{"id":13130,"date":"2022-04-01T09:29:44","date_gmt":"2022-04-01T03:59:44","guid":{"rendered":"https:\/\/ccssmathanswers.com\/?p=13130"},"modified":"2022-04-07T11:10:43","modified_gmt":"2022-04-07T05:40:43","slug":"big-ideas-math-answers-grade-4-chapter-7","status":"publish","type":"post","link":"https:\/\/bigideasmathanswers.com\/big-ideas-math-answers-grade-4-chapter-7\/","title":{"rendered":"Big Ideas Math Answers Grade 4 Chapter 7 Understand Fraction Equivalence and Comparison"},"content":{"rendered":"<p>Other than marks it is important for the students to understand the in-depth concepts in math. So, make your students learn the real-time examples along with learning the concepts. We have given questions with real-time problems so that it will be easy to understand the concept deeply. Refer to our Big Ideas Math Answers Grade 4 Chapter 7 Understand Fraction Equivalence and Comparison for a better understanding of the concept. Keeping the growth of the students in mind our team has prepared the <a href=\"https:\/\/bigideasmathanswers.com\/big-ideas-math-answers-grade-4\/\">Big Ideas Math Answers Grade 4<\/a> Chapter 7 Understand Fraction Equivalence and Comparison topic-wise.<\/p>\n<h2>Big Ideas 4th Grade Math Book Chapter 7 Understand Fraction Equivalence and Comparison Answer Key<\/h2>\n<p>Start your preparation with the Big Ideas 4th Grade Math Book Answer Key. Know your strengths and weaknesses and concentrate on the weak concepts to become a math expert. Find out different problems with a detailed explanation here. We have included problems on every topic individually. therefore, preparing with our Big Ideas Math Book 4th Grade Solution Key Chapter 7 Understand Fraction Equivalence and Comparison is easy and quick. Click on the below-given links and begin practicing the problems.<\/p>\n<p><strong>Lesson: 1 Model Equivalent Fractions<\/strong><\/p>\n<ul>\n<li><a href=\"#Lesson 7.1_Model_Equivalent_Fractions\">Lesson 7.1 Model Equivalent Fractions<\/a><\/li>\n<li><a href=\"#Model_Equivalent_Fractions_Homework_&amp;_Practice_7.1\">Model Equivalent Fractions Homework &amp; Practice 7.1<\/a><\/li>\n<\/ul>\n<p><strong>Lesson: 2 Generate Equivalent Fractions by Multiplying<\/strong><\/p>\n<ul>\n<li><a href=\"#Lesson_7.2_Generate_Equivalent_Fractions_by_Multiplying\">Lesson 7.2 Generate Equivalent Fractions by Multiplying<\/a><\/li>\n<li><a href=\"#Generate_Equivalent_Fractions_by_Multiplying_Homework_&amp;_Practice_7.2\">Generate Equivalent Fractions by Multiplying Homework &amp; Practice 7.2<\/a><\/li>\n<\/ul>\n<p><strong>Lesson: 3 Generate Equivalent Fractions by Dividing<\/strong><\/p>\n<ul>\n<li><a href=\"#Lesson_7.3_Generate_Equivalent_Fractions_by_Dividing\">Lesson 7.3 Generate Equivalent Fractions by Dividing<\/a><\/li>\n<li><a href=\"#Generate_Equivalent_Fractions_by_Dividing_Homework_&amp;_Practice_7.3\">Generate Equivalent Fractions by Dividing Homework &amp; Practice 7.3<\/a><\/li>\n<\/ul>\n<p><strong>Lesson: 4 Compare Fractions Using Benchmarks<\/strong><\/p>\n<ul>\n<li><a href=\"#Lesson_7.4_Compare_Fractions_Using_Benchmarks\">Lesson 7.4 Compare Fractions Using Benchmarks<\/a><\/li>\n<li><a href=\"#Compare_Fractions_Using_Benchmarks_Homework_&amp;_Practice_7.4\">Compare Fractions Using Benchmarks Homework &amp; Practice 7.4<\/a><\/li>\n<\/ul>\n<p><strong>Lesson: 5 Compare Fractions<\/strong><\/p>\n<ul>\n<li><a href=\"#Lesson_7.5_Compare_Fractions\">Lesson 7.5 Compare Fractions<\/a><\/li>\n<li><a href=\"#Compare_Fractions_Practice_7.5\">Compare Fractions Homework &amp; Practice 7.5<\/a><\/li>\n<\/ul>\n<p><strong>Performance Task<\/strong><\/p>\n<ul>\n<li><a href=\"#Understand_Fraction_Equivalence_and_Comparison_Performance_Task\">Understand Fraction Equivalence and Comparison Performance Task<\/a><\/li>\n<li><a href=\"#Understand_Fraction_Equivalence_and_Comparison_Activity\">Understand Fraction Equivalence and Comparison Activity<\/a><\/li>\n<li><a href=\"#Understand_Fraction_Equivalence_and_Comparison_Chapter_Practice\">Understand Fraction Equivalence and Comparison Chapter Practice<\/a><\/li>\n<li><a href=\"#Understand_Fraction_Equivalence_and_Comparison_Cumulative_Practice\">Understand Fraction Equivalence and Comparison of Cumulative Practice<\/a><\/li>\n<li><a href=\"#Understand_Fraction_Equivalence_and_Comparison_STEAM_Performance_Task\">Understand Fraction Equivalence and Comparison STEAM Performance Task<\/a><\/li>\n<\/ul>\n<h3><a id=\"Lesson 7.1_Model_Equivalent_Fractions\"><\/a>Lesson 7.1 Model Equivalent Fractions<\/h3>\n<p><strong>Explore and Grow<\/strong><\/p>\n<p>Use the model to write fractions that are the same size as \\(\\frac{1}{2}\\).<br \/>\n<img loading=\"lazy\" class=\"alignnone size-full wp-image-13131\" src=\"https:\/\/ccssmathanswers.com\/wp-content\/uploads\/2020\/12\/Big-Ideas-Math-Answer-Key-Grade-4-Chapter-7-Understand-Fraction-Equivalence-and-Comparison-7.1-1.png\" alt=\"Big Ideas Math Answer Key Grade 4 Chapter 7 Understand Fraction Equivalence and Comparison 7.1 1\" width=\"582\" height=\"309\" srcset=\"https:\/\/bigideasmathanswers.com\/wp-content\/uploads\/2020\/12\/Big-Ideas-Math-Answer-Key-Grade-4-Chapter-7-Understand-Fraction-Equivalence-and-Comparison-7.1-1.png 582w, https:\/\/bigideasmathanswers.com\/wp-content\/uploads\/2020\/12\/Big-Ideas-Math-Answer-Key-Grade-4-Chapter-7-Understand-Fraction-Equivalence-and-Comparison-7.1-1-300x159.png 300w\" sizes=\"(max-width: 582px) 100vw, 582px\" \/><\/p>\n<p>Answer: Using the model, the fractions that have the same size as \\(\\frac{1}{2}\\) are:<br \/>\n\\(\\frac{2}{4}\\), \\(\\frac{3}{6}\\), \\(\\frac{4}{8}\\), \\(\\frac{6}{12}\\)<\/p>\n<p>Explanation:<br \/>\nGiven model is:<br \/>\n<img loading=\"lazy\" class=\"alignnone size-full wp-image-13131\" src=\"https:\/\/ccssmathanswers.com\/wp-content\/uploads\/2020\/12\/Big-Ideas-Math-Answer-Key-Grade-4-Chapter-7-Understand-Fraction-Equivalence-and-Comparison-7.1-1.png\" alt=\"Big Ideas Math Answer Key Grade 4 Chapter 7 Understand Fraction Equivalence and Comparison 7.1 1\" width=\"582\" height=\"309\" srcset=\"https:\/\/bigideasmathanswers.com\/wp-content\/uploads\/2020\/12\/Big-Ideas-Math-Answer-Key-Grade-4-Chapter-7-Understand-Fraction-Equivalence-and-Comparison-7.1-1.png 582w, https:\/\/bigideasmathanswers.com\/wp-content\/uploads\/2020\/12\/Big-Ideas-Math-Answer-Key-Grade-4-Chapter-7-Understand-Fraction-Equivalence-and-Comparison-7.1-1-300x159.png 300w\" sizes=\"(max-width: 582px) 100vw, 582px\" \/><br \/>\nIn the above table, the whole 1 is divided in to different fractions like \\(\\frac{1}{2}\\),<br \/>\n\\(\\frac{1}{3}\\), \\(\\frac{1}{4}\\), \\(\\frac{1}{5}\\), \\(\\frac{1}{6}\\),<br \/>\n\\(\\frac{1}{8}\\), \\(\\frac{1}{10}\\), and \\(\\frac{1}{12}\\)<br \/>\nSo,<br \/>\nFrom this table, the fractions that give us the same size as of \\(\\frac{1}{2}\\) are:<br \/>\n\\(\\frac{2}{4}\\), \\(\\frac{3}{6}\\), \\(\\frac{4}{8}\\), \\(\\frac{6}{12}\\)<\/p>\n<p>Hence, from the above,<br \/>\nWe can conclude that the fractions that are having the same size as \\(\\frac{1}{2}\\) are:<br \/>\n\\(\\frac{2}{4}\\), \\(\\frac{3}{6}\\), \\(\\frac{4}{8}\\), \\(\\frac{6}{12}\\)<\/p>\n<p><strong>Reasoning<\/strong><br \/>\nCan you write a fraction with a denominator of 12 that is to the same size as \\(\\frac{2}{3}\\) ? Explain.<\/p>\n<p>Answer: The fraction with the denominator 12 that is to the same size as \\(\\frac{2}{3}\\) is:<br \/>\n\\(\\frac{8}{12}\\)<\/p>\n<p>Explanation:<br \/>\nThe given model is:<br \/>\n<img loading=\"lazy\" class=\"alignnone size-full wp-image-13131\" src=\"https:\/\/ccssmathanswers.com\/wp-content\/uploads\/2020\/12\/Big-Ideas-Math-Answer-Key-Grade-4-Chapter-7-Understand-Fraction-Equivalence-and-Comparison-7.1-1.png\" alt=\"Big Ideas Math Answer Key Grade 4 Chapter 7 Understand Fraction Equivalence and Comparison 7.1 1\" width=\"582\" height=\"309\" srcset=\"https:\/\/bigideasmathanswers.com\/wp-content\/uploads\/2020\/12\/Big-Ideas-Math-Answer-Key-Grade-4-Chapter-7-Understand-Fraction-Equivalence-and-Comparison-7.1-1.png 582w, https:\/\/bigideasmathanswers.com\/wp-content\/uploads\/2020\/12\/Big-Ideas-Math-Answer-Key-Grade-4-Chapter-7-Understand-Fraction-Equivalence-and-Comparison-7.1-1-300x159.png 300w\" sizes=\"(max-width: 582px) 100vw, 582px\" \/><br \/>\nFrom the above table, the fractions having denominator 12 have only 1 row.<br \/>\nBut, we want the same value of \\(\\frac{2}{3}\\) by having the denominator 12<br \/>\nSo, from the table,<br \/>\nWhen we add all \\(\\frac{1}{12}\\), we will get the value \\(\\frac{8}{12}\\)<br \/>\nSo,<br \/>\nThe value of \\(\\frac{2}{3}\\) is equal to the \\(\\frac{8}{12}\\)<br \/>\nHence, from the above,<br \/>\nWe can conclude that the fraction with denominator 12 that is having the same size as \\(\\frac{2}{3}\\) is:<br \/>\n\\(\\frac{8}{12}\\)<\/p>\n<p><strong>Think and Grow: Model Equivalent Fractions<\/strong><\/p>\n<p>Two or more numbers that have the same value are. Two or equivalent more fractions that name the same part of a whole are equivalent. Equivalent fractions name the same point on a number line. fractions.<br \/>\nExample<br \/>\nUse models to find equivalent fractions for \\(\\frac{2}{3}\\) .<br \/>\n<img loading=\"lazy\" class=\"alignnone size-full wp-image-13132\" src=\"https:\/\/ccssmathanswers.com\/wp-content\/uploads\/2020\/12\/Big-Ideas-Math-Answer-Key-Grade-4-Chapter-7-Understand-Fraction-Equivalence-and-Comparison-7.1-2.png\" alt=\"Big Ideas Math Answer Key Grade 4 Chapter 7 Understand Fraction Equivalence and Comparison 7.1 2\" width=\"218\" height=\"253\" \/><br \/>\nOne Way:<br \/>\nDraw models that show the same whole divided into different numbers of parts.<\/p>\n<p><img loading=\"lazy\" class=\"alignnone size-full wp-image-23560\" src=\"https:\/\/ccssmathanswers.com\/wp-content\/uploads\/2020\/12\/Big-Ideas-Math-Answers-Grade-4-Chapter-7.jpg\" alt=\"\" width=\"716\" height=\"450\" srcset=\"https:\/\/bigideasmathanswers.com\/wp-content\/uploads\/2020\/12\/Big-Ideas-Math-Answers-Grade-4-Chapter-7.jpg 716w, https:\/\/bigideasmathanswers.com\/wp-content\/uploads\/2020\/12\/Big-Ideas-Math-Answers-Grade-4-Chapter-7-300x189.jpg 300w\" sizes=\"(max-width: 716px) 100vw, 716px\" \/><\/p>\n<p><strong>Show and Grow<\/strong><\/p>\n<p>Use the model to find an equivalent fraction for \\(\\frac{2}{5}\\) .<br \/>\nAnswer:<br \/>\n<img loading=\"lazy\" class=\"alignnone size-full wp-image-13134\" src=\"https:\/\/ccssmathanswers.com\/wp-content\/uploads\/2020\/12\/Big-Ideas-Math-Answer-Key-Grade-4-Chapter-7-Understand-Fraction-Equivalence-and-Comparison-7.1-4.png\" alt=\"Big Ideas Math Answer Key Grade 4 Chapter 7 Understand Fraction Equivalence and Comparison 7.1 4\" width=\"242\" height=\"73\" \/><br \/>\nAnswer: The equivalent fraction for \\(\\frac{2}{5}\\) is: \\(\\frac{4}{10}\\)<\/p>\n<p>Explanation:<br \/>\nThe given model is:<br \/>\n<img loading=\"lazy\" class=\"alignnone size-full wp-image-13134\" src=\"https:\/\/ccssmathanswers.com\/wp-content\/uploads\/2020\/12\/Big-Ideas-Math-Answer-Key-Grade-4-Chapter-7-Understand-Fraction-Equivalence-and-Comparison-7.1-4.png\" alt=\"Big Ideas Math Answer Key Grade 4 Chapter 7 Understand Fraction Equivalence and Comparison 7.1 4\" width=\"242\" height=\"73\" \/><br \/>\nFrom the above model, we can say the fraction is: \\(\\frac{2}{5}\\)<br \/>\nNow, the model for the equivalent fraction of \\(\\frac{2}{5}\\) is:<br \/>\n<img loading=\"lazy\" class=\"alignnone size-full wp-image-23561\" src=\"https:\/\/ccssmathanswers.com\/wp-content\/uploads\/2020\/12\/Big-Ideas-Math-Answers-Grade-4-Chapter-7-1.jpg\" alt=\"\" width=\"489\" height=\"77\" srcset=\"https:\/\/bigideasmathanswers.com\/wp-content\/uploads\/2020\/12\/Big-Ideas-Math-Answers-Grade-4-Chapter-7-1.jpg 489w, https:\/\/bigideasmathanswers.com\/wp-content\/uploads\/2020\/12\/Big-Ideas-Math-Answers-Grade-4-Chapter-7-1-300x47.jpg 300w\" sizes=\"(max-width: 489px) 100vw, 489px\" \/><br \/>\nFrom the above model, we can say that the fraction is: \\(\\frac{4}{10}\\)<br \/>\nHence, from the above,<br \/>\nWe can conclude that the equivalent of \\(\\frac{2}{5}\\) is: \\(\\frac{4}{10}\\)<\/p>\n<p>Question 2.<br \/>\nUse the number line to find an1equivalent fraction for \\(\\frac{1}{6}\\) .<br \/>\nAnswer:<br \/>\n<img loading=\"lazy\" class=\"alignnone size-full wp-image-13135\" src=\"https:\/\/ccssmathanswers.com\/wp-content\/uploads\/2020\/12\/Big-Ideas-Math-Answer-Key-Grade-4-Chapter-7-Understand-Fraction-Equivalence-and-Comparison-7.1-5.1.png\" alt=\"Big Ideas Math Answer Key Grade 4 Chapter 7 Understand Fraction Equivalence and Comparison 7.1 5.1\" width=\"293\" height=\"64\" \/><br \/>\nThe equivalent fraction for \\(\\frac{1}{6}\\) is: \\(\\frac{2}{12}\\)<\/p>\n<p>Explanation:<br \/>\nThe given number line is:<br \/>\n<img loading=\"lazy\" class=\"alignnone size-full wp-image-13135\" src=\"https:\/\/ccssmathanswers.com\/wp-content\/uploads\/2020\/12\/Big-Ideas-Math-Answer-Key-Grade-4-Chapter-7-Understand-Fraction-Equivalence-and-Comparison-7.1-5.1.png\" alt=\"Big Ideas Math Answer Key Grade 4 Chapter 7 Understand Fraction Equivalence and Comparison 7.1 5.1\" width=\"293\" height=\"64\" \/><br \/>\nFrom the given line, we can say that every 2 lines represent \\(\\frac{1}{6}\\) multiple.<br \/>\nSo,<br \/>\nEach line of the given number line represents \\(\\frac{1}{12}\\) multiple<br \/>\nSo,<br \/>\nThe number line with \\(\\frac{1}{12}\\) will be like:<br \/>\n<img loading=\"lazy\" class=\"alignnone size-full wp-image-23562\" src=\"https:\/\/ccssmathanswers.com\/wp-content\/uploads\/2020\/12\/Big-Ideas-Math-Answers-Grade-4-Chapter-7-2.jpg\" alt=\"\" width=\"304\" height=\"103\" srcset=\"https:\/\/bigideasmathanswers.com\/wp-content\/uploads\/2020\/12\/Big-Ideas-Math-Answers-Grade-4-Chapter-7-2.jpg 304w, https:\/\/bigideasmathanswers.com\/wp-content\/uploads\/2020\/12\/Big-Ideas-Math-Answers-Grade-4-Chapter-7-2-300x102.jpg 300w\" sizes=\"(max-width: 304px) 100vw, 304px\" \/><br \/>\nSo, from the above number line,<br \/>\nWe can say that the equivalent fraction of \\(\\frac{1}{6}\\) is: \\(\\frac{1}{12}\\)<\/p>\n<p>Hence, from the above,<br \/>\nWe can conclude that the equivalent fraction of \\(\\frac{1}{6}\\) is: \\(\\frac{1}{12}\\)<\/p>\n<p><strong>Apply and Grow: Practice<\/strong><\/p>\n<p><strong>Use the model to find an equivalent fraction.<\/strong><br \/>\nQuestion 3.<br \/>\n<img loading=\"lazy\" class=\"alignnone size-full wp-image-13136\" src=\"https:\/\/ccssmathanswers.com\/wp-content\/uploads\/2020\/12\/Big-Ideas-Math-Answer-Key-Grade-4-Chapter-7-Understand-Fraction-Equivalence-and-Comparison-7.1-5.png\" alt=\"Big Ideas Math Answer Key Grade 4 Chapter 7 Understand Fraction Equivalence and Comparison 7.1 5\" width=\"196\" height=\"122\" \/><br \/>\nAnswer: The equivalent fraction of \\(\\frac{3}{6}\\) is: \\(\\frac{1}{2}\\)<\/p>\n<p>Explanation:<br \/>\nThe given model is:<br \/>\n<img loading=\"lazy\" class=\"alignnone size-full wp-image-13136\" src=\"https:\/\/ccssmathanswers.com\/wp-content\/uploads\/2020\/12\/Big-Ideas-Math-Answer-Key-Grade-4-Chapter-7-Understand-Fraction-Equivalence-and-Comparison-7.1-5.png\" alt=\"Big Ideas Math Answer Key Grade 4 Chapter 7 Understand Fraction Equivalence and Comparison 7.1 5\" width=\"196\" height=\"122\" \/><br \/>\nFrom the above model, we can say that the fraction is: \\(\\frac{3}{6}\\)<br \/>\nSo,<br \/>\nThe model for the equivalent fraction is:<br \/>\n<img loading=\"lazy\" class=\"alignnone size-full wp-image-23565\" src=\"https:\/\/ccssmathanswers.com\/wp-content\/uploads\/2020\/12\/Big-Ideas-Math-Answers-Grade-4-Chapter-7-3.jpg\" alt=\"\" width=\"489\" height=\"77\" srcset=\"https:\/\/bigideasmathanswers.com\/wp-content\/uploads\/2020\/12\/Big-Ideas-Math-Answers-Grade-4-Chapter-7-3.jpg 489w, https:\/\/bigideasmathanswers.com\/wp-content\/uploads\/2020\/12\/Big-Ideas-Math-Answers-Grade-4-Chapter-7-3-300x47.jpg 300w\" sizes=\"(max-width: 489px) 100vw, 489px\" \/><br \/>\nFrom the above, we can see that the model represents \\(\\frac{1}{2}\\)<br \/>\nNote: \\(\\frac{3}{6}\\) is equal to \\(\\frac{1}{2}\\) because when we divide \\(\\frac{3}{6}\\) with 3, then we can get the answer.<br \/>\nHence, from the above,<br \/>\nWe can conclude that \\(\\frac{3}{6}\\) = \\(\\frac{1}{2}\\)<\/p>\n<p>Question 4.<br \/>\n<img loading=\"lazy\" class=\"alignnone size-full wp-image-13137\" src=\"https:\/\/ccssmathanswers.com\/wp-content\/uploads\/2020\/12\/Big-Ideas-Math-Answer-Key-Grade-4-Chapter-7-Understand-Fraction-Equivalence-and-Comparison-7.1-6.png\" alt=\"Big Ideas Math Answer Key Grade 4 Chapter 7 Understand Fraction Equivalence and Comparison 7.1 6\" width=\"202\" height=\"74\" \/><br \/>\nAnswer: The\u00a0 equivalent fraction of \\(\\frac{1}{5}\\) is: \\(\\frac{2}{10}\\)<\/p>\n<p>Explanation:<br \/>\nThe given model is:<br \/>\n<img loading=\"lazy\" class=\"alignnone size-full wp-image-13137\" src=\"https:\/\/ccssmathanswers.com\/wp-content\/uploads\/2020\/12\/Big-Ideas-Math-Answer-Key-Grade-4-Chapter-7-Understand-Fraction-Equivalence-and-Comparison-7.1-6.png\" alt=\"Big Ideas Math Answer Key Grade 4 Chapter 7 Understand Fraction Equivalence and Comparison 7.1 6\" width=\"202\" height=\"74\" \/><br \/>\nFrom the above model, we can say that the fraction is: \\(\\frac{1}{5}\\)<br \/>\nSo,<br \/>\nThe model for the equivalent fraction is:<br \/>\n<img loading=\"lazy\" class=\"alignnone size-full wp-image-23566\" src=\"https:\/\/ccssmathanswers.com\/wp-content\/uploads\/2020\/12\/Big-Ideas-Math-Answers-Grade-4-Chapter-7-4.jpg\" alt=\"\" width=\"489\" height=\"77\" srcset=\"https:\/\/bigideasmathanswers.com\/wp-content\/uploads\/2020\/12\/Big-Ideas-Math-Answers-Grade-4-Chapter-7-4.jpg 489w, https:\/\/bigideasmathanswers.com\/wp-content\/uploads\/2020\/12\/Big-Ideas-Math-Answers-Grade-4-Chapter-7-4-300x47.jpg 300w\" sizes=\"(max-width: 489px) 100vw, 489px\" \/><br \/>\nSo,<br \/>\nThe equivalent fraction from the above model is: \\(\\frac{2}{10}\\)<br \/>\nSo,<br \/>\nWhen \\(\\frac{2}{10}\\) is divided by 2, we will get the equivalent fraction<br \/>\nHence, from the above,<br \/>\nWe can say that \\(\\frac{1}{5}\\) = \\(\\frac{2}{10}\\)<\/p>\n<p>Question 5.<br \/>\n<img loading=\"lazy\" class=\"alignnone size-full wp-image-13138\" src=\"https:\/\/ccssmathanswers.com\/wp-content\/uploads\/2020\/12\/Big-Ideas-Math-Answer-Key-Grade-4-Chapter-7-Understand-Fraction-Equivalence-and-Comparison-7.1-7.png\" alt=\"Big Ideas Math Answer Key Grade 4 Chapter 7 Understand Fraction Equivalence and Comparison 7.1 7\" width=\"186\" height=\"135\" \/><br \/>\nAnswer: The equivalent fraction of \\(\\frac{4}{5}\\) is: \\(\\frac{8}{10}\\)<\/p>\n<p>Explanation:<br \/>\nThe given model is:<br \/>\n<img loading=\"lazy\" class=\"alignnone size-full wp-image-13138\" src=\"https:\/\/ccssmathanswers.com\/wp-content\/uploads\/2020\/12\/Big-Ideas-Math-Answer-Key-Grade-4-Chapter-7-Understand-Fraction-Equivalence-and-Comparison-7.1-7.png\" alt=\"Big Ideas Math Answer Key Grade 4 Chapter 7 Understand Fraction Equivalence and Comparison 7.1 7\" width=\"186\" height=\"135\" \/><br \/>\nFrom the above model, we can say the fraction is \\(\\frac{4}{5}\\)<br \/>\nSo,<br \/>\nThe model for the equivalent fraction is:<br \/>\n<img loading=\"lazy\" class=\"alignnone size-full wp-image-23567\" src=\"https:\/\/ccssmathanswers.com\/wp-content\/uploads\/2020\/12\/Big-Ideas-Math-Answers-Grade-4-Chapter-7-5.jpg\" alt=\"\" width=\"489\" height=\"77\" srcset=\"https:\/\/bigideasmathanswers.com\/wp-content\/uploads\/2020\/12\/Big-Ideas-Math-Answers-Grade-4-Chapter-7-5.jpg 489w, https:\/\/bigideasmathanswers.com\/wp-content\/uploads\/2020\/12\/Big-Ideas-Math-Answers-Grade-4-Chapter-7-5-300x47.jpg 300w\" sizes=\"(max-width: 489px) 100vw, 489px\" \/><br \/>\nFrom the above model, we can say that the equivalent fraction is: \\(\\frac{8}{10}\\)<br \/>\nSo,<br \/>\nWhen \\(\\frac{8}{10}\\) is divided by 2, we will get the equivalent fraction.<br \/>\nHence, from the above,<br \/>\nWe can conclude that \\(\\frac{4}{5}\\) = \\(\\frac{8}{10}\\)<\/p>\n<p>Question 6.<br \/>\n<img loading=\"lazy\" class=\"alignnone size-full wp-image-13139\" src=\"https:\/\/ccssmathanswers.com\/wp-content\/uploads\/2020\/12\/Big-Ideas-Math-Answer-Key-Grade-4-Chapter-7-Understand-Fraction-Equivalence-and-Comparison-7.1-8.png\" alt=\"Big Ideas Math Answer Key Grade 4 Chapter 7 Understand Fraction Equivalence and Comparison 7.1 8\" width=\"190\" height=\"117\" \/><br \/>\nAnswer: The equivalent fraction of \\(\\frac{1}{2}\\) is: \\(\\frac{5}{10}\\)<\/p>\n<p>Explanation:<br \/>\nThe given model is:<br \/>\n<img loading=\"lazy\" class=\"alignnone size-full wp-image-13139\" src=\"https:\/\/ccssmathanswers.com\/wp-content\/uploads\/2020\/12\/Big-Ideas-Math-Answer-Key-Grade-4-Chapter-7-Understand-Fraction-Equivalence-and-Comparison-7.1-8.png\" alt=\"Big Ideas Math Answer Key Grade 4 Chapter 7 Understand Fraction Equivalence and Comparison 7.1 8\" width=\"190\" height=\"117\" \/><br \/>\nFrom the above model, we can say that the fraction is: \\(\\frac{1}{2}\\)<br \/>\nSo,<br \/>\nThe model for the equivalent fraction is:<br \/>\n<img loading=\"lazy\" class=\"alignnone size-full wp-image-23568\" src=\"https:\/\/ccssmathanswers.com\/wp-content\/uploads\/2020\/12\/Big-Ideas-Math-Answers-Grade-4-Chapter-7-6.jpg\" alt=\"\" width=\"245\" height=\"219\" \/><br \/>\nSo, the model that represents the equivalent fraction is: \\(\\frac{5}{10}\\)<br \/>\nSo,<br \/>\nWhen \\(\\frac{5}{10}\\) is divided by 5, we will get the equivalent fraction<br \/>\nHence, from the above,<br \/>\nWe can conclude that \\(\\frac{1}{2}\\) = \\(\\frac{5}{10}\\)<\/p>\n<p><strong>Use a number line to find an equivalent fraction.<\/strong><br \/>\nQuestion 7.<br \/>\n<img loading=\"lazy\" class=\"alignnone size-full wp-image-13140\" src=\"https:\/\/ccssmathanswers.com\/wp-content\/uploads\/2020\/12\/Big-Ideas-Math-Answer-Key-Grade-4-Chapter-7-Understand-Fraction-Equivalence-and-Comparison-7.1-9.png\" alt=\"Big Ideas Math Answer Key Grade 4 Chapter 7 Understand Fraction Equivalence and Comparison 7.1 9\" width=\"291\" height=\"104\" \/><br \/>\nAnswer: The equivalent fraction of \\(\\frac{3}{4}\\) is: \\(\\frac{6}{8}\\)<\/p>\n<p>Explanation:<br \/>\nThe given number line is:<br \/>\n<img loading=\"lazy\" class=\"alignnone size-full wp-image-13140\" src=\"https:\/\/ccssmathanswers.com\/wp-content\/uploads\/2020\/12\/Big-Ideas-Math-Answer-Key-Grade-4-Chapter-7-Understand-Fraction-Equivalence-and-Comparison-7.1-9.png\" alt=\"Big Ideas Math Answer Key Grade 4 Chapter 7 Understand Fraction Equivalence and Comparison 7.1 9\" width=\"291\" height=\"104\" \/><br \/>\nFrom the above-given number line,<br \/>\nEvery 2 lines represent the value.i.e., \\(\\frac{1}{4}\\)<br \/>\nSo,<br \/>\nThe value of each line represents \\(\\frac{1}{8}\\)<br \/>\nSo,<br \/>\nThe model for the equivalent fraction is:<br \/>\n<img loading=\"lazy\" class=\"alignnone size-full wp-image-23569\" src=\"https:\/\/ccssmathanswers.com\/wp-content\/uploads\/2020\/12\/Big-Ideas-Math-Answers-Grade-4-Chapter-7-7.jpg\" alt=\"\" width=\"319\" height=\"125\" srcset=\"https:\/\/bigideasmathanswers.com\/wp-content\/uploads\/2020\/12\/Big-Ideas-Math-Answers-Grade-4-Chapter-7-7.jpg 319w, https:\/\/bigideasmathanswers.com\/wp-content\/uploads\/2020\/12\/Big-Ideas-Math-Answers-Grade-4-Chapter-7-7-300x118.jpg 300w\" sizes=\"(max-width: 319px) 100vw, 319px\" \/><br \/>\nSo,<br \/>\nFrom the equivalent number line,<br \/>\nWe can say that \\(\\frac{3}{4}\\) is equivalent to \\(\\frac{6}{8}\\)<br \/>\nHence, from the above,<br \/>\nWe can conclude that \\(\\frac{3}{4}\\) = \\(\\frac{6}{8}\\)<\/p>\n<p>Question 8.<br \/>\n<img loading=\"lazy\" class=\"alignnone size-full wp-image-13141\" src=\"https:\/\/ccssmathanswers.com\/wp-content\/uploads\/2020\/12\/Big-Ideas-Math-Answer-Key-Grade-4-Chapter-7-Understand-Fraction-Equivalence-and-Comparison-7.1-10.png\" alt=\"Big Ideas Math Answer Key Grade 4 Chapter 7 Understand Fraction Equivalence and Comparison 7.1 10\" width=\"304\" height=\"111\" srcset=\"https:\/\/bigideasmathanswers.com\/wp-content\/uploads\/2020\/12\/Big-Ideas-Math-Answer-Key-Grade-4-Chapter-7-Understand-Fraction-Equivalence-and-Comparison-7.1-10.png 304w, https:\/\/bigideasmathanswers.com\/wp-content\/uploads\/2020\/12\/Big-Ideas-Math-Answer-Key-Grade-4-Chapter-7-Understand-Fraction-Equivalence-and-Comparison-7.1-10-300x110.png 300w\" sizes=\"(max-width: 304px) 100vw, 304px\" \/><br \/>\nAnswer: The equivalent fraction of \\(\\frac{1}{3}\\) is: \\(\\frac{3}{9}\\)<\/p>\n<p>Explanation:<br \/>\nThe given number line is:<br \/>\n<img loading=\"lazy\" class=\"alignnone size-full wp-image-13141\" src=\"https:\/\/ccssmathanswers.com\/wp-content\/uploads\/2020\/12\/Big-Ideas-Math-Answer-Key-Grade-4-Chapter-7-Understand-Fraction-Equivalence-and-Comparison-7.1-10.png\" alt=\"Big Ideas Math Answer Key Grade 4 Chapter 7 Understand Fraction Equivalence and Comparison 7.1 10\" width=\"304\" height=\"111\" srcset=\"https:\/\/bigideasmathanswers.com\/wp-content\/uploads\/2020\/12\/Big-Ideas-Math-Answer-Key-Grade-4-Chapter-7-Understand-Fraction-Equivalence-and-Comparison-7.1-10.png 304w, https:\/\/bigideasmathanswers.com\/wp-content\/uploads\/2020\/12\/Big-Ideas-Math-Answer-Key-Grade-4-Chapter-7-Understand-Fraction-Equivalence-and-Comparison-7.1-10-300x110.png 300w\" sizes=\"(max-width: 304px) 100vw, 304px\" \/><br \/>\nFrom the above number line,<br \/>\nThe given fraction is: \\(\\frac{1}{3}\\)<br \/>\nFrom the above number line,<br \/>\nEvery 2 lines represent a value.<br \/>\nSo,<br \/>\nif we divide the lines into 3 lines between the values, then we will get each line value with the denominator 9<br \/>\nSo,<br \/>\nThe number line for the equivalent fraction is:<br \/>\n<img loading=\"lazy\" class=\"alignnone size-full wp-image-23570\" src=\"https:\/\/ccssmathanswers.com\/wp-content\/uploads\/2020\/12\/Big-Ideas-Math-Answers-Grade-4-Chapter-7-8.jpg\" alt=\"\" width=\"307\" height=\"133\" srcset=\"https:\/\/bigideasmathanswers.com\/wp-content\/uploads\/2020\/12\/Big-Ideas-Math-Answers-Grade-4-Chapter-7-8.jpg 307w, https:\/\/bigideasmathanswers.com\/wp-content\/uploads\/2020\/12\/Big-Ideas-Math-Answers-Grade-4-Chapter-7-8-300x130.jpg 300w\" sizes=\"(max-width: 307px) 100vw, 307px\" \/><br \/>\nSo, from the above number line,<br \/>\nWe can say that the equivalent fraction of \\(\\frac{1}{3}\\) is: \\(\\frac{3}{9}\\)<br \/>\nHence, from the above,<br \/>\nWe can conclude that \\(\\frac{1}{3}\\) = \\(\\frac{3}{9}\\)<\/p>\n<p>Question 9.<br \/>\n<strong>Open-Ended<\/strong><br \/>\nWrite two equivalent fractions to describe the portion of the eggs that are white<br \/>\n<img loading=\"lazy\" class=\"alignnone size-full wp-image-13142\" src=\"https:\/\/ccssmathanswers.com\/wp-content\/uploads\/2020\/12\/Big-Ideas-Math-Answer-Key-Grade-4-Chapter-7-Understand-Fraction-Equivalence-and-Comparison-7.1-11.png\" alt=\"Big Ideas Math Answer Key Grade 4 Chapter 7 Understand Fraction Equivalence and Comparison 7.1 11\" width=\"192\" height=\"133\" \/><br \/>\nAnswer:<br \/>\nThe two equivalent fractions to describe the portion of eggs that are white are:<br \/>\n\\(\\frac{6}{12}\\) and \\(\\frac{1}{2}\\)<\/p>\n<p>Explanation:<br \/>\nThe given model is:<br \/>\n<img loading=\"lazy\" class=\"alignnone size-full wp-image-13142\" src=\"https:\/\/ccssmathanswers.com\/wp-content\/uploads\/2020\/12\/Big-Ideas-Math-Answer-Key-Grade-4-Chapter-7-Understand-Fraction-Equivalence-and-Comparison-7.1-11.png\" alt=\"Big Ideas Math Answer Key Grade 4 Chapter 7 Understand Fraction Equivalence and Comparison 7.1 11\" width=\"192\" height=\"133\" \/><br \/>\nFrom the above model,<br \/>\nWe can say that,<br \/>\nThe number of colored eggs is: 6<br \/>\nThe number of white eggs is: 6<br \/>\nSo,<br \/>\nThe total number of eggs are: 12<br \/>\nSo,<br \/>\nThe fraction form for the white eggs is = \\(\\frac{Number of white eggs}{Total number of eggs}\\)<br \/>\n= \\(\\frac{6}{12}\\)<br \/>\nEquivalent form for the white eggs:<br \/>\nConsider the colored eggs as 1 group and the white eggs as 1 group<br \/>\nSo,<br \/>\nThe number of White eggs is: 1<br \/>\nThe number of colored eggs is: 1<br \/>\nSo,<br \/>\nThe total number of eggs are: 2<br \/>\nSo,<br \/>\nThe fraction that the eggs are white = \\(\\frac{Number of white eggs}{Total number of eggs}\\)<br \/>\n= \\(\\frac{1}{2}\\)<br \/>\nHence, from the above,<br \/>\nWe can say that<br \/>\nThe two equivalent fractions to describe the portion of eggs that are white are:<br \/>\n\\(\\frac{6}{12}\\) and \\(\\frac{1}{2}\\)<\/p>\n<p>Question 10.<br \/>\n<strong>YOU BE THE TEACHER<\/strong><br \/>\nYour friend says the models show equivalent fractions. Is your friend correct? Explain.<br \/>\n<img loading=\"lazy\" class=\"alignnone size-full wp-image-13143\" src=\"https:\/\/ccssmathanswers.com\/wp-content\/uploads\/2020\/12\/Big-Ideas-Math-Answer-Key-Grade-4-Chapter-7-Understand-Fraction-Equivalence-and-Comparison-7.1-12.png\" alt=\"Big Ideas Math Answer Key Grade 4 Chapter 7 Understand Fraction Equivalence and Comparison 7.1 12\" width=\"225\" height=\"102\" \/><br \/>\nAnswer: Yes, your friend is correct<\/p>\n<p>Explanation:<br \/>\nGiven models are:<br \/>\n<img loading=\"lazy\" class=\"alignnone size-full wp-image-13143\" src=\"https:\/\/ccssmathanswers.com\/wp-content\/uploads\/2020\/12\/Big-Ideas-Math-Answer-Key-Grade-4-Chapter-7-Understand-Fraction-Equivalence-and-Comparison-7.1-12.png\" alt=\"Big Ideas Math Answer Key Grade 4 Chapter 7 Understand Fraction Equivalence and Comparison 7.1 12\" width=\"225\" height=\"102\" \/><br \/>\nLet the two models be named as 1st model and 2nd model.<br \/>\nSo,<br \/>\nFrom the 1st model,<br \/>\nThe total number of parts are: 4<br \/>\nThe colored part is: 1<br \/>\nSo,<br \/>\nThe fraction form is: \\(\\frac{The colored part}{The total number of parts}\\) = \\(\\frac{1}{4}\\)<br \/>\nNow,<br \/>\nFrom the 2nd model,<br \/>\nThe total number of parts are: 4<br \/>\nThe colored part is: 1<br \/>\nSo,<br \/>\nThe fraction form is: \\(\\frac{The colored part}{The total number of parts}\\) = \\(\\frac{1}{4}\\)<br \/>\nHence, from the above,<br \/>\nWe can conclude that the 2 fractions are equal and so, your friend is correct.<\/p>\n<p><strong>Think and Grow: Modeling Real Life<\/strong><\/p>\n<p><strong>Example<\/strong><br \/>\nYou and your friend make braided paper bookmarks. Yours is \\(\\frac{2}{3}\\) foot long. Your friend\u2019s is \\(\\frac{7}{12}\\) foot long. Are the bookmarks the same length?<br \/>\n<img loading=\"lazy\" class=\"alignnone size-full wp-image-13144\" src=\"https:\/\/ccssmathanswers.com\/wp-content\/uploads\/2020\/12\/Big-Ideas-Math-Answer-Key-Grade-4-Chapter-7-Understand-Fraction-Equivalence-and-Comparison-7.1-13.png\" alt=\"Big Ideas Math Answer Key Grade 4 Chapter 7 Understand Fraction Equivalence and Comparison 7.1 13\" width=\"178\" height=\"213\" \/><br \/>\nDetermine whether the fractions are equivalent. Plot the fractions on the same number line. Then compare.<br \/>\n<img loading=\"lazy\" class=\"alignnone size-full wp-image-13145\" src=\"https:\/\/ccssmathanswers.com\/wp-content\/uploads\/2020\/12\/Big-Ideas-Math-Answer-Key-Grade-4-Chapter-7-Understand-Fraction-Equivalence-and-Comparison-7.1-14.png\" alt=\"Big Ideas Math Answer Key Grade 4 Chapter 7 Understand Fraction Equivalence and Comparison 7.1 14\" width=\"449\" height=\"88\" srcset=\"https:\/\/bigideasmathanswers.com\/wp-content\/uploads\/2020\/12\/Big-Ideas-Math-Answer-Key-Grade-4-Chapter-7-Understand-Fraction-Equivalence-and-Comparison-7.1-14.png 449w, https:\/\/bigideasmathanswers.com\/wp-content\/uploads\/2020\/12\/Big-Ideas-Math-Answer-Key-Grade-4-Chapter-7-Understand-Fraction-Equivalence-and-Comparison-7.1-14-300x59.png 300w\" sizes=\"(max-width: 449px) 100vw, 449px\" \/><br \/>\nFrom the above number line,<br \/>\nwe can observe that \\(\\frac{2}{3}\\) is after the \\(\\frac{7}{12}\\)<br \/>\nSo,<br \/>\n\\(\\frac{2}{3}\\) is greater than \\(\\frac{7}{12}\\)<br \/>\nSo,<br \/>\nThe bookmarks do not have the same length.<\/p>\n<p><strong>Show and Grow<\/strong><\/p>\n<p>Question 11.<br \/>\nThe lasagna pans are the same size. Are the amounts of lasagna left in the pans equal?<br \/>\n<img loading=\"lazy\" class=\"alignnone size-full wp-image-13146\" src=\"https:\/\/ccssmathanswers.com\/wp-content\/uploads\/2020\/12\/Big-Ideas-Math-Answer-Key-Grade-4-Chapter-7-Understand-Fraction-Equivalence-and-Comparison-7.1-15.png\" alt=\"Big Ideas Math Answer Key Grade 4 Chapter 7 Understand Fraction Equivalence and Comparison 7.1 15\" width=\"509\" height=\"143\" srcset=\"https:\/\/bigideasmathanswers.com\/wp-content\/uploads\/2020\/12\/Big-Ideas-Math-Answer-Key-Grade-4-Chapter-7-Understand-Fraction-Equivalence-and-Comparison-7.1-15.png 509w, https:\/\/bigideasmathanswers.com\/wp-content\/uploads\/2020\/12\/Big-Ideas-Math-Answer-Key-Grade-4-Chapter-7-Understand-Fraction-Equivalence-and-Comparison-7.1-15-300x84.png 300w\" sizes=\"(max-width: 509px) 100vw, 509px\" \/><br \/>\nAnswer: No, the amount of lasagna left in the pans are not equal<\/p>\n<p>Explanation:<br \/>\nGiven lasagna pans are:<br \/>\n<img loading=\"lazy\" class=\"alignnone size-full wp-image-13146\" src=\"https:\/\/ccssmathanswers.com\/wp-content\/uploads\/2020\/12\/Big-Ideas-Math-Answer-Key-Grade-4-Chapter-7-Understand-Fraction-Equivalence-and-Comparison-7.1-15.png\" alt=\"Big Ideas Math Answer Key Grade 4 Chapter 7 Understand Fraction Equivalence and Comparison 7.1 15\" width=\"509\" height=\"143\" srcset=\"https:\/\/bigideasmathanswers.com\/wp-content\/uploads\/2020\/12\/Big-Ideas-Math-Answer-Key-Grade-4-Chapter-7-Understand-Fraction-Equivalence-and-Comparison-7.1-15.png 509w, https:\/\/bigideasmathanswers.com\/wp-content\/uploads\/2020\/12\/Big-Ideas-Math-Answer-Key-Grade-4-Chapter-7-Understand-Fraction-Equivalence-and-Comparison-7.1-15-300x84.png 300w\" sizes=\"(max-width: 509px) 100vw, 509px\" \/><br \/>\nLet the two lasagna pans be named as 1st model and 2nd model<br \/>\nFrom the first model,<br \/>\nThe total number of parts are: 12<br \/>\nThe number of parts that are occupied is: 4<br \/>\nThe number of parts that are left is: 8<br \/>\nFrom the 2nd model,<br \/>\nThe total number of parts are: 6<br \/>\nThe number of parts that are occupied is: 2<br \/>\nThe number of parts that are left is: 4<br \/>\nHence, from the above,<br \/>\nWe can conclude that the amount of lasagna left in the pans is not equal.<\/p>\n<p>Question 12.<br \/>\n<strong>DIG DEEPER!<\/strong><br \/>\nYou run 3 laps around an outdoor track, where 4 laps are equal to 1 mile. Your friend runs 6 laps around the indoor track shown. Do you and your friend run the same distance? Explain.<br \/>\n<img loading=\"lazy\" class=\"alignnone size-full wp-image-13147\" src=\"https:\/\/ccssmathanswers.com\/wp-content\/uploads\/2020\/12\/Big-Ideas-Math-Answer-Key-Grade-4-Chapter-7-Understand-Fraction-Equivalence-and-Comparison-7.1-16.png\" alt=\"Big Ideas Math Answer Key Grade 4 Chapter 7 Understand Fraction Equivalence and Comparison 7.1 16\" width=\"243\" height=\"208\" \/><br \/>\nAnswer: Yes, you and your friend run the same distance.<\/p>\n<p>Explanation:<br \/>\nGiven that you run 3 laps around the outdoor track whereas for you, 4 laps is equal to 1 mile.<br \/>\nSo,<br \/>\nThe total distance covered by you = \\(\\frac{The number of laps that you run}{The number of laps that is equal to 1 mile}\\)= \\(\\frac{3}{4}\\)<br \/>\nIt is also given that your friend runs 6 laps around the indoor track whereas, for your friend, 8 laps is equal to 1 mile.<br \/>\nSo,<br \/>\nThe total distance covered by your friend = \\(\\frac{The number of laps that your friend run}{The number of laps that is equal to 1 mile}\\) = \\(\\frac{6}{8}\\)<br \/>\nWhen \\(\\frac{3}{4}\\) is multiplied and divide by 2 , we get \\(\\frac{6}{8}\\)<br \/>\nSo,<br \/>\n\\(\\frac{3}{4}\\) = \\(\\frac{6}{8}\\)<br \/>\nHence, from the above,<br \/>\nWe can conclude that you and your friend runs the same distance<\/p>\n<h3><a id=\"Model_Equivalent_Fractions_Homework_&amp;_Practice_7.1\"><\/a>Model Equivalent Fractions Homework &amp; Practice 7.1<\/h3>\n<p><strong>Use the model to find an equivalent fraction.<\/strong><br \/>\nQuestion 1.<br \/>\n<img loading=\"lazy\" class=\"alignnone size-full wp-image-13148\" src=\"https:\/\/ccssmathanswers.com\/wp-content\/uploads\/2020\/12\/Big-Ideas-Math-Answer-Key-Grade-4-Chapter-7-Understand-Fraction-Equivalence-and-Comparison-7.1-17.png\" alt=\"Big Ideas Math Answer Key Grade 4 Chapter 7 Understand Fraction Equivalence and Comparison 7.1 17\" width=\"285\" height=\"82\" \/><br \/>\nAnswer: The equivalent fraction of \\(\\frac{3}{5}\\) is: \\(\\frac{6}{10}\\)<\/p>\n<p>Explanation:<br \/>\nThe given model is:<br \/>\n<img loading=\"lazy\" class=\"alignnone size-full wp-image-13148\" src=\"https:\/\/ccssmathanswers.com\/wp-content\/uploads\/2020\/12\/Big-Ideas-Math-Answer-Key-Grade-4-Chapter-7-Understand-Fraction-Equivalence-and-Comparison-7.1-17.png\" alt=\"Big Ideas Math Answer Key Grade 4 Chapter 7 Understand Fraction Equivalence and Comparison 7.1 17\" width=\"285\" height=\"82\" \/><br \/>\nFrom the above model,<br \/>\nWe can say that the fraction is: \\(\\frac{3}{5}\\)<br \/>\nSo,<br \/>\nThe model for the Equivalent fraction is:<br \/>\n<img loading=\"lazy\" class=\"alignnone size-full wp-image-23706\" src=\"https:\/\/ccssmathanswers.com\/wp-content\/uploads\/2020\/12\/Big-Ideas-Math-Answers-Grade-4-Chapter-7-9.jpg\" alt=\"\" width=\"520\" height=\"133\" srcset=\"https:\/\/bigideasmathanswers.com\/wp-content\/uploads\/2020\/12\/Big-Ideas-Math-Answers-Grade-4-Chapter-7-9.jpg 520w, https:\/\/bigideasmathanswers.com\/wp-content\/uploads\/2020\/12\/Big-Ideas-Math-Answers-Grade-4-Chapter-7-9-300x77.jpg 300w\" sizes=\"(max-width: 520px) 100vw, 520px\" \/><br \/>\nFrom the above model, we can say that the equivalent fraction is: \\(\\frac{6}{10}\\)<br \/>\nSo,<br \/>\nWhen we divide \\(\\frac{6}{10}\\) by 2, we will get the equivalent value.<br \/>\nHence, from the above,<br \/>\nWe can conclude that \\(\\frac{3}{5}\\) = \\(\\frac{6}{10}\\)<\/p>\n<p>Question 2.<br \/>\n<img loading=\"lazy\" class=\"alignnone size-full wp-image-13149\" src=\"https:\/\/ccssmathanswers.com\/wp-content\/uploads\/2020\/12\/Big-Ideas-Math-Answer-Key-Grade-4-Chapter-7-Understand-Fraction-Equivalence-and-Comparison-7.1-18.png\" alt=\"Big Ideas Math Answer Key Grade 4 Chapter 7 Understand Fraction Equivalence and Comparison 7.1 18\" width=\"205\" height=\"154\" \/><br \/>\nAnswer: The equivalent fraction of \\(\\frac{1}{4}\\) is: \\(\\frac{2}{8}\\)<\/p>\n<p>Explanation:<br \/>\nThe given model is:<br \/>\n<img loading=\"lazy\" class=\"alignnone size-full wp-image-13149\" src=\"https:\/\/ccssmathanswers.com\/wp-content\/uploads\/2020\/12\/Big-Ideas-Math-Answer-Key-Grade-4-Chapter-7-Understand-Fraction-Equivalence-and-Comparison-7.1-18.png\" alt=\"Big Ideas Math Answer Key Grade 4 Chapter 7 Understand Fraction Equivalence and Comparison 7.1 18\" width=\"205\" height=\"154\" \/><br \/>\nFrom the above model, we can say that the fraction is: \\(\\frac{1}{4}\\)<br \/>\nSo,<br \/>\nThe model for the equivalent fraction is:<br \/>\n<img loading=\"lazy\" class=\"alignnone size-full wp-image-23709\" src=\"https:\/\/ccssmathanswers.com\/wp-content\/uploads\/2020\/12\/Big-Ideas-Math-Answers-Grade-4-Chapter-7-10.jpg\" alt=\"\" width=\"305\" height=\"264\" srcset=\"https:\/\/bigideasmathanswers.com\/wp-content\/uploads\/2020\/12\/Big-Ideas-Math-Answers-Grade-4-Chapter-7-10.jpg 305w, https:\/\/bigideasmathanswers.com\/wp-content\/uploads\/2020\/12\/Big-Ideas-Math-Answers-Grade-4-Chapter-7-10-300x260.jpg 300w\" sizes=\"(max-width: 305px) 100vw, 305px\" \/><br \/>\nFrom the above model,<br \/>\nSo, we can say that the equivalent fraction is: \\(\\frac{2}{8}\\)<br \/>\nSo,<br \/>\nWhen \\(\\frac{1}{4}\\) is multiplied and divided by 2, we can get the equivalent value.<br \/>\nHence, from the above,<br \/>\nWe can conclude that \\(\\frac{1}{4}\\) = \\(\\frac{2}{8}\\)<\/p>\n<p><strong>Use a number line to find an equivalent fraction.<\/strong><br \/>\nQuestion 3.<br \/>\n<img loading=\"lazy\" class=\"alignnone size-full wp-image-13150\" src=\"https:\/\/ccssmathanswers.com\/wp-content\/uploads\/2020\/12\/Big-Ideas-Math-Answer-Key-Grade-4-Chapter-7-Understand-Fraction-Equivalence-and-Comparison-7.1-19.png\" alt=\"Big Ideas Math Answer Key Grade 4 Chapter 7 Understand Fraction Equivalence and Comparison 7.1 19\" width=\"286\" height=\"122\" \/><br \/>\nAnswer: The equivalent fraction of \\(\\frac{4}{6}\\) is: \\(\\frac{8}{12}\\)<\/p>\n<p>Explanation:<br \/>\nThe given Number line is:<br \/>\n<img loading=\"lazy\" class=\"alignnone size-full wp-image-13150\" src=\"https:\/\/ccssmathanswers.com\/wp-content\/uploads\/2020\/12\/Big-Ideas-Math-Answer-Key-Grade-4-Chapter-7-Understand-Fraction-Equivalence-and-Comparison-7.1-19.png\" alt=\"Big Ideas Math Answer Key Grade 4 Chapter 7 Understand Fraction Equivalence and Comparison 7.1 19\" width=\"286\" height=\"122\" \/><br \/>\nFrom the given number line,<br \/>\nwe can see that every 2 lines represent a value.i.e., \\(\\frac{4}{6}\\)<br \/>\nSo, when there will be 2 lines between 2 values, then each line will become \\(\\frac{1}{12}\\)<br \/>\nSo,<br \/>\nThe model for the equivalent fraction is:<br \/>\n<img loading=\"lazy\" class=\"alignnone size-full wp-image-23713\" src=\"https:\/\/ccssmathanswers.com\/wp-content\/uploads\/2020\/12\/Big-Ideas-Math-Answers-Grade-4-Chapter-7-12.jpg\" alt=\"\" width=\"293\" height=\"114\" \/><br \/>\nSo, from the equivalent number line,<br \/>\nWe can say that \\(\\frac{4}{6}\\) is equal to \\(\\frac{8}{12}\\)<br \/>\nHence, from the above,<br \/>\nWe can conclude that \\(\\frac{4}{6}\\) = \\(\\frac{8}{12}\\)<\/p>\n<p>Question 4.<br \/>\n<img loading=\"lazy\" class=\"alignnone size-full wp-image-13151\" src=\"https:\/\/ccssmathanswers.com\/wp-content\/uploads\/2020\/12\/Big-Ideas-Math-Answer-Key-Grade-4-Chapter-7-Understand-Fraction-Equivalence-and-Comparison-7.1-20.png\" alt=\"Big Ideas Math Answer Key Grade 4 Chapter 7 Understand Fraction Equivalence and Comparison 7.1 20\" width=\"307\" height=\"128\" srcset=\"https:\/\/bigideasmathanswers.com\/wp-content\/uploads\/2020\/12\/Big-Ideas-Math-Answer-Key-Grade-4-Chapter-7-Understand-Fraction-Equivalence-and-Comparison-7.1-20.png 307w, https:\/\/bigideasmathanswers.com\/wp-content\/uploads\/2020\/12\/Big-Ideas-Math-Answer-Key-Grade-4-Chapter-7-Understand-Fraction-Equivalence-and-Comparison-7.1-20-300x125.png 300w\" sizes=\"(max-width: 307px) 100vw, 307px\" \/><br \/>\nAnswer: The equivalent fraction of \\(\\frac{2}{3}\\) is: \\(\\frac{4}{6}\\)<\/p>\n<p>Explanation:<br \/>\nThe given number line is:<br \/>\n<img loading=\"lazy\" class=\"alignnone size-full wp-image-13151\" src=\"https:\/\/ccssmathanswers.com\/wp-content\/uploads\/2020\/12\/Big-Ideas-Math-Answer-Key-Grade-4-Chapter-7-Understand-Fraction-Equivalence-and-Comparison-7.1-20.png\" alt=\"Big Ideas Math Answer Key Grade 4 Chapter 7 Understand Fraction Equivalence and Comparison 7.1 20\" width=\"307\" height=\"128\" srcset=\"https:\/\/bigideasmathanswers.com\/wp-content\/uploads\/2020\/12\/Big-Ideas-Math-Answer-Key-Grade-4-Chapter-7-Understand-Fraction-Equivalence-and-Comparison-7.1-20.png 307w, https:\/\/bigideasmathanswers.com\/wp-content\/uploads\/2020\/12\/Big-Ideas-Math-Answer-Key-Grade-4-Chapter-7-Understand-Fraction-Equivalence-and-Comparison-7.1-20-300x125.png 300w\" sizes=\"(max-width: 307px) 100vw, 307px\" \/><br \/>\nFrom the above number line,<br \/>\nwe can say that 2 lines represent a value. i.e., \\(\\frac{2}{3}\\)<br \/>\nSo,<br \/>\nThe value of each line when divided into 2 parts represent: \\(\\frac{1}{6}\\)<br \/>\nSo,<br \/>\nThe equivalent number line is:<br \/>\n<img loading=\"lazy\" class=\"alignnone size-full wp-image-23715\" src=\"https:\/\/ccssmathanswers.com\/wp-content\/uploads\/2020\/12\/Big-Ideas-Math-Answers-Grade-4-Chapter-7-13.jpg\" alt=\"\" width=\"302\" height=\"110\" srcset=\"https:\/\/bigideasmathanswers.com\/wp-content\/uploads\/2020\/12\/Big-Ideas-Math-Answers-Grade-4-Chapter-7-13.jpg 302w, https:\/\/bigideasmathanswers.com\/wp-content\/uploads\/2020\/12\/Big-Ideas-Math-Answers-Grade-4-Chapter-7-13-300x109.jpg 300w\" sizes=\"(max-width: 302px) 100vw, 302px\" \/><br \/>\nSo, from the above equivalent number line,<br \/>\nWe can see that \\(\\frac{2}{3}\\) is equal to \\(\\frac{4}{6}\\)<br \/>\nHence, from the above,<br \/>\nWe can conclude that \\(\\frac{2}{3}\\) = \\(\\frac{4}{6}\\)<\/p>\n<p><strong>Find the equivalent fraction.<\/strong><br \/>\nQuestion 5.<br \/>\n<img loading=\"lazy\" class=\"alignnone size-full wp-image-13152\" src=\"https:\/\/ccssmathanswers.com\/wp-content\/uploads\/2020\/12\/Big-Ideas-Math-Answer-Key-Grade-4-Chapter-7-Understand-Fraction-Equivalence-and-Comparison-7.1-21.png\" alt=\"Big Ideas Math Answer Key Grade 4 Chapter 7 Understand Fraction Equivalence and Comparison 7.1 21\" width=\"85\" height=\"69\" \/><br \/>\nAnswer: The equivalent fraction of \\(\\frac{1}{6}\\) is: \\(\\frac{2}{12}\\)<\/p>\n<p>Explanation:<br \/>\nWhen we multiply and divide \\(\\frac{1}{6}\\) with 2, we will get the equivalent value of \\(\\frac{1}{6}\\)<br \/>\nSo,<br \/>\n<img loading=\"lazy\" class=\"alignnone size-full wp-image-23718\" src=\"https:\/\/ccssmathanswers.com\/wp-content\/uploads\/2020\/12\/Big-Ideas-Math-Answers-Grade-4-Chapter-7-14.jpg\" alt=\"\" width=\"77\" height=\"48\" \/><br \/>\nHence, from the above,<br \/>\nWe can conclude that \\(\\frac{1}{6}\\) = \\(\\frac{2}{12}\\)<\/p>\n<p>Question 6.<br \/>\n<img loading=\"lazy\" class=\"alignnone size-full wp-image-13153\" src=\"https:\/\/ccssmathanswers.com\/wp-content\/uploads\/2020\/12\/Big-Ideas-Math-Answer-Key-Grade-4-Chapter-7-Understand-Fraction-Equivalence-and-Comparison-7.1-22.png\" alt=\"Big Ideas Math Answer Key Grade 4 Chapter 7 Understand Fraction Equivalence and Comparison 7.1 22\" width=\"71\" height=\"62\" \/><br \/>\nAnswer: The equivalent fraction of \\(\\frac{2}{5}\\) is: \\(\\frac{4}{10}\\)<\/p>\n<p>Explanation:<br \/>\nWhen we multiply and divide \\(\\frac{2}{5}\\) with 2, we will get the equivalent value of \\(\\frac{2}{5}\\)<br \/>\nSo,<br \/>\n<img loading=\"lazy\" class=\"alignnone size-full wp-image-23719\" src=\"https:\/\/ccssmathanswers.com\/wp-content\/uploads\/2020\/12\/Big-Ideas-Math-Answers-Grade-4-Chapter-7-15.jpg\" alt=\"\" width=\"74\" height=\"47\" \/><br \/>\nHence, from the above,<br \/>\nWe can conclude that \\(\\frac{2}{5}\\) = \\(\\frac{4}{10}\\)<\/p>\n<p>Question 7.<br \/>\n<img loading=\"lazy\" class=\"alignnone size-full wp-image-13154\" src=\"https:\/\/ccssmathanswers.com\/wp-content\/uploads\/2020\/12\/Big-Ideas-Math-Answer-Key-Grade-4-Chapter-7-Understand-Fraction-Equivalence-and-Comparison-7.1-23.png\" alt=\"Big Ideas Math Answer Key Grade 4 Chapter 7 Understand Fraction Equivalence and Comparison 7.1 23\" width=\"63\" height=\"62\" \/><br \/>\nAnswer: The equivalent fraction of \\(\\frac{1}{4}\\) is: \\(\\frac{2}{8}\\)<\/p>\n<p>Explanation:<br \/>\nWhen we multiply and divide \\(\\frac{1}{4}\\) with 2, we will get the equivalent value of \\(\\frac{1}{4}\\)<br \/>\nSo,<br \/>\n<img loading=\"lazy\" class=\"alignnone size-full wp-image-23721\" src=\"https:\/\/ccssmathanswers.com\/wp-content\/uploads\/2020\/12\/Big-Ideas-Math-Answers-Grade-4-Chapter-7-16.jpg\" alt=\"\" width=\"63\" height=\"52\" \/><br \/>\nHence, from the above,<br \/>\nWe can conclude that \\(\\frac{1}{4}\\) = \\(\\frac{2}{8}\\)<\/p>\n<p>Question 8.<br \/>\n<img loading=\"lazy\" class=\"alignnone size-full wp-image-13155\" src=\"https:\/\/ccssmathanswers.com\/wp-content\/uploads\/2020\/12\/Big-Ideas-Math-Answer-Key-Grade-4-Chapter-7-Understand-Fraction-Equivalence-and-Comparison-7.1-24.png\" alt=\"Big Ideas Math Answer Key Grade 4 Chapter 7 Understand Fraction Equivalence and Comparison 7.1 24\" width=\"77\" height=\"66\" \/><br \/>\nAnswer: The equivalent fraction of \\(\\frac{9}{12}\\) is: \\(\\frac{3}{4}\\)<\/p>\n<p>Explanation:<br \/>\nWhen we divide the \\(\\frac{9}{12}\\) by 3, we will get the equivalent value of \\(\\frac{9}{12}\\)<br \/>\nSo,<br \/>\n<img loading=\"lazy\" class=\"alignnone size-full wp-image-23723\" src=\"https:\/\/ccssmathanswers.com\/wp-content\/uploads\/2020\/12\/Big-Ideas-Math-Answers-Grade-4-Chapter-7-17.jpg\" alt=\"\" width=\"65\" height=\"48\" \/><br \/>\nHence, from the above,<br \/>\nWe can conclude that \\(\\frac{9}{12}\\) = \\(\\frac{3}{4}\\)<\/p>\n<p>Question 9.<br \/>\n<strong>Which One Doesn\u2019tBelong?<\/strong><br \/>\nWhich model does not belong with the other three? Explain<br \/>\n<img loading=\"lazy\" class=\"alignnone size-full wp-image-13156\" src=\"https:\/\/ccssmathanswers.com\/wp-content\/uploads\/2020\/12\/Big-Ideas-Math-Answer-Key-Grade-4-Chapter-7-Understand-Fraction-Equivalence-and-Comparison-7.1-25.png\" alt=\"Big Ideas Math Answer Key Grade 4 Chapter 7 Understand Fraction Equivalence and Comparison 7.1 25\" width=\"590\" height=\"120\" srcset=\"https:\/\/bigideasmathanswers.com\/wp-content\/uploads\/2020\/12\/Big-Ideas-Math-Answer-Key-Grade-4-Chapter-7-Understand-Fraction-Equivalence-and-Comparison-7.1-25.png 590w, https:\/\/bigideasmathanswers.com\/wp-content\/uploads\/2020\/12\/Big-Ideas-Math-Answer-Key-Grade-4-Chapter-7-Understand-Fraction-Equivalence-and-Comparison-7.1-25-300x61.png 300w\" sizes=\"(max-width: 590px) 100vw, 590px\" \/><br \/>\nAnswer:<br \/>\nLet the given figures be named as A), B), C) and D)<br \/>\nSo,<br \/>\nfrom the fraction values, figure C) does not belong with the other three because the values of the denominators of A), B), D) are all the multiples of 3<\/p>\n<p>Explanation:<br \/>\nThere are 4 given figures.<br \/>\nLet it be named as A), B), C) and D)<br \/>\n<img loading=\"lazy\" class=\"alignnone size-full wp-image-13156\" src=\"https:\/\/ccssmathanswers.com\/wp-content\/uploads\/2020\/12\/Big-Ideas-Math-Answer-Key-Grade-4-Chapter-7-Understand-Fraction-Equivalence-and-Comparison-7.1-25.png\" alt=\"Big Ideas Math Answer Key Grade 4 Chapter 7 Understand Fraction Equivalence and Comparison 7.1 25\" width=\"590\" height=\"120\" srcset=\"https:\/\/bigideasmathanswers.com\/wp-content\/uploads\/2020\/12\/Big-Ideas-Math-Answer-Key-Grade-4-Chapter-7-Understand-Fraction-Equivalence-and-Comparison-7.1-25.png 590w, https:\/\/bigideasmathanswers.com\/wp-content\/uploads\/2020\/12\/Big-Ideas-Math-Answer-Key-Grade-4-Chapter-7-Understand-Fraction-Equivalence-and-Comparison-7.1-25-300x61.png 300w\" sizes=\"(max-width: 590px) 100vw, 590px\" \/><br \/>\nFrom A),<br \/>\nThe total number of parts are: 3<br \/>\nThe colored part is: 1<br \/>\nSo,<br \/>\nThe fraction form is: \\(\\frac{The colored part}{The total number of parts}\\) = \\(\\frac{1}{3}\\)<br \/>\nFrom B),<br \/>\nThe total number of parts are: 6<br \/>\nThe colored part is: 3<br \/>\nSo,<br \/>\nThe fraction form is: \\(\\frac{The colored part}{The total number of parts}\\) = \\(\\frac{3}{6}\\)<br \/>\nFrom C),<br \/>\nThe total number of parts are: 5<br \/>\nThe colored part is: 2<br \/>\nSo,<br \/>\nThe fraction form is: \\(\\frac{The colored part}{The total number of parts}\\) = \\(\\frac{2}{5}\\)<br \/>\nFrom D),<br \/>\nThe total number of parts are: 12<br \/>\nThe colored part is: 4<br \/>\nSo,<br \/>\nThe fraction form is: \\(\\frac{The colored part}{The total number of parts}\\) = \\(\\frac{4}{12}\\)<br \/>\nHence, from all the figures,<br \/>\nWe can conclude that figure C) does not belong with the other three because the values of the denominators of A), B), D) are all the multiples of 3<\/p>\n<p>Question 10.<br \/>\n<strong>Modeling Real Life<\/strong><br \/>\nYour crayon is \\(\\frac{1}{6}\\) foot long. Your friend\u2019s crayon is \\(\\frac{3}{12}\\) foot long. Are the crayons the same length?<br \/>\n<img loading=\"lazy\" class=\"alignnone size-full wp-image-13157\" src=\"https:\/\/ccssmathanswers.com\/wp-content\/uploads\/2020\/12\/Big-Ideas-Math-Answer-Key-Grade-4-Chapter-7-Understand-Fraction-Equivalence-and-Comparison-7.1-26.png\" alt=\"Big Ideas Math Answer Key Grade 4 Chapter 7 Understand Fraction Equivalence and Comparison 7.1 26\" width=\"236\" height=\"240\" \/><br \/>\nAnswer: No, the crayons are not of the same length because your crayon is shorter than the crayon of your friend.<\/p>\n<p>Explanation:<br \/>\nGiven that,<br \/>\nThe length of your crayon is: \\(\\frac{1}{6}\\) foot<br \/>\nThe length of your friend&#8217;s crayon is: \\(\\frac{3}{12}\\) foot<br \/>\nSo,<br \/>\nWhen we compare \\(\\frac{1}{6}\\) foot and \\(\\frac{3}{12}\\) foot,<br \/>\nNow,<br \/>\nMultiply and divide \\(\\frac{1}{6}\\) with 2, we will get \\(\\frac{2}{12}\\) foot<br \/>\nSo,<br \/>\nwe can sayt that \\(\\frac{1}{6}\\) foot is less than \\(\\frac{3}{12}\\) foot<br \/>\nHence, from the above,<br \/>\nWe can conclude that the length of the crayons are not equal.<\/p>\n<p><strong>Review &amp; Refresh<\/strong><\/p>\n<p><strong>Find the product<\/strong><br \/>\nQuestion 11.<br \/>\n5 \u00d7 437 = _______<br \/>\nAnswer: 5 \u00d7 437 = 2,185<\/p>\n<p>Explanation:<br \/>\nBy using the partial products method,<br \/>\n5 \u00d7 437 = 5 \u00d7 ( 400 + 30 + 7 )<br \/>\n= ( 5 \u00d7 400 ) + ( 5 \u00d7 30 ) + ( 5 \u00d7 7 )<br \/>\n= 2,000 + 150 + 35<br \/>\n= 2,185<br \/>\nHence, 5 \u00d7 437 = 2,185<\/p>\n<p>Question 12.<br \/>\n6,982 \u00d7 9 = _______<br \/>\nAnswer: 6,982 \u00d7 9 = 62,838<\/p>\n<p>Explanation:<br \/>\nBy using the partial products method,<br \/>\n6,982 \u00d7 9 = ( 6,000 + 900 + 80 + 2 ) \u00d7 9<br \/>\n= ( 6,000 \u00d7 9 ) + ( 900 \u00d7 9 ) + ( 80 \u00d7 9 ) + ( 2 \u00d7 9 )<br \/>\n= 54,000 + 8,100 + 720 + 18<br \/>\n= 62,838<br \/>\nHence, 6,982 \u00d7 9 = 62,838<\/p>\n<p>Question 13.<br \/>\n8 \u00d7 708 = _______<br \/>\nAnswer: 8 \u00d7 708 = 5,664<\/p>\n<p>Explanation:<br \/>\nBy using the partial products method,<br \/>\n8 \u00d7 708 = 8 \u00d7 ( 700 + 8 )<br \/>\n= ( 8 \u00d7 700 ) + ( 8 \u00d7 8 )<br \/>\n= 5,600 + 64<br \/>\n= 5,664<br \/>\nHence, 8 \u00d7 708 = 5,664<\/p>\n<h3><a id=\"Lesson_7.2_Generate_Equivalent_Fractions_by_Multiplying\"><\/a>Lesson 7.2 Generate Equivalent Fractions by Multiplying<\/h3>\n<p><strong>Explore and Grow<\/strong><\/p>\n<p>Shade the second model in each pair to show an equivalent fraction.Then write the fraction.<br \/>\n<img loading=\"lazy\" class=\"alignnone size-full wp-image-24266\" src=\"https:\/\/ccssmathanswers.com\/wp-content\/uploads\/2020\/12\/Big-Ideas-Math-Answers-Grade-4-Chapter-7-18.jpg\" alt=\"\" width=\"565\" height=\"213\" srcset=\"https:\/\/bigideasmathanswers.com\/wp-content\/uploads\/2020\/12\/Big-Ideas-Math-Answers-Grade-4-Chapter-7-18.jpg 565w, https:\/\/bigideasmathanswers.com\/wp-content\/uploads\/2020\/12\/Big-Ideas-Math-Answers-Grade-4-Chapter-7-18-300x113.jpg 300w\" sizes=\"(max-width: 565px) 100vw, 565px\" \/><br \/>\nDescribe the relationship between each pair of numerators and each pair of denominators.<br \/>\nAnswer: From the three models, we can say that the equivalent fractions of the three models obtained by multiplying and dividing \\(\\frac{1}{2}\\) with 2, 3 and 4<br \/>\nHence,<br \/>\nIn the first model,<br \/>\n\\(\\frac{1}{2}\\) = \\(\\frac{2}{4}\\)<br \/>\nIn the second model,<br \/>\n\\(\\frac{1}{2}\\) = \\(\\frac{3}{6}\\)<br \/>\nIn the third model,<br \/>\n\\(\\frac{1}{2}\\) = \\(\\frac{4}{8}\\)<\/p>\n<p><strong>Structure<\/strong><br \/>\nHow can you use multiplication to write equivalent fractions? Explain. Then use your method to find another fraction that is equivalent to \\(\\frac{1}{2}\\).<br \/>\nAnswer: The equivalent fraction of \\(\\frac{1}{2}\\) is: \\(\\frac{3}{6}\\)<br \/>\nSo,<br \/>\n\\(\\frac{1}{2}\\) = \\(\\frac{3}{6}\\)<\/p>\n<p>Explanation:<br \/>\nWe can multiply the given fraction by another fraction that have the same numerator and denominator to write equivalent fractions.<br \/>\nFor example,<br \/>\nTo write the equivalent fractions of \\(\\frac{1}{2}\\), we can multiply so many fractions with the same numerator and denominator like \\(\\frac{2}{2}\\), \\(\\frac{3}{3}\\) etc.<br \/>\nHence,<br \/>\nThe equivalent fraction of \\(\\frac{1}{2}\\) is: \\(\\frac{3}{6}\\) or \\(\\frac{2}{4}\\) or \\(\\frac{4}{8}\\) or \\(\\frac{5}{10}\\)<\/p>\n<p><strong>Think and Grow: Multiply to find Equivalent Fractions<\/strong><\/p>\n<p>You can find an equivalent fraction by multiplying the numerator and the denominator by the same number.<br \/>\n<img loading=\"lazy\" class=\"alignnone size-full wp-image-13159\" src=\"https:\/\/ccssmathanswers.com\/wp-content\/uploads\/2020\/12\/Big-Ideas-Math-Answers-4th-Grade-Chapter-7-Understand-Fraction-Equivalence-and-Comparison-7.2-2.png\" alt=\"Big Ideas Math Answers 4th Grade Chapter 7 Understand Fraction Equivalence and Comparison 7.2 2\" width=\"137\" height=\"67\" \/><br \/>\nExample<br \/>\nFind an equivalent fraction for \\(\\frac{3}{5}\\).<\/p>\n<p><img loading=\"lazy\" class=\"alignnone size-full wp-image-24268\" src=\"https:\/\/ccssmathanswers.com\/wp-content\/uploads\/2020\/12\/Big-Ideas-Math-Answers-Grade-4-Chapter-7-19.jpg\" alt=\"\" width=\"654\" height=\"435\" srcset=\"https:\/\/bigideasmathanswers.com\/wp-content\/uploads\/2020\/12\/Big-Ideas-Math-Answers-Grade-4-Chapter-7-19.jpg 654w, https:\/\/bigideasmathanswers.com\/wp-content\/uploads\/2020\/12\/Big-Ideas-Math-Answers-Grade-4-Chapter-7-19-300x200.jpg 300w\" sizes=\"(max-width: 654px) 100vw, 654px\" \/><\/p>\n<p><strong>Show and Grow<\/strong><\/p>\n<p><strong>Find an equivalent fraction.<\/strong><br \/>\nQuestion 1.<br \/>\n<img loading=\"lazy\" class=\"alignnone size-full wp-image-13161\" src=\"https:\/\/ccssmathanswers.com\/wp-content\/uploads\/2020\/12\/Big-Ideas-Math-Answers-4th-Grade-Chapter-7-Understand-Fraction-Equivalence-and-Comparison-7.2-4.png\" alt=\"Big Ideas Math Answers 4th Grade Chapter 7 Understand Fraction Equivalence and Comparison 7.2 4\" width=\"177\" height=\"74\" \/><br \/>\nAnswer: The equivalent fraction of \\(\\frac{5}{6}\\) is: \\(\\frac{10}{12}\\)<\/p>\n<p>Explanation:<br \/>\nWhen we multiply the fraction with the fraction having the same number as the numerator as the denominator, we will get the equivalent fraction.<br \/>\nSo,<br \/>\n\\(\\frac{5}{6}\\) is multiplied with \\(\\frac{2}{2}\\)<br \/>\nHence,<br \/>\n<img loading=\"lazy\" class=\"alignnone size-full wp-image-24270\" src=\"https:\/\/ccssmathanswers.com\/wp-content\/uploads\/2020\/12\/Big-Ideas-Math-Answers-Grade-4-Chapter-7-20.jpg\" alt=\"\" width=\"168\" height=\"69\" \/><\/p>\n<p>Question 2.<br \/>\n<img loading=\"lazy\" class=\"alignnone size-full wp-image-13162\" src=\"https:\/\/ccssmathanswers.com\/wp-content\/uploads\/2020\/12\/Big-Ideas-Math-Answers-4th-Grade-Chapter-7-Understand-Fraction-Equivalence-and-Comparison-7.2-5.png\" alt=\"Big Ideas Math Answers 4th Grade Chapter 7 Understand Fraction Equivalence and Comparison 7.2 5\" width=\"178\" height=\"68\" \/><br \/>\nAnswer: The equivalent fraction of \\(\\frac{8}{5}\\) is: \\(\\frac{16}{10}\\)<\/p>\n<p>Explanation:<br \/>\nWhen we multiply the fraction with the fraction having the same number as the numerator as the denominator, we will get the equivalent fraction.<br \/>\nSo,<br \/>\n\\(\\frac{8}{5}\\) is multiplied with \\(\\frac{2}{2}\\)<br \/>\nHence,<br \/>\n<img loading=\"lazy\" class=\"alignnone size-full wp-image-24272\" src=\"https:\/\/ccssmathanswers.com\/wp-content\/uploads\/2020\/12\/Big-Ideas-Math-Answers-Grade-4-Chapter-7-21.jpg\" alt=\"\" width=\"176\" height=\"58\" \/><\/p>\n<p><strong>Find the equivalent fraction.<\/strong><br \/>\nQuestion 3.<br \/>\n<img loading=\"lazy\" class=\"alignnone size-full wp-image-13163\" src=\"https:\/\/ccssmathanswers.com\/wp-content\/uploads\/2020\/12\/Big-Ideas-Math-Answers-4th-Grade-Chapter-7-Understand-Fraction-Equivalence-and-Comparison-7.2-6.png\" alt=\"Big Ideas Math Answers 4th Grade Chapter 7 Understand Fraction Equivalence and Comparison 7.2 6\" width=\"273\" height=\"123\" \/><br \/>\nAnswer: The equivalent fraction of \\(\\frac{1}{2}\\) is: \\(\\frac{4}{8}\\)<\/p>\n<p>Explanation:<br \/>\nThe given model is:<br \/>\n<img loading=\"lazy\" class=\"alignnone size-full wp-image-13163\" src=\"https:\/\/ccssmathanswers.com\/wp-content\/uploads\/2020\/12\/Big-Ideas-Math-Answers-4th-Grade-Chapter-7-Understand-Fraction-Equivalence-and-Comparison-7.2-6.png\" alt=\"Big Ideas Math Answers 4th Grade Chapter 7 Understand Fraction Equivalence and Comparison 7.2 6\" width=\"273\" height=\"123\" \/><br \/>\nThe two models are the original model and its equivalent model.<br \/>\nSo,<br \/>\nAccording to the models,<br \/>\n\\(\\frac{1}{2}\\) = \\(\\frac{4}{8}\\)<br \/>\nWhen we multiply the fraction with the fraction having the same number as the numerator as the denominator, we will get the equivalent fraction.<br \/>\nSo according to the Equivalet model,<br \/>\n\\(\\frac{1}{2}\\) is multiplied with \\(\\frac{4}{4}\\)<br \/>\nHence,<br \/>\n<img loading=\"lazy\" class=\"alignnone size-full wp-image-24274\" src=\"https:\/\/ccssmathanswers.com\/wp-content\/uploads\/2020\/12\/Big-Ideas-Math-Answers-Grade-4-Chapter-7-22.jpg\" alt=\"\" width=\"86\" height=\"51\" \/><\/p>\n<p>Question 4.<br \/>\n<img loading=\"lazy\" class=\"alignnone size-full wp-image-13164\" src=\"https:\/\/ccssmathanswers.com\/wp-content\/uploads\/2020\/12\/Big-Ideas-Math-Answers-4th-Grade-Chapter-7-Understand-Fraction-Equivalence-and-Comparison-7.2-7.png\" alt=\"Big Ideas Math Answers 4th Grade Chapter 7 Understand Fraction Equivalence and Comparison 7.2 7\" width=\"230\" height=\"119\" \/><br \/>\nAnswer: The equivalent fraction is: \\(\\frac{2}{3}\\) is: \\(\\frac{4}{6}\\)<\/p>\n<p>Explanation:<br \/>\nThe given model is:<br \/>\n<img loading=\"lazy\" class=\"alignnone size-full wp-image-13164\" src=\"https:\/\/ccssmathanswers.com\/wp-content\/uploads\/2020\/12\/Big-Ideas-Math-Answers-4th-Grade-Chapter-7-Understand-Fraction-Equivalence-and-Comparison-7.2-7.png\" alt=\"Big Ideas Math Answers 4th Grade Chapter 7 Understand Fraction Equivalence and Comparison 7.2 7\" width=\"230\" height=\"119\" \/><br \/>\nThe two models are the original model and the equivalent model.<br \/>\nSo,<br \/>\nAccording to the models,<br \/>\n\\(\\frac{2}{3}\\) = \\(\\frac{4}{6}\\)<br \/>\nWhen we multiply the fraction with the fraction having the same number as the numerator as the denominator, we will get the equivalent fraction.<br \/>\nSo according to the Equivalent model,<br \/>\n\\(\\frac{1}{2}\\) is multiplied with \\(\\frac{2}{2}\\)<br \/>\nHence,<br \/>\n<img loading=\"lazy\" class=\"alignnone size-full wp-image-24296\" src=\"https:\/\/ccssmathanswers.com\/wp-content\/uploads\/2020\/12\/Big-Ideas-Math-Answers-Grade-4-Chapter-7-23.jpg\" alt=\"\" width=\"85\" height=\"43\" \/><\/p>\n<p><strong>Apply and Grow: Practice<\/strong><\/p>\n<p><strong>Find the equivalent fraction<\/strong>.<br \/>\nQuestion 5.<br \/>\n<img loading=\"lazy\" class=\"alignnone size-full wp-image-13165\" src=\"https:\/\/ccssmathanswers.com\/wp-content\/uploads\/2020\/12\/Big-Ideas-Math-Answers-4th-Grade-Chapter-7-Understand-Fraction-Equivalence-and-Comparison-7.2-8.png\" alt=\"Big Ideas Math Answers 4th Grade Chapter 7 Understand Fraction Equivalence and Comparison 7.2 8\" width=\"279\" height=\"136\" \/><br \/>\nAnswer: The equivalent model of \\(\\frac{3}{4}\\) is: \\(\\frac{6}{8}\\)<\/p>\n<p>Explanation:<br \/>\nThe given model is:<br \/>\n<img loading=\"lazy\" class=\"alignnone size-full wp-image-13165\" src=\"https:\/\/ccssmathanswers.com\/wp-content\/uploads\/2020\/12\/Big-Ideas-Math-Answers-4th-Grade-Chapter-7-Understand-Fraction-Equivalence-and-Comparison-7.2-8.png\" alt=\"Big Ideas Math Answers 4th Grade Chapter 7 Understand Fraction Equivalence and Comparison 7.2 8\" width=\"279\" height=\"136\" \/><br \/>\nThe two models are the original model and the equivalent model.<br \/>\nSo,<br \/>\nAccording to the models,<br \/>\n\\(\\frac{3}{4}\\) = \\(\\frac{6}{8}\\)<br \/>\nWhen we multiply the fraction with the fraction having the same number as the numerator as the denominator, we will get the equivalent fraction.<br \/>\nSo according to the Equivalent model,<br \/>\n\\(\\frac{3}{4}\\) is multiplied with \\(\\frac{2}{2}\\)<br \/>\nHence,<br \/>\n<img loading=\"lazy\" class=\"alignnone size-full wp-image-24301\" src=\"https:\/\/ccssmathanswers.com\/wp-content\/uploads\/2020\/12\/Big-Ideas-Math-Answers-Grade-4-Chapter-7-24.jpg\" alt=\"\" width=\"86\" height=\"47\" \/><\/p>\n<p>Question 6.<br \/>\n<img loading=\"lazy\" class=\"alignnone size-full wp-image-13166\" src=\"https:\/\/ccssmathanswers.com\/wp-content\/uploads\/2020\/12\/Big-Ideas-Math-Answers-4th-Grade-Chapter-7-Understand-Fraction-Equivalence-and-Comparison-7.2-9.png\" alt=\"Big Ideas Math Answers 4th Grade Chapter 7 Understand Fraction Equivalence and Comparison 7.2 9\" width=\"278\" height=\"127\" \/><br \/>\nAnswer: The equivalent fraction of \\(\\frac{1}{3}\\) is: \\(\\frac{4}{12}\\)<\/p>\n<p>Explanation:<br \/>\nThe given model is:<br \/>\n<img loading=\"lazy\" class=\"alignnone size-full wp-image-13166\" src=\"https:\/\/ccssmathanswers.com\/wp-content\/uploads\/2020\/12\/Big-Ideas-Math-Answers-4th-Grade-Chapter-7-Understand-Fraction-Equivalence-and-Comparison-7.2-9.png\" alt=\"Big Ideas Math Answers 4th Grade Chapter 7 Understand Fraction Equivalence and Comparison 7.2 9\" width=\"278\" height=\"127\" \/><br \/>\nThe two models are the original model and the equivalent model.<br \/>\nSo,<br \/>\nAccording to the models,<br \/>\n\\(\\frac{1}{3}\\) = \\(\\frac{4}{12}\\)<br \/>\nWhen we multiply the fraction with the fraction having the same number as the numerator as the denominator, we will get the equivalent fraction.<br \/>\nSo according to the Equivalent model,<br \/>\n\\(\\frac{1}{3}\\) is multiplied with \\(\\frac{4}{4}\\)<br \/>\nHence,<br \/>\n<img loading=\"lazy\" class=\"alignnone size-full wp-image-24416\" src=\"https:\/\/ccssmathanswers.com\/wp-content\/uploads\/2020\/12\/Big-Ideas-Math-Answers-Grade-4-Chapter-7-25.jpg\" alt=\"\" width=\"83\" height=\"53\" \/><\/p>\n<p>Question 7.<br \/>\n<img loading=\"lazy\" class=\"alignnone size-full wp-image-13167\" src=\"https:\/\/ccssmathanswers.com\/wp-content\/uploads\/2020\/12\/Big-Ideas-Math-Answers-4th-Grade-Chapter-7-Understand-Fraction-Equivalence-and-Comparison-7.2-10.png\" alt=\"Big Ideas Math Answers 4th Grade Chapter 7 Understand Fraction Equivalence and Comparison 7.2 10\" width=\"85\" height=\"61\" \/><br \/>\nAnswer: The equivalent fraction of \\(\\frac{9}{6}\\) is: \\(\\frac{18}{12}\\)<\/p>\n<p>Explanation:<br \/>\nWhen we multiply the fraction with the fraction having the same number as the numerator as the denominator, we will get the equivalent fraction.<br \/>\nSo,<br \/>\n\\(\\frac{9}{6}\\) is multiplied with \\(\\frac{2}{2}\\)<br \/>\nHence,<br \/>\n<img loading=\"lazy\" class=\"alignnone size-full wp-image-24419\" src=\"https:\/\/ccssmathanswers.com\/wp-content\/uploads\/2020\/12\/Big-Ideas-Math-Answers-Grade-4-Chapter-7-26.jpg\" alt=\"\" width=\"87\" height=\"49\" \/><\/p>\n<p>Question 8.<br \/>\n<img loading=\"lazy\" class=\"alignnone size-full wp-image-13168\" src=\"https:\/\/ccssmathanswers.com\/wp-content\/uploads\/2020\/12\/Big-Ideas-Math-Answers-4th-Grade-Chapter-7-Understand-Fraction-Equivalence-and-Comparison-7.2-11.png\" alt=\"Big Ideas Math Answers 4th Grade Chapter 7 Understand Fraction Equivalence and Comparison 7.2 11\" width=\"91\" height=\"63\" \/><br \/>\nAnswer: The equivalent fraction of \\(\\frac{7}{5}\\) is: \\(\\frac{140}{100}\\)<\/p>\n<p>Explanation:<br \/>\nWhen we multiply the fraction with the fraction having the same number as the numerator as the denominator, we will get the equivalent fraction.<br \/>\nSo,<br \/>\n\\(\\frac{7}{5}\\) is multiplied with \\(\\frac{20}{20}\\)<br \/>\nHence,<br \/>\n<img loading=\"lazy\" class=\"alignnone size-full wp-image-24420\" src=\"https:\/\/ccssmathanswers.com\/wp-content\/uploads\/2020\/12\/Big-Ideas-Math-Answers-Grade-4-Chapter-7-27.jpg\" alt=\"\" width=\"87\" height=\"50\" \/><\/p>\n<p><strong>Find an equivalent fraction.<br \/>\n<\/strong>Question 9.<br \/>\n\\(\\frac{7}{6}\\)<br \/>\nAnswer: The equivalent fraction of \\(\\frac{7}{6}\\) is: \\(\\frac{14}{12}\\)<\/p>\n<p>Explanation:<br \/>\nWhen we multiply the fraction with the fraction having the same number as the numerator as the denominator, we will get the equivalent fraction.<br \/>\nSo,<br \/>\n\\(\\frac{7}{6}\\) is multiplied with \\(\\frac{2}{2}\\)<br \/>\nHence,<br \/>\n\\(\\frac{7}{6}\\) = \\(\\frac{14}{12}\\)<\/p>\n<p>Question 10.<br \/>\n\\(\\frac{10}{10}\\)<br \/>\nAnswer: The equivalent fraction of \\(\\frac{10}{10}\\) is: \\(\\frac{20}{20}\\)<\/p>\n<p>Explanation:<br \/>\nWhen we multiply the fraction with the fraction having the same number as the numerator as the denominator, we will get the equivalent fraction.<br \/>\nSo,<br \/>\n\\(\\frac{10}{10}\\) is multiplied with \\(\\frac{2}{2}\\)<br \/>\nHence,<br \/>\n\\(\\frac{10}{10}\\) = \\(\\frac{20}{20}\\)<\/p>\n<p>Question 11.<br \/>\n\\(\\frac{2}{4}\\)<br \/>\nAnswer: The equivalent fraction of \\(\\frac{2}{4}\\) is: \\(\\frac{4}{8}\\)<\/p>\n<p>Explanation:<br \/>\nWhen we multiply the fraction with the fraction having the same number as the numerator as the denominator, we will get the equivalent fraction.<br \/>\nSo,<br \/>\n\\(\\frac{2}{4}\\) is multiplied with \\(\\frac{2}{2}\\)<br \/>\nHence,<br \/>\n\\(\\frac{2}{4}\\) = \\(\\frac{4}{8}\\)<\/p>\n<p>Find two equivalent fractions.<br \/>\nQuestion 12.<br \/>\n\\(\\frac{5}{5}\\)<br \/>\nAnswer:<br \/>\nThe two equivalent fractions of \\(\\frac{5}{5}\\) are: \\(\\frac{10}{10}\\) and \\(\\frac{15}{15}\\)<\/p>\n<p>Explanation:<br \/>\nWhen we multiply the fraction with the fraction having the same number as the numerator as the denominator, we will get the equivalent fraction.<br \/>\nSo,<br \/>\n\\(\\frac{5}{5}\\) is multiplied with \\(\\frac{2}{2}\\) and \\(\\frac{3}{3}\\)<br \/>\nHence,<br \/>\n\\(\\frac{5}{5}\\) = \\(\\frac{10}{10}\\) and \\(\\frac{15}{15}\\)<\/p>\n<p>Question 13.<br \/>\n\\(\\frac{4}{3}\\)<br \/>\nAnswer:<br \/>\nThe two equivalent fractions of \\(\\frac{4}{3}\\) are: \\(\\frac{8}{6}\\) and \\(\\frac{12}{9}\\)<\/p>\n<p>Explanation:<br \/>\nWhen we multiply the fraction with the fraction having the same number as the numerator as the denominator, we will get the equivalent fraction.<br \/>\nSo,<br \/>\n\\(\\frac{4}{3}\\) is multiplied with \\(\\frac{2}{2}\\) and \\(\\frac{3}{3}\\)<br \/>\nHence,<br \/>\n\\(\\frac{4}{3}\\) = \\(\\frac{8}{6}\\) and \\(\\frac{12}{9}\\)<\/p>\n<p>Question 14.<br \/>\n\\(\\frac{1}{10}\\)<br \/>\nAnswer:<br \/>\nThe two equivalent fractions of \\(\\frac{1}{10}\\) are: \\(\\frac{2}{20}\\) and \\(\\frac{3}{30}\\)<\/p>\n<p>Explanation:<br \/>\nWhen we multiply the fraction with the fraction having the same number as the numerator as the denominator, we will get the equivalent fraction.<br \/>\nSo,<br \/>\n\\(\\frac{1}{10}\\) is multiplied with \\(\\frac{2}{2}\\) and \\(\\frac{3}{3}\\)<br \/>\nHence,<br \/>\n\\(\\frac{1}{10}\\) = \\(\\frac{2}{20}\\) and \\(\\frac{3}{30}\\)<\/p>\n<p>Question 15.<br \/>\n<strong>Writing<\/strong><br \/>\nExplain how \\(\\frac{1}{4}\\) and \\(\\frac{2}{8}\\) are equivalent using multiplication. Use models to support your answer.<br \/>\nAnswer: The equivalent fraction of \\(\\frac{1}{4}\\) is: \\(\\frac{2}{8}\\)<\/p>\n<p>Explanation:<br \/>\nFor the \\(\\frac{1}{4}\\) and \\(\\frac{2}{8}\\), the models are:<br \/>\n<img loading=\"lazy\" class=\"alignnone size-full wp-image-24429\" src=\"https:\/\/ccssmathanswers.com\/wp-content\/uploads\/2020\/12\/Big-Ideas-Math-Answers-Grade-4-Chapter-7-28.jpg\" alt=\"\" width=\"532\" height=\"175\" srcset=\"https:\/\/bigideasmathanswers.com\/wp-content\/uploads\/2020\/12\/Big-Ideas-Math-Answers-Grade-4-Chapter-7-28.jpg 532w, https:\/\/bigideasmathanswers.com\/wp-content\/uploads\/2020\/12\/Big-Ideas-Math-Answers-Grade-4-Chapter-7-28-300x99.jpg 300w\" sizes=\"(max-width: 532px) 100vw, 532px\" \/><br \/>\nThe two models are the original model and the equivalent model.<br \/>\nSo,<br \/>\nAccording to the original model,<br \/>\nThe total number of parts are: 4<br \/>\nThe colored part is: 1<br \/>\nAccording to the Equivalent model,<br \/>\nThe total number of parts are: 8<br \/>\nThe colored part is: 2<br \/>\nNow,<br \/>\nWhen we multiply the fraction with the fraction having the same number as the numerator as the denominator, we will get the equivalent fraction.<br \/>\nSo,<br \/>\nWhen we multiply \\(\\frac{1}{4}\\) with \\(\\frac{2}{2}\\), we will get the \\(\\frac{2}{8}\\) which is the equivalent value of \\(\\frac{1}{4}\\)<br \/>\nHence,<br \/>\nThe equivalent value of \\(\\frac{1}{4}\\) is: \\(\\frac{2}{8}\\)<\/p>\n<p><strong>DIG DEEPER!<\/strong><br \/>\nWrite true or false for the statement. If false, explain why.<br \/>\nQuestion 16.<br \/>\n<img loading=\"lazy\" class=\"alignnone size-full wp-image-13169\" src=\"https:\/\/ccssmathanswers.com\/wp-content\/uploads\/2020\/12\/Big-Ideas-Math-Answers-4th-Grade-Chapter-7-Understand-Fraction-Equivalence-and-Comparison-7.2-12.png\" alt=\"Big Ideas Math Answers 4th Grade Chapter 7 Understand Fraction Equivalence and Comparison 7.2 12\" width=\"167\" height=\"59\" \/><br \/>\nAnswer: \\(\\frac{4}{2}\\) = \\(\\frac{24}{12}\\)<\/p>\n<p>Explanation:<br \/>\nGiven fractions are: \\(\\frac{4}{2}\\) and \\(\\frac{24}{12}\\)<br \/>\nWhen we multiply the fraction with the fraction having the same number as the numerator as the denominator, we will get the equivalent fraction.<br \/>\nSo,<br \/>\nWhen \\(\\frac{4}{2}\\) is multiplied with \\(\\frac{6}{6}\\), we will get\u00a0 \\(\\frac{24}{12}\\) which is the equivalent value of \\(\\frac{4}{2}\\)<br \/>\nHence,<br \/>\n\\(\\frac{4}{2}\\) = \\(\\frac{24}{12}\\)<\/p>\n<p>Question 17.<br \/>\n<img loading=\"lazy\" class=\"alignnone size-full wp-image-13170\" src=\"https:\/\/ccssmathanswers.com\/wp-content\/uploads\/2020\/12\/Big-Ideas-Math-Answers-4th-Grade-Chapter-7-Understand-Fraction-Equivalence-and-Comparison-7.2-13.png\" alt=\"Big Ideas Math Answers 4th Grade Chapter 7 Understand Fraction Equivalence and Comparison 7.2 13\" width=\"164\" height=\"56\" \/><br \/>\nAnswer: \\(\\frac{3}{5}\\) is not equal to \\(\\frac{6}{100}\\)<\/p>\n<p>Explanation:<br \/>\nGiven fractions are: \\(\\frac{3}{5}\\) and \\(\\frac{6}{100}\\)<br \/>\nWhen we multiply the fraction with the fraction having the same number as the numerator as the denominator, we will get the equivalent fraction.<br \/>\nSo,<br \/>\nWhen \\(\\frac{3}{5}\\) is multiplied with \\(\\frac{2}{2}\\), we will get\u00a0 \\(\\frac{6}{10}\\) which is not the equivalent value of \\(\\frac{3}{5}\\)<br \/>\nHence,<br \/>\n\\(\\frac{3}{5}\\) is not equal to \\(\\frac{6}{100}\\)<\/p>\n<p><strong>Think and Grow: Modeling Real Life<\/strong><\/p>\n<p><strong>Example<\/strong><br \/>\nA recipe calls for \\(\\frac{3}{4}\\) cup of oats. You only have a \\(\\frac{1}{8}\\) cup measuring cup. What fraction of a cup of oats, in eighths,do you need? Use multiplication to write an equivalent fraction for \\(\\frac{3}{4}\\) in eighths.<br \/>\n<img loading=\"lazy\" class=\"alignnone size-full wp-image-13171\" src=\"https:\/\/ccssmathanswers.com\/wp-content\/uploads\/2020\/12\/Big-Ideas-Math-Answers-4th-Grade-Chapter-7-Understand-Fraction-Equivalence-and-Comparison-7.2-14.png\" alt=\"Big Ideas Math Answers 4th Grade Chapter 7 Understand Fraction Equivalence and Comparison 7.2 14\" width=\"237\" height=\"188\" \/><\/p>\n<p><img loading=\"lazy\" class=\"alignnone size-full wp-image-24432\" src=\"https:\/\/ccssmathanswers.com\/wp-content\/uploads\/2020\/12\/Big-Ideas-Math-Answers-Grade-4-Chapter-7-29.jpg\" alt=\"\" width=\"581\" height=\"129\" srcset=\"https:\/\/bigideasmathanswers.com\/wp-content\/uploads\/2020\/12\/Big-Ideas-Math-Answers-Grade-4-Chapter-7-29.jpg 581w, https:\/\/bigideasmathanswers.com\/wp-content\/uploads\/2020\/12\/Big-Ideas-Math-Answers-Grade-4-Chapter-7-29-300x67.jpg 300w\" sizes=\"(max-width: 581px) 100vw, 581px\" \/><\/p>\n<p><strong>Show and Grow<\/strong><\/p>\n<p>Question 18.<br \/>\nYou need \\(\\frac{1}{2}\\) cup of water for a science experiment. You only have a \\(\\frac{1}{4}\\) cup measuring cup. What fraction of a cup of water, in fourths, do you need?<br \/>\nAnswer: You need \\(\\frac{2}{4}\\), in fourths, of a cup of water<\/p>\n<p>Explanation:<br \/>\nGiven that you need \\(\\frac{1}{2}\\) cup of water for a science experiment and you only have a \\(\\frac{1}{4}\\) cup measuring cup.<br \/>\nSo, in terms of \\(\\frac{1}{4}\\), \\(\\frac{1}{2}\\) can be written as:<br \/>\n\\(\\frac{1}{2}\\) = \\(\\frac{1 \u00d7 2}{2 \u00d7 2}\\)<br \/>\n= \\(\\frac{2}{4}\\)<br \/>\nHence, from the above,<br \/>\nWe can conclude that we need \\(\\frac{2}{4}\\) fraction of a cup of water, in fourths<\/p>\n<p>Question 19.<br \/>\nA pedestrian needs to walk \\(\\frac{4}{5}\\) mile to meet her goal. The path is marked at every tenth of a mile. What fraction of a mile, in tenths, should she walk?<br \/>\nAnswer: She should walk \\(\\frac{8}{10}\\), in tenths of a mile<\/p>\n<p>Explanation:<br \/>\nGiven that a pedestrian needs to walk \\(\\frac{4}{5}\\) mile to meet her goal.<br \/>\nIt is also given that the path is marked at every tenth of a mile.<br \/>\nSo, in terms of \\(\\frac{1}{10}\\), \\(\\frac{4}{5}\\) can be written as:<br \/>\n\\(\\frac{4}{5}\\) = \\(\\frac{4 \u00d7 2}{5 \u00d7 2}\\)<br \/>\n= \\(\\frac{8}{10}\\)<br \/>\nHence, from the above,<br \/>\nWe can conclude that she should walk \\(\\frac{8}{10}\\), in tenths of a mile<\/p>\n<p>Question 20.<br \/>\n<strong>DIG DEEPER!<\/strong><br \/>\nYou put together \\(\\frac{7}{10}\\) of a puzzle. The puzzle has pieces. What fraction of the puzzle, in hundredths, is not put together? Explain.<br \/>\n<img loading=\"lazy\" class=\"alignnone size-full wp-image-13173\" src=\"https:\/\/ccssmathanswers.com\/wp-content\/uploads\/2020\/12\/Big-Ideas-Math-Answers-4th-Grade-Chapter-7-Understand-Fraction-Equivalence-and-Comparison-7.2-16.png\" alt=\"Big Ideas Math Answers 4th Grade Chapter 7 Understand Fraction Equivalence and Comparison 7.2 16\" width=\"189\" height=\"125\" \/><br \/>\nAnswer: The fraction of the puzzle not put together, in hundredths is: \\(\\frac{30}{100}\\)<\/p>\n<p>Explanation:<br \/>\nGiven that you put together \\(\\frac{7}{10}\\) of a puzzle.<br \/>\nSo, from this, the part of the puzzle that is not put together is: \\(\\frac{3}{10}\\)<br \/>\nWe have to find the fraction of the puzzle that is not put together, in hundredths<br \/>\nSo, in terms of \\(\\frac{1}{100}\\), \\(\\frac{3}{10}\\) can be written as:<br \/>\n\\(\\frac{3}{10}\\) = \\(\\frac{3 \u00d7 10}{10 \u00d7 10}\\)<br \/>\n= \\(\\frac{30}{100}\\)<br \/>\nHence, from the above,<br \/>\nWe can conclude that the fraction of the puzzle not put together, in hundredths is: \\(\\frac{30}{100}\\)<\/p>\n<p>Question 21.<br \/>\nYou have \\(\\frac{3}{5}\\) of a dollar in coins. What fraction of a dollar, in hundredths, do you have? Write one possible combination of coins that you have.<br \/>\n<img loading=\"lazy\" class=\"alignnone size-full wp-image-13174\" src=\"https:\/\/ccssmathanswers.com\/wp-content\/uploads\/2020\/12\/Big-Ideas-Math-Answers-4th-Grade-Chapter-7-Understand-Fraction-Equivalence-and-Comparison-7.2-17.png\" alt=\"Big Ideas Math Answers 4th Grade Chapter 7 Understand Fraction Equivalence and Comparison 7.2 17\" width=\"188\" height=\"171\" \/><br \/>\nAnswer: The fraction of a dollar in hundredths is: \\(\\frac{60}{100}\\)<\/p>\n<p>Explanation:<br \/>\nGiven that you have \\(\\frac{3}{5}\\) of a dollar in coins.<br \/>\nSo, in terms of \\(\\frac{1}{100}\\), \\(\\frac{3}{5}\\) can be written as:<br \/>\n\\(\\frac{3}{5}\\) = \\(\\frac{3 \u00d7 20}{5 \u00d7 20}\\)<br \/>\n= \\(\\frac{60}{100}\\)<br \/>\nHence, from the above,<br \/>\nWe can conclude that the fraction of a dollar in hundredths is: \\(\\frac{60}{100}\\)<\/p>\n<h3><a id=\"Generate_Equivalent_Fractions_by_Multiplying_Homework_&amp;_Practice_7.2\"><\/a>Generate Equivalent Fractions by Multiplying Homework &amp; Practice 7.2<\/h3>\n<p><strong>Find an equivalent fraction.<\/strong><br \/>\nQuestion 1.<br \/>\n<img loading=\"lazy\" class=\"alignnone size-full wp-image-13175\" src=\"https:\/\/ccssmathanswers.com\/wp-content\/uploads\/2020\/12\/Big-Ideas-Math-Answers-4th-Grade-Chapter-7-Understand-Fraction-Equivalence-and-Comparison-7.2-18.png\" alt=\"Big Ideas Math Answers 4th Grade Chapter 7 Understand Fraction Equivalence and Comparison 7.2 18\" width=\"165\" height=\"65\" \/><br \/>\nAnswer: The equivalent fraction of \\(\\frac{1}{5}\\) is: \\(\\frac{2}{10}\\)<\/p>\n<p>Explanation:<br \/>\nWhen we multiply the fraction with the fraction having the same number as the numerator as the denominator, we will get the equivalent fraction.<br \/>\nSo,<br \/>\n\\(\\frac{1}{5}\\) is multiplied with \\(\\frac{2}{2}\\)<br \/>\nHence,<br \/>\n<img loading=\"lazy\" class=\"alignnone size-full wp-image-24446\" src=\"https:\/\/ccssmathanswers.com\/wp-content\/uploads\/2020\/12\/Big-Ideas-Math-Answers-Grade-4-Chapter-7-30.jpg\" alt=\"\" width=\"163\" height=\"60\" \/><\/p>\n<p>Question 2.<br \/>\n<img loading=\"lazy\" class=\"alignnone size-full wp-image-13176\" src=\"https:\/\/ccssmathanswers.com\/wp-content\/uploads\/2020\/12\/Big-Ideas-Math-Answers-4th-Grade-Chapter-7-Understand-Fraction-Equivalence-and-Comparison-7.2-19.png\" alt=\"Big Ideas Math Answers 4th Grade Chapter 7 Understand Fraction Equivalence and Comparison 7.2 19\" width=\"187\" height=\"66\" \/><br \/>\nAnswer: The equivalent fraction of \\(\\frac{11}{6}\\) is: \\(\\frac{22}{12}\\)<\/p>\n<p>Explanation:<br \/>\nWhen we multiply the fraction with the fraction having the same number as the numerator as the denominator, we will get the equivalent fraction.<br \/>\nSo,<br \/>\n\\(\\frac{11}{6}\\) is multiplied with \\(\\frac{2}{2}\\)<br \/>\nHence,<br \/>\n<img loading=\"lazy\" class=\"alignnone size-full wp-image-24448\" src=\"https:\/\/ccssmathanswers.com\/wp-content\/uploads\/2020\/12\/Big-Ideas-Math-Answers-Grade-4-Chapter-7-31.jpg\" alt=\"\" width=\"186\" height=\"57\" \/><\/p>\n<p><strong>Find an equivalent fraction.<\/strong><br \/>\nQuestion 3.<br \/>\n<img loading=\"lazy\" class=\"alignnone size-full wp-image-13177\" src=\"https:\/\/ccssmathanswers.com\/wp-content\/uploads\/2020\/12\/Big-Ideas-Math-Answers-4th-Grade-Chapter-7-Understand-Fraction-Equivalence-and-Comparison-7.2-20.png\" alt=\"Big Ideas Math Answers 4th Grade Chapter 7 Understand Fraction Equivalence and Comparison 7.2 20\" width=\"286\" height=\"126\" \/><br \/>\nAnswer: The equivalent fraction of \\(\\frac{4}{6}\\) is: \\(\\frac{8}{12}\\)<\/p>\n<p>Explanation:<br \/>\nThe given model is:<br \/>\n<img loading=\"lazy\" class=\"alignnone size-full wp-image-13177\" src=\"https:\/\/ccssmathanswers.com\/wp-content\/uploads\/2020\/12\/Big-Ideas-Math-Answers-4th-Grade-Chapter-7-Understand-Fraction-Equivalence-and-Comparison-7.2-20.png\" alt=\"Big Ideas Math Answers 4th Grade Chapter 7 Understand Fraction Equivalence and Comparison 7.2 20\" width=\"286\" height=\"126\" \/><br \/>\nThe two models are the original model and its equivalent model.<br \/>\nSo,<br \/>\nAccording to the models,<br \/>\n\\(\\frac{4}{6}\\) = \\(\\frac{8}{12}\\)<br \/>\nWhen we multiply the fraction with the fraction having the same number as the numerator as the denominator, we will get the equivalent fraction.<br \/>\nSo according to the Equivalent model,<br \/>\n\\(\\frac{4}{6}\\) is multiplied with \\(\\frac{2}{2}\\)<br \/>\nHence,<br \/>\n<img loading=\"lazy\" class=\"alignnone size-full wp-image-24449\" src=\"https:\/\/ccssmathanswers.com\/wp-content\/uploads\/2020\/12\/Big-Ideas-Math-Answers-Grade-4-Chapter-7-32.jpg\" alt=\"\" width=\"86\" height=\"46\" \/><\/p>\n<p>Question 4.<br \/>\n<img loading=\"lazy\" class=\"alignnone size-full wp-image-13178\" src=\"https:\/\/ccssmathanswers.com\/wp-content\/uploads\/2020\/12\/Big-Ideas-Math-Answers-4th-Grade-Chapter-7-Understand-Fraction-Equivalence-and-Comparison-7.2-21.png\" alt=\"Big Ideas Math Answers 4th Grade Chapter 7 Understand Fraction Equivalence and Comparison 7.2 21\" width=\"246\" height=\"124\" \/><br \/>\nAnswer: The equivalent fraction of \\(\\frac{2}{5}\\) is: \\(\\frac{4}{10}\\)<\/p>\n<p>Explanation:<br \/>\nThe given model is:<br \/>\n<img loading=\"lazy\" class=\"alignnone size-full wp-image-13178\" src=\"https:\/\/ccssmathanswers.com\/wp-content\/uploads\/2020\/12\/Big-Ideas-Math-Answers-4th-Grade-Chapter-7-Understand-Fraction-Equivalence-and-Comparison-7.2-21.png\" alt=\"Big Ideas Math Answers 4th Grade Chapter 7 Understand Fraction Equivalence and Comparison 7.2 21\" width=\"246\" height=\"124\" \/><br \/>\nThe two models are the original model and its equivalent model.<br \/>\nSo,<br \/>\nAccording to the models,<br \/>\n\\(\\frac{2}{5}\\) = \\(\\frac{4}{10}\\)<br \/>\nWhen we multiply the fraction with the fraction having the same number as the numerator as the denominator, we will get the equivalent fraction.<br \/>\nSo according to the Equivalent model,<br \/>\n\\(\\frac{2}{5}\\) is multiplied with \\(\\frac{2}{2}\\)<br \/>\nHence,<br \/>\n<img loading=\"lazy\" class=\"alignnone size-full wp-image-24450\" src=\"https:\/\/ccssmathanswers.com\/wp-content\/uploads\/2020\/12\/Big-Ideas-Math-Answers-Grade-4-Chapter-7-33.jpg\" alt=\"\" width=\"80\" height=\"50\" \/><\/p>\n<p>Question 5.<br \/>\n<img loading=\"lazy\" class=\"alignnone size-full wp-image-13179\" src=\"https:\/\/ccssmathanswers.com\/wp-content\/uploads\/2020\/12\/Big-Ideas-Math-Answers-4th-Grade-Chapter-7-Understand-Fraction-Equivalence-and-Comparison-7.2-22.png\" alt=\"Big Ideas Math Answers 4th Grade Chapter 7 Understand Fraction Equivalence and Comparison 7.2 22\" width=\"107\" height=\"63\" \/><br \/>\nAnswer: The equivalent fraction of \\(\\frac{3}{3}\\) is: \\(\\frac{6}{6}\\)<\/p>\n<p>Explanation:<br \/>\nWhen we multiply the fraction with the fraction having the same number as the numerator as the denominator, we will get the equivalent fraction.<br \/>\nSo,<br \/>\n\\(\\frac{3}{3}\\) is multiplied with \\(\\frac{2}{2}\\)<br \/>\nHence,<br \/>\n<img loading=\"lazy\" class=\"alignnone size-full wp-image-24451\" src=\"https:\/\/ccssmathanswers.com\/wp-content\/uploads\/2020\/12\/Big-Ideas-Math-Answers-Grade-4-Chapter-7-34.jpg\" alt=\"\" width=\"84\" height=\"45\" \/><\/p>\n<p>Question 6.<br \/>\n<img loading=\"lazy\" class=\"alignnone size-full wp-image-13180\" src=\"https:\/\/ccssmathanswers.com\/wp-content\/uploads\/2020\/12\/Big-Ideas-Math-Answers-4th-Grade-Chapter-7-Understand-Fraction-Equivalence-and-Comparison-7.2-23.png\" alt=\"Big Ideas Math Answers 4th Grade Chapter 7 Understand Fraction Equivalence and Comparison 7.2 23\" width=\"102\" height=\"66\" \/><br \/>\nAnswer: The equivalent fraction of \\(\\frac{7}{10}\\) is: \\(\\frac{70}{100}\\)<\/p>\n<p>Explanation:<br \/>\nExplanation:<br \/>\nWhen we multiply the fraction with the fraction having the same number as the numerator as the denominator, we will get the equivalent fraction.<br \/>\nSo,<br \/>\n\\(\\frac{7}{10}\\) is multiplied with \\(\\frac{10}{10}\\)<br \/>\nHence,<br \/>\n<img loading=\"lazy\" class=\"alignnone size-full wp-image-24453\" src=\"https:\/\/ccssmathanswers.com\/wp-content\/uploads\/2020\/12\/Big-Ideas-Math-Answers-Grade-4-Chapter-7-35.jpg\" alt=\"\" width=\"98\" height=\"53\" \/><\/p>\n<p><strong>Find an equivalent fraction.<\/strong><br \/>\nQuestion 7.<br \/>\n\\(\\frac{5}{3}\\)<br \/>\nAnswer: The equivalent value of \\(\\frac{5}{3}\\) is: \\(\\frac{10}{6}\\)<\/p>\n<p>Explanation:<br \/>\nWhen we multiply the fraction with the fraction having the same number as the numerator as the denominator, we will get the equivalent fraction.<br \/>\nSo,<br \/>\n\\(\\frac{5}{3}\\) is multiplied with \\(\\frac{2}{2}\\)<br \/>\nHence,<br \/>\n\\(\\frac{5}{3}\\) = \\(\\frac{10}{6}\\)<\/p>\n<p>Question 8.<br \/>\n\\(\\frac{4}{4}\\)<br \/>\nAnswer: The equivalent value of \\(\\frac{4}{4}\\) is: \\(\\frac{8}{8}\\)<\/p>\n<p>Explanation:<br \/>\nWhen we multiply the fraction with the fraction having the same number as the numerator as the denominator, we will get the equivalent fraction.<br \/>\nSo,<br \/>\n\\(\\frac{4}{4}\\) is multiplied with \\(\\frac{2}{2}\\)<br \/>\nHence,<br \/>\n\\(\\frac{4}{4}\\) = \\(\\frac{8}{8}\\)<\/p>\n<p>Question 9.<br \/>\n\\(\\frac{5}{10}\\)<br \/>\nAnswer: The equivalent value of \\(\\frac{5}{10}\\) is: \\(\\frac{10}{20}\\)<\/p>\n<p>Explanation:<br \/>\nWhen we multiply the fraction with the fraction having the same number as the numerator as the denominator, we will get the equivalent fraction.<br \/>\nSo,<br \/>\n\\(\\frac{5}{10}\\) is multiplied with \\(\\frac{2}{2}\\)<br \/>\nHence,<br \/>\n\\(\\frac{5}{10}\\) = \\(\\frac{10}{20}\\)<\/p>\n<p>Find two equivalent fractions.<br \/>\nQuestion 10.<br \/>\n\\(\\frac{3}{2}\\)<br \/>\nAnswer:<br \/>\nThe two equivalent fractions of \\(\\frac{3}{2}\\) are: \\(\\frac{6}{4}\\) and \\(\\frac{9}{6}\\)<\/p>\n<p>Explanation:<br \/>\nWhen we multiply the fraction with the fraction having the same number as the numerator as the denominator, we will get the equivalent fraction.<br \/>\nSo,<br \/>\n\\(\\frac{3}{2}\\) is multiplied with \\(\\frac{2}{2}\\) and \\(\\frac{3}{3}\\)<br \/>\nHence,<br \/>\n\\(\\frac{3}{2}\\) = \\(\\frac{6}{4}\\) and \\(\\frac{9}{6}\\)<\/p>\n<p>Question 11.<br \/>\n\\(\\frac{4}{10}\\)<br \/>\nAnswer:<br \/>\nThe two equivalent fractions of \\(\\frac{4}{10}\\) are: \\(\\frac{8}{20}\\) and \\(\\frac{12}{30}\\)<\/p>\n<p>Explanation:<br \/>\nWhen we multiply the fraction with the fraction having the same number as the numerator as the denominator, we will get the equivalent fraction.<br \/>\nSo,<br \/>\n\\(\\frac{4}{10}\\) is multiplied with \\(\\frac{2}{2}\\) and \\(\\frac{3}{3}\\)<br \/>\nHence,<br \/>\n\\(\\frac{4}{10}\\) = \\(\\frac{8}{20}\\) and \\(\\frac{12}{30}\\)<\/p>\n<p>Question 12.<br \/>\n\\(\\frac{10}{5}\\)<br \/>\nAnswer:<br \/>\nThe two equivalent fractions of \\(\\frac{10}{5}\\) are: \\(\\frac{20}{10}\\) and \\(\\frac{30}{15}\\)<\/p>\n<p>Explanation:<br \/>\nWhen we multiply the fraction with the fraction having the same number as the numerator as the denominator, we will get the equivalent fraction.<br \/>\nSo,<br \/>\n\\(\\frac{10}{5}\\) is multiplied with \\(\\frac{2}{2}\\) and \\(\\frac{3}{3}\\)<br \/>\nHence,<br \/>\n\\(\\frac{10}{5}\\) = \\(\\frac{20}{10}\\) and \\(\\frac{30}{15}\\)<\/p>\n<p>Question 13.<br \/>\n<strong>DIG DEEPER!<\/strong><br \/>\nWhat is Descartes\u2019s fraction?<br \/>\n<img loading=\"lazy\" class=\"alignnone size-full wp-image-13181\" src=\"https:\/\/ccssmathanswers.com\/wp-content\/uploads\/2020\/12\/Big-Ideas-Math-Answers-4th-Grade-Chapter-7-Understand-Fraction-Equivalence-and-Comparison-7.2-24.png\" alt=\"Big Ideas Math Answers 4th Grade Chapter 7 Understand Fraction Equivalence and Comparison 7.2 24\" width=\"224\" height=\"222\" srcset=\"https:\/\/bigideasmathanswers.com\/wp-content\/uploads\/2020\/12\/Big-Ideas-Math-Answers-4th-Grade-Chapter-7-Understand-Fraction-Equivalence-and-Comparison-7.2-24.png 224w, https:\/\/bigideasmathanswers.com\/wp-content\/uploads\/2020\/12\/Big-Ideas-Math-Answers-4th-Grade-Chapter-7-Understand-Fraction-Equivalence-and-Comparison-7.2-24-150x150.png 150w\" sizes=\"(max-width: 224px) 100vw, 224px\" \/><br \/>\nAnswer:<\/p>\n<p>Question 14.<br \/>\n<strong>YOU BE THE TEACHER<\/strong><br \/>\nYour friend says she can write a fraction equivalent to \\(\\frac{3}{4}\\) that has a denominator of 10 and 4 and a whole number in the numerator. Is your friend correct? Explain.<br \/>\nAnswer: Your friend is not correct<\/p>\n<p>Explanation:<br \/>\nGiven that your friend says she can write a fraction equivalent to \\(\\frac{3}{4}\\) that has a denominator of 10 and 4 and a whole number in the numerator.<br \/>\nWhen we multiply the fraction with the fraction having the same number as the numerator as the denominator, we will get the equivalent fraction.<br \/>\nSo,<br \/>\n\\(\\frac{3}{4}\\) will be multiplied with \\(\\frac{10}{25}\\) to get the value of 10 in the denominator<br \/>\n\\(\\frac{3}{4}\\) will be multiplied \\(\\frac{1}{1}\\) to get the value of 4 in the denomintor.<br \/>\nSo,<br \/>\n\\(\\frac{3}{4}\\) = \\(\\frac{30}{100}\\) But it is said this fraction has to ahve the denominator of 10 but we get the denominator of 100<br \/>\nHence, from the above,<br \/>\nwe can conclude that your friend is not correct<\/p>\n<p>Question 15.<br \/>\n<strong>Modeling Real Life<\/strong><br \/>\nA recipe calls for 1 teaspoon of cinnamon. You only have a \\(\\frac{1}{2}\\) teaspoon measuring spoon. What fraction of a teaspoon of cinnamon, in halves, do you need?<br \/>\n<img loading=\"lazy\" class=\"alignnone size-full wp-image-13182\" src=\"https:\/\/ccssmathanswers.com\/wp-content\/uploads\/2020\/12\/Big-Ideas-Math-Answers-4th-Grade-Chapter-7-Understand-Fraction-Equivalence-and-Comparison-7.2-25.png\" alt=\"Big Ideas Math Answers 4th Grade Chapter 7 Understand Fraction Equivalence and Comparison 7.2 25\" width=\"184\" height=\"143\" \/><br \/>\nAnswer: You need \\(\\frac{1}{2}\\) of a fraction of teaspoon, in halves<\/p>\n<p>Explanation:<br \/>\nGiven that a recipe calls for 1 teaspoon of cinnamon and you only have a \\(\\frac{1}{2}\\) teaspoon measuring spoon.<br \/>\nSo,<br \/>\nIn terms of \\(\\frac{1}{2}\\), we can write \\(\\frac{1}{2}\\) as:<br \/>\n\\(\\frac{1}{2}\\) = \\(\\frac{1\u00d7 1}{2 \u00d7 1}\\)<br \/>\nHence, from the above,<br \/>\nWe can conclude that you need \\(\\frac{1}{2}\\) of a fraction of teaspoon, in halves<\/p>\n<p>Question 16.<br \/>\nA couple lives in Florida for \\(\\frac{1}{3}\\) of the year. Each year has 12 months. What fraction of a year,\u00a0 in twelfths, does the couple live in Florida?<br \/>\nAnswer: The couple lives in Florida for \\(\\frac{4}{12}\\) of a year, in twelfths.<\/p>\n<p>Explanation:<br \/>\nGiven that a couple lives in Florida for \\(\\frac{1}{3}\\) of the year.<br \/>\nIt is also given that each year has 12 months<br \/>\nSo,<br \/>\nIn terms of \\(\\frac{1}{12}\\), we can write \\(\\frac{1}{3}\\) as:<br \/>\n\\(\\frac{1}{3}\\) = \\(\\frac{1\u00d7 4}{3 \u00d7 4}\\)<br \/>\nHence, from the above,<br \/>\nWe can conclude that the couple lives in Florida for \\(\\frac{4}{12}\\) of a year, in twelfths.<\/p>\n<p><strong>Review &amp; Refresh<\/strong><\/p>\n<p><strong>Divide. Then check your answer.<\/strong><br \/>\nQuestion 17.<br \/>\n7\u221a891<br \/>\nAnswer: 891 \u00f7 7 =127 R 2<\/p>\n<p>Explanation:<br \/>\nBy using the partial quotients method,<br \/>\n891 \u00f7 7 = ( 840 + 49 ) \u00f7 7<br \/>\n= ( 840 \u00f7 7 ) + ( 49 \u00f7 7 )<br \/>\n= 120 + 7<br \/>\n= 127 R 2<br \/>\nHence, 891 \u00f7 7 = 127 R 2<\/p>\n<p>Question 18.<br \/>\n3\u221a2,395<br \/>\nAnswer: 2,395 \u00f7 3 =798 R 1<\/p>\n<p>Explanation:<br \/>\nBy using the partial quotients method,<br \/>\n2,395 \u00f7 3 = ( 2,100 + 180 + 39 + 72 + 3 ) \u00f7 3<br \/>\n= ( 2,100 \u00f7 3 ) + ( 180 \u00f7 3 ) + ( 39 \u00f7 3 ) + ( 72 \u00f7 3 ) + ( 3 \u00f7 3 )<br \/>\n=700 + 60 + 13 + 24 + 1<br \/>\n= 798 R 1<br \/>\nHence, 2,395 \u00f7 3 = 798 R 1<\/p>\n<p>Question 19.<br \/>\n6\u221a627<br \/>\nAnswer: 627 \u00f7 6 = 104 R 3<\/p>\n<p>Explanation:<br \/>\nBy using the partial quotients method,<br \/>\n627 \u00f7 6 = ( 600 + 24 ) \u00f7 6<br \/>\n= ( 600 \u00f7 6 ) + ( 24 \u00f7 6 )<br \/>\n= 100 + 4<br \/>\n= 104 R 3<br \/>\nHence, 627 \u00f7 6 = 104 R 3<\/p>\n<h3><a id=\"Lesson_7.3_Generate_Equivalent_Fractions_by_Dividing\"><\/a>Lesson 7.3 Generate Equivalent Fractions by Dividing<\/h3>\n<p><strong>Explore and Grow<\/strong><\/p>\n<p>Shade the second model in each pair to show an equivalent fraction.Then write the fraction.<br \/>\n<img loading=\"lazy\" class=\"alignnone size-full wp-image-24530\" src=\"https:\/\/ccssmathanswers.com\/wp-content\/uploads\/2020\/12\/Big-Ideas-Math-Answers-Grade-4-Chapter-7-36.jpg\" alt=\"\" width=\"568\" height=\"233\" srcset=\"https:\/\/bigideasmathanswers.com\/wp-content\/uploads\/2020\/12\/Big-Ideas-Math-Answers-Grade-4-Chapter-7-36.jpg 568w, https:\/\/bigideasmathanswers.com\/wp-content\/uploads\/2020\/12\/Big-Ideas-Math-Answers-Grade-4-Chapter-7-36-300x123.jpg 300w\" sizes=\"(max-width: 568px) 100vw, 568px\" \/><br \/>\nDescribe the relationship between each pair of numerators and each pair of denominators.<br \/>\nAnswer: The division of the fractions depends on the divisibility rules.<br \/>\nSo,<br \/>\nWhen the numerator and denominator are even numbers, then they can only be divided by even numbers.<br \/>\nWhen the numerator and denominator are the multiples of 3, then they can only be divided by 3.<br \/>\nSo, like these, we will divide the numerator and the denominator<\/p>\n<p><strong>Structure<\/strong><br \/>\nHow can you use division to write equivalent fractions? Explain and then use your method to find a fraction that is equivalent to \\(\\frac{6}{10}\\).<br \/>\nAnswer: The equivalent fraction of \\(\\frac{6}{10}\\) is: \\(\\frac{3}{5}\\)<\/p>\n<p>Explanation:<br \/>\nThe division of the fractions depends on the divisibility rules of the numbers.<br \/>\nNow,<br \/>\nDivisibility rule of 2: If the one&#8217;s digit ends with 0, 2, 4, 6, 8, then that number is divisible by 2<br \/>\nSo,<br \/>\n\\(\\frac{6}{10}\\) has the numbers 6 and 10 which has the one&#8217;s digit of 6 and 0.<br \/>\nSo,<br \/>\nWe can divide the \\(\\frac{6}{10}\\) by 2<br \/>\nSo,<br \/>\nWe will get ,<br \/>\n\\(\\frac{6}{10}=\\frac{6 \\div 2}{10 \\div 2}=\\frac{3}{5}\\)<br \/>\nHence, from the above,<br \/>\nWe can conclude that from the above method, the equivalent of \\(\\frac{6}{10}\\) is: \\(\\frac{3}{5}\\)<\/p>\n<p><strong>Think and Grow: Divide to Find Equivalent Fractions<\/strong><\/p>\n<p>A factor that is shared bytwo or more given numbers is a common factor. You can find an equivalent fraction by dividing the numerator and the denominator by a common factor.<br \/>\n\\(\\frac{2}{4}=\\frac{2 \\div 2}{4 \\div 2}=\\frac{1}{2}\\)<br \/>\n<strong>Example<\/strong><br \/>\nFind an equivalent fraction for \\(\\frac{8}{12}\\) .<br \/>\nFind the common factors of 8 and 12.<\/p>\n<p><img loading=\"lazy\" class=\"alignnone size-full wp-image-24532\" src=\"https:\/\/ccssmathanswers.com\/wp-content\/uploads\/2020\/12\/Big-Ideas-Math-Answers-Grade-4-Chapter-7-37.jpg\" alt=\"\" width=\"618\" height=\"312\" srcset=\"https:\/\/bigideasmathanswers.com\/wp-content\/uploads\/2020\/12\/Big-Ideas-Math-Answers-Grade-4-Chapter-7-37.jpg 618w, https:\/\/bigideasmathanswers.com\/wp-content\/uploads\/2020\/12\/Big-Ideas-Math-Answers-Grade-4-Chapter-7-37-300x151.jpg 300w\" sizes=\"(max-width: 618px) 100vw, 618px\" \/><\/p>\n<p><strong>Show and Grow<\/strong><\/p>\n<p><strong>Find an equivalent fraction.<\/strong><br \/>\nQuestion 1.<br \/>\n<img loading=\"lazy\" class=\"alignnone size-full wp-image-13185\" src=\"https:\/\/ccssmathanswers.com\/wp-content\/uploads\/2020\/12\/Big-Ideas-Math-Answers-Grade-4-Chapter-7-Understand-Fraction-Equivalence-and-Comparison-7.3-3.png\" alt=\"Big Ideas Math Answers Grade 4 Chapter 7 Understand Fraction Equivalence and Comparison 7.3 3\" width=\"136\" height=\"73\" \/><br \/>\nAnswer: The equivalent fraction of \\(\\frac{3}{6}\\) is: \\(\\frac{1}{2}\\)<\/p>\n<p>Explanation:<br \/>\nThe given fraction is \\(\\frac{3}{6}\\)<br \/>\nFrom the above fraction, the numerator and denominator are: 3 and 6<br \/>\n3 and 6 are the multiples of 3.<br \/>\nSo,<br \/>\nWe have to divide the \\(\\frac{3}{6}\\) with 3<br \/>\nSo,<br \/>\n\\(\\frac{3}{6}=\\frac{3 \\div 3}{6 \\div 3}=\\frac{1}{2}\\)<br \/>\nHence,<br \/>\n<img loading=\"lazy\" class=\"alignnone size-full wp-image-24534\" src=\"https:\/\/ccssmathanswers.com\/wp-content\/uploads\/2020\/12\/Big-Ideas-Math-Answers-Grade-4-Chapter-7-38.jpg\" alt=\"\" width=\"137\" height=\"62\" \/><\/p>\n<p>Question 2.<br \/>\n<img loading=\"lazy\" class=\"alignnone size-full wp-image-13186\" src=\"https:\/\/ccssmathanswers.com\/wp-content\/uploads\/2020\/12\/Big-Ideas-Math-Answers-Grade-4-Chapter-7-Understand-Fraction-Equivalence-and-Comparison-7.3-4.png\" alt=\"Big Ideas Math Answers Grade 4 Chapter 7 Understand Fraction Equivalence and Comparison 7.3 4\" width=\"153\" height=\"73\" srcset=\"https:\/\/bigideasmathanswers.com\/wp-content\/uploads\/2020\/12\/Big-Ideas-Math-Answers-Grade-4-Chapter-7-Understand-Fraction-Equivalence-and-Comparison-7.3-4.png 153w, https:\/\/bigideasmathanswers.com\/wp-content\/uploads\/2020\/12\/Big-Ideas-Math-Answers-Grade-4-Chapter-7-Understand-Fraction-Equivalence-and-Comparison-7.3-4-150x73.png 150w\" sizes=\"(max-width: 153px) 100vw, 153px\" \/><br \/>\nAnswer: The equivalent fraction of \\(\\frac{20}{8}\\) is: \\(\\frac{10}{4}\\)<\/p>\n<p>Explanation:<br \/>\nThe given fraction is \\(\\frac{20}{8}\\)<br \/>\nFrom the above fraction, the numerator and denominator are: 20 and 8<br \/>\n20 and 8 are the multiples of 2.( SInce the one&#8217;s digit are 0 and 8)<br \/>\nSo,<br \/>\nWe have to divide the \\(\\frac{20}{8}\\) with 2<br \/>\nSo,<br \/>\n\\(\\frac{20}{8}=\\frac{20 \\div 2}{8 \\div 2}=\\frac{10}{4}\\)<br \/>\nHence,<br \/>\n<img loading=\"lazy\" class=\"alignnone size-full wp-image-24535\" src=\"https:\/\/ccssmathanswers.com\/wp-content\/uploads\/2020\/12\/Big-Ideas-Math-Answers-Grade-4-Chapter-7-39.jpg\" alt=\"\" width=\"157\" height=\"62\" \/><\/p>\n<p><strong>Find the equivalent fraction.<\/strong><br \/>\nQuestion 3.<br \/>\n<img loading=\"lazy\" class=\"alignnone size-full wp-image-13187\" src=\"https:\/\/ccssmathanswers.com\/wp-content\/uploads\/2020\/12\/Big-Ideas-Math-Answers-Grade-4-Chapter-7-Understand-Fraction-Equivalence-and-Comparison-7.3-5.png\" alt=\"Big Ideas Math Answers Grade 4 Chapter 7 Understand Fraction Equivalence and Comparison 7.3 5\" width=\"80\" height=\"58\" \/><br \/>\nAnswer: The equivalent fraction of \\(\\frac{4}{10}\\) is: \\(\\frac{2}{5}\\)<\/p>\n<p>Explanation:<br \/>\nThe given fraction is \\(\\frac{4}{10}\\)<br \/>\nFrom the above fraction, the numerator and denominator are: 4 and 10<br \/>\n4 and 10 are the multiples of 2.( SInce the one&#8217;s digit are 0 and 4)<br \/>\nSo,<br \/>\nWe have to divide the \\(\\frac{4}{10}\\) with 2<br \/>\nSo,<br \/>\n\\(\\frac{4}{10}=\\frac{4 \\div 2}{10 \\div 2}=\\frac{2}{5}\\)<br \/>\nHence,<br \/>\n<img loading=\"lazy\" class=\"alignnone size-full wp-image-24536\" src=\"https:\/\/ccssmathanswers.com\/wp-content\/uploads\/2020\/12\/Big-Ideas-Math-Answers-Grade-4-Chapter-7-40.jpg\" alt=\"\" width=\"77\" height=\"44\" \/><\/p>\n<p>Question 4.<br \/>\n<img loading=\"lazy\" class=\"alignnone size-full wp-image-13188\" src=\"https:\/\/ccssmathanswers.com\/wp-content\/uploads\/2020\/12\/Big-Ideas-Math-Answers-Grade-4-Chapter-7-Understand-Fraction-Equivalence-and-Comparison-7.3-6.png\" alt=\"Big Ideas Math Answers Grade 4 Chapter 7 Understand Fraction Equivalence and Comparison 7.3 6\" width=\"93\" height=\"69\" \/><br \/>\nAnswer: The equivalent fraction of \\(\\frac{90}{100} is: [latex]\\frac{9}{10}<\/p>\n<p>Explanation:<br \/>\nThe given fraction is [latex]\\frac{90}{100}\\)<br \/>\nFrom the above fraction, the numerator and denominator are: 90 and 100<br \/>\n90 and 100 are the multiples of 10.<br \/>\nSo,<br \/>\nWe have to divide the \\(\\frac{90}{100}\\) with 10<br \/>\nSo,<br \/>\n\\(\\frac{90}{100}=\\frac{90 \\div 10}{100 \\div 10}=\\frac{9}{10}\\)<br \/>\nHence,<br \/>\n<img loading=\"lazy\" class=\"alignnone size-full wp-image-25115\" src=\"https:\/\/ccssmathanswers.com\/wp-content\/uploads\/2020\/12\/Big-Ideas-Math-Answers-Grade-4-Chapter-7-41.jpg\" alt=\"\" width=\"77\" height=\"50\" \/><\/p>\n<p>Question 5.<br \/>\n<img loading=\"lazy\" class=\"alignnone size-full wp-image-13189\" src=\"https:\/\/ccssmathanswers.com\/wp-content\/uploads\/2020\/12\/Big-Ideas-Math-Answers-Grade-4-Chapter-7-Understand-Fraction-Equivalence-and-Comparison-7.3-7.png\" alt=\"Big Ideas Math Answers Grade 4 Chapter 7 Understand Fraction Equivalence and Comparison 7.3 7\" width=\"77\" height=\"69\" \/><br \/>\nAnswer: The equivalent fraction of \\(\\frac{14}{4}\\) is: \\(\\frac{7}{2}\\)<\/p>\n<p>Explanation:<br \/>\nThe given fraction is \\(\\frac{14}{4}\\)<br \/>\nFrom the above fraction, the numerator and denominator are: 14 and 4<br \/>\n14 and 4 are the multiples of 2. ( Since, the one&#8217;s digit is 4 )<br \/>\nSo,<br \/>\nWe have to divide the \\(\\frac{14}{4}\\) with 2<br \/>\nSo,<br \/>\n\\(\\frac{14}{4}=\\frac{14 \\div 2}{4 \\div 2}=\\frac{7}{2}\\)<br \/>\nHence,<br \/>\n<img loading=\"lazy\" class=\"alignnone size-full wp-image-25130\" src=\"https:\/\/ccssmathanswers.com\/wp-content\/uploads\/2020\/12\/Big-Ideas-Math-Answers-Grade-4-Chapter-7-42.jpg\" alt=\"\" width=\"79\" height=\"49\" \/><\/p>\n<p><strong>Apply any Grow: Practice<\/strong><\/p>\n<p><strong>Find the equivalent fraction.<\/strong><br \/>\nQuestion 6.<br \/>\n<img loading=\"lazy\" class=\"alignnone size-full wp-image-13190\" src=\"https:\/\/ccssmathanswers.com\/wp-content\/uploads\/2020\/12\/Big-Ideas-Math-Answers-Grade-4-Chapter-7-Understand-Fraction-Equivalence-and-Comparison-7.3-8.png\" alt=\"Big Ideas Math Answers Grade 4 Chapter 7 Understand Fraction Equivalence and Comparison 7.3 8\" width=\"76\" height=\"68\" \/><br \/>\nAnswer: The equivalent fraction of \\(\\frac{2}{6}\\) is: \\(\\frac{1}{3}\\)<\/p>\n<p>Explanation:<br \/>\nThe given fraction is \\(\\frac{2}{6}\\)<br \/>\nFrom the above fraction, the numerator and denominator are: 2 and 6<br \/>\n2 and 6 are the multiples of 2. ( Since, the one&#8217;s digit is 2 and 6 )<br \/>\nSo,<br \/>\nWe have to divide the \\(\\frac{2}{6}\\) with 2<br \/>\nSo,<br \/>\n\\(\\frac{2}{6}=\\frac{2 \\div 2}{6 \\div 2}=\\frac{1}{3}\\)<br \/>\nHence,<br \/>\n<img loading=\"lazy\" class=\"alignnone size-full wp-image-25131\" src=\"https:\/\/ccssmathanswers.com\/wp-content\/uploads\/2020\/12\/Big-Ideas-Math-Answers-Grade-4-Chapter-7-43.jpg\" alt=\"\" width=\"78\" height=\"53\" \/><\/p>\n<p>Question 7.<br \/>\n<img loading=\"lazy\" class=\"alignnone size-full wp-image-13191\" src=\"https:\/\/ccssmathanswers.com\/wp-content\/uploads\/2020\/12\/Big-Ideas-Math-Answers-Grade-4-Chapter-7-Understand-Fraction-Equivalence-and-Comparison-7.3-9.png\" alt=\"Big Ideas Math Answers Grade 4 Chapter 7 Understand Fraction Equivalence and Comparison 7.3 9\" width=\"77\" height=\"69\" \/><br \/>\nAnswer: The equivalent fraction of \\(\\frac{16}{12}\\) is: \\(\\frac{4}{3}\\)<\/p>\n<p>Explanation:<br \/>\nThe given fraction is \\(\\frac{16}{12}\\)<br \/>\nFrom the above fraction, the numerator and denominator are: 16 and 12<br \/>\n16 and 12 are the multiples of 4.<br \/>\nSo,<br \/>\nWe have to divide the \\(\\frac{16}{12}\\) with 4<br \/>\nSo,<br \/>\n\\(\\frac{16}{12}=\\frac{16 \\div 4}{12 \\div 4}=\\frac{4}{3}\\)<br \/>\nHence,<br \/>\n<img loading=\"lazy\" class=\"alignnone size-full wp-image-25134\" src=\"https:\/\/ccssmathanswers.com\/wp-content\/uploads\/2020\/12\/Big-Ideas-Math-Answers-Grade-4-Chapter-7-45.jpg\" alt=\"\" width=\"75\" height=\"53\" \/><\/p>\n<p>Question 8.<br \/>\n<img loading=\"lazy\" class=\"alignnone size-full wp-image-13192\" src=\"https:\/\/ccssmathanswers.com\/wp-content\/uploads\/2020\/12\/Big-Ideas-Math-Answers-Grade-4-Chapter-7-Understand-Fraction-Equivalence-and-Comparison-7.3-10.png\" alt=\"Big Ideas Math Answers Grade 4 Chapter 7 Understand Fraction Equivalence and Comparison 7.3 10\" width=\"86\" height=\"68\" \/><br \/>\nAnswer: The equivalent fraction of \\(\\frac{80}{100}\\) is: \\(\\frac{8}{10}\\)<\/p>\n<p>Explanation:<br \/>\nThe given fraction is \\(\\frac{80}{100}\\)<br \/>\nFrom the above fraction, the numerator and denominator are: 80 and 100<br \/>\n80 and 100 are the multiples of 10.<br \/>\nSo,<br \/>\nWe have to divide the \\(\\frac{80}{100}\\) with 10<br \/>\nSo,<br \/>\n\\(\\frac{80}{100}=\\frac{80 \\div 10}{100 \\div 10}=\\frac{8}{10}\\)<br \/>\nHence,<br \/>\n<img loading=\"lazy\" class=\"alignnone size-full wp-image-25135\" src=\"https:\/\/ccssmathanswers.com\/wp-content\/uploads\/2020\/12\/Big-Ideas-Math-Answers-Grade-4-Chapter-7-46.jpg\" alt=\"\" width=\"85\" height=\"50\" \/><\/p>\n<p>Question 9.<br \/>\n<img loading=\"lazy\" class=\"alignnone size-full wp-image-13193\" src=\"https:\/\/ccssmathanswers.com\/wp-content\/uploads\/2020\/12\/Big-Ideas-Math-Answers-Grade-4-Chapter-7-Understand-Fraction-Equivalence-and-Comparison-7.3-11.png\" alt=\"Big Ideas Math Answers Grade 4 Chapter 7 Understand Fraction Equivalence and Comparison 7.3 11\" width=\"82\" height=\"62\" \/><br \/>\nAnswer: The equivalent fraction of \\(\\frac{8}{8}\\) is: \\(\\frac{1}{1}\\)<\/p>\n<p>Explanation:<br \/>\nThe given fraction is \\(\\frac{8}{8}\\)<br \/>\nFrom the above fraction, the numerator and denominator are: 8 and 8<br \/>\n8 and 8 are the multiples of 8.<br \/>\nSo,<br \/>\nWe have to divide the \\(\\frac{8}{8}\\) with 8<br \/>\nSo,<br \/>\n\\(\\frac{8}{8}=\\frac{8 \\div 8}{8 \\div 8}=\\frac{1}{1}\\)<br \/>\nHence,<br \/>\n<img loading=\"lazy\" class=\"alignnone size-full wp-image-25136\" src=\"https:\/\/ccssmathanswers.com\/wp-content\/uploads\/2020\/12\/Big-Ideas-Math-Answers-Grade-4-Chapter-7-47.jpg\" alt=\"\" width=\"73\" height=\"51\" \/><\/p>\n<p>Question 10.<br \/>\n<img loading=\"lazy\" class=\"alignnone size-full wp-image-13194\" src=\"https:\/\/ccssmathanswers.com\/wp-content\/uploads\/2020\/12\/Big-Ideas-Math-Answers-Grade-4-Chapter-7-Understand-Fraction-Equivalence-and-Comparison-7.3-12.png\" alt=\"Big Ideas Math Answers Grade 4 Chapter 7 Understand Fraction Equivalence and Comparison 7.3 12\" width=\"67\" height=\"63\" \/><br \/>\nAnswer: The equivalent fraction of \\(\\frac{2}{4}\\) is: \\(\\frac{1}{2}\\)<\/p>\n<p>Explanation:<br \/>\nThe given fraction is \\(\\frac{2}{4}\\)<br \/>\nFrom the above fraction, the numerator and denominator are: 2 and 4<br \/>\n2 and 4 are the multiples of 2.<br \/>\nSo,<br \/>\nWe have to divide the \\(\\frac{2}{4}\\) with 2<br \/>\nSo,<br \/>\n\\(\\frac{2}{4}=\\frac{2 \\div 2}{4 \\div 2}=\\frac{1}{2}\\)<br \/>\nHence,<br \/>\n<img loading=\"lazy\" class=\"alignnone size-full wp-image-25137\" src=\"https:\/\/ccssmathanswers.com\/wp-content\/uploads\/2020\/12\/Big-Ideas-Math-Answers-Grade-4-Chapter-7-48.jpg\" alt=\"\" width=\"65\" height=\"52\" \/><\/p>\n<p>Question 11.<br \/>\n<img loading=\"lazy\" class=\"alignnone size-full wp-image-13195\" src=\"https:\/\/ccssmathanswers.com\/wp-content\/uploads\/2020\/12\/Big-Ideas-Math-Answers-Grade-4-Chapter-7-Understand-Fraction-Equivalence-and-Comparison-7.3-13.png\" alt=\"Big Ideas Math Answers Grade 4 Chapter 7 Understand Fraction Equivalence and Comparison 7.3 13\" width=\"85\" height=\"65\" \/><br \/>\nAnswer: The equivalent fraction of \\(\\frac{30}{6}\\) is: \\(\\frac{10}{2}\\)<\/p>\n<p>Explanation:<br \/>\nThe given fraction is \\(\\frac{30}{6}\\)<br \/>\nFrom the above fraction, the numerator and denominator are: 30 and 6<br \/>\n30 and 6 are the multiples of 3.\u00a0 ( Since the sum of the digits of the numerator and the denominator are the multiples of 3 )<br \/>\nSo,<br \/>\nWe have to divide the \\(\\frac{30}{6}\\) with 3<br \/>\nSo,<br \/>\n\\(\\frac{30}{6}=\\frac{30 \\div 3}{6 \\div 3}=\\frac{10}{2}\\)<br \/>\nHence,<br \/>\n<img loading=\"lazy\" class=\"alignnone size-full wp-image-25138\" src=\"https:\/\/ccssmathanswers.com\/wp-content\/uploads\/2020\/12\/Big-Ideas-Math-Answers-Grade-4-Chapter-7-49.jpg\" alt=\"\" width=\"69\" height=\"51\" \/><\/p>\n<p><strong>Find an equivalent fraction for the point on the number line.<\/strong><br \/>\nQuestion 12.<br \/>\n<img loading=\"lazy\" class=\"alignnone size-full wp-image-13196\" src=\"https:\/\/ccssmathanswers.com\/wp-content\/uploads\/2020\/12\/Big-Ideas-Math-Answers-Grade-4-Chapter-7-Understand-Fraction-Equivalence-and-Comparison-7.3-14.png\" alt=\"Big Ideas Math Answers Grade 4 Chapter 7 Understand Fraction Equivalence and Comparison 7.3 14\" width=\"257\" height=\"77\" \/><br \/>\nAnswer: The equivalent fraction of \\(\\frac{6}{8}\\) is: \\(\\frac{3}{4}\\)<\/p>\n<p>Explanation:<br \/>\nThe Given number line is:<br \/>\n<img loading=\"lazy\" class=\"alignnone size-full wp-image-13196\" src=\"https:\/\/ccssmathanswers.com\/wp-content\/uploads\/2020\/12\/Big-Ideas-Math-Answers-Grade-4-Chapter-7-Understand-Fraction-Equivalence-and-Comparison-7.3-14.png\" alt=\"Big Ideas Math Answers Grade 4 Chapter 7 Understand Fraction Equivalence and Comparison 7.3 14\" width=\"257\" height=\"77\" \/><br \/>\nIn the given line, the point on the marked line is at \\(\\frac{6}{8}\\)<br \/>\nSo,<br \/>\nThe numerator and denominator of \\(\\frac{6}{8}\\) are: 6 and 8 which are the multiples of 2<br \/>\nSo,<br \/>\n\\(\\frac{6}{8}\\) is divided by 2<br \/>\nSo,<br \/>\n\\(\\frac{6}{8}=\\frac{6 \\div 2}{8 \\div 2}=\\frac{3}{4}\\)<br \/>\nHence,<br \/>\nThe equivalent fraction of \\(\\frac{6}{8}\\) is: \\(\\frac{3}{4}\\)<\/p>\n<p>Question 13.<br \/>\n<img loading=\"lazy\" class=\"alignnone size-full wp-image-13197\" src=\"https:\/\/ccssmathanswers.com\/wp-content\/uploads\/2020\/12\/Big-Ideas-Math-Answers-Grade-4-Chapter-7-Understand-Fraction-Equivalence-and-Comparison-7.3-15.png\" alt=\"Big Ideas Math Answers Grade 4 Chapter 7 Understand Fraction Equivalence and Comparison 7.3 15\" width=\"277\" height=\"70\" \/><br \/>\nAnswer: The equivalent fraction of \\(\\frac{4}{12}\\) is: \\(\\frac{1}{3}\\)<\/p>\n<p>Explanation:<br \/>\nThe given number line is:<br \/>\n<img loading=\"lazy\" class=\"alignnone size-full wp-image-13197\" src=\"https:\/\/ccssmathanswers.com\/wp-content\/uploads\/2020\/12\/Big-Ideas-Math-Answers-Grade-4-Chapter-7-Understand-Fraction-Equivalence-and-Comparison-7.3-15.png\" alt=\"Big Ideas Math Answers Grade 4 Chapter 7 Understand Fraction Equivalence and Comparison 7.3 15\" width=\"277\" height=\"70\" \/><br \/>\nIn the given line, the point on the marked line is at \\(\\frac{4}{12}\\)<br \/>\nSo,<br \/>\nThe numerator and denominator of \\(\\frac{4}{12}\\) are: 4 and 12 which are the multiples of 2<br \/>\nSo,<br \/>\n\\(\\frac{4}{12}\\) is divided by 2<br \/>\nSo,<br \/>\n\\(\\frac{4}{12}=\\frac{4 \\div 2}{12 \\div 2}=\\frac{2}{6}\\)<br \/>\nHence,<br \/>\nThe equivalent fraction of \\(\\frac{4}{12}\\) is: \\(\\frac{2}{6}\\)<\/p>\n<p><strong>Find an equivalent fraction.<\/strong><br \/>\nQuestion 14.<br \/>\n\\(\\frac{3}{12}\\)<br \/>\nAnswer: The equivalent fraction of \\(\\frac{3}{12}\\) is: \\(\\frac{1}{4}\\)<\/p>\n<p>Explanation:<br \/>\nThe given fraction is \\(\\frac{3}{12}\\)<br \/>\nFrom the above fraction, the numerator and denominator are: 3 and 12<br \/>\n3 and 12 are the multiples of 3.\u00a0 ( Since the sum of the digits of the numerator and the denominator are the multiples of 3 )<br \/>\nSo,<br \/>\nWe have to divide the \\(\\frac{3}{12}\\) with 3<br \/>\nSo,<br \/>\n\\(\\frac{3}{12}=\\frac{3 \\div 3}{12 \\div 3}=\\frac{1}{4}\\)<br \/>\nHence,<br \/>\nThe equivalent fraction of \\(\\frac{3}{12}\\) is: \\(\\frac{1}{4}\\)<\/p>\n<p>Question 15.<br \/>\n\\(\\frac{18}{6}\\)<br \/>\nAnswer: The equivalent fraction of \\(\\frac{18}{6}\\) is: \\(\\frac{6}{2}\\)<\/p>\n<p>Explanation:<br \/>\nThe given fraction is \\(\\frac{18}{6}\\)<br \/>\nFrom the above fraction, the numerator and denominator are: 18 and 6<br \/>\n18 and 6 are the multiples of 3.\u00a0 ( Since the sum of the digits of the numerator and the denominator are the multiples of 3 )<br \/>\nSo,<br \/>\nWe have to divide the \\(\\frac{18}{6}\\) with 3<br \/>\nSo,<br \/>\n\\(\\frac{18}{6}=\\frac{18 \\div 3}{6 \\div 3}=\\frac{6}{2}\\)<br \/>\nHence,<br \/>\nThe equivalent fraction of \\(\\frac{18}{6}\\) is: \\(\\frac{3}{1}\\)<\/p>\n<p><strong>Find two equivalent fractions.<\/strong><br \/>\nQuestion 16.<br \/>\n\\(\\frac{20}{10}\\)<br \/>\nAnswer: The two equivalent fractions of \\(\\frac{20}{10}\\) is: \\(\\frac{2}{1}\\) and \\(\\frac{10}{5}\\)<\/p>\n<p>Explanation:<br \/>\nThe given fraction is \\(\\frac{20}{10}\\)<br \/>\nFrom the above fraction, the numerator and denominator are: 20 and 10<br \/>\n20 and 10 are the multiples of 10 and 2<br \/>\nSo,<br \/>\nWe have to divide the \\(\\frac{20}{10}\\) with 10 and 2<br \/>\nSo,<br \/>\n\\(\\frac{20}{10}=\\frac{20 \\div 10}{10 \\div 10}=\\frac{2}{1}\\)<br \/>\n\\(\\frac{20}{10}=\\frac{20 \\div 2}{10 \\div 2}=\\frac{10}{5}\\)<br \/>\nHence,<br \/>\nThe two equivalent fractions of \\(\\frac{20}{10}\\) is: \\(\\frac{2}{1}\\) and \\(\\frac{10}{5}\\)<\/p>\n<p>Question 17.<br \/>\n\\(\\frac{75}{100}\\)<br \/>\nAnswer: The two equivalent fractions of \\(\\frac{75}{100}\\) is: \\(\\frac{15}{20}\\) and \\(\\frac{3}{4}\\)<\/p>\n<p>Explanation:<br \/>\nThe given fraction is \\(\\frac{75}{100}\\)<br \/>\nFrom the above fraction, the numerator and denominator are: 75 and 100<br \/>\n75 and 100 are the multiples of 5 and 25 ( Since the one&#8217;s digit is 5 and 0 ).<br \/>\nSo,<br \/>\nWe have to divide the \\(\\frac{75}{100}\\) with 5 and 25<br \/>\nSo,<br \/>\n\\(\\frac{75}{100}=\\frac{75 \\div 5}{100 \\div 5}=\\frac{15}{20}\\)<br \/>\n\\(\\frac{75}{100}=\\frac{75 \\div 25}{100 \\div 25}=\\frac{3}{4}\\)<br \/>\nHence,<br \/>\nThe two equivalent fractions of \\(\\frac{75}{100}\\) is: \\(\\frac{15}{20}\\) and \\(\\frac{3}{4}\\)<\/p>\n<p>Question 18.<br \/>\n<strong>Reasoning<\/strong><br \/>\nYour friend begins to divide the numerator and denominator of \\(\\frac{12}{6}\\) by 4 and then gets stuck. Explain why your friend gets stuck.<br \/>\nAnswer: The numerator and denominator of \\(\\frac{12}{6}\\) is 12 and 6<br \/>\nwhen we find out the sum of the digits of the numerator and denominator, we find out that they are the multiples of 3.<br \/>\nSo, we have to divide the \\(\\frac{12}{6}\\) by 3 instead of 4<br \/>\nSo, your friend get struck<\/p>\n<p>Explanation:<br \/>\nThe given fraction is: \\(\\frac{12}{6}\\)<br \/>\nFrom the above fraction, the numerator and the denominator are: 12 and 6<br \/>\nWhen we find the sum of the digits of the numerator and the denominator, we can find out that the sum of the digits is the multiples of 3.<br \/>\nSo,<br \/>\nWe have to divide \\(\\frac{12}{6}\\) by 3 instead of 4<br \/>\nHence, from the above,<br \/>\nWe can conclude that your friend is struck<\/p>\n<p>Question 19.<br \/>\n<strong>DIG DEEPER!<\/strong><br \/>\nCan you write an equivalent fraction with a lesser numerator and denominator when the numerator and denominator of a fraction are both odd numbers? Explain.<br \/>\nAnswer:<br \/>\nLet the fraction with both the numerator and denominator odd numbers is: \\(\\frac{15}{9}\\)<br \/>\nSo,<br \/>\nThe equivalent fraction of \\(\\frac{15}{9}\\) is: \\(\\frac{5}{3}\\)<\/p>\n<p>Explanation:<br \/>\nGiven that you have to write an equivalent fraction with a lesser numerator and denominator when the numerator and denominator of a fraction are both odd numbers.<br \/>\nNow,<br \/>\nLet the fraction with numerator and denominator odd numbers are: \\(\\frac{15}{9}\\)<br \/>\nFrom the above fraction, the numerator and denominator are: 15 and 9<br \/>\n15 and 9 are the multiples of 3 ( Since the sum of the digits is a multiple of 3 ).<br \/>\nSo,<br \/>\nWe have to divide the \\(\\frac{15}{9}\\) with 3<br \/>\nSo,<br \/>\n\\(\\frac{15}{9}=\\frac{15 \\div 3}{9 \\div 3}=\\frac{5}{3}\\)<br \/>\nHence,<br \/>\nThe equivalent fraction of \\(\\frac{15}{9}\\) is: \\(\\frac{5}{3}\\)<\/p>\n<p><strong>Think and Grow: Modeling Real Life<\/strong><\/p>\n<p><strong>Example<\/strong><br \/>\nThe Lechtal High Trail is a 100-kilometer hiking trail in Austria. A hiker has completed 70 kilometers of the trail. What fraction of the trail, in tenths, has the hiker completed?<br \/>\n<img loading=\"lazy\" class=\"alignnone size-full wp-image-13198\" src=\"https:\/\/ccssmathanswers.com\/wp-content\/uploads\/2020\/12\/Big-Ideas-Math-Answers-Grade-4-Chapter-7-Understand-Fraction-Equivalence-and-Comparison-7.3-16.png\" alt=\"Big Ideas Math Answers Grade 4 Chapter 7 Understand Fraction Equivalence and Comparison 7.3 16\" width=\"218\" height=\"177\" \/><br \/>\nUse the distances to write the fraction of the trail the hiker has completed.<\/p>\n<p><img loading=\"lazy\" class=\"alignnone size-full wp-image-25187\" src=\"https:\/\/ccssmathanswers.com\/wp-content\/uploads\/2020\/12\/Big-Ideas-Math-Answers-Grade-4-Chapter-7-50.jpg\" alt=\"\" width=\"611\" height=\"252\" srcset=\"https:\/\/bigideasmathanswers.com\/wp-content\/uploads\/2020\/12\/Big-Ideas-Math-Answers-Grade-4-Chapter-7-50.jpg 611w, https:\/\/bigideasmathanswers.com\/wp-content\/uploads\/2020\/12\/Big-Ideas-Math-Answers-Grade-4-Chapter-7-50-300x124.jpg 300w\" sizes=\"(max-width: 611px) 100vw, 611px\" \/><\/p>\n<p><strong>Show and Grow<\/strong><\/p>\n<p>Question 20.<br \/>\nA puzzle cube has 54 stickers. Nine of the stickers are orange. A cube has 6 faces. What fraction of the stickers, in sixths, are orange?<br \/>\n<img loading=\"lazy\" class=\"alignnone size-full wp-image-13200\" src=\"https:\/\/ccssmathanswers.com\/wp-content\/uploads\/2020\/12\/Big-Ideas-Math-Answers-Grade-4-Chapter-7-Understand-Fraction-Equivalence-and-Comparison-7.3-18.png\" alt=\"Big Ideas Math Answers Grade 4 Chapter 7 Understand Fraction Equivalence and Comparison 7.3 18\" width=\"130\" height=\"140\" \/><br \/>\nAnswer: The fraction of the stickers, in sixths, that are orange is: \\(\\frac{1}{6}\\)<\/p>\n<p>Explanation:<br \/>\nGiven that a puzzle has 54 stickers and each cube has 6 faces.<br \/>\nIt is also given that 9 of the stickers are orange.<br \/>\nSo,<br \/>\nThe fraction of the stickers that are in orange = The number of stickers that are in orange \u00f7 The total number of stickers<br \/>\n= 9 \u00f7 54<br \/>\n=\\(\\frac{1}{6}\\)<br \/>\nHence, from the above,<br \/>\nWe can conclude that the fraction of the stickers, in sixths, that are orange are: \\(\\frac{1}{6}\\)<\/p>\n<p>Question 21.<br \/>\nThere are 28 students in a class. Seven of the students pack their lunch. What fraction of the students, in fourths, pack their lunch?<br \/>\nAnswer: The fraction of the students, in fourths that pack their lunch, is: \\(\\frac{1}{4}\\)<\/p>\n<p>Explanation:<br \/>\nIt is given that there are 28 students in a class and 7 of the students pack their lunch.<br \/>\nSo,<br \/>\nThe fraction of students, in fourths, that pack their lunch = The number of students that pack their lunch \u00f7 The total number of students<br \/>\n= 7 \u00f7 28<br \/>\n= \\(\\frac{1}{4}\\)<br \/>\nHence, from the above,<br \/>\nWe can conclude that the fraction of students, in fourths that pack their lunch, are: \\(\\frac{1}{4}\\)<\/p>\n<p>Question 22.<br \/>\n<strong>DIG DEEPER!<\/strong><br \/>\nThere are 45 apps on a tablet. Nine of the apps are games. What fraction of the apps, in fifths, are not games? Explain.<br \/>\nAnswer: The fraction of the apps, in fifths that are not games, is: \\(\\frac{4}{5}\\)<\/p>\n<p>Explanation:<br \/>\nGiven that there are 45 apps on a tablet and nine of the apps are games.<br \/>\nSo,<br \/>\nThe fraction, in fifths that are games = The number of apps that are games \u00f7 The total number of games<br \/>\n= 9 \u00f7 45<br \/>\n= \\(\\frac{1}{5}\\)<br \/>\nNow,<br \/>\nThe fraction of the apps, in fifths that are not games = 1- ( \\(\\frac{1}{5}\\) )<br \/>\n= ( 5 &#8211; 1 ) \u00f7 5<br \/>\n= \\(\\frac{4}{5}\\)<br \/>\nHence, from the above,<br \/>\nWe can conclude that the fraction of apps, in fifths that are not games, is: \\(\\frac{4}{5}\\)<\/p>\n<h3><a id=\"Generate_Equivalent_Fractions_by_Dividing_Homework_&amp;_Practice_7.3\"><\/a>Generate Equivalent Fractions by Dividing Homework &amp; Practice 7.3<\/h3>\n<p><strong>Find an equivalent fraction.<\/strong><br \/>\nQuestion 1.<br \/>\n<img loading=\"lazy\" class=\"alignnone size-full wp-image-13201\" src=\"https:\/\/ccssmathanswers.com\/wp-content\/uploads\/2020\/12\/Big-Ideas-Math-Answers-Grade-4-Chapter-7-Understand-Fraction-Equivalence-and-Comparison-7.3-19.png\" alt=\"Big Ideas Math Answers Grade 4 Chapter 7 Understand Fraction Equivalence and Comparison 7.3 19\" width=\"152\" height=\"70\" srcset=\"https:\/\/bigideasmathanswers.com\/wp-content\/uploads\/2020\/12\/Big-Ideas-Math-Answers-Grade-4-Chapter-7-Understand-Fraction-Equivalence-and-Comparison-7.3-19.png 152w, https:\/\/bigideasmathanswers.com\/wp-content\/uploads\/2020\/12\/Big-Ideas-Math-Answers-Grade-4-Chapter-7-Understand-Fraction-Equivalence-and-Comparison-7.3-19-150x70.png 150w\" sizes=\"(max-width: 152px) 100vw, 152px\" \/><br \/>\nAnswer: The equivalent fraction of \\(\\frac{8}{10}\\) is: \\(\\frac{4}{5}\\)<\/p>\n<p>Explanation:<br \/>\nThe given fraction is \\(\\frac{8}{10}\\)<br \/>\nFrom the above fraction, the numerator and denominator are: 8 and 10<br \/>\n8 and 10 are the multiples of 2. ( Since, the one&#8217;s digit is 8 and 0 )<br \/>\nSo,<br \/>\nWe have to divide the \\(\\frac{8}{10}\\) with 2<br \/>\nSo,<br \/>\n\\(\\frac{8}{10}=\\frac{8 \\div 2}{10 \\div 2}=\\frac{4}{5}\\)<br \/>\nHence,<br \/>\n<img loading=\"lazy\" class=\"alignnone size-full wp-image-25189\" src=\"https:\/\/ccssmathanswers.com\/wp-content\/uploads\/2020\/12\/Big-Ideas-Math-Answers-Grade-4-Chapter-7-51.jpg\" alt=\"\" width=\"149\" height=\"61\" \/><\/p>\n<p>Question 2.<br \/>\n<img loading=\"lazy\" class=\"alignnone size-full wp-image-13202\" src=\"https:\/\/ccssmathanswers.com\/wp-content\/uploads\/2020\/12\/Big-Ideas-Math-Answers-Grade-4-Chapter-7-Understand-Fraction-Equivalence-and-Comparison-7.3-20.png\" alt=\"Big Ideas Math Answers Grade 4 Chapter 7 Understand Fraction Equivalence and Comparison 7.3 20\" width=\"154\" height=\"69\" \/><br \/>\nAnswer: The equivalent fraction of \\(\\frac{24}{6}\\) is: \\(\\frac{8}{2}\\)<\/p>\n<p>Explanation:<br \/>\nThe given fraction is \\(\\frac{24}{6}\\)<br \/>\nFrom the above fraction, the numerator and denominator are: 24 and 6<br \/>\n24 and 6 are the multiples of 3. ( Since, the sum of the digits is the multiples of 3 )<br \/>\nSo,<br \/>\nWe have to divide the \\(\\frac{24}{6}\\) with 3<br \/>\nSo,<br \/>\n\\(\\frac{24}{6}=\\frac{24 \\div 3}{6 \\div 3}=\\frac{8}{2}\\)<br \/>\nHence,<br \/>\n<img loading=\"lazy\" class=\"alignnone size-full wp-image-25190\" src=\"https:\/\/ccssmathanswers.com\/wp-content\/uploads\/2020\/12\/Big-Ideas-Math-Answers-Grade-4-Chapter-7-52.jpg\" alt=\"\" width=\"156\" height=\"55\" \/><\/p>\n<p><strong>Find the equivalent fraction.<\/strong><br \/>\nQuestion 3.<br \/>\n<img loading=\"lazy\" class=\"alignnone size-full wp-image-13203\" src=\"https:\/\/ccssmathanswers.com\/wp-content\/uploads\/2020\/12\/Big-Ideas-Math-Answers-Grade-4-Chapter-7-Understand-Fraction-Equivalence-and-Comparison-7.3-21.png\" alt=\"Big Ideas Math Answers Grade 4 Chapter 7 Understand Fraction Equivalence and Comparison 7.3 21\" width=\"71\" height=\"68\" \/><br \/>\nAnswer: The equivalent fraction of \\(\\frac{4}{6}\\) is: \\(\\frac{2}{3}\\)<\/p>\n<p>Explanation:<br \/>\nThe given fraction is \\(\\frac{4}{6}\\)<br \/>\nFrom the above fraction, the numerator and denominator are: 4 and 6<br \/>\n4 and 6 are the multiples of 2. ( Since, the one&#8217;s digits are 4 and 6 )<br \/>\nSo,<br \/>\nWe have to divide the \\(\\frac{4}{6}\\) with 2<br \/>\nSo,<br \/>\n\\(\\frac{4}{6}=\\frac{4 \\div 2}{6 \\div 2}=\\frac{2}{3}\\)<br \/>\nHence,<br \/>\n<img loading=\"lazy\" class=\"alignnone size-full wp-image-25191\" src=\"https:\/\/ccssmathanswers.com\/wp-content\/uploads\/2020\/12\/Big-Ideas-Math-Answers-Grade-4-Chapter-7-53.jpg\" alt=\"\" width=\"69\" height=\"50\" \/><\/p>\n<p>Question 4.<br \/>\n<img loading=\"lazy\" class=\"alignnone size-full wp-image-13204\" src=\"https:\/\/ccssmathanswers.com\/wp-content\/uploads\/2020\/12\/Big-Ideas-Math-Answers-Grade-4-Chapter-7-Understand-Fraction-Equivalence-and-Comparison-7.3-22.png\" alt=\"Big Ideas Math Answers Grade 4 Chapter 7 Understand Fraction Equivalence and Comparison 7.3 22\" width=\"90\" height=\"63\" \/><br \/>\nAnswer: The equivalent fraction of \\(\\frac{25}{100}\\) is: \\(\\frac{5}{20}\\)<\/p>\n<p>Explanation:<br \/>\nThe given fraction is \\(\\frac{25}{100}\\)<br \/>\nFrom the above fraction, the numerator and denominator are: 25 and 100<br \/>\n25 and 100 are the multiples of 5. ( Since, the one&#8217;s digits are 5 and 0 )<br \/>\nSo,<br \/>\nWe have to divide the \\(\\frac{25}{100}\\) with 5<br \/>\nSo,<br \/>\n\\(\\frac{25}{100}=\\frac{25 \\div 5}{100 \\div 5}=\\frac{5}{20}\\)<br \/>\nHence,<br \/>\n<img loading=\"lazy\" class=\"alignnone size-full wp-image-25192\" src=\"https:\/\/ccssmathanswers.com\/wp-content\/uploads\/2020\/12\/Big-Ideas-Math-Answers-Grade-4-Chapter-7-54.jpg\" alt=\"\" width=\"84\" height=\"58\" \/><\/p>\n<p><strong>Find an equivalent fraction for the point on the number line.<\/strong><br \/>\nQuestion 5.<br \/>\n<img loading=\"lazy\" class=\"alignnone size-full wp-image-13205\" src=\"https:\/\/ccssmathanswers.com\/wp-content\/uploads\/2020\/12\/Big-Ideas-Math-Answers-Grade-4-Chapter-7-Understand-Fraction-Equivalence-and-Comparison-7.3-23.png\" alt=\"Big Ideas Math Answers Grade 4 Chapter 7 Understand Fraction Equivalence and Comparison 7.3 23\" width=\"275\" height=\"77\" \/><br \/>\nAnswer: The equivalent fraction of \\(\\frac{9}{12}\\) is: \\(\\frac{3}{4}\\)<\/p>\n<p>Explanation:<br \/>\nThe Given number line is:<br \/>\n<img loading=\"lazy\" class=\"alignnone size-full wp-image-13205\" src=\"https:\/\/ccssmathanswers.com\/wp-content\/uploads\/2020\/12\/Big-Ideas-Math-Answers-Grade-4-Chapter-7-Understand-Fraction-Equivalence-and-Comparison-7.3-23.png\" alt=\"Big Ideas Math Answers Grade 4 Chapter 7 Understand Fraction Equivalence and Comparison 7.3 23\" width=\"275\" height=\"77\" \/><br \/>\nIn the given line, the point on the marked line is at \\(\\frac{9}{12}\\)<br \/>\nSo,<br \/>\nThe numerator and denominator of \\(\\frac{9}{12}\\) are: 9 and 12 which are the multiples of 3<br \/>\nSo,<br \/>\n\\(\\frac{9}{12}\\) is divided by 3<br \/>\nSo,<br \/>\n\\(\\frac{9}{12}=\\frac{9 \\div 3}{12 \\div 3}=\\frac{3}{4}\\)<br \/>\nHence,<br \/>\nThe equivalent fraction of \\(\\frac{9}{12}\\) is: \\(\\frac{3}{4}\\)<\/p>\n<p>Question 6.<br \/>\n<img loading=\"lazy\" class=\"alignnone size-full wp-image-13206\" src=\"https:\/\/ccssmathanswers.com\/wp-content\/uploads\/2020\/12\/Big-Ideas-Math-Answers-Grade-4-Chapter-7-Understand-Fraction-Equivalence-and-Comparison-7.3-24.png\" alt=\"Big Ideas Math Answers Grade 4 Chapter 7 Understand Fraction Equivalence and Comparison 7.3 24\" width=\"278\" height=\"72\" \/><br \/>\nAnswer: The equivalent fraction of \\(\\frac{6}{10}\\) is: \\(\\frac{3}{5}\\)<\/p>\n<p>Explanation:<br \/>\nThe Given number line is:<br \/>\n<img loading=\"lazy\" class=\"alignnone size-full wp-image-13206\" src=\"https:\/\/ccssmathanswers.com\/wp-content\/uploads\/2020\/12\/Big-Ideas-Math-Answers-Grade-4-Chapter-7-Understand-Fraction-Equivalence-and-Comparison-7.3-24.png\" alt=\"Big Ideas Math Answers Grade 4 Chapter 7 Understand Fraction Equivalence and Comparison 7.3 24\" width=\"278\" height=\"72\" \/><br \/>\nIn the given line, the point on the marked line is at \\(\\frac{6}{10}\\)<br \/>\nSo,<br \/>\nThe numerator and denominator of \\(\\frac{6}{10}\\) are: 6 and 10 which are the multiples of 2<br \/>\nSo,<br \/>\n\\(\\frac{6}{10}\\) is divided by 2<br \/>\nSo,<br \/>\n\\(\\frac{6}{10}=\\frac{6 \\div 2}{10 \\div 2}=\\frac{3}{5}\\)<br \/>\nHence,<br \/>\nThe equivalent fraction of \\(\\frac{6}{10}\\) is: \\(\\frac{3}{5}\\)<\/p>\n<p><strong>Find an equivalent fraction.<\/strong><br \/>\nQuestion 7.<br \/>\n\\(\\frac{3}{6}\\)<br \/>\nAnswer: The equivalent fraction of \\(\\frac{3}{6}\\) is: \\(\\frac{1}{2}\\)<\/p>\n<p>Explanation:<br \/>\nThe given fraction is \\(\\frac{3}{6}\\)<br \/>\nFrom the above fraction, the numerator and denominator are: 3 and 6<br \/>\n3 and 6 are the multiples of 3.\u00a0 ( Since the\u00a0 the numerator and the denominator are the multiples of 3 )<br \/>\nSo,<br \/>\nWe have to divide the \\(\\frac{3}{6}\\) with 3<br \/>\nSo,<br \/>\n\\(\\frac{3}{6}=\\frac{3 \\div 3}{6 \\div 3}=\\frac{1}{2}\\)<br \/>\nHence,<br \/>\nThe equivalent fraction of \\(\\frac{3}{6}\\) is: \\(\\frac{1}{2}\\)<\/p>\n<p>Question 8.<br \/>\n\\(\\frac{8}{4}\\)<br \/>\nAnswer: The equivalent fraction of \\(\\frac{8}{4}\\) is: \\(\\frac{4}{2}\\)<\/p>\n<p>Explanation:<br \/>\nThe given fraction is \\(\\frac{8}{4}\\)<br \/>\nFrom the above fraction, the numerator and denominator are: 8 and 4<br \/>\n8 and 4 are the multiples of 2.\u00a0 ( Since the one&#8217;s digit is 8 and 4 )<br \/>\nSo,<br \/>\nWe have to divide the \\(\\frac{8}{4}\\) with 2<br \/>\nSo,<br \/>\n\\(\\frac{8}{4}=\\frac{8 \\div 2}{4 \\div 2}=\\frac{4}{2}\\)<br \/>\nHence,<br \/>\nThe equivalent fraction of \\(\\frac{8}{4}\\) is: \\(\\frac{4}{2}\\)<\/p>\n<p>Question 9.<br \/>\n\\(\\frac{15}{5}\\)<br \/>\nAnswer: The equivalent fraction of \\(\\frac{15}{5}\\) is: \\(\\frac{3}{1}\\)<\/p>\n<p>Explanation:<br \/>\nThe given fraction is \\(\\frac{15}{5}\\)<br \/>\nFrom the above fraction, the numerator and denominator are: 15 and 5<br \/>\n15 and 5 are the multiples of 5.\u00a0 ( Since the last digits are 5 )<br \/>\nSo,<br \/>\nWe have to divide the \\(\\frac{15}{5}\\) with 5<br \/>\nSo,<br \/>\n\\(\\frac{15}{5}=\\frac{15 \\div 5}{5 \\div 5}=\\frac{3}{1}\\)<br \/>\nHence,<br \/>\nThe equivalent fraction of \\(\\frac{15}{5}\\) is: \\(\\frac{3}{1}\\)<\/p>\n<p><strong>Find two equivalent fractions.<\/strong><br \/>\nQuestion 10.<br \/>\n\\(\\frac{4}{100}\\)<br \/>\nAnswer: The two equivalent fractions of \\(\\frac{4}{100}\\) is: \\(\\frac{1}{25}\\) and \\(\\frac{2}{50}\\)<\/p>\n<p>Explanation:<br \/>\nThe given fraction is \\(\\frac{4}{100}\\)<br \/>\nFrom the above fraction, the numerator and denominator are: 4 and 100<br \/>\n4 and 100 are the multiples of 2 and 4<br \/>\nSo,<br \/>\nWe have to divide the \\(\\frac{4}{100}\\) with 4 and 2<br \/>\nSo,<br \/>\n\\(\\frac{4}{100}=\\frac{4 \\div 2}{100 \\div 2}=\\frac{2}{50}\\)<br \/>\n\\(\\frac{4}{100}=\\frac{4 \\div 4}{100 \\div 4}=\\frac{1}{25}\\)<br \/>\nHence,<br \/>\nThe two equivalent fractions of \\(\\frac{4}{100}\\) is: \\(\\frac{2}{50}\\) and \\(\\frac{1}{25}\\)<\/p>\n<p>Question 11.<br \/>\n\\(\\frac{6}{6}\\)<br \/>\nAnswer: The two equivalent fractions of \\(\\frac{6}{6}\\) is: \\(\\frac{1}{1}\\) and \\(\\frac{2}{2}\\)<\/p>\n<p>Explanation:<br \/>\nThe given fraction is \\(\\frac{6}{6}\\)<br \/>\nFrom the above fraction, the numerator and denominator are: 6 and 6<br \/>\n6 and 6 are the multiples of 3 and 6<br \/>\nSo,<br \/>\nWe have to divide the \\(\\frac{6}{6}\\) with 6 and 2<br \/>\nSo,<br \/>\n\\(\\frac{6}{6}=\\frac{6 \\div 2}{6 \\div 2}=\\frac{3}{3}\\)<br \/>\n\\(\\frac{6}{6}=\\frac{6 \\div 6}{6 \\div 6}=\\frac{1}{1}\\)<br \/>\nHence,<br \/>\nThe two equivalent fractions of \\(\\frac{6}{6}\\) is: \\(\\frac{1}{1}\\) and \\(\\frac{3}{3}\\)<\/p>\n<p>Question 12.<br \/>\n\\(\\frac{24}{8}\\)<br \/>\nAnswer: The two equivalent fractions of \\(\\frac{24}{8}\\) is: \\(\\frac{6}{2}\\) and \\(\\frac{12}{4}\\)<\/p>\n<p>Explanation:<br \/>\nThe given fraction is \\(\\frac{24}{8}\\)<br \/>\nFrom the above fraction, the numerator and denominator are: 24 and 8<br \/>\n24 and 8 are the multiples of 4 and 2<br \/>\nSo,<br \/>\nWe have to divide the \\(\\frac{24}{8}\\) with 4 and 2<br \/>\nSo,<br \/>\n\\(\\frac{24}{8}=\\frac{24 \\div 4}{8 \\div 4}=\\frac{6}{2}\\)<br \/>\n\\(\\frac{24}{8}=\\frac{24 \\div 2}{2 \\div 2}=\\frac{12}{4}\\)<br \/>\nHence,<br \/>\nThe two equivalent fractions of \\(\\frac{24}{8}\\) is: \\(\\frac{6}{2}\\) and \\(\\frac{12}{4}\\)<\/p>\n<p>Question 13.<br \/>\n<strong>Writing<\/strong><br \/>\nExplain how to find an equivalent fraction using division.<br \/>\nAnswer:<br \/>\nLet the fraction be \\(\\frac{a}{b}\\)<br \/>\nLet the equivalent fraction of \\(\\frac{a}{b}\\) is: \\(\\frac{x}{y}\\)<br \/>\nLet the number that divides \\(\\frac{a}{b}\\) be p.<br \/>\nSo,<br \/>\nNow, by using division,<br \/>\n\\(\\frac{a}{b}=\\frac{a \\div p}{b \\div p}=\\frac{x}{y}\\)<br \/>\nHence, like the above,<br \/>\nWe can find th eequivalent fraction by using division.<\/p>\n<p>Question 14.<br \/>\n<strong>Patterns<\/strong><br \/>\nDescribe and complete the pattern.<br \/>\n<img loading=\"lazy\" class=\"alignnone size-full wp-image-13207\" src=\"https:\/\/ccssmathanswers.com\/wp-content\/uploads\/2020\/12\/Big-Ideas-Math-Answers-Grade-4-Chapter-7-Understand-Fraction-Equivalence-and-Comparison-7.3-25.png\" alt=\"Big Ideas Math Answers Grade 4 Chapter 7 Understand Fraction Equivalence and Comparison 7.3 25\" width=\"217\" height=\"62\" \/><br \/>\nAnswer: The remaining pattern is: \\(\\frac{8}{200}\\) and \\(\\frac{4}{100}\\)<\/p>\n<p>Explanation:<br \/>\nThe given pattern is:<br \/>\n<img loading=\"lazy\" class=\"alignnone size-full wp-image-13207\" src=\"https:\/\/ccssmathanswers.com\/wp-content\/uploads\/2020\/12\/Big-Ideas-Math-Answers-Grade-4-Chapter-7-Understand-Fraction-Equivalence-and-Comparison-7.3-25.png\" alt=\"Big Ideas Math Answers Grade 4 Chapter 7 Understand Fraction Equivalence and Comparison 7.3 25\" width=\"217\" height=\"62\" \/><br \/>\nFrom the above pattern, we can say that the given pattern is divided by 2.<br \/>\nNow,<br \/>\n\\(\\frac{64}{1,600}=\\frac{64 \\div 2}{1,600 \\div 2}=\\frac{32}{800}\\)<br \/>\nSo, like the above,<br \/>\nThe remaining two patterns will be:<br \/>\n\\(\\frac{16}{400}=\\frac{16 \\div 2}{400 \\div 2}=\\frac{8}{200}\\)<br \/>\n\\(\\frac{8}{200}=\\frac{8 \\div 2}{200 \\div 2}=\\frac{4}{100}\\)<br \/>\nHence, from the above,<br \/>\nWe can conclude the pattern will be:<br \/>\n<img loading=\"lazy\" class=\"alignnone size-full wp-image-25194\" src=\"https:\/\/ccssmathanswers.com\/wp-content\/uploads\/2020\/12\/Big-Ideas-Math-Answers-Grade-4-Chapter-7-55.jpg\" alt=\"\" width=\"207\" height=\"53\" \/><\/p>\n<p>Question 15.<br \/>\n<strong>Modeling Real Life<\/strong><br \/>\nA book shows100 hieroglyphic symbols. You have learned the meanings of 30 of them. What fraction of the symbols\u2019 meanings, in tenths, have you learned?<br \/>\n<img loading=\"lazy\" class=\"alignnone size-full wp-image-13208\" src=\"https:\/\/ccssmathanswers.com\/wp-content\/uploads\/2020\/12\/Big-Ideas-Math-Answers-Grade-4-Chapter-7-Understand-Fraction-Equivalence-and-Comparison-7.3-26.png\" alt=\"Big Ideas Math Answers Grade 4 Chapter 7 Understand Fraction Equivalence and Comparison 7.3 26\" width=\"326\" height=\"106\" srcset=\"https:\/\/bigideasmathanswers.com\/wp-content\/uploads\/2020\/12\/Big-Ideas-Math-Answers-Grade-4-Chapter-7-Understand-Fraction-Equivalence-and-Comparison-7.3-26.png 326w, https:\/\/bigideasmathanswers.com\/wp-content\/uploads\/2020\/12\/Big-Ideas-Math-Answers-Grade-4-Chapter-7-Understand-Fraction-Equivalence-and-Comparison-7.3-26-300x98.png 300w\" sizes=\"(max-width: 326px) 100vw, 326px\" \/><br \/>\nAnswer: The fraction of the symbols&#8217; meaning, in tenths you have learned, is: \\(\\frac{3}{10}\\)<\/p>\n<p>Explanation:<br \/>\nGiven that a book shows 100 hieroglyphic symbols<br \/>\nIt is also given that you have learned the meanings of 30 of them.<br \/>\nSo,<br \/>\nThe fraction of the symbols&#8217; meaning, in tenths, you have read = The number of meanings of the symbols&#8217; you have learned \u00f7 The total number of symbols<br \/>\n= 30 \u00f7 100<br \/>\n= \\(\\frac{3}{10}\\)<br \/>\nHence, from the above,<br \/>\nWe can conclude that the fraction of the symbols&#8217; meaning, in tenths, you have learned is: \\(\\frac{3}{10}\\)<\/p>\n<p>Question 16.<br \/>\n<strong>DIG DEEPER!<\/strong><br \/>\nThere are 54 players in a beach volleyball club. Nine of the players cannot attend a game night. The coach needs to make even teams with the players that are there. What fraction of the players, in sixths, are at the game night?<br \/>\n<img loading=\"lazy\" class=\"alignnone size-full wp-image-13209\" src=\"https:\/\/ccssmathanswers.com\/wp-content\/uploads\/2020\/12\/Big-Ideas-Math-Answers-Grade-4-Chapter-7-Understand-Fraction-Equivalence-and-Comparison-7.3-27.png\" alt=\"Big Ideas Math Answers Grade 4 Chapter 7 Understand Fraction Equivalence and Comparison 7.3 27\" width=\"202\" height=\"128\" \/><br \/>\nAnswer: The fraction of the players, in sixths, are at the game night is: \\(\\frac{5}{6}\\)<\/p>\n<p>Explanation:<br \/>\nGiven that there are 54 players in a beach volleyball club.<br \/>\nIt is also given that nine of the players can not attend a game night and also the coach needs to make even teams with the players that are there.<br \/>\nSo,<br \/>\nThe fraction of the players, in sixths, that are not in the game night = \\(\\frac{The number of players that are not in the game night}{The total number of players}\\)<br \/>\n= \\(\\frac{9}{54}\\)<br \/>\nSo,<br \/>\nwe have to divide \\(\\frac{9}{54}\\) with 9 ( Since 9 and 54 are the multiples of 9 )<br \/>\nSo,<br \/>\n\\(\\frac{9}{54}=\\frac{9 \\div 9}{54 \\div 9}=\\frac{1}{6}\\)<br \/>\nSo,<br \/>\nThe fraction of players, in sixths, that attended a game night = 1 &#8211; \\(\\frac{1}{6}\\)<br \/>\n= \\(\\frac{5}{6}\\)<br \/>\nHence, from the above,<br \/>\nWe can conclude that the fraction of the players, in sixths, that attended a game night is: \\(\\frac{5}{6}\\)<\/p>\n<p><strong>Review &amp; Refresh<\/strong><\/p>\n<p><strong>Find the product. Check whether your answer is reasonable.<\/strong><br \/>\nQuestion 17.<br \/>\n71 \u00d7 63 = _______<br \/>\nAnswer: 71 \u00d7 63 = 4,473<\/p>\n<p>Explanation:<br \/>\nLet 71 be rounded to 70<br \/>\nLet 63 be rounded to 65<br \/>\nSo,<br \/>\nBy using the place-value method,<br \/>\n70 \u00d7 65 = 7 tens \u00d7 65<br \/>\n= 455 tens<br \/>\n= 4,550<br \/>\nHence, from the above 2 values 4,473 and 4,550,<br \/>\nWe can conclude that the answer is not reasonable.<\/p>\n<p>Question 18.<br \/>\n24 \u00d7 98 = _______<br \/>\nAnswer: 24 \u00d7 98 = 2,352<\/p>\n<p>Explanation:<br \/>\nLet 24 be rounded to 25<br \/>\nLet 98 be rounded to 100<br \/>\nSo,<br \/>\nBy using the place-value method,<br \/>\n25 \u00d7 100 = 10 tens \u00d7 25<br \/>\n= 250 tens<br \/>\n= 2,500<br \/>\nHence, from the above 2 values 2,352 and 2,500,<br \/>\nWe can conclude that the answer is not reasonable<\/p>\n<p>Question 19.<br \/>\n85 \u00d7 27 = _______<br \/>\nAnswer: 85 \u00d7 27 = 2,295<\/p>\n<p>Explanation:<br \/>\nLet 27 be rounded to 25<br \/>\nSo,<br \/>\nBy using the partial products method,<br \/>\n85 \u00d7 25 = ( 80 + 5 ) \u00d7 ( 20 + 5 )<br \/>\n= ( 80 \u00d7 20 ) + ( 80 \u00d7 5 ) + ( 5 \u00d7 20 ) + ( 5 \u00d7 5 )<br \/>\n= 1,600 + 400 + 100 + 25<br \/>\n= 2,125<br \/>\nHence, from the above 2 values 2,295 and 2,125,<br \/>\nWe can conclude that the answer is not reasonable<\/p>\n<h3><a id=\"Lesson_7.4_Compare_Fractions_Using_Benchmarks\"><\/a>Lesson 7.4 Compare Fractions Using Benchmarks<\/h3>\n<p><strong>Explore and Grow<\/strong><\/p>\n<p><img loading=\"lazy\" class=\"alignnone size-full wp-image-13210\" src=\"https:\/\/ccssmathanswers.com\/wp-content\/uploads\/2020\/12\/Big-Ideas-Math-Solutions-Grade-4-Chapter-7-Understand-Fraction-Equivalence-and-Comparison-7.4-1.png\" alt=\"Big Ideas Math Solutions Grade 4 Chapter 7 Understand Fraction Equivalence and Comparison 7.4 1\" width=\"381\" height=\"319\" srcset=\"https:\/\/bigideasmathanswers.com\/wp-content\/uploads\/2020\/12\/Big-Ideas-Math-Solutions-Grade-4-Chapter-7-Understand-Fraction-Equivalence-and-Comparison-7.4-1.png 381w, https:\/\/bigideasmathanswers.com\/wp-content\/uploads\/2020\/12\/Big-Ideas-Math-Solutions-Grade-4-Chapter-7-Understand-Fraction-Equivalence-and-Comparison-7.4-1-300x251.png 300w\" sizes=\"(max-width: 381px) 100vw, 381px\" \/><br \/>\nAnswer:\u00a0 <img loading=\"lazy\" class=\"alignnone size-full wp-image-25196\" src=\"https:\/\/ccssmathanswers.com\/wp-content\/uploads\/2020\/12\/Big-Ideas-Math-Answers-Grade-4-Chapter-7-56.jpg\" alt=\"\" width=\"440\" height=\"219\" srcset=\"https:\/\/bigideasmathanswers.com\/wp-content\/uploads\/2020\/12\/Big-Ideas-Math-Answers-Grade-4-Chapter-7-56.jpg 440w, https:\/\/bigideasmathanswers.com\/wp-content\/uploads\/2020\/12\/Big-Ideas-Math-Answers-Grade-4-Chapter-7-56-300x149.jpg 300w\" sizes=\"(max-width: 440px) 100vw, 440px\" \/><br \/>\n<img loading=\"lazy\" class=\"alignnone size-full wp-image-25197\" src=\"https:\/\/ccssmathanswers.com\/wp-content\/uploads\/2020\/12\/Big-Ideas-Math-Answers-Grade-4-Chapter-7-57.jpg\" alt=\"\" width=\"440\" height=\"221\" srcset=\"https:\/\/bigideasmathanswers.com\/wp-content\/uploads\/2020\/12\/Big-Ideas-Math-Answers-Grade-4-Chapter-7-57.jpg 440w, https:\/\/bigideasmathanswers.com\/wp-content\/uploads\/2020\/12\/Big-Ideas-Math-Answers-Grade-4-Chapter-7-57-300x151.jpg 300w\" sizes=\"(max-width: 440px) 100vw, 440px\" \/><br \/>\nBy using the above models,<br \/>\n5 is greater than half of the value of 8 i.e., 4<br \/>\nSo,<br \/>\nWe can conclude that \\(\\frac{5}{8}\\) is greater than \\(\\frac{2}{5}\\)<\/p>\n<p><strong>Structure<\/strong><br \/>\nHow does the numerator of a fraction compare tothe11denominator when the fraction is less than \\(\\frac{1}{2}\\)? greater than \\(\\frac{1}{2}\\) ? equal to \\(\\frac{1}{2}\\)? Explain.<br \/>\nAnswer:<\/p>\n<p><strong>Think and Grow: Compare Fractions Using Benchmarks<\/strong><\/p>\n<p>A benchmark is a commonly used number that you can use to compare other numbers. You can use the benchmarks \\(\\frac{1}{2}\\) and 1 to help you compare fractions.<br \/>\n<img loading=\"lazy\" class=\"alignnone size-full wp-image-13211\" src=\"https:\/\/ccssmathanswers.com\/wp-content\/uploads\/2020\/12\/Big-Ideas-Math-Solutions-Grade-4-Chapter-7-Understand-Fraction-Equivalence-and-Comparison-7.4-2.png\" alt=\"Big Ideas Math Solutions Grade 4 Chapter 7 Understand Fraction Equivalence and Comparison 7.4 2\" width=\"207\" height=\"253\" \/><br \/>\n<strong>Example<\/strong><br \/>\nUse fraction strips to compare \\(\\frac{7}{10}\\) and \\(\\frac{3}{8}\\).<\/p>\n<p><img loading=\"lazy\" class=\"alignnone size-full wp-image-25206\" src=\"https:\/\/ccssmathanswers.com\/wp-content\/uploads\/2020\/12\/Big-Ideas-Math-Answers-Grade-4-Chapter-7-61.jpg\" alt=\"\" width=\"615\" height=\"388\" srcset=\"https:\/\/bigideasmathanswers.com\/wp-content\/uploads\/2020\/12\/Big-Ideas-Math-Answers-Grade-4-Chapter-7-61.jpg 615w, https:\/\/bigideasmathanswers.com\/wp-content\/uploads\/2020\/12\/Big-Ideas-Math-Answers-Grade-4-Chapter-7-61-300x189.jpg 300w\" sizes=\"(max-width: 615px) 100vw, 615px\" \/><\/p>\n<p><strong>Show and Grow<\/strong><\/p>\n<p><strong>Compare. Use a model to help<\/strong><br \/>\nQuestion 1.<br \/>\n<img loading=\"lazy\" class=\"alignnone size-full wp-image-13213\" src=\"https:\/\/ccssmathanswers.com\/wp-content\/uploads\/2020\/12\/Big-Ideas-Math-Solutions-Grade-4-Chapter-7-Understand-Fraction-Equivalence-and-Comparison-7.4-4.png\" alt=\"Big Ideas Math Solutions Grade 4 Chapter 7 Understand Fraction Equivalence and Comparison 7.4 4\" width=\"91\" height=\"59\" \/><br \/>\nAnswer: \\(\\frac{5}{12}\\) is less than \\(\\frac{3}{5}\\)<\/p>\n<p>Explanation:<br \/>\n<img loading=\"lazy\" class=\"alignnone size-full wp-image-25201\" src=\"https:\/\/ccssmathanswers.com\/wp-content\/uploads\/2020\/12\/Big-Ideas-Math-Answers-Grade-4-Chapter-7-59.jpg\" alt=\"\" width=\"530\" height=\"221\" srcset=\"https:\/\/bigideasmathanswers.com\/wp-content\/uploads\/2020\/12\/Big-Ideas-Math-Answers-Grade-4-Chapter-7-59.jpg 530w, https:\/\/bigideasmathanswers.com\/wp-content\/uploads\/2020\/12\/Big-Ideas-Math-Answers-Grade-4-Chapter-7-59-300x125.jpg 300w\" sizes=\"(max-width: 530px) 100vw, 530px\" \/><br \/>\nFrom the above model,<br \/>\n5 is less than half of the value of 12 i.e., 6<br \/>\nSo,<br \/>\nWe can conclude that \\(\\frac{5}{12}\\) is less than \\(\\frac{3}{5}\\)<\/p>\n<p>Question 2.<br \/>\n<img loading=\"lazy\" class=\"alignnone size-full wp-image-13214\" src=\"https:\/\/ccssmathanswers.com\/wp-content\/uploads\/2020\/12\/Big-Ideas-Math-Solutions-Grade-4-Chapter-7-Understand-Fraction-Equivalence-and-Comparison-7.4-5.png\" alt=\"Big Ideas Math Solutions Grade 4 Chapter 7 Understand Fraction Equivalence and Comparison 7.4 5\" width=\"71\" height=\"63\" \/><br \/>\nAnswer: \\(\\frac{3}{4}\\) is equal to \\(\\frac{6}{8}\\) which is the equivalent fraction of \\(\\frac{3}{4}\\)<\/p>\n<p>Explanation:<br \/>\n<img loading=\"lazy\" class=\"alignnone size-full wp-image-25205\" src=\"https:\/\/ccssmathanswers.com\/wp-content\/uploads\/2020\/12\/Big-Ideas-Math-Answers-Grade-4-Chapter-7-60.jpg\" alt=\"\" width=\"440\" height=\"221\" srcset=\"https:\/\/bigideasmathanswers.com\/wp-content\/uploads\/2020\/12\/Big-Ideas-Math-Answers-Grade-4-Chapter-7-60.jpg 440w, https:\/\/bigideasmathanswers.com\/wp-content\/uploads\/2020\/12\/Big-Ideas-Math-Answers-Grade-4-Chapter-7-60-300x151.jpg 300w\" sizes=\"(max-width: 440px) 100vw, 440px\" \/><br \/>\nFrom the above model,<br \/>\nWhen we simplify \\(\\frac{6}{8}\\) i.e., divide it by 2, we will get \\(\\frac{3}{4}\\)<br \/>\nSo,<br \/>\nWe can conclude that \\(\\frac{3}{4}\\) is equal to \\(\\frac{6}{8}\\)<\/p>\n<p>Question 3.<br \/>\n<img loading=\"lazy\" class=\"alignnone size-full wp-image-13215\" src=\"https:\/\/ccssmathanswers.com\/wp-content\/uploads\/2020\/12\/Big-Ideas-Math-Solutions-Grade-4-Chapter-7-Understand-Fraction-Equivalence-and-Comparison-7.4-6.png\" alt=\"Big Ideas Math Solutions Grade 4 Chapter 7 Understand Fraction Equivalence and Comparison 7.4 6\" width=\"82\" height=\"67\" \/><br \/>\nAnswer: \\(\\frac{6}{5}\\) is greater than \\(\\frac{9}{10}\\)<\/p>\n<p>Explanation:<br \/>\n<img loading=\"lazy\" class=\"alignnone size-full wp-image-25207\" src=\"https:\/\/ccssmathanswers.com\/wp-content\/uploads\/2020\/12\/Big-Ideas-Math-Answers-Grade-4-Chapter-7-62.jpg\" alt=\"\" width=\"440\" height=\"221\" srcset=\"https:\/\/bigideasmathanswers.com\/wp-content\/uploads\/2020\/12\/Big-Ideas-Math-Answers-Grade-4-Chapter-7-62.jpg 440w, https:\/\/bigideasmathanswers.com\/wp-content\/uploads\/2020\/12\/Big-Ideas-Math-Answers-Grade-4-Chapter-7-62-300x151.jpg 300w\" sizes=\"(max-width: 440px) 100vw, 440px\" \/><br \/>\nFrom the above model,<br \/>\n6 is greater than half of the value of 5.<br \/>\nSo,<br \/>\nWe can conclude that \\(\\frac{6}{5}\\) is greater than \\(\\frac{9}{10}\\)<\/p>\n<p><strong>Apply and Grow: Practice<\/strong><\/p>\n<p><strong>Compare. Use a model to help<\/strong><br \/>\nQuestion 4.<br \/>\n<img loading=\"lazy\" class=\"alignnone size-full wp-image-13216\" src=\"https:\/\/ccssmathanswers.com\/wp-content\/uploads\/2020\/12\/Big-Ideas-Math-Solutions-Grade-4-Chapter-7-Understand-Fraction-Equivalence-and-Comparison-7.4-7.png\" alt=\"Big Ideas Math Solutions Grade 4 Chapter 7 Understand Fraction Equivalence and Comparison 7.4 7\" width=\"95\" height=\"61\" \/><br \/>\nAnswer: \\(\\frac{4}{12}\\) is less than \\(\\frac{7}{10}\\)<\/p>\n<p>Explanation:<br \/>\nGiven fractions are: \\(\\frac{4}{12}\\) and \\(\\frac{7}{10}\\)<br \/>\nNow,<br \/>\nFrom \\(\\frac{4}{12}\\),<br \/>\nwe can see that 4 is less than half of the value of 12 ie., 6<br \/>\nHence,<br \/>\nWe can conclude that \\(\\frac{4}{12}\\) is less than \\(\\frac{7}{10}\\)<\/p>\n<p>Question 5.<br \/>\n<img loading=\"lazy\" class=\"alignnone size-full wp-image-13217\" src=\"https:\/\/ccssmathanswers.com\/wp-content\/uploads\/2020\/12\/Big-Ideas-Math-Solutions-Grade-4-Chapter-7-Understand-Fraction-Equivalence-and-Comparison-7.4-8.png\" alt=\"Big Ideas Math Solutions Grade 4 Chapter 7 Understand Fraction Equivalence and Comparison 7.4 8\" width=\"73\" height=\"64\" \/><br \/>\nAnswer: \\(\\frac{1}{2}\\) is equal to \\(\\frac{3}{6}\\) which is the equivalent fraction of \\(\\frac{3}{6}\\)<\/p>\n<p>Explanation:<br \/>\nGiven fractions are: \\(\\frac{1}{2}\\) and \\(\\frac{3}{6}\\)<br \/>\nNow,<br \/>\nWhen we simplify \\(\\frac{3}{6}\\), by divideing with 3, we will get \\(\\frac{1}{2}\\)<br \/>\nSo,<br \/>\nWe can conclude that \\(\\frac{1}{2}\\) isequal to \\(\\frac{3}{6}\\) which is the equivalent fraction of<br \/>\n\\(\\frac{3}{6}\\)<\/p>\n<p>Question 6.<br \/>\n<img loading=\"lazy\" class=\"alignnone size-full wp-image-13218\" src=\"https:\/\/ccssmathanswers.com\/wp-content\/uploads\/2020\/12\/Big-Ideas-Math-Solutions-Grade-4-Chapter-7-Understand-Fraction-Equivalence-and-Comparison-7.4-9.png\" alt=\"Big Ideas Math Solutions Grade 4 Chapter 7 Understand Fraction Equivalence and Comparison 7.4 9\" width=\"74\" height=\"62\" \/><br \/>\nAnswer: \\(\\frac{2}{10}\\) is less than \\(\\frac{5}{6}\\)<\/p>\n<p>Explanation:<br \/>\nGiven fractions are: \\(\\frac{2}{10}\\) and \\(\\frac{5}{6}\\)<br \/>\nNow,<br \/>\nFrom\u00a0 \\(\\frac{2}{10}\\),<br \/>\nWe can see that 2 is less than half of the value of 10 i.e., 5<br \/>\nSo,<br \/>\nWe can conclude that \\(\\frac{2}{10}\\) is less than \\(\\frac{5}{6}\\)<\/p>\n<p>Question 7.<br \/>\n<img loading=\"lazy\" class=\"alignnone size-full wp-image-13219\" src=\"https:\/\/ccssmathanswers.com\/wp-content\/uploads\/2020\/12\/Big-Ideas-Math-Solutions-Grade-4-Chapter-7-Understand-Fraction-Equivalence-and-Comparison-7.4-10.png\" alt=\"Big Ideas Math Solutions Grade 4 Chapter 7 Understand Fraction Equivalence and Comparison 7.4 10\" width=\"87\" height=\"50\" \/><br \/>\nAnswer: \\(\\frac{5}{5}\\) is equal to \\(\\frac{12}{12}\\)<\/p>\n<p>Explanation:<br \/>\nGiven fractions are: \\(\\frac{5}{5}\\) and \\(\\frac{12}{12}\\)<br \/>\nNow,<br \/>\nFrom \\(\\frac{5}{5}\\),<br \/>\nWe can see that the numerator and denominator are equal, so we will get the same result in both the numerator and the denominator<br \/>\nSo,<br \/>\nWe can conclude that \\(\\frac{5}{5}\\) is equal to \\(\\frac{12}{12}\\)<\/p>\n<p>Question 8.<br \/>\n<img loading=\"lazy\" class=\"alignnone size-full wp-image-13220\" src=\"https:\/\/ccssmathanswers.com\/wp-content\/uploads\/2020\/12\/Big-Ideas-Math-Solutions-Grade-4-Chapter-7-Understand-Fraction-Equivalence-and-Comparison-7.4-11.png\" alt=\"Big Ideas Math Solutions Grade 4 Chapter 7 Understand Fraction Equivalence and Comparison 7.4 11\" width=\"82\" height=\"61\" \/><br \/>\nAnswer: \\(\\frac{4}{2}\\) is greater than \\(\\frac{7}{10}\\)<\/p>\n<p>Explanation:<br \/>\nGiven fractions are: \\(\\frac{4}{2}\\) and \\(\\frac{7}{10}\\)<br \/>\nNow,<br \/>\nFrom \\(\\frac{4}{2}\\),<br \/>\nWe can see that 4 is greater than half of the value of 2.<br \/>\nSo,<br \/>\nWe can conclude that \\(\\frac{4}{2}\\) is greater than \\(\\frac{7}{10}\\)<\/p>\n<p>Question 9.<br \/>\n<img loading=\"lazy\" class=\"alignnone size-full wp-image-13221\" src=\"https:\/\/ccssmathanswers.com\/wp-content\/uploads\/2020\/12\/Big-Ideas-Math-Solutions-Grade-4-Chapter-7-Understand-Fraction-Equivalence-and-Comparison-7.4-12.png\" alt=\"Big Ideas Math Solutions Grade 4 Chapter 7 Understand Fraction Equivalence and Comparison 7.4 12\" width=\"83\" height=\"59\" \/><br \/>\nAnswer: \\(\\frac{4}{6}\\) is greater than \\(\\frac{1}{3}\\)<\/p>\n<p>Explanation:<br \/>\nGiven fractions are: \\(\\frac{4}{6}\\) and \\(\\frac{1}{3}\\)<br \/>\nWhen we simplify \\(\\frac{4}{6}\\), we will get \\(\\frac{2}{3}\\)<br \/>\nNow,<br \/>\nFrom \\(\\frac{2}{3}\\),<br \/>\nWe can see that 2 is greater than half of the value of 3.<br \/>\nSo,<br \/>\nWe can conclude that \\(\\frac{4}{6}\\) is greater than \\(\\frac{1}{3}\\)<\/p>\n<p>Question 10.<br \/>\n<img loading=\"lazy\" class=\"alignnone size-full wp-image-13222\" src=\"https:\/\/ccssmathanswers.com\/wp-content\/uploads\/2020\/12\/Big-Ideas-Math-Solutions-Grade-4-Chapter-7-Understand-Fraction-Equivalence-and-Comparison-7.4-13.png\" alt=\"Big Ideas Math Solutions Grade 4 Chapter 7 Understand Fraction Equivalence and Comparison 7.4 13\" width=\"83\" height=\"59\" \/><br \/>\nAnswer: \\(\\frac{5}{4}\\) is greater than \\(\\frac{3}{8}\\)<\/p>\n<p>Explanation:<br \/>\nGiven fractions are: \\(\\frac{5}{4}\\) and \\(\\frac{3}{8}\\)<br \/>\nNow,<br \/>\nFrom \\(\\frac{5}{4}\\),<br \/>\nWe can say that 5 is greater than half of the value of 4 i.e., 2<br \/>\nSo,<br \/>\nWe can conclude that \\(\\frac{5}{4}\\) is greater than \\(\\frac{3}{8}\\)<\/p>\n<p>Question 11.<br \/>\n<img loading=\"lazy\" class=\"alignnone size-full wp-image-13223\" src=\"https:\/\/ccssmathanswers.com\/wp-content\/uploads\/2020\/12\/Big-Ideas-Math-Solutions-Grade-4-Chapter-7-Understand-Fraction-Equivalence-and-Comparison-7.4-14.png\" alt=\"Big Ideas Math Solutions Grade 4 Chapter 7 Understand Fraction Equivalence and Comparison 7.4 14\" width=\"79\" height=\"56\" \/><br \/>\nAnswer: \\(\\frac{6}{12}\\) is less than \\(\\frac{4}{5}\\)<\/p>\n<p>Explanation:<br \/>\nGiven fractions are: \\(\\frac{6}{12}\\) and \\(\\frac{4}{5}\\)<br \/>\nWhen we simplify \\(\\frac{6}{12}\\), we will get \\(\\frac{1}{2}\\)<br \/>\nNow,<br \/>\nFrom \\(\\frac{4}{5}\\),<br \/>\nWe can say that 4 is greater than half of the value of 5<br \/>\nSo,<br \/>\nWe can conclude that \\(\\frac{6}{12}\\) is less than \\(\\frac{4}{5}\\)<\/p>\n<p>Question 12.<br \/>\n<img loading=\"lazy\" class=\"alignnone size-full wp-image-13224\" src=\"https:\/\/ccssmathanswers.com\/wp-content\/uploads\/2020\/12\/Big-Ideas-Math-Solutions-Grade-4-Chapter-7-Understand-Fraction-Equivalence-and-Comparison-7.4-15.png\" alt=\"Big Ideas Math Solutions Grade 4 Chapter 7 Understand Fraction Equivalence and Comparison 7.4 15\" width=\"87\" height=\"54\" \/><br \/>\nAnswer: \\(\\frac{3}{2}\\) is greater than \\(\\frac{80}{100}\\)<\/p>\n<p>Explanation:<br \/>\nThe given fractions are: \\(\\frac{3}{2}\\) and \\(\\frac{80}{100}\\)<br \/>\nWhen we simplify \\(\\frac{80}{100}\\) by dividing with 20, we will get \\(\\frac{4}{5}\\)<br \/>\nNow,<br \/>\nFrom \\(\\frac{3}{2}\\),<br \/>\nWe can say that 3 is greater than half of the value of 2 i.e., 1<br \/>\nSo,<br \/>\nWe can conclude that \\(\\frac{3}{2}\\) is greater than \\(\\frac{80}{100}\\)<\/p>\n<p>Question 13.<br \/>\nA black bear hibernates for \\(\\frac{7}{12}\\) of 1 year. A bat hibernates for \\(\\frac{1}{4}\\) of 1 year. Which animal hibernates longer? How do you know?<br \/>\n<img loading=\"lazy\" class=\"alignnone size-full wp-image-13225\" src=\"https:\/\/ccssmathanswers.com\/wp-content\/uploads\/2020\/12\/Big-Ideas-Math-Solutions-Grade-4-Chapter-7-Understand-Fraction-Equivalence-and-Comparison-7.4-16.png\" alt=\"Big Ideas Math Solutions Grade 4 Chapter 7 Understand Fraction Equivalence and Comparison 7.4 16\" width=\"189\" height=\"145\" \/><\/p>\n<p>Answer: The black bear hibernates for a longer time than the bat<\/p>\n<p>Explanation:<br \/>\nIt is given that a black bear hibernates for \\(\\frac{7}{12}\\) of 1 year and a bat hibernates for \\(\\frac{1}{4}\\) of 1 year.<br \/>\nSo,<br \/>\nThe time that a black bear hibernates is: \\(\\frac{7}{12}\\) of 1 year<br \/>\nThe time that a bat hibernates is: \\(\\frac{1}{4}\\) of 1 year<br \/>\nSo,<br \/>\nTo make the total time 1 year, we have to multiply\u00a0 \\(\\frac{1}{4}\\) with \\(\\frac{3}{3}\\)<br \/>\nSo,<br \/>\n\\(\\frac{1}{4}\\) = \\(\\frac{3}{12}\\)<br \/>\nHence,<br \/>\nWhen we compare \\(\\frac{7}{12}\\) and \\(\\frac{3}{12}\\),<br \/>\nWe can conclude that a black bear hibernates for a long time.<\/p>\n<p>Question 14.<br \/>\n<strong>Writing<\/strong><br \/>\nExplain how you can tell whether a fraction is greater than, less than, or equal to1, just by looking at the numerator and the denominator<br \/>\nAnswer: We will compare the numerator with half of the value of the denominator. In this way, we will determine the relationship between the fractions.<br \/>\nNow,<br \/>\nLet the 2 fractions be \\(\\frac{a}{b}\\) and \\(\\frac{x}{y}\\)<br \/>\nSo,<br \/>\nCompare the first fraction&#8217;s a and b<br \/>\nWhen a &gt; ( b \/ 2 ), \\(\\frac{a}{b}\\) &gt; \\(\\frac{x}{y}\\)<br \/>\nWhen a &lt; ( b \/ 2 ), \\(\\frac{a}{b}\\) &lt; \\(\\frac{x}{y}\\)<br \/>\nWhen a = ( b \/ 2 ), \\(\\frac{a}{b}\\) = \\(\\frac{x}{y}\\)<br \/>\nHence, from the above,<br \/>\nWe can conclude that we can compare the two fractions just by looking at the numerator and the denominator<\/p>\n<p>Question 15.<br \/>\n<strong>DIG DEEPER.!<\/strong><br \/>\nYou and your friend pack lunch. You eat \\(\\frac{2}{6}\\) of your lunch. Your friend eats \\(\\frac{3}{4}\\) of his lunch. Can you tell who ate more? Explain.<br \/>\nAnswer: Your friend ate more lunch than you<\/p>\n<p>Explanation:<br \/>\nGiven that you and your friend pack lunch.<br \/>\nIt is also given that you eat \\(\\frac{2}{6}\\) of your lunch and your friend eats \\(\\frac{3}{4}\\) of his lunch.<br \/>\nSo,<br \/>\nThe amount of lunch you ate = \\(\\frac{2}{6}\\)<br \/>\nBy simplifying \\(\\frac{2}{6}\\) i.e., dividing by 2, we will get \\(\\frac{1}{3}\\)<br \/>\nSo,<br \/>\nThe amount of lunch you ate = \\(\\frac{1}{3}\\)<br \/>\nNow,<br \/>\nThe amount of lunch your friend ate = \\(\\frac{3}{4}\\)<br \/>\nSo, when we compare \\(\\frac{1}{3}\\) and \\(\\frac{3}{4}\\),<br \/>\nNow,<br \/>\nFrom \\(\\frac{1}{3}\\),<br \/>\n1 is less than half of the value of the 3<br \/>\nFrom \\(\\frac{3}{4}\\),<br \/>\n3 is greater than half of the value of 4<br \/>\nHence, from the above,<br \/>\nWe can conclude that your friend ate more than you<\/p>\n<p><strong>Think and Grow: Modeling Real Life<\/strong><\/p>\n<p><strong>Example<\/strong><br \/>\nYou have \\(\\frac{3}{5}\\) of a bottle of blue paint and \\(\\frac{7}{8}\\) of a bottle of yellow paint. Do you have enough of each paint color to make the recipe? Explain.<br \/>\n<img loading=\"lazy\" class=\"alignnone size-full wp-image-13226\" src=\"https:\/\/ccssmathanswers.com\/wp-content\/uploads\/2020\/12\/Big-Ideas-Math-Solutions-Grade-4-Chapter-7-Understand-Fraction-Equivalence-and-Comparison-7.4-17.png\" alt=\"Big Ideas Math Solutions Grade 4 Chapter 7 Understand Fraction Equivalence and Comparison 7.4 17\" width=\"210\" height=\"249\" \/><br \/>\nCompare each fraction of a paint bottle to the benchmark \\(\\frac{1}{2}\\).<br \/>\n<img loading=\"lazy\" class=\"alignnone size-full wp-image-25224\" src=\"https:\/\/ccssmathanswers.com\/wp-content\/uploads\/2020\/12\/Big-Ideas-Math-Answers-Grade-4-Chapter-7-63.jpg\" alt=\"\" width=\"411\" height=\"94\" srcset=\"https:\/\/bigideasmathanswers.com\/wp-content\/uploads\/2020\/12\/Big-Ideas-Math-Answers-Grade-4-Chapter-7-63.jpg 411w, https:\/\/bigideasmathanswers.com\/wp-content\/uploads\/2020\/12\/Big-Ideas-Math-Answers-Grade-4-Chapter-7-63-300x69.jpg 300w\" sizes=\"(max-width: 411px) 100vw, 411px\" \/><br \/>\nSo,<br \/>\nYou have enough of each paint color to make the recipe.<\/p>\n<p><strong>Show and Grow<\/strong><\/p>\n<p>Question 16.<br \/>\nYou have \\(\\frac{3}{8}\\) tablespoon of baking soda, \\(\\frac{2}{3}\\) tablespoon of contact lens solution, and \\(\\frac{5}{3}\\) cups of glue. Do you have enough of each ingredient to make the recipe? Explain.<br \/>\n<img loading=\"lazy\" class=\"alignnone size-full wp-image-13228\" src=\"https:\/\/ccssmathanswers.com\/wp-content\/uploads\/2020\/12\/Big-Ideas-Math-Solutions-Grade-4-Chapter-7-Understand-Fraction-Equivalence-and-Comparison-7.4-19.png\" alt=\"Big Ideas Math Solutions Grade 4 Chapter 7 Understand Fraction Equivalence and Comparison 7.4 19\" width=\"266\" height=\"146\" \/><\/p>\n<p>Answer: You have enough ingredients of contact lens solution and glue.<\/p>\n<p>Explanation:<br \/>\nIt is given that you have \\(\\frac{3}{8}\\) tablespoon of baking soda, \\(\\frac{2}{3}\\) tablespoon of contact lens solution, and \\(\\frac{5}{3}\\) cups of glue.<br \/>\nBut it is given that<br \/>\n<img loading=\"lazy\" class=\"alignnone size-full wp-image-13228\" src=\"https:\/\/ccssmathanswers.com\/wp-content\/uploads\/2020\/12\/Big-Ideas-Math-Solutions-Grade-4-Chapter-7-Understand-Fraction-Equivalence-and-Comparison-7.4-19.png\" alt=\"Big Ideas Math Solutions Grade 4 Chapter 7 Understand Fraction Equivalence and Comparison 7.4 19\" width=\"266\" height=\"146\" \/><br \/>\nSo, when we compare the two values,<br \/>\nFor the tablespoon of baking soda,<br \/>\n\\(\\frac{3}{8}\\) is less than \\(\\frac{3}{4}\\)<br \/>\nFor the tablespoon of contact lens solution,<br \/>\n\\(\\frac{2}{3}\\) is less than \\(\\frac{3}{2}\\)<br \/>\nFor the tablespoon of glue,<br \/>\n\\(\\frac{5}{3}\\) is greater than \\(\\frac{6}{8}\\)<br \/>\nHence, from the above,<br \/>\nWe can conclude that you have enough ingredients to make the recipe.<\/p>\n<p>Question 17.<br \/>\n<strong>DIG DEEPER!<\/strong><br \/>\nYou and your friend are making posters for a science fair. The posters are the same size. Your poster has 8 equal parts and you are halfway done. Your friend\u2019s poster has 12 equal parts. Your friend has completed \\(\\frac{9}{12}\\) of her poster. Who has a greater amount of posters left to complete?<\/p>\n<p>Answer: You have a greater amount of posters left to complete<\/p>\n<p>Explanation:<br \/>\nGiven that you and your friend are making posters for a science fair and the posters are the same size.<br \/>\nGiven that,<br \/>\nYour poster has 8 equal parts and you are halfway done.<br \/>\nSo,<br \/>\nThe representation of your work is: \\(\\frac{4}{8}\\)<br \/>\nThe simple form of \\(\\frac{4}{8}\\) is: \\(\\frac{1}{2}\\)<br \/>\nNow,<br \/>\nIt is also given that your friend&#8217;s poster has 12 equal parts and you have completed \\(\\frac{9}{12}\\) of her poster.<br \/>\nSo,<br \/>\nThe representation of your friend&#8217;s work is: \\(\\frac{9}{12}\\)<br \/>\nThe simplified form of \\(\\frac{9}{12}\\) is: \\(\\frac{3}{4}\\)<br \/>\nSo,<br \/>\nThe amount of work left by you is: \\(\\frac{1}{2}\\)<br \/>\nThe amount of work left by your friend is: \\(\\frac{1}{4}\\)<br \/>\nHence, from the above,<br \/>\nWe can conclude that you have a greater amount of posters left to complete.<\/p>\n<h3><a id=\"Compare_Fractions_Using_Benchmarks_Homework_&amp;_Practice_7.4\"><\/a>Compare Fractions Using Benchmarks Homework &amp; Practice 7.4<\/h3>\n<p><strong>Compare. Use a model to help.<\/strong><br \/>\nQuestion 1.<br \/>\n<img loading=\"lazy\" class=\"alignnone size-full wp-image-13229\" src=\"https:\/\/ccssmathanswers.com\/wp-content\/uploads\/2020\/12\/Big-Ideas-Math-Solutions-Grade-4-Chapter-7-Understand-Fraction-Equivalence-and-Comparison-7.4-20.png\" alt=\"Big Ideas Math Solutions Grade 4 Chapter 7 Understand Fraction Equivalence and Comparison 7.4 20\" width=\"82\" height=\"57\" \/><br \/>\nAnswer: \\(\\frac{8}{12}\\) is less than \\(\\frac{1}{4}\\)<\/p>\n<p>Explanation:<br \/>\nThe given fractions are: \\(\\frac{8}{12}\\) and \\(\\frac{8}{6}\\)<br \/>\nNow,<br \/>\nThe simple form of \\(\\frac{8}{12}\\) is: \\(\\frac{2}{3}\\)<br \/>\nThe simple form of \\(\\frac{8}{6}\\) is: \\(\\frac{4}{3}\\)<br \/>\nSo,<br \/>\nWhen we compare \\(\\frac{2}{3}\\) and \\(\\frac{4}{3}\\),<br \/>\nWe can say that \\(\\frac{2}{3}\\) is less than \\(\\frac{4}{3}\\)<\/p>\n<p>Question 2.<br \/>\n<img loading=\"lazy\" class=\"alignnone size-full wp-image-13230\" src=\"https:\/\/ccssmathanswers.com\/wp-content\/uploads\/2020\/12\/Big-Ideas-Math-Solutions-Grade-4-Chapter-7-Understand-Fraction-Equivalence-and-Comparison-7.4-21.png\" alt=\"Big Ideas Math Solutions Grade 4 Chapter 7 Understand Fraction Equivalence and Comparison 7.4 21\" width=\"76\" height=\"61\" \/><br \/>\nAnswer: \\(\\frac{9}{10}\\) is greater than \\(\\frac{1}{3}\\)<\/p>\n<p>Explanation:<br \/>\nThe given fractions are: \\(\\frac{9}{10}\\) and \\(\\frac{1}{3}\\)<br \/>\nFor \\(\\frac{9}{10}\\) and \\(\\frac{1}{3}\\)<br \/>\nWhen we compare 9 with half of the value of 10 i.e., 5, and when we compare 1 with half of the value of 3,<br \/>\nWe will conclude that \\(\\frac{9}{10}\\) is greater than \\(\\frac{1}{3}\\)<\/p>\n<p>Question 3.<br \/>\n<img loading=\"lazy\" class=\"alignnone size-full wp-image-13231\" src=\"https:\/\/ccssmathanswers.com\/wp-content\/uploads\/2020\/12\/Big-Ideas-Math-Solutions-Grade-4-Chapter-7-Understand-Fraction-Equivalence-and-Comparison-7.4-22.png\" alt=\"Big Ideas Math Solutions Grade 4 Chapter 7 Understand Fraction Equivalence and Comparison 7.4 22\" width=\"71\" height=\"66\" \/><br \/>\nAnswer: \\(\\frac{5}{2}\\) is greater than \\(\\frac{7}{8}\\)<\/p>\n<p>Explanation:<br \/>\nThe given fractions are: \\(\\frac{5}{2}\\) and \\(\\frac{7}{8}\\)<br \/>\nFor \\(\\frac{5}{2}\\) and \\(\\frac{7}{8}\\)<br \/>\nWhen we compare 5 with half of the value of 2 i.e., 1, and when we compare 7 with half of the value of 8,<br \/>\nWe will conclude that \\(\\frac{5}{2}\\) is greater than \\(\\frac{7}{8}\\)<\/p>\n<p>Question 4.<br \/>\n<img loading=\"lazy\" class=\"alignnone size-full wp-image-13232\" src=\"https:\/\/ccssmathanswers.com\/wp-content\/uploads\/2020\/12\/Big-Ideas-Math-Solutions-Grade-4-Chapter-7-Understand-Fraction-Equivalence-and-Comparison-7.4-23.png\" alt=\"Big Ideas Math Solutions Grade 4 Chapter 7 Understand Fraction Equivalence and Comparison 7.4 23\" width=\"75\" height=\"57\" \/><br \/>\nAnswer: \\(\\frac{1}{4}\\) is less than \\(\\frac{7}{12}\\)<\/p>\n<p>Explanation:<br \/>\nThe given fractions are: \\(\\frac{1}{4}\\) and \\(\\frac{7}{12}\\)<br \/>\nFor \\(\\frac{1}{4}\\) and \\(\\frac{7}{12}\\)<br \/>\nWhen we compare 1 with half of the value of 4 i.e., 2, and when we compare 7 with half of the value of 6,<br \/>\nWe will conclude that \\(\\frac{1}{4}\\) is less than \\(\\frac{7}{1}\\)<\/p>\n<p>Question 5.<br \/>\n<img loading=\"lazy\" class=\"alignnone size-full wp-image-13233\" src=\"https:\/\/ccssmathanswers.com\/wp-content\/uploads\/2020\/12\/Big-Ideas-Math-Solutions-Grade-4-Chapter-7-Understand-Fraction-Equivalence-and-Comparison-7.4-24.png\" alt=\"Big Ideas Math Solutions Grade 4 Chapter 7 Understand Fraction Equivalence and Comparison 7.4 24\" width=\"85\" height=\"61\" \/><br \/>\nAnswer: \\(\\frac{2}{2}\\) is less than \\(\\frac{10}{8}\\)<\/p>\n<p>Explanation:<br \/>\nThe given fractions are: \\(\\frac{2}{2}\\) and \\(\\frac{10}{8}\\)<br \/>\nFor \\(\\frac{2}{2}\\) and \\(\\frac{10}{8}\\)<br \/>\nWhen we compare 2 with the value of 2, and when we compare 10 with half of the value of 8,<br \/>\nWe will conclude that \\(\\frac{2}{2}\\) is less than \\(\\frac{10}{8}\\)<\/p>\n<p>Question 6.<br \/>\n<img loading=\"lazy\" class=\"alignnone size-full wp-image-13234\" src=\"https:\/\/ccssmathanswers.com\/wp-content\/uploads\/2020\/12\/Big-Ideas-Math-Solutions-Grade-4-Chapter-7-Understand-Fraction-Equivalence-and-Comparison-7.4-25.png\" alt=\"Big Ideas Math Solutions Grade 4 Chapter 7 Understand Fraction Equivalence and Comparison 7.4 25\" width=\"89\" height=\"62\" \/><br \/>\nAnswer: \\(\\frac{60}{100}\\) is equal to \\(\\frac{3}{5}\\)<\/p>\n<p>Explanation:<br \/>\nThe given two fractions are: \\(\\frac{60}{100}\\) and \\(\\frac{3}{5}\\)<br \/>\nWhen we simplify (i.e., divide by 20) \\(\\frac{60}{100}\\), we will get \\(\\frac{3}{5}\\)<br \/>\nSo,<br \/>\nWhen we compare the two fractions,<br \/>\nWe will conclude that \\(\\frac{60}{100}\\) is equal to \\(\\frac{3}{5}\\)<\/p>\n<p>Question 7.<br \/>\n<img loading=\"lazy\" class=\"alignnone size-full wp-image-13235\" src=\"https:\/\/ccssmathanswers.com\/wp-content\/uploads\/2020\/12\/Big-Ideas-Math-Solutions-Grade-4-Chapter-7-Understand-Fraction-Equivalence-and-Comparison-7.4-26.png\" alt=\"Big Ideas Math Solutions Grade 4 Chapter 7 Understand Fraction Equivalence and Comparison 7.4 26\" width=\"87\" height=\"56\" \/><br \/>\nAnswer: \\(\\frac{4}{12}\\) is equal to \\(\\frac{2}{6}\\)<\/p>\n<p>Explanation:<br \/>\nThe two given fractions are: \\(\\frac{4}{12}\\) and \\(\\frac{2}{6}\\)<br \/>\nWhen \\(\\frac{4}{12}\\) is divided by 4, we will get \\(\\frac{1}{3}\\)<br \/>\nWhen \\(\\frac{2}{6}\\) is divided by 2, we will get \\(\\frac{1}{3}\\)<br \/>\nSo, when we compare the two fractions,<br \/>\nWe will conclude that the two fractions are equal.<\/p>\n<p>Question 8.<br \/>\n<img loading=\"lazy\" class=\"alignnone size-full wp-image-13236\" src=\"https:\/\/ccssmathanswers.com\/wp-content\/uploads\/2020\/12\/Big-Ideas-Math-Solutions-Grade-4-Chapter-7-Understand-Fraction-Equivalence-and-Comparison-7.4-27.png\" alt=\"Big Ideas Math Solutions Grade 4 Chapter 7 Understand Fraction Equivalence and Comparison 7.4 27\" width=\"96\" height=\"58\" \/><br \/>\nAnswer: \\(\\frac{4}{6}\\) is greater than \\(\\frac{5}{100}\\)<\/p>\n<p>Explanation:<br \/>\nThe given two fractions are: \\(\\frac{4}{6}\\) and \\(\\frac{5}{100}\\)<br \/>\nWhen \\(\\frac{4}{6}\\) is divided by 2, we will get \\(\\frac{2}{3}\\)<br \/>\nWhen \\(\\frac{5}{100}\\) is divided by 5, we will get \\(\\frac{1}{20}\\)<br \/>\nSo,<br \/>\nWhen we compare 2 with half of the value of 3,<br \/>\nWe will conclude that \\(\\frac{4}{6}\\) is greater than \\(\\frac{5}{100}\\)<\/p>\n<p>Question 9.<br \/>\n<img loading=\"lazy\" class=\"alignnone size-full wp-image-13237\" src=\"https:\/\/ccssmathanswers.com\/wp-content\/uploads\/2020\/12\/Big-Ideas-Math-Solutions-Grade-4-Chapter-7-Understand-Fraction-Equivalence-and-Comparison-7.4-28.png\" alt=\"Big Ideas Math Solutions Grade 4 Chapter 7 Understand Fraction Equivalence and Comparison 7.4 28\" width=\"82\" height=\"62\" \/><br \/>\nAnswer: \\(\\frac{8}{10}\\) is less than \\(\\frac{9}{1}\\)<\/p>\n<p>Explanation:<br \/>\nThe given two fractions are: \\(\\frac{8}{10}\\) and \\(\\frac{9}{1}\\)<br \/>\nWhen we cross multiply the two fractions, i.e., 8 \u00d7 1 and 9 \u00d7 10,<br \/>\nWe will get the values of 8 and 90,<br \/>\nSo, from the above,<br \/>\nWe will conclude that \\(\\frac{8}{10}\\) is less than \\(\\frac{9}{1}\\)<\/p>\n<p>Question 10.<br \/>\nIn a litter of kittens, \\(\\frac{3}{4}\\) are white, and \\(\\frac{2}{8}\\) are gray. Are there more white or more gray kittens?<br \/>\n<img loading=\"lazy\" class=\"alignnone size-full wp-image-13238\" src=\"https:\/\/ccssmathanswers.com\/wp-content\/uploads\/2020\/12\/Big-Ideas-Math-Solutions-Grade-4-Chapter-7-Understand-Fraction-Equivalence-and-Comparison-7.4-29.png\" alt=\"Big Ideas Math Solutions Grade 4 Chapter 7 Understand Fraction Equivalence and Comparison 7.4 29\" width=\"273\" height=\"146\" \/><br \/>\nAnswer: There are more white kittens than grey kittens<\/p>\n<p>Explanation:<br \/>\nGiven that,<br \/>\nThe number of white kittens are: \\(\\frac{3}{4}\\)<br \/>\nThe number of gray kittens are: \\(\\frac{2}{8}\\)<br \/>\nSimplify \\(\\frac{2}{8}\\) by dividing it with 2<br \/>\nSo,<br \/>\n\\(\\frac{2}{8}\\) = \\(\\frac{1}{4}\\)<br \/>\nSo,<br \/>\nThe number of white kittens are: \\(\\frac{1}{4}\\)<br \/>\nThe number of gray kittens are: \\(\\frac{3}{4}\\)<br \/>\nSo,<br \/>\nWhen we compare the number of white and gray kittens,<br \/>\nWe will conclude that white kittens are more than gray kittens<\/p>\n<p><strong>Open-Ended<\/strong><br \/>\n<strong>Complete the statement.<\/strong><br \/>\nQuestion 11.<br \/>\n<img loading=\"lazy\" class=\"alignnone size-full wp-image-13239\" src=\"https:\/\/ccssmathanswers.com\/wp-content\/uploads\/2020\/12\/Big-Ideas-Math-Solutions-Grade-4-Chapter-7-Understand-Fraction-Equivalence-and-Comparison-7.4-30.png\" alt=\"Big Ideas Math Solutions Grade 4 Chapter 7 Understand Fraction Equivalence and Comparison 7.4 30\" width=\"72\" height=\"66\" \/><br \/>\nAnswer: The missing fraction is: \\(\\frac{1}{3}\\)<\/p>\n<p>Explanation:<br \/>\nThe given fraction is: \\(\\frac{5}{6}\\)<br \/>\nLet the missing fraction be: \\(\\frac{1}{3}\\)<br \/>\nSo,<br \/>\nWhen we compare the 2 fractions by cross multiplying the two fractions,<br \/>\nWe will conclude that<br \/>\n<img loading=\"lazy\" class=\"alignnone size-full wp-image-25248\" src=\"https:\/\/ccssmathanswers.com\/wp-content\/uploads\/2020\/12\/Big-Ideas-Math-Answers-Grade-4-Chapter-7-65.jpg\" alt=\"\" width=\"66\" height=\"53\" \/><\/p>\n<p>Question 12.<br \/>\n<img loading=\"lazy\" class=\"alignnone size-full wp-image-13240\" src=\"https:\/\/ccssmathanswers.com\/wp-content\/uploads\/2020\/12\/Big-Ideas-Math-Solutions-Grade-4-Chapter-7-Understand-Fraction-Equivalence-and-Comparison-7.4-31.png\" alt=\"Big Ideas Math Solutions Grade 4 Chapter 7 Understand Fraction Equivalence and Comparison 7.4 31\" width=\"77\" height=\"64\" \/><br \/>\nAnswer: The missing fraction is:\\(\\frac{5}{8}\\)<\/p>\n<p>Explanation:<br \/>\nThe given fraction is: \\(\\frac{7}{8}\\)<br \/>\nLet the missing fraction be: \\(\\frac{5}{8}\\)<br \/>\nSo,<br \/>\nWhen we compare the two fractions by cross multiplying the two fractions,<br \/>\nWe will conclude that<br \/>\n<img loading=\"lazy\" class=\"alignnone size-full wp-image-25249\" src=\"https:\/\/ccssmathanswers.com\/wp-content\/uploads\/2020\/12\/Big-Ideas-Math-Answers-Grade-4-Chapter-7-66.jpg\" alt=\"\" width=\"76\" height=\"50\" \/><\/p>\n<p>Question 13.<br \/>\n<img loading=\"lazy\" class=\"alignnone size-full wp-image-13241\" src=\"https:\/\/ccssmathanswers.com\/wp-content\/uploads\/2020\/12\/Big-Ideas-Math-Solutions-Grade-4-Chapter-7-Understand-Fraction-Equivalence-and-Comparison-7.4-32.png\" alt=\"Big Ideas Math Solutions Grade 4 Chapter 7 Understand Fraction Equivalence and Comparison 7.4 32\" width=\"80\" height=\"68\" \/><br \/>\nAnswer: The missing fraction is:\u00a0 \\(\\frac{2}{5}\\)<\/p>\n<p>Explanation:<br \/>\nThe given fraction is: \\(\\frac{12}{5}\\)<br \/>\nLet the missing fraction be: \\(\\frac{2}{5}\\)<br \/>\nSo,<br \/>\nWhen we compare the two fractions by cross multiplication,<br \/>\nWe will conclude that<br \/>\n<img loading=\"lazy\" class=\"alignnone size-full wp-image-25250\" src=\"https:\/\/ccssmathanswers.com\/wp-content\/uploads\/2020\/12\/Big-Ideas-Math-Answers-Grade-4-Chapter-7-67.jpg\" alt=\"\" width=\"76\" height=\"57\" \/><\/p>\n<p>Question 14.<br \/>\n<strong>Number Sense<\/strong><br \/>\nWhich statements are true<br \/>\n<img loading=\"lazy\" class=\"alignnone size-full wp-image-13242\" src=\"https:\/\/ccssmathanswers.com\/wp-content\/uploads\/2020\/12\/Big-Ideas-Math-Solutions-Grade-4-Chapter-7-Understand-Fraction-Equivalence-and-Comparison-7.4-33.png\" alt=\"Big Ideas Math Solutions Grade 4 Chapter 7 Understand Fraction Equivalence and Comparison 7.4 33\" width=\"492\" height=\"63\" srcset=\"https:\/\/bigideasmathanswers.com\/wp-content\/uploads\/2020\/12\/Big-Ideas-Math-Solutions-Grade-4-Chapter-7-Understand-Fraction-Equivalence-and-Comparison-7.4-33.png 492w, https:\/\/bigideasmathanswers.com\/wp-content\/uploads\/2020\/12\/Big-Ideas-Math-Solutions-Grade-4-Chapter-7-Understand-Fraction-Equivalence-and-Comparison-7.4-33-300x38.png 300w\" sizes=\"(max-width: 492px) 100vw, 492px\" \/><\/p>\n<p>Answer:<br \/>\nLet the given statements be named as A), B), ) and D)<br \/>\nSo,<br \/>\nFrom these four statements, A), B) statements are true<\/p>\n<p>Explanation:<br \/>\nLet the four statements be named as: A), B), C) and D)<br \/>\nNow, the given statements are:<br \/>\n<img loading=\"lazy\" class=\"alignnone size-full wp-image-13242\" src=\"https:\/\/ccssmathanswers.com\/wp-content\/uploads\/2020\/12\/Big-Ideas-Math-Solutions-Grade-4-Chapter-7-Understand-Fraction-Equivalence-and-Comparison-7.4-33.png\" alt=\"Big Ideas Math Solutions Grade 4 Chapter 7 Understand Fraction Equivalence and Comparison 7.4 33\" width=\"492\" height=\"63\" srcset=\"https:\/\/bigideasmathanswers.com\/wp-content\/uploads\/2020\/12\/Big-Ideas-Math-Solutions-Grade-4-Chapter-7-Understand-Fraction-Equivalence-and-Comparison-7.4-33.png 492w, https:\/\/bigideasmathanswers.com\/wp-content\/uploads\/2020\/12\/Big-Ideas-Math-Solutions-Grade-4-Chapter-7-Understand-Fraction-Equivalence-and-Comparison-7.4-33-300x38.png 300w\" sizes=\"(max-width: 492px) 100vw, 492px\" \/><br \/>\nCross multiply each statement<br \/>\nSo,<br \/>\nFrom A), we will get 48 &gt;15<br \/>\nFrom B), we will get 100 &gt;48<br \/>\nFrom C), we will get 12 &lt; 9<br \/>\nFrom D), we will get 8 &lt; 8<br \/>\nHence, from the above,<br \/>\nWe can conclude that A) and B) statements are true<\/p>\n<p>Question 15.<br \/>\n<strong>Modeling Real Life<\/strong><br \/>\nYou have \\(\\frac{1}{3}\\) cup of oranges and \\(\\frac{5}{4}\\) cups of strawberries. Do you have enough of each ingredient to make the smoothie? Explain.<br \/>\n<img loading=\"lazy\" class=\"alignnone size-full wp-image-13243\" src=\"https:\/\/ccssmathanswers.com\/wp-content\/uploads\/2020\/12\/Big-Ideas-Math-Solutions-Grade-4-Chapter-7-Understand-Fraction-Equivalence-and-Comparison-7.4-34.png\" alt=\"Big Ideas Math Solutions Grade 4 Chapter 7 Understand Fraction Equivalence and Comparison 7.4 34\" width=\"230\" height=\"107\" \/><\/p>\n<p>Answer: We have only enough strawberries ingredient<\/p>\n<p>Explanation:<br \/>\nThe given recipe is:<br \/>\n<img loading=\"lazy\" class=\"alignnone size-full wp-image-13243\" src=\"https:\/\/ccssmathanswers.com\/wp-content\/uploads\/2020\/12\/Big-Ideas-Math-Solutions-Grade-4-Chapter-7-Understand-Fraction-Equivalence-and-Comparison-7.4-34.png\" alt=\"Big Ideas Math Solutions Grade 4 Chapter 7 Understand Fraction Equivalence and Comparison 7.4 34\" width=\"230\" height=\"107\" \/><br \/>\nIt is also given that you have \\(\\frac{1}{3}\\) cup of oranges and \\(\\frac{5}{4}\\) cups of strawberries.<br \/>\nBut, from the recipe,<\/p>\n<p>It is given that \\(\\frac{3}{2}\\) cup of oranges and \\(\\frac{7}{8}\\) cups of strawberries.<br \/>\nSo,<br \/>\nWhen we compare \\(\\frac{1}{3}\\) and \\(\\frac{3}{2}\\) cup of oranges, we can say that we have less amount of oranges to make the recipe.<br \/>\nWhen we compare \\(\\frac{5}{4}\\) and \\(\\frac{7}{8}\\) cups of strawberries, we can say that we have enough amount of strawberries to make the recipe.<br \/>\nHence, from the above,<br \/>\nWe can conclude that we have only enough strawberry ingredients to make the recipe.<\/p>\n<p>Question 16.<br \/>\n<strong>DIG DEEPER!<\/strong><br \/>\nNewton and Descartes are picking apples at a farm. Newton\u2019s bag of 4apples weighs \\(\\frac{4}{5}\\) pound. Descartes\u2019s bag weighs \\(\\frac{3}{2}\\) pounds. How much money will Newton and Descartes each pay for their bag of apples?<br \/>\n<img loading=\"lazy\" class=\"alignnone size-full wp-image-13244\" src=\"https:\/\/ccssmathanswers.com\/wp-content\/uploads\/2020\/12\/Big-Ideas-Math-Solutions-Grade-4-Chapter-7-Understand-Fraction-Equivalence-and-Comparison-7.4-35.png\" alt=\"Big Ideas Math Solutions Grade 4 Chapter 7 Understand Fraction Equivalence and Comparison 7.4 35\" width=\"285\" height=\"193\" \/><br \/>\nAnswer: The amount of money will Newton and Descartes each pay for their bag of apples is: $301<\/p>\n<p>Explanation:<br \/>\nIt is given that Newton and Descartes are picking apples at a farm.<br \/>\nIt is also given that Newton&#8217;s bag of 4 apples weighs \\(\\frac{4}{5}\\) pound.<br \/>\n<img loading=\"lazy\" class=\"alignnone size-full wp-image-13244\" src=\"https:\/\/ccssmathanswers.com\/wp-content\/uploads\/2020\/12\/Big-Ideas-Math-Solutions-Grade-4-Chapter-7-Understand-Fraction-Equivalence-and-Comparison-7.4-35.png\" alt=\"Big Ideas Math Solutions Grade 4 Chapter 7 Understand Fraction Equivalence and Comparison 7.4 35\" width=\"285\" height=\"193\" \/><br \/>\nSo,<br \/>\n\\(\\frac{4}{5}\\) is in between \\(\\frac{1}{2}\\) pound and 1 pound<br \/>\nSo,<br \/>\nAs per the figure, the pice of Newton&#8217;s bag is: $75<br \/>\nSo,<br \/>\nThe amount paid by Newton = 4 \u00d7 75 = $300<br \/>\nIt is also given that Descartes&#8217;s bag weighs \\(\\frac{3}{2}\\) pounds.<br \/>\nSo,<br \/>\n\\(\\frac{3}{2}\\) is greater than 1 pound<br \/>\nSo,<br \/>\nThe amount paid by Descartes is: $1<br \/>\nHence, from the above,<br \/>\nThe amount paid by Newton and Descartes = 300 + 1 = $301<\/p>\n<p><strong>Review &amp; Refresh<\/strong><\/p>\n<p><strong>Find the factor pairs for the number.<\/strong><br \/>\nQuestion 17.<br \/>\n12<br \/>\nAnswer: The factor pairs of 12 are: 1 and 12, 2 and 6, 3 and 4<\/p>\n<p>Explanation:<br \/>\nFactors are the numbers that divide the original number completely.<br \/>\nHence,<br \/>\nThe factor pairs of 12 are: 1 \u00d7 12, 2 \u00d7 6, 3 \u00d7 4<\/p>\n<p>Question 18.<br \/>\n50<br \/>\nAnswer: The factor pairs of 50 are: 1 and 50, 2 and 25, 5 and 10<\/p>\n<p>Explanation:<br \/>\nFactors are the numbers that divide the original number completely.<br \/>\nHence,<br \/>\nThe factor pairs of 50 are: 1 \u00d7 50, 2 \u00d7 25, 5 \u00d7 10<\/p>\n<p>Question 19.<br \/>\n17<br \/>\nAnswer: The factor pairs of 17 are: 1 and 17, 17 and 1<\/p>\n<p>Explanation:<br \/>\nFactors are the numbers that divide the original number completely.<br \/>\nhence,<br \/>\nThe factor pairs of 17 are: 1 \u00d7 17, 17 \u00d7 1<\/p>\n<h3><a id=\"Lesson_7.5_Compare_Fractions\"><\/a>Lesson 7.5 Compare Fractions<\/h3>\n<p><strong>Explore and Grow<\/strong><\/p>\n<p>Shade each pair of models to compare \\(\\frac{1}{3}\\) and \\(\\frac{5}{12}\\). Explain how each pair of models helps you compare the fractions differently.<br \/>\n<img loading=\"lazy\" class=\"alignnone size-full wp-image-13245\" src=\"https:\/\/ccssmathanswers.com\/wp-content\/uploads\/2020\/12\/Big-Ideas-Math-Answer-Key-Grade-4-Chapter-7-Understand-Fraction-Equivalence-and-Comparison-7.5-1.png\" alt=\"Big Ideas Math Answer Key Grade 4 Chapter 7 Understand Fraction Equivalence and Comparison 7.5 1\" width=\"456\" height=\"322\" srcset=\"https:\/\/bigideasmathanswers.com\/wp-content\/uploads\/2020\/12\/Big-Ideas-Math-Answer-Key-Grade-4-Chapter-7-Understand-Fraction-Equivalence-and-Comparison-7.5-1.png 456w, https:\/\/bigideasmathanswers.com\/wp-content\/uploads\/2020\/12\/Big-Ideas-Math-Answer-Key-Grade-4-Chapter-7-Understand-Fraction-Equivalence-and-Comparison-7.5-1-300x212.png 300w\" sizes=\"(max-width: 456px) 100vw, 456px\" \/><br \/>\nAnswer:<br \/>\n<img loading=\"lazy\" class=\"alignnone size-full wp-image-25256\" src=\"https:\/\/ccssmathanswers.com\/wp-content\/uploads\/2020\/12\/Big-Ideas-Math-Answers-Grade-4-Chapter-7-68.jpg\" alt=\"\" width=\"438\" height=\"327\" srcset=\"https:\/\/bigideasmathanswers.com\/wp-content\/uploads\/2020\/12\/Big-Ideas-Math-Answers-Grade-4-Chapter-7-68.jpg 438w, https:\/\/bigideasmathanswers.com\/wp-content\/uploads\/2020\/12\/Big-Ideas-Math-Answers-Grade-4-Chapter-7-68-300x224.jpg 300w\" sizes=\"(max-width: 438px) 100vw, 438px\" \/><br \/>\nFrom the first pattern,<br \/>\nThe first fraction is:<br \/>\n\\(\\frac{1}{3}\\) = \\(\\frac{4}{12}\\)<br \/>\nThe second fraction is: \\(\\frac{5}{12}\\)<br \/>\nBy comparing the two fractions&#8217; numerators,<br \/>\nWe can conclude that \\(\\frac{4}{12}\\) is less than \\(\\frac{5}{12}\\)<br \/>\nFrom the second pattern,<br \/>\nThe first fraction is:<br \/>\n\\(\\frac{1}{3}\\) = \\(\\frac{5}{15}\\)<br \/>\nThe second fraction is: \\(\\frac{5}{12}\\)<br \/>\nBy comparing the two fractions&#8217; denominators,<br \/>\nWe can conclude that \\(\\frac{5}{15}\\) is greater than \\(\\frac{5}{12}\\)<\/p>\n<p><strong>Reasoning<\/strong><br \/>\nHow can you use equivalent fractions to compare fractions with different numerators and different denominators?<br \/>\nAnswer:<br \/>\nWe can use the equivalent fractions to compare the different numerators and different denominators by making either both the fractions&#8217; numerators or both the fractions&#8217; denominators.<\/p>\n<p><strong>Think and Grow: Compare Fractions<\/strong><\/p>\n<p><strong>Example<\/strong><br \/>\nCompare \\(\\frac{3}{5}\\) and \\(\\frac{9}{10}\\).<br \/>\nOne Way:<br \/>\nUse a like denominator. Find an equivalent fraction for \\(\\frac{3}{5}\\) that has a denominator of 10.<br \/>\nMultiply the numerator and the denominator of \\(\\frac{3}{5}\\) by 2<br \/>\n<img loading=\"lazy\" class=\"alignnone size-full wp-image-25257\" src=\"https:\/\/ccssmathanswers.com\/wp-content\/uploads\/2020\/12\/Big-Ideas-Math-Answers-Grade-4-Chapter-7-69.jpg\" alt=\"\" width=\"319\" height=\"355\" srcset=\"https:\/\/bigideasmathanswers.com\/wp-content\/uploads\/2020\/12\/Big-Ideas-Math-Answers-Grade-4-Chapter-7-69.jpg 319w, https:\/\/bigideasmathanswers.com\/wp-content\/uploads\/2020\/12\/Big-Ideas-Math-Answers-Grade-4-Chapter-7-69-270x300.jpg 270w\" sizes=\"(max-width: 319px) 100vw, 319px\" \/><\/p>\n<p>Another Way:<br \/>\nUse a like numerator. Find an equivalent fraction for \\(\\frac{3}{5}\\) that has a numerator of 10.<br \/>\nMultiply the numerator and the denominator of \\(\\frac{3}{5}\\) by 3<br \/>\n<img loading=\"lazy\" class=\"alignnone size-full wp-image-25258\" src=\"https:\/\/ccssmathanswers.com\/wp-content\/uploads\/2020\/12\/Big-Ideas-Math-Answers-Grade-4-Chapter-7-70.jpg\" alt=\"\" width=\"336\" height=\"362\" srcset=\"https:\/\/bigideasmathanswers.com\/wp-content\/uploads\/2020\/12\/Big-Ideas-Math-Answers-Grade-4-Chapter-7-70.jpg 336w, https:\/\/bigideasmathanswers.com\/wp-content\/uploads\/2020\/12\/Big-Ideas-Math-Answers-Grade-4-Chapter-7-70-278x300.jpg 278w\" sizes=\"(max-width: 336px) 100vw, 336px\" \/><\/p>\n<p><strong>Show and Grow<\/strong><\/p>\n<p><strong>Compare. Use a model to help.<\/strong><br \/>\nQuestion 1.<br \/>\n<img loading=\"lazy\" class=\"alignnone size-full wp-image-13248\" src=\"https:\/\/ccssmathanswers.com\/wp-content\/uploads\/2020\/12\/Big-Ideas-Math-Answer-Key-Grade-4-Chapter-7-Understand-Fraction-Equivalence-and-Comparison-7.5-4.png\" alt=\"Big Ideas Math Answer Key Grade 4 Chapter 7 Understand Fraction Equivalence and Comparison 7.5 4\" width=\"73\" height=\"54\" \/><br \/>\nAnswer: \\(\\frac{7}{8}\\) is greater than \\(\\frac{3}{4}\\)<\/p>\n<p>Explanation:<br \/>\nThe given fractions are: \\(\\frac{7}{8}\\) and \\(\\frac{3}{4}\\)<br \/>\nSo,<br \/>\nLet make the denominator of the two fractions equal so that we can compare the numerators<br \/>\nTo make the denominators equal, multiply the second fraction with 2<br \/>\nSo,<br \/>\n\\(\\frac{3}{4}\\) = \\(\\frac{6}{8}\\)<br \/>\nSo, when we compare the 2 fractions,<br \/>\nWe can conclude that \\(\\frac{7}{8}\\) is greater than \\(\\frac{3}{4}\\)<\/p>\n<p>Question 2.<br \/>\n<img loading=\"lazy\" class=\"alignnone size-full wp-image-13249\" src=\"https:\/\/ccssmathanswers.com\/wp-content\/uploads\/2020\/12\/Big-Ideas-Math-Answer-Key-Grade-4-Chapter-7-Understand-Fraction-Equivalence-and-Comparison-7.5-5.png\" alt=\"Big Ideas Math Answer Key Grade 4 Chapter 7 Understand Fraction Equivalence and Comparison 7.5 5\" width=\"68\" height=\"56\" \/><br \/>\nAnswer: \\(\\frac{4}{6}\\) is equal to \\(\\frac{2}{3}\\)<\/p>\n<p>Explanation:<br \/>\nThe given fractions are: \\(\\frac{4}{6}\\) and \\(\\frac{2}{3}\\)<br \/>\nSo,<br \/>\nLet make the denominator of the two fractions equal so that we can compare the numerators<br \/>\nTo make the denominators equal, multiply the second fraction with 2<br \/>\nSo,<br \/>\n\\(\\frac{2}{3}\\) = \\(\\frac{4}{6}\\)<br \/>\nSo, when we compare the 2 fractions,<br \/>\nWe can conclude that \\(\\frac{4}{6}\\) is equal to \\(\\frac{2}{3}\\)<\/p>\n<p>Question 3.<br \/>\n<img loading=\"lazy\" class=\"alignnone size-full wp-image-13250\" src=\"https:\/\/ccssmathanswers.com\/wp-content\/uploads\/2020\/12\/Big-Ideas-Math-Answer-Key-Grade-4-Chapter-7-Understand-Fraction-Equivalence-and-Comparison-7.5-6.png\" alt=\"Big Ideas Math Answer Key Grade 4 Chapter 7 Understand Fraction Equivalence and Comparison 7.5 6\" width=\"78\" height=\"58\" \/><br \/>\nAnswer: \\(\\frac{4}{3}\\) is greater than \\(\\frac{5}{4}\\)<\/p>\n<p>Explanation:<br \/>\nThe given fractions are: \\(\\frac{4}{3}\\) and \\(\\frac{5}{4}\\)<br \/>\nSo,<br \/>\nLet make the denominator of the two fractions equal so that we can compare the numerators<br \/>\nTo make the denominators equal, multiply the first fraction with 4 and the second fraction with 3<br \/>\nSo,<br \/>\n\\(\\frac{4}{3}\\) = \\(\\frac{16}{12}\\)<br \/>\n\\(\\frac{5}{4}\\) = \\(\\frac{15}{12}\\)<br \/>\nSo, when we compare the 2 fractions,<br \/>\nWe can conclude that \\(\\frac{4}{3}\\) is greater than \\(\\frac{5}{4}\\)<\/p>\n<p><strong>Apply and Grow: Practice<\/strong><\/p>\n<p><strong>Compare. Use a model to help<\/strong><br \/>\nQuestion 4.<br \/>\n<img loading=\"lazy\" class=\"alignnone size-full wp-image-13251\" src=\"https:\/\/ccssmathanswers.com\/wp-content\/uploads\/2020\/12\/Big-Ideas-Math-Answer-Key-Grade-4-Chapter-7-Understand-Fraction-Equivalence-and-Comparison-7.5-7.png\" alt=\"Big Ideas Math Answer Key Grade 4 Chapter 7 Understand Fraction Equivalence and Comparison 7.5 7\" width=\"85\" height=\"51\" \/><br \/>\nAnswer: \\(\\frac{56}{12}\\) is greater than \\(\\frac{1}{3}\\)<\/p>\n<p>Explanation:<br \/>\nThe given fractions are: \\(\\frac{6}{12}\\) and \\(\\frac{1}{3}\\)<br \/>\nSo,<br \/>\nLet make the denominator of the two fractions equal so that we can compare the numerators<br \/>\nTo make the denominators equal, multiply the second fraction with 4<br \/>\nSo,<br \/>\n\\(\\frac{1}{3}\\) = \\(\\frac{4}{12}\\)<br \/>\nSo, when we compare the 2 fractions,<br \/>\nWe can conclude that \\(\\frac{6}{12}\\) is greater than \\(\\frac{1}{3}\\)<\/p>\n<p>Question 5.<br \/>\n<img loading=\"lazy\" class=\"alignnone size-full wp-image-13252\" src=\"https:\/\/ccssmathanswers.com\/wp-content\/uploads\/2020\/12\/Big-Ideas-Math-Answer-Key-Grade-4-Chapter-7-Understand-Fraction-Equivalence-and-Comparison-7.5-8.png\" alt=\"Big Ideas Math Answer Key Grade 4 Chapter 7 Understand Fraction Equivalence and Comparison 7.5 8\" width=\"80\" height=\"51\" \/><br \/>\nAnswer: \\(\\frac{8}{10}\\) is equal to \\(\\frac{4}{5}\\)<\/p>\n<p>Explanation:<br \/>\nThe given fractions are: \\(\\frac{8}{10}\\) and \\(\\frac{4}{5}\\)<br \/>\nSo,<br \/>\nLet make the denominator of the two fractions equal so that we can compare the numerstors<br \/>\nTo make the denominators equal, multiply the second fraction with 2<br \/>\nSo,<br \/>\n\\(\\frac{4}{5}\\) = \\(\\frac{8}{10}\\)<br \/>\nSo, when we compare the 2 fractions,<br \/>\nWe can conclude that \\(\\frac{8}{10}\\) is equal to \\(\\frac{4}{5}\\)<\/p>\n<p>Question 6.<br \/>\n<img loading=\"lazy\" class=\"alignnone size-full wp-image-13253\" src=\"https:\/\/ccssmathanswers.com\/wp-content\/uploads\/2020\/12\/Big-Ideas-Math-Answer-Key-Grade-4-Chapter-7-Understand-Fraction-Equivalence-and-Comparison-7.5-9.png\" alt=\"Big Ideas Math Answer Key Grade 4 Chapter 7 Understand Fraction Equivalence and Comparison 7.5 9\" width=\"81\" height=\"61\" \/><br \/>\nAnswer: \\(\\frac{3}{10}\\) is greater than \\(\\frac{1}{4}\\)<\/p>\n<p>Explanation:<br \/>\nThe given two fractions are: \\(\\frac{3}{10}\\) and \\(\\frac{1}{4}\\)<br \/>\nSo,<br \/>\nLet make the denominators equal so that we can compare the numerators<br \/>\nSo,<br \/>\nTo make the denominators equal, multiply the first fraction with 4 and the second fraction with 10<br \/>\nSo,<br \/>\n\\(\\frac{3}{10}\\) = \\(\\frac{12}{40}\\)<br \/>\n\\(\\frac{1}{4}\\) = \\(\\frac{10}{40}\\)<br \/>\nSo, when we compare the 2 fractions,<br \/>\nWe can conclude that \\(\\frac{3}{10}\\) is greater than \\(\\frac{1}{4}\\)<\/p>\n<p>Question 7.<br \/>\n<img loading=\"lazy\" class=\"alignnone size-full wp-image-13254\" src=\"https:\/\/ccssmathanswers.com\/wp-content\/uploads\/2020\/12\/Big-Ideas-Math-Answer-Key-Grade-4-Chapter-7-Understand-Fraction-Equivalence-and-Comparison-7.5-10.png\" alt=\"Big Ideas Math Answer Key Grade 4 Chapter 7 Understand Fraction Equivalence and Comparison 7.5 10\" width=\"71\" height=\"53\" \/><br \/>\nAnswer: \\(\\frac{3}{8}\\) is less than \\(\\frac{2}{5}\\)<\/p>\n<p>Explanation:<br \/>\nThe given two fractions are: \\(\\frac{3}{8}\\) and \\(\\frac{2}{5}\\)<br \/>\nSo,<br \/>\nLet make the denominators equal so that we can compare the numerators<br \/>\nSo,<br \/>\nTo make the denominators equal, multiply the first fraction with 5 and the second fraction with 8<br \/>\nSo,<br \/>\n\\(\\frac{3}{8}\\) = \\(\\frac{15}{40}\\)<br \/>\n\\(\\frac{2}{5}\\) = \\(\\frac{16}{40}\\)<br \/>\nSo, when we compare the 2 fractions,<br \/>\nWe can conclude that \\(\\frac{3}{8}\\) is less than \\(\\frac{2}{5}\\)<\/p>\n<p>Question 8.<br \/>\n<img loading=\"lazy\" class=\"alignnone size-full wp-image-13255\" src=\"https:\/\/ccssmathanswers.com\/wp-content\/uploads\/2020\/12\/Big-Ideas-Math-Answer-Key-Grade-4-Chapter-7-Understand-Fraction-Equivalence-and-Comparison-7.5-11.png\" alt=\"Big Ideas Math Answer Key Grade 4 Chapter 7 Understand Fraction Equivalence and Comparison 7.5 11\" width=\"72\" height=\"53\" \/><br \/>\nAnswer: \\(\\frac{9}{6}\\) is equal to \\(\\frac{15}{10}\\)<\/p>\n<p>Explanation:<br \/>\nThe given two fractions are: \\(\\frac{9}{6}\\) and \\(\\frac{15}{10}\\)<br \/>\nSo,<br \/>\nLet make the denominators equal so that we can compare the numerators<br \/>\nSo,<br \/>\nTo make the denominators equal, multiply the first fraction with 10 and the second fraction with 6<br \/>\nSo,<br \/>\n\\(\\frac{9}{6}\\) = \\(\\frac{90}{60}\\)<br \/>\n\\(\\frac{15}{10}\\) = \\(\\frac{90}{60}\\)<br \/>\nSo, when we compare the 2 fractions,<br \/>\nWe can conclude that \\(\\frac{9}{6}\\) is equal to \\(\\frac{15}{10}\\)<\/p>\n<p>Question 9.<br \/>\n<img loading=\"lazy\" class=\"alignnone size-full wp-image-13256\" src=\"https:\/\/ccssmathanswers.com\/wp-content\/uploads\/2020\/12\/Big-Ideas-Math-Answer-Key-Grade-4-Chapter-7-Understand-Fraction-Equivalence-and-Comparison-7.5-12.png\" alt=\"Big Ideas Math Answer Key Grade 4 Chapter 7 Understand Fraction Equivalence and Comparison 7.5 12\" width=\"95\" height=\"55\" \/><br \/>\nAnswer: \\(\\frac{7}{10}\\) is less than \\(\\frac{9}{12}\\)<\/p>\n<p>Explanation:<br \/>\nThe given two fractions are: \\(\\frac{7}{10}\\) and \\(\\frac{9}{12}\\)<br \/>\nSo,<br \/>\nLet make the denominators equal so that we can compare the numerators<br \/>\nSo,<br \/>\nTo make the denominators equal, multiply the first fraction with 12 and the second fraction with 10<br \/>\nSo,<br \/>\n\\(\\frac{7}{10}\\) = \\(\\frac{84}{120}\\)<br \/>\n\\(\\frac{9}{12}\\) = \\(\\frac{90}{120}\\)<br \/>\nSo, when we compare the 2 fractions,<br \/>\nWe can conclude that \\(\\frac{7}{10}\\) is less than \\(\\frac{9}{12}\\)<\/p>\n<p>Question 10.<br \/>\n<strong>Writing<\/strong><br \/>\nExplain why writing fractions with like denominators or like numerators is helpful when comparing them.<br \/>\nAnswer: If we write the fractions with the like numerators and like denominators, then the comparison will be easy when we do the cross multiplication of the fractions.<\/p>\n<p>Explanation:<br \/>\n\\(\\frac{1}{2}\\) is less than \\(\\frac{3}{4}\\)<br \/>\nSo, to make the like denominators, multiply the first fraction with 2<br \/>\nSo, \\(\\frac{1}{2}\\) = \\(\\frac{2}{4}\\)<br \/>\nSince the denominators are equal, compare the numerstors and we will get the conclusion \\(\\frac{1}{2}\\) is less than \\(\\frac{3}{4}\\)<\/p>\n<p>Question 11.<br \/>\n<strong>DIG DEEPER!<\/strong><br \/>\nUse the fractions and symbols to make two true statements.<br \/>\n<img loading=\"lazy\" class=\"alignnone size-full wp-image-13257\" src=\"https:\/\/ccssmathanswers.com\/wp-content\/uploads\/2020\/12\/Big-Ideas-Math-Answer-Key-Grade-4-Chapter-7-Understand-Fraction-Equivalence-and-Comparison-7.5-13.png\" alt=\"Big Ideas Math Answer Key Grade 4 Chapter 7 Understand Fraction Equivalence and Comparison 7.5 13\" width=\"363\" height=\"132\" srcset=\"https:\/\/bigideasmathanswers.com\/wp-content\/uploads\/2020\/12\/Big-Ideas-Math-Answer-Key-Grade-4-Chapter-7-Understand-Fraction-Equivalence-and-Comparison-7.5-13.png 363w, https:\/\/bigideasmathanswers.com\/wp-content\/uploads\/2020\/12\/Big-Ideas-Math-Answer-Key-Grade-4-Chapter-7-Understand-Fraction-Equivalence-and-Comparison-7.5-13-300x109.png 300w\" sizes=\"(max-width: 363px) 100vw, 363px\" \/><br \/>\nAnswer:<br \/>\nThe two statements are:<br \/>\n\\(\\frac{9}{12}\\) &lt; \\(\\frac{5}{6}\\)<br \/>\n\\(\\frac{7}{8}\\) &gt; \\(\\frac{2}{3}\\)<\/p>\n<p>Explanation:<br \/>\nGiven pattern is:<br \/>\n<img loading=\"lazy\" class=\"alignnone size-full wp-image-13257\" src=\"https:\/\/ccssmathanswers.com\/wp-content\/uploads\/2020\/12\/Big-Ideas-Math-Answer-Key-Grade-4-Chapter-7-Understand-Fraction-Equivalence-and-Comparison-7.5-13.png\" alt=\"Big Ideas Math Answer Key Grade 4 Chapter 7 Understand Fraction Equivalence and Comparison 7.5 13\" width=\"363\" height=\"132\" srcset=\"https:\/\/bigideasmathanswers.com\/wp-content\/uploads\/2020\/12\/Big-Ideas-Math-Answer-Key-Grade-4-Chapter-7-Understand-Fraction-Equivalence-and-Comparison-7.5-13.png 363w, https:\/\/bigideasmathanswers.com\/wp-content\/uploads\/2020\/12\/Big-Ideas-Math-Answer-Key-Grade-4-Chapter-7-Understand-Fraction-Equivalence-and-Comparison-7.5-13-300x109.png 300w\" sizes=\"(max-width: 363px) 100vw, 363px\" \/><br \/>\nGiven fractions from the above are:<br \/>\n\\(\\frac{9}{12}\\), \\(\\frac{5}{6}\\), \\(\\frac{7}{8}\\) and \\(\\frac{2}{3}\\)<br \/>\nNow, first take the 2 fractions for comparison.<br \/>\nThe 2 fractions are:\u00a0\\(\\frac{9}{12}\\), \\(\\frac{5}{6}\\)<br \/>\nSo, to make the denominators of these 2 fractions equal, multiply the second fraction with 2<br \/>\nSo,<br \/>\n\\(\\frac{5}{6}\\) = \\(\\frac{10}{12}\\)<br \/>\nHence,<br \/>\nThe first statement is:<br \/>\n\\(\\frac{9}{12}\\) &lt; \\(\\frac{5}{6}\\)<br \/>\nNow, take the remaining 2 fractions.<br \/>\nThe remaining 2 fractions are: \\(\\frac{7}{8}\\) and \\(\\frac{2}{3}\\)<br \/>\nSo, to make the denominators of these 2 fractions equal, multiply the first fraction with 3 and the second fraction with 8<br \/>\nSo,<br \/>\n\\(\\frac{7}{8}\\) = \\(\\frac{21}{24}\\)<br \/>\n\\(\\frac{2}{3}\\) \\(\\frac{16}{24}\\)<br \/>\nHence,<br \/>\nThe second statement is:<br \/>\n\\(\\frac{7}{8}\\) &gt; \\(\\frac{2}{3}\\)<\/p>\n<p><strong>Think and Grow: Modeling Real Life<\/strong><\/p>\n<p><strong>Example<\/strong><br \/>\nYou try to use a \\(\\frac{13}{16}\\)-inch socket to tighten a bolt, but it is too big. Should you try a \\(\\frac{3}{4}\\) -inch socket or a \\(\\frac{7}{8}\\)-inch socket next?<br \/>\n<img loading=\"lazy\" class=\"alignnone size-full wp-image-13258\" src=\"https:\/\/ccssmathanswers.com\/wp-content\/uploads\/2020\/12\/Big-Ideas-Math-Answer-Key-Grade-4-Chapter-7-Understand-Fraction-Equivalence-and-Comparison-7.5-14.png\" alt=\"Big Ideas Math Answer Key Grade 4 Chapter 7 Understand Fraction Equivalence and Comparison 7.5 14\" width=\"176\" height=\"160\" \/><br \/>\nWrite each fraction using a like denominator.<br \/>\nBecause 4 and 8 are both factors of 16, use 16 as the denominator.<\/p>\n<p><img loading=\"lazy\" class=\"alignnone size-full wp-image-25272\" src=\"https:\/\/ccssmathanswers.com\/wp-content\/uploads\/2020\/12\/Big-Ideas-Math-Answers-Grade-4-Chapter-7-72.jpg\" alt=\"\" width=\"574\" height=\"281\" srcset=\"https:\/\/bigideasmathanswers.com\/wp-content\/uploads\/2020\/12\/Big-Ideas-Math-Answers-Grade-4-Chapter-7-72.jpg 574w, https:\/\/bigideasmathanswers.com\/wp-content\/uploads\/2020\/12\/Big-Ideas-Math-Answers-Grade-4-Chapter-7-72-300x147.jpg 300w\" sizes=\"(max-width: 574px) 100vw, 574px\" \/><\/p>\n<p><strong>Show and Grow<\/strong><\/p>\n<p>Question 12.<br \/>\nYou drill a hole using a \\(\\frac{5}{16}\\) -inch drill bit. The hole is too small. Which drill bit should you use to enlarge the hole?<br \/>\n<img loading=\"lazy\" class=\"alignnone size-full wp-image-13260\" src=\"https:\/\/ccssmathanswers.com\/wp-content\/uploads\/2020\/12\/Big-Ideas-Math-Answer-Key-Grade-4-Chapter-7-Understand-Fraction-Equivalence-and-Comparison-7.5-16.png\" alt=\"Big Ideas Math Answer Key Grade 4 Chapter 7 Understand Fraction Equivalence and Comparison 7.5 16\" width=\"225\" height=\"105\" \/><br \/>\nAnswer: You should use \\(\\frac{3}{8}\\)&#8211; inch drill bit to enlarge the hole.<\/p>\n<p>Explanation:<br \/>\nIt is given that you drill a hole using a \\(\\frac{5}{16}\\) and by using this, the hole is too small.<br \/>\nTo enlarge a drill bit, it is also given 2 types of drill bits. They are:<br \/>\nA) \\(\\frac{3}{8}\\) B) \\(\\frac{1}{4}\\)<br \/>\nNow, to find the type of drill bit which is used to enlarge the hole, compare \\(\\frac{5}{16}\\) with the given 2 drill bits<br \/>\nNow,<br \/>\nA) \\(\\frac{3}{8}\\) and \\(\\frac{5}{16}\\)<br \/>\nSo, to make the denominators equal, \\(\\frac{3}{8}\\) with 2.<br \/>\nSo,<br \/>\n\\(\\frac{3}{8}\\)= \\(\\frac{6}{16}\\)<br \/>\nHence,<br \/>\n\\(\\frac{6}{16}\\) &gt; \\(\\frac{5}{16}\\)<br \/>\nNow,<br \/>\nB) \\(\\frac{5}{16}\\) and \\(\\frac{1}{4}\\)<br \/>\nSo, to make the denominators equal, multiply \\(\\frac{1}{4}\\) with 4<br \/>\nSo,<br \/>\n\\(\\frac{1}{4}\\) = \\(\\frac{4}{16}\\)<br \/>\nHence,<br \/>\n\\(\\frac{5}{16}\\) &lt; \\(\\frac{4}{16}\\)<br \/>\nHence, from the above two,<br \/>\nWe can conclude that we can use \\(\\frac{3}{8}\\) &#8211; inch bit drill to enlarge a hole which is made by \\(\\frac{5}{16}\\) &#8211; inch bit drill<\/p>\n<p>Question 13.<br \/>\n<strong>DIG DEEPER!<\/strong><br \/>\nOrder the animals from lightest to heaviest.<br \/>\n<img loading=\"lazy\" class=\"alignnone size-full wp-image-13261\" src=\"https:\/\/ccssmathanswers.com\/wp-content\/uploads\/2020\/12\/Big-Ideas-Math-Answer-Key-Grade-4-Chapter-7-Understand-Fraction-Equivalence-and-Comparison-7.5-17.png\" alt=\"Big Ideas Math Answer Key Grade 4 Chapter 7 Understand Fraction Equivalence and Comparison 7.5 17\" width=\"241\" height=\"187\" \/><br \/>\nAnswer: The order of animals from the lightest to heaviest is: Elk &lt; Grizzly Bear &lt; Mouse<\/p>\n<p>Explanation:<br \/>\nThe given table is:<br \/>\n<img loading=\"lazy\" class=\"alignnone size-full wp-image-13261\" src=\"https:\/\/ccssmathanswers.com\/wp-content\/uploads\/2020\/12\/Big-Ideas-Math-Answer-Key-Grade-4-Chapter-7-Understand-Fraction-Equivalence-and-Comparison-7.5-17.png\" alt=\"Big Ideas Math Answer Key Grade 4 Chapter 7 Understand Fraction Equivalence and Comparison 7.5 17\" width=\"241\" height=\"187\" \/><br \/>\nSo,<br \/>\nThe weights of the animals from the above table are:<br \/>\nMouse: \\(\\frac{4}{5}\\)<br \/>\nElk: \\(\\frac{1}{3}\\)<br \/>\nGrizzly bear: \\(\\frac{3}{8}\\)<br \/>\nTo find the weights of all the 3 animals, we have to make the denominators of the three equal.<br \/>\nSo, to make the denominators equal, multiply the three fractions by 120.<br \/>\nSo, we will get<br \/>\nThe weight of Mouse is:<br \/>\n\\(\\frac{4}{5}\\) = \\(\\frac{96}{120}\\)<br \/>\nThe weight of Elk is:<br \/>\n\\(\\frac{1}{3}\\) = \\(\\frac{40}{120}\\)<br \/>\nThe weight of Grizzly bear is:<br \/>\n\\(\\frac{3}{8}\\) = \\(\\frac{45}{120}\\)<br \/>\nHence, from the above,<br \/>\nWe can say that the order of the weights of the animals from the lightest to heaviest is: Elk &lt; Grizzly Bear &lt; Mouse<\/p>\n<h3><a id=\"Compare_Fractions_Practice_7.5\"><\/a>Compare Fractions Homework &amp; Practice 7.5<\/h3>\n<p><strong>Compare. Use model to help.<\/strong><br \/>\nQuestion 1.<br \/>\n<img loading=\"lazy\" class=\"alignnone size-full wp-image-13262\" src=\"https:\/\/ccssmathanswers.com\/wp-content\/uploads\/2020\/12\/Big-Ideas-Math-Answer-Key-Grade-4-Chapter-7-Understand-Fraction-Equivalence-and-Comparison-7.5-18.png\" alt=\"Big Ideas Math Answer Key Grade 4 Chapter 7 Understand Fraction Equivalence and Comparison 7.5 18\" width=\"80\" height=\"52\" \/><br \/>\nAnswer: \\(\\frac{3}{10}\\) is greater than \\(\\frac{1}{5}\\)<\/p>\n<p>Explanation:<br \/>\nThe given two fractions are: \\(\\frac{3}{10}\\) and \\(\\frac{1}{5}\\)<br \/>\nSo,<br \/>\nLet make the denominators equal so that we can compare the numerators<br \/>\nSo,<br \/>\nTo make the denominators equal, multiply the second fraction with 2<br \/>\nSo,<br \/>\n\\(\\frac{1}{5}\\) = \\(\\frac{2}{10}\\)<br \/>\nSo, when we compare the 2 fractions,<br \/>\nWe can conclude that \\(\\frac{3}{10}\\) is greater than \\(\\frac{1}{5}\\)<\/p>\n<p>Question 2.<br \/>\n<img loading=\"lazy\" class=\"alignnone size-full wp-image-13263\" src=\"https:\/\/ccssmathanswers.com\/wp-content\/uploads\/2020\/12\/Big-Ideas-Math-Answer-Key-Grade-4-Chapter-7-Understand-Fraction-Equivalence-and-Comparison-7.5-19.png\" alt=\"Big Ideas Math Answer Key Grade 4 Chapter 7 Understand Fraction Equivalence and Comparison 7.5 19\" width=\"88\" height=\"62\" \/><br \/>\nAnswer: \\(\\frac{4}{5}\\) is greater than \\(\\frac{2}{3}\\)<\/p>\n<p>Explanation:<br \/>\nThe given two fractions are: \\(\\frac{4}{5}\\) and \\(\\frac{2}{3}\\)<br \/>\nSo,<br \/>\nLet make the denominators equal so that we can compare the numerators<br \/>\nSo,<br \/>\nTo make the denominators equal, multiply the first fraction with 3 and the second fraction with 5<br \/>\nSo,<br \/>\n\\(\\frac{4}{5}\\) = \\(\\frac{12}{15}\\)<br \/>\n\\(\\frac{2}{3}\\) = \\(\\frac{10}{15}\\)<br \/>\nSo, when we compare the 2 fractions,<br \/>\nWe can conclude that \\(\\frac{4}{5}\\) is greater than \\(\\frac{2}{3}\\)<\/p>\n<p>Question 3.<br \/>\n<img loading=\"lazy\" class=\"alignnone size-full wp-image-13264\" src=\"https:\/\/ccssmathanswers.com\/wp-content\/uploads\/2020\/12\/Big-Ideas-Math-Answer-Key-Grade-4-Chapter-7-Understand-Fraction-Equivalence-and-Comparison-7.5-20.png\" alt=\"Big Ideas Math Answer Key Grade 4 Chapter 7 Understand Fraction Equivalence and Comparison 7.5 20\" width=\"86\" height=\"69\" \/><br \/>\nAnswer: \\(\\frac{5}{8}\\) is less than \\(\\frac{2}{1}\\)<\/p>\n<p>Explanation:<br \/>\nThe given two fractions are: \\(\\frac{5}{8}\\) and \\(\\frac{2}{1}\\)<br \/>\nSo,<br \/>\nLet make the denominators equal so that we can compare the numerators<br \/>\nSo,<br \/>\nTo make the denominators equal, multiply the second fraction with 8<br \/>\nSo,<br \/>\n\\(\\frac{2}{1}\\) = \\(\\frac{16}{8}\\)<br \/>\nSo, when we compare the 2 fractions,<br \/>\nWe can conclude that \\(\\frac{5}{8}\\) is less than \\(\\frac{2}{1}\\)<\/p>\n<p><strong>Compare. Use a model to help.<\/strong><br \/>\nQuestion 4.<br \/>\n<img loading=\"lazy\" class=\"alignnone size-full wp-image-13265\" src=\"https:\/\/ccssmathanswers.com\/wp-content\/uploads\/2020\/12\/Big-Ideas-Math-Answer-Key-Grade-4-Chapter-7-Understand-Fraction-Equivalence-and-Comparison-7.5-21.png\" alt=\"Big Ideas Math Answer Key Grade 4 Chapter 7 Understand Fraction Equivalence and Comparison 7.5 21\" width=\"88\" height=\"52\" \/><br \/>\nAnswer: \\(\\frac{9}{10}\\) is less than \\(\\frac{97}{100}\\)<\/p>\n<p>Explanation:<br \/>\nThe given two fractions are: \\(\\frac{9}{10}\\) and \\(\\frac{97}{100}\\)<br \/>\nSo,<br \/>\nLet make the denominators equal so that we can compare the numerators<br \/>\nSo,<br \/>\nTo make the denominators equal, multiply the first fraction with 10<br \/>\nSo,<br \/>\n\\(\\frac{9}{10}\\) = \\(\\frac{90}{100}\\)<br \/>\nSo, when we compare the 2 fractions,<br \/>\nWe can conclude that \\(\\frac{9}{10}\\) is less than \\(\\frac{97}{100}\\)<\/p>\n<p>Question 5.<br \/>\n<img loading=\"lazy\" class=\"alignnone size-full wp-image-13266\" src=\"https:\/\/ccssmathanswers.com\/wp-content\/uploads\/2020\/12\/Big-Ideas-Math-Answer-Key-Grade-4-Chapter-7-Understand-Fraction-Equivalence-and-Comparison-7.5-22.png\" alt=\"Big Ideas Math Answer Key Grade 4 Chapter 7 Understand Fraction Equivalence and Comparison 7.5 22\" width=\"75\" height=\"54\" \/><br \/>\nAnswer: \\(\\frac{3}{8}\\) is greater than \\(\\frac{2}{6}\\)<\/p>\n<p>Explanation:<br \/>\nThe given two fractions are: \\(\\frac{3}{8}\\) and \\(\\frac{2}{6}\\)<br \/>\nSo,<br \/>\nLet make the denominators equal so that we can compare the numerators<br \/>\nSo,<br \/>\nTo make the denominators equal, multiply the first fraction with 3 and the second fraction with 4<br \/>\nSo,<br \/>\n\\(\\frac{3}{8}\\) = \\(\\frac{9}{24}\\)<br \/>\n\\(\\frac{2}{6}\\) = \\(\\frac{8}{24}\\)<br \/>\nSo, when we compare the 2 fractions,<br \/>\nWe can conclude that \\(\\frac{3}{8}\\) is greater than \\(\\frac{2}{6}\\)<\/p>\n<p>Question 6.<br \/>\n<img loading=\"lazy\" class=\"alignnone size-full wp-image-13267\" src=\"https:\/\/ccssmathanswers.com\/wp-content\/uploads\/2020\/12\/Big-Ideas-Math-Answer-Key-Grade-4-Chapter-7-Understand-Fraction-Equivalence-and-Comparison-7.5-23.png\" alt=\"Big Ideas Math Answer Key Grade 4 Chapter 7 Understand Fraction Equivalence and Comparison 7.5 23\" width=\"85\" height=\"60\" \/><br \/>\nAnswer: \\(\\frac{1}{3}\\) is equal to \\(\\frac{4}{12}\\)<\/p>\n<p>Explanation:<br \/>\nThe given two fractions are: \\(\\frac{1}{3}\\) and \\(\\frac{4}{12}\\)<br \/>\nSo,<br \/>\nLet make the denominators equal so that we can compare the numerators<br \/>\nSo,<br \/>\nTo make the denominators equal, multiply the first fraction with 4<br \/>\nSo,<br \/>\n\\(\\frac{1}{3}\\) = \\(\\frac{4}{12}\\)<br \/>\nSo, when we compare the 2 fractions,<br \/>\nWe can conclude that \\(\\frac{1}{3}\\) is equal to \\(\\frac{4}{12}\\)<\/p>\n<p>Question 7.<br \/>\n<img loading=\"lazy\" class=\"alignnone size-full wp-image-13268\" src=\"https:\/\/ccssmathanswers.com\/wp-content\/uploads\/2020\/12\/Big-Ideas-Math-Answer-Key-Grade-4-Chapter-7-Understand-Fraction-Equivalence-and-Comparison-7.5-24.png\" alt=\"Big Ideas Math Answer Key Grade 4 Chapter 7 Understand Fraction Equivalence and Comparison 7.5 24\" width=\"76\" height=\"54\" \/><br \/>\nAnswer: \\(\\frac{7}{2}\\) is greater than \\(\\frac{6}{5}\\)<\/p>\n<p>Explanation:<br \/>\nThe given two fractions are: \\(\\frac{7}{2}\\) and \\(\\frac{6}{5}\\)<br \/>\nSo,<br \/>\nLet make the denominators equal so that we can compare the numerators<br \/>\nSo,<br \/>\nTo make the denominators equal, multiply the first fraction with 5 and the second fraction with 2<br \/>\nSo,<br \/>\n\\(\\frac{7}{2}\\) = \\(\\frac{35}{10}\\)<br \/>\n\\(\\frac{6}{5}\\) = \\(\\frac{12}{10}\\)<br \/>\nSo, when we compare the 2 fractions,<br \/>\nWe can conclude that \\(\\frac{7}{2}\\) is less than \\(\\frac{6}{5}\\)<\/p>\n<p>Question 8.<br \/>\n<img loading=\"lazy\" class=\"alignnone size-full wp-image-13269\" src=\"https:\/\/ccssmathanswers.com\/wp-content\/uploads\/2020\/12\/Big-Ideas-Math-Answer-Key-Grade-4-Chapter-7-Understand-Fraction-Equivalence-and-Comparison-7.5-25.png\" alt=\"Big Ideas Math Answer Key Grade 4 Chapter 7 Understand Fraction Equivalence and Comparison 7.5 25\" width=\"89\" height=\"51\" \/><br \/>\nAnswer: \\(\\frac{1}{10}\\) is less than \\(\\frac{2}{12}\\)<\/p>\n<p>Explanation:<br \/>\nThe given two fractions are: \\(\\frac{1}{10}\\) and \\(\\frac{2}{12}\\)<br \/>\nSo,<br \/>\nLet make the denominators equal so that we can compare the numerators<br \/>\nSo,<br \/>\nTo make the denominators equal, multiply the first fraction with 12 and the second fraction with 10<br \/>\nSo,<br \/>\n\\(\\frac{1}{10}\\) = \\(\\frac{12}{120}\\)<br \/>\n\\(\\frac{2}{12}\\) = \\(\\frac{20}{120}\\)<br \/>\nSo, when we compare the 2 fractions,<br \/>\nWe can conclude that \\(\\frac{1}{10}\\) is less than \\(\\frac{2}{12}\\)<\/p>\n<p>Question 9.<br \/>\n<img loading=\"lazy\" class=\"alignnone size-full wp-image-13270\" src=\"https:\/\/ccssmathanswers.com\/wp-content\/uploads\/2020\/12\/Big-Ideas-Math-Answer-Key-Grade-4-Chapter-7-Understand-Fraction-Equivalence-and-Comparison-7.5-26.png\" alt=\"Big Ideas Math Answer Key Grade 4 Chapter 7 Understand Fraction Equivalence and Comparison 7.5 26\" width=\"81\" height=\"57\" \/><br \/>\nAnswer: \\(\\frac{3}{4}\\) is greater than \\(\\frac{4}{6}\\)<\/p>\n<p>Explanation:<br \/>\nThe given two fractions are: \\(\\frac{3}{4}\\) and \\(\\frac{4}{6}\\)<br \/>\nSo,<br \/>\nLet make the denominators equal so that we can compare the numerators<br \/>\nSo,<br \/>\nTo make the denominators equal, multiply the first fraction with 3 and the second fraction with 2<br \/>\nSo,<br \/>\n\\(\\frac{3}{4}\\) = \\(\\frac{9}{12}\\)<br \/>\n\\(\\frac{4}{6}\\) = \\(\\frac{8}{12}\\)<br \/>\nSo, when we compare the 2 fractions,<br \/>\nWe can conclude that \\(\\frac{3}{4}\\) is greater than \\(\\frac{4}{6}\\)<\/p>\n<p>Question 10.<br \/>\n<strong>Structure<\/strong><br \/>\nCompare \\(\\frac{3}{8}\\) and \\(\\frac{1}{4}\\) two different ways.<\/p>\n<p>Answer: \\(\\frac{3}{8}\\) is greater than \\(\\frac{1}{4}\\)<\/p>\n<p>Explanation:<br \/>\nThe given two fractions are: \\(\\frac{3}{8}\\) and \\(\\frac{1}{4}\\)<br \/>\nFirst way of Comparison:<br \/>\nLet make the denominators equal so that we can compare the numerators<br \/>\nSo,<br \/>\nTo make the denominators equal, multiply the second fraction with 2<br \/>\nSo,<br \/>\n\\(\\frac{1}{4}\\) = \\(\\frac{2}{8}\\)<br \/>\nSo, when we compare the 2 fractions,<br \/>\nWe can conclude that \\(\\frac{3}{8}\\) is greater than \\(\\frac{1}{4}\\)<br \/>\nSecond Way of Comparison:<br \/>\nThe given two fractions are: \\(\\frac{3}{8}\\) and \\(\\frac{1}{4}\\)<br \/>\nSo,<br \/>\nLet make the numerators equal so that we can compare the denominators<br \/>\nSo,<br \/>\nTo make the numerators equal, multiply the second fraction with 3<br \/>\nSo,<br \/>\n\\(\\frac{1}{4}\\) = \\(\\frac{3}{4}\\)<br \/>\nSo, when we compare the 2 fractions,<br \/>\nWe can conclude that \\(\\frac{3}{8}\\) is greater than \\(\\frac{1}{4}\\)<\/p>\n<p>Question 11.<br \/>\n<strong>Modeling Real Life<\/strong><br \/>\nA sailor is making a ship in a bottle. The last thing he needs to do is seal the bottle with a cork stopper. He tries a \\(\\frac{3}{4}\\) -inch cork stopper, but it is too small. Should he try a \\(\\frac{1}{2}\\)-inch cork stopper or a \\(\\frac{4}{5}\\)-inch cork stopper next? Explain.<br \/>\n<img loading=\"lazy\" class=\"alignnone size-full wp-image-13271\" src=\"https:\/\/ccssmathanswers.com\/wp-content\/uploads\/2020\/12\/Big-Ideas-Math-Answer-Key-Grade-4-Chapter-7-Understand-Fraction-Equivalence-and-Comparison-7.5-27.png\" alt=\"Big Ideas Math Answer Key Grade 4 Chapter 7 Understand Fraction Equivalence and Comparison 7.5 27\" width=\"270\" height=\"94\" \/><br \/>\nAnswer: He had to use \\(\\frac{4}{5}\\) -inch cork stopper<\/p>\n<p>Explanation:<br \/>\nIt is given that a sailor is making a ship in a bottle and he needs to seal the bottle after making the ship.<br \/>\nIt is also given that he tried a \\(\\frac{3}{4}\\) -inch cork stopper which is small<br \/>\nSo, to make the big cork stopper so that it can close the bottle, there are 2 choices given.<br \/>\nThe two choices are:<br \/>\nA) \\(\\frac{1}{2}\\) B) \\(\\frac{4}{5}\\)<br \/>\nNow,<br \/>\nCompare \\(\\frac{1}{2}\\) with \\(\\frac{3}{4}\\)<br \/>\nNow,<br \/>\nLet make the denominators equal so that we can compare the numerators<br \/>\nSo,<br \/>\nTo make the denominators equal, multiply the second fraction with 2<br \/>\nSo,<br \/>\n\\(\\frac{1}{2}\\) = \\(\\frac{2}{4}\\)<br \/>\nSo, when we compare the 2 fractions,<br \/>\nWe can conclude that \\(\\frac{1}{2}\\) is less than \\(\\frac{3}{4}\\)<br \/>\nNow,<br \/>\nCompare \\(\\frac{4}{5}\\) with \\(\\frac{3}{4}\\)<br \/>\nNow,<br \/>\nLet make the denominators equal so that we can compare the numerators<br \/>\nSo,<br \/>\nTo make the denominators equal, multiply the\u00a0 first fraction with 4 and the second fraction with 5<br \/>\nSo,<br \/>\n\\(\\frac{4}{5}\\) = \\(\\frac{16}{20}\\)<br \/>\n\\(\\frac{3}{4}\\) = \\(\\frac{15}{20}\\)<br \/>\nSo, when we compare the 2 fractions,<br \/>\nWe can conclude that \\(\\frac{4}{5}\\) is greater than \\(\\frac{3}{4}\\)<br \/>\nHence, from the above 2 comparisons,<br \/>\nWe can conclude that we can use \\(\\frac{4}{5}\\) &#8211; inch cork stopper.<\/p>\n<p>Question 12.<br \/>\n<strong>DIG DEEPER!<\/strong><br \/>\nOrder the lengths of hair donated from greatest to least.<br \/>\n<img loading=\"lazy\" class=\"alignnone size-full wp-image-13272\" src=\"https:\/\/ccssmathanswers.com\/wp-content\/uploads\/2020\/12\/Big-Ideas-Math-Answer-Key-Grade-4-Chapter-7-Understand-Fraction-Equivalence-and-Comparison-7.5-28.png\" alt=\"Big Ideas Math Answer Key Grade 4 Chapter 7 Understand Fraction Equivalence and Comparison 7.5 28\" width=\"232\" height=\"203\" \/><\/p>\n<p>Answer: The order of lengths of hair donated from the greatest to the least is: C &gt; B &gt; A<\/p>\n<p>Explanation:<br \/>\nThe given table is:<br \/>\n<img loading=\"lazy\" class=\"alignnone size-full wp-image-13272\" src=\"https:\/\/ccssmathanswers.com\/wp-content\/uploads\/2020\/12\/Big-Ideas-Math-Answer-Key-Grade-4-Chapter-7-Understand-Fraction-Equivalence-and-Comparison-7.5-28.png\" alt=\"Big Ideas Math Answer Key Grade 4 Chapter 7 Understand Fraction Equivalence and Comparison 7.5 28\" width=\"232\" height=\"203\" \/><br \/>\nFrom the above table,<br \/>\nThe length of the hair donated by student A is: \\(\\frac{3}{4}\\)<br \/>\nThe length of the hair donated by student B is: \\(\\frac{11}{12}\\)<br \/>\nThe length of the hair donated by student C is: \\(\\frac{5}{6}\\)<br \/>\nNow,<br \/>\nLet make the denominators equal so that we can compare the numerators<br \/>\nSo,<br \/>\nTo make the denominators equal, multiply the first fraction with 3, the second fraction with 1 and the third fraction with 2<br \/>\nSo,<br \/>\n\\(\\frac{3}{4}\\) = \\(\\frac{9}{12}\\)<br \/>\n\\(\\frac{5}{6}\\) = \\(\\frac{10}{12}\\)<br \/>\n\\(\\frac{11}{12}\\) = \\(\\frac{11}{12}\\)<br \/>\nSo, when we compare the 3 fractions,<br \/>\nWe can conclude that the order of the lengths of hair donated from highest to least is: C &gt; B &gt; A<\/p>\n<p><strong>Review &amp; Refresh<\/strong><\/p>\n<p>Question 13.<br \/>\nExtend the pattern of shapes by repeating the rule \u201ctriangle, pentagon, octagon.\u201dWhat is the 48th shape in the pattern?<br \/>\n<img loading=\"lazy\" class=\"alignnone size-full wp-image-13273\" src=\"https:\/\/ccssmathanswers.com\/wp-content\/uploads\/2020\/12\/Big-Ideas-Math-Answer-Key-Grade-4-Chapter-7-Understand-Fraction-Equivalence-and-Comparison-7.5-29.png\" alt=\"Big Ideas Math Answer Key Grade 4 Chapter 7 Understand Fraction Equivalence and Comparison 7.5 29\" width=\"515\" height=\"74\" srcset=\"https:\/\/bigideasmathanswers.com\/wp-content\/uploads\/2020\/12\/Big-Ideas-Math-Answer-Key-Grade-4-Chapter-7-Understand-Fraction-Equivalence-and-Comparison-7.5-29.png 515w, https:\/\/bigideasmathanswers.com\/wp-content\/uploads\/2020\/12\/Big-Ideas-Math-Answer-Key-Grade-4-Chapter-7-Understand-Fraction-Equivalence-and-Comparison-7.5-29-300x43.png 300w\" sizes=\"(max-width: 515px) 100vw, 515px\" \/><br \/>\nAnswer: The 48th shape in the given pattern is: Octagon<\/p>\n<p>Explanation:<br \/>\nThe given pattern is:<br \/>\n<img loading=\"lazy\" class=\"alignnone size-full wp-image-13273\" src=\"https:\/\/ccssmathanswers.com\/wp-content\/uploads\/2020\/12\/Big-Ideas-Math-Answer-Key-Grade-4-Chapter-7-Understand-Fraction-Equivalence-and-Comparison-7.5-29.png\" alt=\"Big Ideas Math Answer Key Grade 4 Chapter 7 Understand Fraction Equivalence and Comparison 7.5 29\" width=\"515\" height=\"74\" srcset=\"https:\/\/bigideasmathanswers.com\/wp-content\/uploads\/2020\/12\/Big-Ideas-Math-Answer-Key-Grade-4-Chapter-7-Understand-Fraction-Equivalence-and-Comparison-7.5-29.png 515w, https:\/\/bigideasmathanswers.com\/wp-content\/uploads\/2020\/12\/Big-Ideas-Math-Answer-Key-Grade-4-Chapter-7-Understand-Fraction-Equivalence-and-Comparison-7.5-29-300x43.png 300w\" sizes=\"(max-width: 515px) 100vw, 515px\" \/><br \/>\nFrom the above pattern,<br \/>\nThe given rule is: Triangle, pentagon, octagon<br \/>\nSo,<br \/>\nThe total number of figures in the given pattern = 3<br \/>\nSo,<br \/>\nThe 48th figure in the given pattern = 48 \u00f7 3<br \/>\nNow,<br \/>\nBy using the partial quotients method,<br \/>\n48 \u00f7 3 = ( 30 + 18 ) \u00f7 3<br \/>\n= ( 30 \u00f7 3 ) + ( 18 \u00f7 3 )<br \/>\n= 10 + 6<br \/>\n= 16 R 0<br \/>\nHence, from the above,<br \/>\nWe can conclude that the 48th figure in the given pattern is: Octagon<\/p>\n<h3><a id=\"Understand_Fraction_Equivalence_and_Comparison_Performance_Task\"><\/a>Understand Fraction Equivalence and Comparison Performance Task<\/h3>\n<p>Question 1.<br \/>\na. Your art teacher wants you to complete the design below. Half of the squares are colored black. Complete the table. Then use the table to finish the design.<br \/>\n<img loading=\"lazy\" class=\"alignnone size-full wp-image-25337\" src=\"https:\/\/ccssmathanswers.com\/wp-content\/uploads\/2020\/12\/Big-Ideas-Math-Answers-Grade-4-Chapter-7-73.jpg\" alt=\"\" width=\"686\" height=\"407\" srcset=\"https:\/\/bigideasmathanswers.com\/wp-content\/uploads\/2020\/12\/Big-Ideas-Math-Answers-Grade-4-Chapter-7-73.jpg 686w, https:\/\/bigideasmathanswers.com\/wp-content\/uploads\/2020\/12\/Big-Ideas-Math-Answers-Grade-4-Chapter-7-73-300x178.jpg 300w\" sizes=\"(max-width: 686px) 100vw, 686px\" \/><br \/>\nb.Which two colors cover the same portion of the design? Explain.<\/p>\n<p>Answer: Green and Blue colors cover the same portion of the design<br \/>\nExplanation:<br \/>\nThe teacher has given a board that has a total of 100 squares and according to the table, we have to complete the design of the squares.<br \/>\nThe table is:<br \/>\n<img loading=\"lazy\" class=\"alignnone size-full wp-image-25339\" src=\"https:\/\/ccssmathanswers.com\/wp-content\/uploads\/2020\/12\/Big-Ideas-Math-Answers-Grade-4-Chapter-7-74.jpg\" alt=\"\" width=\"242\" height=\"377\" srcset=\"https:\/\/bigideasmathanswers.com\/wp-content\/uploads\/2020\/12\/Big-Ideas-Math-Answers-Grade-4-Chapter-7-74.jpg 242w, https:\/\/bigideasmathanswers.com\/wp-content\/uploads\/2020\/12\/Big-Ideas-Math-Answers-Grade-4-Chapter-7-74-193x300.jpg 193w\" sizes=\"(max-width: 242px) 100vw, 242px\" \/><br \/>\nHence, from the above table,<br \/>\nWe can conclude that Blue and Yellow colors cover the same portion of the design.<\/p>\n<p>Question 2.<br \/>\nYour teacher displays 30 designs in a rectangular array on the wall. Show two different ways your teacher can arrange the designs.<\/p>\n<p>Answer: The\u00a0 different ways that your teacher can arrange the designs are: 1 \u00d7 30, 2 \u00d7 15, 3 \u00d7 5, 5 \u00d7 3, 15 \u00d7 2, 30 \u00d7 1<\/p>\n<p>Explanation:<br \/>\nIt is given that your teacher displays 30 designs in a rectangular array on the wall.<br \/>\nSo, we can arrange the 30 designs in different ways by using the factor pairs of 30<br \/>\nNow,<br \/>\nThe factor pairs of 30 are: 1 \u00d7 30, 2 \u00d7 15, 3 \u00d7 5, 5 \u00d7 3, 15 \u00d7 2, 30 \u00d7 1<br \/>\nHence, from the above,<br \/>\nWe can conclude that the different ways to arrange the 30 designs in a rectangular array is: 1 \u00d7 30, 2 \u00d7 15, 3 \u00d7 5, 5 \u00d7 3, 15 \u00d7 2, 30 \u00d7 1<\/p>\n<h3><a id=\"Understand_Fraction_Equivalence_and_Comparison_Activity\"><\/a>Understand Fraction Equivalence and Comparison Activity<\/h3>\n<p><strong>Fraction Boss<\/strong><br \/>\n<strong>Directions:<\/strong><br \/>\n1. Divide the Fraction Boss Cards equally between both players.<br \/>\n2. Each player flips a Fraction Boss Card.<br \/>\n3. Players compare their fractions. The player with the greater fraction takes both cards.<br \/>\n4. If the fractions are equal, each player flips another card. Players compare their fractions. The player with the greater fraction takes all four cards.<br \/>\n5. The player with the most cards at the end of the round wins!<br \/>\n<img loading=\"lazy\" class=\"alignnone size-full wp-image-13275\" src=\"https:\/\/ccssmathanswers.com\/wp-content\/uploads\/2020\/12\/Big-Ideas-Math-Answers-4th-Grade-Chapter-7-Understand-Fraction-Equivalence-and-Comparison-2.png\" alt=\"Big Ideas Math Answers 4th Grade Chapter 7 Understand Fraction Equivalence and Comparison 2\" width=\"694\" height=\"701\" srcset=\"https:\/\/bigideasmathanswers.com\/wp-content\/uploads\/2020\/12\/Big-Ideas-Math-Answers-4th-Grade-Chapter-7-Understand-Fraction-Equivalence-and-Comparison-2.png 694w, https:\/\/bigideasmathanswers.com\/wp-content\/uploads\/2020\/12\/Big-Ideas-Math-Answers-4th-Grade-Chapter-7-Understand-Fraction-Equivalence-and-Comparison-2-297x300.png 297w\" sizes=\"(max-width: 694px) 100vw, 694px\" \/><\/p>\n<h3><a id=\"Understand_Fraction_Equivalence_and_Comparison_Chapter_Practice\"><\/a>Understand Fraction Equivalence and Comparison Chapter Practice<\/h3>\n<p><strong>7.1 Model Equivalent Fractions<\/strong><\/p>\n<p>Question 1.<br \/>\nUse the model to find an equivalent fraction for \\(\\frac{3}{4}\\).<br \/>\n<img loading=\"lazy\" class=\"alignnone size-full wp-image-13276\" src=\"https:\/\/ccssmathanswers.com\/wp-content\/uploads\/2020\/12\/Big-Ideas-Math-Answers-4th-Grade-Chapter-7-Understand-Fraction-Equivalence-and-Comparison-chp-1.png\" alt=\"Big Ideas Math Answers 4th Grade Chapter 7 Understand Fraction Equivalence and Comparison chp 1\" width=\"207\" height=\"71\" \/><br \/>\nAnswer: The equivalent fraction of \\(\\frac{3}{4}\\) is: \\(\\frac{6}{8}\\)<\/p>\n<p>Explanation:<br \/>\nThe given model is:<br \/>\n<img loading=\"lazy\" class=\"alignnone size-full wp-image-13276\" src=\"https:\/\/ccssmathanswers.com\/wp-content\/uploads\/2020\/12\/Big-Ideas-Math-Answers-4th-Grade-Chapter-7-Understand-Fraction-Equivalence-and-Comparison-chp-1.png\" alt=\"Big Ideas Math Answers 4th Grade Chapter 7 Understand Fraction Equivalence and Comparison chp 1\" width=\"207\" height=\"71\" \/><br \/>\nFrom the above model,<br \/>\nWe can say that the fraction is: \\(\\frac{3}{4}\\)<br \/>\nSo,<br \/>\nThe model for the Equivalent fraction is:<br \/>\n<img loading=\"lazy\" class=\"alignnone size-full wp-image-25340\" src=\"https:\/\/ccssmathanswers.com\/wp-content\/uploads\/2020\/12\/Big-Ideas-Math-Answers-Grade-4-Chapter-7-75.jpg\" alt=\"\" width=\"471\" height=\"84\" srcset=\"https:\/\/bigideasmathanswers.com\/wp-content\/uploads\/2020\/12\/Big-Ideas-Math-Answers-Grade-4-Chapter-7-75.jpg 471w, https:\/\/bigideasmathanswers.com\/wp-content\/uploads\/2020\/12\/Big-Ideas-Math-Answers-Grade-4-Chapter-7-75-300x54.jpg 300w\" sizes=\"(max-width: 471px) 100vw, 471px\" \/><br \/>\nFrom the above model, we can say that the equivalent fraction is: \\(\\frac{6}{8}\\)<br \/>\nSo,<br \/>\nWhen we divide \\(\\frac{6}{8}\\) by 2, we will get the equivalent value.<br \/>\nHence, from the above,<br \/>\nWe can conclude that \\(\\frac{3}{4}\\) = \\(\\frac{6}{8}\\)<\/p>\n<p>Question 2.<br \/>\nUse the number line to find an equivalent fraction for \\(\\frac{2}{5}\\).<br \/>\n<img loading=\"lazy\" class=\"alignnone size-full wp-image-13277\" src=\"https:\/\/ccssmathanswers.com\/wp-content\/uploads\/2020\/12\/Big-Ideas-Math-Answers-4th-Grade-Chapter-7-Understand-Fraction-Equivalence-and-Comparison-chp-2.png\" alt=\"Big Ideas Math Answers 4th Grade Chapter 7 Understand Fraction Equivalence and Comparison chp 2\" width=\"291\" height=\"59\" \/><br \/>\nAnswer: The equivalent fraction of \\(\\frac{2}{5}\\) is: \\(\\frac{4}{10}\\)<\/p>\n<p>Explanation:<br \/>\nThe given number line is:<br \/>\n<img loading=\"lazy\" class=\"alignnone size-full wp-image-13277\" src=\"https:\/\/ccssmathanswers.com\/wp-content\/uploads\/2020\/12\/Big-Ideas-Math-Answers-4th-Grade-Chapter-7-Understand-Fraction-Equivalence-and-Comparison-chp-2.png\" alt=\"Big Ideas Math Answers 4th Grade Chapter 7 Understand Fraction Equivalence and Comparison chp 2\" width=\"291\" height=\"59\" \/><br \/>\nFrom the above number line,<br \/>\nwe can say that 2 lines represent a value. i.e., \\(\\frac{2}{5}\\)<br \/>\nSo,<br \/>\nThe value of each line when divided into 2 parts represent: \\(\\frac{1}{10}\\)<br \/>\nSo,<br \/>\nThe equivalent number line is:<br \/>\n<img loading=\"lazy\" class=\"alignnone size-full wp-image-25341\" src=\"https:\/\/ccssmathanswers.com\/wp-content\/uploads\/2020\/12\/Big-Ideas-Math-Answers-Grade-4-Chapter-7-76.jpg\" alt=\"\" width=\"292\" height=\"140\" \/><br \/>\nSo, from the above equivalent number line,<br \/>\nWe can see that \\(\\frac{2}{5}\\) is equal to \\(\\frac{4}{10}\\)<br \/>\nHence, from the above,<br \/>\nWe can conclude that \\(\\frac{2}{5}\\) = \\(\\frac{4}{10}\\)<\/p>\n<p>Question 3.<br \/>\n<strong>Open-Ended<\/strong><br \/>\nWrite two equivalent fractions to describe the portion of the apples that are red.<br \/>\n<img loading=\"lazy\" class=\"alignnone size-full wp-image-13278\" src=\"https:\/\/ccssmathanswers.com\/wp-content\/uploads\/2020\/12\/Big-Ideas-Math-Answers-4th-Grade-Chapter-7-Understand-Fraction-Equivalence-and-Comparison-chp-3.png\" alt=\"Big Ideas Math Answers 4th Grade Chapter 7 Understand Fraction Equivalence and Comparison chp 3\" width=\"188\" height=\"111\" \/><br \/>\nAnswer:<br \/>\nThe two equivalent fractions to describe the portion of apples that are red is:<br \/>\n\\(\\frac{4}{8}\\) and \\(\\frac{1}{2}\\)<\/p>\n<p>Explanation:<br \/>\nThe given model is:<br \/>\n<img loading=\"lazy\" class=\"alignnone size-full wp-image-13278\" src=\"https:\/\/ccssmathanswers.com\/wp-content\/uploads\/2020\/12\/Big-Ideas-Math-Answers-4th-Grade-Chapter-7-Understand-Fraction-Equivalence-and-Comparison-chp-3.png\" alt=\"Big Ideas Math Answers 4th Grade Chapter 7 Understand Fraction Equivalence and Comparison chp 3\" width=\"188\" height=\"111\" \/><br \/>\nFrom the above model,<br \/>\nWe can say that,<br \/>\nThe number of colored apples is: 4<br \/>\nThe number of red apples is: 4<br \/>\nSo,<br \/>\nThe total number of apples are: 8<br \/>\nSo,<br \/>\nThe fraction form for the red apples is = \\(\\frac{Number of red apples}{Total number of apples}\\)<br \/>\n= \\(\\frac{4}{8}\\)<br \/>\nEquivalent form for the red apples:<br \/>\nConsider the colored apples as 1 group and the red apples as 1 group<br \/>\nSo,<br \/>\nThe number of red apples is: 1<br \/>\nThe number of colored apples is: 1<br \/>\nSo,<br \/>\nThe total number of apples are: 2<br \/>\nSo,<br \/>\nThe fraction that the apples are red = \\(\\frac{Number of red apples}{Total number of apples}\\)<br \/>\n= \\(\\frac{1}{2}\\)<br \/>\nHence, from the above,<br \/>\nWe can say that<br \/>\nThe two equivalent fractions to describe the portion of apples that are red are:<br \/>\n\\(\\frac{4}{8}\\) and \\(\\frac{1}{2}\\)<\/p>\n<p><strong>7.2 Generate Equivalent Fractions by Multiplying<\/strong><\/p>\n<p><strong>Find the equivalent fraction.<\/strong><br \/>\nQuestion 4.<br \/>\n<img loading=\"lazy\" class=\"alignnone size-full wp-image-13279\" src=\"https:\/\/ccssmathanswers.com\/wp-content\/uploads\/2020\/12\/Big-Ideas-Math-Answers-4th-Grade-Chapter-7-Understand-Fraction-Equivalence-and-Comparison-chp-4.png\" alt=\"Big Ideas Math Answers 4th Grade Chapter 7 Understand Fraction Equivalence and Comparison chp 4\" width=\"92\" height=\"65\" \/><br \/>\nAnswer: The equivalent fraction of \\(\\frac{3}{4}\\) is: \\(\\frac{9}{12}\\)<\/p>\n<p>Explanation:<br \/>\nThe given fraction is \\(\\frac{3}{4}\\)<br \/>\nFrom the above fraction, the numerator and denominator are: 3 and 4<br \/>\nIt is given that the denominator value is 12.<br \/>\nSo, to make the value 12 from 4, we have to multiply the fraction with 3<br \/>\nSo,<br \/>\n\\(\\frac{3}{4} is multiplied with [latex]\\frac{3}{3}.<br \/>\nHence,<br \/>\n<img loading=\"lazy\" class=\"alignnone size-full wp-image-25342\" src=\"https:\/\/ccssmathanswers.com\/wp-content\/uploads\/2020\/12\/Big-Ideas-Math-Answers-Grade-4-Chapter-7-77.jpg\" alt=\"\" width=\"82\" height=\"53\" \/><\/p>\n<p>Question 5.<br \/>\n<img loading=\"lazy\" class=\"alignnone size-full wp-image-13280\" src=\"https:\/\/ccssmathanswers.com\/wp-content\/uploads\/2020\/12\/Big-Ideas-Math-Answers-4th-Grade-Chapter-7-Understand-Fraction-Equivalence-and-Comparison-chp-5.png\" alt=\"Big Ideas Math Answers 4th Grade Chapter 7 Understand Fraction Equivalence and Comparison chp 5\" width=\"91\" height=\"61\" \/><br \/>\nAnswer: The equivalent fraction of [latex]\\frac{1}{2}\\) is: \\(\\frac{5}{10}\\)<\/p>\n<p>Explanation:<br \/>\nThe given fraction is \\(\\frac{1}{2}\\)<br \/>\nFrom the above fraction, the numerator and denominator are: 1 and 2<br \/>\nIt is given that the numerator value is 5.<br \/>\nSo, to make the value 5 from 1, we have to multiply the fraction with 5<br \/>\nSo,<br \/>\n\\(\\frac{1}{2} is multiplied with [latex]\\frac{5}{5}.<br \/>\nHence,<br \/>\n<img loading=\"lazy\" class=\"alignnone size-full wp-image-25343\" src=\"https:\/\/ccssmathanswers.com\/wp-content\/uploads\/2020\/12\/Big-Ideas-Math-Answers-Grade-4-Chapter-7-78.jpg\" alt=\"\" width=\"82\" height=\"52\" \/><\/p>\n<p>Question 6.<br \/>\n<img loading=\"lazy\" class=\"alignnone size-full wp-image-13281\" src=\"https:\/\/ccssmathanswers.com\/wp-content\/uploads\/2020\/12\/Big-Ideas-Math-Answers-4th-Grade-Chapter-7-Understand-Fraction-Equivalence-and-Comparison-chp-6.png\" alt=\"Big Ideas Math Answers 4th Grade Chapter 7 Understand Fraction Equivalence and Comparison chp 6\" width=\"92\" height=\"61\" \/><br \/>\nAnswer: The equivalent fraction of [latex]\\frac{8}{5}\\) is: \\(\\frac{160}{100}\\)<\/p>\n<p>Explanation:<br \/>\nThe given fraction is \\(\\frac{8}{5}\\)<br \/>\nFrom the above fraction, the numerator and denominator are: 8 and 5<br \/>\nIt is given that the denominator value is 100.<br \/>\nSo, to make the value 100 from 5, we have to multiply the fraction with 20<br \/>\nSo,<br \/>\n\\(\\frac{8}{5} is multiplied with [latex]\\frac{20}{20}.<br \/>\nHence,<br \/>\n<img loading=\"lazy\" class=\"alignnone size-full wp-image-25345\" src=\"https:\/\/ccssmathanswers.com\/wp-content\/uploads\/2020\/12\/Big-Ideas-Math-Answers-Grade-4-Chapter-7-79.jpg\" alt=\"\" width=\"81\" height=\"53\" \/><\/p>\n<p><strong>Find an equivalent fraction.<\/strong><br \/>\nQuestion 7.<br \/>\n[latex]\\frac{1}{6}\\)<br \/>\nAnswer: The equivalent fraction of \\(\\frac{1}{6}\\) is: \\(\\frac{2}{12}\\)<\/p>\n<p>Explanation:<br \/>\nWhen we multiply the fraction with the fraction having the same number as the numerator as the denominator, we will get the equivalent fraction.<br \/>\nSo,<br \/>\n\\(\\frac{1}{6}\\) is multiplied with \\(\\frac{2}{2}\\)<br \/>\nHence,<br \/>\n\\(\\frac{1}{6}\\) = \\(\\frac{2}{12}\\)<\/p>\n<p>Question 8.<br \/>\n\\(\\frac{5}{5}\\)<br \/>\nAnswer: The equivalent fraction of \\(\\frac{5}{5}\\) is: \\(\\frac{10}{10}\\)<\/p>\n<p>Explanation:<br \/>\nWhen we multiply the fraction with the fraction having the same number as the numerator as the denominator, we will get the equivalent fraction.<br \/>\nSo,<br \/>\n\\(\\frac{5}{5}\\) is multiplied with \\(\\frac{2}{2}\\)<br \/>\nHence,<br \/>\n\\(\\frac{5}{5}\\) = \\(\\frac{10}{10}\\)<\/p>\n<p>Question 9.<br \/>\n\\(\\frac{1}{4}\\)<br \/>\nAnswer: The equivalent fraction of \\(\\frac{1}{4}\\) is: \\(\\frac{2}{8}\\)<\/p>\n<p>Explanation:<br \/>\nWhen we multiply the fraction with the fraction having the same number as the numerator as the denominator, we will get the equivalent fraction.<br \/>\nSo,<br \/>\n\\(\\frac{1}{4}\\) is multiplied with \\(\\frac{2}{2}\\)<br \/>\nHence,<br \/>\n\\(\\frac{1}{4}\\) = \\(\\frac{2}{8}\\)<\/p>\n<p><strong>Find two equivalent fractions.<\/strong><br \/>\nQuestion 10.<br \/>\n\\(\\frac{3}{2}\\)<br \/>\nAnswer:<br \/>\nThe two equivalent fractions of \\(\\frac{3}{2}\\) is: \\(\\frac{6}{4}\\) and \\(\\frac{9}{6}\\)<span id=\"MathJax-Element-280-Frame\" class=\"MathJax\"><span id=\"MathJax-Span-1797\" class=\"math\"><span id=\"MathJax-Span-1798\" class=\"mrow\"><span id=\"MathJax-Span-1799\" class=\"mfrac\"><\/span><\/span><\/span><\/span><\/p>\n<p>Explanation:<br \/>\nWhen we multiply the fraction with the fraction having the same number as the numerator as the denominator, we will get the equivalent fraction.<br \/>\nSo,<br \/>\n\\(\\frac{3}{2}\\) is multiplied with \\(\\frac{2}{2}\\) and \\(\\frac{3}{3}\\)<br \/>\nHence,<br \/>\n\\(\\frac{3}{2}\\) = \\(\\frac{6}{4}\\) and \\(\\frac{9}{6}\\)<\/p>\n<p>Question 11.<br \/>\n\\(\\frac{1}{3}\\)<br \/>\nAnswer:<br \/>\nThe two equivalent fractions of \\(\\frac{1}{3}\\) is: \\(\\frac{2}{6}\\) and \\(\\frac{3}{9}\\)<span id=\"MathJax-Element-280-Frame\" class=\"MathJax\"><span id=\"MathJax-Span-1797\" class=\"math\"><span id=\"MathJax-Span-1798\" class=\"mrow\"><span id=\"MathJax-Span-1799\" class=\"mfrac\"><\/span><\/span><\/span><\/span><\/p>\n<p>Explanation:<br \/>\nWhen we multiply the fraction with the fraction having the same number as the numerator as the denominator, we will get the equivalent fraction.<br \/>\nSo,<br \/>\n\\(\\frac{1}{3}\\) is multiplied with \\(\\frac{2}{2}\\) and \\(\\frac{3}{3}\\)<br \/>\nHence,<br \/>\n\\(\\frac{1}{3}\\) = \\(\\frac{2}{6}\\) and \\(\\frac{3}{9}\\)<\/p>\n<p>Question 12.<br \/>\n\\(\\frac{4}{5}\\)<br \/>\nAnswer:<br \/>\nThe two equivalent fractions of \\(\\frac{4}{5}\\) is: \\(\\frac{8}{10}\\) and \\(\\frac{12}{15}\\)<span id=\"MathJax-Element-280-Frame\" class=\"MathJax\"><span id=\"MathJax-Span-1797\" class=\"math\"><span id=\"MathJax-Span-1798\" class=\"mrow\"><span id=\"MathJax-Span-1799\" class=\"mfrac\"><\/span><\/span><\/span><\/span><\/p>\n<p>Explanation:<br \/>\nWhen we multiply the fraction with the fraction having the same number as the numerator as the denominator, we will get the equivalent fraction.<br \/>\nSo,<br \/>\n\\(\\frac{4}{5}\\) is multiplied with \\(\\frac{2}{2}\\) and \\(\\frac{3}{3}\\)<br \/>\nHence,<br \/>\n\\(\\frac{4}{5}\\) = \\(\\frac{8}{10}\\) and \\(\\frac{12}{15}\\)<\/p>\n<p><strong>7.3 Generate Equivalent Fractions by Dividing<\/strong><\/p>\n<p><strong>Find the equivalent fraction.<\/strong><br \/>\nQuestion 13.<br \/>\n<img loading=\"lazy\" class=\"alignnone size-full wp-image-13282\" src=\"https:\/\/ccssmathanswers.com\/wp-content\/uploads\/2020\/12\/Big-Ideas-Math-Answers-4th-Grade-Chapter-7-Understand-Fraction-Equivalence-and-Comparison-chp-13.png\" alt=\"Big Ideas Math Answers 4th Grade Chapter 7 Understand Fraction Equivalence and Comparison chp 13\" width=\"93\" height=\"55\" \/><br \/>\nAnswer: The equivalent fraction of \\(\\frac{3}{12}\\) is: \\(\\frac{1}{4}\\)<\/p>\n<p>Explanation:<br \/>\nThe given fraction is: \\(\\frac{3}{12}\\)<br \/>\nFrom the above fraction, the numerator and denominator are: 3 and 12<br \/>\n3 and 12 are the multiples of 3.<br \/>\nSo,<br \/>\n\\(\\frac{3}{12}=\\frac{3 \\div 3}{12 \\div 3}=\\frac{1}{4}\\)<br \/>\nHence,<br \/>\n<img loading=\"lazy\" class=\"alignnone size-full wp-image-25349\" src=\"https:\/\/ccssmathanswers.com\/wp-content\/uploads\/2020\/12\/Big-Ideas-Math-Answers-Grade-4-Chapter-7-80.jpg\" alt=\"\" width=\"86\" height=\"52\" \/><\/p>\n<p>Question 14.<br \/>\n<img loading=\"lazy\" class=\"alignnone size-full wp-image-13283\" src=\"https:\/\/ccssmathanswers.com\/wp-content\/uploads\/2020\/12\/Big-Ideas-Math-Answers-4th-Grade-Chapter-7-Understand-Fraction-Equivalence-and-Comparison-chp-14.png\" alt=\"Big Ideas Math Answers 4th Grade Chapter 7 Understand Fraction Equivalence and Comparison chp 14\" width=\"113\" height=\"65\" \/><br \/>\nAnswer: The equivalent fraction of \\(\\frac{18}{100}\\) is: \\(\\frac{9}{50}\\)<\/p>\n<p>Explanation:<br \/>\nThe given fraction is: \\(\\frac{18}{100}\\)<br \/>\nFrom the above fraction, the numerator and denominator are: 18 and 100<br \/>\n18 and 100 are the multiples of 2.<br \/>\nSo,<br \/>\n\\(\\frac{18}{100}=\\frac{18 \\div 2}{100 \\div 2}=\\frac{9}{50}\\)<br \/>\nHence,<br \/>\n<img loading=\"lazy\" class=\"alignnone size-full wp-image-25351\" src=\"https:\/\/ccssmathanswers.com\/wp-content\/uploads\/2020\/12\/Big-Ideas-Math-Answers-Grade-4-Chapter-7-81.jpg\" alt=\"\" width=\"97\" height=\"56\" \/><\/p>\n<p>Question 15.<br \/>\n<img loading=\"lazy\" class=\"alignnone size-full wp-image-13284\" src=\"https:\/\/ccssmathanswers.com\/wp-content\/uploads\/2020\/12\/Big-Ideas-Math-Answers-4th-Grade-Chapter-7-Understand-Fraction-Equivalence-and-Comparison-chp-15.png\" alt=\"Big Ideas Math Answers 4th Grade Chapter 7 Understand Fraction Equivalence and Comparison chp 15\" width=\"94\" height=\"63\" \/><br \/>\nAnswer: The equivalent fraction of \\(\\frac{20}{10}\\) is: \\(\\frac{4}{2}\\)<\/p>\n<p>Explanation:<br \/>\nThe given fraction is: \\(\\frac{20}{10}\\)<br \/>\nFrom the above fraction, the numerator and denominator are: 20 and 10<br \/>\n20 and 10 are the multiples of 5. ( 20 and 10 are also multiples of 2 and 10 but in the denominator, 2i s given which can only be obtained by divideing 10 with 5 )<br \/>\nSo,<br \/>\n\\(\\frac{20}{10}=\\frac{20 \\div 5}{10 \\div 5}=\\frac{4}{2}\\)<br \/>\nHence,<br \/>\n<img loading=\"lazy\" class=\"alignnone size-full wp-image-25353\" src=\"https:\/\/ccssmathanswers.com\/wp-content\/uploads\/2020\/12\/Big-Ideas-Math-Answers-Grade-4-Chapter-7-82.jpg\" alt=\"\" width=\"95\" height=\"51\" \/><\/p>\n<p><strong>Find an equivalent fraction.<\/strong><br \/>\nQuestion 16.<br \/>\n\\(\\frac{4}{6}\\)<br \/>\nAnswer: The equivalent fraction of \\(\\frac{4}{6}\\) is: \\(\\frac{2}{3}\\)<\/p>\n<p>Explanation:<br \/>\nThe given fraction is: \\(\\frac{4}{6}\\)<br \/>\nFrom the above fraction, the numerator and denominator are: 4 and 6<br \/>\n4 and 6 are the multiples of 2. ( 4 and 6 are multiples of 2 )<br \/>\nSo,<br \/>\n\\(\\frac{4}{6}=\\frac{4 \\div 2}{6 \\div 2}=\\frac{2}{3}\\)<br \/>\nHence,<br \/>\nThe equivalent fraction of \\(\\frac{4}{6}\\) is: \\(\\frac{2}{3}\\)<\/p>\n<p>Question 17.<br \/>\n\\(\\frac{16}{4}\\)<br \/>\nAnswer: The equivalent fraction of \\(\\frac{16}{4}\\) is: \\(\\frac{8}{2}\\)<\/p>\n<p>Explanation:<br \/>\nThe given fraction is: \\(\\frac{16}{4}\\)<br \/>\nFrom the above fraction, the numerator and denominator are: 16 and 4<br \/>\n16 and 4 are the multiples of 2.<br \/>\nSo,<br \/>\n\\(\\frac{16}{4}=\\frac{16 \\div 2}{4 \\div 2}=\\frac{8}{2}\\)<br \/>\nHence,<br \/>\nThe equivalent fraction of \\(\\frac{16}{4}\\) is: \\(\\frac{8}{2}\\)<\/p>\n<p>Question 18.<br \/>\n\\(\\frac{20}{8}\\)<br \/>\nAnswer: The equivalent fraction of \\(\\frac{20}{8}\\) is: \\(\\frac{10}{4}\\)<\/p>\n<p>Explanation:<br \/>\nThe given fraction is: \\(\\frac{20}{8}\\)<br \/>\nFrom the above fraction, the numerator and denominator are: 20 and 8<br \/>\n20 and 8 are the multiples of 2.<br \/>\nSo,<br \/>\n\\(\\frac{20}{8}=\\frac{20 \\div 2}{8 \\div 2}=\\frac{10}{4}\\)<br \/>\nHence,<br \/>\nThe equivalent fraction of \\(\\frac{20}{8}\\) is: \\(\\frac{10}{4}\\)<\/p>\n<p><strong>Find two equivalent fractions.<\/strong><br \/>\nQuestion 19.<br \/>\n\\(\\frac{80}{100}\\)<br \/>\nAnswer: The two equivalent fractions of \\(\\frac{80}{100}\\) is: \\(\\frac{4}{5}\\) and \\(\\frac{20}{25}\\)<\/p>\n<p>Explanation:<br \/>\nThe given fraction is: \\(\\frac{80}{100}\\)<br \/>\nFrom the above fraction, the numerator and denominator are: 80 and 100<br \/>\n80 and 100 are the multiples of 20 and 4<br \/>\nSo,<br \/>\nWe have to divide \\(\\frac{80}{100}\\) with 20and 4<br \/>\nSo,<br \/>\n\\(\\frac{80}{100}=\\frac{80 \\div 20}{100 \\div 20}=\\frac{4}{5}\\)<br \/>\n\\(\\frac{80}{100}=\\frac{80 \\div 4}{100 \\div 4}=\\frac{20}{25}\\)<br \/>\nHence,<br \/>\nThe two equivalent fractions of \\(\\frac{80}{100}\\) is: \\(\\frac{4}{5}\\) and \\(\\frac{20}{25}\\)<\/p>\n<p>Question 20.<br \/>\n\\(\\frac{6}{12}\\)<br \/>\nAnswer: The two equivalent fractions of \\(\\frac{6}{12}\\) is: \\(\\frac{2}{4}\\) and \\(\\frac{1}{2}\\)<\/p>\n<p>Explanation:<br \/>\nThe given fraction is: \\(\\frac{6}{12}\\)<br \/>\nFrom the above fraction, the numerator and denominator are: 6 and 12<br \/>\n6 and 12 are the multiples of 3 and 6<br \/>\nSo,<br \/>\nWe have to divide \\(\\frac{6}{12}\\) with 3 and 6<br \/>\nSo,<br \/>\n\\(\\frac{6}{12}=\\frac{6 \\div 3}{12 \\div 3}=\\frac{2}{4}\\)<br \/>\n\\(\\frac{6}{12}=\\frac{6 \\div 6}{12 \\div 6}=\\frac{1}{2}\\)<br \/>\nHence,<br \/>\nThe two equivalent fractions of \\(\\frac{6}{12}\\) is: \\(\\frac{2}{4}\\) and \\(\\frac{1}{2}\\)<\/p>\n<p>Question 21.<br \/>\n\\(\\frac{40}{4}\\)<br \/>\nAnswer: The two equivalent fractions of \\(\\frac{40}{4}\\) is: \\(\\frac{20}{2}\\) and \\(\\frac{10}{1}\\)<\/p>\n<p>Explanation:<br \/>\nThe given fraction is: \\(\\frac{40}{4}\\)<br \/>\nFrom the above fraction, the numerator and denominator are: 40 and 4<br \/>\n40 and 4 are the multiples of 2 and 4<br \/>\nSo,<br \/>\nWe have to divide \\(\\frac{40}{4}\\) with 2 and 4<br \/>\nSo,<br \/>\n\\(\\frac{40}{4}=\\frac{40 \\div 2}{4 \\div 2}=\\frac{20}{2}\\)<br \/>\n\\(\\frac{40}{4}=\\frac{40 \\div 4}{4 \\div 4}=\\frac{10}{1}\\)<br \/>\nHence,<br \/>\nThe two equivalent fractions of \\(\\frac{40}{4}\\) is: \\(\\frac{20}{2}\\) and \\(\\frac{10}{1}\\)<\/p>\n<p>Question 22.<br \/>\n<strong>Modeling Real Life<\/strong><br \/>\nYou have 90$. What fraction of a dollar, in tenths, do you have?<br \/>\nAnswer: The fraction of a dollar, in tenths, is: \\(\\frac{1}{10}\\)<\/p>\n<p>Explanation:<br \/>\nIt is given that you have 90$<br \/>\nSo,<br \/>\nThe fraction of a dollar, in tenths that pack their lunch = The number of dollars \u00f7 The total number of dollars<br \/>\n= 90 \u00f7 100<br \/>\n= \\(\\frac{9}{10}\\)<br \/>\nHence, from the above,<br \/>\nWe can conclude that the number of dollars, in tenths, is: \\(\\frac{9}{10}\\)<\/p>\n<p><strong>7.4 Compare Fractions Using Benchmarks<\/strong><\/p>\n<p><strong>Compare. Use a model to help.<\/strong><br \/>\nQuestion 23.<br \/>\n<img loading=\"lazy\" class=\"alignnone size-full wp-image-13285\" src=\"https:\/\/ccssmathanswers.com\/wp-content\/uploads\/2020\/12\/Big-Ideas-Math-Answers-4th-Grade-Chapter-7-Understand-Fraction-Equivalence-and-Comparison-chp-23.png\" alt=\"Big Ideas Math Answers 4th Grade Chapter 7 Understand Fraction Equivalence and Comparison chp 23\" width=\"87\" height=\"58\" \/><br \/>\nAnswer: \\(\\frac{7}{8}\\) is greater than \\(\\frac{2}{5}\\)<\/p>\n<p>Explanation:<br \/>\nThe given fractions are: \\(\\frac{7}{8}\\) and \\(\\frac{2}{5}\\)<br \/>\nFor the two fractions, the models are:<br \/>\n<img loading=\"lazy\" class=\"alignnone size-full wp-image-25370\" src=\"https:\/\/ccssmathanswers.com\/wp-content\/uploads\/2020\/12\/Big-Ideas-Math-Answers-Grade-4-Chapter-7-83.jpg\" alt=\"\" width=\"540\" height=\"204\" srcset=\"https:\/\/bigideasmathanswers.com\/wp-content\/uploads\/2020\/12\/Big-Ideas-Math-Answers-Grade-4-Chapter-7-83.jpg 540w, https:\/\/bigideasmathanswers.com\/wp-content\/uploads\/2020\/12\/Big-Ideas-Math-Answers-Grade-4-Chapter-7-83-300x113.jpg 300w\" sizes=\"(max-width: 540px) 100vw, 540px\" \/><br \/>\nSo,<br \/>\nLet make the denominators equal so that we can compare the numerators<br \/>\nSo,<br \/>\nTo make the denominators equal, multiply the first fraction with 5 and the second fraction with 8<br \/>\nSo,<br \/>\n\\(\\frac{7}{8}\\) = \\(\\frac{35}{40}\\)<br \/>\n\\(\\frac{2}{5}\\) = \\(\\frac{16}{40}\\)<br \/>\nSo, when we compare the 2 fractions,<br \/>\nWe can conclude that \\(\\frac{7}{8}\\) is greater than \\(\\frac{2}{5}\\)<\/p>\n<p>Question 24.<br \/>\n<img loading=\"lazy\" class=\"alignnone size-full wp-image-13286\" src=\"https:\/\/ccssmathanswers.com\/wp-content\/uploads\/2020\/12\/Big-Ideas-Math-Answers-4th-Grade-Chapter-7-Understand-Fraction-Equivalence-and-Comparison-chp-24.png\" alt=\"Big Ideas Math Answers 4th Grade Chapter 7 Understand Fraction Equivalence and Comparison chp 24\" width=\"100\" height=\"54\" \/><br \/>\nAnswer: \\(\\frac{6}{10}\\) is less than \\(\\frac{4}{3}\\)<\/p>\n<p>Explanation:<br \/>\nThe given fractions are: \\(\\frac{6}{10}\\) and \\(\\frac{4}{3}\\)<br \/>\nFor the two fractions, the models are:<br \/>\n<img loading=\"lazy\" class=\"alignnone size-full wp-image-25373\" src=\"https:\/\/ccssmathanswers.com\/wp-content\/uploads\/2020\/12\/Big-Ideas-Math-Answers-Grade-4-Chapter-7-84.jpg\" alt=\"\" width=\"540\" height=\"204\" srcset=\"https:\/\/bigideasmathanswers.com\/wp-content\/uploads\/2020\/12\/Big-Ideas-Math-Answers-Grade-4-Chapter-7-84.jpg 540w, https:\/\/bigideasmathanswers.com\/wp-content\/uploads\/2020\/12\/Big-Ideas-Math-Answers-Grade-4-Chapter-7-84-300x113.jpg 300w\" sizes=\"(max-width: 540px) 100vw, 540px\" \/><br \/>\nSo,<br \/>\nLet make the denominators equal so that we can compare the numerators<br \/>\nSo,<br \/>\nTo make the denominators equal, multiply the first fraction with 3 and the second fraction with 10<br \/>\nSo,<br \/>\n\\(\\frac{6}{10}\\) = \\(\\frac{18}{30}\\)<br \/>\n\\(\\frac{4}{3}\\) = \\(\\frac{40}{30}\\)<br \/>\nSo, when we compare the 2 fractions,<br \/>\nWe can conclude that \\(\\frac{6}{10}\\) is less than \\(\\frac{4}{3}\\)<\/p>\n<p>Question 25.<br \/>\n<img loading=\"lazy\" class=\"alignnone size-full wp-image-13287\" src=\"https:\/\/ccssmathanswers.com\/wp-content\/uploads\/2020\/12\/Big-Ideas-Math-Answers-4th-Grade-Chapter-7-Understand-Fraction-Equivalence-and-Comparison-chp-25.png\" alt=\"Big Ideas Math Answers 4th Grade Chapter 7 Understand Fraction Equivalence and Comparison chp 25\" width=\"91\" height=\"57\" \/><br \/>\nAnswer: \\(\\frac{1}{6}\\) is equal to \\(\\frac{2}{12}\\)<\/p>\n<p>Explanation:<br \/>\nThe given fractions are: \\(\\frac{1}{6}\\) and \\(\\frac{2}{12}\\)<br \/>\nFor the two fractions, the models are:<br \/>\n<img loading=\"lazy\" class=\"alignnone size-full wp-image-25375\" src=\"https:\/\/ccssmathanswers.com\/wp-content\/uploads\/2020\/12\/Big-Ideas-Math-Answers-Grade-4-Chapter-7-85.jpg\" alt=\"\" width=\"540\" height=\"204\" srcset=\"https:\/\/bigideasmathanswers.com\/wp-content\/uploads\/2020\/12\/Big-Ideas-Math-Answers-Grade-4-Chapter-7-85.jpg 540w, https:\/\/bigideasmathanswers.com\/wp-content\/uploads\/2020\/12\/Big-Ideas-Math-Answers-Grade-4-Chapter-7-85-300x113.jpg 300w\" sizes=\"(max-width: 540px) 100vw, 540px\" \/><br \/>\nSo,<br \/>\nLet make the denominators equal so that we can compare the numerators<br \/>\nSo,<br \/>\nTo make the denominators equal, multiply the first fraction with 2<br \/>\nSo,<br \/>\n\\(\\frac{1}{6}\\) = \\(\\frac{2}{12}\\)<br \/>\nSo, when we compare the 2 fractions,<br \/>\nWe can conclude that \\(\\frac{1}{6}\\) is equal to \\(\\frac{2}{12}\\)<\/p>\n<p><strong>7.5 Compare Fractions<\/strong><\/p>\n<p><strong>Compare. Use a model to help.<\/strong><br \/>\nQuestion 26.<br \/>\n<img loading=\"lazy\" class=\"alignnone size-full wp-image-13288\" src=\"https:\/\/ccssmathanswers.com\/wp-content\/uploads\/2020\/12\/Big-Ideas-Math-Answers-4th-Grade-Chapter-7-Understand-Fraction-Equivalence-and-Comparison-chp-26.png\" alt=\"Big Ideas Math Answers 4th Grade Chapter 7 Understand Fraction Equivalence and Comparison chp 26\" width=\"79\" height=\"53\" \/><br \/>\nAnswer: \\(\\frac{1}{4}\\) is equal to \\(\\frac{3}{12}\\)<\/p>\n<p>Explanation:<br \/>\nThe given two fractions are: \\(\\frac{1}{4}\\) and \\(\\frac{3}{12}\\)<br \/>\nSo,<br \/>\nLet make the denominators equal so that we can compare the numerators<br \/>\nSo,<br \/>\nTo make the denominators equal, multiply the first fraction with 3<br \/>\nSo,<br \/>\n\\(\\frac{1}{4}\\) = \\(\\frac{3}{12}\\)<br \/>\nSo, when we compare the 2 fractions,<br \/>\nWe can conclude that \\(\\frac{1}{4}\\) is equal to \\(\\frac{3}{12}\\)<\/p>\n<p>Question 27.<br \/>\n<img loading=\"lazy\" class=\"alignnone size-full wp-image-13289\" src=\"https:\/\/ccssmathanswers.com\/wp-content\/uploads\/2020\/12\/Big-Ideas-Math-Answers-4th-Grade-Chapter-7-Understand-Fraction-Equivalence-and-Comparison-chp-27.png\" alt=\"Big Ideas Math Answers 4th Grade Chapter 7 Understand Fraction Equivalence and Comparison chp 27\" width=\"77\" height=\"57\" \/><br \/>\nAnswer: \\(\\frac{2}{3}\\) is greater than \\(\\frac{6}{10}\\)<\/p>\n<p>Explanation:<br \/>\nThe given two fractions are: \\(\\frac{2}{3}\\) and \\(\\frac{6}{10}\\)<br \/>\nSo,<br \/>\nLet make the denominators equal so that we can compare the numerators<br \/>\nSo,<br \/>\nTo make the denominators equal, multiply the first fraction with 10 and the second fraction with 3<br \/>\nSo,<br \/>\n\\(\\frac{2}{3}\\) = \\(\\frac{20}{30}\\)<br \/>\n\\(\\frac{6}{10}\\) = \\(\\frac{18}{30}\\)<br \/>\nSo, when we compare the 2 fractions,<br \/>\nWe can conclude that \\(\\frac{2}{3}\\) is greater than \\(\\frac{6}{10}\\)<\/p>\n<p>Question 28.<br \/>\n<img loading=\"lazy\" class=\"alignnone size-full wp-image-13290\" src=\"https:\/\/ccssmathanswers.com\/wp-content\/uploads\/2020\/12\/Big-Ideas-Math-Answers-4th-Grade-Chapter-7-Understand-Fraction-Equivalence-and-Comparison-chp-28.png\" alt=\"Big Ideas Math Answers 4th Grade Chapter 7 Understand Fraction Equivalence and Comparison chp 28\" width=\"86\" height=\"63\" \/><br \/>\nAnswer: \\(\\frac{7}{8}\\) is greater than \\(\\frac{5}{6}\\)<\/p>\n<p>Explanation:<br \/>\nThe given two fractions are: \\(\\frac{7}{8}\\) and \\(\\frac{5}{6}\\)<br \/>\nSo,<br \/>\nLet make the denominators equal so that we can compare the numerators<br \/>\nSo,<br \/>\nTo make the denominators equal, multiply the first fraction with 6 and the second fraction with 8<br \/>\nSo,<br \/>\n\\(\\frac{7}{8}\\) = \\(\\frac{42}{48}\\)<br \/>\n\\(\\frac{5}{6}\\) = \\(\\frac{40}{48}\\)<br \/>\nSo, when we compare the 2 fractions,<br \/>\nWe can conclude that \\(\\frac{7}{8}\\) is greater than \\(\\frac{5}{6}\\)<\/p>\n<h3><a id=\"Understand_Fraction_Equivalence_and_Comparison_Cumulative_Practice\"><\/a>Understand Fraction Equivalence and Comparison of Cumulative Practice<\/h3>\n<p>Question 1.<br \/>\nWhich number is a common factor of 12, 16, and 40?<br \/>\nA. 5<br \/>\nB. 8<br \/>\nC. 3<br \/>\nD. 4<br \/>\nAnswer: D) 4<\/p>\n<p>Explanation:<br \/>\nGiven numbers are: 12, 16 and 40<br \/>\nThe factors are the numbers that divide the original number completely.<br \/>\nSo,<br \/>\nThe factors of 12 are: 1, 2, 3, 4, 6, 12<br \/>\nThe factors of 16 are: 1, 2, 4, 8, 16<br \/>\nThe factors of 40 are: 1, 2, 4, 5, 8, 10, 20, 40<br \/>\nSo,<br \/>\nThe common factors of 12, 16, and 20 are: 1, 2, 4<\/p>\n<p>Question 2.<br \/>\nWhich statements describe the difference between 77,986 and 21,403?<br \/>\n<img loading=\"lazy\" class=\"alignnone size-full wp-image-13291\" src=\"https:\/\/ccssmathanswers.com\/wp-content\/uploads\/2020\/12\/Big-Ideas-Math-Answers-Grade-4-Chapter-7-Understand-Fraction-Equivalence-and-Comparison-cp-2.png\" alt=\"Big Ideas Math Answers Grade 4 Chapter 7 Understand Fraction Equivalence and Comparison cp 2\" width=\"618\" height=\"95\" srcset=\"https:\/\/bigideasmathanswers.com\/wp-content\/uploads\/2020\/12\/Big-Ideas-Math-Answers-Grade-4-Chapter-7-Understand-Fraction-Equivalence-and-Comparison-cp-2.png 618w, https:\/\/bigideasmathanswers.com\/wp-content\/uploads\/2020\/12\/Big-Ideas-Math-Answers-Grade-4-Chapter-7-Understand-Fraction-Equivalence-and-Comparison-cp-2-300x46.png 300w\" sizes=\"(max-width: 618px) 100vw, 618px\" \/><\/p>\n<p>Answer: The given numbers are: 77,986 and 21,403<br \/>\nSo,<br \/>\nThe difference between 77,986 and 21,403 is: 56,583<br \/>\nThe below statements describe the difference between 77,986 and 21,403<br \/>\n<img loading=\"lazy\" class=\"alignnone size-full wp-image-25379\" src=\"https:\/\/ccssmathanswers.com\/wp-content\/uploads\/2020\/12\/Big-Ideas-Math-Answers-Grade-4-Chapter-7-86.jpg\" alt=\"\" width=\"605\" height=\"93\" srcset=\"https:\/\/bigideasmathanswers.com\/wp-content\/uploads\/2020\/12\/Big-Ideas-Math-Answers-Grade-4-Chapter-7-86.jpg 605w, https:\/\/bigideasmathanswers.com\/wp-content\/uploads\/2020\/12\/Big-Ideas-Math-Answers-Grade-4-Chapter-7-86-300x46.jpg 300w\" sizes=\"(max-width: 605px) 100vw, 605px\" \/><\/p>\n<p>Question 3.<br \/>\nWhich product is between 5,050 and 5,100?<br \/>\nA. 652 \u00d7 8<br \/>\nB. 566 \u00d7 9<br \/>\nC. 1,023 \u00d7 5<br \/>\nD. 1,257 \u00d7 4<\/p>\n<p>Answer: B) 566 \u00d7 9<\/p>\n<p>Explanation:<br \/>\nLet the given product Expressions be named as\u00a0 A), B), C) and D)<br \/>\nSo,<br \/>\nThe given products are:<br \/>\nA) 652 \u00d7 8\u00a0 \u00a0B) 566 \u00d7 9\u00a0 C) 1,023 \u00d7 5\u00a0 D) 1,257 \u00d7 4<br \/>\nNow,<br \/>\nBy using the partial products method,<br \/>\nA. 652 \u00d7 8 = 5,216<br \/>\nB. 566 \u00d7 9 = 5,094<br \/>\nC. 1,023 \u00d7 5 = 5,115<br \/>\nD. 1,257 \u00d7 4 = 5,028<br \/>\nSo,<br \/>\nFrom the above values,<br \/>\nThe product that is between 5,050 and 5,100 is: 566 \u00d7 9<\/p>\n<p>Question 4.<br \/>\nUse the advertisement to answer the question.<br \/>\n<img loading=\"lazy\" class=\"alignnone size-full wp-image-13292\" src=\"https:\/\/ccssmathanswers.com\/wp-content\/uploads\/2020\/12\/Big-Ideas-Math-Answers-Grade-4-Chapter-7-Understand-Fraction-Equivalence-and-Comparison-cp-4.png\" alt=\"Big Ideas Math Answers Grade 4 Chapter 7 Understand Fraction Equivalence and Comparison cp 4\" width=\"254\" height=\"191\" \/><br \/>\nWhat is the greatest number of miles that the car could have been driven?<br \/>\nA. 84,699<br \/>\nB. 84,750<br \/>\nC. 84,749<br \/>\nD. 84,650<br \/>\nAnswer: The greatest number of miles that the car should have been driven is: 84,699 miles<\/p>\n<p>Explanation:<br \/>\nGiven that the car should have been driven approximate 84,700 miles ( rounded to the nearest 100 )<br \/>\nThe given options are: A) 84,699 B) 84,750 C) 84,749 D) 84,650<br \/>\nThe greatest number that is close to 84,700 is: 84, 699<br \/>\nHence, from the above,<br \/>\nWe can conclude that the greatest number of miles that the car should have been driven is: 84,699 miles<\/p>\n<p>Question 5.<br \/>\nWhich multiplication expressions could be represented by the area model?<br \/>\n<img loading=\"lazy\" class=\"alignnone size-full wp-image-25381\" src=\"https:\/\/ccssmathanswers.com\/wp-content\/uploads\/2020\/12\/Big-Ideas-Math-Answers-Grade-4-Chapter-7-88.jpg\" alt=\"\" width=\"380\" height=\"226\" srcset=\"https:\/\/bigideasmathanswers.com\/wp-content\/uploads\/2020\/12\/Big-Ideas-Math-Answers-Grade-4-Chapter-7-88.jpg 380w, https:\/\/bigideasmathanswers.com\/wp-content\/uploads\/2020\/12\/Big-Ideas-Math-Answers-Grade-4-Chapter-7-88-300x178.jpg 300w\" sizes=\"(max-width: 380px) 100vw, 380px\" \/><br \/>\nAnswer: The multiplication Expression represented by the area model is: 84 \u00d7 34<\/p>\n<p>Explanation:<br \/>\nThe given area model is:<br \/>\n<img loading=\"lazy\" class=\"alignnone size-full wp-image-25380\" src=\"https:\/\/ccssmathanswers.com\/wp-content\/uploads\/2020\/12\/Big-Ideas-Math-Answers-Grade-4-Chapter-7-87.jpg\" alt=\"\" width=\"153\" height=\"143\" \/><br \/>\nSo, from the area model,<br \/>\nThe factor pairs of 2,400 are: 80 \u00d7 30, 60 \u00d7 40<br \/>\nThe factor pairs of 120 are: 4 \u00d7 30, 6 \u00d7 20<br \/>\nFrom the above two factors, we can say that<br \/>\nThe area model can be formed from 80, 4 and 30<br \/>\nHence,<br \/>\nThe product for the given area model is: 84 \u00d7 34<\/p>\n<p>Question 6.<br \/>\nYour neighbor buys yogurt in packages of 4. If your neighbor only buys complete packages, how many yogurts could he have bought?<br \/>\n<img loading=\"lazy\" class=\"alignnone size-full wp-image-13294\" src=\"https:\/\/ccssmathanswers.com\/wp-content\/uploads\/2020\/12\/Big-Ideas-Math-Answers-Grade-4-Chapter-7-Understand-Fraction-Equivalence-and-Comparison-cp-6.png\" alt=\"Big Ideas Math Answers Grade 4 Chapter 7 Understand Fraction Equivalence and Comparison cp 6\" width=\"203\" height=\"143\" \/><br \/>\nA. 2<br \/>\nB. 20<br \/>\nC. 34<br \/>\nD. 18<br \/>\nAnswer: The complete packages of yogurts that he could have brought is: 20<\/p>\n<p>Explanation:<br \/>\nIt is given that your neighbor bought yogurt in packages of 4<br \/>\nSo, for complete packages, the number of packages that he takes should not have any extra yogurt i.e., remainder yogurt when packing completely in the packs of 4.<br \/>\nSo,<br \/>\nFrom the above options,<br \/>\nWe have only 20 yogurts that can be packed completely in packs of 4.<\/p>\n<p>Question 7.<br \/>\nWhich fraction makes the statement true?<br \/>\n<img loading=\"lazy\" class=\"alignnone size-full wp-image-13295\" src=\"https:\/\/ccssmathanswers.com\/wp-content\/uploads\/2020\/12\/Big-Ideas-Math-Answers-Grade-4-Chapter-7-Understand-Fraction-Equivalence-and-Comparison-cp-7.png\" alt=\"Big Ideas Math Answers Grade 4 Chapter 7 Understand Fraction Equivalence and Comparison cp 7\" width=\"343\" height=\"157\" srcset=\"https:\/\/bigideasmathanswers.com\/wp-content\/uploads\/2020\/12\/Big-Ideas-Math-Answers-Grade-4-Chapter-7-Understand-Fraction-Equivalence-and-Comparison-cp-7.png 343w, https:\/\/bigideasmathanswers.com\/wp-content\/uploads\/2020\/12\/Big-Ideas-Math-Answers-Grade-4-Chapter-7-Understand-Fraction-Equivalence-and-Comparison-cp-7-300x137.png 300w\" sizes=\"(max-width: 343px) 100vw, 343px\" \/><br \/>\nAnswer: \\(\\frac{1}{4}\\) makes the statement true.<\/p>\n<p>Explanation:<br \/>\nGiven fraction is: \\(\\frac{6}{8}\\)<br \/>\nSo,<br \/>\nWe have to compare \\(\\frac{6}{8}\\) with the given options to satisfy the relation the option &lt; \\(\\frac{6}{8}\\)<br \/>\nNow,<br \/>\nA) The two fractions are:\u00a0 \\(\\frac{1}{4}\\) and \\(\\frac{6}{8}\\)<br \/>\nSo, to make the denominators equal, multiply the first fraction with 2<br \/>\nSo,<br \/>\n\\(\\frac{1}{4}\\) = \\(\\frac{2}{8}\\)<br \/>\nHence,<br \/>\n\\(\\frac{1}{4}\\) &lt;\u00a0\\(\\frac{6}{8}\\)<\/p>\n<p>Question 8.<br \/>\nWhich division equation is represented by the counters?<br \/>\n<img loading=\"lazy\" class=\"alignnone size-full wp-image-13296\" src=\"https:\/\/ccssmathanswers.com\/wp-content\/uploads\/2020\/12\/Big-Ideas-Math-Answers-Grade-4-Chapter-7-Understand-Fraction-Equivalence-and-Comparison-cp-8.png\" alt=\"Big Ideas Math Answers Grade 4 Chapter 7 Understand Fraction Equivalence and Comparison cp 8\" width=\"506\" height=\"197\" srcset=\"https:\/\/bigideasmathanswers.com\/wp-content\/uploads\/2020\/12\/Big-Ideas-Math-Answers-Grade-4-Chapter-7-Understand-Fraction-Equivalence-and-Comparison-cp-8.png 506w, https:\/\/bigideasmathanswers.com\/wp-content\/uploads\/2020\/12\/Big-Ideas-Math-Answers-Grade-4-Chapter-7-Understand-Fraction-Equivalence-and-Comparison-cp-8-300x117.png 300w\" sizes=\"(max-width: 506px) 100vw, 506px\" \/><br \/>\nAnswer: D) 26 \u00f7 6 = 4 R 2<\/p>\n<p>Explanation:<br \/>\nGiven counters are:<br \/>\n<img loading=\"lazy\" class=\"alignnone size-full wp-image-25383\" src=\"https:\/\/ccssmathanswers.com\/wp-content\/uploads\/2020\/12\/Big-Ideas-Math-Answers-Grade-4-Chapter-7-89.jpg\" alt=\"\" width=\"492\" height=\"77\" srcset=\"https:\/\/bigideasmathanswers.com\/wp-content\/uploads\/2020\/12\/Big-Ideas-Math-Answers-Grade-4-Chapter-7-89.jpg 492w, https:\/\/bigideasmathanswers.com\/wp-content\/uploads\/2020\/12\/Big-Ideas-Math-Answers-Grade-4-Chapter-7-89-300x47.jpg 300w\" sizes=\"(max-width: 492px) 100vw, 492px\" \/><br \/>\nFrom the above model,<br \/>\nThe total number of counters are: 6<br \/>\nThe number of parts that each counter has: 4<br \/>\nThe number of parts that has leftover is: 2<br \/>\nSo,<br \/>\nThe total number of parts in 6 counters = 4 + 4 + 4 + 4 + 4 + 4 = 24<br \/>\nThe total number of parts = The number of parts in 6 counters + The number of parts leftover = 24 + 2 = 26<br \/>\nHence, from the above, the division Expression can be represented as:<br \/>\n26 \u00f7 6 = 4 R 2<\/p>\n<p>Question 9.<br \/>\nWhich statements are true?<br \/>\n<img loading=\"lazy\" class=\"alignnone size-full wp-image-13297\" src=\"https:\/\/ccssmathanswers.com\/wp-content\/uploads\/2020\/12\/Big-Ideas-Math-Answers-Grade-4-Chapter-7-Understand-Fraction-Equivalence-and-Comparison-cp-9.png\" alt=\"Big Ideas Math Answers Grade 4 Chapter 7 Understand Fraction Equivalence and Comparison cp 9\" width=\"631\" height=\"155\" srcset=\"https:\/\/bigideasmathanswers.com\/wp-content\/uploads\/2020\/12\/Big-Ideas-Math-Answers-Grade-4-Chapter-7-Understand-Fraction-Equivalence-and-Comparison-cp-9.png 631w, https:\/\/bigideasmathanswers.com\/wp-content\/uploads\/2020\/12\/Big-Ideas-Math-Answers-Grade-4-Chapter-7-Understand-Fraction-Equivalence-and-Comparison-cp-9-300x74.png 300w\" sizes=\"(max-width: 631px) 100vw, 631px\" \/><br \/>\nAnswer: The below statements are true:<br \/>\n<img loading=\"lazy\" class=\"alignnone size-full wp-image-25384\" src=\"https:\/\/ccssmathanswers.com\/wp-content\/uploads\/2020\/12\/Big-Ideas-Math-Answers-Grade-4-Chapter-7-90.jpg\" alt=\"\" width=\"635\" height=\"149\" srcset=\"https:\/\/bigideasmathanswers.com\/wp-content\/uploads\/2020\/12\/Big-Ideas-Math-Answers-Grade-4-Chapter-7-90.jpg 635w, https:\/\/bigideasmathanswers.com\/wp-content\/uploads\/2020\/12\/Big-Ideas-Math-Answers-Grade-4-Chapter-7-90-300x70.jpg 300w\" sizes=\"(max-width: 635px) 100vw, 635px\" \/><br \/>\nPrime numbers:<br \/>\nThe numbers that have exactly 2 factors 1 and itself are &#8221; Prime numbers&#8221;<br \/>\nComposite numbers:<br \/>\nThe numbers that have more than 2 factors are &#8220;Composite numbers&#8221;<\/p>\n<p>Question 10.<br \/>\nWhat is the quotient of 3,258 and 3?<br \/>\n<img loading=\"lazy\" class=\"alignnone size-full wp-image-13298\" src=\"https:\/\/ccssmathanswers.com\/wp-content\/uploads\/2020\/12\/Big-Ideas-Math-Answers-Grade-4-Chapter-7-Understand-Fraction-Equivalence-and-Comparison-cp-10.png\" alt=\"Big Ideas Math Answers Grade 4 Chapter 7 Understand Fraction Equivalence and Comparison cp 10\" width=\"85\" height=\"63\" \/><br \/>\nAnswer: The quotient of 3,258 and 3 is: 1,086<\/p>\n<p>Explanation:<br \/>\nBy using the partial quotients method,<br \/>\n3,258 \u00f7 3 = ( 3,000 + 240 + 18 ) \u00f7 3<br \/>\n= ( 3,000 \u00f7 3 ) + ( 240 \u00f7 3 ) + ( 18 \u00f7 3 )<br \/>\n= 1,000 + 80 + 6<br \/>\n= 1,086<br \/>\nHence, from the above,<br \/>\nThe quotient of 3,258 and 3 is: 1,086<\/p>\n<p>Question 11.<br \/>\nWhich model shows an equivalent fraction for the fraction shown by the model below?<br \/>\n<img loading=\"lazy\" class=\"alignnone size-full wp-image-13299\" src=\"https:\/\/ccssmathanswers.com\/wp-content\/uploads\/2020\/12\/Big-Ideas-Math-Answers-Grade-4-Chapter-7-Understand-Fraction-Equivalence-and-Comparison-cp-11.png\" alt=\"Big Ideas Math Answers Grade 4 Chapter 7 Understand Fraction Equivalence and Comparison cp 11\" width=\"449\" height=\"248\" srcset=\"https:\/\/bigideasmathanswers.com\/wp-content\/uploads\/2020\/12\/Big-Ideas-Math-Answers-Grade-4-Chapter-7-Understand-Fraction-Equivalence-and-Comparison-cp-11.png 449w, https:\/\/bigideasmathanswers.com\/wp-content\/uploads\/2020\/12\/Big-Ideas-Math-Answers-Grade-4-Chapter-7-Understand-Fraction-Equivalence-and-Comparison-cp-11-300x166.png 300w\" sizes=\"(max-width: 449px) 100vw, 449px\" \/><br \/>\nAnswer: The equivalent fraction for the given model in shown in Option C)<\/p>\n<p>Explanation:<br \/>\nFrom the given model,<br \/>\nThe fraction is:\\(\\frac{3}{6}\\)<br \/>\nFrom\\(\\frac{3}{6}\\),<br \/>\nThe number of colored parts is: 3<br \/>\nThe total number of parts are: 6<br \/>\nSo,<br \/>\nAs 3 and 6 are the multiples of 3, divide \\(\\frac{3}{6}\\) with 3<br \/>\nSo, we get<br \/>\n\\(\\frac{3}{6}\\) = \\(\\frac{1}{2}\\)<br \/>\nSo,<br \/>\nThe equivalent fraction of \\(\\frac{3}{6}\\) is \\(\\frac{1}{2}\\) which is shown in the model of Option C)<\/p>\n<p>Question 12.<br \/>\nWhat is the product of 68 and 45?<br \/>\nA. 8,420<br \/>\nB. 3,060<br \/>\nC. 612<br \/>\nD. 27,360<br \/>\nAnswer: 68 \u00d7 45 = 3,060<\/p>\n<p>Explanation:<br \/>\nBy using the partial products method,<br \/>\n68 \u00d7 45 = ( 60 + 8 ) \u00d7 ( 40 + 5 )<br \/>\n= ( 60 \u00d7 40 ) + ( 8 \u00d7 5 ) + ( 60 \u00d7 5 ) + ( 8 \u00d7 40 )<br \/>\n= 2,400 + 40 + 300 + 320<br \/>\n= 3,060<br \/>\nHence,<br \/>\n68 \u00d7 45 = 3,060 which is Option B)<\/p>\n<p>Question 13.<br \/>\nWhich pattern uses the same rule as the pattern below?<br \/>\n2, 10, 18, 26, 34, 42<br \/>\nA. 15, 23, 31, 39, 47, 55<br \/>\nB. 5, 25, 125, 625, 3, 125, 15, 625,<br \/>\nC. 70, 62, 54, 46, 38, 30<br \/>\nD. 25, 34, 43, 52, 61, 70<br \/>\nAnswer: Option A) follows the same pattern as the given pattern<\/p>\n<p>Explanation:<br \/>\nGiven pattern is: 2, 10, 18, 26, 34, 42<br \/>\nFrom the above pattern,<br \/>\nThe rule is: Add 8<br \/>\nSo,<br \/>\nBy checking the options,<br \/>\nWe can conclude that option A) satisfies the same rule as in the given pattern<\/p>\n<p>Question 14.<br \/>\nWhich statements are true?<br \/>\n<img loading=\"lazy\" class=\"alignnone size-full wp-image-13300\" src=\"https:\/\/ccssmathanswers.com\/wp-content\/uploads\/2020\/12\/Big-Ideas-Math-Answers-Grade-4-Chapter-7-Understand-Fraction-Equivalence-and-Comparison-cp-12.png\" alt=\"Big Ideas Math Answers Grade 4 Chapter 7 Understand Fraction Equivalence and Comparison cp 12\" width=\"508\" height=\"114\" srcset=\"https:\/\/bigideasmathanswers.com\/wp-content\/uploads\/2020\/12\/Big-Ideas-Math-Answers-Grade-4-Chapter-7-Understand-Fraction-Equivalence-and-Comparison-cp-12.png 508w, https:\/\/bigideasmathanswers.com\/wp-content\/uploads\/2020\/12\/Big-Ideas-Math-Answers-Grade-4-Chapter-7-Understand-Fraction-Equivalence-and-Comparison-cp-12-300x67.png 300w\" sizes=\"(max-width: 508px) 100vw, 508px\" \/><br \/>\nAnswer: The statements that are true are:<br \/>\n<img loading=\"lazy\" class=\"alignnone size-full wp-image-25388\" src=\"https:\/\/ccssmathanswers.com\/wp-content\/uploads\/2020\/12\/Big-Ideas-Math-Answers-Grade-4-Chapter-7-91.jpg\" alt=\"\" width=\"500\" height=\"108\" srcset=\"https:\/\/bigideasmathanswers.com\/wp-content\/uploads\/2020\/12\/Big-Ideas-Math-Answers-Grade-4-Chapter-7-91.jpg 500w, https:\/\/bigideasmathanswers.com\/wp-content\/uploads\/2020\/12\/Big-Ideas-Math-Answers-Grade-4-Chapter-7-91-300x65.jpg 300w\" sizes=\"(max-width: 500px) 100vw, 500px\" \/><\/p>\n<p>Explanation:<br \/>\nCompare the given fractions by making either both the denominators or the numerators equal.<\/p>\n<p>Question 15.<br \/>\nPart A At a summer camp, 67 students are in a line to rent kayaks. Each kayak can hold 4 people. How many kayaks will be full?<br \/>\nThink<br \/>\nSolve<br \/>\nExplain<br \/>\n<img loading=\"lazy\" class=\"alignnone size-full wp-image-13301\" src=\"https:\/\/ccssmathanswers.com\/wp-content\/uploads\/2020\/12\/Big-Ideas-Math-Answers-Grade-4-Chapter-7-Understand-Fraction-Equivalence-and-Comparison-cp-15.png\" alt=\"Big Ideas Math Answers Grade 4 Chapter 7 Understand Fraction Equivalence and Comparison cp 15\" width=\"183\" height=\"145\" \/><br \/>\nPart B How many kayaks will be used?<br \/>\nPart C How many students will be in the last kayak? Explain.<\/p>\n<p>Answer:<br \/>\nPart A: 16 kayaks will be full<br \/>\nPart B: 17 kayaks will be used<br \/>\nPart C: 3 students will be in the last kayak<\/p>\n<p>Explanation:<br \/>\nGiven that there are 67 students standing in a line to rent a kayak and each kayak holds 4 people.<br \/>\nSo,<br \/>\nThe number of kayaks is: 67 \u00f7 4<br \/>\nNow,<br \/>\n67 \u00f7 4 = ( 60 + 4 ) \u00f7 4<br \/>\n= ( 60 \u00f7 4 ) + ( 4 \u00f7 4 )<br \/>\n= 15 + 1<br \/>\n= 16 R 3<br \/>\nHence, from the above<br \/>\nThe number of kayaks that are full is: 16<br \/>\nThe number of kayaks that will be used is: 17<br \/>\nThe number of students that will be in the last kayak is: 3<\/p>\n<p>Question 16.<br \/>\nHow many zeros will the product of 80 and 50 have?<br \/>\nA. 1<br \/>\nB. 2<br \/>\nC. 3<br \/>\nD. 4<br \/>\nAnswer: The product of 80 and 50 will have 3 zeroes<\/p>\n<p>Explanation:<br \/>\nBy using the place-value method,<br \/>\n80 \u00d7 50 = 8 tens \u00d7 50<br \/>\n= 400 tens<br \/>\n= 4,000<br \/>\nHence,<br \/>\nThe number of zeroes in 80 \u00d7 50 is: 3<\/p>\n<p>Question 17.<br \/>\nThere are 57 electronic books checked out of a library. There are 8 times as many printed books checked out as electronic books. How many total books are checked out of the library?<br \/>\nA. 513<br \/>\nB. 4,113<br \/>\nC. 122<br \/>\nD. 456<br \/>\nAnswer: A) The total number of books that are checked out of the library: 513<\/p>\n<p>Explanation:<br \/>\nIt is given that there are 57 electronic books checked out of a library.<br \/>\nIt is also given that there are 8 times as many printed books checked out as electronic books<br \/>\nSo,<br \/>\nThe total number of printed books = 57 \u00d7 8 = 456<br \/>\nHence,<br \/>\nThe total number of books = The number of electronic books + The number of printed books<br \/>\n= 57 + 456<br \/>\n= 513 books<\/p>\n<p>Question 18.<br \/>\nWhich number is equal to 100,000 + 5,000 + 80 + 4?<br \/>\nA. 1,584<br \/>\nB. 105084<br \/>\nC. 15,084<br \/>\nD. 105,840<br \/>\nAnswer: B) 1,05,084<\/p>\n<p>Explanation:<br \/>\nThe given Expanded form is: 100,000 + 0 + 5,000 + 0 + 80 + 4<br \/>\nHence,<br \/>\nThe standard form is: 105,084<\/p>\n<h3><a id=\"Understand_Fraction_Equivalence_and_Comparison_STEAM_Performance_Task\"><\/a>Understand Fraction Equivalence and Comparison STEAM Performance Task<\/h3>\n<p>Question 1.<br \/>\nSea level is the average level of the oceans on Earth. The global sea level is rising about \\(\\frac{1}{8}\\) inch each year.<br \/>\na. If this pattern continues, how much will the sea level rise in 80 years?<br \/>\nb. You read from another source that the sea level is1rising about \\(\\frac{1}{2}\\) inch every 4 years. Did your source use the same fact as above? Explain.<br \/>\n<img loading=\"lazy\" class=\"alignnone size-full wp-image-13302\" src=\"https:\/\/ccssmathanswers.com\/wp-content\/uploads\/2020\/12\/Big-Ideas-Math-Answers-Grade-4-Chapter-7-Understand-Fraction-Equivalence-and-Comparison-spt-1.png\" alt=\"Big Ideas Math Answers Grade 4 Chapter 7 Understand Fraction Equivalence and Comparison spt 1\" width=\"288\" height=\"199\" \/><br \/>\nc. In 10 years, will the sea level rise more or less than an inch? Explain.<br \/>\n<img loading=\"lazy\" class=\"alignnone size-full wp-image-13303\" src=\"https:\/\/ccssmathanswers.com\/wp-content\/uploads\/2020\/12\/Big-Ideas-Math-Answers-Grade-4-Chapter-7-Understand-Fraction-Equivalence-and-Comparison-spt-2.png\" alt=\"Big Ideas Math Answers Grade 4 Chapter 7 Understand Fraction Equivalence and Comparison spt 2\" width=\"200\" height=\"230\" \/><br \/>\nd. How many years will it take the sea level to rise about 1 foot?<br \/>\ne. Use the Internet or some other resource to learn about rising sea levels. Write one interesting fact that you learn.<br \/>\nAnswer:<br \/>\na) The amount of sea-level rise in 80 years is: 10 inches<br \/>\nb) Yes, your source does not use the same fact as above<br \/>\nc) In 10 years, the sea level will be an inch.<br \/>\nd) The amount of years that the sea-level will rise to about 1 foot is: 96 years<br \/>\ne) The sea-level will be more in the coastal areas<\/p>\n<p>Explanation:<br \/>\nIt is given that the global sea-level is rising about \\(\\frac{1}{8}\\)\u00a0 inch every year<br \/>\nSo,<br \/>\nThe amount of sea-level that will rise in 80 years = 80 \u00d7 \\(\\frac{1}{8}\\) = 10 inches<br \/>\nIt is also given that another Internet source given that the sea-level is rising about \\(\\frac{1}{4}\\) inches every 4 years<br \/>\nSo,<br \/>\nThe amount of sea-level that will rise every year = \\(\\frac{1}{4}\\) \u00d7 \\(\\frac{1}{4}\\) = \\(\\frac{1}{16}\\)<br \/>\nSo,<br \/>\nYour source does not use the same source as above<br \/>\nWe know that,<br \/>\n1 inch = 12 foot<br \/>\nBut from above,<br \/>\nWe can see that the amount of sea-level that will rise in 80 years in only 10 inch<br \/>\nSo,<br \/>\nThe amount os sea-level will be less than an inch in 10 year<br \/>\nThe number of years that will take for the sea-level that will rise about 1 foot = 96 years<\/p>\n<p>Question 2.<br \/>\nThe gravitational pull of the moon affects the high and low tides of the oceans on Earth. Cities along the coasts use tide tables each day. Use the tide table to answer the questions.<br \/>\n<img loading=\"lazy\" class=\"alignnone size-full wp-image-13304\" src=\"https:\/\/ccssmathanswers.com\/wp-content\/uploads\/2020\/12\/Big-Ideas-Math-Answers-Grade-4-Chapter-7-Understand-Fraction-Equivalence-and-Comparison-spt-3.png\" alt=\"Big Ideas Math Answers Grade 4 Chapter 7 Understand Fraction Equivalence and Comparison spt 3\" width=\"189\" height=\"328\" srcset=\"https:\/\/bigideasmathanswers.com\/wp-content\/uploads\/2020\/12\/Big-Ideas-Math-Answers-Grade-4-Chapter-7-Understand-Fraction-Equivalence-and-Comparison-spt-3.png 189w, https:\/\/bigideasmathanswers.com\/wp-content\/uploads\/2020\/12\/Big-Ideas-Math-Answers-Grade-4-Chapter-7-Understand-Fraction-Equivalence-and-Comparison-spt-3-173x300.png 173w\" sizes=\"(max-width: 189px) 100vw, 189px\" \/><br \/>\na. When swimming, why is it important to understand tide tables?<br \/>\nAnswer: When swimming, the tide tables is important because we can&#8217;t swim when there will be high tides. Otherwise, there is a chance, that we will be suffocated by water and die<\/p>\n<p>b. What are the common factors of the water heights?<br \/>\nAnswer: The common factors of water heights are: 1, 2, 4<br \/>\nc. Make a picture graph of the water heights.<br \/>\n<img loading=\"lazy\" class=\"alignnone size-full wp-image-13305\" src=\"https:\/\/ccssmathanswers.com\/wp-content\/uploads\/2020\/12\/Big-Ideas-Math-Answers-Grade-4-Chapter-7-Understand-Fraction-Equivalence-and-Comparison-spt-4.png\" alt=\"Big Ideas Math Answers Grade 4 Chapter 7 Understand Fraction Equivalence and Comparison spt 4\" width=\"566\" height=\"308\" srcset=\"https:\/\/bigideasmathanswers.com\/wp-content\/uploads\/2020\/12\/Big-Ideas-Math-Answers-Grade-4-Chapter-7-Understand-Fraction-Equivalence-and-Comparison-spt-4.png 566w, https:\/\/bigideasmathanswers.com\/wp-content\/uploads\/2020\/12\/Big-Ideas-Math-Answers-Grade-4-Chapter-7-Understand-Fraction-Equivalence-and-Comparison-spt-4-300x163.png 300w\" sizes=\"(max-width: 566px) 100vw, 566px\" \/><br \/>\nd. What pattern do you notice about the water heights? Explain.<br \/>\nAnswer: All water heights are the multiples of 4<\/p>\n<p><em>Conclusion:<\/em><br \/>\nFree PDF of Big Ideas Math Answers Grade 4 Chapter 7 Understand Fraction Equivalence and Comparison is available here. Learn the easy tricks and tips to solve Grade 4 questions. Practice Books and questions are provided along with the explanations. Refer to Big Ideas Math Answers Grade 4 Chapter 7 Understand Fraction Equivalence and Comparison and score marks in the exams.<\/p>\n","protected":false},"excerpt":{"rendered":"<p>Other than marks it is important for the students to understand the in-depth concepts in math. So, make your students learn the real-time examples along with learning the concepts. We have given questions with real-time problems so that it will be easy to understand the concept deeply. Refer to our Big Ideas Math Answers Grade &#8230; <a title=\"Big Ideas Math Answers Grade 4 Chapter 7 Understand Fraction Equivalence and Comparison\" class=\"read-more\" href=\"https:\/\/bigideasmathanswers.com\/big-ideas-math-answers-grade-4-chapter-7\/\" aria-label=\"More on Big Ideas Math Answers Grade 4 Chapter 7 Understand Fraction Equivalence and Comparison\">Read more<\/a><\/p>\n","protected":false},"author":7,"featured_media":89643,"comment_status":"open","ping_status":"open","sticky":false,"template":"","format":"standard","meta":{"spay_email":""},"categories":[4],"tags":[],"jetpack_featured_media_url":"https:\/\/bigideasmathanswers.com\/wp-content\/uploads\/2020\/12\/Big-Ideas-Math-Answers-Grade-4-Chapter-7.png","_links":{"self":[{"href":"https:\/\/bigideasmathanswers.com\/wp-json\/wp\/v2\/posts\/13130"}],"collection":[{"href":"https:\/\/bigideasmathanswers.com\/wp-json\/wp\/v2\/posts"}],"about":[{"href":"https:\/\/bigideasmathanswers.com\/wp-json\/wp\/v2\/types\/post"}],"author":[{"embeddable":true,"href":"https:\/\/bigideasmathanswers.com\/wp-json\/wp\/v2\/users\/7"}],"replies":[{"embeddable":true,"href":"https:\/\/bigideasmathanswers.com\/wp-json\/wp\/v2\/comments?post=13130"}],"version-history":[{"count":1,"href":"https:\/\/bigideasmathanswers.com\/wp-json\/wp\/v2\/posts\/13130\/revisions"}],"predecessor-version":[{"id":90285,"href":"https:\/\/bigideasmathanswers.com\/wp-json\/wp\/v2\/posts\/13130\/revisions\/90285"}],"wp:featuredmedia":[{"embeddable":true,"href":"https:\/\/bigideasmathanswers.com\/wp-json\/wp\/v2\/media\/89643"}],"wp:attachment":[{"href":"https:\/\/bigideasmathanswers.com\/wp-json\/wp\/v2\/media?parent=13130"}],"wp:term":[{"taxonomy":"category","embeddable":true,"href":"https:\/\/bigideasmathanswers.com\/wp-json\/wp\/v2\/categories?post=13130"},{"taxonomy":"post_tag","embeddable":true,"href":"https:\/\/bigideasmathanswers.com\/wp-json\/wp\/v2\/tags?post=13130"}],"curies":[{"name":"wp","href":"https:\/\/api.w.org\/{rel}","templated":true}]}}