\\(\\frac{1}{2}\\)+\\(\\frac{1}{2}\\)+<br \/>\n\\(\\frac{1}{2}\\)+\\(\\frac{1}{2}\\)+\\(\\frac{1}{2}\\)+\\(\\frac{1}{2}\\)<br \/>\nand multiplication as \\(\\frac{9}{2}\\) represents 9 parts that are \\(\\frac{1}{2}\\) of the whole,<br \/>\n\\(\\frac{9}{2}\\)= 9 X \\(\\frac{1}{2}\\).<\/p>\n<p>Question 7.<br \/>\n\\(\\frac{8}{8}\\)<br \/>\nAnswer:<br \/>\n\\(\\frac{8}{8}\\)=1=\\(\\frac{1}{8}\\)+\\(\\frac{1}{8}\\)+\\(\\frac{1}{8}\\)+<br \/>\n\\(\\frac{1}{8}\\)+\\(\\frac{1}{8}\\)+\\(\\frac{1}{8}\\)+\\(\\frac{1}{8}\\)+<br \/>\n\\(\\frac{1}{8}\\) = \\(\\frac{8}{8}\\) = 8 X \\(\\frac{1}{8}\\).<\/p>\n<p>Explanation:<br \/>\n\\(\\frac{8}{8}\\)= 1 ,but we write the fraction as a addition of a unit fraction and multiple of a unit fraction,<br \/>\nWe write \\(\\frac{8}{8}\\) in addition equation as \\(\\frac{8}{8}\\) = \\(\\frac{1}{8}\\)+<br \/>\n\\(\\frac{1}{8}\\)+\\(\\frac{1}{8}\\)+\\(\\frac{1}{8}\\)+\\(\\frac{1}{8}\\)+<br \/>\n\\(\\frac{1}{8}\\)+\\(\\frac{1}{8}\\)+\\(\\frac{1}{8}\\) and multiplication as \\(\\frac{8}{8}\\)<br \/>\nrepresents 8 parts that are \\(\\frac{1}{8}\\) of the whole,\\(\\frac{8}{8}\\)= 8 X \\(\\frac{1}{8}\\).<\/p>\n<p>Question 8.<br \/>\n\\(\\frac{6}{3}\\)<br \/>\nAnswer:<br \/>\n\\(\\frac{6}{3}\\)=2,\\(\\frac{6}{3}\\)= \\(\\frac{1}{3}\\)+\\(\\frac{1}{3}\\)+<br \/>\n\\(\\frac{1}{3}\\)+\\(\\frac{1}{3}\\)+\\(\\frac{1}{3}\\)+\\(\\frac{1}{3}\\)<br \/>\n= 6 X \\(\\frac{1}{3}\\).<\/p>\n<p>Explanantion:<br \/>\n\\(\\frac{6}{3}\\)= 2 ,but we write the fraction as a addition of a unit fraction and multiple of a unit fraction,<br \/>\nWe write \\(\\frac{6}{3}\\) in addition equation as \\(\\frac{6}{3}\\)= \\(\\frac{1}{3}\\)+<br \/>\n\\(\\frac{1}{3}\\)+\\(\\frac{1}{3}\\)+\\(\\frac{1}{3}\\)+\\(\\frac{1}{3}\\)+<br \/>\n\\(\\frac{1}{3}\\) and multiplication as \\(\\frac{6}{3}\\) represents 6 parts that are<br \/>\n\\(\\frac{1}{3}\\) of the whole,\\(\\frac{6}{3}\\)= 6 X \\(\\frac{1}{3}\\).<\/p>\n<p>Question 9.<br \/>\n<strong>Logic<\/strong><br \/>\nWhat is Newton\u2019s fraction? Write the fraction as a multiple of a unit fraction.<br \/>\n<img decoding=\"async\" loading=\"lazy\" class=\"alignnone size-full wp-image-13061\" src=\"https:\/\/ccssanswers.com\/wp-content\/uploads\/2020\/12\/Big-Ideas-Math-Solutions-Grade-4-Chapter-9-Multiply-Whole-Numbers-and-Fractions-7.png\" alt=\"Big Ideas Math Solutions Grade 4 Chapter 9 Multiply Whole Numbers and Fractions 7\" width=\"203\" height=\"214\" \/><br \/>\nAnswer:<br \/>\nNewton&#8217;s fraction = \\(\\frac{9}{12}\\)=\\(\\frac{1}{12}\\) +\\(\\frac{1}{12}\\) +<br \/>\n\\(\\frac{1}{12}\\) +\\(\\frac{1}{12}\\) +\\(\\frac{1}{12}\\) +\\(\\frac{1}{12}\\) +<br \/>\n\\(\\frac{1}{12}\\) +\\(\\frac{1}{12}\\) +\\(\\frac{1}{12}\\) = 9 X \\(\\frac{1}{12}\\).<\/p>\n<p>Explanation:<br \/>\nGiven that Newton&#8217;s fraction as sum of 9 unit fractions and each unit fraction is one twelfth of a whole.<br \/>\nSo Newton&#8217;s fraction is \\(\\frac{9}{12}\\) we write \\(\\frac{9}{12}\\) in addition equation as<br \/>\n\\(\\frac{9}{12}\\)=\u00a0 \\(\\frac{1}{12}\\) +\\(\\frac{1}{12}\\) +\\(\\frac{1}{12}\\) +<br \/>\n\\(\\frac{1}{12}\\) +\\(\\frac{1}{12}\\) +\\(\\frac{1}{12}\\) +\\(\\frac{1}{12}\\) +<br \/>\n\\(\\frac{1}{12}\\) +\\(\\frac{1}{12}\\) and multiplication as \\(\\frac{9}{12}\\) represents 9 parts<br \/>\nthat are \\(\\frac{1}{12}\\) of the whole,\\(\\frac{9}{12}\\)= 9 X \\(\\frac{1}{12}\\).<\/p>\n<p>Question 10<br \/>\n<strong>Structure<\/strong><br \/>\nWrite a multiplication equation that represents the grapefruit halves.<br \/>\n<img decoding=\"async\" loading=\"lazy\" class=\"alignnone size-full wp-image-13062\" src=\"https:\/\/ccssanswers.com\/wp-content\/uploads\/2020\/12\/Big-Ideas-Math-Solutions-Grade-4-Chapter-9-Multiply-Whole-Numbers-and-Fractions-8.png\" alt=\"Big Ideas Math Solutions Grade 4 Chapter 9 Multiply Whole Numbers and Fractions 8\" width=\"284\" height=\"64\" \/><br \/>\nAnswer:<br \/>\n\\(\\frac{6}{2}\\)=\\(\\frac{1}{2}\\)+\\(\\frac{1}{2}\\)+\\(\\frac{1}{2}\\)+<br \/>\n\\(\\frac{1}{2}\\)+\\(\\frac{1}{2}\\)+\\(\\frac{1}{2}\\)<br \/>\n= 6 X \\(\\frac{1}{2}\\).<\/p>\n<p>Explanation:<br \/>\nGiven 6 number of grapefruit halves so there are total grapefruit as \\(\\frac{6}{2}\\) we write<br \/>\n\\(\\frac{6}{2}\\) in addition equation as \\(\\frac{6}{2}\\)=\\(\\frac{1}{2}\\)+<br \/>\n\\(\\frac{1}{2}\\)+\\(\\frac{1}{2}\\)+\\(\\frac{1}{2}\\)+\\(\\frac{1}{2}\\)+<br \/>\n\\(\\frac{1}{2}\\),so the multiplication equation is \\(\\frac{6}{2}\\) represents 6 parts that are<br \/>\n\\(\\frac{1}{2}\\) of the whole,\\(\\frac{6}{2}\\)= 6 X \\(\\frac{1}{2}\\).<\/p>\n<p>Question 11.<br \/>\n<strong>Which One Doesn&#8217;t Belong?<\/strong><br \/>\nWhich expression does not belong with the other three?<br \/>\n<img decoding=\"async\" loading=\"lazy\" class=\"alignnone size-full wp-image-13063\" src=\"https:\/\/ccssanswers.com\/wp-content\/uploads\/2020\/12\/Big-Ideas-Math-Solutions-Grade-4-Chapter-9-Multiply-Whole-Numbers-and-Fractions-9.png\" alt=\"Big Ideas Math Solutions Grade 4 Chapter 9 Multiply Whole Numbers and Fractions 9\" width=\"431\" height=\"63\" srcset=\"https:\/\/ccssanswers.com\/wp-content\/uploads\/2020\/12\/Big-Ideas-Math-Solutions-Grade-4-Chapter-9-Multiply-Whole-Numbers-and-Fractions-9.png 431w, https:\/\/ccssanswers.com\/wp-content\/uploads\/2020\/12\/Big-Ideas-Math-Solutions-Grade-4-Chapter-9-Multiply-Whole-Numbers-and-Fractions-9-300x44.png 300w\" sizes=\"(max-width: 431px) 100vw, 431px\" \/><br \/>\nAnswer:<br \/>\n4 X \\(\\frac{1}{5}\\) expression does not belong with the other three, as all the other expressions values results are same =\\(\\frac{5}{4}\\) only 4 X \\(\\frac{1}{5}\\) expression is not.<\/p>\n<p>Explanation:<br \/>\n1. 5 X \\(\\frac{1}{4}\\) = \\(\\frac{5}{4}\\)<br \/>\n2. \\(\\frac{1}{4}\\)+\\(\\frac{1}{4}\\)+\\(\\frac{1}{4}\\)+\\(\\frac{1}{4}\\)=<br \/>\n5 X \\(\\frac{1}{4}\\)= \\(\\frac{5}{4}\\)<br \/>\n3. \\(\\frac{5}{4}\\) =\\(\\frac{5}{4}\\)<br \/>\n4. 4 X \\(\\frac{1}{5}\\)= \\(\\frac{4}{5}\\)\u2260\u00a0 \\(\\frac{5}{4}\\)<br \/>\nSo in the above expressions only 4 X \\(\\frac{1}{5}\\)\u00a0 does not belong with the other three expressions.<\/p>\n<p>Question 12.<br \/>\n<strong>Modeling Real Life<\/strong><br \/>\nYou are making blueberry pancakes. You have \\(\\frac{6}{8}\\) cup of blueberries. You put \\(\\frac{1}{8}\\) cup of blueberries in each pancake. How many pancakes do you make?<br \/>\n<img decoding=\"async\" loading=\"lazy\" class=\"alignnone size-full wp-image-13064\" src=\"https:\/\/ccssanswers.com\/wp-content\/uploads\/2020\/12\/Big-Ideas-Math-Solutions-Grade-4-Chapter-9-Multiply-Whole-Numbers-and-Fractions-10.png\" alt=\"Big Ideas Math Solutions Grade 4 Chapter 9 Multiply Whole Numbers and Fractions 10\" width=\"230\" height=\"107\" \/><br \/>\nAnswer:<br \/>\n6 pancakes i can make.<\/p>\n<p>Explanation:<br \/>\nI have \\(\\frac{6}{8}\\) cup of blueberries and i can put \\(\\frac{1}{8}\\) cup of blueberries<br \/>\nin each pan cake so total number of pancakes made are \\(\\frac{6}{8}\\) divided by \\(\\frac{1}{8}\\) =<br \/>\n\\(\\frac{6}{8}\\) X \\(\\frac{8}{1}\\)= 6 pancakes.<\/p>\n<p>Question 13.<br \/>\n<strong>DIG DEEPER!<\/strong><br \/>\nYou cut a loaf of zucchini bread into 20 equal slices. You and your friends eat \\(\\frac{3}{10}\\) of the slices.<br \/>\nYou want to put each leftover slice into its own bag. How many bags do you need?<br \/>\nAnswer:<br \/>\n14 bags are needed.<\/p>\n<p>Explanation :<br \/>\nGiven a loaf of zucchini bread is cut\u00a0 into 20 equal slices and i ,friend eat \\(\\frac{3}{10}\\) of the slices,<br \/>\nTotal number of slices of zucchini bread =20, Number of slices ate = \\(\\frac{3}{10}\\) means it says<br \/>\nout of 10 slices 3 were ate, so out of 20 slices\u00a0 2 x 3= 6 slices were eaten. Number of slices left = 20 &#8211; 6 =14 slices<br \/>\nand one bag contains only one slice. Therefore number of bags needed are 14.<\/p>\n<p>Question 14.<br \/>\nIs 46 a multiple of 45.<br \/>\nAnswer:<br \/>\nNo 46 is not a multiple of 45.<\/p>\n<p>Explanation:<br \/>\nA\u00a0multiple\u00a0is a\u00a0number that can be divided by another number a certain number of times without a remainder.<br \/>\n45 when divided by 46 a certain times will leave a remainder, So 46 is not a multiple of 45<br \/>\nor a factor\u00a0is\u00a0one of two or more numbers that divides a given number without a remainder.<br \/>\nAs factors of 45 are 1,3,5,9,15 and factors of 46 are 1,2,23, both do not have common factors so 46 is not a multiple of 45.<\/p>\n<p>Question 15.<br \/>\nIs 3 a factor of 75?<br \/>\nAnswer:<br \/>\nYes 3 is a factor of 75<br \/>\nExplanation:<br \/>\nWe know that a factor is one that divides a given number without a remainder and 75 when divided by 3<br \/>\nleaves no remainder, So 3 is a factor of 75.<\/p>\n<h3><a id=\"Lesson_9.2_Understand_Multiples_of_Fractions\"><\/a>Lesson 9.2 Understand Multiples of Fractions<\/h3>\n<p>Draw a model for each expression. Then write a multiplication expression to represent each model.<br \/>\n<img decoding=\"async\" loading=\"lazy\" class=\"alignnone size-full wp-image-13065\" src=\"https:\/\/ccssanswers.com\/wp-content\/uploads\/2020\/12\/Big-Ideas-Math-Solutions-Grade-4-Chapter-9-Multiply-Whole-Numbers-and-Fractions-11.png\" alt=\"Big Ideas Math Solutions Grade 4 Chapter 9 Multiply Whole Numbers and Fractions 11\" width=\"140\" height=\"58\" \/><br \/>\n<img decoding=\"async\" loading=\"lazy\" class=\"alignnone size-full wp-image-13066\" src=\"https:\/\/ccssanswers.com\/wp-content\/uploads\/2020\/12\/Big-Ideas-Math-Solutions-Grade-4-Chapter-9-Multiply-Whole-Numbers-and-Fractions-12.png\" alt=\"Big Ideas Math Solutions Grade 4 Chapter 9 Multiply Whole Numbers and Fractions 12\" width=\"252\" height=\"60\" \/><br \/>\nAnswer:<br \/>\n<img decoding=\"async\" loading=\"lazy\" class=\"alignnone wp-image-23873 size-full\" src=\"https:\/\/ccssanswers.com\/wp-content\/uploads\/2020\/12\/9-Multiply-Whole-Numbers-and-Fractions-7-1.bmp\" alt=\"\" width=\"1258\" height=\"468\" srcset=\"https:\/\/ccssanswers.com\/wp-content\/uploads\/2020\/12\/9-Multiply-Whole-Numbers-and-Fractions-7-1.bmp 1258w, https:\/\/ccssanswers.com\/wp-content\/uploads\/2020\/12\/9-Multiply-Whole-Numbers-and-Fractions-7-1-300x112.jpg 300w, https:\/\/ccssanswers.com\/wp-content\/uploads\/2020\/12\/9-Multiply-Whole-Numbers-and-Fractions-7-1-1024x381.jpg 1024w, https:\/\/ccssanswers.com\/wp-content\/uploads\/2020\/12\/9-Multiply-Whole-Numbers-and-Fractions-7-1-768x286.jpg 768w\" sizes=\"(max-width: 1258px) 100vw, 1258px\" \/><\/p>\n<p>The multiplication expression is \\(\\frac{2}{6}\\) +\\(\\frac{2}{6}\\) +\\(\\frac{2}{6}\\) +<br \/>\n\\(\\frac{2}{6}\\) = 4 X \\(\\frac{2}{6}\\) =<br \/>\n\\(\\frac{1}{6}\\) +\\(\\frac{1}{6}\\)+ \\(\\frac{1}{6}\\) +\\(\\frac{1}{6}\\)+<br \/>\n\\(\\frac{1}{6}\\) +\\(\\frac{1}{6}\\)+ \\(\\frac{1}{6}\\) +\\(\\frac{1}{6}\\) =<br \/>\n8 X \\(\\frac{1}{6}\\).<\/p>\n<p>Explanation:<br \/>\n\\(\\frac{2}{6}\\) +\\(\\frac{2}{6}\\) +\\(\\frac{2}{6}\\) +\\(\\frac{2}{6}\\)<br \/>\nthe multiplication equation is\u00a0 4 parts that are \\(\\frac{2}{6}\\) of the whole as\u00a0 4 X \\(\\frac{2}{6}\\)<br \/>\n\\(\\frac{1}{6}\\) +\\(\\frac{1}{6}\\)+ \\(\\frac{1}{6}\\) +\\(\\frac{1}{6}\\)+<br \/>\n\\(\\frac{1}{6}\\) +\\(\\frac{1}{6}\\)+ \\(\\frac{1}{6}\\) +\\(\\frac{1}{6}\\) =<br \/>\n8 X \\(\\frac{1}{6}\\) the multiplication equation is 8 parts that are \\(\\frac{1}{6}\\) of the whole as<br \/>\n8 X \\(\\frac{1}{6}\\).<\/p>\n<p><strong>Structure<\/strong><br \/>\nCompare your expressions. How are they the same? How are they different?<br \/>\nSame means the result of both expressions is same = \\(\\frac{8}{6}\\)<br \/>\nDifferent means in one expression we take value of \\(\\frac{2}{6}\\) 4 times and in another<br \/>\nexpression we take \\(\\frac{1}{6}\\) 8 times.<\/p>\n<p>Explanation:<br \/>\nSame means \\(\\frac{2}{6}\\) +\\(\\frac{2}{6}\\) +\\(\\frac{2}{6}\\) +\\(\\frac{2}{6}\\) =<br \/>\n4 X \\(\\frac{2}{6}\\) = \\(\\frac{8}{6}\\) and \\(\\frac{1}{6}\\) +\\(\\frac{1}{6}\\)+<br \/>\n\\(\\frac{1}{6}\\) +\\(\\frac{1}{6}\\)+\\(\\frac{1}{6}\\) +\\(\\frac{1}{6}\\)+<br \/>\n\\(\\frac{1}{6}\\) +\\(\\frac{1}{6}\\) = 8 X \\(\\frac{1}{6}\\) =\\(\\frac{8}{6}\\) ,<br \/>\nboth have results similar as \\(\\frac{8}{6}\\), Different means here we are taking expressions as addition values of\u00a0 \\(\\frac{2}{6}\\) by 4 times and in other expression we are taking addition values of \\(\\frac{1}{6}\\) by 8 times.<\/p>\n<p><strong>Think and Grow: Multiples of Fractions<\/strong><\/p>\n<p>A multiple of any fraction can be written as a multiple of a unit fraction with a like denominator.<br \/>\n<img decoding=\"async\" loading=\"lazy\" class=\"alignnone size-full wp-image-13067\" src=\"https:\/\/ccssanswers.com\/wp-content\/uploads\/2020\/12\/Big-Ideas-Math-Solutions-Grade-4-Chapter-9-Multiply-Whole-Numbers-and-Fractions-13.png\" alt=\"Big Ideas Math Solutions Grade 4 Chapter 9 Multiply Whole Numbers and Fractions 13\" width=\"677\" height=\"365\" srcset=\"https:\/\/ccssanswers.com\/wp-content\/uploads\/2020\/12\/Big-Ideas-Math-Solutions-Grade-4-Chapter-9-Multiply-Whole-Numbers-and-Fractions-13.png 677w, https:\/\/ccssanswers.com\/wp-content\/uploads\/2020\/12\/Big-Ideas-Math-Solutions-Grade-4-Chapter-9-Multiply-Whole-Numbers-and-Fractions-13-300x162.png 300w\" sizes=\"(max-width: 677px) 100vw, 677px\" \/><br \/>\nAnswer:<br \/>\n<img decoding=\"async\" loading=\"lazy\" class=\"alignnone wp-image-22811 size-full\" src=\"https:\/\/ccssanswers.com\/wp-content\/uploads\/2020\/12\/9-Multiply-Whole-Numbers-and-Fractions-8.bmp\" alt=\"\" width=\"562\" height=\"354\" srcset=\"https:\/\/ccssanswers.com\/wp-content\/uploads\/2020\/12\/9-Multiply-Whole-Numbers-and-Fractions-8.bmp 562w, https:\/\/ccssanswers.com\/wp-content\/uploads\/2020\/12\/9-Multiply-Whole-Numbers-and-Fractions-8-300x189.jpg 300w\" sizes=\"(max-width: 562px) 100vw, 562px\" \/><\/p>\n<p><strong><br \/>\n<\/strong>Explanation:<br \/>\nTo write 2 X \\(\\frac{3}{5}\\) multiple of unit fraction first we write \\(\\frac{3}{5}\\) as multiple of<br \/>\n3 X \\(\\frac{1}{5}\\) then we multiply it by 2 as 2 X 3 X \\(\\frac{1}{5}\\)=6 X \\(\\frac{1}{5}\\).<br \/>\n<strong><br \/>\nShow and Grow<\/strong><\/p>\n<p>Write the product as a multiple of a unit fraction. Then find the product.<\/p>\n<p>Question 1.<br \/>\n<img decoding=\"async\" loading=\"lazy\" class=\"alignnone size-full wp-image-13068\" src=\"https:\/\/ccssanswers.com\/wp-content\/uploads\/2020\/12\/Big-Ideas-Math-Solutions-Grade-4-Chapter-9-Multiply-Whole-Numbers-and-Fractions-14.png\" alt=\"Big Ideas Math Solutions Grade 4 Chapter 9 Multiply Whole Numbers and Fractions 14\" width=\"55\" height=\"51\" \/><br \/>\nAnswer:<br \/>\n2 X \\(\\frac{4}{5}\\) = 2 X 4 X \\(\\frac{1}{5}\\) = 8 X \\(\\frac{1}{5}\\) = \\(\\frac{8}{5}\\).<\/p>\n<p>Explanation:<br \/>\nFirst we write \\(\\frac{4}{5}\\)\u00a0 as \u00a0\\(\\frac{1}{5}\\) + \\(\\frac{1}{5}\\) +<br \/>\n\\(\\frac{1}{5}\\) + \\(\\frac{1}{5}\\) = 4 X \\(\\frac{1}{5}\\) then multiply it by 2<br \/>\nwhich is\u00a0 2 X 4 X \\(\\frac{1}{5}\\) = 8 X \\(\\frac{1}{5}\\) = \\(\\frac{8}{5}\\).<\/p>\n<p>Question 2.<br \/>\n<img decoding=\"async\" loading=\"lazy\" class=\"alignnone size-full wp-image-13069\" src=\"https:\/\/ccssanswers.com\/wp-content\/uploads\/2020\/12\/Big-Ideas-Math-Solutions-Grade-4-Chapter-9-Multiply-Whole-Numbers-and-Fractions-15.png\" alt=\"Big Ideas Math Solutions Grade 4 Chapter 9 Multiply Whole Numbers and Fractions 15\" width=\"64\" height=\"50\" \/><br \/>\nAnswer:<br \/>\n3 X \\(\\frac{2}{10}\\) = 3 X 2 X \u00a0\\(\\frac{1}{10}\\) = 6 X \\(\\frac{1}{10}\\) =\\(\\frac{6}{10}\\).<\/p>\n<p>Explanation:<br \/>\nFirst we write \\(\\frac{2}{10}\\) as \\(\\frac{1}{10}\\) +\\(\\frac{1}{10}\\) = 2 X \\(\\frac{1}{10}\\)<br \/>\nthen multiply it by 3 which is 3 X 2 X \\(\\frac{1}{10}\\) = 6 X \\(\\frac{1}{10}\\) =\\(\\frac{6}{10}\\).<\/p>\n<p>Question 3.<br \/>\n<img decoding=\"async\" loading=\"lazy\" class=\"alignnone size-full wp-image-13070\" src=\"https:\/\/ccssanswers.com\/wp-content\/uploads\/2020\/12\/Big-Ideas-Math-Solutions-Grade-4-Chapter-9-Multiply-Whole-Numbers-and-Fractions-16.png\" alt=\"Big Ideas Math Solutions Grade 4 Chapter 9 Multiply Whole Numbers and Fractions 16\" width=\"60\" height=\"58\" \/><br \/>\nAnswer:<br \/>\n4 X \\(\\frac{3}{2}\\) = 4 X 3 X \\(\\frac{1}{2}\\) = 12 X \\(\\frac{1}{2}\\) = \\(\\frac{12}{2}\\) = 6.<\/p>\n<p>Explanation:<br \/>\nFirst we write \\(\\frac{3}{2}\\) as \\(\\frac{1}{2}\\) +\\(\\frac{1}{2}\\) + \\(\\frac{1}{2}\\) = 3 X \\(\\frac{1}{2}\\) then we multiply it by 4 which is 4 X 3 X \\(\\frac{1}{2}\\)= 12 X \\(\\frac{1}{2}\\)= \\(\\frac{12}{2}\\)=6.<\/p>\n<p><strong>Apply and Grow: Practice<\/strong><\/p>\n<p>Write the product as a multiple of a unit fraction. Then \ufb01nd the product.<\/p>\n<p>Question 4.<br \/>\n<img decoding=\"async\" loading=\"lazy\" class=\"alignnone size-full wp-image-13071\" src=\"https:\/\/ccssanswers.com\/wp-content\/uploads\/2020\/12\/Big-Ideas-Math-Solutions-Grade-4-Chapter-9-Multiply-Whole-Numbers-and-Fractions-17.png\" alt=\"Big Ideas Math Solutions Grade 4 Chapter 9 Multiply Whole Numbers and Fractions 17\" width=\"62\" height=\"57\" \/><br \/>\nAnswer:<br \/>\n5 X \\(\\frac{2}{3}\\) = 5 X 2 X \\(\\frac{1}{3}\\) = 10 X \\(\\frac{1}{3}\\)=<br \/>\n\\(\\frac{10}{3}\\).<\/p>\n<p>Explanation:<br \/>\nFirst we write \\(\\frac{2}{3}\\) as \\(\\frac{1}{3}\\)+\\(\\frac{1}{3}\\)=<br \/>\n2 X \\(\\frac{1}{3}\\) then multiply it by 5 which is 5 X 2 X \\(\\frac{1}{3}\\)=<br \/>\n10 X \\(\\frac{1}{3}\\)= \\(\\frac{10}{3}\\).<\/p>\n<p>Question 5.<br \/>\n<img decoding=\"async\" loading=\"lazy\" class=\"alignnone size-full wp-image-13072\" src=\"https:\/\/ccssanswers.com\/wp-content\/uploads\/2020\/12\/Big-Ideas-Math-Solutions-Grade-4-Chapter-9-Multiply-Whole-Numbers-and-Fractions-18.png\" alt=\"Big Ideas Math Solutions Grade 4 Chapter 9 Multiply Whole Numbers and Fractions 18\" width=\"64\" height=\"54\" \/><br \/>\nAnswer:<br \/>\n6 X \\(\\frac{5}{8}\\)= 6 X 5 X \\(\\frac{1}{8}\\)= 30 X \\(\\frac{1}{8}\\) =<br \/>\n\\(\\frac{30}{8}\\).<\/p>\n<p>Explanation:<br \/>\nFirst we write \\(\\frac{5}{8}\\) as \\(\\frac{1}{8}\\)+ \\(\\frac{1}{8}\\)+<br \/>\n\\(\\frac{1}{8}\\) + \\(\\frac{1}{8}\\)+ \\(\\frac{1}{8}\\) = 5 X \\(\\frac{1}{8}\\)<br \/>\nthen multiply it by 6 which is 6 X 5 X \\(\\frac{1}{8}\\)=30 X \\(\\frac{1}{8}\\)= \\(\\frac{30}{8}\\).<\/p>\n<p>Question 6.<br \/>\n<img decoding=\"async\" loading=\"lazy\" class=\"alignnone size-full wp-image-13073\" src=\"https:\/\/ccssanswers.com\/wp-content\/uploads\/2020\/12\/Big-Ideas-Math-Solutions-Grade-4-Chapter-9-Multiply-Whole-Numbers-and-Fractions-19.png\" alt=\"Big Ideas Math Solutions Grade 4 Chapter 9 Multiply Whole Numbers and Fractions 19\" width=\"67\" height=\"70\" \/><br \/>\nAnswer:<br \/>\n9 X \\(\\frac{7}{4}\\) = 9 X 7 X\\(\\frac{1}{4}\\)= 63 X \\(\\frac{1}{4}\\) =<br \/>\n\\(\\frac{63}{4}\\).<\/p>\n<p>Explanation:<br \/>\nFirst we write \\(\\frac{7}{4}\\) as \\(\\frac{1}{4}\\)+\\(\\frac{1}{4}\\)+<br \/>\n\\(\\frac{1}{4}\\)+ \\(\\frac{1}{4}\\)+\\(\\frac{1}{4}\\)+\\(\\frac{1}{4}\\)+<br \/>\n\\(\\frac{1}{4}\\) = 7 x \\(\\frac{1}{4}\\)<br \/>\nthen we multiply it by 9 which is 9 X 7 X \\(\\frac{1}{4}\\)= 63 X \\(\\frac{1}{4}\\) =<br \/>\n\\(\\frac{63}{4}\\).<\/p>\n<p>Question 7.<br \/>\n<img decoding=\"async\" loading=\"lazy\" class=\"alignnone size-full wp-image-13074\" src=\"https:\/\/ccssanswers.com\/wp-content\/uploads\/2020\/12\/Big-Ideas-Math-Solutions-Grade-4-Chapter-9-Multiply-Whole-Numbers-and-Fractions-20.png\" alt=\"Big Ideas Math Solutions Grade 4 Chapter 9 Multiply Whole Numbers and Fractions 20\" width=\"65\" height=\"44\" \/><br \/>\nAnswer:<br \/>\n7 X \\(\\frac{4}{12}\\)=7 X 4 X \\(\\frac{1}{12}\\)= 28 X \\(\\frac{1}{12}\\)=<br \/>\n\\(\\frac{28}{12}\\) also 7 X \\(\\frac{4}{12}\\)= 7 X \u00a0\\(\\frac{1}{3}\\)= \\(\\frac{7}{3}\\).<\/p>\n<p>Explanation:<br \/>\nFirst we write \\(\\frac{4}{12}\\) as \\(\\frac{1}{12}\\)+ \\(\\frac{1}{12}\\)+<br \/>\n\\(\\frac{1}{12}\\)+\\(\\frac{1}{12}\\)= 4 X \\(\\frac{1}{12}\\) then we multiply it by 7<br \/>\nwhich is 7 X 4 X \\(\\frac{1}{12}\\)= 28 X \\(\\frac{1}{12}\\)=\\(\\frac{28}{12}\\)<br \/>\nwe can also simplify 7 X \\(\\frac{4}{12}\\) as 4,12 can be divided by 4 we can also write<br \/>\n7 X \\(\\frac{4}{12}\\) as 7 X \u00a0\\(\\frac{1}{3}\\)= \\(\\frac{7}{3}\\).<\/p>\n<p>Question 8.<br \/>\n<img decoding=\"async\" loading=\"lazy\" class=\"alignnone size-full wp-image-13075\" src=\"https:\/\/ccssanswers.com\/wp-content\/uploads\/2020\/12\/Big-Ideas-Math-Solutions-Grade-4-Chapter-9-Multiply-Whole-Numbers-and-Fractions-21.png\" alt=\"Big Ideas Math Solutions Grade 4 Chapter 9 Multiply Whole Numbers and Fractions 21\" width=\"60\" height=\"46\" \/><br \/>\nAnswer:<br \/>\n\\(\\frac{9}{6}\\) X 8 = 9 X \\(\\frac{1}{6}\\) X 8 = 72 X \\(\\frac{1}{6}\\) =<br \/>\n\\(\\frac{72}{6}\\) =12.<\/p>\n<p>Explanation:<br \/>\nFirst we write \\(\\frac{9}{6}\\) as \\(\\frac{1}{6}\\) +\\(\\frac{1}{6}\\) +<br \/>\n\\(\\frac{1}{6}\\) + \\(\\frac{1}{6}\\) +\\(\\frac{1}{6}\\) +\\(\\frac{1}{6}\\) +<br \/>\n\\(\\frac{1}{6}\\) + \\(\\frac{1}{6}\\) +\\(\\frac{1}{6}\\) =9 X \\(\\frac{1}{6}\\)<br \/>\nthen we multiply it by 8 which is 9 X 8 X \\(\\frac{1}{6}\\) = 72 X \\(\\frac{1}{6}\\) =<br \/>\n\\(\\frac{72}{6}\\)\u00a0 further as 6 can divide 72 and leaving no remainder we write \\(\\frac{72}{6}\\) =12.<\/p>\n<p>Question 9.<br \/>\n<img decoding=\"async\" loading=\"lazy\" class=\"alignnone size-full wp-image-13076\" src=\"https:\/\/ccssanswers.com\/wp-content\/uploads\/2020\/12\/Big-Ideas-Math-Solutions-Grade-4-Chapter-9-Multiply-Whole-Numbers-and-Fractions-22.png\" alt=\"Big Ideas Math Solutions Grade 4 Chapter 9 Multiply Whole Numbers and Fractions 22\" width=\"87\" height=\"54\" \/><br \/>\nAnswer:<br \/>\n10 X \\(\\frac{20}{100}\\) = 10 X \\(\\frac{2}{10}\\)=2 X 10 X \\(\\frac{1}{10}\\)=<br \/>\n20 \\(\\frac{1}{10}\\)=\\(\\frac{20}{10}\\)=2.<\/p>\n<p>Explanation:<br \/>\nFirst we write \\(\\frac{20}{100}\\) = \\(\\frac{2}{10}\\) as \\(\\frac{1}{10}\\) +<br \/>\n\\(\\frac{1}{10}\\) = 2 X \\(\\frac{1}{10}\\) then multiply it by 10 which is<br \/>\n2 X 10 X \\(\\frac{1}{10}\\)= 20 X \\(\\frac{1}{10}\\)=\\(\\frac{20}{10}\\)<br \/>\nand 10 can divide 20 leaving no remainder further we can write \\(\\frac{20}{10}\\) as 2.<\/p>\n<p><strong>Number Sense<\/strong><br \/>\nFind the unknown number.<\/p>\n<p>Question 10.<br \/>\n<img decoding=\"async\" loading=\"lazy\" class=\"alignnone size-full wp-image-13077\" src=\"https:\/\/ccssanswers.com\/wp-content\/uploads\/2020\/12\/Big-Ideas-Math-Solutions-Grade-4-Chapter-9-Multiply-Whole-Numbers-and-Fractions-23.png\" alt=\"Big Ideas Math Solutions Grade 4 Chapter 9 Multiply Whole Numbers and Fractions 23\" width=\"125\" height=\"61\" \/><br \/>\nAnswer:<br \/>\nThe unknown number is 2.<\/p>\n<p>Explanation:<br \/>\n___ X \\(\\frac{8}{10}\\) = \\(\\frac{16}{10}\\)= to get the unknown number we take it as P,<br \/>\nP X \\(\\frac{8}{10}\\) = \\(\\frac{16}{10}\\) means P = \\(\\frac{16}{10}\\) X<br \/>\n\\(\\frac{10}{8}\\)\u00a0 we get 2 , so P=2.<\/p>\n<p>Question 11.<br \/>\n<img decoding=\"async\" loading=\"lazy\" class=\"alignnone size-full wp-image-13078\" src=\"https:\/\/ccssanswers.com\/wp-content\/uploads\/2020\/12\/Big-Ideas-Math-Solutions-Grade-4-Chapter-9-Multiply-Whole-Numbers-and-Fractions-24.png\" alt=\"Big Ideas Math Solutions Grade 4 Chapter 9 Multiply Whole Numbers and Fractions 24\" width=\"122\" height=\"74\" \/><br \/>\nAnswer:<br \/>\nThe unknown number is 5.<\/p>\n<p>Explanation:<br \/>\nLet us take unknown letter as P so 4 X \\(\\frac{P}{2}\\) = \\(\\frac{20}{2}\\) ,<br \/>\n4 X P= 2 X \\(\\frac{20}{2}\\) to get value of P we take 4 to other side ,<br \/>\nTherefore P=20 X \\(\\frac{1}{4}\\) = 5, so the unknown number is 5.<\/p>\n<p>Question 12.<br \/>\n<img decoding=\"async\" loading=\"lazy\" class=\"alignnone size-full wp-image-13079\" src=\"https:\/\/ccssanswers.com\/wp-content\/uploads\/2020\/12\/Big-Ideas-Math-Solutions-Grade-4-Chapter-9-Multiply-Whole-Numbers-and-Fractions-25.png\" alt=\"Big Ideas Math Solutions Grade 4 Chapter 9 Multiply Whole Numbers and Fractions 25\" width=\"129\" height=\"74\" \/><br \/>\nAnswer:<br \/>\nThe unknown number is 100.<\/p>\n<p>Explanation:<br \/>\nLet us take unknown number as P given 3 X \\(\\frac{9}{P}\\) = \\(\\frac{27}{100}\\) ,<br \/>\n27 X[ latex]\\frac{1}{P}[\/latex] = \\(\\frac{27}{100}\\), Therefore P= 27 X \\(\\frac{100}{27}\\)=100.<\/p>\n<p>Question 13.<br \/>\n<strong>Reasoning<\/strong><br \/>\nWithout calculating, would you plot the product of 5 and \\(\\frac{3}{6}\\) to the left or to the right of 5 on a number line? Explain.<br \/>\n<img decoding=\"async\" loading=\"lazy\" class=\"alignnone size-full wp-image-13080\" src=\"https:\/\/ccssanswers.com\/wp-content\/uploads\/2020\/12\/Big-Ideas-Math-Solutions-Grade-4-Chapter-9-Multiply-Whole-Numbers-and-Fractions-26.png\" alt=\"Big Ideas Math Solutions Grade 4 Chapter 9 Multiply Whole Numbers and Fractions 26\" width=\"303\" height=\"75\" srcset=\"https:\/\/ccssanswers.com\/wp-content\/uploads\/2020\/12\/Big-Ideas-Math-Solutions-Grade-4-Chapter-9-Multiply-Whole-Numbers-and-Fractions-26.png 303w, https:\/\/ccssanswers.com\/wp-content\/uploads\/2020\/12\/Big-Ideas-Math-Solutions-Grade-4-Chapter-9-Multiply-Whole-Numbers-and-Fractions-26-300x74.png 300w\" sizes=\"(max-width: 303px) 100vw, 303px\" \/><br \/>\nAnswer:<br \/>\nYes , without calculating we can plot 5 and \\(\\frac{3}{6}\\) to the left of 5<br \/>\n<img decoding=\"async\" loading=\"lazy\" class=\"alignnone wp-image-23250 size-full\" src=\"https:\/\/ccssanswers.com\/wp-content\/uploads\/2020\/12\/9-Multiply-Whole-Numbers-and-Fractions-9.bmp\" alt=\"\" width=\"350\" height=\"76\" srcset=\"https:\/\/ccssanswers.com\/wp-content\/uploads\/2020\/12\/9-Multiply-Whole-Numbers-and-Fractions-9.bmp 350w, https:\/\/ccssanswers.com\/wp-content\/uploads\/2020\/12\/9-Multiply-Whole-Numbers-and-Fractions-9-300x65.jpg 300w\" sizes=\"(max-width: 350px) 100vw, 350px\" \/><\/p>\n<p>Explanation:<br \/>\n5 X \\(\\frac{3}{6}\\)= 5 X\u00a0 \\(\\frac{1}{2}\\) since the denominator of each given fraction is <span style=\"font-size: 16px;\">2<br \/>\ndivide the space between every pairs of two consecutive integers (on the number line) in 2 equal parts each part<br \/>\nso obtained will represent the fraction \\(\\frac{1}{2}\\) , so on the number line we move 5 parts on the<br \/>\nright-side of zero as shown in the figure.<br \/>\n<\/span><\/p>\n<p>Question 14.<br \/>\n<strong>Patterns<\/strong><br \/>\nDescribe and complete the pattern.<br \/>\n<img decoding=\"async\" loading=\"lazy\" class=\"alignnone size-full wp-image-13081\" src=\"https:\/\/ccssanswers.com\/wp-content\/uploads\/2020\/12\/Big-Ideas-Math-Solutions-Grade-4-Chapter-9-Multiply-Whole-Numbers-and-Fractions-27.png\" alt=\"Big Ideas Math Solutions Grade 4 Chapter 9 Multiply Whole Numbers and Fractions 27\" width=\"207\" height=\"290\" \/><br \/>\nAnswer:<br \/>\n<img decoding=\"async\" loading=\"lazy\" class=\"alignnone wp-image-23251 size-full\" src=\"https:\/\/ccssanswers.com\/wp-content\/uploads\/2020\/12\/9-Multiply-Whole-Numbers-and-Fractions-10.bmp\" alt=\"\" width=\"265\" height=\"308\" srcset=\"https:\/\/ccssanswers.com\/wp-content\/uploads\/2020\/12\/9-Multiply-Whole-Numbers-and-Fractions-10.bmp 265w, https:\/\/ccssanswers.com\/wp-content\/uploads\/2020\/12\/9-Multiply-Whole-Numbers-and-Fractions-10-258x300.jpg 258w\" sizes=\"(max-width: 265px) 100vw, 265px\" \/><br \/>\nExplanation:<br \/>\nWe first write the expressions as multiple of unit fraction and find the product so<br \/>\n1. 3 X \\(\\frac{1}{5}\\) can be written as\u00a0 product of 3 X 1 X\u00a0 \\(\\frac{1}{5}\\)=<br \/>\n3 X \\(\\frac{1}{5}\\) = \\(\\frac{3}{5}\\)<br \/>\n2. 3 X \\(\\frac{2}{5}\\)\u00a0 can be written as product of\u00a0 3 X 2 X \\(\\frac{1}{5}\\) =<br \/>\n6 X \\(\\frac{1}{5}\\) = \\(\\frac{6}{5}\\)<br \/>\n3. 3 X \\(\\frac{3}{5}\\) can be written as product of 3 X 3 X \\(\\frac{1}{5}\\) =<br \/>\n9 X \\(\\frac{1}{5}\\) = \\(\\frac{9}{5}\\)<br \/>\n4. 3 X \\(\\frac{4}{5}\\) can be written as product of\u00a0 3 X 4 X \\(\\frac{1}{5}\\) =<br \/>\n12 X \\(\\frac{1}{5}\\) = \\(\\frac{12}{5}\\)<br \/>\n5. 3 X \\(\\frac{5}{5}\\) can be written as product of 3 X 5 X \\(\\frac{1}{5}\\) =<br \/>\n15 X \\(\\frac{1}{5}\\) = \\(\\frac{15}{5}\\) further can be simplified as 15,5 goes in 5,<br \/>\nso dividing by 5 we get \\(\\frac{15}{5}\\) =\u00a0 3.<\/p>\n<p><strong>Think and Grow: Modeling Real Life<\/strong><\/p>\n<p>A bird keeper uses a \\(\\frac{1}{3}\\) cup scoop to feed 3 birds. He feeds each bird \\(\\frac{2}{3}\\) cup of birdseed. How many times does he fill the scoop?<br \/>\nThree birds each need \\(\\frac{2}{3}\\) cup of birdseed, so find 3 \u00d7 \\(\\frac{2}{3}\\).<br \/>\n<img decoding=\"async\" loading=\"lazy\" class=\"alignnone size-full wp-image-13082\" src=\"https:\/\/ccssanswers.com\/wp-content\/uploads\/2020\/12\/Big-Ideas-Math-Solutions-Grade-4-Chapter-9-Multiply-Whole-Numbers-and-Fractions-28.png\" alt=\"Big Ideas Math Solutions Grade 4 Chapter 9 Multiply Whole Numbers and Fractions 28\" width=\"210\" height=\"159\" \/><br \/>\n<img decoding=\"async\" loading=\"lazy\" class=\"alignnone size-full wp-image-13083\" src=\"https:\/\/ccssanswers.com\/wp-content\/uploads\/2020\/12\/Big-Ideas-Math-Solutions-Grade-4-Chapter-9-Multiply-Whole-Numbers-and-Fractions-29.png\" alt=\"Big Ideas Math Solutions Grade 4 Chapter 9 Multiply Whole Numbers and Fractions 29\" width=\"588\" height=\"188\" srcset=\"https:\/\/ccssanswers.com\/wp-content\/uploads\/2020\/12\/Big-Ideas-Math-Solutions-Grade-4-Chapter-9-Multiply-Whole-Numbers-and-Fractions-29.png 588w, https:\/\/ccssanswers.com\/wp-content\/uploads\/2020\/12\/Big-Ideas-Math-Solutions-Grade-4-Chapter-9-Multiply-Whole-Numbers-and-Fractions-29-300x96.png 300w\" sizes=\"(max-width: 588px) 100vw, 588px\" \/><br \/>\nAnswer:<br \/>\n<img decoding=\"async\" loading=\"lazy\" class=\"alignnone wp-image-23312 size-full\" src=\"https:\/\/ccssanswers.com\/wp-content\/uploads\/2020\/12\/9-Multiply-Whole-Numbers-and-Fractions-11.bmp\" alt=\"\" width=\"588\" height=\"188\" srcset=\"https:\/\/ccssanswers.com\/wp-content\/uploads\/2020\/12\/9-Multiply-Whole-Numbers-and-Fractions-11.bmp 588w, https:\/\/ccssanswers.com\/wp-content\/uploads\/2020\/12\/9-Multiply-Whole-Numbers-and-Fractions-11-300x96.jpg 300w\" sizes=\"(max-width: 588px) 100vw, 588px\" \/><\/p>\n<p>Explanation :<br \/>\nGiven A bird keeper uses a \\(\\frac{1}{3}\\) cup scoop to feed 3 birds each bird he feeds<br \/>\n\\(\\frac{2}{3}\\) cup of birdseed, Three birds each need \\(\\frac{2}{3}\\) cup of birdseed<br \/>\nso the bird keeper fills the scoop as 3 X \\(\\frac{2}{3}\\) = 3 X _____P______ X \\(\\frac{1}{3}\\) here<br \/>\nP is the\u00a0 number of times the bird keeper fills the cup scoop.<br \/>\n3 X 2 X \\(\\frac{1}{3}\\) =\u00a0 3 X P X \\(\\frac{1}{3}\\) , when we equate both sides,<br \/>\nwe get 3 X 2 = 3 X P , therefore P = 2.<br \/>\n<strong>Show and Grow<\/strong><\/p>\n<p>Question 15.<br \/>\nA chef makes 4 servings of honey1oatmeal. She uses a \\(\\frac{1}{2}\\) tablespoon measuring spoon to measure \\(\\frac{3}{2}\\) tablespoons of honey for each serving. How many times does she fill the measuring spoon?<br \/>\nAnswer:<br \/>\n3 times the chef fill the measuring spoon.<\/p>\n<p>Explanation:<br \/>\nChef uses a \\(\\frac{1}{2}\\) table spoon as measuring spoon, To measure honey for each serving<br \/>\nshe needed for each serving is \\(\\frac{3}{2}\\) , so 4 X \\(\\frac{3}{2}\\) ,<br \/>\nLet us take P as number of times of measuring spoon , Given 4 X \\(\\frac{3}{2}\\) =<br \/>\n4 X <span style=\"text-decoration: underline;\">_P_<\/span> X \\(\\frac{1}{2}\\), 4 X <span style=\"text-decoration: underline;\">___3___<\/span> X \\(\\frac{1}{2}\\)= 4 X <span style=\"text-decoration: underline;\">_P_<\/span> X \\(\\frac{1}{2}\\) ,<br \/>\nwe equate both sides\u00a0 we get value of P as 3 , therefore 3 times the chef fill the measuring spoon.<\/p>\n<p>Question 16.<br \/>\nYou have 7 magnetic blocks that are each \\(\\frac{9}{100}\\) meter long. You connect the ends of the blocks to make a snake. What fraction of a meter is the block snake?<br \/>\nAnswer:<br \/>\n\\(\\frac{63}{100}\\) meter is the block snake.<\/p>\n<p>Explanation:<br \/>\nGiven 7 magnetic blocks and each are \\(\\frac{9}{100}\\) meter long. After connecting the ends<br \/>\nof the blocks to make a snake is 7 X \\(\\frac{9}{100}\\) = 7 X 9 X \\(\\frac{1}{100}\\) =<br \/>\n63 X \\(\\frac{1}{100}\\) = \\(\\frac{63}{100}\\) meter.<\/p>\n<p>Question 17.<br \/>\nYour friend roller-skates \\(\\frac{15}{10}\\) miles each day for 5 days. How many miles does your friend roller-skate in all?<br \/>\n<img decoding=\"async\" loading=\"lazy\" class=\"alignnone size-full wp-image-13084\" src=\"https:\/\/ccssanswers.com\/wp-content\/uploads\/2020\/12\/Big-Ideas-Math-Solutions-Grade-4-Chapter-9-Multiply-Whole-Numbers-and-Fractions-30.png\" alt=\"Big Ideas Math Solutions Grade 4 Chapter 9 Multiply Whole Numbers and Fractions 30\" width=\"175\" height=\"158\" \/><br \/>\nAnswer:<br \/>\nMy friend roller skate \\(\\frac{15}{2}\\) miles in all.<\/p>\n<p>Explanation:<br \/>\nGiven friend roller-skates \\(\\frac{15}{10}\\) miles each day means \\(\\frac{3}{2}\\) miles<br \/>\neach day so for 5 days it is 5 X \\(\\frac{3}{2}\\) = 5 X 3 X \\(\\frac{1}{2}\\) =<br \/>\n15 X \\(\\frac{1}{2}\\) = \\(\\frac{15}{2}\\) miles.<\/p>\n<h3><a id=\"Understand_Multiples_of_Fractions_Homework_&amp;_Practice_9.2\"><\/a>Understand Multiples of Fractions Homework &amp; Practice 9.2<\/h3>\n<p>Write the product as a multiple of a unit fraction. Then find the product.<\/p>\n<p>Question 1.<br \/>\n<img decoding=\"async\" loading=\"lazy\" class=\"alignnone size-full wp-image-13085\" src=\"https:\/\/ccssanswers.com\/wp-content\/uploads\/2020\/12\/Big-Ideas-Math-Solutions-Grade-4-Chapter-9-Multiply-Whole-Numbers-and-Fractions-31.png\" alt=\"Big Ideas Math Solutions Grade 4 Chapter 9 Multiply Whole Numbers and Fractions 31\" width=\"64\" height=\"50\" \/><br \/>\nAnswer:<br \/>\n2 X \\(\\frac{2}{3}\\) = 2 X 2 X \\(\\frac{1}{3}\\) = 4 X (\\(\\frac{1}{3}\\)) =<br \/>\n\\(\\frac{4}{3}\\)<\/p>\n<p>Explanation:<br \/>\nTo write the product as a multiple of a unit fraction we write it \\(\\frac{2}{3}\\)<br \/>\nas 2 X \\(\\frac{1}{3}\\) and multiply by 2 = 2 X 2 X \\(\\frac{1}{3}\\) =<br \/>\n4 X \\(\\frac{1}{3}\\) = \\(\\frac{4}{3}\\)<\/p>\n<p>Question 2.<br \/>\n<img decoding=\"async\" loading=\"lazy\" class=\"alignnone size-full wp-image-13086\" src=\"https:\/\/ccssanswers.com\/wp-content\/uploads\/2020\/12\/Big-Ideas-Math-Solutions-Grade-4-Chapter-9-Multiply-Whole-Numbers-and-Fractions-32.png\" alt=\"Big Ideas Math Solutions Grade 4 Chapter 9 Multiply Whole Numbers and Fractions 32\" width=\"59\" height=\"53\" \/><br \/>\nAnswer:<br \/>\n3 X \\(\\frac{5}{8}\\) = 3 X 5 X \\(\\frac{1}{8}\\) = 15 X (\\(\\frac{1}{8}\\)) =<br \/>\n\\(\\frac{15}{8}\\).<\/p>\n<p>Explanation:<br \/>\nTo write the product as a multiple of a unit fraction we write it \\(\\frac{5}{8}\\) as<br \/>\n5 X \\(\\frac{1}{8}\\) and multiply by 3 = 3 X 5 X \\(\\frac{1}{8}\\) = 15 X \\(\\frac{1}{8}\\)<br \/>\n= \\(\\frac{15}{8}\\)<\/p>\n<p>Question 3.<br \/>\n<img decoding=\"async\" loading=\"lazy\" class=\"alignnone size-full wp-image-13087\" src=\"https:\/\/ccssanswers.com\/wp-content\/uploads\/2020\/12\/Big-Ideas-Math-Solutions-Grade-4-Chapter-9-Multiply-Whole-Numbers-and-Fractions-33.png\" alt=\"Big Ideas Math Solutions Grade 4 Chapter 9 Multiply Whole Numbers and Fractions 33\" width=\"64\" height=\"57\" \/><br \/>\nAnswer:<br \/>\n4 X \\(\\frac{8}{2}\\) = 4 X 8 X \\(\\frac{1}{2}\\) = 32 X (\\(\\frac{1}{2}\\)) =<br \/>\n\\(\\frac{32}{2}\\) =16.<\/p>\n<p>Explanation:<br \/>\nTo write the product as a multiple of a unit fraction we write it \\(\\frac{8}{2}\\) as<br \/>\n8 X \\(\\frac{1}{2}\\) and multiply by 4 = 4 X 8 X \\(\\frac{1}{2}\\) =<br \/>\n32 X \\(\\frac{1}{2}\\) = \\(\\frac{32}{2}\\) = 16.<\/p>\n<p>Question 4.<br \/>\n<img decoding=\"async\" loading=\"lazy\" class=\"alignnone size-full wp-image-13088\" src=\"https:\/\/ccssanswers.com\/wp-content\/uploads\/2020\/12\/Big-Ideas-Math-Solutions-Grade-4-Chapter-9-Multiply-Whole-Numbers-and-Fractions-34.png\" alt=\"Big Ideas Math Solutions Grade 4 Chapter 9 Multiply Whole Numbers and Fractions 34\" width=\"78\" height=\"58\" \/><br \/>\nAnswer:<br \/>\n5 X \\(\\frac{9}{10}\\) = 5 X 9 X \\(\\frac{1}{10}\\) = 45 X (\\(\\frac{1}{10}\\)) =<br \/>\n\\(\\frac{45}{10}\\) = \\(\\frac{9}{2}\\)<\/p>\n<p>Explanation:<br \/>\nTo write the product as a multiple of a unit fraction we write it \\(\\frac{9}{10}\\) as<br \/>\n9 X \\(\\frac{1}{10}\\) and multiply by 5 = 5 X 9 X \\(\\frac{1}{10}\\) =<br \/>\n45 X \\(\\frac{1}{10}\\) = \\(\\frac{45}{10}\\) = \\(\\frac{9}{2}\\).<\/p>\n<p>Question 5.<br \/>\n<img decoding=\"async\" loading=\"lazy\" class=\"alignnone size-full wp-image-13089\" src=\"https:\/\/ccssanswers.com\/wp-content\/uploads\/2020\/12\/Big-Ideas-Math-Solutions-Grade-4-Chapter-9-Multiply-Whole-Numbers-and-Fractions-35.png\" alt=\"Big Ideas Math Solutions Grade 4 Chapter 9 Multiply Whole Numbers and Fractions 35\" width=\"59\" height=\"52\" \/><br \/>\nAnswer:<br \/>\n8 X \\(\\frac{6}{5}\\) = 8 X 6 X \\(\\frac{1}{5}\\) = 48X (\\(\\frac{1}{5}\\)) =<br \/>\n\\(\\frac{48}{5}\\)<\/p>\n<p>Explanation:<br \/>\nTo write the product as a multiple of a unit fraction we write it \\(\\frac{6}{5}\\) as<br \/>\n6 X \\(\\frac{1}{5}\\) and multiply by 8 = 8 X 6 X \\(\\frac{1}{5}\\) =<br \/>\n48 X \\(\\frac{1}{5}\\) = \\(\\frac{48}{5}\\).<\/p>\n<p>Question 6.<br \/>\n<img decoding=\"async\" loading=\"lazy\" class=\"alignnone size-full wp-image-13090\" src=\"https:\/\/ccssanswers.com\/wp-content\/uploads\/2020\/12\/Big-Ideas-Math-Solutions-Grade-4-Chapter-9-Multiply-Whole-Numbers-and-Fractions-36.png\" alt=\"Big Ideas Math Solutions Grade 4 Chapter 9 Multiply Whole Numbers and Fractions 36\" width=\"62\" height=\"50\" \/><br \/>\nAnswer:<br \/>\n10 X \\(\\frac{2}{4}\\) = 10 X 2 X \\(\\frac{1}{4}\\) = 20 X (\\(\\frac{1}{4}\\)) =<br \/>\n\\(\\frac{20}{4}\\) = \\(\\frac{10}{2}\\).<\/p>\n<p>Explanation:<br \/>\nTo write the product as a multiple of a unit fraction we write it \\(\\frac{2}{4}\\) as 2 X \\(\\frac{1}{4}\\)<br \/>\nand multiply by 10 = 2 X 10 X \\(\\frac{1}{4}\\) = 20 X \\(\\frac{1}{4}\\) = \\(\\frac{20}{4}\\) =<br \/>\n\\(\\frac{10}{2}\\).<\/p>\n<p>Question 7.<br \/>\n<strong>Number Sense<\/strong><br \/>\nWhich expression are equivalent to <img decoding=\"async\" loading=\"lazy\" class=\"alignnone size-full wp-image-13091\" src=\"https:\/\/ccssanswers.com\/wp-content\/uploads\/2020\/12\/Big-Ideas-Math-Solutions-Grade-4-Chapter-9-Multiply-Whole-Numbers-and-Fractions-37.png\" alt=\"Big Ideas Math Solutions Grade 4 Chapter 9 Multiply Whole Numbers and Fractions 37\" width=\"45\" height=\"41\" \/> ?<br \/>\n<img decoding=\"async\" loading=\"lazy\" class=\"alignnone size-full wp-image-13092\" src=\"https:\/\/ccssanswers.com\/wp-content\/uploads\/2020\/12\/Big-Ideas-Math-Solutions-Grade-4-Chapter-9-Multiply-Whole-Numbers-and-Fractions-38.png\" alt=\"Big Ideas Math Solutions Grade 4 Chapter 9 Multiply Whole Numbers and Fractions 38\" width=\"518\" height=\"56\" srcset=\"https:\/\/ccssanswers.com\/wp-content\/uploads\/2020\/12\/Big-Ideas-Math-Solutions-Grade-4-Chapter-9-Multiply-Whole-Numbers-and-Fractions-38.png 518w, https:\/\/ccssanswers.com\/wp-content\/uploads\/2020\/12\/Big-Ideas-Math-Solutions-Grade-4-Chapter-9-Multiply-Whole-Numbers-and-Fractions-38-300x32.png 300w\" sizes=\"(max-width: 518px) 100vw, 518px\" \/><br \/>\nAnswer:<br \/>\nThe expressions equivalent to 4 X \\(\\frac{7}{8}\\) are\u00a0 (4 X 7) x \\(\\frac{1}{8}\\) ,<br \/>\n\\(\\frac{28}{8}\\),\\(\\frac{7}{8}\\)+\\(\\frac{7}{8}\\)+\\(\\frac{7}{8}\\) +<br \/>\n\\(\\frac{7}{8}\\).<\/p>\n<p>Explanation:<br \/>\nWe have the value of expression of 4 X \\(\\frac{7}{8}\\) as \\(\\frac{28}{8}\\) So<br \/>\n1.(4 X 7) x \\(\\frac{1}{8}\\)= \\(\\frac{28}{8}\\)<br \/>\n2. \\(\\frac{28}{8}\\)=\\(\\frac{28}{8}\\)<br \/>\n3. 4 X 7 \u2260 \\(\\frac{28}{8}\\)<br \/>\n4. \\(\\frac{32}{7}\\) \u2260 \\(\\frac{28}{8}\\)<br \/>\n5. \\(\\frac{7}{8}\\)+\\(\\frac{7}{8}\\)+\\(\\frac{7}{8}\\)+\\(\\frac{7}{8}\\) =<br \/>\n\\(\\frac{28}{8}\\), Therefore expressions 1,2,5 are equivalent to \\(\\frac{28}{8}\\).<br \/>\nThe expressions equivalent to 4 X \\(\\frac{7}{8}\\) are\u00a0 (4 X 7) x \\(\\frac{1}{8}\\) , \\(\\frac{28}{8}\\),\\(\\frac{7}{8}\\)+\\(\\frac{7}{8}\\)+\\(\\frac{7}{8}\\)+\\(\\frac{7}{8}\\)<\/p>\n<p>Question 8.<br \/>\nWhich is greater, <img decoding=\"async\" loading=\"lazy\" class=\"alignnone size-full wp-image-13094\" src=\"https:\/\/ccssanswers.com\/wp-content\/uploads\/2020\/12\/Big-Ideas-Math-Solutions-Grade-4-Chapter-9-Multiply-Whole-Numbers-and-Fractions-39.png\" alt=\"Big Ideas Math Solutions Grade 4 Chapter 9 Multiply Whole Numbers and Fractions 39\" width=\"111\" height=\"41\" \/> ? Explain.<br \/>\nAnswer:<br \/>\n6 X \\(\\frac{6}{2}\\) is greater<\/p>\n<p>Explanation:<br \/>\n6 X \\(\\frac{6}{2}\\)= 6 X 6 X \\(\\frac{1}{2}\\)=36 X \\(\\frac{1}{2}\\)=<br \/>\n\\(\\frac{36}{2}\\) and 5 X \\(\\frac{7}{2}\\) =5 X 7 X \\(\\frac{1}{2}\\)=<br \/>\n35 X \\(\\frac{1}{2}\\), Now comparing both sides 36 X \\(\\frac{1}{2}\\) and<br \/>\n35 X \\(\\frac{1}{2}\\) we see 36 X \\(\\frac{1}{2}\\) &gt; 35 X \\(\\frac{1}{2}\\)<br \/>\nso 6 X \\(\\frac{6}{2}\\) is greater.<\/p>\n<p>Question 9.<br \/>\n<strong>Structure<\/strong><br \/>\nYour friend fills a \\(\\frac{3}{4}\\) &#8211; cup measuring cup with rice 2 times.<br \/>\nWrite an equation to show how much rice she uses.<\/p>\n<p>Answer:<br \/>\nFriend uses \\(\\frac{3}{2}\\) cups.<\/p>\n<p>Explanation:<br \/>\nFriend fills a \\(\\frac{3}{4}\\) &#8211; cup with rice 2 times, so she uses 2 X \\(\\frac{3}{4}\\) =<br \/>\n2 X 3 x \\(\\frac{1}{4}\\) = 6 X \\(\\frac{1}{4}\\)= \\(\\frac{6}{4}\\)=<br \/>\n\\(\\frac{3}{2}\\).<\/p>\n<p>Question 10.<br \/>\n<strong>Modeling Real Life<\/strong><br \/>\nYou are making a tornado in each of 2 bottles. Each bottle needs to contain \\(\\frac{20}{4}\\) cups of water.<br \/>\nYou only have a \\(\\frac{1}{4}\\) &#8211; cup measuring cup. How many times do you need to fill the measuring cup?<br \/>\n<img decoding=\"async\" loading=\"lazy\" class=\"alignnone size-full wp-image-13093\" src=\"https:\/\/ccssanswers.com\/wp-content\/uploads\/2020\/12\/Big-Ideas-Math-Solutions-Grade-4-Chapter-9-Multiply-Whole-Numbers-and-Fractions-39.1.png\" alt=\"Big Ideas Math Solutions Grade 4 Chapter 9 Multiply Whole Numbers and Fractions 39.1\" width=\"179\" height=\"196\" \/><br \/>\nAnswer:<br \/>\nTo make a tornado we require 40 cups of water.<\/p>\n<p>Explanation:<br \/>\nEach bottle needs \\(\\frac{20}{4}\\) cups of water and have a \\(\\frac{1}{4}\\) &#8211; cup<br \/>\nmeasuring cup, Now we take P as number of times for filling so \\(\\frac{20}{4}\\) =<br \/>\nP X \\(\\frac{1}{4}\\), 20 X \\(\\frac{1}{4}\\)=P X \\(\\frac{1}{4}\\),<br \/>\nEquating both sides we get\u00a0 P = 20,\u00a0 so it is 20 times to fill the measuring cups of water<br \/>\nfor one bottle, Given that to make a tornado we require 2 bottles, 2 X 20 cups of water = 40 cups of water.<\/p>\n<p>Question 11.<br \/>\n<strong>DIG DEEPER!<\/strong><br \/>\nYou and your friend are each selling 12 coupon books. So far, you have sold \\(\\frac{2}{6}\\)<br \/>\nof your books. Your friend has sold 3 times as many as you. What fraction of your friend\u2019s coupon books has she sold?<\/p>\n<p>Answer:<br \/>\nWe will get the fraction as whole 1 so friend has sold all the 12 coupon books.<\/p>\n<p>Explanation:<br \/>\nSo far i sold \\(\\frac{2}{6}\\) books out of 12 coupon books. Lets us take P number of books,<br \/>\ni have sold P out of 12 coupon books, P= 12 X \\(\\frac{2}{6}\\) =12 X 2 X \\(\\frac{1}{6}\\) =<br \/>\n24 X \\(\\frac{1}{6}\\) = \\(\\frac{24}{6}\\) =4 , So i have sold 4 coupon books,<br \/>\nGiven friend has sold 3 times as many as I, Means 3 X 4 =12 means friend has sold all the coupon books<\/p>\n<p><strong>Review &amp; Refresh<\/strong><\/p>\n<p>Find the product.<\/p>\n<p>Question 12.<br \/>\n12 \u00d7 47 = ___<br \/>\nAnswer:<br \/>\n12 X 47 = 564<\/p>\n<p>Explanation:<br \/>\nWhen 12 is multiplied by 47 we get the product as 564.<\/p>\n<p>Question 13.<br \/>\n35 \u00d7 31 = ___<br \/>\nAnswer:<br \/>\n35 X 31 =1,085<\/p>\n<p>Explanation:<br \/>\nWhen 35 is multiplied by 31 we get the product as 1,085.<\/p>\n<p>Question 14.<br \/>\n58 \u00d7 49 = ___<br \/>\nAnswer:<br \/>\n58 X 49 = 2,842<\/p>\n<p>Explanation:<br \/>\nWhen 58 is multiplied by 49 we get the product as 2,842.<\/p>\n<h3><a id=\"Lesson_9.3_Multiply_Whole_Numbers_and_Fractions\"><\/a>Lesson 9.3 Multiply Whole Numbers and 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 decoding=\"async\" loading=\"lazy\" class=\"alignnone size-full wp-image-13095\" src=\"https:\/\/ccssanswers.com\/wp-content\/uploads\/2020\/12\/Big-Ideas-Math-Solutions-Grade-4-Chapter-9-Multiply-Whole-Numbers-and-Fractions-40.png\" alt=\"Big Ideas Math Solutions Grade 4 Chapter 9 Multiply Whole Numbers and Fractions 40\" width=\"208\" height=\"307\" srcset=\"https:\/\/ccssanswers.com\/wp-content\/uploads\/2020\/12\/Big-Ideas-Math-Solutions-Grade-4-Chapter-9-Multiply-Whole-Numbers-and-Fractions-40.png 208w, https:\/\/ccssanswers.com\/wp-content\/uploads\/2020\/12\/Big-Ideas-Math-Solutions-Grade-4-Chapter-9-Multiply-Whole-Numbers-and-Fractions-40-203x300.png 203w\" sizes=\"(max-width: 208px) 100vw, 208px\" \/><br \/>\n<strong>Construct Arguments<\/strong><br \/>\nExplain how to \ufb01nd the product of a whole number and a fraction without using models.<br \/>\nAnswer:<br \/>\n<img decoding=\"async\" loading=\"lazy\" class=\"alignnone wp-image-23521 size-full\" src=\"https:\/\/ccssanswers.com\/wp-content\/uploads\/2020\/12\/9-Multiply-Whole-Numbers-and-Fractions-12.bmp\" alt=\"\" width=\"1366\" height=\"768\" srcset=\"https:\/\/ccssanswers.com\/wp-content\/uploads\/2020\/12\/9-Multiply-Whole-Numbers-and-Fractions-12.bmp 1366w, https:\/\/ccssanswers.com\/wp-content\/uploads\/2020\/12\/9-Multiply-Whole-Numbers-and-Fractions-12-300x169.jpg 300w, https:\/\/ccssanswers.com\/wp-content\/uploads\/2020\/12\/9-Multiply-Whole-Numbers-and-Fractions-12-1024x576.jpg 1024w, https:\/\/ccssanswers.com\/wp-content\/uploads\/2020\/12\/9-Multiply-Whole-Numbers-and-Fractions-12-768x432.jpg 768w\" sizes=\"(max-width: 1366px) 100vw, 1366px\" \/><img decoding=\"async\" loading=\"lazy\" class=\"alignnone size-full wp-image-30844\" src=\"https:\/\/ccssanswers.com\/wp-content\/uploads\/2020\/12\/9-Multiply-Whole-Numbers-and-Fractions-12-1.bmp\" alt=\"\" width=\"1366\" height=\"768\" srcset=\"https:\/\/ccssanswers.com\/wp-content\/uploads\/2020\/12\/9-Multiply-Whole-Numbers-and-Fractions-12-1.bmp 1366w, https:\/\/ccssanswers.com\/wp-content\/uploads\/2020\/12\/9-Multiply-Whole-Numbers-and-Fractions-12-1-300x169.jpg 300w, https:\/\/ccssanswers.com\/wp-content\/uploads\/2020\/12\/9-Multiply-Whole-Numbers-and-Fractions-12-1-1024x576.jpg 1024w, https:\/\/ccssanswers.com\/wp-content\/uploads\/2020\/12\/9-Multiply-Whole-Numbers-and-Fractions-12-1-768x432.jpg 768w\" sizes=\"(max-width: 1366px) 100vw, 1366px\" \/><img decoding=\"async\" loading=\"lazy\" class=\"alignnone size-full wp-image-30844\" src=\"https:\/\/ccssanswers.com\/wp-content\/uploads\/2020\/12\/9-Multiply-Whole-Numbers-and-Fractions-12-1.bmp\" alt=\"\" width=\"1366\" height=\"768\" srcset=\"https:\/\/ccssanswers.com\/wp-content\/uploads\/2020\/12\/9-Multiply-Whole-Numbers-and-Fractions-12-1.bmp 1366w, https:\/\/ccssanswers.com\/wp-content\/uploads\/2020\/12\/9-Multiply-Whole-Numbers-and-Fractions-12-1-300x169.jpg 300w, https:\/\/ccssanswers.com\/wp-content\/uploads\/2020\/12\/9-Multiply-Whole-Numbers-and-Fractions-12-1-1024x576.jpg 1024w, https:\/\/ccssanswers.com\/wp-content\/uploads\/2020\/12\/9-Multiply-Whole-Numbers-and-Fractions-12-1-768x432.jpg 768w\" sizes=\"(max-width: 1366px) 100vw, 1366px\" \/><br \/>\nExplanation:<\/p>\n<p>We notice that each expression can be written as the product as a multiple of a unit fraction,<br \/>\nThe product of a number and a counting number is a multiple of the number. We can find multiples<br \/>\nof unit fractions. To \ufb01nd the product of a whole number and a fraction without using models,<br \/>\nFirst we multiply the numerator by the whole number, then rewrite the expression as a multiple<br \/>\nof a unit fraction and denominator stays the same we get the product results.<\/p>\n<p><strong>Think and Grow: Multiply Whole Numbers and Fractions<\/strong><\/p>\n<p>You can \ufb01nd the product of a whole number and a fraction by multiplying the numerator by the whole number.<br \/>\nThe denominator stays the same.<br \/>\n<img decoding=\"async\" loading=\"lazy\" class=\"alignnone size-full wp-image-13096\" src=\"https:\/\/ccssanswers.com\/wp-content\/uploads\/2020\/12\/Big-Ideas-Math-Solutions-Grade-4-Chapter-9-Multiply-Whole-Numbers-and-Fractions-41.png\" alt=\"Big Ideas Math Solutions Grade 4 Chapter 9 Multiply Whole Numbers and Fractions 41\" width=\"619\" height=\"551\" srcset=\"https:\/\/ccssanswers.com\/wp-content\/uploads\/2020\/12\/Big-Ideas-Math-Solutions-Grade-4-Chapter-9-Multiply-Whole-Numbers-and-Fractions-41.png 619w, https:\/\/ccssanswers.com\/wp-content\/uploads\/2020\/12\/Big-Ideas-Math-Solutions-Grade-4-Chapter-9-Multiply-Whole-Numbers-and-Fractions-41-300x267.png 300w\" sizes=\"(max-width: 619px) 100vw, 619px\" \/><br \/>\nAnswer:<br \/>\n<img decoding=\"async\" loading=\"lazy\" class=\"alignnone wp-image-23722 size-full\" src=\"https:\/\/ccssanswers.com\/wp-content\/uploads\/2020\/12\/9-Multiply-Whole-Numbers-and-Fractions-13.bmp\" alt=\"\" width=\"784\" height=\"548\" srcset=\"https:\/\/ccssanswers.com\/wp-content\/uploads\/2020\/12\/9-Multiply-Whole-Numbers-and-Fractions-13.bmp 784w, https:\/\/ccssanswers.com\/wp-content\/uploads\/2020\/12\/9-Multiply-Whole-Numbers-and-Fractions-13-300x210.jpg 300w, https:\/\/ccssanswers.com\/wp-content\/uploads\/2020\/12\/9-Multiply-Whole-Numbers-and-Fractions-13-768x537.jpg 768w\" sizes=\"(max-width: 784px) 100vw, 784px\" \/><\/p>\n<p>Explanation:<br \/>\nTo find 4 X \\(\\frac{2}{3}\\)<br \/>\nMethod 1:\u00a0 Multiply the numerator by the whole number as 4 X 2 and divide by 3= \\(\\frac{8}{3}\\)<br \/>\nMethod 2 : Then writing the expression as a multiple of unit fraction \\(\\frac{2}{3}\\)=<br \/>\n4 X ( 2 X \\(\\frac{1}{3}\\) ) applying associative property of multiplication<br \/>\n(4 X 2) X \\(\\frac{1}{3}\\)= 8 X \\(\\frac{1}{3}\\)=\\(\\frac{8}{3}\\)<\/p>\n<p>Show and Grow<\/p>\n<p>Multiply.<\/p>\n<p>Question 1.<br \/>\n<img decoding=\"async\" loading=\"lazy\" class=\"alignnone size-full wp-image-13097\" src=\"https:\/\/ccssanswers.com\/wp-content\/uploads\/2020\/12\/Big-Ideas-Math-Solutions-Grade-4-Chapter-9-Multiply-Whole-Numbers-and-Fractions-42.png\" alt=\"Big Ideas Math Solutions Grade 4 Chapter 9 Multiply Whole Numbers and Fractions 42\" width=\"126\" height=\"47\" \/><br \/>\nAnswer:<br \/>\n4 X \\(\\frac{1}{6}\\) = \\(\\frac{4}{6}\\) also equals to \\(\\frac{2}{3}\\)<br \/>\nExplanation :<br \/>\nAlready the expression is in multiple of unit fraction so 4 X \\(\\frac{1}{6}\\) = \\(\\frac{4}{6}\\) and further simplification it is equal to \\(\\frac{2}{3}\\)<\/p>\n<p>Question 2.<br \/>\n<img decoding=\"async\" loading=\"lazy\" class=\"alignnone size-full wp-image-13098\" src=\"https:\/\/ccssanswers.com\/wp-content\/uploads\/2020\/12\/Big-Ideas-Math-Solutions-Grade-4-Chapter-9-Multiply-Whole-Numbers-and-Fractions-43.png\" alt=\"Big Ideas Math Solutions Grade 4 Chapter 9 Multiply Whole Numbers and Fractions 43\" width=\"116\" height=\"50\" \/><br \/>\nAnswer:<br \/>\n3 X \\(\\frac{2}{4}\\) = 3 X \\(\\frac{1}{2}\\) = \\(\\frac{3}{2}\\).<\/p>\n<p>Explanation:<br \/>\n3 X \\(\\frac{2}{4}\\) can be simplified as 3 X \\(\\frac{1}{2}\\) now the expression is in<br \/>\nmultiple of unit fraction so\u00a0 3 X \\(\\frac{1}{2}\\) =\\(\\frac{3}{2}\\).<\/p>\n<p>Question 3.<br \/>\n<img decoding=\"async\" loading=\"lazy\" class=\"alignnone size-full wp-image-13099\" src=\"https:\/\/ccssanswers.com\/wp-content\/uploads\/2020\/12\/Big-Ideas-Math-Solutions-Grade-4-Chapter-9-Multiply-Whole-Numbers-and-Fractions-44.png\" alt=\"Big Ideas Math Solutions Grade 4 Chapter 9 Multiply Whole Numbers and Fractions 44\" width=\"125\" height=\"51\" \/><br \/>\nAnswer:<br \/>\n7 X \u00a0\\(\\frac{3}{2}\\) = 7 x 3 X \u00a0\\(\\frac{1}{2}\\) = 21 X \\(\\frac{1}{2}\\) =<br \/>\n\\(\\frac{21}{2}\\).<\/p>\n<p>Explanation:<br \/>\n7 X \\(\\frac{3}{2}\\)\u00a0 first we write the expression as multiple of unit fraction so<br \/>\n7 X ( 3 X \\(\\frac{1}{2}\\) ) applying associative property of multiplication<br \/>\n( 7 X\u00a0 3) X \\(\\frac{1}{2}\\) ) = 21 X \\(\\frac{1}{2}\\) = \\(\\frac{21}{2}\\)<\/p>\n<p><strong>Apply and Grow: Practice<\/strong><\/p>\n<p>Multiply.<\/p>\n<p>Question 4.<br \/>\n<img decoding=\"async\" loading=\"lazy\" class=\"alignnone size-full wp-image-13100\" src=\"https:\/\/ccssanswers.com\/wp-content\/uploads\/2020\/12\/Big-Ideas-Math-Solutions-Grade-4-Chapter-9-Multiply-Whole-Numbers-and-Fractions-45.png\" alt=\"Big Ideas Math Solutions Grade 4 Chapter 9 Multiply Whole Numbers and Fractions 45\" width=\"119\" height=\"45\" \/><br \/>\nAnswer:<br \/>\n2 X \\(\\frac{1}{5}\\) = \\(\\frac{2}{5}\\).<\/p>\n<p>Explanation :<br \/>\nAlready the expression 2 X \\(\\frac{1}{5}\\) is a multiple of unit fraction so we multiply<br \/>\nthe whole with the numerator and numerator is being same, 2 X \\(\\frac{1}{5}\\) =<br \/>\n\\(\\frac{2}{5}\\).<\/p>\n<p>Question 5.<br \/>\n<img decoding=\"async\" loading=\"lazy\" class=\"alignnone size-full wp-image-13101\" src=\"https:\/\/ccssanswers.com\/wp-content\/uploads\/2020\/12\/Big-Ideas-Math-Solutions-Grade-4-Chapter-9-Multiply-Whole-Numbers-and-Fractions-46.png\" alt=\"Big Ideas Math Solutions Grade 4 Chapter 9 Multiply Whole Numbers and Fractions 46\" width=\"128\" height=\"53\" \/><br \/>\nAnswer:<br \/>\n5 X \\(\\frac{3}{10}\\) = \\(\\frac{15}{10}\\)=\\(\\frac{3}{2}\\).<\/p>\n<p>Explanation:<br \/>\n5 X \\(\\frac{3}{10}\\), we write the expression as multiple of unit fraction so<br \/>\n5 X 3 X \\(\\frac{1}{10}\\)= 15 X \\(\\frac{1}{10}\\)= \\(\\frac{15}{10}\\)<br \/>\nfurther it can be simplified, as both numerator and denominator can be divided by 5 so<br \/>\n\\(\\frac{15}{10}\\)=\\(\\frac{3}{2}\\).<\/p>\n<p>Question 6.<br \/>\n<img decoding=\"async\" loading=\"lazy\" class=\"alignnone size-full wp-image-13102\" src=\"https:\/\/ccssanswers.com\/wp-content\/uploads\/2020\/12\/Big-Ideas-Math-Solutions-Grade-4-Chapter-9-Multiply-Whole-Numbers-and-Fractions-47.png\" alt=\"Big Ideas Math Solutions Grade 4 Chapter 9 Multiply Whole Numbers and Fractions 47\" width=\"121\" height=\"63\" \/><br \/>\nAnswer:<br \/>\n6 X \\(\\frac{7}{8}\\)= \\(\\frac{42}{8}\\)= \\(\\frac{21}{4}\\).<\/p>\n<p>Explanation:<br \/>\n6 X\u00a0 \\(\\frac{7}{8}\\), we write the expression as multiple of unit fraction so<br \/>\n6 X 7 X \\(\\frac{1}{8}\\) applying associative property of multiplication<br \/>\n6 X ( 7 X \\(\\frac{1}{8}\\) )= ( 6 X 7 ) X \\(\\frac{1}{8}\\)= 42 X \\(\\frac{1}{8}\\)=<br \/>\n\\(\\frac{42}{8}\\) and further also the fraction can be simplified, as both numerator and denominator<br \/>\ncan be divided by 2, making \\(\\frac{42}{8}\\) as \\(\\frac{21}{4}\\).<\/p>\n<p>Question 7.<br \/>\n<img decoding=\"async\" loading=\"lazy\" class=\"alignnone size-full wp-image-13103\" src=\"https:\/\/ccssanswers.com\/wp-content\/uploads\/2020\/12\/Big-Ideas-Math-Solutions-Grade-4-Chapter-9-Multiply-Whole-Numbers-and-Fractions-48.png\" alt=\"Big Ideas Math Solutions Grade 4 Chapter 9 Multiply Whole Numbers and Fractions 48\" width=\"126\" height=\"52\" \/><br \/>\nAnswer:<br \/>\n8 X \\(\\frac{9}{10}\\)= \\(\\frac{72}{10}\\)=\\(\\frac{36}{5}\\).<\/p>\n<p>Explanation:<br \/>\n8 X\u00a0 \\(\\frac{9}{10}\\), we write the expression as multiple of unit fraction<br \/>\nso 8 X 9 X \\(\\frac{1}{10}\\) applying associative property of multiplication<br \/>\n8 X ( 9 X \\(\\frac{1}{10}\\) )= (8 X 9 ) X \\(\\frac{1}{10}\\)=<br \/>\n72 X \\(\\frac{1}{10}\\)= \\(\\frac{72}{10}\\) and further also the fraction can be simplified,<br \/>\nas both numerator and denominator can be divided by 2, making \\(\\frac{72}{10}\\) as \\(\\frac{36}{5}\\).<\/p>\n<p>Question 8.<br \/>\n<img decoding=\"async\" loading=\"lazy\" class=\"alignnone size-full wp-image-13104\" src=\"https:\/\/ccssanswers.com\/wp-content\/uploads\/2020\/12\/Big-Ideas-Math-Solutions-Grade-4-Chapter-9-Multiply-Whole-Numbers-and-Fractions-49.png\" alt=\"Big Ideas Math Solutions Grade 4 Chapter 9 Multiply Whole Numbers and Fractions 49\" width=\"139\" height=\"64\" \/><br \/>\nAnswer:<br \/>\n3 X \\(\\frac{60}{100}\\) =\\(\\frac{180}{100}\\) =\\(\\frac{18}{10}\\).<\/p>\n<p>Explanation:<br \/>\n3 X\u00a0 \\(\\frac{60}{100}\\),\u00a0 we write the expression as multiple of unit fraction,<br \/>\nSo 3 X 60 X \\(\\frac{1}{100}\\) applying associative property of multiplication<br \/>\n3 X (60 X \\(\\frac{1}{100}\\) )= (3 X 60 ) X \\(\\frac{1}{100}\\)= 180 X \\(\\frac{1}{100}\\)=<br \/>\n\\(\\frac{180}{100}\\) and further also the fraction can be simplified,<br \/>\nas both numerator and denominator can be divided by 10, making \\(\\frac{180}{100}\\)<br \/>\nas \\(\\frac{18}{10}\\).<\/p>\n<p>Question 9.<br \/>\n<img decoding=\"async\" loading=\"lazy\" class=\"alignnone size-full wp-image-13105\" src=\"https:\/\/ccssanswers.com\/wp-content\/uploads\/2020\/12\/Big-Ideas-Math-Solutions-Grade-4-Chapter-9-Multiply-Whole-Numbers-and-Fractions-50.png\" alt=\"Big Ideas Math Solutions Grade 4 Chapter 9 Multiply Whole Numbers and Fractions 50\" width=\"132\" height=\"50\" \/><br \/>\nAnswer:<br \/>\n\\(\\frac{4}{2}\\) X 10 = 20.<\/p>\n<p>Explanation :<br \/>\n\\(\\frac{4}{2}\\) X 10 , we write the expression as multiple of unit fraction,<br \/>\nSo 4 X \\(\\frac{1}{2}\\) X 10= 40 X \\(\\frac{1}{2}\\)=\\(\\frac{40}{2}\\)<br \/>\nas the fraction can be further simplified as both numerator and denominator can be divided by 2, making it as 20.<\/p>\n<p>Compare.<\/p>\n<p>Question 10.<br \/>\n<img decoding=\"async\" loading=\"lazy\" class=\"alignnone size-full wp-image-13106\" src=\"https:\/\/ccssanswers.com\/wp-content\/uploads\/2020\/12\/Big-Ideas-Math-Solutions-Grade-4-Chapter-9-Multiply-Whole-Numbers-and-Fractions-51.png\" alt=\"Big Ideas Math Solutions Grade 4 Chapter 9 Multiply Whole Numbers and Fractions 51\" width=\"133\" height=\"56\" \/><br \/>\nAnswer:<br \/>\n7 X \\(\\frac{2}{4}\\) =\\(\\frac{14}{4}\\) is smaller &lt;\u00a0 5 X \\(\\frac{3}{4}\\)=<br \/>\n\\(\\frac{15}{4}\\).<\/p>\n<p>Explanation:<br \/>\n7 X \\(\\frac{2}{4}\\), First we write expression as a multiple of unit fraction<br \/>\n7 X 2 X \\(\\frac{1}{4}\\) =14 X \\(\\frac{1}{4}\\) = \\(\\frac{14}{4}\\)<br \/>\nNow 5 X \\(\\frac{3}{4}\\) is also written as a multiple of unit fraction 5 X 3 X \\(\\frac{1}{4}\\) =<br \/>\n15 X \\(\\frac{1}{4}\\) =\\(\\frac{15}{4}\\) comparing \\(\\frac{14}{4}\\) and<br \/>\n\\(\\frac{15}{4}\\) as the denominators are same same 4 and in numerators 15 is great than 14,<br \/>\nSo\u00a0 \\(\\frac{14}{4}\\)\u00a0 is less than or smaller or &lt; \\(\\frac{15}{4}\\) ,<br \/>\n7 X \\(\\frac{2}{4}\\) is smaller &lt; 5 X \\(\\frac{3}{4}\\)<\/p>\n<p>Question 11.<br \/>\n<img decoding=\"async\" loading=\"lazy\" class=\"alignnone size-full wp-image-13107\" src=\"https:\/\/ccssanswers.com\/wp-content\/uploads\/2020\/12\/Big-Ideas-Math-Solutions-Grade-4-Chapter-9-Multiply-Whole-Numbers-and-Fractions-52.png\" alt=\"Big Ideas Math Solutions Grade 4 Chapter 9 Multiply Whole Numbers and Fractions 52\" width=\"140\" height=\"59\" \/><\/p>\n<p>Answer:<br \/>\n4 X \\(\\frac{1}{8}\\) is greater than &gt; 4 X \\(\\frac{1}{10}\\).<\/p>\n<p>Explanation:<br \/>\n4 X \\(\\frac{1}{8}\\) already the expression is in multiple of unit fraction,<br \/>\nwe write as \\(\\frac{4}{8}\\) and even the expression 4 X \\(\\frac{1}{10}\\)<br \/>\nis in multiple of unit fraction we write as \\(\\frac{4}{10}\\) because in order to compare<br \/>\nthe fractions we must first turn their different denominators into the same denominators to make<br \/>\ndenominators same we multiply 4 X \\(\\frac{1}{8}\\) by 10 \/10 the value will not change =<br \/>\n4 X 10 X \\(\\frac{1}{80}\\)=40 X \\(\\frac{1}{80}\\) =\u00a0 \\(\\frac{40}{80}\\)<br \/>\nnow other expression 4 X \\(\\frac{1}{10}\\) by 8\/8 so that the value = 4 X 8 X \\(\\frac{1}{80}\\) =<br \/>\n32 X \\(\\frac{1}{80}\\) now as denominator are same we can compare only numerators<br \/>\n\\(\\frac{40}{80}\\) with \\(\\frac{32}{80}\\) as 40 is greater than 32,<br \/>\nSo \u00a0\\(\\frac{4}{8}\\) is greater than &gt; \\(\\frac{4}{10}\\) ,<br \/>\n4 X \\(\\frac{1}{8}\\) is greater than &gt; 4 X \\(\\frac{1}{10}\\).<\/p>\n<p>Question 12.<br \/>\n<img decoding=\"async\" loading=\"lazy\" class=\"alignnone size-full wp-image-13108\" src=\"https:\/\/ccssanswers.com\/wp-content\/uploads\/2020\/12\/Big-Ideas-Math-Solutions-Grade-4-Chapter-9-Multiply-Whole-Numbers-and-Fractions-53.png\" alt=\"Big Ideas Math Solutions Grade 4 Chapter 9 Multiply Whole Numbers and Fractions 53\" width=\"141\" height=\"59\" \/><br \/>\nAnswer:<br \/>\n\\(\\frac{4}{3}\\) X 9 = 6 X \\(\\frac{6}{3}\\) both are equal.<\/p>\n<p>Explanation:<br \/>\nFirst we write expressions as a multiple of unit fraction \\(\\frac{4}{3}\\) X 9 =<br \/>\n9 X 4 X \\(\\frac{1}{3}\\) =36 X \\(\\frac{1}{3}\\) =\\(\\frac{36}{3}\\)<br \/>\nnow other expression\u00a0 6 X \\(\\frac{6}{3}\\) as = 6 X 6 X \\(\\frac{1}{3}\\) =<br \/>\n36 X \\(\\frac{1}{3}\\) = \\(\\frac{36}{3}\\) ,<br \/>\nAs denominator is same in the both expression we compare numerators and even<br \/>\nthe numerators are same in both the expression so given both products are equal .<br \/>\nTherefore \\(\\frac{4}{3}\\) X 9 =, is equal to 6 X \\(\\frac{6}{3}\\).<\/p>\n<p>Question 13.<br \/>\n<strong>YOU BE THE TEACHER<\/strong><br \/>\nYour friend says the product of 6 and \\(\\frac{5}{8}\\) is \\(\\frac{5}{48}\\). Is your friend correct? Explain.<br \/>\nAnswer:<br \/>\nNo she is not correct as the product of\u00a0 6 X \\(\\frac{5}{8}\\) \u2260 \\(\\frac{5}{48}\\).<\/p>\n<p>Explanation:<br \/>\nWe write the expression as a product\u00a0 6 and \\(\\frac{5}{8}\\) = 6 X \\(\\frac{5}{8}\\)<br \/>\nto \ufb01nd the product of a whole number and a fraction we multiply the numerator by the whole number.<br \/>\nThe denominator stays the same. 6 X 5 X\u00a0 \\(\\frac{1}{8}\\) =30 X \\(\\frac{1}{8}\\) =<br \/>\n\\(\\frac{30}{8}\\) now comparing with \\(\\frac{5}{48}\\) as denominators are different in order<br \/>\nto compare the fractions we must first turn their different denominators into the <em>same<\/em> denominators<br \/>\nto make denominators same we multiply \\(\\frac{30}{8}\\) with numerator and denominator<br \/>\nas 6= \\(\\frac{30}{8}\\) X \\(\\frac{6}{6}\\) we get \\(\\frac{180}{48}\\),<br \/>\nnow comparing with \\(\\frac{5}{48}\\) being denominators same, now numerators 180,5 both are<br \/>\nnot same so friend is not correct as the product of\u00a0 6 X \\(\\frac{5}{8}\\) \u2260 \\(\\frac{5}{48}\\).<\/p>\n<p>Question 14.<br \/>\n<strong>Open-Ended<\/strong><br \/>\nThe product of a whole number and a fraction is \\(\\frac{24}{10}\\). What could the two factors be?<br \/>\nAnswer:<br \/>\nThe product is given as \\(\\frac{24}{10}\\) and the two factors can be (1,24) or (2,12) or (3,8) or (4,6)<br \/>\nwith multiple of \\(\\frac{1}{10}\\).<\/p>\n<p>Explanation:<br \/>\nGiven the product of a whole number and a fraction is \\(\\frac{24}{10}\\) to find the two factors,<br \/>\nwe first write the product as whole with multiple of unit fraction,\\(\\frac{24}{10}\\),<br \/>\nwe write as 24 X \\(\\frac{1}{10}\\), now the whole part is 24 we find the factors for 24,<br \/>\ntwo more numbers that multiply to make 24 are 1 x 24 = 2 x 12 = 3 x 8 = 4 x 6 = 24.<br \/>\nThis means the factors of 24 are 1, 2, 3, 4, 6, 8, 12 and 24 so the two factors can be<br \/>\n(1,24) X \\(\\frac{1}{10}\\) or\u00a0 (2,12) X \u00a0\\(\\frac{1}{10}\\) or (3,8) X \\(\\frac{1}{10}\\)<br \/>\nor (4,6) X \\(\\frac{1}{10}\\) = 24 X \\(\\frac{1}{10}\\) = \\(\\frac{24}{10}\\).<\/p>\n<p><strong>Think and Grow: Modeling Real Life<\/strong><\/p>\n<p><strong>Example<\/strong><br \/>\nA short roller-coaster track is \\(\\frac{3}{10}\\) mile long. A longer roller-coaster track is about 4 times as long as the short track. About how long is the longer roller-coaster track?<br \/>\nMultiply the shorter roller-coaster track length by 4.<br \/>\n<img decoding=\"async\" loading=\"lazy\" class=\"alignnone size-full wp-image-13110\" src=\"https:\/\/ccssanswers.com\/wp-content\/uploads\/2020\/12\/Big-Ideas-Math-Solutions-Grade-4-Chapter-9-Multiply-Whole-Numbers-and-Fractions-54.png\" alt=\"Big Ideas Math Solutions Grade 4 Chapter 9 Multiply Whole Numbers and Fractions 54\" width=\"209\" height=\"151\" \/><br \/>\n<img decoding=\"async\" loading=\"lazy\" class=\"alignnone size-full wp-image-13109\" src=\"https:\/\/ccssanswers.com\/wp-content\/uploads\/2020\/12\/Big-Ideas-Math-Solutions-Grade-4-Chapter-9-Multiply-Whole-Numbers-and-Fractions-54.1.png\" alt=\"Big Ideas Math Solutions Grade 4 Chapter 9 Multiply Whole Numbers and Fractions 54.1\" width=\"155\" height=\"127\" \/><br \/>\nSo, the longer roller-coaster track is about _<span style=\"text-decoration: underline;\">\\(\\frac{12}{10}\\) _<\/span> miles long or \\(\\frac{6}{5}\\) miles long<br \/>\nAnswer:<br \/>\nThe longer roller-coaster track is about \\(\\frac{12}{10}\\) miles long or \\(\\frac{6}{5}\\).<\/p>\n<p>Explanation:<br \/>\nGiven a short roller-coaster track is \\(\\frac{3}{10}\\) mile long and longer roller-coaster<br \/>\ntrack is about 4 times as long as the short track to find how long is the longer roller-coaster track<br \/>\nwe multiply short roller-coaster track\u00a0 \\(\\frac{3}{10}\\) mile by 4, 4 X \\(\\frac{3}{10}\\)<br \/>\nnow we write expression as a multiple of unit fraction so 4 X 3 X \\(\\frac{1}{10}\\) =<br \/>\n12 X \\(\\frac{1}{10}\\) =\\(\\frac{12}{10}\\)\u00a0 as numerator and denominator<br \/>\ncan be further simplified as both can be divided by 2 making it as \\(\\frac{6}{5}\\).<\/p>\n<p><strong>Show and Grow<\/strong><\/p>\n<p>Question 15.<br \/>\nThe Renaissance Tower in Dallas, Texas is \\(\\frac{27}{100}\\) kilometer tall. The Burj Khalifa is about 3 times as tall as the Renaissance Tower. About how tall is the Burj Khalifa?<br \/>\n<img decoding=\"async\" loading=\"lazy\" class=\"alignnone size-full wp-image-13111\" src=\"https:\/\/ccssanswers.com\/wp-content\/uploads\/2020\/12\/Big-Ideas-Math-Solutions-Grade-4-Chapter-9-Multiply-Whole-Numbers-and-Fractions-55.png\" alt=\"Big Ideas Math Solutions Grade 4 Chapter 9 Multiply Whole Numbers and Fractions 55\" width=\"199\" height=\"272\" \/><br \/>\nAnswer:<br \/>\nThe Burj Khalifa is \\(\\frac{81}{100}\\) kilometers tall.<\/p>\n<p>Explanation:<br \/>\nGiven the Renaissance Tower in Dallas, Texas is \\(\\frac{27}{100}\\) kilometer tall and<br \/>\nThe Burj Khalifa is about 3 times as tall as the Renaissance Tower, To find how tall is the Burj Khalifa<br \/>\nwe multiply the Renaissance Tower in Dallas, Texas length by 3,<br \/>\n3 X \\(\\frac{27}{100}\\) we write expression as a multiple of unit fraction<br \/>\n3 X 27 X \\(\\frac{1}{100}\\) = 81 X \\(\\frac{1}{100}\\) =\\(\\frac{81}{100}\\),<br \/>\nSo the Burj Khalifa is \\(\\frac{81}{100}\\) kilometers tall.<\/p>\n<p>Question 16.<br \/>\nYou water 6 plants using \\(\\frac{3}{5}\\) liter of water for each. How many liters of water do you use?<br \/>\nBetween which two whole numbers does your answer lie?<br \/>\nAnswer:<br \/>\n\\(\\frac{18}{5}\\) liters of water is used, The answer will lie in between 3 and 4.<\/p>\n<p>Explanation:<br \/>\nGiven \\(\\frac{3}{5}\\) liter of water for each is watered, for 6 plants total number of liters of water<br \/>\nused is 6 X \\(\\frac{3}{5},now we write as multiple of unit fraction as 6 X 3 X [latex]\\frac{1}{5}\\) =<br \/>\n18 X \\(\\frac{1}{5}\\)= \\(\\frac{18}{5}\\) liters of water is used.<\/p>\n<p>Now we divide \\(\\frac{18}{5}\\) we get the value as 3.6,means between 3 and 4 whole numbers our answer will lie.<\/p>\n<p>Question 17.<br \/>\n<strong>DIG DEEPER!<\/strong><br \/>\nYou have 6 cups of strawberries. You want to make 4 strawberry-banana smoothies and 4 strawberry-kiwi smoothies. Each smoothie needs \\(\\frac{2}{3}\\) cup of strawberries. Do you have enough? If not, how many more cups of strawberries do you need?<br \/>\nAnswer:<br \/>\nYes we have enough cups of strawberries, we dont require more cups of strawberries.<\/p>\n<p>Explanation:<br \/>\nGiven to make each smoothie we need \\(\\frac{2}{3}\\) cup of strawberries<br \/>\nfirst to make 4 strawberry-banana smoothies we need 4 X \\(\\frac{2}{3}\\) cup of strawberries<br \/>\n= 4 X 2 X \\(\\frac{1}{3}\\)= 8 X \\(\\frac{1}{3}\\) =\\(\\frac{8}{3}\\),<br \/>\nNow similarly for making 4 strawberry-kiwi smoothies we need 4 X \\(\\frac{2}{3}\\)<br \/>\ncup of strawberries = 4 X 2 X \\(\\frac{1}{3}\\)= 8 X \\(\\frac{1}{3}\\) =<br \/>\n\\(\\frac{8}{3}\\),Now total cups of strawberries requried to make smoothie is<br \/>\n\\(\\frac{8}{3}\\) + \\(\\frac{8}{3}\\) = 2 X \\(\\frac{8}{3}\\)=<br \/>\n2 X 8 X \\(\\frac{1}{3}\\)=16 X \\(\\frac{1}{3}\\)= \\(\\frac{16}{3}\\) totals cups<br \/>\nof strawberries required to make smoothies. Now we compare \\(\\frac{16}{3}\\) with 6,<br \/>\nTo compare first we make both denominators same so we multiply 6 with \\(\\frac{3}{3}\\)=<br \/>\n6 X \\(\\frac{3}{3}\\)= 6 X 3 X \\(\\frac{1}{3}\\)= 18 X \\(\\frac{1}{3}\\)=<br \/>\n\\(\\frac{18}{3}\\) as both the denominators are same we compare<br \/>\n\\(\\frac{16}{3}\\) and \\(\\frac{18}{3}\\) by seeing numerator<br \/>\n16 is less than 18 means we have enough cups of strawberries.<\/p>\n<h3><a id=\"Multiply_Whole_Numbers_and_Fractions_Homework_&amp;_practice_9.3\"><\/a>Multiply Whole Numbers and Fractions Homework &amp; practice 9.3<\/h3>\n<p>Multiply<\/p>\n<p>Question 1.<br \/>\n<img decoding=\"async\" loading=\"lazy\" class=\"alignnone size-full wp-image-13112\" src=\"https:\/\/ccssanswers.com\/wp-content\/uploads\/2020\/12\/Big-Ideas-Math-Solutions-Grade-4-Chapter-9-Multiply-Whole-Numbers-and-Fractions-56.png\" alt=\"Big Ideas Math Solutions Grade 4 Chapter 9 Multiply Whole Numbers and Fractions 56\" width=\"119\" height=\"55\" \/><br \/>\nAnswer:<br \/>\n2 X \\(\\frac{1}{4}\\) = \\(\\frac{2}{4}\\)=\\(\\frac{1}{2}\\)<br \/>\nExplanation:<br \/>\nAs the given expression is already a unit fraction we multiply it as 2 X \\(\\frac{1}{4} =<br \/>\n\\)\\(\\frac{2}{4}\\) and further both numerator and denominator can be divided by 2<br \/>\nmaking it as \\(\\frac{1}{2}\\)<\/p>\n<p>Question 2.<br \/>\n<img decoding=\"async\" loading=\"lazy\" class=\"alignnone size-full wp-image-13113\" src=\"https:\/\/ccssanswers.com\/wp-content\/uploads\/2020\/12\/Big-Ideas-Math-Solutions-Grade-4-Chapter-9-Multiply-Whole-Numbers-and-Fractions-57.png\" alt=\"Big Ideas Math Solutions Grade 4 Chapter 9 Multiply Whole Numbers and Fractions 57\" width=\"121\" height=\"61\" \/><br \/>\nAnswer:<br \/>\n3 X \\(\\frac{3}{5}\\)= \\(\\frac{9}{5}\\).<\/p>\n<p>Explanation:<br \/>\n3 X \\(\\frac{3}{5}\\) can be written as multiple of unit fraction as<br \/>\n3 X (3 X \\(\\frac{1}{5}\\)) applying associative property of multiplication<br \/>\n( 3 X 3 ) X \\(\\frac{1}{5}\\)= 9 X \\(\\frac{1}{5}\\) = \\(\\frac{9}{5}\\).<\/p>\n<p>Question 3.<br \/>\n<img decoding=\"async\" loading=\"lazy\" class=\"alignnone size-full wp-image-13114\" src=\"https:\/\/ccssanswers.com\/wp-content\/uploads\/2020\/12\/Big-Ideas-Math-Solutions-Grade-4-Chapter-9-Multiply-Whole-Numbers-and-Fractions-58.png\" alt=\"Big Ideas Math Solutions Grade 4 Chapter 9 Multiply Whole Numbers and Fractions 58\" width=\"125\" height=\"58\" \/><br \/>\nAnswer:<br \/>\n1 X \\(\\frac{6}{8}\\)= \\(\\frac{6}{8}\\)= \\(\\frac{3}{4}\\).<\/p>\n<p>Explanation:<br \/>\n1 X \\(\\frac{6}{8}\\) can be written as multiple of unit fraction as 1 X ( 6 X\u00a0 \\(\\frac{1}{8}\\))<br \/>\napplying associative property of multiplication ( 1 X 6 ) X \\(\\frac{1}{8}\\) = 6 X \\(\\frac{1}{8}\\)=<br \/>\n\\(\\frac{6}{8}\\) as numerator and denominator can be further simplified as both can be divided by 2<br \/>\nmaking as \\(\\frac{6}{8}\\)= \\(\\frac{3}{4}\\)X \\(\\frac{2}{2}\\)=\\(\\frac{3}{4}\\).<\/p>\n<p>Question 4.<br \/>\n<img decoding=\"async\" loading=\"lazy\" class=\"alignnone size-full wp-image-13115\" src=\"https:\/\/ccssanswers.com\/wp-content\/uploads\/2020\/12\/Big-Ideas-Math-Solutions-Grade-4-Chapter-9-Multiply-Whole-Numbers-and-Fractions-59.png\" alt=\"Big Ideas Math Solutions Grade 4 Chapter 9 Multiply Whole Numbers and Fractions 59\" width=\"123\" height=\"55\" \/><br \/>\nAnswer:<br \/>\n4 X \\(\\frac{10}{12}\\)= \\(\\frac{40}{12}\\)= \\(\\frac{10}{3}\\)<\/p>\n<p>Explanation:<br \/>\n4 X \\(\\frac{10}{12}\\) can be written as multiple of unit fraction as 4 X ( 10 X\u00a0 \\(\\frac{1}{12}\\))<br \/>\napplying associative property of multiplication ( 4 X 10 ) X \\(\\frac{1}{12}\\) = 40 X \\(\\frac{1}{12}\\)=<br \/>\n\\(\\frac{40}{12}\\) as numerator and denominator can be further simplified as both can be divided by 4<br \/>\nas \\(\\frac{40}{12}\\)= \\(\\frac{10}{3}\\) X \\(\\frac{4}{4}\\)=\\(\\frac{10}{3}\\) X 1 =<br \/>\n\\(\\frac{10}{3}\\).<\/p>\n<p>Question 5.<br \/>\n<img decoding=\"async\" loading=\"lazy\" class=\"alignnone size-full wp-image-13116\" src=\"https:\/\/ccssanswers.com\/wp-content\/uploads\/2020\/12\/Big-Ideas-Math-Solutions-Grade-4-Chapter-9-Multiply-Whole-Numbers-and-Fractions-60.png\" alt=\"Big Ideas Math Solutions Grade 4 Chapter 9 Multiply Whole Numbers and Fractions 60\" width=\"127\" height=\"58\" \/><br \/>\nAnswer:<br \/>\n7 X \\(\\frac{6}{10}\\) = \\(\\frac{42}{10}\\)= \\(\\frac{21}{5}\\)<\/p>\n<p>Explanation:<br \/>\n7 X \\(\\frac{6}{10}\\) can be written as multiple of unit fraction as 7 X ( 6 X\u00a0 \\(\\frac{1}{10}\\))<br \/>\napplying associative property of multiplication ( 7 X 6 ) X \\(\\frac{1}{10}\\) =<br \/>\n42 X \\(\\frac{1}{10}\\)= \\(\\frac{42}{10}\\) as numerator and denominator<br \/>\ncan be further simplified as both can be divided by 2 as \\(\\frac{42}{10}\\)=<br \/>\n\\(\\frac{21}{5}\\) X \\(\\frac{2}{2}\\)=\\(\\frac{21}{5}\\) X 1 = \\(\\frac{21}{5}\\).<\/p>\n<p>Question 6.<br \/>\n<img decoding=\"async\" loading=\"lazy\" class=\"alignnone size-full wp-image-13117\" src=\"https:\/\/ccssanswers.com\/wp-content\/uploads\/2020\/12\/Big-Ideas-Math-Solutions-Grade-4-Chapter-9-Multiply-Whole-Numbers-and-Fractions-61.png\" alt=\"Big Ideas Math Solutions Grade 4 Chapter 9 Multiply Whole Numbers and Fractions 61\" width=\"118\" height=\"53\" \/><br \/>\nAnswer:<br \/>\n\\(\\frac{4}{6}\\) X 5 =\\(\\frac{20}{6}\\) =\\(\\frac{10}{3}\\).<\/p>\n<p>Explanation:<br \/>\n\\(\\frac{4}{6}\\) X 5\u00a0 can be written as multiple of unit fraction as 5 X ( 4 X\u00a0 \\(\\frac{1}{6}\\))<br \/>\napplying associative property of multiplication ( 5 X 4 ) X \\(\\frac{1}{6}\\) =<br \/>\n20 X \\(\\frac{1}{6}\\)= \\(\\frac{20}{6}\\) as numerator and denominator<br \/>\ncan be further simplified as both can be divided by 2 as \\(\\frac{20}{6}\\) =<br \/>\n\\(\\frac{10}{3}\\) X \\(\\frac{2}{2}\\)=\\(\\frac{10}{3}\\) X 1 =\\(\\frac{10}{3}\\).<\/p>\n<p>Question 7.<br \/>\n<img decoding=\"async\" loading=\"lazy\" class=\"alignnone size-full wp-image-13118\" src=\"https:\/\/ccssanswers.com\/wp-content\/uploads\/2020\/12\/Big-Ideas-Math-Solutions-Grade-4-Chapter-9-Multiply-Whole-Numbers-and-Fractions-62.png\" alt=\"Big Ideas Math Solutions Grade 4 Chapter 9 Multiply Whole Numbers and Fractions 62\" width=\"123\" height=\"56\" \/><br \/>\nAnswer:<br \/>\n8 X \\(\\frac{5}{2}\\) = \\(\\frac{40}{2}\\) =20.<\/p>\n<p>Explanation:<br \/>\n8 X \\(\\frac{5}{2}\\) can be written as multiple of unit fraction as<br \/>\n8 X ( 5 X\u00a0 \\(\\frac{1}{2}\\)) applying associative property of multiplication<br \/>\n( 8 X 5 ) X \\(\\frac{1}{2}\\) = 40 X \\(\\frac{1}{2}\\) = \\(\\frac{40}{2}\\)<br \/>\nfurther it can be simplified as \\(\\frac{40}{2}\\)=20<\/p>\n<p>Question 8.<br \/>\n<img decoding=\"async\" loading=\"lazy\" class=\"alignnone size-full wp-image-13119\" src=\"https:\/\/ccssanswers.com\/wp-content\/uploads\/2020\/12\/Big-Ideas-Math-Solutions-Grade-4-Chapter-9-Multiply-Whole-Numbers-and-Fractions-63.png\" alt=\"Big Ideas Math Solutions Grade 4 Chapter 9 Multiply Whole Numbers and Fractions 63\" width=\"143\" height=\"65\" \/><br \/>\nAnswer:<br \/>\n\\(\\frac{70}{100}\\) X 6 = \\(\\frac{420}{100}\\) = \\(\\frac{42}{10}\\).<\/p>\n<p>Explanation:<br \/>\n\\(\\frac{70}{100}\\) X 6\u00a0 can be written as multiple of unit fraction as<br \/>\n6 X ( 70 X\u00a0 \\(\\frac{1}{100}\\)) applying associative property of multiplication<br \/>\n( 6 X 70 ) X \\(\\frac{1}{100}\\) = 420 X \\(\\frac{1}{100}\\)= \\(\\frac{420}{100}\\)<br \/>\nas numerator and denominator can be further simplified as both can be divided by 10 as \\(\\frac{420}{100}\\)= \\(\\frac{42}{10}\\) X \\(\\frac{10}{10}\\)=\\(\\frac{42}{10}\\) X 1 =\\(\\frac{42}{10}\\).<\/p>\n<p>Question 9.<br \/>\n<img decoding=\"async\" loading=\"lazy\" class=\"alignnone size-full wp-image-13120\" src=\"https:\/\/ccssanswers.com\/wp-content\/uploads\/2020\/12\/Big-Ideas-Math-Solutions-Grade-4-Chapter-9-Multiply-Whole-Numbers-and-Fractions-64.png\" alt=\"Big Ideas Math Solutions Grade 4 Chapter 9 Multiply Whole Numbers and Fractions 64\" width=\"129\" height=\"63\" \/><br \/>\nAnswer:<br \/>\n10 X \\(\\frac{9}{3}\\)=\\(\\frac{90}{3}\\)=30.<\/p>\n<p>Explanation:<br \/>\n10 X \\(\\frac{9}{3}\\) can be written as multiple of unit fraction as<br \/>\n10 X ( 9 X\u00a0 \\(\\frac{1}{3}\\)) applying associative property of multiplication<br \/>\n( 10 X 9 ) X \\(\\frac{1}{3}\\) = 90 X \\(\\frac{1}{3}\\)= \\(\\frac{90}{3}\\)<br \/>\nfurther it can be simplified\u00a0 because 90 can be divided by 3 without leaving remainder making<br \/>\n\\(\\frac{90}{3}\\) as 30.<\/p>\n<p>Compare.<\/p>\n<p>Question 10.<br \/>\n<img decoding=\"async\" loading=\"lazy\" class=\"alignnone size-full wp-image-13121\" src=\"https:\/\/ccssanswers.com\/wp-content\/uploads\/2020\/12\/Big-Ideas-Math-Solutions-Grade-4-Chapter-9-Multiply-Whole-Numbers-and-Fractions-65.png\" alt=\"Big Ideas Math Solutions Grade 4 Chapter 9 Multiply Whole Numbers and Fractions 65\" width=\"142\" height=\"60\" \/><br \/>\nAnswer:<br \/>\n2 X \\(\\frac{4}{2}\\) = 8 X \\(\\frac{1}{2}\\).<\/p>\n<p>Explanation:<br \/>\n2 X \\(\\frac{4}{2}\\) we write as multiple of unit fraction 2 X 4 X \\(\\frac{1}{2}\\) =<br \/>\n8 X \\(\\frac{1}{2}\\) = \u00a0\\(\\frac{8}{2}\\) and<br \/>\n8 X \\(\\frac{1}{2}\\) is already multiple of unit fraction = latex]\\frac{8}{2}[\/latex]<br \/>\nnow we can compare both sides\u00a0 as the denominators are same and numerators are same<br \/>\nboth the expressions are equal 2 X \\(\\frac{4}{2}\\) = 8 X \\(\\frac{1}{2}\\).<\/p>\n<p>Question 11.<br \/>\n<img decoding=\"async\" loading=\"lazy\" class=\"alignnone size-full wp-image-13122\" src=\"https:\/\/ccssanswers.com\/wp-content\/uploads\/2020\/12\/Big-Ideas-Math-Solutions-Grade-4-Chapter-9-Multiply-Whole-Numbers-and-Fractions-66.png\" alt=\"Big Ideas Math Solutions Grade 4 Chapter 9 Multiply Whole Numbers and Fractions 66\" width=\"146\" height=\"60\" \/><br \/>\nAnswer:<br \/>\n9 X \\(\\frac{1}{5}\\) &gt; \\(\\frac{9}{12}\\)<\/p>\n<p>Explanation:<br \/>\n9 X \\(\\frac{1}{5}\\) already it is multiple of unit fraction we write it as \\(\\frac{9}{5}\\)<br \/>\nand 9 X \\(\\frac{1}{12}\\) is also a multiple of unit fraction we write it as \\(\\frac{9}{12}\\)<br \/>\nnow comparing first we make both denominators same so the multiples of 5 are 5,10,15,20,25,30,35,40,45,50,55,60,65<br \/>\nand multiples of 12 are 12,24,36,48,60,72 so the least common multiple of both 5 and 12 is 60 ,<br \/>\nSo to get denominator 60 we multiply top and bottom by 12 for \\(\\frac{9}{5}\\) =<br \/>\n\\(\\frac{9}{5}\\) X \\(\\frac{12}{12}\\)= \\(\\frac{108}{60}\\) ,<br \/>\nSo to get denominator 60 we multiply top and bottom by 5 for \\(\\frac{9}{12}\\)=<br \/>\n\\(\\frac{9}{12}\\) X \\(\\frac{5}{5}\\)= \\(\\frac{45}{60}\\)<br \/>\nNow comparing \\(\\frac{108}{60}\\) with \\(\\frac{45}{60}\\)\u00a0 as both denominator are same,<br \/>\nAs we see numerator it is clear that 108 is more than 45 so \\(\\frac{108}{60}\\) &gt; \\(\\frac{45}{60}\\) ,<br \/>\n9 X \\(\\frac{1}{5}\\) &gt; \\(\\frac{9}{12}\\).<\/p>\n<p>Question 12.<br \/>\n<img decoding=\"async\" loading=\"lazy\" class=\"alignnone size-full wp-image-13123\" src=\"https:\/\/ccssanswers.com\/wp-content\/uploads\/2020\/12\/Big-Ideas-Math-Solutions-Grade-4-Chapter-9-Multiply-Whole-Numbers-and-Fractions-67.png\" alt=\"Big Ideas Math Solutions Grade 4 Chapter 9 Multiply Whole Numbers and Fractions 67\" width=\"161\" height=\"71\" \/><\/p>\n<p>Answer:<br \/>\n\\(\\frac{6}{10}\\)X 4 &lt; 9 X \\(\\frac{3}{10}\\).<\/p>\n<p>Explanation:<br \/>\n\\(\\frac{6}{10}\\)X 4 we write as multiple of unit fraction 4 X 6 X \\(\\frac{1}{10}\\)=<br \/>\n24 X \\(\\frac{1}{10}\\) =\\(\\frac{24}{10}\\) and 9 X \\(\\frac{3}{10}\\) as<br \/>\n9 X 3 X \\(\\frac{1}{10}\\)= 27 X \\(\\frac{1}{10}\\)=\\(\\frac{27}{10}\\),<br \/>\nWe can compare both as denominators of both are 10 we compare numerators as 24 with 27<br \/>\nas 27 is great,\\(\\frac{24}{10}\\) &lt; \\(\\frac{27}{10}\\),<br \/>\n\\(\\frac{6}{10}\\) X 4 &lt; 9 X \\(\\frac{3}{10}\\).<\/p>\n<p>Question 13.<br \/>\n<strong>Writing<\/strong><br \/>\nExplain one way to multiply a whole number by a fraction.<br \/>\nAnswer:<br \/>\nFirst we write fraction as multiple of unit fraction then applying associative property of multiplication<br \/>\nwe multiply the whole numbers first then with the unit fraction,later writing product.<\/p>\n<p>Explanation:<br \/>\nLet us take the whole number as 2 and fraction as \\(\\frac{3}{5}\\),Here first we write fraction as<br \/>\nmultiple of unit fraction as 2 X 3 X \\(\\frac{1}{5}\\) now applying associative property of multiplication,<br \/>\nwe multiply the whole numbers first then with the unit fraction,<br \/>\n6 X \\(\\frac{1}{5}\\) as \\(\\frac{6}{5}\\).<\/p>\n<p>Question 14.<br \/>\n<strong>Number Sense<\/strong><br \/>\nBetween which two whole numbers does the product of 10 and \\(\\frac{5}{6}\\) lie ?<br \/>\nAnswer:<br \/>\nIn between 8 and 9 whole numbers the product of 10 and \\(\\frac{5}{6}\\) lies.<\/p>\n<p>Explanation:<br \/>\n10 X \\(\\frac{5}{6}\\) we first write it as multiple of unit fraction as<br \/>\n10 X ( 5 X \\(\\frac{1}{6}\\)) applying associative property of multiplication,<br \/>\nWe write (10 X 5) X \\(\\frac{1}{6}\\)= 50 X \\(\\frac{1}{6}\\) = \\(\\frac{50}{6}\\)<br \/>\nif we divide \\(\\frac{50}{6}\\))\u00a0 we get 8.333 which is in between 8 and 9 whole numbers.<\/p>\n<p>Question 15.<br \/>\n<strong>Modeling Real Life<\/strong><br \/>\nA seamstress makes fabric dog collars. An extra small dog collar is \\(\\frac{1}{3}\\) yard long.<br \/>\nA large dog collar is 2 times as long as the extra small dog collar. How long is the large dog collar?<br \/>\nAnswer:<br \/>\nThe large dog collar is \\(\\frac{2}{3}\\) yards long.<\/p>\n<p>Explanation:<br \/>\nGiven the extra small dog collar is \\(\\frac{1}{3}\\) yard long and a large dog collar is<br \/>\n2 times as long as the extra small dog collar, so the large dog collar = 2 X \\(\\frac{1}{3}\\)<br \/>\nas the fraction is multiple of unit fraction we write as \\(\\frac{2}{3}\\) ,<br \/>\ntherefore the large dog collar is \\(\\frac{2}{3}\\) yards long.<\/p>\n<p>Question 16.<br \/>\n<strong>DIG DEEPER!<\/strong><br \/>\nNewton has 16 baseball cards. Descartes has \\(\\frac{1}{4}\\) as many cards as Newton, and your friend has \\(\\frac{1}{2}\\) as many cards as Descartes. How many baseball cards do Newton, Descartes, and your friend have in all?<br \/>\n<img decoding=\"async\" loading=\"lazy\" class=\"alignnone size-full wp-image-13124\" src=\"https:\/\/ccssanswers.com\/wp-content\/uploads\/2020\/12\/Big-Ideas-Math-Solutions-Grade-4-Chapter-9-Multiply-Whole-Numbers-and-Fractions-68.png\" alt=\"Big Ideas Math Solutions Grade 4 Chapter 9 Multiply Whole Numbers and Fractions 68\" width=\"151\" height=\"148\" \/><\/p>\n<p>Answer:<br \/>\nNewton has 16 baseball cards, Descartes has 4 baseball cards and my friend has 2 baseball cards,<br \/>\nover all there are total 22 baseball cards.<\/p>\n<p>Explanation:<br \/>\nGiven Newton has 16 baseball cards and Descartes has \\(\\frac{1}{4}\\) as many cards as<br \/>\nNewton so\\(\\frac{1}{4}\\) of 16 = 16 X \\(\\frac{1}{4}\\) cards\u00a0 it is already<br \/>\nas multiple of unit fraction we can write as \\(\\frac{16}{4}\\) further can be simplified<br \/>\nbecause 16 can be divide by 4 so we get as 4 means Descartes has 4 cards.Now my friend has<br \/>\n\\(\\frac{1}{2}\\) as many cards as Descartes So Descartes has 4 cards means my friend has<br \/>\n\\(\\frac{1}{2}\\) out of 4= 4 X \\(\\frac{1}{2}\\)\u00a0 as it is already a multiple of unit fracrtion,<br \/>\nwe take it as \\(\\frac{4}{2}\\) further we can simplify as 4 is divisiblle by 2 we get 2 cards.<br \/>\nNewton has 16 baseball cards,Descartes has 4 baseball cards and my friend has 2 baseball cards,<br \/>\nover all there are total 22 baseball cards.<\/p>\n<p><strong>Review &amp; Refresh<\/strong><\/p>\n<p>Divide<\/p>\n<p>Question 17.<br \/>\n<img decoding=\"async\" loading=\"lazy\" class=\"alignnone size-full wp-image-13125\" src=\"https:\/\/ccssanswers.com\/wp-content\/uploads\/2020\/12\/Big-Ideas-Math-Solutions-Grade-4-Chapter-9-Multiply-Whole-Numbers-and-Fractions-69.png\" alt=\"Big Ideas Math Solutions Grade 4 Chapter 9 Multiply Whole Numbers and Fractions 69\" width=\"52\" height=\"36\" \/><br \/>\nAnswer:<br \/>\n<img decoding=\"async\" loading=\"lazy\" class=\"alignnone size-full wp-image-13125\" src=\"https:\/\/ccssanswers.com\/wp-content\/uploads\/2020\/12\/Big-Ideas-Math-Solutions-Grade-4-Chapter-9-Multiply-Whole-Numbers-and-Fractions-69.png\" alt=\"Big Ideas Math Solutions Grade 4 Chapter 9 Multiply Whole Numbers and Fractions 69\" width=\"52\" height=\"36\" \/>= 19.<\/p>\n<p>Explanation:<br \/>\n<img decoding=\"async\" loading=\"lazy\" class=\"alignnone wp-image-24465 size-full\" src=\"https:\/\/ccssanswers.com\/wp-content\/uploads\/2020\/12\/9-Multiply-Whole-Numbers-and-Fractions-14-1.bmp\" alt=\"\" width=\"1007\" height=\"739\" srcset=\"https:\/\/ccssanswers.com\/wp-content\/uploads\/2020\/12\/9-Multiply-Whole-Numbers-and-Fractions-14-1.bmp 1007w, https:\/\/ccssanswers.com\/wp-content\/uploads\/2020\/12\/9-Multiply-Whole-Numbers-and-Fractions-14-1-300x220.jpg 300w, https:\/\/ccssanswers.com\/wp-content\/uploads\/2020\/12\/9-Multiply-Whole-Numbers-and-Fractions-14-1-768x564.jpg 768w\" sizes=\"(max-width: 1007px) 100vw, 1007px\" \/><\/p>\n<p>Question 18.<br \/>\n<img decoding=\"async\" loading=\"lazy\" class=\"alignnone size-full wp-image-13126\" src=\"https:\/\/ccssanswers.com\/wp-content\/uploads\/2020\/12\/Big-Ideas-Math-Solutions-Grade-4-Chapter-9-Multiply-Whole-Numbers-and-Fractions-70.png\" alt=\"Big Ideas Math Solutions Grade 4 Chapter 9 Multiply Whole Numbers and Fractions 70\" width=\"59\" height=\"40\" \/><br \/>\nAnswer:<br \/>\n<img decoding=\"async\" loading=\"lazy\" class=\"alignnone size-full wp-image-13126\" src=\"https:\/\/ccssanswers.com\/wp-content\/uploads\/2020\/12\/Big-Ideas-Math-Solutions-Grade-4-Chapter-9-Multiply-Whole-Numbers-and-Fractions-70.png\" alt=\"Big Ideas Math Solutions Grade 4 Chapter 9 Multiply Whole Numbers and Fractions 70\" width=\"59\" height=\"40\" \/>=81 with 4 as remainder.<\/p>\n<p>Explanation:<br \/>\nStep 1:Start by setting it up with the divisor 7 on the left side and the dividend 571 on the right side,<br \/>\n<img decoding=\"async\" loading=\"lazy\" class=\"alignnone size-full wp-image-13126\" src=\"https:\/\/ccssanswers.com\/wp-content\/uploads\/2020\/12\/Big-Ideas-Math-Solutions-Grade-4-Chapter-9-Multiply-Whole-Numbers-and-Fractions-70.png\" alt=\"Big Ideas Math Solutions Grade 4 Chapter 9 Multiply Whole Numbers and Fractions 70\" width=\"59\" height=\"40\" \/><br \/>\nStep 2: The divisor (7) does not\u00a0 goes into the first digit of the dividend (5), So we take second digit also , The divisor (7) goes into the two digits of the dividend (57) by 8 time(s),there fore put 8 on the top<br \/>\n8<br \/>\n<img decoding=\"async\" loading=\"lazy\" class=\"alignnone size-full wp-image-13126\" src=\"https:\/\/ccssanswers.com\/wp-content\/uploads\/2020\/12\/Big-Ideas-Math-Solutions-Grade-4-Chapter-9-Multiply-Whole-Numbers-and-Fractions-70.png\" alt=\"Big Ideas Math Solutions Grade 4 Chapter 9 Multiply Whole Numbers and Fractions 70\" width=\"59\" height=\"40\" \/><br \/>\nStep 3: Multiply the divisor by the result in the previous step. Therefore, put 8 on top (7 x 9 = 56) and write that answer below the dividend.<br \/>\n8<br \/>\n<img decoding=\"async\" loading=\"lazy\" class=\"alignnone size-full wp-image-13126\" src=\"https:\/\/ccssanswers.com\/wp-content\/uploads\/2020\/12\/Big-Ideas-Math-Solutions-Grade-4-Chapter-9-Multiply-Whole-Numbers-and-Fractions-70.png\" alt=\"Big Ideas Math Solutions Grade 4 Chapter 9 Multiply Whole Numbers and Fractions 70\" width=\"59\" height=\"40\" \/><br \/>\n56<br \/>\nStep 4: Subtract the result in the previous step from the two digits of the dividend (57 -56 = 1) and write the answer below.<br \/>\n8<br \/>\n<img decoding=\"async\" loading=\"lazy\" class=\"alignnone size-full wp-image-13126\" src=\"https:\/\/ccssanswers.com\/wp-content\/uploads\/2020\/12\/Big-Ideas-Math-Solutions-Grade-4-Chapter-9-Multiply-Whole-Numbers-and-Fractions-70.png\" alt=\"Big Ideas Math Solutions Grade 4 Chapter 9 Multiply Whole Numbers and Fractions 70\" width=\"59\" height=\"40\" \/><br \/>\n<span style=\"text-decoration: underline;\">\u00a056<\/span><br \/>\n1<br \/>\nStep 5: Move down the 3rd digit of the dividend (1)<br \/>\n8<br \/>\n<img decoding=\"async\" loading=\"lazy\" class=\"alignnone size-full wp-image-13126\" src=\"https:\/\/ccssanswers.com\/wp-content\/uploads\/2020\/12\/Big-Ideas-Math-Solutions-Grade-4-Chapter-9-Multiply-Whole-Numbers-and-Fractions-70.png\" alt=\"Big Ideas Math Solutions Grade 4 Chapter 9 Multiply Whole Numbers and Fractions 70\" width=\"59\" height=\"40\" \/><br \/>\n<span style=\"text-decoration: underline;\">\u00a056<\/span><br \/>\n11<br \/>\nStep 6:The divisor (7) goes into the bottom number (11),\u00a0 time(s). Therefore, put 1 on top:<br \/>\n81<br \/>\n<img decoding=\"async\" loading=\"lazy\" class=\"alignnone size-full wp-image-13126\" src=\"https:\/\/ccssanswers.com\/wp-content\/uploads\/2020\/12\/Big-Ideas-Math-Solutions-Grade-4-Chapter-9-Multiply-Whole-Numbers-and-Fractions-70.png\" alt=\"Big Ideas Math Solutions Grade 4 Chapter 9 Multiply Whole Numbers and Fractions 70\" width=\"59\" height=\"40\" \/><br \/>\n<span style=\"text-decoration: underline;\">\u00a0 \u00a0 \u00a056<\/span><br \/>\n11<br \/>\nStep 7 : Multiply the divisor by the result in the previous step (7 x 1 = 7) and write that answer at the bottom:<br \/>\n81<br \/>\n<img decoding=\"async\" loading=\"lazy\" class=\"alignnone size-full wp-image-13126\" src=\"https:\/\/ccssanswers.com\/wp-content\/uploads\/2020\/12\/Big-Ideas-Math-Solutions-Grade-4-Chapter-9-Multiply-Whole-Numbers-and-Fractions-70.png\" alt=\"Big Ideas Math Solutions Grade 4 Chapter 9 Multiply Whole Numbers and Fractions 70\" width=\"59\" height=\"40\" \/><br \/>\n<span style=\"text-decoration: underline;\">\u00a0 \u00a0 \u00a056<\/span><br \/>\n11<br \/>\n07<br \/>\nStep 8 : Subtract the result in the previous step from the number written above it. (11 &#8211; 7 = 04) and write the answer at the bottom<br \/>\n81<br \/>\n<img decoding=\"async\" loading=\"lazy\" class=\"alignnone size-full wp-image-13126\" src=\"https:\/\/ccssanswers.com\/wp-content\/uploads\/2020\/12\/Big-Ideas-Math-Solutions-Grade-4-Chapter-9-Multiply-Whole-Numbers-and-Fractions-70.png\" alt=\"Big Ideas Math Solutions Grade 4 Chapter 9 Multiply Whole Numbers and Fractions 70\" width=\"59\" height=\"40\" \/><br \/>\n<span style=\"text-decoration: underline;\">\u00a056<\/span><br \/>\n11<br \/>\n<span style=\"text-decoration: underline;\"> \u00a0 \u00a0 07<\/span><br \/>\n4<br \/>\nWe stop here as 4 is less than 7 and further we get in decimals , So <img decoding=\"async\" loading=\"lazy\" class=\"alignnone size-full wp-image-13126\" src=\"https:\/\/ccssanswers.com\/wp-content\/uploads\/2020\/12\/Big-Ideas-Math-Solutions-Grade-4-Chapter-9-Multiply-Whole-Numbers-and-Fractions-70.png\" alt=\"Big Ideas Math Solutions Grade 4 Chapter 9 Multiply Whole Numbers and Fractions 70\" width=\"59\" height=\"40\" \/>=81 with 4 as remainder<br \/>\nQuestion 19.<br \/>\n<img decoding=\"async\" loading=\"lazy\" class=\"alignnone size-full wp-image-13127\" src=\"https:\/\/ccssanswers.com\/wp-content\/uploads\/2020\/12\/Big-Ideas-Math-Solutions-Grade-4-Chapter-9-Multiply-Whole-Numbers-and-Fractions-71.png\" alt=\"Big Ideas Math Solutions Grade 4 Chapter 9 Multiply Whole Numbers and Fractions 71\" width=\"63\" height=\"43\" \/><br \/>\nAnswer:<br \/>\n<img decoding=\"async\" loading=\"lazy\" class=\"alignnone size-full wp-image-13127\" src=\"https:\/\/ccssanswers.com\/wp-content\/uploads\/2020\/12\/Big-Ideas-Math-Solutions-Grade-4-Chapter-9-Multiply-Whole-Numbers-and-Fractions-71.png\" alt=\"Big Ideas Math Solutions Grade 4 Chapter 9 Multiply Whole Numbers and Fractions 71\" width=\"63\" height=\"43\" \/>= 184 with 3 as remainder.<\/p>\n<p>Explanation:<br \/>\nStep 1:Start by setting it up with the divisor 5 on the left side and the dividend 923 on the right side,<br \/>\n<img decoding=\"async\" loading=\"lazy\" class=\"alignnone size-full wp-image-13127\" src=\"https:\/\/ccssanswers.com\/wp-content\/uploads\/2020\/12\/Big-Ideas-Math-Solutions-Grade-4-Chapter-9-Multiply-Whole-Numbers-and-Fractions-71.png\" alt=\"Big Ideas Math Solutions Grade 4 Chapter 9 Multiply Whole Numbers and Fractions 71\" width=\"63\" height=\"43\" \/><br \/>\nStep 2: The divisor (5)\u00a0 \u00a0goes into the first digit of the dividend (9)\u00a0 by 8 time there fore put 1 on the top<br \/>\n1<br \/>\n<img decoding=\"async\" loading=\"lazy\" class=\"alignnone size-full wp-image-13127\" src=\"https:\/\/ccssanswers.com\/wp-content\/uploads\/2020\/12\/Big-Ideas-Math-Solutions-Grade-4-Chapter-9-Multiply-Whole-Numbers-and-Fractions-71.png\" alt=\"Big Ideas Math Solutions Grade 4 Chapter 9 Multiply Whole Numbers and Fractions 71\" width=\"63\" height=\"43\" \/><br \/>\nStep 3: Multiply the divisor by the result in the previous step\u00a0 (5 x 1 = 5) and write that answer below the dividend.<br \/>\n1<br \/>\n<img decoding=\"async\" loading=\"lazy\" class=\"alignnone size-full wp-image-13127\" src=\"https:\/\/ccssanswers.com\/wp-content\/uploads\/2020\/12\/Big-Ideas-Math-Solutions-Grade-4-Chapter-9-Multiply-Whole-Numbers-and-Fractions-71.png\" alt=\"Big Ideas Math Solutions Grade 4 Chapter 9 Multiply Whole Numbers and Fractions 71\" width=\"63\" height=\"43\" \/><br \/>\n5<br \/>\nStep 4: Subtract the result in the previous step from the first digit of the dividend (9 -5 = 4) and write the answer below.<br \/>\n1<br \/>\n<img decoding=\"async\" loading=\"lazy\" class=\"alignnone size-full wp-image-13127\" src=\"https:\/\/ccssanswers.com\/wp-content\/uploads\/2020\/12\/Big-Ideas-Math-Solutions-Grade-4-Chapter-9-Multiply-Whole-Numbers-and-Fractions-71.png\" alt=\"Big Ideas Math Solutions Grade 4 Chapter 9 Multiply Whole Numbers and Fractions 71\" width=\"63\" height=\"43\" \/><br \/>\n<span style=\"text-decoration: underline;\"> \u00a0 \u00a05<br \/>\n<\/span>\u00a0 \u00a0 4<br \/>\nStep 5: Move down the 2nd digit of the dividend (2),like below<br \/>\n1<br \/>\n<img decoding=\"async\" loading=\"lazy\" class=\"alignnone size-full wp-image-13127\" src=\"https:\/\/ccssanswers.com\/wp-content\/uploads\/2020\/12\/Big-Ideas-Math-Solutions-Grade-4-Chapter-9-Multiply-Whole-Numbers-and-Fractions-71.png\" alt=\"Big Ideas Math Solutions Grade 4 Chapter 9 Multiply Whole Numbers and Fractions 71\" width=\"63\" height=\"43\" \/><br \/>\n<span style=\"text-decoration: underline;\"> \u00a0 \u00a05<br \/>\n<\/span>\u00a0 \u00a0 \u00a042<br \/>\nStep 6:The divisor (5) goes into the bottom number (40),\u00a0 8 time(s). Therefore, put 8 on top:<br \/>\n18<br \/>\n<img decoding=\"async\" loading=\"lazy\" class=\"alignnone size-full wp-image-13127\" src=\"https:\/\/ccssanswers.com\/wp-content\/uploads\/2020\/12\/Big-Ideas-Math-Solutions-Grade-4-Chapter-9-Multiply-Whole-Numbers-and-Fractions-71.png\" alt=\"Big Ideas Math Solutions Grade 4 Chapter 9 Multiply Whole Numbers and Fractions 71\" width=\"63\" height=\"43\" \/><br \/>\n<span style=\"text-decoration: underline;\"> \u00a0 \u00a05<br \/>\n<\/span>\u00a0 \u00a0 \u00a042<br \/>\nStep 7 : Multiply the divisor by the result in the previous step (5 x 8 = 40) and write that answer at the bottom:<br \/>\n18<br \/>\n<img decoding=\"async\" loading=\"lazy\" class=\"alignnone size-full wp-image-13127\" src=\"https:\/\/ccssanswers.com\/wp-content\/uploads\/2020\/12\/Big-Ideas-Math-Solutions-Grade-4-Chapter-9-Multiply-Whole-Numbers-and-Fractions-71.png\" alt=\"Big Ideas Math Solutions Grade 4 Chapter 9 Multiply Whole Numbers and Fractions 71\" width=\"63\" height=\"43\" \/><br \/>\n<span style=\"text-decoration: underline;\"> \u00a0 \u00a05<br \/>\n<\/span>\u00a0 \u00a0 \u00a042<br \/>\n40<br \/>\nStep 8: Subtract the result in the previous step from the number written above it. (42 &#8211; 40 = 04) and write the answer at the bottom<br \/>\n18<br \/>\n<img decoding=\"async\" loading=\"lazy\" class=\"alignnone size-full wp-image-13127\" src=\"https:\/\/ccssanswers.com\/wp-content\/uploads\/2020\/12\/Big-Ideas-Math-Solutions-Grade-4-Chapter-9-Multiply-Whole-Numbers-and-Fractions-71.png\" alt=\"Big Ideas Math Solutions Grade 4 Chapter 9 Multiply Whole Numbers and Fractions 71\" width=\"63\" height=\"43\" \/><br \/>\n<span style=\"text-decoration: underline;\"> \u00a0 \u00a05<br \/>\n<\/span>\u00a0 \u00a0 \u00a042<br \/>\n<span style=\"text-decoration: underline;\">\u00a0 \u00a0 \u00a040\u00a0 \u00a0<\/span><br \/>\n2<br \/>\nStep 9 :Move down the 3nd digit of the dividend (3),like below<br \/>\n18<br \/>\n<img decoding=\"async\" loading=\"lazy\" class=\"alignnone size-full wp-image-13127\" src=\"https:\/\/ccssanswers.com\/wp-content\/uploads\/2020\/12\/Big-Ideas-Math-Solutions-Grade-4-Chapter-9-Multiply-Whole-Numbers-and-Fractions-71.png\" alt=\"Big Ideas Math Solutions Grade 4 Chapter 9 Multiply Whole Numbers and Fractions 71\" width=\"63\" height=\"43\" \/><br \/>\n<span style=\"text-decoration: underline;\"> \u00a0 \u00a05<br \/>\n<\/span>\u00a0 \u00a0 \u00a042<br \/>\n<span style=\"text-decoration: underline;\">\u00a0 \u00a0 \u00a040\u00a0 \u00a0<\/span><br \/>\n23<br \/>\nStep 10 : The divisor (5) goes into the bottom number (20),\u00a0 4 time(s). Therefore, put 4 on top:<br \/>\n184<br \/>\n<img decoding=\"async\" loading=\"lazy\" class=\"alignnone size-full wp-image-13127\" src=\"https:\/\/ccssanswers.com\/wp-content\/uploads\/2020\/12\/Big-Ideas-Math-Solutions-Grade-4-Chapter-9-Multiply-Whole-Numbers-and-Fractions-71.png\" alt=\"Big Ideas Math Solutions Grade 4 Chapter 9 Multiply Whole Numbers and Fractions 71\" width=\"63\" height=\"43\" \/><br \/>\n<span style=\"text-decoration: underline;\">\u00a0 \u00a0 \u00a05<br \/>\n<\/span>\u00a0 \u00a0 \u00a042<br \/>\n<span style=\"text-decoration: underline;\">\u00a0 \u00a0 \u00a040\u00a0 \u00a0<\/span><br \/>\n23<br \/>\n20<br \/>\nStep 11 : Subtract the result in the previous step from the number written above it. (23 &#8211; 20 = 03) and write the answer at the bottom<br \/>\n184<br \/>\n<img decoding=\"async\" loading=\"lazy\" class=\"alignnone size-full wp-image-13127\" src=\"https:\/\/ccssanswers.com\/wp-content\/uploads\/2020\/12\/Big-Ideas-Math-Solutions-Grade-4-Chapter-9-Multiply-Whole-Numbers-and-Fractions-71.png\" alt=\"Big Ideas Math Solutions Grade 4 Chapter 9 Multiply Whole Numbers and Fractions 71\" width=\"63\" height=\"43\" \/><br \/>\n<span style=\"text-decoration: underline;\">\u00a0 \u00a0 \u00a05<br \/>\n<\/span>\u00a0 \u00a0 \u00a042<br \/>\n<span style=\"text-decoration: underline;\">\u00a0 \u00a0 \u00a040\u00a0 \u00a0<\/span><br \/>\n23<br \/>\n<span style=\"text-decoration: underline;\"> \u00a0 \u00a0 \u00a020<br \/>\n<\/span>\u00a0 \u00a0 \u00a0 \u00a003<br \/>\nWe stop here as 3 is less than 5 and further we get in decimals , So <img decoding=\"async\" loading=\"lazy\" class=\"alignnone size-full wp-image-13127\" src=\"https:\/\/ccssanswers.com\/wp-content\/uploads\/2020\/12\/Big-Ideas-Math-Solutions-Grade-4-Chapter-9-Multiply-Whole-Numbers-and-Fractions-71.png\" alt=\"Big Ideas Math Solutions Grade 4 Chapter 9 Multiply Whole Numbers and Fractions 71\" width=\"63\" height=\"43\" \/>= 184 with 3 as remainder.<\/p>\n<h3><a id=\"Lesson_9.4_Multiply_Whole_Numbers_and_Mixed_Numbers\"><\/a>Lesson 9.4 Multiply Whole Numbers and Mixed Numbers<\/h3>\n<p><strong>Explore and Grow<\/strong><\/p>\n<p>Use models to help you complete the table.<br \/>\n<img decoding=\"async\" loading=\"lazy\" class=\"alignnone size-full wp-image-13034\" src=\"https:\/\/ccssanswers.com\/wp-content\/uploads\/2020\/12\/Big-Ideas-Math-Answers-Grade-4-Chapter-9-Multiply-Whole-Numbers-and-Fractions-72.png\" alt=\"Big Ideas Math Answers Grade 4 Chapter 9 Multiply Whole Numbers and Fractions 72\" width=\"210\" height=\"312\" srcset=\"https:\/\/ccssanswers.com\/wp-content\/uploads\/2020\/12\/Big-Ideas-Math-Answers-Grade-4-Chapter-9-Multiply-Whole-Numbers-and-Fractions-72.png 210w, https:\/\/ccssanswers.com\/wp-content\/uploads\/2020\/12\/Big-Ideas-Math-Answers-Grade-4-Chapter-9-Multiply-Whole-Numbers-and-Fractions-72-202x300.png 202w\" sizes=\"(max-width: 210px) 100vw, 210px\" \/><\/p>\n<p><strong>Structure<\/strong><br \/>\nHow does the Distributive Property relate to your models? Explain.<\/p>\n<p>Answer:<br \/>\n<img decoding=\"async\" loading=\"lazy\" class=\"alignnone wp-image-25117 size-full\" src=\"https:\/\/ccssanswers.com\/wp-content\/uploads\/2020\/12\/9-Multiply-Whole-Numbers-and-Fractions-15-3.bmp\" alt=\"\" width=\"791\" height=\"511\" srcset=\"https:\/\/ccssanswers.com\/wp-content\/uploads\/2020\/12\/9-Multiply-Whole-Numbers-and-Fractions-15-3.bmp 791w, https:\/\/ccssanswers.com\/wp-content\/uploads\/2020\/12\/9-Multiply-Whole-Numbers-and-Fractions-15-3-300x194.jpg 300w, https:\/\/ccssanswers.com\/wp-content\/uploads\/2020\/12\/9-Multiply-Whole-Numbers-and-Fractions-15-3-768x496.jpg 768w\" sizes=\"(max-width: 791px) 100vw, 791px\" \/><\/p>\n<p>Explanation:<br \/>\nAccording to the distributive property, multiplying the sum of two or more addends by a number<br \/>\nwill give the same result as multiplying each addend individually by the number and then adding the products together.<br \/>\nWe use distribute property while relating the models first we draw each multiplying addend individually and<br \/>\nthen add the products together to give the result.<br \/>\nExample : 2 X 1 \\(\\frac{3}{8}\\) using the distributive property we write<br \/>\n2 X 1 \\(\\frac{3}{8}\\) as 2 X ( 1 + \\(\\frac{3}{8}\\) )here first we draw model of<br \/>\n2 X 1 then we draw model of 2 X \\(\\frac{3}{8}\\) then we add the products together as<br \/>\n2 + \\(\\frac{6}{8}\\)= 2 + \\(\\frac{3}{4}\\)=\\(\\frac{11}{4}\\).<br \/>\n<strong>Think and Grow: Multiply Whole Numbers and Mixed Numbers<\/strong><\/p>\n<p>You can \ufb01nd the product of a whole number and a mixed number by writing the mixed number as a fraction or by using the Distributive Property<br \/>\n<img decoding=\"async\" loading=\"lazy\" class=\"alignnone size-full wp-image-13035\" src=\"https:\/\/ccssanswers.com\/wp-content\/uploads\/2020\/12\/Big-Ideas-Math-Answers-Grade-4-Chapter-9-Multiply-Whole-Numbers-and-Fractions-73.png\" alt=\"Big Ideas Math Answers Grade 4 Chapter 9 Multiply Whole Numbers and Fractions 73\" width=\"205\" height=\"55\" \/><br \/>\n<strong>One Way:<\/strong> Write the mixed number as a fraction, then multiply.<br \/>\n<img decoding=\"async\" loading=\"lazy\" class=\"alignnone size-full wp-image-13036\" src=\"https:\/\/ccssanswers.com\/wp-content\/uploads\/2020\/12\/Big-Ideas-Math-Answers-Grade-4-Chapter-9-Multiply-Whole-Numbers-and-Fractions-74.png\" alt=\"Big Ideas Math Answers Grade 4 Chapter 9 Multiply Whole Numbers and Fractions 74\" width=\"171\" height=\"234\" \/><br \/>\n<strong>Another Way:<\/strong> Use the Distributive Property.<br \/>\n<img decoding=\"async\" loading=\"lazy\" class=\"alignnone size-full wp-image-13037\" src=\"https:\/\/ccssanswers.com\/wp-content\/uploads\/2020\/12\/Big-Ideas-Math-Answers-Grade-4-Chapter-9-Multiply-Whole-Numbers-and-Fractions-75.png\" alt=\"Big Ideas Math Answers Grade 4 Chapter 9 Multiply Whole Numbers and Fractions 75\" width=\"302\" height=\"303\" srcset=\"https:\/\/ccssanswers.com\/wp-content\/uploads\/2020\/12\/Big-Ideas-Math-Answers-Grade-4-Chapter-9-Multiply-Whole-Numbers-and-Fractions-75.png 302w, https:\/\/ccssanswers.com\/wp-content\/uploads\/2020\/12\/Big-Ideas-Math-Answers-Grade-4-Chapter-9-Multiply-Whole-Numbers-and-Fractions-75-300x300.png 300w, https:\/\/ccssanswers.com\/wp-content\/uploads\/2020\/12\/Big-Ideas-Math-Answers-Grade-4-Chapter-9-Multiply-Whole-Numbers-and-Fractions-75-150x150.png 150w\" sizes=\"(max-width: 302px) 100vw, 302px\" \/><br \/>\n<img decoding=\"async\" loading=\"lazy\" class=\"alignnone size-full wp-image-13038\" src=\"https:\/\/ccssanswers.com\/wp-content\/uploads\/2020\/12\/Big-Ideas-Math-Answers-Grade-4-Chapter-9-Multiply-Whole-Numbers-and-Fractions-76.png\" alt=\"Big Ideas Math Answers Grade 4 Chapter 9 Multiply Whole Numbers and Fractions 76\" width=\"596\" height=\"191\" srcset=\"https:\/\/ccssanswers.com\/wp-content\/uploads\/2020\/12\/Big-Ideas-Math-Answers-Grade-4-Chapter-9-Multiply-Whole-Numbers-and-Fractions-76.png 596w, https:\/\/ccssanswers.com\/wp-content\/uploads\/2020\/12\/Big-Ideas-Math-Answers-Grade-4-Chapter-9-Multiply-Whole-Numbers-and-Fractions-76-300x96.png 300w\" sizes=\"(max-width: 596px) 100vw, 596px\" \/><br \/>\nAnswer:<br \/>\n3 X 1 \\(\\frac{1}{2}\\) = \\(\\frac{9}{2}\\)<br \/>\nExplanation:<br \/>\nFirst we write the mixed number as a fraction then multiply, so 1 \\(\\frac{1}{2}\\) =<br \/>\n1+ \\(\\frac{1}{2}\\) = 2 x 1+1 by 2=\u00a0 \\(\\frac{3}{2}\\) now we multiply it with the whole ,<br \/>\n3 X \\(\\frac{3}{2}\\) now we write in unit fraction and multiply\u00a0 3 X 3 X \\(\\frac{1}{2}\\)=<br \/>\n9 X\u00a0 \\(\\frac{1}{2}\\)= \\(\\frac{9}{2}\\).<\/p>\n<p><strong>Show and Grow<\/strong><\/p>\n<p>Multiply<\/p>\n<p>Question 1.<br \/>\n<img decoding=\"async\" loading=\"lazy\" class=\"alignnone size-full wp-image-13039\" src=\"https:\/\/ccssanswers.com\/wp-content\/uploads\/2020\/12\/Big-Ideas-Math-Answers-Grade-4-Chapter-9-Multiply-Whole-Numbers-and-Fractions-77.png\" alt=\"Big Ideas Math Answers Grade 4 Chapter 9 Multiply Whole Numbers and Fractions 77\" width=\"135\" height=\"51\" \/><br \/>\nAnswer:<br \/>\n<img decoding=\"async\" loading=\"lazy\" class=\"alignnone size-full wp-image-13039\" src=\"https:\/\/ccssanswers.com\/wp-content\/uploads\/2020\/12\/Big-Ideas-Math-Answers-Grade-4-Chapter-9-Multiply-Whole-Numbers-and-Fractions-77.png\" alt=\"Big Ideas Math Answers Grade 4 Chapter 9 Multiply Whole Numbers and Fractions 77\" width=\"135\" height=\"51\" \/> = \\(\\frac{27}{4}\\)=6 \\(\\frac{3}{4}\\)<br \/>\nExplanation:<br \/>\nFirst we write the mixed number as a fraction then multiply, so 2 \\(\\frac{1}{4}\\) =<br \/>\n2 + \\(\\frac{1}{4}\\)=(2 X 4 + 1) by 4 = \\(\\frac{9}{4}\\) now we multiply it with the whole,<br \/>\n3 X \\(\\frac{9}{4}\\) now we write in unit fraction and multiply\u00a0 3 X 9 X \\(\\frac{1}{4}\\) =<br \/>\n27 X \\(\\frac{1}{4}\\) = \\(\\frac{27}{4}\\), we can write the product as mixed fraction as<br \/>\n<span id=\"MathJax-Element-5-Frame\" class=\"mjx-chtml MathJax_CHTML\"><span id=\"MJXc-Node-26\" class=\"mjx-math\"><span id=\"MJXc-Node-27\" class=\"mjx-mrow\"><span id=\"MJXc-Node-28\" class=\"mjx-mstyle\"><span id=\"MJXc-Node-29\" class=\"mjx-mrow\"><span id=\"MJXc-Node-30\" class=\"mjx-mn\"><span class=\"mjx-char MJXc-TeX-main-R\">4<\/span><\/span><\/span><\/span><\/span><\/span><\/span>\u00a0goes in\u00a0<span id=\"MathJax-Element-6-Frame\" class=\"mjx-chtml MathJax_CHTML\"><span id=\"MJXc-Node-31\" class=\"mjx-math\"><span id=\"MJXc-Node-32\" class=\"mjx-mrow\"><span id=\"MJXc-Node-33\" class=\"mjx-mstyle\"><span id=\"MJXc-Node-34\" class=\"mjx-mrow\"><span id=\"MJXc-Node-35\" class=\"mjx-mn\"><span class=\"mjx-char MJXc-TeX-main-R\">6<\/span><\/span><\/span><\/span><\/span><\/span><\/span> times. 6 will be our whole number <span id=\"MathJax-Element-7-Frame\" class=\"mjx-chtml MathJax_CHTML\"><span id=\"MJXc-Node-36\" class=\"mjx-math\"><span id=\"MJXc-Node-37\" class=\"mjx-mrow\"><span id=\"MJXc-Node-38\" class=\"mjx-mstyle\"><span id=\"MJXc-Node-39\" class=\"mjx-mrow\"><span id=\"MJXc-Node-40\" class=\"mjx-mn\"><span class=\"mjx-char MJXc-TeX-main-R\">4 X <\/span><\/span><span id=\"MJXc-Node-42\" class=\"mjx-mn\"><span class=\"mjx-char MJXc-TeX-main-R\">6<\/span><\/span><\/span><\/span><\/span><\/span><\/span>\u00a0is\u00a0<span id=\"MathJax-Element-8-Frame\" class=\"mjx-chtml MathJax_CHTML\"><span id=\"MJXc-Node-43\" class=\"mjx-math\"><span id=\"MJXc-Node-44\" class=\"mjx-mrow\"><span id=\"MJXc-Node-45\" class=\"mjx-mstyle\"><span id=\"MJXc-Node-46\" class=\"mjx-mrow\"><span id=\"MJXc-Node-47\" class=\"mjx-mn\"><span class=\"mjx-char MJXc-TeX-main-R\">24<\/span><\/span><\/span><\/span><\/span><\/span><\/span>\u00a0and we have\u00a0<span id=\"MathJax-Element-9-Frame\" class=\"mjx-chtml MathJax_CHTML\"><span id=\"MJXc-Node-48\" class=\"mjx-math\"><span id=\"MJXc-Node-49\" class=\"mjx-mrow\"><span id=\"MJXc-Node-50\" class=\"mjx-mstyle\"><span id=\"MJXc-Node-51\" class=\"mjx-mrow\"><span id=\"MJXc-Node-52\" class=\"mjx-mn\"><span class=\"mjx-char MJXc-TeX-main-R\">3<\/span><\/span><\/span><\/span><\/span><\/span><\/span>\u00a0left over (<span id=\"MathJax-Element-10-Frame\" class=\"mjx-chtml MathJax_CHTML\"><span id=\"MJXc-Node-53\" class=\"mjx-math\"><span id=\"MJXc-Node-54\" class=\"mjx-mrow\"><span id=\"MJXc-Node-55\" class=\"mjx-mstyle\"><span id=\"MJXc-Node-56\" class=\"mjx-mrow\"><span id=\"MJXc-Node-57\" class=\"mjx-mn\"><span class=\"mjx-char MJXc-TeX-main-R\">27<\/span><\/span><span id=\"MJXc-Node-58\" class=\"mjx-mo\"><span class=\"mjx-char MJXc-TeX-main-R\">\u2212<\/span><\/span><span id=\"MJXc-Node-59\" class=\"mjx-mn\"><span class=\"mjx-char MJXc-TeX-main-R\">24<\/span><\/span><\/span><\/span><\/span><\/span><\/span>),<br \/>\n3 will be our numerator and our denominator will stay the same 4= \\(\\frac{27}{4}\\)=<br \/>\n6 \\(\\frac{3}{4}\\).<\/p>\n<p>Question 2.<br \/>\n<img decoding=\"async\" loading=\"lazy\" class=\"alignnone size-full wp-image-13040\" src=\"https:\/\/ccssanswers.com\/wp-content\/uploads\/2020\/12\/Big-Ideas-Math-Answers-Grade-4-Chapter-9-Multiply-Whole-Numbers-and-Fractions-78.png\" alt=\"Big Ideas Math Answers Grade 4 Chapter 9 Multiply Whole Numbers and Fractions 78\" width=\"145\" height=\"56\" \/><br \/>\nAnswer:<br \/>\n<img decoding=\"async\" loading=\"lazy\" class=\"alignnone size-full wp-image-13040\" src=\"https:\/\/ccssanswers.com\/wp-content\/uploads\/2020\/12\/Big-Ideas-Math-Answers-Grade-4-Chapter-9-Multiply-Whole-Numbers-and-Fractions-78.png\" alt=\"Big Ideas Math Answers Grade 4 Chapter 9 Multiply Whole Numbers and Fractions 78\" width=\"145\" height=\"56\" \/> \\(\\frac{38}{12}\\)= 3 \\(\\frac{2}{12}\\).<\/p>\n<p>Explanation:<br \/>\nFirst we write the mixed number as a fraction then multiply, so 1 \\(\\frac{7}{12}\\)=<br \/>\n1 + \\(\\frac{7}{12}\\)= (1 X 12 + 7 ) by 12 = \\(\\frac{19}{12}\\)<br \/>\nnow we multiply it with the whole, 2 X \\(\\frac{19}{12}\\) now we write in unit fraction and<br \/>\nmultiply\u00a0 2 X 19 X \\(\\frac{1}{12}\\)= 38 X \\(\\frac{1}{12}\\) = \\(\\frac{38}{12}\\),<br \/>\nwe can write the product as mixed fraction as 12 goes in 3 times. 3 will be our whole number 12<span id=\"MathJax-Element-7-Frame\" class=\"mjx-chtml MathJax_CHTML\"><span id=\"MJXc-Node-36\" class=\"mjx-math\"><span id=\"MJXc-Node-37\" class=\"mjx-mrow\"><span id=\"MJXc-Node-38\" class=\"mjx-mstyle\"><span id=\"MJXc-Node-39\" class=\"mjx-mrow\"><span id=\"MJXc-Node-40\" class=\"mjx-mn\"><span class=\"mjx-char MJXc-TeX-main-R\"> X 3<\/span><\/span><\/span><\/span><\/span><\/span><\/span> is 36\u00a0and<br \/>\nwe have 2\u00a0left over (38<span id=\"MathJax-Element-10-Frame\" class=\"mjx-chtml MathJax_CHTML\"><span id=\"MJXc-Node-53\" class=\"mjx-math\"><span id=\"MJXc-Node-54\" class=\"mjx-mrow\"><span id=\"MJXc-Node-55\" class=\"mjx-mstyle\"><span id=\"MJXc-Node-56\" class=\"mjx-mrow\"><span id=\"MJXc-Node-58\" class=\"mjx-mo\"><span class=\"mjx-char MJXc-TeX-main-R\">\u221236<\/span><\/span><\/span><\/span><\/span><\/span><\/span>). 2 will be our numerator and our denominator will be the same 12<br \/>\n= \\(\\frac{38}{12}\\)=\u00a0 3 \\(\\frac{2}{12}\\).<\/p>\n<p>Question 3.<br \/>\n<img decoding=\"async\" loading=\"lazy\" class=\"alignnone size-full wp-image-13041\" src=\"https:\/\/ccssanswers.com\/wp-content\/uploads\/2020\/12\/Big-Ideas-Math-Answers-Grade-4-Chapter-9-Multiply-Whole-Numbers-and-Fractions-79.png\" alt=\"Big Ideas Math Answers Grade 4 Chapter 9 Multiply Whole Numbers and Fractions 79\" width=\"137\" height=\"61\" \/><br \/>\nAnswer:<br \/>\n<img decoding=\"async\" loading=\"lazy\" class=\"alignnone size-full wp-image-13041\" src=\"https:\/\/ccssanswers.com\/wp-content\/uploads\/2020\/12\/Big-Ideas-Math-Answers-Grade-4-Chapter-9-Multiply-Whole-Numbers-and-Fractions-79.png\" alt=\"Big Ideas Math Answers Grade 4 Chapter 9 Multiply Whole Numbers and Fractions 79\" width=\"137\" height=\"61\" \/>= \\(\\frac{116}{8}\\)= 14 \\(\\frac{4}{8}\\)<br \/>\nExplanation:<br \/>\nFirst we write the mixed number as a fraction then multiply, so 3 \\(\\frac{5}{8}\\)=<br \/>\n3 + \\(\\frac{5}{8}\\)= (3 X 8 + 5) by 8 = \\(\\frac{29}{8}\\) now we multiply it with the whole,<br \/>\n4 X \\(\\frac{29}{8}\\) now we write in unit fraction and multiply\u00a0 4 X 29 X \\(\\frac{1}{8}\\)=<br \/>\n116 X \\(\\frac{1}{8}\\) = \\(\\frac{116}{8}\\), we can write the product as mixed fraction as<br \/>\n8 goes in 14 times. 14 will be our whole number 8<span id=\"MathJax-Element-7-Frame\" class=\"mjx-chtml MathJax_CHTML\"><span id=\"MJXc-Node-36\" class=\"mjx-math\"><span id=\"MJXc-Node-37\" class=\"mjx-mrow\"><span id=\"MJXc-Node-38\" class=\"mjx-mstyle\"><span id=\"MJXc-Node-39\" class=\"mjx-mrow\"><span id=\"MJXc-Node-40\" class=\"mjx-mn\"><span class=\"mjx-char MJXc-TeX-main-R\"> X 14<\/span><\/span><\/span><\/span><\/span><\/span><\/span> is 112 and we have 4 left over (116<span id=\"MathJax-Element-10-Frame\" class=\"mjx-chtml MathJax_CHTML\"><span id=\"MJXc-Node-53\" class=\"mjx-math\"><span id=\"MJXc-Node-54\" class=\"mjx-mrow\"><span id=\"MJXc-Node-55\" class=\"mjx-mstyle\"><span id=\"MJXc-Node-56\" class=\"mjx-mrow\"><span id=\"MJXc-Node-58\" class=\"mjx-mo\"><span class=\"mjx-char MJXc-TeX-main-R\">\u2212112<\/span><\/span><\/span><\/span><\/span><\/span><\/span>).<br \/>\n4 will be our numerator and our denominator will be the same 8= \\(\\frac{116}{8}\\)=<br \/>\n14 \\(\\frac{4}{8}\\).<\/p>\n<p><strong>Apply and Grow: Practice<\/strong><\/p>\n<p>Multiply.<\/p>\n<p>Question 4.<br \/>\n<img decoding=\"async\" loading=\"lazy\" class=\"alignnone size-full wp-image-13042\" src=\"https:\/\/ccssanswers.com\/wp-content\/uploads\/2020\/12\/Big-Ideas-Math-Answers-Grade-4-Chapter-9-Multiply-Whole-Numbers-and-Fractions-80.png\" alt=\"Big Ideas Math Answers Grade 4 Chapter 9 Multiply Whole Numbers and Fractions 80\" width=\"142\" height=\"56\" \/><br \/>\nAnswer:<br \/>\n<img decoding=\"async\" loading=\"lazy\" class=\"alignnone size-full wp-image-13042\" src=\"https:\/\/ccssanswers.com\/wp-content\/uploads\/2020\/12\/Big-Ideas-Math-Answers-Grade-4-Chapter-9-Multiply-Whole-Numbers-and-Fractions-80.png\" alt=\"Big Ideas Math Answers Grade 4 Chapter 9 Multiply Whole Numbers and Fractions 80\" width=\"142\" height=\"56\" \/>= \\(\\frac{50}{3}\\)=16 \\(\\frac{2}{3}\\)<br \/>\nExplanation:<br \/>\nFirst we write the mixed number as a fraction then multiply, so 1 \\(\\frac{2}{3}\\)=<br \/>\n1 + \\(\\frac{2}{3}\\)= (1 X 3 + 2) by 3 = \\(\\frac{5}{3}\\) now we multiply it with the whole,<br \/>\n10 X \\(\\frac{5}{3}\\) now we write in unit fraction and multiply\u00a0 10 X 5 X \\(\\frac{1}{3}\\)=<br \/>\n50 X \\(\\frac{1}{3}\\) = \\(\\frac{50}{3}\\), we can write the product as mixed fraction as<br \/>\n3 goes in 16 times. 16 will be our whole number 3<span id=\"MathJax-Element-7-Frame\" class=\"mjx-chtml MathJax_CHTML\"><span id=\"MJXc-Node-36\" class=\"mjx-math\"><span id=\"MJXc-Node-37\" class=\"mjx-mrow\"><span id=\"MJXc-Node-38\" class=\"mjx-mstyle\"><span id=\"MJXc-Node-39\" class=\"mjx-mrow\"><span id=\"MJXc-Node-40\" class=\"mjx-mn\"><span class=\"mjx-char MJXc-TeX-main-R\"> X 16<\/span><\/span><\/span><\/span><\/span><\/span><\/span> is 48 and we have 2 left over (50<span id=\"MathJax-Element-10-Frame\" class=\"mjx-chtml MathJax_CHTML\"><span id=\"MJXc-Node-53\" class=\"mjx-math\"><span id=\"MJXc-Node-54\" class=\"mjx-mrow\"><span id=\"MJXc-Node-55\" class=\"mjx-mstyle\"><span id=\"MJXc-Node-56\" class=\"mjx-mrow\"><span id=\"MJXc-Node-58\" class=\"mjx-mo\"><span class=\"mjx-char MJXc-TeX-main-R\">\u221248<\/span><\/span><\/span><\/span><\/span><\/span><\/span>).<br \/>\n2 will be our numerator and our denominator will be the same 3= \\(\\frac{50}{3}\\)= 16 \\(\\frac{2}{3}\\).<\/p>\n<p>Question 5.<br \/>\n<img decoding=\"async\" loading=\"lazy\" class=\"alignnone size-full wp-image-13043\" src=\"https:\/\/ccssanswers.com\/wp-content\/uploads\/2020\/12\/Big-Ideas-Math-Answers-Grade-4-Chapter-9-Multiply-Whole-Numbers-and-Fractions-81.png\" alt=\"Big Ideas Math Answers Grade 4 Chapter 9 Multiply Whole Numbers and Fractions 81\" width=\"138\" height=\"61\" \/><br \/>\nAnswer:<br \/>\n<img decoding=\"async\" loading=\"lazy\" class=\"alignnone size-full wp-image-13043\" src=\"https:\/\/ccssanswers.com\/wp-content\/uploads\/2020\/12\/Big-Ideas-Math-Answers-Grade-4-Chapter-9-Multiply-Whole-Numbers-and-Fractions-81.png\" alt=\"Big Ideas Math Answers Grade 4 Chapter 9 Multiply Whole Numbers and Fractions 81\" width=\"138\" height=\"61\" \/>= \\(\\frac{25}{2}\\)=12 \\(\\frac{1}{2}\\)<\/p>\n<p>Explanation:<br \/>\nFirst we write the mixed number as a fraction then multiply, so 2 \\(\\frac{1}{2}\\)=<br \/>\n2 + \\(\\frac{1}{2}\\)= (2 X 2 + 1) by 2 = \\(\\frac{5}{2}\\)<br \/>\nnow we multiply it with the whole, 5 X \\(\\frac{5}{2}\\) .<br \/>\nWe write in unit fraction and multiply\u00a0 5 X 5 X \\(\\frac{1}{2}\\)=<br \/>\n25 X \\(\\frac{1}{2}\\) = \\(\\frac{25}{2}\\), we can write the product as mixed fraction<br \/>\nas 2 goes in 12 times. 12 will be our whole number 2<span id=\"MathJax-Element-7-Frame\" class=\"mjx-chtml MathJax_CHTML\"><span id=\"MJXc-Node-36\" class=\"mjx-math\"><span id=\"MJXc-Node-37\" class=\"mjx-mrow\"><span id=\"MJXc-Node-38\" class=\"mjx-mstyle\"><span id=\"MJXc-Node-39\" class=\"mjx-mrow\"><span id=\"MJXc-Node-40\" class=\"mjx-mn\"><span class=\"mjx-char MJXc-TeX-main-R\"> X 12<\/span><\/span><\/span><\/span><\/span><\/span><\/span> is 24 and we have 1 left over (25<span id=\"MathJax-Element-10-Frame\" class=\"mjx-chtml MathJax_CHTML\"><span id=\"MJXc-Node-53\" class=\"mjx-math\"><span id=\"MJXc-Node-54\" class=\"mjx-mrow\"><span id=\"MJXc-Node-55\" class=\"mjx-mstyle\"><span id=\"MJXc-Node-56\" class=\"mjx-mrow\"><span id=\"MJXc-Node-58\" class=\"mjx-mo\"><span class=\"mjx-char MJXc-TeX-main-R\">\u221224<\/span><\/span><\/span><\/span><\/span><\/span><\/span>).<br \/>\n1 will be our numerator and our denominator will be the same 2= \\(\\frac{25}{2}\\)=<br \/>\n12 \\(\\frac{1}{2}\\)<\/p>\n<p>Question 6.<br \/>\n<img decoding=\"async\" loading=\"lazy\" class=\"alignnone size-full wp-image-13044\" src=\"https:\/\/ccssanswers.com\/wp-content\/uploads\/2020\/12\/Big-Ideas-Math-Answers-Grade-4-Chapter-9-Multiply-Whole-Numbers-and-Fractions-82.png\" alt=\"Big Ideas Math Answers Grade 4 Chapter 9 Multiply Whole Numbers and Fractions 82\" width=\"138\" height=\"73\" \/><br \/>\nAnswer:<br \/>\n<img decoding=\"async\" loading=\"lazy\" class=\"alignnone size-full wp-image-13044\" src=\"https:\/\/ccssanswers.com\/wp-content\/uploads\/2020\/12\/Big-Ideas-Math-Answers-Grade-4-Chapter-9-Multiply-Whole-Numbers-and-Fractions-82.png\" alt=\"Big Ideas Math Answers Grade 4 Chapter 9 Multiply Whole Numbers and Fractions 82\" width=\"138\" height=\"73\" \/>= \\(\\frac{184}{6}\\)=\\(\\frac{92}{3}\\)=30 \\(\\frac{4}{6}\\).<\/p>\n<p>Explanation:<br \/>\nFirst we write the mixed number as a fraction then multiply, so 7 \\(\\frac{4}{6}\\)=<br \/>\n7 + \\(\\frac{4}{6}\\)=(7 X 6 + 4) by 6 = \\(\\frac{46}{6}\\) now we multiply it with the whole,<br \/>\n4 X \\(\\frac{46}{6}\\) now we write in unit fraction and multiply\u00a0 4 X 46 X \\(\\frac{1}{6}\\)=<br \/>\n184 X \\(\\frac{1}{6}\\) = \\(\\frac{184}{6}\\), we can write the product as mixed fraction as<br \/>\n6 goes in 30 times. 30 will be our whole number 6<span id=\"MathJax-Element-7-Frame\" class=\"mjx-chtml MathJax_CHTML\"><span id=\"MJXc-Node-36\" class=\"mjx-math\"><span id=\"MJXc-Node-37\" class=\"mjx-mrow\"><span id=\"MJXc-Node-38\" class=\"mjx-mstyle\"><span id=\"MJXc-Node-39\" class=\"mjx-mrow\"><span id=\"MJXc-Node-40\" class=\"mjx-mn\"><span class=\"mjx-char MJXc-TeX-main-R\"> X 30<\/span><\/span><\/span><\/span><\/span><\/span><\/span> is 180 and we have 4 left over (184<span id=\"MathJax-Element-10-Frame\" class=\"mjx-chtml MathJax_CHTML\"><span id=\"MJXc-Node-53\" class=\"mjx-math\"><span id=\"MJXc-Node-54\" class=\"mjx-mrow\"><span id=\"MJXc-Node-55\" class=\"mjx-mstyle\"><span id=\"MJXc-Node-56\" class=\"mjx-mrow\"><span id=\"MJXc-Node-58\" class=\"mjx-mo\"><span class=\"mjx-char MJXc-TeX-main-R\">\u2212180<\/span><\/span><\/span><\/span><\/span><\/span><\/span>).<br \/>\n4 will be our numerator and our denominator will be the same 6= \\(\\frac{184}{6}\\)=<br \/>\n30 \\(\\frac{4}{6}\\) and \\(\\frac{184}{6}\\) can also written as \\(\\frac{92}{3}\\)<br \/>\nbecause both 184 and 6 can also be further divided by 2.<\/p>\n<p>Question 7.<br \/>\n<img decoding=\"async\" loading=\"lazy\" class=\"alignnone size-full wp-image-13045\" src=\"https:\/\/ccssanswers.com\/wp-content\/uploads\/2020\/12\/Big-Ideas-Math-Answers-Grade-4-Chapter-9-Multiply-Whole-Numbers-and-Fractions-83.png\" alt=\"Big Ideas Math Answers Grade 4 Chapter 9 Multiply Whole Numbers and Fractions 83\" width=\"131\" height=\"57\" \/><br \/>\nAnswer:<br \/>\n<img decoding=\"async\" loading=\"lazy\" class=\"alignnone size-full wp-image-13045\" src=\"https:\/\/ccssanswers.com\/wp-content\/uploads\/2020\/12\/Big-Ideas-Math-Answers-Grade-4-Chapter-9-Multiply-Whole-Numbers-and-Fractions-83.png\" alt=\"Big Ideas Math Answers Grade 4 Chapter 9 Multiply Whole Numbers and Fractions 83\" width=\"131\" height=\"57\" \/>= \\(\\frac{243}{5}\\)= 48 \\(\\frac{3}{5}\\)<br \/>\nExplanation:<br \/>\nFirst we write the mixed number as a fraction then multiply, so 5 \\(\\frac{2}{5}\\)=<br \/>\n5 + \\(\\frac{2}{5}\\)= (5 X 5 + 2) by 5 = \\(\\frac{27}{5}\\) now we multiply it with the whole,<br \/>\n9 X \\(\\frac{27}{5}\\) now we write in unit fraction and multiply\u00a0 9 X 27 X \\(\\frac{1}{5}\\)=<br \/>\n243 X \\(\\frac{1}{5}\\) = \\(\\frac{243}{5}\\), we can write the product as mixed fraction as<br \/>\n5 goes in 48 times. 48 will be our whole number 5<span id=\"MathJax-Element-7-Frame\" class=\"mjx-chtml MathJax_CHTML\"><span id=\"MJXc-Node-36\" class=\"mjx-math\"><span id=\"MJXc-Node-37\" class=\"mjx-mrow\"><span id=\"MJXc-Node-38\" class=\"mjx-mstyle\"><span id=\"MJXc-Node-39\" class=\"mjx-mrow\"><span id=\"MJXc-Node-40\" class=\"mjx-mn\"><span class=\"mjx-char MJXc-TeX-main-R\"> X 48<\/span><\/span><\/span><\/span><\/span><\/span><\/span> is 240 and we have 3 left over (243<span id=\"MathJax-Element-10-Frame\" class=\"mjx-chtml MathJax_CHTML\"><span id=\"MJXc-Node-53\" class=\"mjx-math\"><span id=\"MJXc-Node-54\" class=\"mjx-mrow\"><span id=\"MJXc-Node-55\" class=\"mjx-mstyle\"><span id=\"MJXc-Node-56\" class=\"mjx-mrow\"><span id=\"MJXc-Node-58\" class=\"mjx-mo\"><span class=\"mjx-char MJXc-TeX-main-R\">\u2212240<\/span><\/span><\/span><\/span><\/span><\/span><\/span>).<br \/>\n3 will be our numerator and our denominator will be the same 5= \\(\\frac{243}{5}\\)=<br \/>\n48 \\(\\frac{3}{5}\\).<\/p>\n<p>Question 8.<br \/>\n<img decoding=\"async\" loading=\"lazy\" class=\"alignnone size-full wp-image-13046\" src=\"https:\/\/ccssanswers.com\/wp-content\/uploads\/2020\/12\/Big-Ideas-Math-Answers-Grade-4-Chapter-9-Multiply-Whole-Numbers-and-Fractions-84.png\" alt=\"Big Ideas Math Answers Grade 4 Chapter 9 Multiply Whole Numbers and Fractions 84\" width=\"139\" height=\"65\" \/><br \/>\nAnswer:<br \/>\n<img decoding=\"async\" loading=\"lazy\" class=\"alignnone size-full wp-image-13046\" src=\"https:\/\/ccssanswers.com\/wp-content\/uploads\/2020\/12\/Big-Ideas-Math-Answers-Grade-4-Chapter-9-Multiply-Whole-Numbers-and-Fractions-84.png\" alt=\"Big Ideas Math Answers Grade 4 Chapter 9 Multiply Whole Numbers and Fractions 84\" width=\"139\" height=\"65\" \/>= \\(\\frac{312}{10}\\)= 31\u00a0\\(\\frac{2}{10}\\)<\/p>\n<p>Explanation:<br \/>\nFirst we write the mixed number as a fraction then multiply, so 3 \\(\\frac{9}{10}\\)=<br \/>\n3 + \\(\\frac{9}{10}\\)= (3 X 10 + 9) by 10 = \\(\\frac{39}{10}\\)<br \/>\nnow we multiply it with the whole, 8 X \\(\\frac{39}{10}\\) now we write in unit fraction<br \/>\nand multiply\u00a0 8 X 39 X \\(\\frac{1}{10}\\)= 312 X \\(\\frac{1}{10}\\) =<br \/>\n\\(\\frac{312}{10}\\), we can write the product as mixed fraction as 10 goes in 31 times.<br \/>\n31 will be our whole number 10<span id=\"MathJax-Element-7-Frame\" class=\"mjx-chtml MathJax_CHTML\"><span id=\"MJXc-Node-36\" class=\"mjx-math\"><span id=\"MJXc-Node-37\" class=\"mjx-mrow\"><span id=\"MJXc-Node-38\" class=\"mjx-mstyle\"><span id=\"MJXc-Node-39\" class=\"mjx-mrow\"><span id=\"MJXc-Node-40\" class=\"mjx-mn\"><span class=\"mjx-char MJXc-TeX-main-R\"> X 31<\/span><\/span><\/span><\/span><\/span><\/span><\/span> is 310 and we have 2 left over (312<span id=\"MathJax-Element-10-Frame\" class=\"mjx-chtml MathJax_CHTML\"><span id=\"MJXc-Node-53\" class=\"mjx-math\"><span id=\"MJXc-Node-54\" class=\"mjx-mrow\"><span id=\"MJXc-Node-55\" class=\"mjx-mstyle\"><span id=\"MJXc-Node-56\" class=\"mjx-mrow\"><span id=\"MJXc-Node-58\" class=\"mjx-mo\"><span class=\"mjx-char MJXc-TeX-main-R\">\u2212310<\/span><\/span><\/span><\/span><\/span><\/span><\/span>).<br \/>\n2 will be our numerator and our denominator will be the same 10= \\(\\frac{312}{10}\\)=<br \/>\n31 \\(\\frac{2}{10}\\).<\/p>\n<p>Question 9.<br \/>\n<img decoding=\"async\" loading=\"lazy\" class=\"alignnone size-full wp-image-13047\" src=\"https:\/\/ccssanswers.com\/wp-content\/uploads\/2020\/12\/Big-Ideas-Math-Answers-Grade-4-Chapter-9-Multiply-Whole-Numbers-and-Fractions-85.png\" alt=\"Big Ideas Math Answers Grade 4 Chapter 9 Multiply Whole Numbers and Fractions 85\" width=\"146\" height=\"58\" \/><br \/>\nAnswer:<br \/>\n<img decoding=\"async\" loading=\"lazy\" class=\"alignnone size-full wp-image-13047\" src=\"https:\/\/ccssanswers.com\/wp-content\/uploads\/2020\/12\/Big-Ideas-Math-Answers-Grade-4-Chapter-9-Multiply-Whole-Numbers-and-Fractions-85.png\" alt=\"Big Ideas Math Answers Grade 4 Chapter 9 Multiply Whole Numbers and Fractions 85\" width=\"146\" height=\"58\" \/>= \\(\\frac{5466}{100}\\)=54 \\(\\frac{66}{100}\\).<br \/>\nExplanation:<br \/>\nFirst we write the mixed number as a fraction then multiply, so 9 \\(\\frac{11}{100}\\)=<br \/>\n9 + \\(\\frac{11}{100}\\)= (9 X 100 + 11) by 100 = \\(\\frac{911}{100}\\)<br \/>\nnow we multiply it with the whole, 6 X \\(\\frac{911}{100}\\) now we write in unit fraction<br \/>\nand multiply\u00a0 6 X 911 X \\(\\frac{1}{100}\\)= 5466 X \\(\\frac{1}{100}\\) =<br \/>\n\\(\\frac{5466}{100}\\), we can write the product as mixed fraction as 100 goes in 54 times.<br \/>\n54 will be our whole number 100<span id=\"MathJax-Element-7-Frame\" class=\"mjx-chtml MathJax_CHTML\"><span id=\"MJXc-Node-36\" class=\"mjx-math\"><span id=\"MJXc-Node-37\" class=\"mjx-mrow\"><span id=\"MJXc-Node-38\" class=\"mjx-mstyle\"><span id=\"MJXc-Node-39\" class=\"mjx-mrow\"><span id=\"MJXc-Node-40\" class=\"mjx-mn\"><span class=\"mjx-char MJXc-TeX-main-R\"> X 54<\/span><\/span><\/span><\/span><\/span><\/span><\/span> is 5400 and we have 66 left over (5466<span id=\"MathJax-Element-10-Frame\" class=\"mjx-chtml MathJax_CHTML\"><span id=\"MJXc-Node-53\" class=\"mjx-math\"><span id=\"MJXc-Node-54\" class=\"mjx-mrow\"><span id=\"MJXc-Node-55\" class=\"mjx-mstyle\"><span id=\"MJXc-Node-56\" class=\"mjx-mrow\"><span id=\"MJXc-Node-58\" class=\"mjx-mo\"><span class=\"mjx-char MJXc-TeX-main-R\">\u22125400<\/span><\/span><\/span><\/span><\/span><\/span><\/span>).<br \/>\n66 will be our numerator and our denominator will be the same 100= \\(\\frac{5466}{100}\\)=<br \/>\n54 \\(\\frac{66}{100}\\).<\/p>\n<p>Question 10.<br \/>\n<strong>Reasoning<\/strong><br \/>\nHow can you check whether your answer in Exercise 9 is reasonable?<br \/>\nAnswer:<br \/>\nExercise 9 is reasonable.<\/p>\n<p>Explanation:<br \/>\nIn the above problem 6 X 9 \\(\\frac{11}{100}\\) we got product as<br \/>\n\\(\\frac{5466}{100}\\) =54 \\(\\frac{66}{100}\\)\u00a0 we can write the product as mixed fraction<br \/>\nas 100 goes in 54 times. 54 will be our whole number 100<span id=\"MathJax-Element-7-Frame\" class=\"mjx-chtml MathJax_CHTML\"><span id=\"MJXc-Node-36\" class=\"mjx-math\"><span id=\"MJXc-Node-37\" class=\"mjx-mrow\"><span id=\"MJXc-Node-38\" class=\"mjx-mstyle\"><span id=\"MJXc-Node-39\" class=\"mjx-mrow\"><span id=\"MJXc-Node-40\" class=\"mjx-mn\"><span class=\"mjx-char MJXc-TeX-main-R\"> X 54<\/span><\/span><\/span><\/span><\/span><\/span><\/span> is 5400 and 5466-5400,<br \/>\nleaving 66 as remainder so we consider the whole part 54,As 54 is reasonable close to 100.<\/p>\n<p>Question 11.<br \/>\n<strong>YOU BE THE TEACHER<\/strong><br \/>\nYour friend \ufb01nds the product of 9 and 6\\(\\frac{1}{3}\\). Is your friend correct? Explain.<br \/>\n<img decoding=\"async\" loading=\"lazy\" class=\"alignnone size-full wp-image-13048\" src=\"https:\/\/ccssanswers.com\/wp-content\/uploads\/2020\/12\/Big-Ideas-Math-Answers-Grade-4-Chapter-9-Multiply-Whole-Numbers-and-Fractions-86.png\" alt=\"Big Ideas Math Answers Grade 4 Chapter 9 Multiply Whole Numbers and Fractions 86\" width=\"147\" height=\"123\" \/><br \/>\nAnswer:<br \/>\nYes friend is correct.<\/p>\n<p>Explanation:<br \/>\nFirst we write the mixed number as a fraction then multiply, so 6 \\(\\frac{1}{3}\\)= 6 + \\(\\frac{1}{3}\\)= (6 X 3 + 1) by 3 = \\(\\frac{19}{3}\\) now we multiply it with the whole, 9 X \\(\\frac{19}{3}\\) now we write in unit fraction and multiply\u00a0 9 X 19 X \\(\\frac{1}{3}\\)= 171 X \\(\\frac{1}{3}\\) = \\(\\frac{171}{3}\\), As 3 goes 57 times leaving no remainder so we get 9 X 6 \\(\\frac{1}{3}\\)=57 which matches with the friend&#8217;s product so friend is correct.<\/p>\n<p>Question 12.<br \/>\n<strong>DIG DEEPER!<\/strong><br \/>\nWithout multiplying, can you tell which expression is greater, <img decoding=\"async\" loading=\"lazy\" class=\"alignnone size-full wp-image-13050\" src=\"https:\/\/ccssanswers.com\/wp-content\/uploads\/2020\/12\/Big-Ideas-Math-Answers-Grade-4-Chapter-9-Multiply-Whole-Numbers-and-Fractions-87.png\" alt=\"Big Ideas Math Answers Grade 4 Chapter 9 Multiply Whole Numbers and Fractions 87\" width=\"127\" height=\"46\" \/> ? Explain.<br \/>\nAnswer:<br \/>\n5 X 6 \\(\\frac{1}{4}\\) &lt; 6 X 5 \\(\\frac{1}{4}\\)<\/p>\n<p>Explanation:<\/p>\n<p>By drawing models also we can say<br \/>\n<img decoding=\"async\" loading=\"lazy\" class=\"alignnone wp-image-25118 size-full\" src=\"https:\/\/ccssanswers.com\/wp-content\/uploads\/2020\/12\/9-Multiply-Whole-Numbers-and-Fractions-16-1.bmp\" alt=\"\" width=\"435\" height=\"375\" srcset=\"https:\/\/ccssanswers.com\/wp-content\/uploads\/2020\/12\/9-Multiply-Whole-Numbers-and-Fractions-16-1.bmp 435w, https:\/\/ccssanswers.com\/wp-content\/uploads\/2020\/12\/9-Multiply-Whole-Numbers-and-Fractions-16-1-300x259.jpg 300w\" sizes=\"(max-width: 435px) 100vw, 435px\" \/><br \/>\nIf the denominators are the same, then the fraction with the greater numerator is the greater fraction.<br \/>\nThe fraction with the lesser numerator is the lesser fraction, But first we write the mixed number as a fraction<br \/>\nso in 5 X 6 \\(\\frac{1}{4}\\), 6 \\(\\frac{1}{4}\\)= 6+ \\(\\frac{1}{4}\\)=<br \/>\n(6 X 4 +1) by 4 =\u00a0 \\(\\frac{25}{4}\\) now we multiply it with the whole as<br \/>\n5 X \\(\\frac{25}{4}\\) now we write the mixed fraction 5 \\(\\frac{1}{4}\\)<br \/>\nas 5+ \\(\\frac{1}{4}\\) = 5 x 4 +1 by 4=5 \\(\\frac{21}{4}\\)<br \/>\nnow we multiply it with\u00a0 the whole as 6 X \\(\\frac{21}{4}\\) ,<br \/>\nNow comparing 5 X\u00a0 \\(\\frac{25}{4}\\)\u00a0 and\u00a0 6 X \\(\\frac{21}{4}\\)<br \/>\nin both denominators are same and numerators 5 X \\(\\frac{25}{4}\\) is less than<br \/>\n6 X \\(\\frac{21}{4}\\) so 5 X 6 \\(\\frac{1}{4}\\) &lt; 6 X 5 \\(\\frac{1}{4}\\)<\/p>\n<p><strong>Think and Grow: Modeling Real Life<\/strong><\/p>\n<p><strong>Example<\/strong><br \/>\nAn elephant sleeps 2\\(\\frac{1}{2}\\) hours in 1 day. A koala sleeps 6 times as long as the elephant in the same day. How many hours does the koala sleep that day?<br \/>\n<img decoding=\"async\" loading=\"lazy\" class=\"alignnone size-full wp-image-13049\" src=\"https:\/\/ccssanswers.com\/wp-content\/uploads\/2020\/12\/Big-Ideas-Math-Answers-Grade-4-Chapter-9-Multiply-Whole-Numbers-and-Fractions-87.1.png\" alt=\"Big Ideas Math Answers Grade 4 Chapter 9 Multiply Whole Numbers and Fractions 87.1\" width=\"212\" height=\"147\" \/><br \/>\nMultiply the number of hours the elephant sleeps by 6.<br \/>\n<img decoding=\"async\" loading=\"lazy\" class=\"alignnone size-full wp-image-13051\" src=\"https:\/\/ccssanswers.com\/wp-content\/uploads\/2020\/12\/Big-Ideas-Math-Answers-Grade-4-Chapter-9-Multiply-Whole-Numbers-and-Fractions-88.png\" alt=\"Big Ideas Math Answers Grade 4 Chapter 9 Multiply Whole Numbers and Fractions 88\" width=\"585\" height=\"212\" srcset=\"https:\/\/ccssanswers.com\/wp-content\/uploads\/2020\/12\/Big-Ideas-Math-Answers-Grade-4-Chapter-9-Multiply-Whole-Numbers-and-Fractions-88.png 585w, https:\/\/ccssanswers.com\/wp-content\/uploads\/2020\/12\/Big-Ideas-Math-Answers-Grade-4-Chapter-9-Multiply-Whole-Numbers-and-Fractions-88-300x109.png 300w\" sizes=\"(max-width: 585px) 100vw, 585px\" \/><br \/>\nAnswer:<br \/>\nThe koala sleeps<span style=\"text-decoration: underline;\"> 5<\/span> hours that day.<\/p>\n<p>Explanation:<br \/>\nFirst we write mixed fraction as fraction so 2 \\(\\frac{1}{2}\\) =( 2 X 2 + 1 ) by 2<br \/>\n= \\(\\frac{5}{2}\\) , now we multiply with whole number 2 = 2 X \\(\\frac{5}{2}\\) =<br \/>\n2 X 5 X \\(\\frac{1}{2}\\) = 10 X \\(\\frac{1}{2}\\) = \\(\\frac{10}{2}\\)<br \/>\nfurther it can be simplified as both 10,2 can be divided by 2 so \\(\\frac{10}{2}\\) = 5 hours that day.<\/p>\n<p><strong>Show and Grow<\/strong><\/p>\n<p>Question 13.<br \/>\nA small bag of popcorn has 1\\(\\frac{7}{8}\\) cups of popcorn. A large bag has 7 times as many cups of popcorn as the small bag. How many cups of popcorn are in the large bag?<br \/>\nAnswer:<br \/>\nThe large bag has \\(\\frac{105}{8}\\) cups of popcorn or 13 \\(\\frac{1}{8}\\) cups of popcorn.<\/p>\n<p>Explanation:<br \/>\nGiven A small bag of popcorn has 1\\(\\frac{7}{8}\\) cups of popcorn so first we write mixed fraction<br \/>\nas fraction as 1 \\(\\frac{7}{8}\\)= ( 1 X 8 + 7 ) by 8 =\\(\\frac{15}{8}\\) ,as a large bag has<br \/>\n7 times as many cups of popcorn as the small bag so 7 times \\(\\frac{15}{8}\\)=<br \/>\n7 X 15 X \\(\\frac{1}{8}\\)=105 X \\(\\frac{1}{8}\\)=\\(\\frac{105}{8}\\) cups of popcorn.<br \/>\nWe can write the product as mixed fraction as 8 goes in 13 times.<br \/>\n13 will be our whole number 8<span id=\"MathJax-Element-7-Frame\" class=\"mjx-chtml MathJax_CHTML\"><span id=\"MJXc-Node-36\" class=\"mjx-math\"><span id=\"MJXc-Node-37\" class=\"mjx-mrow\"><span id=\"MJXc-Node-38\" class=\"mjx-mstyle\"><span id=\"MJXc-Node-39\" class=\"mjx-mrow\"><span id=\"MJXc-Node-40\" class=\"mjx-mn\"><span class=\"mjx-char MJXc-TeX-main-R\"> X 13<\/span><\/span><\/span><\/span><\/span><\/span><\/span> is 104 and we have 1 left over (105<span id=\"MathJax-Element-10-Frame\" class=\"mjx-chtml MathJax_CHTML\"><span id=\"MJXc-Node-53\" class=\"mjx-math\"><span id=\"MJXc-Node-54\" class=\"mjx-mrow\"><span id=\"MJXc-Node-55\" class=\"mjx-mstyle\"><span id=\"MJXc-Node-56\" class=\"mjx-mrow\"><span id=\"MJXc-Node-58\" class=\"mjx-mo\"><span class=\"mjx-char MJXc-TeX-main-R\">\u2212104<\/span><\/span><\/span><\/span><\/span><\/span><\/span>).<br \/>\n1 will be our numerator and our denominator will be the same 8= \\(\\frac{105}{8}\\)=<br \/>\n13 \\(\\frac{1}{8}\\) cups of popcorn.<\/p>\n<p>Question 14.<br \/>\n<strong>DIG DEEPER!<\/strong><br \/>\nA deli worker prepares 4 packages of meat. Each package contains 3\\(\\frac{1}{3}\\) pounds of meat.<br \/>\nYour friend says the deli worker uses between 12 and 13 pounds of meat. Is your friend correct? Explain.<br \/>\nAnswer:<br \/>\nNo, friend is not correct as deli worker uses between 13 and 14 pounds of meat,<br \/>\nnot between 12 and 13 pounds of meat.<\/p>\n<p>Explanation:<br \/>\nGiven each package contains 3\\(\\frac{1}{3}\\) pounds of meat.<br \/>\nFirst we write mixed fraction as fraction as ( 3 X 3 +1 ) by 3= \\(\\frac{10}{3}\\)<br \/>\nnow deli worker prepares 4 packages of meat so 4 times\u00a0 \\(\\frac{10}{3}\\)=<br \/>\n4 X 10 X \\(\\frac{1}{3}\\)= 40 X \\(\\frac{1}{3}\\)=\\(\\frac{40}{3}\\) ,<br \/>\nwe will write the product as mixed fraction as 3 goes in 13 times. 13 will be our whole number<br \/>\n3<span id=\"MathJax-Element-7-Frame\" class=\"mjx-chtml MathJax_CHTML\"><span id=\"MJXc-Node-36\" class=\"mjx-math\"><span id=\"MJXc-Node-37\" class=\"mjx-mrow\"><span id=\"MJXc-Node-38\" class=\"mjx-mstyle\"><span id=\"MJXc-Node-39\" class=\"mjx-mrow\"><span id=\"MJXc-Node-40\" class=\"mjx-mn\"><span class=\"mjx-char MJXc-TeX-main-R\">\u00a0X 13<\/span><\/span><\/span><\/span><\/span><\/span><\/span> is 39 and we have 1 left over (40<span id=\"MathJax-Element-10-Frame\" class=\"mjx-chtml MathJax_CHTML\"><span id=\"MJXc-Node-53\" class=\"mjx-math\"><span id=\"MJXc-Node-54\" class=\"mjx-mrow\"><span id=\"MJXc-Node-55\" class=\"mjx-mstyle\"><span id=\"MJXc-Node-56\" class=\"mjx-mrow\"><span id=\"MJXc-Node-58\" class=\"mjx-mo\"><span class=\"mjx-char MJXc-TeX-main-R\">\u221239<\/span><\/span><\/span><\/span><\/span><\/span><\/span>). 1 will be our numerator and our denominator<br \/>\nwill be the same 3= \\(\\frac{105}{8}\\)= 13 \\(\\frac{1}{3}\\),<br \/>\nso the whole number is greater than 13 means deli worker uses between 13 and 14 pounds of meat<br \/>\nnot between 12 and 13 pounds of meat.<\/p>\n<p>Question 15.<br \/>\n<strong>DIG DEEPER!<\/strong><br \/>\nAn athlete\u2019s goal is to run at least 80 miles in 1 week. He runs 5\\(\\frac{3}{4}\\) miles 2 times each day for 1 week. Does the athlete meet his goal? Explain.<br \/>\n<img decoding=\"async\" loading=\"lazy\" class=\"alignnone size-full wp-image-13052\" src=\"https:\/\/ccssanswers.com\/wp-content\/uploads\/2020\/12\/Big-Ideas-Math-Answers-Grade-4-Chapter-9-Multiply-Whole-Numbers-and-Fractions-89.png\" alt=\"Big Ideas Math Answers Grade 4 Chapter 9 Multiply Whole Numbers and Fractions 89\" width=\"192\" height=\"226\" \/><br \/>\nAnswer:<br \/>\nAthlete runs more than 80 miles in 1 week so he meets his goal.<\/p>\n<p>Explanation:<br \/>\nGiven an athlete runs 5\\(\\frac{3}{4}\\) miles 2 times each day, First we write mixed fraction<br \/>\nas fraction as ( 5 X 4 +3) by 4 =\\(\\frac{23}{4}\\) now we multiply by 2 ,<br \/>\n2 X \\(\\frac{23}{4}\\)= 2 X 23 X \\(\\frac{1}{4}\\)=46 x \\(\\frac{1}{4}\\)=<br \/>\n\\(\\frac{46}{4}\\), Now for 1 week it is 7 X \\(\\frac{46}{4}\\)= 7 X 46 X \\(\\frac{1}{4}\\)=<br \/>\n322 X \\(\\frac{1}{4}\\)= \\(\\frac{322}{4}\\) now we will write the product as mixed fraction<br \/>\nas 4 goes in 80 times. 80 will be our whole number 4<span id=\"MathJax-Element-7-Frame\" class=\"mjx-chtml MathJax_CHTML\"><span id=\"MJXc-Node-36\" class=\"mjx-math\"><span id=\"MJXc-Node-37\" class=\"mjx-mrow\"><span id=\"MJXc-Node-38\" class=\"mjx-mstyle\"><span id=\"MJXc-Node-39\" class=\"mjx-mrow\"><span id=\"MJXc-Node-40\" class=\"mjx-mn\"><span class=\"mjx-char MJXc-TeX-main-R\"> X 80<\/span><\/span><\/span><\/span><\/span><\/span><\/span> is 320 and we have 2 left over (322<span id=\"MathJax-Element-10-Frame\" class=\"mjx-chtml MathJax_CHTML\"><span id=\"MJXc-Node-53\" class=\"mjx-math\"><span id=\"MJXc-Node-54\" class=\"mjx-mrow\"><span id=\"MJXc-Node-55\" class=\"mjx-mstyle\"><span id=\"MJXc-Node-56\" class=\"mjx-mrow\"><span id=\"MJXc-Node-58\" class=\"mjx-mo\"><span class=\"mjx-char MJXc-TeX-main-R\">\u2212320<\/span><\/span><\/span><\/span><\/span><\/span><\/span>).<br \/>\n2 will be our numerator and our denominator will be the same 4= \\(\\frac{322}{4}\\)= 80 \\(\\frac{2}{4}\\) ,<br \/>\nAs 80 \\(\\frac{2}{4}\\) is greater than 80,\u00a0 athlete runs more than 80 miles in 1 week he meets his goal.<\/p>\n<h3><a id=\"Multiply_Whole_Numbers_and_Mixed_Numbers_Homework_&amp;_Practice_9.4\"><\/a>Multiply Whole Numbers and Mixed Numbers Homework &amp; Practice 9.4<\/h3>\n<p>Multiply<\/p>\n<p>Question 1.<br \/>\n<img decoding=\"async\" loading=\"lazy\" class=\"alignnone size-full wp-image-13053\" src=\"https:\/\/ccssanswers.com\/wp-content\/uploads\/2020\/12\/Big-Ideas-Math-Answers-Grade-4-Chapter-9-Multiply-Whole-Numbers-and-Fractions-90.png\" alt=\"Big Ideas Math Answers Grade 4 Chapter 9 Multiply Whole Numbers and Fractions 90\" width=\"147\" height=\"49\" \/><br \/>\nAnswer:<br \/>\n2 X 1 \\(\\frac{1}{12}\\) = \\(\\frac{26}{12}\\) = \\(\\frac{13}{6}\\)=<br \/>\n2 \\(\\frac{1}{6}\\).<\/p>\n<p>Explanation:<br \/>\nFirst we write the mixed number as a fraction then multiply, so 1 \\(\\frac{1}{12}\\) =<br \/>\n1 + \\(\\frac{1}{12}\\) = ( 1 X 12 + 1 )by 12 = \\(\\frac{13}{12}\\) now we multiply it with the whole,<br \/>\n2 X \\(\\frac{13}{12}\\) now we write in unit fraction and multiply\u00a0 2 X 13 X \\(\\frac{1}{12}\\)=<br \/>\n26 X \\(\\frac{1}{12}\\) = \\(\\frac{26}{6}\\), Now the fraction can be further divided by 2<br \/>\nas 26,6 both goes in 2 after dividing it becomes as \\(\\frac{13}{6}\\) now we can write the product<br \/>\nas mixed fraction as 6 goes in 2 times. 2 will be our whole number 6<span id=\"MathJax-Element-7-Frame\" class=\"mjx-chtml MathJax_CHTML\"><span id=\"MJXc-Node-36\" class=\"mjx-math\"><span id=\"MJXc-Node-37\" class=\"mjx-mrow\"><span id=\"MJXc-Node-38\" class=\"mjx-mstyle\"><span id=\"MJXc-Node-39\" class=\"mjx-mrow\"><span id=\"MJXc-Node-40\" class=\"mjx-mn\"><span class=\"mjx-char MJXc-TeX-main-R\"> X 2<\/span><\/span><\/span><\/span><\/span><\/span><\/span> is 12 and we have 1 left over (13<span id=\"MathJax-Element-10-Frame\" class=\"mjx-chtml MathJax_CHTML\"><span id=\"MJXc-Node-53\" class=\"mjx-math\"><span id=\"MJXc-Node-54\" class=\"mjx-mrow\"><span id=\"MJXc-Node-55\" class=\"mjx-mstyle\"><span id=\"MJXc-Node-56\" class=\"mjx-mrow\"><span id=\"MJXc-Node-58\" class=\"mjx-mo\"><span class=\"mjx-char MJXc-TeX-main-R\">\u221212<\/span><\/span><\/span><\/span><\/span><\/span><\/span>).<br \/>\n1 will be our numerator and our denominator will be the same 6= \\(\\frac{13}{6}\\)=<br \/>\n2 \\(\\frac{1}{6}\\).<\/p>\n<p>Question 2.<br \/>\n<img decoding=\"async\" loading=\"lazy\" class=\"alignnone size-full wp-image-13012\" src=\"https:\/\/ccssanswers.com\/wp-content\/uploads\/2020\/12\/Big-Ideas-Math-Answers-4th-Grade-Chapter-9-Multiply-Whole-Numbers-and-Fractions-91.png\" alt=\"Big Ideas Math Answers 4th Grade Chapter 9 Multiply Whole Numbers and Fractions 91\" width=\"125\" height=\"66\" \/><br \/>\nAnswer:<br \/>\n2 X 3\\(\\frac{5}{6}\\)=\\(\\frac{46}{6}\\) = \\(\\frac{23}{3}\\)= 7 \\(\\frac{2}{3}\\)<\/p>\n<p>Explanation:<br \/>\nFirst we write the mixed number as a fraction then multiply, so 3 \\(\\frac{5}{6}\\) =<br \/>\n3 + \\(\\frac{5}{6}\\) =(3 X 6 + 5) by 6 = \\(\\frac{23}{6}\\) now we multiply it with the whole,<br \/>\n2 X \\(\\frac{23}{6}\\) now we write in unit fraction and multiply\u00a0 2 X 23 X \\(\\frac{1}{6}\\)=<br \/>\n46 X \\(\\frac{1}{6}\\) = \\(\\frac{46}{6}\\), Now the fraction can be further divided by 2<br \/>\nas 46,6 both goes in 2 after dividing it becomes as 23,3 = \\(\\frac{23}{3}\\)<br \/>\nnow we can write the product as mixed fraction as 3 goes in 7 times. 3<span id=\"MathJax-Element-7-Frame\" class=\"mjx-chtml MathJax_CHTML\"><span id=\"MJXc-Node-36\" class=\"mjx-math\"><span id=\"MJXc-Node-37\" class=\"mjx-mrow\"><span id=\"MJXc-Node-38\" class=\"mjx-mstyle\"><span id=\"MJXc-Node-39\" class=\"mjx-mrow\"><span id=\"MJXc-Node-40\" class=\"mjx-mn\"><span class=\"mjx-char MJXc-TeX-main-R\"> X 7 <\/span><\/span><\/span><\/span><\/span><\/span><\/span>\u00a0is 21 ,<br \/>\n7 will be our whole number and\u00a0 (23<span id=\"MathJax-Element-10-Frame\" class=\"mjx-chtml MathJax_CHTML\"><span id=\"MJXc-Node-53\" class=\"mjx-math\"><span id=\"MJXc-Node-54\" class=\"mjx-mrow\"><span id=\"MJXc-Node-55\" class=\"mjx-mstyle\"><span id=\"MJXc-Node-56\" class=\"mjx-mrow\"><span id=\"MJXc-Node-58\" class=\"mjx-mo\"><span class=\"mjx-char MJXc-TeX-main-R\">\u221221<\/span><\/span><\/span><\/span><\/span><\/span><\/span>) we have 2 left over. 2 will be our numerator and<br \/>\nour denominator will be the same 3= \\(\\frac{23}{3}\\)= 7 \\(\\frac{2}{3}\\).<\/p>\n<p>Question 3.<br \/>\n<img decoding=\"async\" loading=\"lazy\" class=\"alignnone size-full wp-image-13013\" src=\"https:\/\/ccssanswers.com\/wp-content\/uploads\/2020\/12\/Big-Ideas-Math-Answers-4th-Grade-Chapter-9-Multiply-Whole-Numbers-and-Fractions-92.png\" alt=\"Big Ideas Math Answers 4th Grade Chapter 9 Multiply Whole Numbers and Fractions 92\" width=\"147\" height=\"62\" \/><br \/>\nAnswer:<br \/>\n4 X 3 \\(\\frac{6}{10}\\) = \\(\\frac{144}{10}\\) = \\(\\frac{72}{5}\\) = 14 \\(\\frac{2}{5}\\).<\/p>\n<p>Explanation:<br \/>\nFirst we write the mixed number as a fraction then multiply, so 3 \\(\\frac{6}{10}\\) =<br \/>\n3 + \\(\\frac{6}{10}\\) =( 3 X 10 + 6 ) by 10 = \\(\\frac{36}{10}\\) now we multiply it with the whole,<br \/>\n4 X \\(\\frac{36}{10}\\) now we write in unit fraction and multiply\u00a0 4 X 36 X \\(\\frac{1}{10}\\)=<br \/>\n144 X \\(\\frac{1}{10}\\) = \\(\\frac{144}{10}\\), Now the fraction can be further divided by 2<br \/>\nas 144,10 both goes in 2 after dividing it becomes as 72,5 = \\(\\frac{72}{5}\\)<br \/>\nnow we can write the product as mixed fraction as 5 goes in 14 times. 5<span id=\"MathJax-Element-7-Frame\" class=\"mjx-chtml MathJax_CHTML\"><span id=\"MJXc-Node-36\" class=\"mjx-math\"><span id=\"MJXc-Node-37\" class=\"mjx-mrow\"><span id=\"MJXc-Node-38\" class=\"mjx-mstyle\"><span id=\"MJXc-Node-39\" class=\"mjx-mrow\"><span id=\"MJXc-Node-40\" class=\"mjx-mn\"><span class=\"mjx-char MJXc-TeX-main-R\"> X 14 <\/span><\/span><\/span><\/span><\/span><\/span><\/span>\u00a0is 70 ,14 will be our whole number<br \/>\nand\u00a0 (72<span id=\"MathJax-Element-10-Frame\" class=\"mjx-chtml MathJax_CHTML\"><span id=\"MJXc-Node-53\" class=\"mjx-math\"><span id=\"MJXc-Node-54\" class=\"mjx-mrow\"><span id=\"MJXc-Node-55\" class=\"mjx-mstyle\"><span id=\"MJXc-Node-56\" class=\"mjx-mrow\"><span id=\"MJXc-Node-58\" class=\"mjx-mo\"><span class=\"mjx-char MJXc-TeX-main-R\">\u221270<\/span><\/span><\/span><\/span><\/span><\/span><\/span>) we have 2 left over. 2 will be our numerator and our denominator will be the same 5<br \/>\n= \\(\\frac{72}{5}\\)= 14 \\(\\frac{2}{5}\\).<\/p>\n<p>Question 4.<br \/>\n<img decoding=\"async\" loading=\"lazy\" class=\"alignnone size-full wp-image-13014\" src=\"https:\/\/ccssanswers.com\/wp-content\/uploads\/2020\/12\/Big-Ideas-Math-Answers-4th-Grade-Chapter-9-Multiply-Whole-Numbers-and-Fractions-93.png\" alt=\"Big Ideas Math Answers 4th Grade Chapter 9 Multiply Whole Numbers and Fractions 93\" width=\"134\" height=\"64\" \/><br \/>\nAnswer:<br \/>\n2 \\(\\frac{3}{8}\\) X 5 = \\(\\frac{95}{8}\\) =11 \\(\\frac{7}{8}\\).<\/p>\n<p>Explanation:<br \/>\nFirst we write the mixed number as a fraction then multiply, so 2 \\(\\frac{3}{8}\\) =<br \/>\n2 + \\(\\frac{3}{8}\\) =(2 X 8 + 3) by 8 = \\(\\frac{19}{8}\\) now we multiply it with the whole,<br \/>\n5 X \\(\\frac{19}{8}\\) now we write in unit fraction and multiply\u00a0 5 X 19 X \\(\\frac{1}{8}\\)=<br \/>\n95 X \\(\\frac{1}{8}\\) = \\(\\frac{95}{8}\\), Now we can write the product as mixed fraction as<br \/>\n8 goes in 11 times. 8<span id=\"MathJax-Element-7-Frame\" class=\"mjx-chtml MathJax_CHTML\"><span id=\"MJXc-Node-36\" class=\"mjx-math\"><span id=\"MJXc-Node-37\" class=\"mjx-mrow\"><span id=\"MJXc-Node-38\" class=\"mjx-mstyle\"><span id=\"MJXc-Node-39\" class=\"mjx-mrow\"><span id=\"MJXc-Node-40\" class=\"mjx-mn\"><span class=\"mjx-char MJXc-TeX-main-R\"> X 11 <\/span><\/span><\/span><\/span><\/span><\/span><\/span>\u00a0is 88 ,11 will be our whole number and\u00a0 (95<span id=\"MathJax-Element-10-Frame\" class=\"mjx-chtml MathJax_CHTML\"><span id=\"MJXc-Node-53\" class=\"mjx-math\"><span id=\"MJXc-Node-54\" class=\"mjx-mrow\"><span id=\"MJXc-Node-55\" class=\"mjx-mstyle\"><span id=\"MJXc-Node-56\" class=\"mjx-mrow\"><span id=\"MJXc-Node-58\" class=\"mjx-mo\"><span class=\"mjx-char MJXc-TeX-main-R\">\u221288<\/span><\/span><\/span><\/span><\/span><\/span><\/span>) we have 7 left over.<br \/>\n7 will be our numerator and our denominator will be the same 8= \\(\\frac{95}{8}\\)=<br \/>\n11 \\(\\frac{7}{8}\\).<\/p>\n<p>Question 5.<br \/>\n<img decoding=\"async\" loading=\"lazy\" class=\"alignnone size-full wp-image-13015\" src=\"https:\/\/ccssanswers.com\/wp-content\/uploads\/2020\/12\/Big-Ideas-Math-Answers-4th-Grade-Chapter-9-Multiply-Whole-Numbers-and-Fractions-94.png\" alt=\"Big Ideas Math Answers 4th Grade Chapter 9 Multiply Whole Numbers and Fractions 94\" width=\"137\" height=\"62\" \/><br \/>\nAnswer:<br \/>\n4 X 6 \\(\\frac{4}{5}\\) = \\(\\frac{136}{5}\\) = 27 \\(\\frac{1}{5}\\)<br \/>\nExplanation:<br \/>\nFirst we write the mixed number as a fraction then multiply, so 6 \\(\\frac{4}{5}\\) =<br \/>\n6 + \\(\\frac{4}{5}\\) =(6 X 5 + 4) by 5 = \\(\\frac{34}{5}\\) now we multiply it with the whole,<br \/>\n4 X \\(\\frac{34}{5}\\) now we write in unit fraction and multiply\u00a0 4 X 34 X \\(\\frac{1}{5}\\) =<br \/>\n136 X \\(\\frac{1}{5}\\) = \\(\\frac{136}{5}\\), now we can write the product as mixed fraction as<br \/>\n5 goes in 27 times. 5<span id=\"MathJax-Element-7-Frame\" class=\"mjx-chtml MathJax_CHTML\"><span id=\"MJXc-Node-36\" class=\"mjx-math\"><span id=\"MJXc-Node-37\" class=\"mjx-mrow\"><span id=\"MJXc-Node-38\" class=\"mjx-mstyle\"><span id=\"MJXc-Node-39\" class=\"mjx-mrow\"><span id=\"MJXc-Node-40\" class=\"mjx-mn\"><span class=\"mjx-char MJXc-TeX-main-R\"> X 27 <\/span><\/span><\/span><\/span><\/span><\/span><\/span>\u00a0is 135 , 27 will be our whole number and\u00a0 (136<span id=\"MathJax-Element-10-Frame\" class=\"mjx-chtml MathJax_CHTML\"><span id=\"MJXc-Node-53\" class=\"mjx-math\"><span id=\"MJXc-Node-54\" class=\"mjx-mrow\"><span id=\"MJXc-Node-55\" class=\"mjx-mstyle\"><span id=\"MJXc-Node-56\" class=\"mjx-mrow\"><span id=\"MJXc-Node-58\" class=\"mjx-mo\"><span class=\"mjx-char MJXc-TeX-main-R\">\u2212135<\/span><\/span><\/span><\/span><\/span><\/span><\/span>) we have 1 left over.<br \/>\n1 will be our numerator and our denominator will be the same 5 = \\(\\frac{136}{5}\\)=<br \/>\n27 \\(\\frac{1}{5}\\).<\/p>\n<p>Question 6.<br \/>\n<img decoding=\"async\" loading=\"lazy\" class=\"alignnone size-full wp-image-13016\" src=\"https:\/\/ccssanswers.com\/wp-content\/uploads\/2020\/12\/Big-Ideas-Math-Answers-4th-Grade-Chapter-9-Multiply-Whole-Numbers-and-Fractions-95.png\" alt=\"Big Ideas Math Answers 4th Grade Chapter 9 Multiply Whole Numbers and Fractions 95\" width=\"161\" height=\"70\" \/><br \/>\nAnswer:<br \/>\n8 \\(\\frac{20}{100}\\) X 10 = \\(\\frac{8200}{100}\\) = 82.<\/p>\n<p>Explanation:<br \/>\nFirst we write the mixed number as a fraction then multiply, so 8 \\(\\frac{20}{100}\\) =<br \/>\n8 + \\(\\frac{20}{100}\\) = ( 8 X 100 + 20 ) by 100 = \\(\\frac{820}{100}\\)<br \/>\nnow we multiply it with the whole, 100 X \\(\\frac{820}{100}\\) now we write in unit fraction<br \/>\nand multiply\u00a0 10 X 820 X \\(\\frac{1}{100}\\) = 8200 X \\(\\frac{1}{100}\\) =<br \/>\n\\(\\frac{8200}{100}\\), Now the fraction can be further divided by 100 as 8200,100<br \/>\nboth goes in 100 after dividing by 100\u00a0 it becomes as 82.<\/p>\n<p>Question 7.<br \/>\n<strong>Reasoning<\/strong><br \/>\nWithout calculating, is the product of 7 and 5\\(\\frac{3}{4}\\) greater than or less than 35? Explain.<br \/>\nAnswer:<br \/>\n7 X 5 \\(\\frac{3}{4}\\) is greater than ( &gt; ) 35.<\/p>\n<p>Explanation:<br \/>\nGiven to compare between 7 X 5 \\(\\frac{3}{4}\\) and 35, first we take 7 X 5 \\(\\frac{3}{4}\\)<br \/>\nto this expression if we apply distributive property means if multiplying the sum of two or more addends<br \/>\nby a number will give the same result as multiplying each addend individually by the number and<br \/>\nthen adding the products together. example a X b \\(\\frac{c}{d}\\) = a X b + a X \\(\\frac{c}{d}\\)<br \/>\nSo 7 X 5 \\(\\frac{3}{4}\\) = 7 X 5 + 7 X \\(\\frac{3}{4}\\) means 35 + 7 X\u00a0 \\(\\frac{3}{4}\\)<br \/>\nSo by comparing left side it is addition of 35 plus some value ,it will be more than 35 only and right hand side<br \/>\nit it 35 so obiviously 7 X 5 \\(\\frac{3}{4}\\) is greater than ( &gt; ) 35.<\/p>\n<p>Question 8.<br \/>\n<strong>YOU BE THE TEACHER<\/strong><br \/>\nYour friend \ufb01nds the product of 4 and 2\\(\\frac{8}{10}\\). Is your friend correct? Explain.<br \/>\n<img decoding=\"async\" loading=\"lazy\" class=\"alignnone size-full wp-image-13017\" src=\"https:\/\/ccssanswers.com\/wp-content\/uploads\/2020\/12\/Big-Ideas-Math-Answers-4th-Grade-Chapter-9-Multiply-Whole-Numbers-and-Fractions-96.png\" alt=\"Big Ideas Math Answers 4th Grade Chapter 9 Multiply Whole Numbers and Fractions 96\" width=\"234\" height=\"179\" \/><br \/>\nAnswer:<br \/>\nYes friend is correct, because the value is same as 11 \\(\\frac{2}{10}\\) .<\/p>\n<p>Explanation:<br \/>\nTo caluculate the value of 4 X 2 \\(\\frac{8}{10}\\) , First we write the mixed number as a<br \/>\nfraction then multiply, so 2 \\(\\frac{8}{10}\\) = 2 + \\(\\frac{8}{10}\\) =<br \/>\n( 2 X 10 + 8 ) by 10 = \\(\\frac{28}{10}\\) now we multiply it with the whole,<br \/>\n4 X \\(\\frac{28}{10}\\) now we write in unit fraction and multiply\u00a0 4 X 28 X \\(\\frac{1}{10}\\)=<br \/>\n112 X \\(\\frac{1}{10}\\) = \\(\\frac{112}{10}\\), now we can write the product as mixed fraction<br \/>\nas 10 goes in 11 times. 10<span id=\"MathJax-Element-7-Frame\" class=\"mjx-chtml MathJax_CHTML\"><span id=\"MJXc-Node-36\" class=\"mjx-math\"><span id=\"MJXc-Node-37\" class=\"mjx-mrow\"><span id=\"MJXc-Node-38\" class=\"mjx-mstyle\"><span id=\"MJXc-Node-39\" class=\"mjx-mrow\"><span id=\"MJXc-Node-40\" class=\"mjx-mn\"><span class=\"mjx-char MJXc-TeX-main-R\"> X 11 <\/span><\/span><\/span><\/span><\/span><\/span><\/span>\u00a0is 110 , 11 will be our whole number and\u00a0 (112<span id=\"MathJax-Element-10-Frame\" class=\"mjx-chtml MathJax_CHTML\"><span id=\"MJXc-Node-53\" class=\"mjx-math\"><span id=\"MJXc-Node-54\" class=\"mjx-mrow\"><span id=\"MJXc-Node-55\" class=\"mjx-mstyle\"><span id=\"MJXc-Node-56\" class=\"mjx-mrow\"><span id=\"MJXc-Node-58\" class=\"mjx-mo\"><span class=\"mjx-char MJXc-TeX-main-R\">\u2212110<\/span><\/span><\/span><\/span><\/span><\/span><\/span>) we have 2 left over.<br \/>\n2 will be our numerator and our denominator will be the same 10= \\(\\frac{112}{10}\\)=<br \/>\n11 \\(\\frac{2}{10}\\) is same as friend, So friend is correct.<\/p>\n<p>Question 9.<br \/>\n<strong>Number Sense<\/strong><br \/>\nBetween which two whole numbers does the product of 9 and 7 \\(\\frac{1}{8}\\) lie?<br \/>\nAnswer:<br \/>\nThe product of 9 and 7 \\(\\frac{1}{8}\\) lies in between 64 and 65.<\/p>\n<p>Explanation:<br \/>\nFirst we write the mixed number 7 \\(\\frac{1}{8}\\) as a fraction then multiply, so 7 \\(\\frac{1}{8}\\) =<br \/>\n7 + \\(\\frac{1}{8}\\) = 7 X 8 + 1 by 8 = \\(\\frac{57}{8}\\) now we multiply it with the whole,<br \/>\n9 X \\(\\frac{57}{8}\\) now we write in unit fraction and multiply\u00a0 9 X 57 X \\(\\frac{1}{8}\\) =<br \/>\n513 X \\(\\frac{1}{8}\\) = \\(\\frac{513}{8}\\), now we can write the product as mixed fraction as<br \/>\n8 goes in 64 times. 8<span id=\"MathJax-Element-7-Frame\" class=\"mjx-chtml MathJax_CHTML\"><span id=\"MJXc-Node-36\" class=\"mjx-math\"><span id=\"MJXc-Node-37\" class=\"mjx-mrow\"><span id=\"MJXc-Node-38\" class=\"mjx-mstyle\"><span id=\"MJXc-Node-39\" class=\"mjx-mrow\"><span id=\"MJXc-Node-40\" class=\"mjx-mn\"><span class=\"mjx-char MJXc-TeX-main-R\"> X 64 <\/span><\/span><\/span><\/span><\/span><\/span><\/span>\u00a0is 512 , 64 will be our whole number and\u00a0 (513<span id=\"MathJax-Element-10-Frame\" class=\"mjx-chtml MathJax_CHTML\"><span id=\"MJXc-Node-53\" class=\"mjx-math\"><span id=\"MJXc-Node-54\" class=\"mjx-mrow\"><span id=\"MJXc-Node-55\" class=\"mjx-mstyle\"><span id=\"MJXc-Node-56\" class=\"mjx-mrow\"><span id=\"MJXc-Node-58\" class=\"mjx-mo\"><span class=\"mjx-char MJXc-TeX-main-R\">\u2212512<\/span><\/span><\/span><\/span><\/span><\/span><\/span>) we have 1 left over.<br \/>\n1 will be our numerator and our denominator will be the same 8 = \\(\\frac{513}{8}\\)= 64<br \/>\n\\(\\frac{1}{8}\\). Any how we got 64 whole number and next whole number is 65 means<br \/>\nthe product of 9 and 7 \\(\\frac{1}{8}\\) lies in between 64 and 65.<\/p>\n<p>Question 10.<br \/>\n<strong>Modeling Real Life<\/strong><br \/>\nAthlete A holds a 2\\(\\frac{1}{2}\\) &#8211; kilogram plate while doing squats. Athlete B holds a plate that is 4 times heavier than Athlete A\u2019s. How many kilograms is the plate held by Athlete B?<br \/>\n<img decoding=\"async\" loading=\"lazy\" class=\"alignnone size-full wp-image-13018\" src=\"https:\/\/ccssanswers.com\/wp-content\/uploads\/2020\/12\/Big-Ideas-Math-Answers-4th-Grade-Chapter-9-Multiply-Whole-Numbers-and-Fractions-97.png\" alt=\"Big Ideas Math Answers 4th Grade Chapter 9 Multiply Whole Numbers and Fractions 97\" width=\"135\" height=\"113\" \/><br \/>\nAnswer:<br \/>\nAthlete B holds 10 kilograms of plate while doing squats.<\/p>\n<p>Explanation:<br \/>\nGiven Athlete A hold a 2 \\(\\frac{1}{2}\\) kilogram plate while doing squats,<br \/>\nAthlete B holds a plate that is 4 times heavier than Athlete A&#8217;s, So Athlete B holds<br \/>\n4 X 2 \\(\\frac{1}{2}\\), First we write the mixed number as a fraction then multiply,<br \/>\nso 2 \\(\\frac{1}{2}\\) = 2 + \\(\\frac{1}{2}\\) = ( 2 X 2 + 1 ) by 2 = \\(\\frac{5}{2}\\)<br \/>\nnow we multiply it with the whole, 4 X \\(\\frac{5}{2}\\) now we write in unit fraction and<br \/>\nmultiply\u00a0 4 X 5 X \\(\\frac{1}{2}\\) = 20 X \\(\\frac{1}{2}\\) = \\(\\frac{20}{2}\\)<br \/>\nas 20,2 goes by 2 we further divide both by 2 we get 10,1 = \\(\\frac{20}{2}\\) = 10,<br \/>\ntherefore Athlete B holds 10 kilograms of plate while doing squats.<\/p>\n<p>Question 11.<br \/>\n<strong>DIG DEEPER!<\/strong><br \/>\nA zoo nutritionist orders 5 \\(\\frac{1}{4}\\) tons of apples and 7\\(\\frac{2}{4}\\)tons of bananas each year to feed the animals. She orders 6 times as many tons of herbivore pellets than tons of fruit. How many tons of herbivore pellets does the nutritionist order?<br \/>\nAnswer:<br \/>\nExplanation:<\/p>\n<p><strong>Review &amp; Refresh<\/strong><\/p>\n<p>Subtract.<\/p>\n<p>Question 12.<br \/>\n<img decoding=\"async\" loading=\"lazy\" class=\"alignnone size-full wp-image-13019\" src=\"https:\/\/ccssanswers.com\/wp-content\/uploads\/2020\/12\/Big-Ideas-Math-Answers-4th-Grade-Chapter-9-Multiply-Whole-Numbers-and-Fractions-98.png\" alt=\"Big Ideas Math Answers 4th Grade Chapter 9 Multiply Whole Numbers and Fractions 98\" width=\"143\" height=\"63\" \/><br \/>\nAnswer:<br \/>\n<img decoding=\"async\" loading=\"lazy\" class=\"alignnone size-full wp-image-13019\" src=\"https:\/\/ccssanswers.com\/wp-content\/uploads\/2020\/12\/Big-Ideas-Math-Answers-4th-Grade-Chapter-9-Multiply-Whole-Numbers-and-Fractions-98.png\" alt=\"Big Ideas Math Answers 4th Grade Chapter 9 Multiply Whole Numbers and Fractions 98\" width=\"143\" height=\"63\" \/>= \\(\\frac{12}{4}\\) = 3<br \/>\nExplanation:<\/p>\n<p>First we write the mixed numbers into fractions and subtract, So 9 \\(\\frac{1}{4}\\) =<br \/>\n9 +\\(\\frac{1}{4}\\) = (9 x 4 + 1) by 4 = \\(\\frac{37}{4}\\) and\u00a0 6 \\(\\frac{1}{4}\\) =<br \/>\n6 + \\(\\frac{1}{4}\\) = 6 X 4 + 1 by 4 = \\(\\frac{25}{4}\\) now subtracting<br \/>\n\\(\\frac{37}{4}\\) &#8211; \\(\\frac{25}{4}\\) to subtract a fraction from another<br \/>\nwe need to first make sure both fractions have the same denominator as both denominators<br \/>\nhave same value 4 now we can subtract one numerator from the other to make one fraction as 37 &#8211; 25 by 4 = \\(\\frac{12}{4}\\) as 12, 4 goes by 4 we further can divide both by 4 we get 12,1 = \\(\\frac{12}{4}\\) = 3 .<\/p>\n<p>Question 13.<br \/>\n<img decoding=\"async\" loading=\"lazy\" class=\"alignnone size-full wp-image-13020\" src=\"https:\/\/ccssanswers.com\/wp-content\/uploads\/2020\/12\/Big-Ideas-Math-Answers-4th-Grade-Chapter-9-Multiply-Whole-Numbers-and-Fractions-99.png\" alt=\"Big Ideas Math Answers 4th Grade Chapter 9 Multiply Whole Numbers and Fractions 99\" width=\"142\" height=\"59\" \/><br \/>\nAnswer:<br \/>\n<img decoding=\"async\" loading=\"lazy\" class=\"alignnone size-full wp-image-13020\" src=\"https:\/\/ccssanswers.com\/wp-content\/uploads\/2020\/12\/Big-Ideas-Math-Answers-4th-Grade-Chapter-9-Multiply-Whole-Numbers-and-Fractions-99.png\" alt=\"Big Ideas Math Answers 4th Grade Chapter 9 Multiply Whole Numbers and Fractions 99\" width=\"142\" height=\"59\" \/> = \\(\\frac{11}{3}\\) = 3 \\(\\frac{2}{3}\\)<br \/>\nExplanation:<br \/>\nFirst we write the mixed numbers into fractions and subtract, So 6 \\(\\frac{1}{3}\\) =<br \/>\n6 +\\(\\frac{1}{3}\\) =(6 x 3 + 1) by 3 = \\(\\frac{19}{3}\\) and\u00a0 2 \\(\\frac{2}{3}\\) =<br \/>\n2 + \\(\\frac{2}{3}\\) = 2 X 3 + 2 by 3 = \\(\\frac{8}{3}\\) now subtracting<br \/>\n\\(\\frac{19}{3}\\) &#8211; \\(\\frac{8}{3}\\) to subtract a fraction from another<br \/>\nwe need to first make sure both fractions have the same denominator as both denominators<br \/>\nhave same value 3 now we can subtract one numerator from the other to make one fraction as 19 &#8211; 8 by 3<br \/>\n= \\(\\frac{11}{3}\\) since the numerator is greater than the denominator,<br \/>\nwe can further simplify it into a mixed fraction as 3 goes in 3 times. 3<span id=\"MathJax-Element-7-Frame\" class=\"mjx-chtml MathJax_CHTML\"><span id=\"MJXc-Node-36\" class=\"mjx-math\"><span id=\"MJXc-Node-37\" class=\"mjx-mrow\"><span id=\"MJXc-Node-38\" class=\"mjx-mstyle\"><span id=\"MJXc-Node-39\" class=\"mjx-mrow\"><span id=\"MJXc-Node-40\" class=\"mjx-mn\"><span class=\"mjx-char MJXc-TeX-main-R\"> X 3 <\/span><\/span><\/span><\/span><\/span><\/span><\/span>\u00a0is 9 , 3 will be our<br \/>\nwhole number and\u00a0 (11<span id=\"MathJax-Element-10-Frame\" class=\"mjx-chtml MathJax_CHTML\"><span id=\"MJXc-Node-53\" class=\"mjx-math\"><span id=\"MJXc-Node-54\" class=\"mjx-mrow\"><span id=\"MJXc-Node-55\" class=\"mjx-mstyle\"><span id=\"MJXc-Node-56\" class=\"mjx-mrow\"><span id=\"MJXc-Node-58\" class=\"mjx-mo\"><span class=\"mjx-char MJXc-TeX-main-R\">\u22129<\/span><\/span><\/span><\/span><\/span><\/span><\/span>) we have 2 left over. 2 will be our numerator and our denominator will be the same 3<br \/>\n= \\(\\frac{11}{3}\\) = 3 \\(\\frac{2}{3}\\) .<\/p>\n<p>Question 14.<br \/>\n<img decoding=\"async\" loading=\"lazy\" class=\"alignnone size-full wp-image-13021\" src=\"https:\/\/ccssanswers.com\/wp-content\/uploads\/2020\/12\/Big-Ideas-Math-Answers-4th-Grade-Chapter-9-Multiply-Whole-Numbers-and-Fractions-100.png\" alt=\"Big Ideas Math Answers 4th Grade Chapter 9 Multiply Whole Numbers and Fractions 100\" width=\"165\" height=\"69\" \/><br \/>\nAnswer:<\/p>\n<p><img decoding=\"async\" loading=\"lazy\" class=\"alignnone size-full wp-image-13021\" src=\"https:\/\/ccssanswers.com\/wp-content\/uploads\/2020\/12\/Big-Ideas-Math-Answers-4th-Grade-Chapter-9-Multiply-Whole-Numbers-and-Fractions-100.png\" alt=\"Big Ideas Math Answers 4th Grade Chapter 9 Multiply Whole Numbers and Fractions 100\" width=\"165\" height=\"69\" \/>= \\(\\frac{78}{12}\\) = 6 \\(\\frac{6}{12}\\) or<br \/>\n\\(\\frac{78}{12}\\) = \\(\\frac{39}{6}\\) = \\(\\frac{13}{2}\\) =\u00a0 6 \\(\\frac{1}{2}\\).<\/p>\n<p>Explanation:<br \/>\nFirst we write the mixed numbers into fractions and subtract, So 8 \\(\\frac{4}{12}\\) =<br \/>\n8 +\\(\\frac{4}{12}\\) = ( 8 x 12 + 4 ) by 12 = \\(\\frac{100}{12}\\) and\u00a0 1 \\(\\frac{10}{12}\\) = 1 + \\(\\frac{10}{12}\\) = 1 X 12 + 10 by 12 = \\(\\frac{22}{12}\\) now subtracting \\(\\frac{100}{12}\\) &#8211; \\(\\frac{22}{12}\\) to subtract a fraction from another we need to first make sure both fractions<br \/>\nhave the same denominator as both denominators have same value 3 now we can subtract one numerator<br \/>\nfrom the other to make one fraction as 100 &#8211; 22 by 12 = \\(\\frac{78}{12}\\) since the numerator<br \/>\nis greater than the denominator , we can further simplify it into a mixed fraction as 12 goes in 6 times.<br \/>\n12<span id=\"MathJax-Element-7-Frame\" class=\"mjx-chtml MathJax_CHTML\"><span id=\"MJXc-Node-36\" class=\"mjx-math\"><span id=\"MJXc-Node-37\" class=\"mjx-mrow\"><span id=\"MJXc-Node-38\" class=\"mjx-mstyle\"><span id=\"MJXc-Node-39\" class=\"mjx-mrow\"><span id=\"MJXc-Node-40\" class=\"mjx-mn\"><span class=\"mjx-char MJXc-TeX-main-R\"> X 6 <\/span><\/span><\/span><\/span><\/span><\/span><\/span>\u00a0is 72 , 6 will be our whole number and\u00a0 (78<span id=\"MathJax-Element-10-Frame\" class=\"mjx-chtml MathJax_CHTML\"><span id=\"MJXc-Node-53\" class=\"mjx-math\"><span id=\"MJXc-Node-54\" class=\"mjx-mrow\"><span id=\"MJXc-Node-55\" class=\"mjx-mstyle\"><span id=\"MJXc-Node-56\" class=\"mjx-mrow\"><span id=\"MJXc-Node-58\" class=\"mjx-mo\"><span class=\"mjx-char MJXc-TeX-main-R\">\u221212<\/span><\/span><\/span><\/span><\/span><\/span><\/span>) we have 6 left over. 6 will be our numerator and<br \/>\nour denominator will be the same 12, 6 \\(\\frac{6}{12}\\) , Further \\(\\frac{78}{12}\\)<br \/>\ncan be simplified as 78,12 both goes by\u00a0 2 making them as 39, 6=\\(\\frac{39}{6}\\),<br \/>\neven further \\(\\frac{39}{6}\\) can be simplified as 39,6 both goes by 3 making them as 13,2<br \/>\n=\\(\\frac{13}{2}\\), Since the numerator is greater than the denominator , we can further simplify<br \/>\nit into a mixed fraction as 2 goes in 6 times. 6<span id=\"MathJax-Element-7-Frame\" class=\"mjx-chtml MathJax_CHTML\"><span id=\"MJXc-Node-36\" class=\"mjx-math\"><span id=\"MJXc-Node-37\" class=\"mjx-mrow\"><span id=\"MJXc-Node-38\" class=\"mjx-mstyle\"><span id=\"MJXc-Node-39\" class=\"mjx-mrow\"><span id=\"MJXc-Node-40\" class=\"mjx-mn\"><span class=\"mjx-char MJXc-TeX-main-R\"> X 2 <\/span><\/span><\/span><\/span><\/span><\/span><\/span>\u00a0is 12 , 6 will be our whole number and\u00a0 (13<span id=\"MathJax-Element-10-Frame\" class=\"mjx-chtml MathJax_CHTML\"><span id=\"MJXc-Node-53\" class=\"mjx-math\"><span id=\"MJXc-Node-54\" class=\"mjx-mrow\"><span id=\"MJXc-Node-55\" class=\"mjx-mstyle\"><span id=\"MJXc-Node-56\" class=\"mjx-mrow\"><span id=\"MJXc-Node-58\" class=\"mjx-mo\"><span class=\"mjx-char MJXc-TeX-main-R\">\u221212<\/span><\/span><\/span><\/span><\/span><\/span><\/span>) we have 1 left over.<br \/>\n1 will be our numerator and our denominator will be the same 3 = \\(\\frac{78}{12}\\) =<br \/>\n6 \\(\\frac{6}{12}\\) or \\(\\frac{78}{12}\\) = \\(\\frac{39}{6}\\) = \\(\\frac{13}{2}\\) =<br \/>\n6 \\(\\frac{1}{2}\\).<\/p>\n<h3><a id=\"Lesson_9.5_Problem_Solving:_Fraction_Operations\"><\/a>Lesson 9.5 Problem Solving: Fraction Operations<\/h3>\n<p><strong>Explore and Grow<\/strong><\/p>\n<p>You want to make 3 batches of the recipe. Explain how to find how much of each ingredient you need.<br \/>\n<img decoding=\"async\" loading=\"lazy\" class=\"alignnone size-full wp-image-13022\" src=\"https:\/\/ccssanswers.com\/wp-content\/uploads\/2020\/12\/Big-Ideas-Math-Answers-4th-Grade-Chapter-9-Multiply-Whole-Numbers-and-Fractions-101.png\" alt=\"Big Ideas Math Answers 4th Grade Chapter 9 Multiply Whole Numbers and Fractions 101\" width=\"543\" height=\"354\" srcset=\"https:\/\/ccssanswers.com\/wp-content\/uploads\/2020\/12\/Big-Ideas-Math-Answers-4th-Grade-Chapter-9-Multiply-Whole-Numbers-and-Fractions-101.png 543w, https:\/\/ccssanswers.com\/wp-content\/uploads\/2020\/12\/Big-Ideas-Math-Answers-4th-Grade-Chapter-9-Multiply-Whole-Numbers-and-Fractions-101-300x196.png 300w\" sizes=\"(max-width: 543px) 100vw, 543px\" \/><\/p>\n<p><strong>Reasoning<\/strong><br \/>\nExplain how you can tell whether you need more than or less than 6 cups of blueberries without calculating<br \/>\nAnswer:<br \/>\nTo make 3 batches of recipe we require \\(\\frac{21}{4}\\) pounds of strawberries or<br \/>\n5 \\(\\frac{1}{4}\\) pounds of strawberries required,<br \/>\n\\(\\frac{3}{2}\\) cups of orange juice or 1 \\(\\frac{1}{2}\\) cups of orange juice,<br \/>\n12 tablespoons of lemon juice,12 tablespoons of honey and<br \/>\n\\(\\frac{27}{4}\\) cups of blue berries are required or 6 \\(\\frac{3}{4}\\) cups of blueberries are required.<br \/>\nWe require more than 6 cups of blueberries why because if we see product required is<br \/>\n3 X 2 \\(\\frac{1}{4}\\) cups of blue berries without calculating , Applying distributive property<br \/>\nwe get (3 X 2 ) + ( 3 X \\(\\frac{1}{4}\\) ) = 6 + ( 3 X \\(\\frac{1}{4}\\) ) it clearly shows that<br \/>\nwe require more than 6 cups of blueberries.<\/p>\n<p>Explanation:<br \/>\nGiven\u00a0 to make 1 batch of Recipe Ladybug Ice pops we require\u00a0 1 \\(\\frac{3}{4}\\) pounds of strawberries ,<br \/>\n\\(\\frac{1}{2}\\) cup of orange juice , 4 tablespoons of lemon juice, 4 tablespoons of honey,<br \/>\n2 \\(\\frac{1}{4}\\) cups of blue berries.<br \/>\nTo find out how much of each ingredient needed to make 3 batches of recipe we multiply each ingredient with 3.<br \/>\nStrawberries needed are 3 X 1 \\(\\frac{3}{4}\\), First we write the mixed number as a<br \/>\nfraction then multiply so 1 \\(\\frac{3}{4}\\) = ( 1 X 4 + 3 ) by 4 = \\(\\frac{7}{4}\\) ,<br \/>\nso 3\u00a0 X\u00a0 \\(\\frac{7}{4}\\)\u00a0 now we write in unit fraction and multiply\u00a0 3 X 7 X \\(\\frac{1}{4}\\) =<br \/>\n21 X \\(\\frac{1}{4}\\) = \\(\\frac{21}{4}\\) pounds of strawberries required,<br \/>\nSince the numerator is greater than the denominator , we can further simplify it into a mixed fraction as<br \/>\n4 goes in 5 times. 5<span id=\"MathJax-Element-7-Frame\" class=\"mjx-chtml MathJax_CHTML\"><span id=\"MJXc-Node-36\" class=\"mjx-math\"><span id=\"MJXc-Node-37\" class=\"mjx-mrow\"><span id=\"MJXc-Node-38\" class=\"mjx-mstyle\"><span id=\"MJXc-Node-39\" class=\"mjx-mrow\"><span id=\"MJXc-Node-40\" class=\"mjx-mn\"><span class=\"mjx-char MJXc-TeX-main-R\"> X 4 <\/span><\/span><\/span><\/span><\/span><\/span><\/span>\u00a0is 20 , 5 will be our whole number and\u00a0 (21<span id=\"MathJax-Element-10-Frame\" class=\"mjx-chtml MathJax_CHTML\"><span id=\"MJXc-Node-53\" class=\"mjx-math\"><span id=\"MJXc-Node-54\" class=\"mjx-mrow\"><span id=\"MJXc-Node-55\" class=\"mjx-mstyle\"><span id=\"MJXc-Node-56\" class=\"mjx-mrow\"><span id=\"MJXc-Node-58\" class=\"mjx-mo\"><span class=\"mjx-char MJXc-TeX-main-R\">\u221220<\/span><\/span><\/span><\/span><\/span><\/span><\/span>) we have 1 left over.<br \/>\n1 will be our numerator and our denominator will be the same 4 =5 \\(\\frac{1}{4}\\)<br \/>\npounds of strawberries required,<br \/>\nOrange juice required 3 X \\(\\frac{1}{2}\\) already it is in unit fraction<br \/>\nso we require \\(\\frac{3}{2}\\) cups of orange juice Since the numerator is greater than the denominator ,<br \/>\nwe can further simplify it into a mixed fraction as 2 goes in 1 times. 1 X 2 is 2, 1 will be our whole number and (3-2),<br \/>\nwe have 1 left over. 1 will be our numerator and our denominator will be the same<br \/>\n2 = 1 \\(\\frac{1}{2}\\) cups of orange juice.<br \/>\nLemon juice required is 3 X 4 = 12 tablespoons of lemon juice, 3 X 4 = 12 tablespoons of honey,<br \/>\nnow blue berries required are 3 X 2 \\(\\frac{1}{4}\\) cups, First we write the mixed number as a<br \/>\nfraction then multiply so 2 \\(\\frac{1}{4}\\) = ( 2 X 4 + 1 ) by 4 = \\(\\frac{9}{4}\\) ,<br \/>\nnow\u00a0 3\u00a0 X\u00a0 \\(\\frac{9}{4}\\)\u00a0 now we write in unit fraction and multiply\u00a0 3 X 9 X \\(\\frac{1}{4}\\) =<br \/>\n27 X \\(\\frac{1}{4}\\) = \\(\\frac{27}{4}\\) cups of blue berries are required,<br \/>\nSince the numerator is greater than the denominator , we can further simplify it into a mixed fraction as<br \/>\n4 goes in 6 times. 6 X 4 is 24, 6 will be our whole number and (27-24) we have 3 left over.<br \/>\n3 will be our numerator and our denominator will be the same 4 = 6 \\(\\frac{3}{4}\\) cups of blueberries are required.<br \/>\nNow comparing blueberries we require more than 6 cups of blueberries why because we use is<br \/>\n3 X 2 \\(\\frac{1}{4}\\) cups of blue berries are required without calculating,<br \/>\nApplying distributive property\u00a0 we get (3 X 2 ) +( 3 X \\(\\frac{1}{4}\\) )=<br \/>\n6 +( 3 X \\(\\frac{1}{4}\\)), it clearly shows that we require more than 6 cups of blueberries.<\/p>\n<p><strong>Think and Grow: Problem Solving: Fraction Operations<\/strong><\/p>\n<p><strong>Example<\/strong><br \/>\nTo convert a temperature from degrees Celsius to degrees Fahrenheit, multiply the Celsius temperature by \\(\\frac{9}{5}\\), then add 32. What is the temperature shown by the thermometer in degrees Fahrenheit?<br \/>\n<img decoding=\"async\" loading=\"lazy\" class=\"alignnone size-full wp-image-13023\" src=\"https:\/\/ccssanswers.com\/wp-content\/uploads\/2020\/12\/Big-Ideas-Math-Answers-4th-Grade-Chapter-9-Multiply-Whole-Numbers-and-Fractions-102.png\" alt=\"Big Ideas Math Answers 4th Grade Chapter 9 Multiply Whole Numbers and Fractions 102\" width=\"68\" height=\"197\" \/><br \/>\nAnswer:<br \/>\nThe temperature shown by the thermometer is 50<sup>0<\/sup> Fahrenheit.<\/p>\n<p>Explanation:<br \/>\nWe know to convert a temperature from degrees Celsius to degrees Fahrenheit is Fahrenheit =<br \/>\nCelsius temperature X \\(\\frac{9}{5}\\) + 32 .<br \/>\nSo multiply the Celsius temperature by \\(\\frac{9}{5}\\), then add 32,<br \/>\nGiven the Celsius temperature as 10<sup>0 <\/sup>in the figure above, First we write \\(\\frac{9}{5}\\) in unit fraction and<br \/>\nmultiply by Celsius temperature so \\(\\frac{9}{5}\\)=9 X \\(\\frac{1}{5}\\)<br \/>\nnow we multiply by 10 as 10 X 9 X \\(\\frac{1}{5}\\) = 90 X \\(\\frac{1}{5}\\) =<br \/>\n\\(\\frac{90}{5}\\) this value can be further simplified as 90,5 both goes by\u00a0 5 making them as 18,1,<br \/>\nNow we got result as 18 , We add 18 + 32\u00a0 we will get 50<sup>0 <\/sup>Fahrenheit.<\/p>\n<p><strong>Understand the Problem<\/strong><\/p>\n<p>What do you know?<\/p>\n<ul>\n<li>To convert a temperature from degrees Celsius to degrees Fahrenheit, multiply the Celsius temperature by \\(\\frac{9}{5}\\), then add 32.<\/li>\n<li>The thermometer shows 10 degrees Celsius.<br \/>\nWhat do you need to find?<\/li>\n<li>You need to find the temperature shown by the thermometer in degrees Fahrenheit.<\/li>\n<\/ul>\n<p><strong>Make a Plan<\/strong><\/p>\n<p>How will you solve?<\/p>\n<ul>\n<li>First, multiply the Celsius temperature, 10 degrees, by \\(\\frac{9}{5}\\).<\/li>\n<li>Then add 32 to the product.<\/li>\n<\/ul>\n<p><strong>Solve<\/strong><br \/>\n<img decoding=\"async\" loading=\"lazy\" class=\"alignnone size-full wp-image-13024\" src=\"https:\/\/ccssanswers.com\/wp-content\/uploads\/2020\/12\/Big-Ideas-Math-Answers-4th-Grade-Chapter-9-Multiply-Whole-Numbers-and-Fractions-103.png\" alt=\"Big Ideas Math Answers 4th Grade Chapter 9 Multiply Whole Numbers and Fractions 103\" width=\"258\" height=\"215\" \/><br \/>\n<img decoding=\"async\" loading=\"lazy\" class=\"alignnone size-full wp-image-13025\" src=\"https:\/\/ccssanswers.com\/wp-content\/uploads\/2020\/12\/Big-Ideas-Math-Answers-4th-Grade-Chapter-9-Multiply-Whole-Numbers-and-Fractions-104.png\" alt=\"Big Ideas Math Answers 4th Grade Chapter 9 Multiply Whole Numbers and Fractions 104\" width=\"237\" height=\"145\" \/><br \/>\nSo, the temperature shown by the thermometer is _50<sup>0<\/sup>_ degrees Fahrenheit.<br \/>\nAnswer:<br \/>\nThe temperature shown by the thermometer is 50<sup>0<\/sup>\u00a0Fahrenheit.<\/p>\n<p>Explanation :<br \/>\nTo convert a temperature from degrees Celsius to degrees Fahrenheit, Let us take\u00a0 p as multiply of<br \/>\nCelsius temperature by \\(\\frac{9}{5}\\), Now we take f as p+32,<br \/>\nFirst we write \\(\\frac{9}{5}\\) in unit fraction and multiply by Celsius temperature,<br \/>\nso \\(\\frac{9}{5}\\)=9 X \\(\\frac{1}{5}\\) now multiply by 10 = 10 X 9 X \\(\\frac{1}{5}\\) =<br \/>\n90 X \\(\\frac{1}{5}\\) = \\(\\frac{90}{5}\\) this value we take as p this can be further simplified<br \/>\nas 90,5 both goes by\u00a0 5 making them as 18, Now we got p as 18 we add 32 to p ,<br \/>\nwe get f, So f = 18 + 32 =\u00a050<sup>0<br \/>\n<\/sup>So the temperature shown by the thermometer is 50<sup>0<\/sup> Fahrenheit.<\/p>\n<p><strong>Show and Grow<\/strong><\/p>\n<p>Question 1.<br \/>\nShow how to solve the example above using one equation.<br \/>\nAnswer:<br \/>\nF= C X \\(\\frac{9}{5}\\) + 32 degrees.<\/p>\n<p>Explanation:<br \/>\nTo solve the example above using one equation, Let us take Fahrenheit as F ,<br \/>\nCelsius as C so to convert a temperature from degrees Celsius to degrees Fahrenheit we multiply<br \/>\nC with \\(\\frac{9}{5}\\) and add 32.<\/p>\n<p><strong>Apply and Grow: Practice<\/strong><\/p>\n<p>Understand the problem. What do you know? What do you need to find? Explain.<\/p>\n<p>Answer:<br \/>\nWe know Celsius temperature, We need to find the temperature shown by the thermometer in degrees Fahrenheit.<\/p>\n<p>Explanation:<br \/>\nGiven the temperature in Celsius and we know the formula to convert from Celsius temperature to<br \/>\nFahrenheit as F= C X \\(\\frac{9}{5}\\) + 32 degrees so we substitute the values and find the temperature.<\/p>\n<p>Question 2.<br \/>\nYou make a friendship bracelet with 3 pink strings and 2 blue strings. Each string is 3\\(\\frac{3}{4}\\) feet long.<br \/>\nHow many feet of string do you use?<\/p>\n<p>Answer:<br \/>\n\\(\\frac{75}{4}\\) feet long strings is used or 18 \\(\\frac{3}{4}\\) feet long strings is used.<\/p>\n<p>Explanation:<br \/>\nGiven to make a friendship bracelet we use 3 pink strings , 2 blue strings means total 5 strings are needed<br \/>\nand each string is 3\\(\\frac{3}{4}\\) feet long, First we convert mixed fraction into fraction as<br \/>\n( 3 X 4 + 3 ) by 4 = \\(\\frac{15}{4}\\) ,Now we will convert into unit fraction as 15 X \\(\\frac{1}{4}\\)<br \/>\nnow we multiply with 5 , 5 X 15 X \\(\\frac{1}{4}\\) =\\(\\frac{75}{4}\\),<br \/>\nsince the numerator is greater than the denominator , we can further simplify it into a mixed fraction as<br \/>\n4 goes in 18 times. 18 X 4 is 72, 18 will be our whole number and (75-72) we have 3 left over.<br \/>\n3 will be our numerator and our denominator will be the same 4 = 18 \\(\\frac{3}{4}\\),<br \/>\nSo \\(\\frac{75}{4}\\) feet long strings is used or 18 \\(\\frac{3}{4}\\) feet long strings is used.<\/p>\n<p>Question 3.<br \/>\nA smoothie store worker makes 4 peanut butter banana smoothies and 2 fruit smoothies. The worker uses \\(\\frac{2}{3}\\) cup of bananas in each smoothie. How many cups of bananas does the worker need?<\/p>\n<p>Answer:<br \/>\nThe worker needed\u00a0 \\(\\frac{12}{3}\\) cups of bananas or 4 cups of bananas are needed to make smoothie.<\/p>\n<p>Explanation:<br \/>\nGiven a smoothie store worker makes 4 peanut butter banana smoothies and 2 fruit smoothies.<br \/>\nThe worker uses \\(\\frac{2}{3}\\) cup of bananas in each smoothie so the number of cups of bananas<br \/>\nthe worker needed are 4 X latex]\\frac{2}{3}[\/latex] plus 2 X \\(\\frac{2}{3}\\) first we convert<br \/>\nboth into unit fractions and multiply 4 X 2 X \\(\\frac{1}{3}\\) = 8 X \\(\\frac{1}{3}\\) =<br \/>\n\\(\\frac{8}{3}\\)\u00a0 of peanut butter banana smoothies and 2 X 2 X \\(\\frac{1}{3}\\) =<br \/>\n4 X \\(\\frac{1}{3}\\) = \\(\\frac{4}{3}\\) fruit smoothies, now we add both \\(\\frac{8}{3}\\) +<br \/>\n\\(\\frac{4}{3}\\) as both denominators are same we add numerators as 8 + 4 =12 as numerator and<br \/>\ndenominator as 3 = \\(\\frac{12}{3}\\) as numerator is greater than denominator further can be simplified and<br \/>\n12 divides by 3 gives 4 with 0 remainder so the worker needed\u00a0 \\(\\frac{12}{3}\\) cups of bananas or<br \/>\n4 cups of bananas are needed to make smoothie.<\/p>\n<p>Understand the problem. Then make a plan. How will you solve? Explain.<\/p>\n<p>Question 4.<br \/>\nYour friend walks her dog for \\(\\frac{1}{4}\\) mile each day. She then runs 2\\(\\frac{3}{4}\\) miles each day.<br \/>\nHow many total miles does she walk her dog and run in 1 week?<\/p>\n<p>Answer:<br \/>\nTotal 21 miles my friend walks her dog and run in 1 week.<\/p>\n<p>Explanation:<br \/>\nGiven my friend walks her dog for \\(\\frac{1}{4}\\) mile each day , She then runs<br \/>\n2\\(\\frac{3}{4}\\) miles each day. So in each day she walk her dog and run\u00a0 is<br \/>\n\\(\\frac{1}{4}\\) mile + 2\\(\\frac{3}{4}\\) miles, Then we multiply with<br \/>\n7 because we have to calculate for 1 week. First we convert mixed fraction into fraction<br \/>\n2 \\(\\frac{3}{4}\\) , ( 2 X 4 + 3 ) by 4 = \\(\\frac{11}{4}\\), Now we add with<br \/>\n\\(\\frac{1}{4}\\) + \\(\\frac{11}{4}\\) = \\(\\frac{12}{4}\\)<br \/>\nas numerator is greater than denominator further can be simplified and 12 divides by 4<br \/>\ngives 3 with 0 remainder, so 3 miles for each day, Now for 1 week it is 7 X 3\u00a0 = 21 miles.<br \/>\nMy friend walks 21 miles her dog and run in 1 week.<\/p>\n<p>Question 5.<br \/>\nHair donations must be 12 inches longer. Your friend\u2019s hair is 7 inches long. Her hair grows<br \/>\nabout \\(\\frac{1}{2}\\) inch each month. Can she donate her hair in 8 months?<\/p>\n<p>Answer:<\/p>\n<p>No friend cannot donate her hair in 8 months as in 8 months it grows to 11 inches long and for<br \/>\nhair donations it must be 12 inches longer.<\/p>\n<p>Explanation:<\/p>\n<p>Given friend\u2019s hair is 7 inches long. Her hair grows about \\(\\frac{1}{2}\\) inch each month.<br \/>\nIn 8 months it grows 8\u00a0 X \\(\\frac{1}{2}\\) = \\(\\frac{8}{2}\\) as numerator is<br \/>\ngreater than denominator further can be simplified and 8 divides by 2 gives 4 with 0 remainder,<br \/>\nin 8 months it will grow 4 inches , So after 8 months it will be 7 + 4 =11 inches long as 11 is less than 12<br \/>\nand hair donations must be 12 inches longer so friend cannot donate her hair in 8 months.<\/p>\n<p>Question 6.<br \/>\nToday you walk \\(\\frac{6}{10}\\) mile from the Martin Luther King Jr. Memorial to the Washington Monument. Tomorrow you will walk about 4 times as far from the Washington Monument to the White House. About how much farther will you walk tomorrow?<\/p>\n<p>Answer:<\/p>\n<p>Tomorrow i will walk father \\(\\frac{18}{10}\\) miles\u00a0 or \\(\\frac{9}{5}\\) miles or 1 \\(\\frac{4}{5}\\) .<\/p>\n<p>Explanation:<\/p>\n<p>Given today i walked \\(\\frac{6}{10}\\) mile from the Martin Luther King Jr. Memorial<br \/>\nto the Washington Monument, Tomorrow i will walk about 4 times as far from the Washington Monument<br \/>\nto the White House , So number of miles walked tomorrow will be 4 X \\(\\frac{6}{10}\\)<br \/>\nfirst we write in unit fraction 4 X 6 X \\(\\frac{1}{10}\\) = 24 X \\(\\frac{1}{10}\\)\u00a0 =<br \/>\n\\(\\frac{24}{10}\\) as numerator is greater than denominator further can be simplified as<br \/>\n24,10 both can be divided by 2 gives 12,5 so \\(\\frac{24}{10}\\) = \\(\\frac{12}{5}\\)<br \/>\nnow farther i will walk tomorrow will be \\(\\frac{24}{10}\\) &#8211; \\(\\frac{6}{10}\\) as denominator<br \/>\nof both are same we substract numerators , 24 &#8211; 6 =18 and denominator will remain same 10 =<br \/>\n\\(\\frac{18}{10}\\) miles or further can be simplified and 18,10 both can be divided by by 2<br \/>\ngives 9, 5 = \\(\\frac{18}{10}\\) miles = \\(\\frac{9}{5}\\) miles as numerator is greater than<br \/>\ndenominator we can write it in mixed fraction as 5 goes in 1 times. 5<span id=\"MathJax-Element-7-Frame\" class=\"mjx-chtml MathJax_CHTML\"><span id=\"MJXc-Node-36\" class=\"mjx-math\"><span id=\"MJXc-Node-37\" class=\"mjx-mrow\"><span id=\"MJXc-Node-38\" class=\"mjx-mstyle\"><span id=\"MJXc-Node-39\" class=\"mjx-mrow\"><span id=\"MJXc-Node-40\" class=\"mjx-mn\"><span class=\"mjx-char MJXc-TeX-main-R\"> X 1 <\/span><\/span><\/span><\/span><\/span><\/span><\/span>is 5 , 1 will be our whole number and<br \/>\n(9<span id=\"MathJax-Element-10-Frame\" class=\"mjx-chtml MathJax_CHTML\"><span id=\"MJXc-Node-53\" class=\"mjx-math\"><span id=\"MJXc-Node-54\" class=\"mjx-mrow\"><span id=\"MJXc-Node-55\" class=\"mjx-mstyle\"><span id=\"MJXc-Node-56\" class=\"mjx-mrow\"><span id=\"MJXc-Node-58\" class=\"mjx-mo\"><span class=\"mjx-char MJXc-TeX-main-R\">\u22125<\/span><\/span><\/span><\/span><\/span><\/span><\/span>) we have 4 left over. 4 will be our numerator and our denominator will be the same 5 = 1 \\(\\frac{4}{5}\\) .<\/p>\n<p><strong>Think and Grow: Modeling Real Life<\/strong><\/p>\n<p><strong>Example<\/strong><br \/>\nA 20-pound dog and a 60-pound dog eat the recommended amounts of dog food each day. How much more food does the 60-pound dog eat in 1 week than the 20-pound dog?<br \/>\nThink: What do you know? What do you need to find? How will you solve?<br \/>\n<img decoding=\"async\" loading=\"lazy\" class=\"alignnone size-full wp-image-13026\" src=\"https:\/\/ccssanswers.com\/wp-content\/uploads\/2020\/12\/Big-Ideas-Math-Answers-4th-Grade-Chapter-9-Multiply-Whole-Numbers-and-Fractions-105.png\" alt=\"Big Ideas Math Answers 4th Grade Chapter 9 Multiply Whole Numbers and Fractions 105\" width=\"212\" height=\"221\" \/><br \/>\n<img decoding=\"async\" loading=\"lazy\" class=\"alignnone size-full wp-image-13027\" src=\"https:\/\/ccssanswers.com\/wp-content\/uploads\/2020\/12\/Big-Ideas-Math-Answers-4th-Grade-Chapter-9-Multiply-Whole-Numbers-and-Fractions-106.png\" alt=\"Big Ideas Math Answers 4th Grade Chapter 9 Multiply Whole Numbers and Fractions 106\" width=\"312\" height=\"463\" srcset=\"https:\/\/ccssanswers.com\/wp-content\/uploads\/2020\/12\/Big-Ideas-Math-Answers-4th-Grade-Chapter-9-Multiply-Whole-Numbers-and-Fractions-106.png 312w, https:\/\/ccssanswers.com\/wp-content\/uploads\/2020\/12\/Big-Ideas-Math-Answers-4th-Grade-Chapter-9-Multiply-Whole-Numbers-and-Fractions-106-202x300.png 202w\" sizes=\"(max-width: 312px) 100vw, 312px\" \/><br \/>\n<img decoding=\"async\" loading=\"lazy\" class=\"alignnone size-full wp-image-13028\" src=\"https:\/\/ccssanswers.com\/wp-content\/uploads\/2020\/12\/Big-Ideas-Math-Answers-4th-Grade-Chapter-9-Multiply-Whole-Numbers-and-Fractions-107.png\" alt=\"Big Ideas Math Answers 4th Grade Chapter 9 Multiply Whole Numbers and Fractions 107\" width=\"297\" height=\"463\" srcset=\"https:\/\/ccssanswers.com\/wp-content\/uploads\/2020\/12\/Big-Ideas-Math-Answers-4th-Grade-Chapter-9-Multiply-Whole-Numbers-and-Fractions-107.png 297w, https:\/\/ccssanswers.com\/wp-content\/uploads\/2020\/12\/Big-Ideas-Math-Answers-4th-Grade-Chapter-9-Multiply-Whole-Numbers-and-Fractions-107-192x300.png 192w\" sizes=\"(max-width: 297px) 100vw, 297px\" \/><br \/>\nSo, the 60-pound dog eats 10 \\(\\frac{1}{2}\\)\u00a0 more cups of food than the 20-pound dog in 1 week.<\/p>\n<p>Answer:<\/p>\n<p>The 60-pound dog eats 10 \\(\\frac{1}{2}\\)\u00a0 more cups of food than the 20-pound dog in 1 week.<\/p>\n<p>Explanation:<\/p>\n<p>Given A 20-pound dog eats 1 \\(\\frac{1}{2}\\) cups\u00a0 and a 60-pound dog eats 3 cups,<br \/>\nthe recommended amount of food each day. Now we need to calculate how much more food does<br \/>\nthe 60-pound dog eat in 1 week than the 20-pound dog,<br \/>\nSo Step 1 : First we find how much food the 20-pound dog eats in 1 week,<br \/>\nlet us take it as b = 7 X 1 \\(\\frac{1}{2}\\) we write mixed fraction as fraction<br \/>\n1 \\(\\frac{1}{2}\\) = ( 1 X 2 + 1 )by 2 = \\(\\frac{3}{2}\\) now multiply by 7 =<br \/>\n7 X \\(\\frac{3}{2}\\) we write into unit fraction 7 X 3 X \\(\\frac{1}{2}\\) =<br \/>\n21 X \\(\\frac{1}{2}\\) = \\(\\frac{21}{2}\\) cups,<br \/>\nStep 2: Now we find how much food the 60-pound dog eats in 1 week let us take it as c = 7 X 3 = 21 cups,<br \/>\nStep 3: Subtract b from c to find how much more food the 60-pound dog eats in 1 week.<br \/>\nc- b = 21 &#8211; \\(\\frac{21}{2}\\) to subtract first we make both denominators same,<br \/>\nwe multiply and divide 21 by 2 making as (21 x 2) by 2 = \\(\\frac{42}{2}\\) &#8211;\\(\\frac{21}{2}\\)<br \/>\nas denominators are same we subtarct numerators 42-21=21 will be numerator and denominator is same 2<br \/>\n=\\(\\frac{21}{2}\\) as numerator is greater than denominator and 2 goes 10 times, 2 <span id=\"MathJax-Element-7-Frame\" class=\"mjx-chtml MathJax_CHTML\"><span id=\"MJXc-Node-36\" class=\"mjx-math\"><span id=\"MJXc-Node-37\" class=\"mjx-mrow\"><span id=\"MJXc-Node-38\" class=\"mjx-mstyle\"><span id=\"MJXc-Node-39\" class=\"mjx-mrow\"><span id=\"MJXc-Node-40\" class=\"mjx-mn\"><span class=\"mjx-char MJXc-TeX-main-R\">X 10 <\/span><\/span><\/span><\/span><\/span><\/span><\/span>is 20 ,<br \/>\n10 will be our whole number and\u00a0 (21<span id=\"MathJax-Element-10-Frame\" class=\"mjx-chtml MathJax_CHTML\"><span id=\"MJXc-Node-53\" class=\"mjx-math\"><span id=\"MJXc-Node-54\" class=\"mjx-mrow\"><span id=\"MJXc-Node-55\" class=\"mjx-mstyle\"><span id=\"MJXc-Node-56\" class=\"mjx-mrow\"><span id=\"MJXc-Node-58\" class=\"mjx-mo\"><span class=\"mjx-char MJXc-TeX-main-R\">\u221220<\/span><\/span><\/span><\/span><\/span><\/span><\/span>) we have 1 left over. 1 will be our numerator and our denominator<br \/>\nwill be the same 2 = 10 \\(\\frac{1}{2}\\) . Therefore the 60-pound dog eats 10 \\(\\frac{1}{2}\\)<br \/>\nmore cups of food than the 20-pound dog in 1 week.<\/p>\n<p><strong>Show and Grow<\/strong><\/p>\n<p>Question 7.<br \/>\nUse the table above. A 40-pound dog and a 100-pound dog eat the recommended amounts of dog food each day. How much food is needed to feed both dogs for 1 week?<br \/>\n<img decoding=\"async\" loading=\"lazy\" class=\"alignnone size-full wp-image-13029\" src=\"https:\/\/ccssanswers.com\/wp-content\/uploads\/2020\/12\/Big-Ideas-Math-Answers-4th-Grade-Chapter-9-Multiply-Whole-Numbers-and-Fractions-108.png\" alt=\"Big Ideas Math Answers 4th Grade Chapter 9 Multiply Whole Numbers and Fractions 108\" width=\"136\" height=\"158\" \/><\/p>\n<p>Answer:<br \/>\nTo feed the food for both dogs for 1 week we require \\(\\frac{182}{4}\\) cups or \\(\\frac{91}{2}\\) or 45 \\(\\frac{1}{2}\\) cups.<\/p>\n<p>Explanation:<br \/>\nFrom the table 40-pound dog eats 2 \\(\\frac{1}{4}\\) and 100-pound dog eats<br \/>\n4 \\(\\frac{1}{4}\\) the recommended amounts of dog food each day,<br \/>\nto find how much food is needed to feed both dogs for 1 week first we calculate for<br \/>\n40-pound dog= 7 X 2 \\(\\frac{1}{4}\\) we write the mixed fraction as a fraction<br \/>\n2 x 4 + 1 by 4 = \\(\\frac{9}{4}\\) and multiply by 7 , 7 X \\(\\frac{9}{4}\\)<br \/>\nnow we write in unit fraction 7 X 9 X \\(\\frac{1}{4}\\) = 63 X \\(\\frac{1}{4}\\) =<br \/>\n\\(\\frac{63}{4}\\) now we calculate for 100-pound dog eats 4 \\(\\frac{1}{4}\\) in 1 week is<br \/>\n7 X 4 \\(\\frac{1}{4}\\) we write the mixed fraction as a fraction ( 4 X 4 + 1 )by 4 =<br \/>\n\\(\\frac{17}{4}\\) and multiply by 7 , 7 X \\(\\frac{17}{4}\\) now we write in unit fraction<br \/>\n7 X 17 X \\(\\frac{1}{4}\\) = 119 X \\(\\frac{1}{4}\\) = \\(\\frac{119}{4}\\).<br \/>\nNow to feed the food for both dogs for 1 week is \\(\\frac{63}{4}\\) + \\(\\frac{119}{4}\\)<br \/>\nas denominators are same we add numerators we get 63 + 119 = 182 as numerator, \\(\\frac{182}{4}\\)<br \/>\nfurther can be simplifed as 182 and 4 goes by 2 we write as \\(\\frac{91}{2}\\) numerator is greater<br \/>\nwe can write in mixed fraction as 2 goes 45 times, 2 <span id=\"MathJax-Element-7-Frame\" class=\"mjx-chtml MathJax_CHTML\"><span id=\"MJXc-Node-36\" class=\"mjx-math\"><span id=\"MJXc-Node-37\" class=\"mjx-mrow\"><span id=\"MJXc-Node-38\" class=\"mjx-mstyle\"><span id=\"MJXc-Node-39\" class=\"mjx-mrow\"><span id=\"MJXc-Node-40\" class=\"mjx-mn\"><span class=\"mjx-char MJXc-TeX-main-R\">X 45 <\/span><\/span><\/span><\/span><\/span><\/span><\/span>is 90 , 45 will be our whole number and<br \/>\n(91<span id=\"MathJax-Element-10-Frame\" class=\"mjx-chtml MathJax_CHTML\"><span id=\"MJXc-Node-53\" class=\"mjx-math\"><span id=\"MJXc-Node-54\" class=\"mjx-mrow\"><span id=\"MJXc-Node-55\" class=\"mjx-mstyle\"><span id=\"MJXc-Node-56\" class=\"mjx-mrow\"><span id=\"MJXc-Node-58\" class=\"mjx-mo\"><span class=\"mjx-char MJXc-TeX-main-R\">\u221290<\/span><\/span><\/span><\/span><\/span><\/span><\/span>) we have 1 left over. 1 will be our numerator and our denominator will be the same 2,<br \/>\nmaking as 45 \\(\\frac{1}{2}\\) cups.<\/p>\n<h3><a id=\"Problem_Solving:_Fraction_Operations_Homework_&amp;_Practice_9.5\"><\/a>Problem Solving: Fraction Operations Homework &amp; Practice 9.5<\/h3>\n<p>Understand the problem. Then make a plan. How will you solve? Explain.<\/p>\n<p>Question 1.<br \/>\nYour friend makes strawberry jam and raspberry jam. He makes enough strawberry jam to \ufb01ll \\(\\frac{1}{2}\\) of a jar. He makes 5 times as much raspberry jam as strawberry jam. How many full jars of raspberry jam does he make?<br \/>\n<img decoding=\"async\" loading=\"lazy\" class=\"alignnone size-full wp-image-13030\" src=\"https:\/\/ccssanswers.com\/wp-content\/uploads\/2020\/12\/Big-Ideas-Math-Answers-4th-Grade-Chapter-9-Multiply-Whole-Numbers-and-Fractions-109.png\" alt=\"Big Ideas Math Answers 4th Grade Chapter 9 Multiply Whole Numbers and Fractions 109\" width=\"148\" height=\"102\" \/><br \/>\nAnswer:<br \/>\nFriend makes \\(\\frac{5}{2}\\) jars= 2 \\(\\frac{1}{2}\\) jars in that full jars are 2,<br \/>\nSo 2 jars of raspberry jam he makes.<\/p>\n<p>Explanation:<br \/>\nGiven friend makes strawberry jam to fill \\(\\frac{1}{2}\\) of a jar and makes 5 times as<br \/>\nmuch raspberry jam as strawberry jam means he makes 5 X \\(\\frac{1}{2}\\) of jars of<br \/>\nraspberry jam now we write as fraction \\(\\frac{5}{2}\\) as numerator is greater,<br \/>\nwe can write in mixed fraction as 2 goes 2 times, 2 <span id=\"MathJax-Element-7-Frame\" class=\"mjx-chtml MathJax_CHTML\"><span id=\"MJXc-Node-36\" class=\"mjx-math\"><span id=\"MJXc-Node-37\" class=\"mjx-mrow\"><span id=\"MJXc-Node-38\" class=\"mjx-mstyle\"><span id=\"MJXc-Node-39\" class=\"mjx-mrow\"><span id=\"MJXc-Node-40\" class=\"mjx-mn\"><span class=\"mjx-char MJXc-TeX-main-R\">X 2 <\/span><\/span><\/span><\/span><\/span><\/span><\/span>is 4 , 2 will be our whole number and<br \/>\n(5<span id=\"MathJax-Element-10-Frame\" class=\"mjx-chtml MathJax_CHTML\"><span id=\"MJXc-Node-53\" class=\"mjx-math\"><span id=\"MJXc-Node-54\" class=\"mjx-mrow\"><span id=\"MJXc-Node-55\" class=\"mjx-mstyle\"><span id=\"MJXc-Node-56\" class=\"mjx-mrow\"><span id=\"MJXc-Node-58\" class=\"mjx-mo\"><span class=\"mjx-char MJXc-TeX-main-R\">\u22124<\/span><\/span><\/span><\/span><\/span><\/span><\/span>) we have 1 left over. 1 will be our numerator and our denominator will be the same 2,<br \/>\nmaking as 2 \\(\\frac{1}{2}\\) ,here 2 is whole there fore full jars of raspberry jam is 2.<br \/>\nSo friend makes \\(\\frac{5}{2}\\) jars= 2 \\(\\frac{1}{2}\\) jars in that full jars are 2,<br \/>\nSo 2 jars of raspberry jam he makes.<\/p>\n<p>Question 2.<br \/>\nYou buy a pair of jeans that originally cost $22. The pair of jeans is \\(\\frac{1}{2}\\) off the original price.<br \/>\nYou pay with a $20 bill. How much change do you receive?<br \/>\nAnswer:<br \/>\nI receive $9 as change.<br \/>\nExplanation:<br \/>\nThe pair of jeans is \\(\\frac{1}{2}\\) off the original price and original cost is $ 22,<br \/>\nSo the cost to be paid is $22 X \\(\\frac{1}{2}\\) = \\(\\frac{22}{2}\\)<br \/>\nfurther this can be simplified as both can be divided by 2 numerator becomes 11 and denominator as 1 = 11,<br \/>\ntherefore the original cost for the pair of jeans is $ 11, Now i have paid $ 20bill,<br \/>\ni will receive a change that is $20 &#8211; $11= $9, i receive $9 as a change.<\/p>\n<p>Question 3.<br \/>\nThe observation deck of the Space Needle in Seattle is 520 feet above ground.<br \/>\nThe tip of the Space Needle is 85 feet above the observation deck.<br \/>\nAn artist makes a replica that is \\(\\frac{1}{100}\\) the height of the entire Space Needle. How tall is the replica?<br \/>\n<img decoding=\"async\" loading=\"lazy\" class=\"alignnone size-full wp-image-13031\" src=\"https:\/\/ccssanswers.com\/wp-content\/uploads\/2020\/12\/Big-Ideas-Math-Answers-4th-Grade-Chapter-9-Multiply-Whole-Numbers-and-Fractions-110.png\" alt=\"Big Ideas Math Answers 4th Grade Chapter 9 Multiply Whole Numbers and Fractions 110\" width=\"134\" height=\"269\" \/><br \/>\nAnswer:<br \/>\nThe height of replica is \\(\\frac{605}{100}\\) =\\(\\frac{121}{20}\\) or<br \/>\n6 \\(\\frac{1}{20}\\) feet.<\/p>\n<p>Explanation:<br \/>\nGiven the observation deck of the Space Needle in Seattle is 520 feet above ground and<br \/>\nthe tip of the Space Needle is 85 feet above the observation deck means the height of<br \/>\nthe entire Space Needle is 520 + 85 = 605 feet above the ground to tip,<br \/>\nnow an artist makes a replica that is \\(\\frac{1}{100}\\)<br \/>\nthe height of the entire Space Needle. So the height of the replica is<br \/>\n605 X \\(\\frac{1}{100}\\) = \\(\\frac{605}{100}\\)<br \/>\nfurther can be simplifed as 605 and 100 goes by 5 we get numerator as 121 and denominator as 20 =<br \/>\n\\(\\frac{121}{20}\\) as numerator is greater we can write in mixed fraction as 20 goes<br \/>\n6 times, 20 <span id=\"MathJax-Element-7-Frame\" class=\"mjx-chtml MathJax_CHTML\"><span id=\"MJXc-Node-36\" class=\"mjx-math\"><span id=\"MJXc-Node-37\" class=\"mjx-mrow\"><span id=\"MJXc-Node-38\" class=\"mjx-mstyle\"><span id=\"MJXc-Node-39\" class=\"mjx-mrow\"><span id=\"MJXc-Node-40\" class=\"mjx-mn\"><span class=\"mjx-char MJXc-TeX-main-R\">X 6 <\/span><\/span><\/span><\/span><\/span><\/span><\/span>is 120 , 6 will be our whole number and\u00a0 (121<span id=\"MathJax-Element-10-Frame\" class=\"mjx-chtml MathJax_CHTML\"><span id=\"MJXc-Node-53\" class=\"mjx-math\"><span id=\"MJXc-Node-54\" class=\"mjx-mrow\"><span id=\"MJXc-Node-55\" class=\"mjx-mstyle\"><span id=\"MJXc-Node-56\" class=\"mjx-mrow\"><span id=\"MJXc-Node-58\" class=\"mjx-mo\"><span class=\"mjx-char MJXc-TeX-main-R\">\u2212120<\/span><\/span><\/span><\/span><\/span><\/span><\/span>) we have 1 left over.<br \/>\n1 will be our numerator and our denominator will be the same 20, making as 6 \\(\\frac{1}{20}\\) feet tall.<\/p>\n<p>Question 4.<br \/>\n<strong>Modeling Real Life<\/strong><br \/>\nHow many sheets of orange and black paper does a teacher need so that 30 students can each complete the art project?<br \/>\n<img decoding=\"async\" loading=\"lazy\" class=\"alignnone size-full wp-image-13032\" src=\"https:\/\/ccssanswers.com\/wp-content\/uploads\/2020\/12\/Big-Ideas-Math-Answers-4th-Grade-Chapter-9-Multiply-Whole-Numbers-and-Fractions-111.png\" alt=\"Big Ideas Math Answers 4th Grade Chapter 9 Multiply Whole Numbers and Fractions 111\" width=\"262\" height=\"211\" \/><br \/>\nAnswer:<br \/>\nFor 30 students to complete the Art Project orange sheets required are 11 \\(\\frac{2}{8}\\) and<br \/>\n18 \\(\\frac{6}{8}\\)\u00a0 black sheets of paper is required.<\/p>\n<p>Explanation:<br \/>\nGiven paper needed for Art Project orange is \\(\\frac{3}{8}\\) and for 30 students it is<br \/>\n30 X \\(\\frac{3}{8}\\) we write in unit fraction as 30 X 3 X \\(\\frac{1}{8}\\) =<br \/>\n90 X \\(\\frac{1}{8}\\) = \\(\\frac{90}{8}\\) as numerator is greater we can write in mixed fraction<br \/>\nas 8 goes 11 times, 8 <span id=\"MathJax-Element-7-Frame\" class=\"mjx-chtml MathJax_CHTML\"><span id=\"MJXc-Node-36\" class=\"mjx-math\"><span id=\"MJXc-Node-37\" class=\"mjx-mrow\"><span id=\"MJXc-Node-38\" class=\"mjx-mstyle\"><span id=\"MJXc-Node-39\" class=\"mjx-mrow\"><span id=\"MJXc-Node-40\" class=\"mjx-mn\"><span class=\"mjx-char MJXc-TeX-main-R\">X 11 <\/span><\/span><\/span><\/span><\/span><\/span><\/span>is 88, 11 will be our whole number and\u00a0 (90<span id=\"MathJax-Element-10-Frame\" class=\"mjx-chtml MathJax_CHTML\"><span id=\"MJXc-Node-53\" class=\"mjx-math\"><span id=\"MJXc-Node-54\" class=\"mjx-mrow\"><span id=\"MJXc-Node-55\" class=\"mjx-mstyle\"><span id=\"MJXc-Node-56\" class=\"mjx-mrow\"><span id=\"MJXc-Node-58\" class=\"mjx-mo\"><span class=\"mjx-char MJXc-TeX-main-R\">\u221288<\/span><\/span><\/span><\/span><\/span><\/span><\/span>) we have 2 left over.<br \/>\n2 will be our numerator and our denominator will be the same 8, making as<br \/>\n11 \\(\\frac{2}{8}\\) sheets of orange is required, given black paper needed for<br \/>\nArt Project is \\(\\frac{5}{8}\\) and for 30 students it is 30 X \\(\\frac{5}{8}\\)<br \/>\nwe write in unit fraction as 30 X 5 X \\(\\frac{1}{8}\\) = 150 X \\(\\frac{1}{8}\\) =<br \/>\n\\(\\frac{150}{8}\\) as numerator is greater we can write in mixed fraction as 8 goes 18 times,<br \/>\n8 <span id=\"MathJax-Element-7-Frame\" class=\"mjx-chtml MathJax_CHTML\"><span id=\"MJXc-Node-36\" class=\"mjx-math\"><span id=\"MJXc-Node-37\" class=\"mjx-mrow\"><span id=\"MJXc-Node-38\" class=\"mjx-mstyle\"><span id=\"MJXc-Node-39\" class=\"mjx-mrow\"><span id=\"MJXc-Node-40\" class=\"mjx-mn\"><span class=\"mjx-char MJXc-TeX-main-R\">X 18 <\/span><\/span><\/span><\/span><\/span><\/span><\/span>is 144, 18 will be our whole number and\u00a0 (150<span id=\"MathJax-Element-10-Frame\" class=\"mjx-chtml MathJax_CHTML\"><span id=\"MJXc-Node-53\" class=\"mjx-math\"><span id=\"MJXc-Node-54\" class=\"mjx-mrow\"><span id=\"MJXc-Node-55\" class=\"mjx-mstyle\"><span id=\"MJXc-Node-56\" class=\"mjx-mrow\"><span id=\"MJXc-Node-58\" class=\"mjx-mo\"><span class=\"mjx-char MJXc-TeX-main-R\">\u2212144<\/span><\/span><\/span><\/span><\/span><\/span><\/span>) we have 6 left over.<br \/>\n6 will be our numerator and our denominator will be the same 8, making as<br \/>\n18 \\(\\frac{6}{8}\\) black sheets are required.<br \/>\nTherefore for 30 students to complete the Art Project orange sheets required are<br \/>\n11 \\(\\frac{2}{8}\\) and 18 \\(\\frac{6}{8}\\) black sheets of paper is required.<\/p>\n<p>Question 5.<br \/>\n<strong>Writing<\/strong><br \/>\nWrite and solve a two-step word problem with mixed numbers that can be solved using multiplication.<\/p>\n<p>Answer:<br \/>\nA two-step problem is a word problem that requires two operations to solve it.<br \/>\nWe take two mixed numbers and slove using multiplication. In step one<br \/>\nwe use multiplication and add and in another step we use addition and again use multiplication<br \/>\nas explained below with an example,<\/p>\n<p>Explanation:<br \/>\nFor example: Percy walks 2 \\(\\frac{5}{4}\\) kilometers for 2 days and<br \/>\n1 \\(\\frac{1}{4}\\) kilometers for 5 days , how many kilometers does Percy walks in 1 week?<br \/>\nGiven in first 2 days Percy walks 2 \\(\\frac{5}{4}\\) kilometers so In first step<br \/>\nwe change mixed fraction to fraction by using multiplication and then add 2 X 4 + 5 by 4 =<br \/>\n\\(\\frac{13}{4}\\) kilometers for 1 day for 2 days it is 2 X \\(\\frac{13}{4}\\) =<br \/>\n2 X 13 X \\(\\frac{1}{4}\\) = 26 X \\(\\frac{1}{4}\\) = \\(\\frac{26}{4}\\) kilometers<span style=\"font-size: 16px;\"> for 2 days ,<br \/>\nNow for rest of 5 days we calculate. Here 1 \\(\\frac{1}{4}\\) we change the mixed fraction to fraction as<br \/>\n( 1 X 4 + 1 ) by 4 = \\(\\frac{5}{4}\\) for 1 day, For 5 days it will be 5 X \\(\\frac{5}{4}\\),<br \/>\n5 X 5 X \\(\\frac{1}{4}\\) = 25 X \\(\\frac{1}{4}\\) = \\(\\frac{25}{4}\\) kilometers for rest 5 days ,<br \/>\nNow total number of kilometers Percy walks is\u00a0 \\(\\frac{26}{4}\\) + \\(\\frac{25}{4}\\) as denominators<br \/>\nare same we add numerators we get 26 + 25 as 51 and denominator being same as 4 = \\(\\frac{51}{4}\\) kilometers<br \/>\nPercy walks in 1 week and further can be simplified as numerator is greater we can write in mixed fraction as<br \/>\n4 goes 12 times, 4 <span id=\"MathJax-Element-7-Frame\" class=\"mjx-chtml MathJax_CHTML\"><span id=\"MJXc-Node-36\" class=\"mjx-math\"><span id=\"MJXc-Node-37\" class=\"mjx-mrow\"><span id=\"MJXc-Node-38\" class=\"mjx-mstyle\"><span id=\"MJXc-Node-39\" class=\"mjx-mrow\"><span id=\"MJXc-Node-40\" class=\"mjx-mn\"><span class=\"mjx-char MJXc-TeX-main-R\">X 12 <\/span><\/span><\/span><\/span><\/span><\/span><\/span>is 48, 12 will be our whole number and\u00a0 (51<span id=\"MathJax-Element-10-Frame\" class=\"mjx-chtml MathJax_CHTML\"><span id=\"MJXc-Node-53\" class=\"mjx-math\"><span id=\"MJXc-Node-54\" class=\"mjx-mrow\"><span id=\"MJXc-Node-55\" class=\"mjx-mstyle\"><span id=\"MJXc-Node-56\" class=\"mjx-mrow\"><span id=\"MJXc-Node-58\" class=\"mjx-mo\"><span class=\"mjx-char MJXc-TeX-main-R\">\u221248<\/span><\/span><\/span><\/span><\/span><\/span><\/span>) we have 3 left over.<br \/>\n3 will be our numerator and our denominator will be the same 4, making as<br \/>\n12 \\(\\frac{3}{4}\\) kilometers Percy walks in 1 week.<\/span><\/p>\n<p>Question 6.<br \/>\n<strong>Modeling Real Life<\/strong><br \/>\nIn science class, you test how many grams different-sized bundles of spaghetti can hold. You predict that a bundle of 5 spaghetti noodles can hold 10 quarters before breaking. You predict that a bundle of 10 spaghetti noodles can hold 20 quarters before breaking. Each quarter 5\\(\\frac{67}{100}\\) grams. According to your predictions, how many more grams can the bundle of 10 noodles hold than the bundle of 5 noodles?<br \/>\n<img decoding=\"async\" loading=\"lazy\" class=\"alignnone size-full wp-image-12985\" src=\"https:\/\/ccssanswers.com\/wp-content\/uploads\/2020\/12\/Big-Ideas-Math-Answer-Key-Grade-4-Chapter-9-Multiply-Whole-Numbers-and-Fractions-112.png\" alt=\"Big Ideas Math Answer Key Grade 4 Chapter 9 Multiply Whole Numbers and Fractions 112\" width=\"266\" height=\"162\" \/><br \/>\nAnswer:<br \/>\n\\(\\frac{970}{100}\\) grams more the bundle of 10 noodles hold than the bundle of 5 noodles<br \/>\nor \\(\\frac{97}{10}\\) grams more the bundle of 10 noodles hold than the bundle of 5 noodles<br \/>\nor <span style=\"font-size: 16px;\">9 \\(\\frac{7}{10}\\) grams more the bundle of 10 noodles hold than the bundle of 5 noodles.<\/span><br \/>\nExplanation:<br \/>\nGiven that bundle of 5 noodles can hold 10 quarters means 5 noodles can hold<br \/>\n10 X 5 \\(\\frac{67}{100}\\) grams first we change mixed fraction to fraction by<br \/>\nusing multiplication and then add as 5 \\(\\frac{67}{100}\\) = 5 X 6 + 67 by 100 =<br \/>\n\\(\\frac{97}{100}\\) now we multiply by 10, 10 X \\(\\frac{97}{100}\\) =<br \/>\n10 X 97 X \\(\\frac{1}{100}\\) = 970 X \\(\\frac{1}{100}\\) = \\(\\frac{970}{100}\\) grams ,<br \/>\nso 5 spaghetti noodles can hold \\(\\frac{970}{100}\\) grams before breaking,<br \/>\nNow given 10 spaghetti noodles can hold 20 quarters means 10 spaghetti noodles can hold<br \/>\n20 X 5 \\(\\frac{67}{100}\\) grams again first we change mixed fraction to fraction<br \/>\nby using multiplication and then add as 5 \\(\\frac{67}{100}\\) = ( 5 X 6 + 67 ) by 100 =<br \/>\n\\(\\frac{97}{100}\\) now we multiply by 20, 20 X \\(\\frac{97}{100}\\) =<br \/>\n20 X 97 X \\(\\frac{1}{100}\\) = 1940 X \\(\\frac{1}{100}\\) = \\(\\frac{1940}{100}\\) grams ,<br \/>\nso 10 spaghetti noodles can hold \\(\\frac{1940}{100}\\) grams before breaking now to calculate<br \/>\nhow many more grams can the bundle of 10 noodles hold than the bundle of 5 noodles we subtract<br \/>\n\\(\\frac{1940}{100}\\) grams &#8211; \\(\\frac{970}{100}\\) grams as denominators are same first<br \/>\nwe substract numerators as 1940 &#8211; 970 = 970 as numerator and denominator being same 100<br \/>\nwe get \\(\\frac{970}{100}\\) grams more the bundle of 10 noodles hold than the bundle of 5 noodles,<br \/>\nfurther can be simplified as 970 and 100 both can be divided by 10 making it as \\(\\frac{97}{10}\\) grams<br \/>\nmore the bundle of 10 noodles hold than the bundle of 5 noodles and as <span style=\"font-size: 16px;\">numerator is greater ,<br \/>\nwe can write in mixed fraction as 10 goes 9 times, 10 <span id=\"MathJax-Element-7-Frame\" class=\"mjx-chtml MathJax_CHTML\"><span id=\"MJXc-Node-36\" class=\"mjx-math\"><span id=\"MJXc-Node-37\" class=\"mjx-mrow\"><span id=\"MJXc-Node-38\" class=\"mjx-mstyle\"><span id=\"MJXc-Node-39\" class=\"mjx-mrow\"><span id=\"MJXc-Node-40\" class=\"mjx-mn\"><span class=\"mjx-char MJXc-TeX-main-R\">X 9 <\/span><\/span><\/span><\/span><\/span><\/span><\/span>is 90, 9 will be our whole number and\u00a0 (97<span id=\"MathJax-Element-10-Frame\" class=\"mjx-chtml MathJax_CHTML\"><span id=\"MJXc-Node-53\" class=\"mjx-math\"><span id=\"MJXc-Node-54\" class=\"mjx-mrow\"><span id=\"MJXc-Node-55\" class=\"mjx-mstyle\"><span id=\"MJXc-Node-56\" class=\"mjx-mrow\"><span id=\"MJXc-Node-58\" class=\"mjx-mo\"><span class=\"mjx-char MJXc-TeX-main-R\">\u221290<\/span><\/span><\/span><\/span><\/span><\/span><\/span>)<br \/>\nwe have 7 left over. 7 will be our numerator and our denominator will be the same 10,<br \/>\nmaking as 9 \\(\\frac{7}{10}\\) grams more the bundle of 10 noodles hold than the bundle of 5 noodles.<\/span><\/p>\n<p><strong>Review &amp; Refresh<\/strong><\/p>\n<p>Compare<\/p>\n<p>Question 7.<br \/>\n<img decoding=\"async\" loading=\"lazy\" class=\"alignnone size-full wp-image-12986\" src=\"https:\/\/ccssanswers.com\/wp-content\/uploads\/2020\/12\/Big-Ideas-Math-Answer-Key-Grade-4-Chapter-9-Multiply-Whole-Numbers-and-Fractions-113.png\" alt=\"Big Ideas Math Answer Key Grade 4 Chapter 9 Multiply Whole Numbers and Fractions 113\" width=\"92\" height=\"60\" \/><br \/>\nAnswer:<br \/>\n\\(\\frac{9}{10}\\) is greater than &gt; \\(\\frac{4}{5}\\) or<br \/>\n\\(\\frac{9}{10}\\) is greater than &gt; \\(\\frac{8}{10}\\)<\/p>\n<p>Explanation:<br \/>\nIn order to compare the fractions we must first turn their different denominators into<br \/>\nthe same denominators to make denominators same we multiply \\(\\frac{4}{5}\\)<br \/>\nwith both numerator and denominator by 2 the value will not change =<br \/>\n\\(\\frac{4}{5}\\) \u00a0X \\(\\frac{2}{2}\\)= \\(\\frac{8}{10}\\)<br \/>\nnow as denominators are same 10 we can compare only numerators<br \/>\n\\(\\frac{9}{10}\\) with \\(\\frac{8}{10}\\) as 9 is greater than 8,<br \/>\nSo \\(\\frac{9}{10}\\) is greater than &gt; \\(\\frac{8}{10}\\) or<br \/>\n\\(\\frac{9}{10}\\) is greater than &gt; \\(\\frac{4}{5}\\)<\/p>\n<p>Question 8.<br \/>\n<img decoding=\"async\" loading=\"lazy\" class=\"alignnone size-full wp-image-12987\" src=\"https:\/\/ccssanswers.com\/wp-content\/uploads\/2020\/12\/Big-Ideas-Math-Answer-Key-Grade-4-Chapter-9-Multiply-Whole-Numbers-and-Fractions-114.png\" alt=\"Big Ideas Math Answer Key Grade 4 Chapter 9 Multiply Whole Numbers and Fractions 114\" width=\"76\" height=\"59\" \/><br \/>\nAnswer:<br \/>\n\\(\\frac{3}{8}\\) &lt; is less than \\(\\frac{5}{6}\\) or<br \/>\n\\(\\frac{9}{24}\\) &lt; is less than \\(\\frac{20}{24}\\).<\/p>\n<p>Explanation:<br \/>\nIn order to compare the fractions we must first turn their different denominators into<br \/>\nthe same denominators to make denominators same ,<br \/>\nwe find the least common multiplier of 8 ,6 as ( 2 X 2 X 2 X 3 ) = 24,<br \/>\n<img decoding=\"async\" loading=\"lazy\" class=\"alignnone\" src=\"https:\/\/haygot.s3.amazonaws.com\/questions\/1632716_1778536_ans_1eecbaefff954e9c969f1224d2918e0d.JPG\" alt=\"solution\" width=\"162\" height=\"205\" \/><\/p>\n<p class=\"Solution_html__31bvW\">Now convert each one of \\(\\frac{3}{8}\\) and \\(\\frac{5}{6}\\)<br \/>\ninto an equivalent fraction having\u00a0<span class=\"katex\"><span class=\"katex-html\" aria-hidden=\"true\"><span class=\"base\"><span class=\"mord\">2<\/span><span class=\"mord\">4<\/span><\/span><\/span><\/span> as denominator,<br \/>\n\\(\\frac{3}{8}\\) = \\(\\frac{3}{8}\\) X \\(\\frac{3}{3}\\) =<br \/>\n\\(\\frac{9}{24}\\) and \\(\\frac{5}{6}\\) = \\(\\frac{5}{6}\\) X \\(\\frac{4}{4}\\) =<br \/>\n\\(\\frac{20}{24}\\) now as denominators are same 24 we can compare only numerators<br \/>\n\\(\\frac{9}{24}\\) with \\(\\frac{20}{24}\\) as 9 is less than 20,<br \/>\nso \\(\\frac{9}{24}\\) &lt; is less than \\(\\frac{20}{24}\\) or<br \/>\n\\(\\frac{3}{8}\\) &lt; is less than \\(\\frac{5}{6}\\)<\/p>\n<p>Question 9.<br \/>\n<img decoding=\"async\" loading=\"lazy\" class=\"alignnone size-full wp-image-12988\" src=\"https:\/\/ccssanswers.com\/wp-content\/uploads\/2020\/12\/Big-Ideas-Math-Answer-Key-Grade-4-Chapter-9-Multiply-Whole-Numbers-and-Fractions-115.png\" alt=\"Big Ideas Math Answer Key Grade 4 Chapter 9 Multiply Whole Numbers and Fractions 115\" width=\"82\" height=\"53\" \/><br \/>\nAnswer:<br \/>\n\\(\\frac{1}{3}\\) = is equal to\u00a0 \\(\\frac{4}{12}\\) or<br \/>\n\\(\\frac{1}{3}\\) = is equal to\u00a0 \\(\\frac{1}{3}\\)<br \/>\nExplanation:<br \/>\nHere first we simplify \\(\\frac{4}{12}\\) as both can be divided by 4 if we dividey<br \/>\nboth numerator and denominator by 4 we get numerator as 1 and denominator as 4 =<br \/>\n\\(\\frac{1}{3}\\) now comparing both sides, as values are same<br \/>\nso \\(\\frac{1}{3}\\) = is equal to\u00a0 \\(\\frac{4}{12}\\) or<br \/>\n\\(\\frac{1}{3}\\) = is equal to\u00a0 \\(\\frac{1}{3}\\).<\/p>\n<h3><a id=\"Multiply_Whole_Numbers_and_Fractions_Performance_Task\"><\/a>Multiply Whole Numbers and Fractions Performance Task<\/h3>\n<p>Question 1.<br \/>\nYou use identical glass jars, colored water, and a spoon to learn about sounds. When you tap a spoon on a jar, the vibrations make a sound. The jar that has the least amount of water makes the lowest sound.<br \/>\n<img decoding=\"async\" loading=\"lazy\" class=\"alignnone size-full wp-image-12989\" src=\"https:\/\/ccssanswers.com\/wp-content\/uploads\/2020\/12\/Big-Ideas-Math-Answer-Key-Grade-4-Chapter-9-Multiply-Whole-Numbers-and-Fractions-116.png\" alt=\"Big Ideas Math Answer Key Grade 4 Chapter 9 Multiply Whole Numbers and Fractions 116\" width=\"705\" height=\"258\" srcset=\"https:\/\/ccssanswers.com\/wp-content\/uploads\/2020\/12\/Big-Ideas-Math-Answer-Key-Grade-4-Chapter-9-Multiply-Whole-Numbers-and-Fractions-116.png 705w, https:\/\/ccssanswers.com\/wp-content\/uploads\/2020\/12\/Big-Ideas-Math-Answer-Key-Grade-4-Chapter-9-Multiply-Whole-Numbers-and-Fractions-116-300x110.png 300w\" sizes=\"(max-width: 705px) 100vw, 705px\" \/><br \/>\na. You fill each glass using a \\(\\frac{3}{4}\\)-cup measuring cup. Complete the table to find the total amount of water in each jar.<br \/>\nb. How much more water is in the purple jar than the green jar?<br \/>\nc. How many cups of water are used in all?<br \/>\nd. Each jar can hold 4 cups of water. Is it possible to add another \\(\\frac{3}{4}\\) cup of water to the purple jar? Explain.<br \/>\ne. Which jars are more than half full?<br \/>\nf. You add another \\(\\frac{3}{4}\\) cup of water to the green jar. How does that affect the sound?<br \/>\nAnswer:<br \/>\na. <img decoding=\"async\" loading=\"lazy\" class=\"alignnone wp-image-25575 size-full\" src=\"https:\/\/ccssanswers.com\/wp-content\/uploads\/2020\/12\/9-Multiply-Whole-Numbers-and-Fractions-17.bmp\" alt=\"\" width=\"291\" height=\"290\" srcset=\"https:\/\/ccssanswers.com\/wp-content\/uploads\/2020\/12\/9-Multiply-Whole-Numbers-and-Fractions-17.bmp 291w, https:\/\/ccssanswers.com\/wp-content\/uploads\/2020\/12\/9-Multiply-Whole-Numbers-and-Fractions-17-150x150.jpg 150w\" sizes=\"(max-width: 291px) 100vw, 291px\" \/><br \/>\nb. Purple jar is 3 cups more than the Green jar or Purple jar is \\(\\frac{12}{4}\\) cups more than the Green jar.<br \/>\nc. T<span style=\"font-size: 16px;\">otal number of cups of water used in all is \\(\\frac{45}{4}\\) cups or 11 \\(\\frac{1}{4}\\) cups.<br \/>\n<\/span>d. No, it is not possible to add another \\(\\frac{3}{4}\\) cup of water to the purple jar as if we add it will become <span style=\"font-size: 16px;\">\\(\\frac{18}{4}\\) cups = 4 \\(\\frac{2}{4}\\) = 4 + \\(\\frac{2}{4}\\) cups of water<br \/>\nto the purple jar cups which is more than 4 cups it will overflow so it is not possible to add another<br \/>\n\\(\\frac{3}{4}\\) cup of water to the purple jar.<br \/>\n<\/span>e. Jars which are more than half full are Orange, Red and Purple.<br \/>\nf. After adding add another \\(\\frac{3}{4}\\) cup of water to the green jar it becomes<br \/>\n\\(\\frac{6}{4}\\) which is equal to blue color jar, <span style=\"font-size: 16px;\">we know the jar that has the least amount of water<br \/>\nmakes the lowest sound before it was the green jar which had least amount of water so it had lowest sound,<br \/>\nso now after adding \\(\\frac{3}{4}\\) cup of water to green jar it has become equal to blue jar<br \/>\nso now both green and blue jar has least amount of water so they both make the lowest sound.<br \/>\n<\/span><br \/>\nExplanantion:<br \/>\na. Given we fill each glass \\(\\frac{3}{4}\\)-cup measuring cup so total water cups used for each color are<br \/>\nGreen 1 means 1 X \\(\\frac{3}{4}\\) cup = \\(\\frac{3}{4}\\) cup<br \/>\nBlue 2 of \\(\\frac{3}{4}\\) = 2 X \\(\\frac{3}{4}\\) = 2 X 3 X \\(\\frac{1}{4}\\) =<br \/>\n6 X \\(\\frac{1}{4}\\)= \\(\\frac{6}{4}\\) cups , as both numerator and denominator<br \/>\ncan be divided by 2 we get \\(\\frac{3}{2}\\) cups<br \/>\nOrange 3 of \\(\\frac{3}{4}\\) = 3 X \\(\\frac{3}{4}\\) = 3 X 3 X \\(\\frac{1}{4}\\) =<br \/>\n9 X \\(\\frac{1}{4}\\) = \\(\\frac{9}{4}\\) cups<br \/>\nRed 4 of \\(\\frac{3}{4}\\) = 4 X \\(\\frac{3}{4}\\) = 4 X 3 X \\(\\frac{1}{4}\\) =<br \/>\n12 X \\(\\frac{1}{4}\\) = \\(\\frac{12}{4}\\) as both numerator and denominator can be divided by 4<br \/>\nwe get numerator as 3 and denominator 1 making Red 4 of \\(\\frac{3}{4}\\) = 3 cups.<br \/>\nPurple 5 of \\(\\frac{3}{4}\\) = 5 X \\(\\frac{3}{4}\\) = 5 X 3 X \\(\\frac{1}{4}\\) =<br \/>\n15 X \\(\\frac{1}{4}\\) =<br \/>\n\\(\\frac{15}{4}\\) cups.<\/p>\n<p>b. To calculate how much more water is in the Purple jar than the Green jar we subtract<br \/>\nthe quantity of purple jar minus quantity in green jar as \\(\\frac{15}{4}\\) cups &#8211; \\(\\frac{3}{4}\\) cup,<br \/>\nas denominators are same for the both we will sustract numerators 15-3 = 12 and<br \/>\ndenominator remains the same as 4, \\(\\frac{12}{4}\\) as both numerator and<br \/>\ndenominator can be divided by 4 we get numerator as 3 and denominator 1 so Purple Jar is 3 cups<br \/>\nmore than the Green jar.<\/p>\n<p>c. Total number of cups of water are used in all is adding Green, Blue, Orange, Red,<br \/>\nPurple &#8211; \\(\\frac{3}{4}\\) + \\(\\frac{6}{4}\\) + \\(\\frac{9}{4}\\)\u00a0 + \\(\\frac{12}{4}\\) +<br \/>\n\\(\\frac{15}{4}\\) as denominators are same we add numerators as 3 + 6 + 9 + 12 + 15 = 45 and<br \/>\ndenominator being same as 4 = \\(\\frac{45}{4}\\) as numerator is greater we can also write in mixed fraction<br \/>\nas 4 goes 11 ,<span style=\"font-size: 16px;\"> 4\u00a0<span id=\"MathJax-Element-7-Frame\" class=\"mjx-chtml MathJax_CHTML\"><span id=\"MJXc-Node-36\" class=\"mjx-math\"><span id=\"MJXc-Node-37\" class=\"mjx-mrow\"><span id=\"MJXc-Node-38\" class=\"mjx-mstyle\"><span id=\"MJXc-Node-39\" class=\"mjx-mrow\"><span id=\"MJXc-Node-40\" class=\"mjx-mn\"><span class=\"mjx-char MJXc-TeX-main-R\">X 11 <\/span><\/span><\/span><\/span><\/span><\/span><\/span>is 44, 11 will be our whole number and\u00a0 (45<span id=\"MathJax-Element-10-Frame\" class=\"mjx-chtml MathJax_CHTML\"><span id=\"MJXc-Node-53\" class=\"mjx-math\"><span id=\"MJXc-Node-54\" class=\"mjx-mrow\"><span id=\"MJXc-Node-55\" class=\"mjx-mstyle\"><span id=\"MJXc-Node-56\" class=\"mjx-mrow\"><span id=\"MJXc-Node-58\" class=\"mjx-mo\"><span class=\"mjx-char MJXc-TeX-main-R\">\u221244<\/span><\/span><\/span><\/span><\/span><\/span><\/span>) we have 1 left over.<br \/>\n1 will be our numerator and our denominator will be the same 4, making as 11 \\(\\frac{1}{4}\\),<br \/>\ntherfore total number of cups of water used in all is \\(\\frac{45}{4}\\) cups or 11 \\(\\frac{1}{4}\\) cups.<\/span><\/p>\n<p>d. We got Purple jar contains \\(\\frac{15}{4}\\) cups to this we will \u00a0add another<br \/>\n\\(\\frac{3}{4}\\) cup of water = \\(\\frac{15}{4}\\) + \\(\\frac{3}{4}\\) as denominator is<br \/>\nsame we add numerators as 15 + 3 = 18 and denominator is same 4 so now the Purple jar contains<br \/>\n\\(\\frac{18}{4}\\) cups , to find the whole value we write in mixed fraction as 4 goes , 4 <span id=\"MathJax-Element-7-Frame\" class=\"mjx-chtml MathJax_CHTML\"><span id=\"MJXc-Node-36\" class=\"mjx-math\"><span id=\"MJXc-Node-37\" class=\"mjx-mrow\"><span id=\"MJXc-Node-38\" class=\"mjx-mstyle\"><span id=\"MJXc-Node-39\" class=\"mjx-mrow\"><span id=\"MJXc-Node-40\" class=\"mjx-mn\"><span class=\"mjx-char MJXc-TeX-main-R\">X 4 <\/span><\/span><\/span><\/span><\/span><\/span><\/span>is 16, 4<br \/>\nwill be our whole number and\u00a0 (18<span id=\"MathJax-Element-10-Frame\" class=\"mjx-chtml MathJax_CHTML\"><span id=\"MJXc-Node-53\" class=\"mjx-math\"><span id=\"MJXc-Node-54\" class=\"mjx-mrow\"><span id=\"MJXc-Node-55\" class=\"mjx-mstyle\"><span id=\"MJXc-Node-56\" class=\"mjx-mrow\"><span id=\"MJXc-Node-58\" class=\"mjx-mo\"><span class=\"mjx-char MJXc-TeX-main-R\">\u221216<\/span><\/span><\/span><\/span><\/span><\/span><\/span>) we have 2 left over. 2 will be our numerator and our denominator<br \/>\nwill be the same 4, making as 4 \\(\\frac{2}{4}\\) = 4 + \\(\\frac{2}{4}\\) and<br \/>\ngiven that each jar can hold 4 cups of water but as we are getting more than 4 it will overflow,<br \/>\nso it is not possible to add another \\(\\frac{3}{4}\\) cup of water to the purple jar.<br \/>\ne. Jars more than half full means each jars should be above<span style=\"font-size: 16px;\"> 2 cups means to check we need<br \/>\ndenominator to be same that is 4 so we multiply denominator and numerator by 4,<br \/>\nwe get \\(\\frac{8}{4}\\) to be more than half full means each jars numerators should be more than 8 and all jars denominators being same as 4, now we check with green jar, \\(\\frac{8}{4}\\)\u00a0 and<br \/>\n\\(\\frac{3}{4}\\) as 3 is not greater than 8 so not green jar, blue jar we have \\(\\frac{6}{4}\\) cups<br \/>\nhere also numerator 6 is not more than 8 so even we will not conside blue jar,<br \/>\norange jar \\(\\frac{9}{4}\\) now here numerator 8 is less than 9 so we will consider orange jar,<br \/>\nNow red jar as red jar has 3 cups which is above 2 cups we consider red jar and we have purple jar as<br \/>\n\\(\\frac{15}{4}\\) here numerator 15 is more than numerator 8 so we consider purple jar,<br \/>\ntherefore jars with more than half full are Orange, Red and Purple.<\/span><\/p>\n<p>f. Now we will add another \\(\\frac{3}{4}\\) cup of water to the green jar means<br \/>\n\\(\\frac{3}{4}\\) + \\(\\frac{3}{4}\\) as denominators as same we add numerators<br \/>\nwe get \\(\\frac{6}{4}\\) which is equal to blue color jar, we know the jar that has the<br \/>\nleast amount of water makes the lowest sound before it was the green jar which had least amount of water,<br \/>\nso it had lowest sound, so now after adding \\(\\frac{3}{4}\\) cup of water to green jar it has become equal<br \/>\nto blue jar so now both green and blue jar has least amount of water so they both make the lowest sound.<\/p>\n<h3><a id=\"Multiply_Whole_Numbers_and_Fractions_Activity\"><\/a>Multiply Whole Numbers and Fractions Activity<\/h3>\n<p>Three In a Row: Fraction Multiplication<\/p>\n<p><strong>Directions:<\/strong><\/p>\n<ol>\n<li>Players take turns.<\/li>\n<li>On your turn, spin both spinners.<\/li>\n<li>Multiply the whole number and the fraction or mixed number. Cover the product.<\/li>\n<li>If the product is already covered, you lose your turn.<\/li>\n<li>The \ufb01rst player to get three in a row wins!<\/li>\n<\/ol>\n<p><img decoding=\"async\" loading=\"lazy\" class=\"alignnone size-full wp-image-12990\" src=\"https:\/\/ccssanswers.com\/wp-content\/uploads\/2020\/12\/Big-Ideas-Math-Answer-Key-Grade-4-Chapter-9-Multiply-Whole-Numbers-and-Fractions-117.png\" alt=\"Big Ideas Math Answer Key Grade 4 Chapter 9 Multiply Whole Numbers and Fractions 117\" width=\"613\" height=\"613\" srcset=\"https:\/\/ccssanswers.com\/wp-content\/uploads\/2020\/12\/Big-Ideas-Math-Answer-Key-Grade-4-Chapter-9-Multiply-Whole-Numbers-and-Fractions-117.png 613w, https:\/\/ccssanswers.com\/wp-content\/uploads\/2020\/12\/Big-Ideas-Math-Answer-Key-Grade-4-Chapter-9-Multiply-Whole-Numbers-and-Fractions-117-300x300.png 300w, https:\/\/ccssanswers.com\/wp-content\/uploads\/2020\/12\/Big-Ideas-Math-Answer-Key-Grade-4-Chapter-9-Multiply-Whole-Numbers-and-Fractions-117-150x150.png 150w\" sizes=\"(max-width: 613px) 100vw, 613px\" \/><br \/>\nAnswer:<\/p>\n<h3><a id=\"Multiply_Whole_Numbers_and_Fractions_Chapter_Practice\"><\/a>Multiply Whole Numbers and Fractions Chapter Practice<\/h3>\n<p><strong>9.1 Understand Multiples of Unit Fractions<\/strong><\/p>\n<p>Write the fraction as a multiple of a unit fraction.<\/p>\n<p>Question 1.<br \/>\n<img decoding=\"async\" loading=\"lazy\" class=\"alignnone size-full wp-image-12991\" src=\"https:\/\/ccssanswers.com\/wp-content\/uploads\/2020\/12\/Big-Ideas-Math-Answer-Key-Grade-4-Chapter-9-Multiply-Whole-Numbers-and-Fractions-118.png\" alt=\"Big Ideas Math Answer Key Grade 4 Chapter 9 Multiply Whole Numbers and Fractions 118\" width=\"162\" height=\"112\" \/><br \/>\nAnswer:<br \/>\n\\(\\frac{3}{10}\\)= \\(\\frac{1}{10}\\) + \\(\\frac{1}{10}\\) + \\(\\frac{1}{10}\\)<br \/>\n= 3 X \\(\\frac{1}{10}\\).<\/p>\n<p>Explanation:<br \/>\nWe write \\(\\frac{3}{10}\\) in addition equation as \\(\\frac{3}{100}\\)=<br \/>\n\\(\\frac{1}{10}\\) + \\(\\frac{1}{10}\\) + \\(\\frac{1}{10}\\) and<br \/>\nmultiplication as unit fraction \\(\\frac{3}{10}\\) represents 3 parts that are \\(\\frac{1}{10}\\) of the whole, \\(\\frac{3}{10}\\) = 3 X \\(\\frac{1}{10}\\)<\/p>\n<p>Question 2.<br \/>\n<img decoding=\"async\" loading=\"lazy\" class=\"alignnone size-full wp-image-12992\" src=\"https:\/\/ccssanswers.com\/wp-content\/uploads\/2020\/12\/Big-Ideas-Math-Answer-Key-Grade-4-Chapter-9-Multiply-Whole-Numbers-and-Fractions-119.png\" alt=\"Big Ideas Math Answer Key Grade 4 Chapter 9 Multiply Whole Numbers and Fractions 119\" width=\"215\" height=\"122\" \/><br \/>\nAnswer:<br \/>\n\\(\\frac{4}{8}\\)= \\(\\frac{1}{8}\\) + \\(\\frac{1}{8}\\) +<br \/>\n\\(\\frac{1}{8}\\) + \\(\\frac{1}{8}\\) = 4 X \\(\\frac{1}{8}\\).<\/p>\n<p>Explanation:<br \/>\nWe write \\(\\frac{4}{8}\\) in addition equation as \\(\\frac{4}{8}\\)=<br \/>\n\\(\\frac{1}{8}\\) + \\(\\frac{1}{8}\\) + \\(\\frac{1}{8}\\) +<br \/>\n\\(\\frac{1}{8}\\) and multiplication as unit fraction \\(\\frac{4}{8}\\) represents 4 parts<br \/>\nthat are \\(\\frac{1}{8}\\) of the whole, \\(\\frac{4}{8}\\) = 4 X \\(\\frac{1}{8}\\)<\/p>\n<p>Question 3.<br \/>\n\\(\\frac{7}{2}\\)<br \/>\nAnswer:<br \/>\n\\(\\frac{7}{2}\\) = \\(\\frac{1}{2}\\) + \\(\\frac{1}{2}\\) +<br \/>\n\\(\\frac{1}{2}\\) + \\(\\frac{1}{2}\\) + \\(\\frac{1}{2}\\) +<br \/>\n\\(\\frac{1}{2}\\) + \\(\\frac{1}{2}\\) = 7 X \\(\\frac{1}{2}\\).<\/p>\n<p>Explanation:<br \/>\nwe write \\(\\frac{7}{2}\\) in addition equation as\u00a0 \\(\\frac{7}{2}\\) =<br \/>\n\\(\\frac{1}{2}\\) + \\(\\frac{1}{2}\\) + \\(\\frac{1}{2}\\) + \\(\\frac{1}{2}\\)<br \/>\n+ \\(\\frac{1}{2}\\) + \\(\\frac{1}{2}\\) + \\(\\frac{1}{2}\\) = 7 X \\(\\frac{1}{2}\\)<br \/>\nand multiplication as unit fraction \\(\\frac{7}{2}\\) represents 7 parts that are<br \/>\n\\(\\frac{1}{2}\\) of the whole, \\(\\frac{7}{2}\\) = 7 X \\(\\frac{1}{2}\\).<\/p>\n<p>Question 4.<br \/>\n\\(\\frac{56}{100}\\)<br \/>\nAnswer:<br \/>\n\\(\\frac{56}{100}\\)\u00a0 = \\(\\frac{14}{25}\\) = \\(\\frac{1}{25}\\) +<br \/>\n\\(\\frac{1}{25}\\) + \\(\\frac{1}{25}\\) + \\(\\frac{1}{25}\\) +<br \/>\n\\(\\frac{1}{25}\\) + \\(\\frac{1}{25}\\) + \\(\\frac{1}{25}\\) +<br \/>\n\\(\\frac{1}{25}\\) + \\(\\frac{1}{25}\\) + \\(\\frac{1}{25}\\) +<br \/>\n\\(\\frac{1}{25}\\) + \\(\\frac{1}{25}\\) + \\(\\frac{1}{25}\\) +<br \/>\n\\(\\frac{1}{25}\\) = 14 X \\(\\frac{1}{25}\\)<\/p>\n<p>Explanation:<br \/>\n\\(\\frac{56}{100}\\) first we simplify as both numerator and denominator can be<br \/>\ndivided by 4 we get numerator as 14 and denominatior as 25 =\u00a0 \\(\\frac{14}{25}\\)<br \/>\nnow we write \\(\\frac{14}{25}\\) in addition equation as \\(\\frac{14}{25}\\) =<br \/>\n\\(\\frac{1}{25}\\) + \\(\\frac{1}{25}\\) + \\(\\frac{1}{25}\\) + \\(\\frac{1}{25}\\) +<br \/>\n\\(\\frac{1}{25}\\) + \\(\\frac{1}{25}\\) + \\(\\frac{1}{25}\\) + \\(\\frac{1}{25}\\) +<br \/>\n\\(\\frac{1}{25}\\) + \\(\\frac{1}{25}\\) + \\(\\frac{1}{25}\\) + \\(\\frac{1}{25}\\) +<br \/>\n\\(\\frac{1}{25}\\) + \\(\\frac{1}{25}\\) = 14 X \\(\\frac{1}{25}\\) and multiplication as unit fraction \\(\\frac{14}{25}\\) represents 14 parts that are \\(\\frac{1}{25}\\) of the whole,<br \/>\n\\(\\frac{14}{25}\\) = 14 X \\(\\frac{1}{25}\\) .<\/p>\n<p>Question 5.<br \/>\n<strong>Logic<\/strong><br \/>\nWhat is Newton\u2019s fraction? Write the fraction as a multiple of a unit fraction.<br \/>\n<img decoding=\"async\" loading=\"lazy\" class=\"alignnone size-full wp-image-12993\" src=\"https:\/\/ccssanswers.com\/wp-content\/uploads\/2020\/12\/Big-Ideas-Math-Answer-Key-Grade-4-Chapter-9-Multiply-Whole-Numbers-and-Fractions-120.png\" alt=\"Big Ideas Math Answer Key Grade 4 Chapter 9 Multiply Whole Numbers and Fractions 120\" width=\"227\" height=\"209\" \/><br \/>\nAnswer:<br \/>\nNewton&#8217;s fraction is 5 X \\(\\frac{1}{6}\\), The fraction is already a multiple of a unit fraction =<br \/>\n5 X \\(\\frac{1}{6}\\) , 5 is multiple and \\(\\frac{1}{6}\\) is a unit fraction.<\/p>\n<p>Explanation:<br \/>\nGiven unit fraction is one sixth of a whole is \\(\\frac{1}{6}\\) and Newton&#8217;s fraction is 5 unit fractions<br \/>\nmeans it is equal to \\(\\frac{1}{6}\\) + \\(\\frac{1}{6}\\) + \\(\\frac{1}{6}\\) +<br \/>\n\\(\\frac{1}{6}\\) + \\(\\frac{1}{6}\\) = 5 X \\(\\frac{1}{6}\\) already the<br \/>\nfraction is a multiple of a unit fraction = 5 X \\(\\frac{1}{6}\\) , 5 is multiple and<br \/>\n\\(\\frac{1}{6}\\) is a unit fraction.<\/p>\n<p><strong>9.2 Understand Multiples of Fractions<\/strong><\/p>\n<p>Write the product as a multiple of a unit fraction. Then find the product.<\/p>\n<p>Question 6.<br \/>\n<img decoding=\"async\" loading=\"lazy\" class=\"alignnone size-full wp-image-12994\" src=\"https:\/\/ccssanswers.com\/wp-content\/uploads\/2020\/12\/Big-Ideas-Math-Answer-Key-Grade-4-Chapter-9-Multiply-Whole-Numbers-and-Fractions-121.png\" alt=\"Big Ideas Math Answer Key Grade 4 Chapter 9 Multiply Whole Numbers and Fractions 121\" width=\"57\" height=\"49\" \/><br \/>\nAnswer:<br \/>\n2 X \\(\\frac{2}{4}\\) = 2 X 2 X \\(\\frac{1}{4}\\) = 4 X \\(\\frac{1}{4}\\) = \\(\\frac{4}{4}\\)= 1<\/p>\n<p>Explanation:<br \/>\nFirst we write \\(\\frac{2}{4}\\)\u00a0 as \u00a0\\(\\frac{1}{4}\\) + \\(\\frac{1}{4}\\) =<br \/>\n2 X \\(\\frac{1}{4}\\) then multiply it by 2 which is\u00a0 2 X 2 X \\(\\frac{1}{4}\\) =<br \/>\n4 X \\(\\frac{1}{4}\\) = \\(\\frac{4}{4}\\) as numerator and denominator are same<br \/>\nboth get cancelled so we get 1 , \\(\\frac{4}{4}\\) = 1.<\/p>\n<p>Question 7.<br \/>\n<img decoding=\"async\" loading=\"lazy\" class=\"alignnone size-full wp-image-12995\" src=\"https:\/\/ccssanswers.com\/wp-content\/uploads\/2020\/12\/Big-Ideas-Math-Answer-Key-Grade-4-Chapter-9-Multiply-Whole-Numbers-and-Fractions-122.png\" alt=\"Big Ideas Math Answer Key Grade 4 Chapter 9 Multiply Whole Numbers and Fractions 122\" width=\"63\" height=\"46\" \/><br \/>\nAnswer:<br \/>\n3 X \\(\\frac{9}{12}\\) = 3 X \\(\\frac{3}{4}\\) = 9 X \\(\\frac{1}{4}\\) =<br \/>\n\\(\\frac{9}{4}\\)<\/p>\n<p>Explanantion:<br \/>\nAs \\(\\frac{9}{12}\\) can be simplified as both 9,12 can go with 3 leaving numerator as<br \/>\n3 and denominator as 4= \\(\\frac{3}{4}\\), First we write \\(\\frac{3}{4}\\)\u00a0 as \u00a0\\(\\frac{1}{4}\\) +<br \/>\n\\(\\frac{1}{4}\\) + \\(\\frac{1}{4}\\) = 3 X \\(\\frac{1}{4}\\) then multiply it by 3<br \/>\nwhich is\u00a0 3 X 3 X \\(\\frac{1}{4}\\) = 9 X \\(\\frac{1}{4}\\) is multiple of unit fraction,<br \/>\nThe product is \\(\\frac{9}{4}\\) .<\/p>\n<p>Question 8.<br \/>\n<img decoding=\"async\" loading=\"lazy\" class=\"alignnone size-full wp-image-12996\" src=\"https:\/\/ccssanswers.com\/wp-content\/uploads\/2020\/12\/Big-Ideas-Math-Answer-Key-Grade-4-Chapter-9-Multiply-Whole-Numbers-and-Fractions-123.png\" alt=\"Big Ideas Math Answer Key Grade 4 Chapter 9 Multiply Whole Numbers and Fractions 123\" width=\"57\" height=\"53\" \/><br \/>\nAnswer:<br \/>\n\\(\\frac{3}{5}\\) X 4 = 12 X \\(\\frac{1}{5}\\) = \\(\\frac{12}{5}\\).<\/p>\n<p>Explanation:<br \/>\nFirst we write \\(\\frac{3}{5}\\)\u00a0 as \u00a0\\(\\frac{1}{5}\\) + \\(\\frac{1}{5}\\) +<br \/>\n\\(\\frac{1}{5}\\) = 3 X \\(\\frac{1}{5}\\) then multiply it by 4 which is<br \/>\n4 X 3 X \\(\\frac{1}{5}\\) = 12 X \\(\\frac{1}{5}\\) = \\(\\frac{12}{5}\\).<\/p>\n<p>Question 9.<br \/>\n<img decoding=\"async\" loading=\"lazy\" class=\"alignnone size-full wp-image-12997\" src=\"https:\/\/ccssanswers.com\/wp-content\/uploads\/2020\/12\/Big-Ideas-Math-Answer-Key-Grade-4-Chapter-9-Multiply-Whole-Numbers-and-Fractions-124.png\" alt=\"Big Ideas Math Answer Key Grade 4 Chapter 9 Multiply Whole Numbers and Fractions 124\" width=\"71\" height=\"51\" \/><br \/>\nAnswer:<br \/>\n\\(\\frac{8}{10}\\) X 7= \\(\\frac{4}{5}\\) X 7 = 28 X \\(\\frac{1}{5}\\) is<br \/>\nmultiple of unit fraction, The product is \\(\\frac{28}{5}\\).<\/p>\n<p>Explanantion:<br \/>\nAs \\(\\frac{8}{10}\\) can be simplified as both 8,10 can go with 2, leaving numerator as 4<br \/>\nand denominator as 5 = \\(\\frac{4}{5}\\), First we write \\(\\frac{4}{5}\\)\u00a0 as<br \/>\n\\(\\frac{1}{5}\\) + \\(\\frac{1}{5}\\) + \\(\\frac{1}{5}\\) + \\(\\frac{1}{5}\\) =<br \/>\n4 X \\(\\frac{1}{5}\\) then multiply it by 7 which is\u00a0 7 X 4 X \\(\\frac{1}{5}\\) =<br \/>\n28 X \\(\\frac{1}{5}\\) is multiple of unit fraction, The product is \\(\\frac{28}{5}\\).<\/p>\n<p>Question 10.<br \/>\n<img decoding=\"async\" loading=\"lazy\" class=\"alignnone size-full wp-image-12998\" src=\"https:\/\/ccssanswers.com\/wp-content\/uploads\/2020\/12\/Big-Ideas-Math-Answer-Key-Grade-4-Chapter-9-Multiply-Whole-Numbers-and-Fractions-125.png\" alt=\"Big Ideas Math Answer Key Grade 4 Chapter 9 Multiply Whole Numbers and Fractions 125\" width=\"62\" height=\"53\" \/><br \/>\nAnswer:<br \/>\n8 X \\(\\frac{6}{3}\\) = 8 X 2 = 16 as we got \\(\\frac{6}{3}\\) =2,<br \/>\nSo we get results as whole not in fraction.<\/p>\n<p>Explanation:<br \/>\nAs \\(\\frac{6}{3}\\) can be simplified as both can be divided by 2, leaving numerator as 2 and denominator as 1 ,\u00a0 \\(\\frac{6}{3}\\) = 2\u00a0 , now it is 8 X 2 = 16 as we got \\(\\frac{6}{3}\\) =2, so we get results as whole not in fraction.<\/p>\n<p>Question 11.<br \/>\n<img decoding=\"async\" loading=\"lazy\" class=\"alignnone size-full wp-image-12999\" src=\"https:\/\/ccssanswers.com\/wp-content\/uploads\/2020\/12\/Big-Ideas-Math-Answer-Key-Grade-4-Chapter-9-Multiply-Whole-Numbers-and-Fractions-126.png\" alt=\"Big Ideas Math Answer Key Grade 4 Chapter 9 Multiply Whole Numbers and Fractions 126\" width=\"76\" height=\"55\" \/><br \/>\nAnswer:<br \/>\n10 X \\(\\frac{30}{8}\\) = 10 X \\(\\frac{15}{4}\\) = 150 X \\(\\frac{1}{4}\\) =<br \/>\n\\(\\frac{150}{4}\\) = \\(\\frac{75}{2}\\).<\/p>\n<p>Explanation:<br \/>\nAs \\(\\frac{30}{8}\\) can be simplified as both can be divided by 2 , we get numerator as 15 and denominator as 4, \\(\\frac{30}{8}\\) = \\(\\frac{15}{4}\\) = \\(\\frac{1}{4}\\) + \\(\\frac{1}{4}\\) +<br \/>\n\\(\\frac{1}{4}\\) + \\(\\frac{1}{4}\\) + \\(\\frac{1}{4}\\) + \\(\\frac{1}{4}\\) +<br \/>\n\\(\\frac{1}{4}\\) + \\(\\frac{1}{4}\\) + \\(\\frac{1}{4}\\) + \\(\\frac{1}{4}\\) +<br \/>\n\\(\\frac{1}{4}\\) + \\(\\frac{1}{4}\\) + \\(\\frac{1}{4}\\) + \\(\\frac{1}{4}\\) +<br \/>\n\\(\\frac{1}{4}\\) = 15 X \\(\\frac{1}{4}\\) now multiply with 10 X 15 X \\(\\frac{1}{4}\\)<br \/>\n= 150 X \\(\\frac{1}{4}\\) = \\(\\frac{150}{4}\\)\u00a0 this can be further simplified as 150 and 4 both<br \/>\ncan be further divided by 2 making numerator as 75 and denominator as 2 = \\(\\frac{75}{2}\\) .<\/p>\n<p><strong>9.3 Multiply Whole Numbers and Fractions<\/strong><\/p>\n<p>Multiply<\/p>\n<p>Question 12.<br \/>\n<img decoding=\"async\" loading=\"lazy\" class=\"alignnone size-full wp-image-13000\" src=\"https:\/\/ccssanswers.com\/wp-content\/uploads\/2020\/12\/Big-Ideas-Math-Answer-Key-Grade-4-Chapter-9-Multiply-Whole-Numbers-and-Fractions-127.png\" alt=\"Big Ideas Math Answer Key Grade 4 Chapter 9 Multiply Whole Numbers and Fractions 127\" width=\"129\" height=\"52\" \/><br \/>\nAnswer:<br \/>\n2 X \\(\\frac{1}{2}\\) = \\(\\frac{2}{2}\\) = 1<br \/>\nExplanation:<br \/>\nAlready it is in unit fraction so 2 X \\(\\frac{1}{2}\\) = \\(\\frac{2}{2}\\) = 1.<\/p>\n<p>Question 13.<br \/>\n<img decoding=\"async\" loading=\"lazy\" class=\"alignnone size-full wp-image-13001\" src=\"https:\/\/ccssanswers.com\/wp-content\/uploads\/2020\/12\/Big-Ideas-Math-Answer-Key-Grade-4-Chapter-9-Multiply-Whole-Numbers-and-Fractions-128.png\" alt=\"Big Ideas Math Answer Key Grade 4 Chapter 9 Multiply Whole Numbers and Fractions 128\" width=\"125\" height=\"59\" \/><br \/>\nAnswer:<br \/>\n4 X \\(\\frac{5}{8}\\) = \\(\\frac{20}{8}\\) = \\(\\frac{10}{4}\\) =<br \/>\n\\(\\frac{5}{2}\\).<\/p>\n<p>Explanation :<br \/>\nFirst we write \\(\\frac{5}{8}\\) in unit fraction as 5 X \\(\\frac{1}{8}\\)<br \/>\nnow we multiply with whole 4 X 5 X \\(\\frac{1}{8}\\) = \\(\\frac{20}{8}\\)<br \/>\nfurther can be simplifed as 20,8 both can be divided by 4 we get numerator as 5 and denominator 2,<br \/>\ntherefore 4 X \\(\\frac{5}{8}\\) = \\(\\frac{5}{2}\\) .<\/p>\n<p>Question 14.<br \/>\n<img decoding=\"async\" loading=\"lazy\" class=\"alignnone size-full wp-image-13002\" src=\"https:\/\/ccssanswers.com\/wp-content\/uploads\/2020\/12\/Big-Ideas-Math-Answer-Key-Grade-4-Chapter-9-Multiply-Whole-Numbers-and-Fractions-129.png\" alt=\"Big Ideas Math Answer Key Grade 4 Chapter 9 Multiply Whole Numbers and Fractions 129\" width=\"119\" height=\"60\" \/><br \/>\nAnswer:<br \/>\n3 X \\(\\frac{9}{6}\\) =\u00a0\\(\\frac{9}{2}\\).<\/p>\n<p>Explanantion:<br \/>\nWe can simplify \\(\\frac{9}{6}\\) as both goes by 3 giving numerator as 3 and<br \/>\ndenominator as 2 so we get \\(\\frac{9}{6}\\) = \\(\\frac{3}{2}\\) now we write in unit fraction<br \/>\nas 3 X \\(\\frac{1}{2}\\) now we multiply by 3, 3 X 3 X \\(\\frac{1}{2}\\) =<br \/>\n9 X \\(\\frac{1}{2}\\) = \\(\\frac{9}{2}\\).<\/p>\n<p>Question 15.<br \/>\n<img decoding=\"async\" loading=\"lazy\" class=\"alignnone size-full wp-image-13003\" src=\"https:\/\/ccssanswers.com\/wp-content\/uploads\/2020\/12\/Big-Ideas-Math-Answer-Key-Grade-4-Chapter-9-Multiply-Whole-Numbers-and-Fractions-130.png\" alt=\"Big Ideas Math Answer Key Grade 4 Chapter 9 Multiply Whole Numbers and Fractions 130\" width=\"130\" height=\"63\" \/><br \/>\nAnswer:<br \/>\n5 X \u00a0\\(\\frac{7}{12}\\) = \\(\\frac{35}{12}\\).<\/p>\n<p>Explanation:<br \/>\nfirst we write \\(\\frac{7}{12}\\) as unit fraction = 7 X \\(\\frac{1}{12}\\),<br \/>\nnow we multiply with 5 as 5 X 7 X \\(\\frac{1}{12}\\) = 35 X \\(\\frac{1}{12}\\) =<br \/>\n\\(\\frac{35}{12}\\) .<\/p>\n<p>Question 16.<br \/>\n<img decoding=\"async\" loading=\"lazy\" class=\"alignnone size-full wp-image-13004\" src=\"https:\/\/ccssanswers.com\/wp-content\/uploads\/2020\/12\/Big-Ideas-Math-Answer-Key-Grade-4-Chapter-9-Multiply-Whole-Numbers-and-Fractions-131.png\" alt=\"Big Ideas Math Answer Key Grade 4 Chapter 9 Multiply Whole Numbers and Fractions 131\" width=\"128\" height=\"60\" \/><br \/>\nAnswer:<br \/>\n7 X \\(\\frac{30}{100}\\) = 7 X \\(\\frac{3}{10}\\) = \\(\\frac{21}{10}\\).<\/p>\n<p>Explanation:<br \/>\nWe can simplify \\(\\frac{30}{100}\\) as both goes by 10 giving numerator as 3 and<br \/>\ndenominator as 10 so we get \\(\\frac{3}{10}\\)\u00a0 now we write in unit fraction as<br \/>\n3 X \\(\\frac{1}{10}\\) and multiply by 7 , 7 X 3 X \\(\\frac{1}{10}\\)\u00a0 = 21 X \\(\\frac{1}{10}\\)<br \/>\n=\u00a0 \\(\\frac{21}{10}\\) .<\/p>\n<p>Question 17.<br \/>\n<img decoding=\"async\" loading=\"lazy\" class=\"alignnone size-full wp-image-13005\" src=\"https:\/\/ccssanswers.com\/wp-content\/uploads\/2020\/12\/Big-Ideas-Math-Answer-Key-Grade-4-Chapter-9-Multiply-Whole-Numbers-and-Fractions-132.png\" alt=\"Big Ideas Math Answer Key Grade 4 Chapter 9 Multiply Whole Numbers and Fractions 132\" width=\"123\" height=\"60\" \/><br \/>\nAnswer:<br \/>\n\\(\\frac{8}{4}\\) X 9 = 2 X 9 = 18.<\/p>\n<p>Explanantion:<br \/>\nWe can simplify \\(\\frac{8}{4}\\) as both goes by 4 giving numerator as 2 and denominator<br \/>\nas 1 so we get 2 as whole, now we multiply with 9 we get 2 X 9 = 18.<\/p>\n<p><strong>9.4 Multiply Whole Numbers and Mixed Numbers<\/strong><\/p>\n<p>Multiply<\/p>\n<p>Question 18.<br \/>\n<img decoding=\"async\" loading=\"lazy\" class=\"alignnone size-full wp-image-13006\" src=\"https:\/\/ccssanswers.com\/wp-content\/uploads\/2020\/12\/Big-Ideas-Math-Answer-Key-Grade-4-Chapter-9-Multiply-Whole-Numbers-and-Fractions-133.png\" alt=\"Big Ideas Math Answer Key Grade 4 Chapter 9 Multiply Whole Numbers and Fractions 133\" width=\"132\" height=\"59\" \/><br \/>\nAnswer:<br \/>\n<img decoding=\"async\" loading=\"lazy\" class=\"alignnone size-full wp-image-13006\" src=\"https:\/\/ccssanswers.com\/wp-content\/uploads\/2020\/12\/Big-Ideas-Math-Answer-Key-Grade-4-Chapter-9-Multiply-Whole-Numbers-and-Fractions-133.png\" alt=\"Big Ideas Math Answer Key Grade 4 Chapter 9 Multiply Whole Numbers and Fractions 133\" width=\"132\" height=\"59\" \/>= \\(\\frac{5}{2}\\)= 2 \\(\\frac{1}{2}\\)<br \/>\nExplanation:<br \/>\nFirst we write the mixed number as a fraction then multiply, so 1 \\(\\frac{1}{4}\\)=<br \/>\n1 + \\(\\frac{1}{4}\\)= (1 X 4 + 1) by 4 = \\(\\frac{5}{4}\\) now we multiply it with the whole,<br \/>\n2 X \\(\\frac{5}{4}\\) now we write in unit fraction and multiply\u00a0 2 X 5 X \\(\\frac{1}{4}\\)=<br \/>\n10 X \\(\\frac{1}{4}\\) = \\(\\frac{10}{4}\\) further we can simplify as 10,4<br \/>\nboth can be divided by 2 we get numerator as 5 and denominator as 2, \\(\\frac{5}{2}\\)<br \/>\nas numerator is greater than denominator we can write in mixed fraction as 2 goes in 2 times.<br \/>\n2 will be our whole number 2<span id=\"MathJax-Element-7-Frame\" class=\"mjx-chtml MathJax_CHTML\"><span id=\"MJXc-Node-36\" class=\"mjx-math\"><span id=\"MJXc-Node-37\" class=\"mjx-mrow\"><span id=\"MJXc-Node-38\" class=\"mjx-mstyle\"><span id=\"MJXc-Node-39\" class=\"mjx-mrow\"><span id=\"MJXc-Node-40\" class=\"mjx-mn\"><span class=\"mjx-char MJXc-TeX-main-R\"> X 2<\/span><\/span><\/span><\/span><\/span><\/span><\/span> is\u00a0<span id=\"MathJax-Element-8-Frame\" class=\"mjx-chtml MathJax_CHTML\"><span id=\"MJXc-Node-43\" class=\"mjx-math\"><span id=\"MJXc-Node-44\" class=\"mjx-mrow\"><span id=\"MJXc-Node-45\" class=\"mjx-mstyle\"><span id=\"MJXc-Node-46\" class=\"mjx-mrow\"><span id=\"MJXc-Node-47\" class=\"mjx-mn\"><span class=\"mjx-char MJXc-TeX-main-R\">4<\/span><\/span><\/span><\/span><\/span><\/span><\/span> and we have 1 left over (5<span id=\"MathJax-Element-10-Frame\" class=\"mjx-chtml MathJax_CHTML\"><span id=\"MJXc-Node-53\" class=\"mjx-math\"><span id=\"MJXc-Node-54\" class=\"mjx-mrow\"><span id=\"MJXc-Node-55\" class=\"mjx-mstyle\"><span id=\"MJXc-Node-56\" class=\"mjx-mrow\"><span id=\"MJXc-Node-58\" class=\"mjx-mo\"><span class=\"mjx-char MJXc-TeX-main-R\">\u2212<\/span><\/span><span id=\"MJXc-Node-59\" class=\"mjx-mn\"><span class=\"mjx-char MJXc-TeX-main-R\">4<\/span><\/span><\/span><\/span><\/span><\/span><\/span>), 1 will be our numerator and our<br \/>\ndenominator will stay the same 2, \\(\\frac{5}{2}\\)= 2 \\(\\frac{1}{2}\\).<\/p>\n<p>Question 19.<br \/>\n<img decoding=\"async\" loading=\"lazy\" class=\"alignnone size-full wp-image-13007\" src=\"https:\/\/ccssanswers.com\/wp-content\/uploads\/2020\/12\/Big-Ideas-Math-Answer-Key-Grade-4-Chapter-9-Multiply-Whole-Numbers-and-Fractions-134.png\" alt=\"Big Ideas Math Answer Key Grade 4 Chapter 9 Multiply Whole Numbers and Fractions 134\" width=\"150\" height=\"63\" \/><br \/>\nAnswer:<br \/>\n<img decoding=\"async\" loading=\"lazy\" class=\"alignnone size-full wp-image-13007\" src=\"https:\/\/ccssanswers.com\/wp-content\/uploads\/2020\/12\/Big-Ideas-Math-Answer-Key-Grade-4-Chapter-9-Multiply-Whole-Numbers-and-Fractions-134.png\" alt=\"Big Ideas Math Answer Key Grade 4 Chapter 9 Multiply Whole Numbers and Fractions 134\" width=\"150\" height=\"63\" \/>= \\(\\frac{69}{6}\\) = \\(\\frac{23}{2}\\) = 11 \\(\\frac{1}{2}\\)<br \/>\nExplanation:<br \/>\nFirst we write the mixed number as a fraction then multiply, so 3 \\(\\frac{10}{12}\\)=<br \/>\n( 3 X 12 + 10 ) by 12 = \\(\\frac{46}{12}\\) this can be further simplified as both 46,12 goes by 2<br \/>\nwe get numerator as 23 and denominator as 6 , \\(\\frac{23}{6}\\) now we multiply by 3 =<br \/>\n3 X \\(\\frac{23}{6}\\) = \\(\\frac{69}{6}\\) it can be more simplified as both 69,6 goes by 3<br \/>\nwe get numerator as 23 and denominator as 2 making \\(\\frac{69}{6}\\) as \\(\\frac{23}{2}\\)<br \/>\nas numerator is greater than denominator we can write in mixed fraction as 2 goes in 11 times.<br \/>\n11 will be our whole number 2<span id=\"MathJax-Element-7-Frame\" class=\"mjx-chtml MathJax_CHTML\"><span id=\"MJXc-Node-36\" class=\"mjx-math\"><span id=\"MJXc-Node-37\" class=\"mjx-mrow\"><span id=\"MJXc-Node-38\" class=\"mjx-mstyle\"><span id=\"MJXc-Node-39\" class=\"mjx-mrow\"><span id=\"MJXc-Node-40\" class=\"mjx-mn\"><span class=\"mjx-char MJXc-TeX-main-R\"> X 11<\/span><\/span><\/span><\/span><\/span><\/span><\/span> is 22 and we have 1 left over (23<span id=\"MathJax-Element-10-Frame\" class=\"mjx-chtml MathJax_CHTML\"><span id=\"MJXc-Node-53\" class=\"mjx-math\"><span id=\"MJXc-Node-54\" class=\"mjx-mrow\"><span id=\"MJXc-Node-55\" class=\"mjx-mstyle\"><span id=\"MJXc-Node-56\" class=\"mjx-mrow\"><span id=\"MJXc-Node-58\" class=\"mjx-mo\"><span class=\"mjx-char MJXc-TeX-main-R\">\u221222<\/span><\/span><\/span><\/span><\/span><\/span><\/span>), 1 will be our numerator<br \/>\nand our denominator will stay the same 2, \\(\\frac{23}{2}\\) = 11 \\(\\frac{1}{2}\\).<\/p>\n<p>Question 20.<br \/>\n<img decoding=\"async\" loading=\"lazy\" class=\"alignnone size-full wp-image-13008\" src=\"https:\/\/ccssanswers.com\/wp-content\/uploads\/2020\/12\/Big-Ideas-Math-Answer-Key-Grade-4-Chapter-9-Multiply-Whole-Numbers-and-Fractions-135.png\" alt=\"Big Ideas Math Answer Key Grade 4 Chapter 9 Multiply Whole Numbers and Fractions 135\" width=\"127\" height=\"53\" \/><br \/>\nAnswer:<br \/>\n<img decoding=\"async\" loading=\"lazy\" class=\"alignnone size-full wp-image-13008\" src=\"https:\/\/ccssanswers.com\/wp-content\/uploads\/2020\/12\/Big-Ideas-Math-Answer-Key-Grade-4-Chapter-9-Multiply-Whole-Numbers-and-Fractions-135.png\" alt=\"Big Ideas Math Answer Key Grade 4 Chapter 9 Multiply Whole Numbers and Fractions 135\" width=\"127\" height=\"53\" \/>= \\(\\frac{84}{8}\\) = \\(\\frac{21}{2}\\) = 10 \\(\\frac{1}{2}\\).<br \/>\nExplanantion:<\/p>\n<p>First we write the mixed number as a fraction then multiply, so 2 \\(\\frac{5}{8}\\) =<br \/>\n( 2 X 8 + 5 ) by 8 = \\(\\frac{21}{8}\\) now we multiply by 4 we get 4 X \\(\\frac{21}{8}\\) =<br \/>\n4 X 21 X \\(\\frac{1}{8}\\) = 84 X \\(\\frac{1}{8}\\) =\\(\\frac{84}{8}\\)<br \/>\nfurther can be simplified as both 84,8 goes by 4 we get numerator as 21 and denominator as 2<br \/>\n=\\(\\frac{21}{2}\\) as numerator is greater than denominator we can write in mixed fraction<br \/>\nas 2 goes in 10 times. 10 will be our whole number 2<span id=\"MathJax-Element-7-Frame\" class=\"mjx-chtml MathJax_CHTML\"><span id=\"MJXc-Node-36\" class=\"mjx-math\"><span id=\"MJXc-Node-37\" class=\"mjx-mrow\"><span id=\"MJXc-Node-38\" class=\"mjx-mstyle\"><span id=\"MJXc-Node-39\" class=\"mjx-mrow\"><span id=\"MJXc-Node-40\" class=\"mjx-mn\"><span class=\"mjx-char MJXc-TeX-main-R\"> X 10<\/span><\/span><\/span><\/span><\/span><\/span><\/span> is 20 and we have 1 left over (21<span id=\"MathJax-Element-10-Frame\" class=\"mjx-chtml MathJax_CHTML\"><span id=\"MJXc-Node-53\" class=\"mjx-math\"><span id=\"MJXc-Node-54\" class=\"mjx-mrow\"><span id=\"MJXc-Node-55\" class=\"mjx-mstyle\"><span id=\"MJXc-Node-56\" class=\"mjx-mrow\"><span id=\"MJXc-Node-58\" class=\"mjx-mo\"><span class=\"mjx-char MJXc-TeX-main-R\">\u221220<\/span><\/span><\/span><\/span><\/span><\/span><\/span>),<br \/>\n1 will be our numerator and our denominator will stay the same 2,<br \/>\n\\(\\frac{21}{2}\\) = 10 \\(\\frac{1}{2}\\).<\/p>\n<p>Question 21.<br \/>\n<img decoding=\"async\" loading=\"lazy\" class=\"alignnone size-full wp-image-13009\" src=\"https:\/\/ccssanswers.com\/wp-content\/uploads\/2020\/12\/Big-Ideas-Math-Answer-Key-Grade-4-Chapter-9-Multiply-Whole-Numbers-and-Fractions-136.png\" alt=\"Big Ideas Math Answer Key Grade 4 Chapter 9 Multiply Whole Numbers and Fractions 136\" width=\"130\" height=\"61\" \/><br \/>\nAnswer:<br \/>\n<img decoding=\"async\" loading=\"lazy\" class=\"alignnone size-full wp-image-13009\" src=\"https:\/\/ccssanswers.com\/wp-content\/uploads\/2020\/12\/Big-Ideas-Math-Answer-Key-Grade-4-Chapter-9-Multiply-Whole-Numbers-and-Fractions-136.png\" alt=\"Big Ideas Math Answer Key Grade 4 Chapter 9 Multiply Whole Numbers and Fractions 136\" width=\"130\" height=\"61\" \/>= \\(\\frac{40}{3}\\) = 13 \\(\\frac{1}{3}\\)<br \/>\nExplanation:<br \/>\nFirst we write the mixed number as a fraction then multiply, so 2 \\(\\frac{4}{6}\\) =<br \/>\n( 2 X 6 + 4 ) by 6 = \\(\\frac{16}{6}\\) this can be simplified as 16,6 both goes by 2<br \/>\nwe get numerator as 8 and denominator as 3 we get \u00a0\\(\\frac{8}{3}\\)<br \/>\nnow we multiply by 5 we get 5 X \\(\\frac{8}{3}\\) = 5 X 8 X \\(\\frac{1}{3}\\) =<br \/>\n40 X \\(\\frac{1}{3}\\) = \\(\\frac{40}{3}\\) as numerator is greater than denominator<br \/>\nwe can write in mixed fraction as 3 goes in 13 times. 13 will be our whole number 3<span id=\"MathJax-Element-7-Frame\" class=\"mjx-chtml MathJax_CHTML\"><span id=\"MJXc-Node-36\" class=\"mjx-math\"><span id=\"MJXc-Node-37\" class=\"mjx-mrow\"><span id=\"MJXc-Node-38\" class=\"mjx-mstyle\"><span id=\"MJXc-Node-39\" class=\"mjx-mrow\"><span id=\"MJXc-Node-40\" class=\"mjx-mn\"><span class=\"mjx-char MJXc-TeX-main-R\"> X 13<\/span><\/span><\/span><\/span><\/span><\/span><\/span> is 39 and<br \/>\nwe have 1 left over (40<span id=\"MathJax-Element-10-Frame\" class=\"mjx-chtml MathJax_CHTML\"><span id=\"MJXc-Node-53\" class=\"mjx-math\"><span id=\"MJXc-Node-54\" class=\"mjx-mrow\"><span id=\"MJXc-Node-55\" class=\"mjx-mstyle\"><span id=\"MJXc-Node-56\" class=\"mjx-mrow\"><span id=\"MJXc-Node-58\" class=\"mjx-mo\"><span class=\"mjx-char MJXc-TeX-main-R\">\u221239<\/span><\/span><\/span><\/span><\/span><\/span><\/span>), 1 will be our numerator and our denominator will stay the same 3,<br \/>\nwe get mixed fraction as 13 \\(\\frac{1}{3}\\) .<\/p>\n<p>Question 22.<br \/>\n<img decoding=\"async\" loading=\"lazy\" class=\"alignnone size-full wp-image-13010\" src=\"https:\/\/ccssanswers.com\/wp-content\/uploads\/2020\/12\/Big-Ideas-Math-Answer-Key-Grade-4-Chapter-9-Multiply-Whole-Numbers-and-Fractions-137.png\" alt=\"Big Ideas Math Answer Key Grade 4 Chapter 9 Multiply Whole Numbers and Fractions 137\" width=\"133\" height=\"65\" \/><br \/>\nAnswer:<br \/>\n<img decoding=\"async\" loading=\"lazy\" class=\"alignnone size-full wp-image-13010\" src=\"https:\/\/ccssanswers.com\/wp-content\/uploads\/2020\/12\/Big-Ideas-Math-Answer-Key-Grade-4-Chapter-9-Multiply-Whole-Numbers-and-Fractions-137.png\" alt=\"Big Ideas Math Answer Key Grade 4 Chapter 9 Multiply Whole Numbers and Fractions 137\" width=\"133\" height=\"65\" \/>= \\(\\frac{140}{3}\\)\u00a0 = 46 \\(\\frac{2}{3}\\)<br \/>\nExplanation:<br \/>\nFirst we write the mixed number as a fraction then multiply, so 6 \\(\\frac{2}{3}\\) =<br \/>\n( 6 X 3 + 2 ) by 3 = \\(\\frac{20}{3}\\)\u00a0 now we multiply by 7\u00a0 X \\(\\frac{20}{3}\\) =<br \/>\n7 X 20 x \\(\\frac{1}{3}\\)\u00a0 = 140 X \\(\\frac{1}{3}\\) =\\(\\frac{140}{3}\\)<br \/>\nas numerator is greater than denominator we can write in mixed fraction as 3 goes in 46 times.<br \/>\n46 will be our whole number 3<span id=\"MathJax-Element-7-Frame\" class=\"mjx-chtml MathJax_CHTML\"><span id=\"MJXc-Node-36\" class=\"mjx-math\"><span id=\"MJXc-Node-37\" class=\"mjx-mrow\"><span id=\"MJXc-Node-38\" class=\"mjx-mstyle\"><span id=\"MJXc-Node-39\" class=\"mjx-mrow\"><span id=\"MJXc-Node-40\" class=\"mjx-mn\"><span class=\"mjx-char MJXc-TeX-main-R\"> X 46<\/span><\/span><\/span><\/span><\/span><\/span><\/span> is 138 and we have 2 left over (140<span id=\"MathJax-Element-10-Frame\" class=\"mjx-chtml MathJax_CHTML\"><span id=\"MJXc-Node-53\" class=\"mjx-math\"><span id=\"MJXc-Node-54\" class=\"mjx-mrow\"><span id=\"MJXc-Node-55\" class=\"mjx-mstyle\"><span id=\"MJXc-Node-56\" class=\"mjx-mrow\"><span id=\"MJXc-Node-58\" class=\"mjx-mo\"><span class=\"mjx-char MJXc-TeX-main-R\">\u2212138<\/span><\/span><\/span><\/span><\/span><\/span><\/span>), 2 will be our numerator<br \/>\nand our denominator will stay the same 3, we get mixed fraction as 46 \\(\\frac{2}{3}\\) .<\/p>\n<p>Question 23.<br \/>\n<img decoding=\"async\" loading=\"lazy\" class=\"alignnone size-full wp-image-13011\" src=\"https:\/\/ccssanswers.com\/wp-content\/uploads\/2020\/12\/Big-Ideas-Math-Answer-Key-Grade-4-Chapter-9-Multiply-Whole-Numbers-and-Fractions-138.png\" alt=\"Big Ideas Math Answer Key Grade 4 Chapter 9 Multiply Whole Numbers and Fractions 138\" width=\"137\" height=\"64\" \/><br \/>\nAnswer:<br \/>\n<img decoding=\"async\" loading=\"lazy\" class=\"alignnone size-full wp-image-13011\" src=\"https:\/\/ccssanswers.com\/wp-content\/uploads\/2020\/12\/Big-Ideas-Math-Answer-Key-Grade-4-Chapter-9-Multiply-Whole-Numbers-and-Fractions-138.png\" alt=\"Big Ideas Math Answer Key Grade 4 Chapter 9 Multiply Whole Numbers and Fractions 138\" width=\"137\" height=\"64\" \/>= \\(\\frac{470}{5}\\) = 94<br \/>\nExplanation:<br \/>\nFirst we write the mixed number as a fraction then multiply, so 9 \\(\\frac{2}{5}\\) =<br \/>\n( 9 X 5 + 2 ) by 5 = \\(\\frac{47}{5}\\) now we multiply by 10 = 10 X \\(\\frac{47}{5}\\) =<br \/>\n\\(\\frac{470}{5}\\) this can be further simplified as both can be divided by 5 we get numerator as<br \/>\n94 and denominator as 1 so we get only whole number 94.<\/p>\n<p><strong>9.5 Problem Solving: Fraction Operations<\/strong><\/p>\n<p>Question 24.<br \/>\n<strong>Modeling Real Life<\/strong><br \/>\nYour friend rides her bike \\(\\frac{2}{6}\\) mile to your house and \\(\\frac{2}{6}\\)<br \/>\nmile back home 4 times in 1 week. How far does she bike in all?<br \/>\nAnswer:<br \/>\nMy friend rides her bike by \\(\\frac{8}{3}\\) miles or 2 \\(\\frac{2}{3}\\) miles.<\/p>\n<p>Explanation:<br \/>\nGiven friend rides her bike \\(\\frac{2}{6}\\) mile to your house and \\(\\frac{2}{6}\\) mile<br \/>\nback home, first we calculate for 1 time, so first we will add \\(\\frac{2}{6}\\) + \\(\\frac{2}{6}\\)<br \/>\nas both have same denominators we will add numerators as ( 2 + 2 = 4 ).<br \/>\nSo we get \\(\\frac{4}{6}\\) miles for 1 time , now she rides 4 times means 4 X \\(\\frac{4}{6}\\) =<br \/>\n\\(\\frac{16}{6}\\) this can be further simplified as 16,6 both goes by 2 we get numerator as 8 and<br \/>\ndenominator as 3 = \\(\\frac{8}{3}\\) as numerator is greater than denominator we can write in<br \/>\nmixed fraction as 3 goes in 2 times. 2 will be our whole number 3<span id=\"MathJax-Element-7-Frame\" class=\"mjx-chtml MathJax_CHTML\"><span id=\"MJXc-Node-36\" class=\"mjx-math\"><span id=\"MJXc-Node-37\" class=\"mjx-mrow\"><span id=\"MJXc-Node-38\" class=\"mjx-mstyle\"><span id=\"MJXc-Node-39\" class=\"mjx-mrow\"><span id=\"MJXc-Node-40\" class=\"mjx-mn\"><span class=\"mjx-char MJXc-TeX-main-R\">\u00a0X 2<\/span><\/span><\/span><\/span><\/span><\/span><\/span> is 6 and<br \/>\nwe have 2 left over (8<span id=\"MathJax-Element-10-Frame\" class=\"mjx-chtml MathJax_CHTML\"><span id=\"MJXc-Node-53\" class=\"mjx-math\"><span id=\"MJXc-Node-54\" class=\"mjx-mrow\"><span id=\"MJXc-Node-55\" class=\"mjx-mstyle\"><span id=\"MJXc-Node-56\" class=\"mjx-mrow\"><span id=\"MJXc-Node-58\" class=\"mjx-mo\"><span class=\"mjx-char MJXc-TeX-main-R\">\u22126<\/span><\/span><\/span><\/span><\/span><\/span><\/span>), 2 will be our numerator and our denominator will stay the same 3,<br \/>\nwe get mixed fraction as 2 \\(\\frac{2}{3}\\) miles.<\/p>\n<p><em>Conclusion:<\/em><\/p>\n<p>Access the links given in the Big Ideas Math Book 4th Grade Answer Key Chapter 9 Multiply Whole Numbers and Fractions and practice well for the exams. We have solved all the questions in an easy and simple manner. We hope the information provided in this article has brought a smile to your face. Share Big Ideas Math Grade 4 Answer Key Chapter 9 Multiply Whole Numbers and Fractions.<\/p>\n","protected":false},"excerpt":{"rendered":"<p>Download Big Ideas Math Answers Grade 4 Chapter 9 Multiply Whole Numbers and Fractions for free of cost. We are here to help you to overcome the difficulties in maths. Enhance your math skills by practicing the problems from our Big Ideas Math Answers Grade 4 Chapter 9 Multiply Whole Numbers and Fractions. 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