{"id":4780,"date":"2022-03-27T19:32:12","date_gmt":"2022-03-27T14:02:12","guid":{"rendered":"https:\/\/ccssmathanswers.com\/?p=4780"},"modified":"2022-04-07T12:28:31","modified_gmt":"2022-04-07T06:58:31","slug":"go-math-grade-6-answer-key-chapter-2-fractions-and-decimals","status":"publish","type":"post","link":"https:\/\/bigideasmathanswers.com\/go-math-grade-6-answer-key-chapter-2-fractions-and-decimals\/","title":{"rendered":"Go Math Grade 6 Answer Key Chapter 2 Fractions and Decimals"},"content":{"rendered":"<p>Are you looking for the best material to score top in the exams? Then, you are in the right place. HMH Go Math Grade 6 Answer Key Chapter 2 Fractions and Decimals is the best material for the 6th standard students. Here you can find the explanations for each and every question in different methods. Refer to Go Math Grade 6 Chapter 2 Fractions and Decimals Solution Key to learn the concepts of the chapter. So, Download HMH <a href=\"https:\/\/ccssmathanswers.com\/go-math-grade-6-answer-key\/\" target=\"_blank\" rel=\"noopener noreferrer\">Go Math Grade 6 Answer Key<\/a> Chapter 2 Fractions and Decimals for free.<\/p>\n<h2>Download Go Math Grade 6 Chapter 2 Fractions and Decimals Answer Key PDF<\/h2>\n<p>The Go Math Grade 6 Chapter 2 Fractions and Decimals Solution Key consists of various topics like compare and order fractions and decimals, multiply fractions, Divide Fractions, Model Mixed Number Division, etc. We have provided detailed explanations in simple methods here. All the solutions are prepared according to the topics in the Fractions and Decimals Chapter. So, access the links and start your preparation for the exams.<\/p>\n<p><strong>Lesson 1: Fractions and Decimals<\/strong><\/p>\n<ul>\n<li><a href=\"#Fractions_and_Decimals_-_Page_No._71\">Fractions and Decimals &#8211; Page No. 71<\/a><\/li>\n<li><a href=\"#Fractions_and_Decimals_-_Page_No._72\">Fractions and Decimals &#8211; Page No. 72<\/a><\/li>\n<li><a href=\"#Fractions_and_Decimals_Lesson_Check_-_Page_No._73\">Fractions and Decimals Lesson Check &#8211; Page No. 73<\/a><\/li>\n<li><a href=\"#Fractions_and_Decimals_Lesson_Check_1_-_Page_No._74\">Fractions and Decimals Lesson Check 1 &#8211; Page No. 74<\/a><\/li>\n<\/ul>\n<p><strong>Lesson 2: Compare and Order Fractions and Decimals<\/strong><\/p>\n<ul>\n<li><a href=\"#Compare_and_Order_Fractions_and_Decimals_-_Page_No._77\">Compare and Order Fractions and Decimals &#8211; Page No. 77<\/a><\/li>\n<li><a href=\"#Compare_and_Order_Fractions_and_Decimals_-_Page_No._78\">Compare and Order Fractions and Decimals &#8211; Page No. 78<\/a><\/li>\n<li><a href=\"#Compare_and_Order_Fractions_and_Decimals_Lesson_Check_-_Page_No._79\">Compare and Order Fractions and Decimals Lesson Check &#8211; Page No. 79<\/a><\/li>\n<li><a href=\"#Compare_and_Order_Fractions_and_Decimals_Lesson_Check_1_-_Page_No._80\">Compare and Order Fractions and Decimals Lesson Check 1 &#8211; Page No. 80<\/a><\/li>\n<\/ul>\n<p><strong>Lesson 3: Multiply Fractions<\/strong><\/p>\n<ul>\n<li><a href=\"#Multiply_Fractions_-_Page_No._83\">Multiply Fractions &#8211; Page No. 83<\/a><\/li>\n<li><a href=\"#Multiply_Fractions_-_Page_No._84\">Multiply Fractions &#8211; Page No. 84<\/a><\/li>\n<li><a href=\"#Multiply_Fractions_Lesson_Check_-_Page_No._85\">Multiply Fractions Lesson Check &#8211; Page No. 85<\/a><\/li>\n<li><a href=\"#Multiply_Fractions_Lesson_Check_1_-_Page_No._86\">Multiply Fractions Lesson Check 1 &#8211; Page No. 86<\/a><\/li>\n<\/ul>\n<p><strong>Lesson 4: Simplify Factors<\/strong><\/p>\n<ul>\n<li><a href=\"#Simplify_Factors_-_Page_No._89\">Simplify Factors &#8211; Page No. 89<\/a><\/li>\n<li><a href=\"#Simplify_Factors_-_Page_No._90\">Simplify Factors &#8211; Page No. 90<\/a><\/li>\n<li><a href=\"#Simplify_Factors_Lesson_Check_-_Page_No._91\">Simplify Factors Lesson Check &#8211; Page No. 91<\/a><\/li>\n<li><a href=\"#Simplify_Factors_Lesson_Check_1_-_Page_No._92\">Simplify Factors Lesson Check 1 &#8211; Page No. 92<\/a><\/li>\n<\/ul>\n<p><strong>Mid-Chapter Checkpoint<\/strong><\/p>\n<ul>\n<li><a href=\"#Mid-Chapter_Checkpoint_-_Page_No._93\">Mid-Chapter Checkpoint &#8211; Page No. 93<\/a><\/li>\n<li><a href=\"#Mid-Chapter_Checkpoint_Lesson_Check_-_Page_No._94\">Mid-Chapter Checkpoint Lesson Check &#8211; Page No. 94<\/a><\/li>\n<\/ul>\n<p><strong>Lesson 5: Investigate \u2022 Model Fraction Division<\/strong><\/p>\n<ul>\n<li><a href=\"#Model_Fraction_Division_\u2013_Page_No._97\">Model Fraction Division \u2013 Page No. 97<\/a><\/li>\n<li><a href=\"#Model_Fraction_Division_\u2013_Page_No._98\">Model Fraction Division \u2013 Page No. 98<\/a><\/li>\n<li><a href=\"#Model_Fraction_Division_Lesson_Check_\u2013_Page_No._99\">Model Fraction Division Lesson Check \u2013 Page No. 99<\/a><\/li>\n<li><a href=\"#Model_Fraction_Division_Lesson_Check_1_\u2013_Page_No._100\">Model Fraction Division Lesson Check 1 \u2013 Page No. 100<\/a><\/li>\n<\/ul>\n<p><strong>Lesson 6: Estimate Quotients<\/strong><\/p>\n<ul>\n<li><a href=\"#Estimate_Quotients_\u2013_Page_No._103\">Estimate Quotients \u2013 Page No. 103<\/a><\/li>\n<li><a href=\"#Estimate_Quotients_\u2013_Page_No._104\">Estimate Quotients \u2013 Page No. 104<\/a><\/li>\n<li><a href=\"#Estimate_Quotients_Lesson_Check_\u2013_Page_No._105\">Estimate Quotients Lesson Check \u2013 Page No. 105<\/a><\/li>\n<li><a href=\"#Estimate_Quotients_Lesson_Check_1_\u2013_Page_No._106\">Estimate Quotients Lesson Check 1 \u2013 Page No. 106<\/a><\/li>\n<\/ul>\n<p><strong>Lesson 7: Divide Fractions<\/strong><\/p>\n<ul>\n<li><a href=\"#Divide_Fractions_\u2013_Page_No._109\">Divide Fractions \u2013 Page No. 109<\/a><\/li>\n<li><a href=\"#Divide_Fractions_\u2013_Page_No._110\">Divide Fractions \u2013 Page No. 110<\/a><\/li>\n<li><a href=\"#Divide_Fractions_Lesson_Check_\u2013_Page_No._111\">Divide Fractions Lesson Check \u2013 Page No. 111<\/a><\/li>\n<li><a href=\"#Divide_Fractions_Lesson_Check_1_\u2013_Page_No._112\">Divide Fractions Lesson Check 1 \u2013 Page No. 112<\/a><\/li>\n<\/ul>\n<p><strong>Lesson 8: Investigate \u2022 Model Mixed Number Division<\/strong><\/p>\n<ul>\n<li><a href=\"#Model_Mixed_Number_Division_\u2013_Page_No._115\">Model Mixed Number Division \u2013 Page No. 115<\/a><\/li>\n<li><a href=\"#Model_Mixed_Number_Division_\u2013_Page_No._116\">Model Mixed Number Division \u2013 Page No. 116<\/a><\/li>\n<li><a href=\"#Model_Mixed_Number_Division_Lesson_Check_\u2013_Page_No._117\">Model Mixed Number Division Lesson Check \u2013 Page No. 117<\/a><\/li>\n<li><a href=\"#Model_Mixed_Number_Division_Lesson_Check_1_\u2013_Page_No._118\">Model Mixed Number Division Lesson Check 1 \u2013 Page No. 118<\/a><\/li>\n<\/ul>\n<p><strong>Lesson 9: Divide Mixed Numbers<\/strong><\/p>\n<ul>\n<li><a href=\"#Divide_Mixed_Numbers_\u2013_Page_No._121\">Divide Mixed Numbers \u2013 Page No. 121<\/a><\/li>\n<li><a href=\"#Divide_Mixed_Numbers_\u2013_Page_No._122\">Divide Mixed Numbers \u2013 Page No. 122<\/a><\/li>\n<li><a href=\"#Divide_Mixed_Numbers_Lesson_Check_\u2013_Page_No._123\">Divide Mixed Numbers Lesson Check \u2013 Page No. 123<\/a><\/li>\n<li><a href=\"#Divide_Mixed_Numbers_Lesson_Check_1\u2013_Page_No._124\">Divide Mixed Numbers Lesson Check 1\u2013 Page No. 124<\/a><\/li>\n<\/ul>\n<p><strong>Lesson 10: Problem Solving \u2022 Fraction Operations<\/strong><\/p>\n<ul>\n<li><a href=\"#Fraction_Operations_\u2013_Page_No._127\">Fraction Operations \u2013 Page No. 127<\/a><\/li>\n<li><a href=\"#Fraction_Operations_\u2013_Page_No._128\">Fraction Operations \u2013 Page No. 128<\/a><\/li>\n<li><a href=\"#Fraction_Operations_Lesson_Check_\u2013_Page_No._129\">Fraction Operations Lesson Check \u2013 Page No. 129<\/a><\/li>\n<li><a href=\"#Fraction_Operations_Lesson_Check_1\u2013_Page_No._130\">Fraction Operations Lesson Check 1\u2013 Page No. 130<\/a><\/li>\n<\/ul>\n<p><strong>Chapter 2 Review\/Test<\/strong><\/p>\n<ul>\n<li><a href=\"#Review\/Test_-_Page_No._131\">Review\/Test &#8211; Page No. 131<\/a><\/li>\n<li><a href=\"#Review\/Test_-_Page_No._132\">Review\/Test &#8211; Page No. 132<\/a><\/li>\n<li><a href=\"#Review\/Test_-_Page_No._133\">Review\/Test &#8211; Page No. 133<\/a><\/li>\n<li><a href=\"#Review\/Test_-_Page_No._134\">Review\/Test &#8211; Page No. 134<\/a><\/li>\n<li><a href=\"#Review\/Test_-_Page_No._135\">Review\/Test &#8211; Page No. 135<\/a><\/li>\n<li><a href=\"#Review\/Test_-_Page_No._136\">Review\/Test &#8211; Page No. 136<\/a><\/li>\n<\/ul>\n<h3><a id=\"Fractions_and_Decimals_-_Page_No._71\"><\/a>Share and Show &#8211; Page No. 71<\/h3>\n<p><strong>Write as a fraction or as a mixed number in simplest form.<\/strong><\/p>\n<p>Question 1.<br \/>\n95.5<br \/>\n_____ \\(\\frac{\u25a1}{\u25a1}\\)<\/p>\n<p>Answer:<br \/>\n\\(\\frac{1}{2}\\)<\/p>\n<p>Explanation:<br \/>\n95.5<br \/>\n95.5 is 95 ones and 5 tenths.<br \/>\n5 tenths = \\(\\frac{5}{10}\\)<br \/>\nSimplify using the GCF.<br \/>\nThe GCF of 5 and 10 is 10.<br \/>\nDivide the numerator and the denominator by 10<br \/>\n\\(\\frac{5 \u00f7 10}{10 \u00f7 10}\\) = \\(\\frac{1}{2}\\)<\/p>\n<p>Question 2.<br \/>\n0.6<br \/>\n\\(\\frac{\u25a1}{\u25a1}\\)<\/p>\n<p>Answer:<br \/>\n\\(\\frac{3}{5}\\)<\/p>\n<p>Explanation:<br \/>\n0.6<br \/>\n6 tenths = \\(\\frac{6}{10}\\)<br \/>\nSimplify using the GCF.<br \/>\nThe GCF of 6 and 10 is 2.<br \/>\nDivide the numerator and the denominator by 10<br \/>\n\\(\\frac{6 \u00f7 2}{10 \u00f7 2}\\) = \\(\\frac{3}{5}\\)<\/p>\n<p>Question 3.<br \/>\n5.75<br \/>\n_____ \\(\\frac{\u25a1}{\u25a1}\\)<\/p>\n<p>Answer:<br \/>\n5\\(\\frac{3}{4}\\)<\/p>\n<p>Explanation:<br \/>\n5.75 is 5 ones and 75 hundredths.<br \/>\n75 hundredths = \\(\\frac{75}{100}\\)<br \/>\nSimplify using the GCF.<br \/>\nThe GCF of 75 and 100 is 25.<br \/>\nDivide the numerator and the denominator by 25<br \/>\n5\\(\\frac{75 \u00f7 25}{100 \u00f7 25}\\) = 5\\(\\frac{3}{4}\\)<\/p>\n<p><strong>Write as a decimal.<\/strong><\/p>\n<p>Question 4.<br \/>\n\\(\\frac{7}{8}\\)<br \/>\n_____<\/p>\n<p>Answer:<br \/>\n0.875<\/p>\n<p>Explanation:<br \/>\nUse division to rename the fraction part as a decimal.<br \/>\n7\/8 = 0.875<br \/>\nThe quotient has 3 decimal places.<br \/>\nAdd the whole number to the decimal.<br \/>\n0 + 0.875 = 0.875.<br \/>\nSo, \\(\\frac{7}{8}\\) = 0.875<\/p>\n<p>Question 5.<br \/>\n\\(\\frac{13}{20}\\)<br \/>\n_____<\/p>\n<p>Answer:<br \/>\n0.65<\/p>\n<p>Explanation:<br \/>\nUse division to rename the fraction part as a decimal.<br \/>\n\\(\\frac{13}{20}\\) = 0.65<br \/>\nThe quotient has 2 decimal places.<br \/>\nAdd the whole number to the decimal.<br \/>\n0 + 0.65 = 0.65.<br \/>\nSo, \\(\\frac{13}{20}\\) = 0.65<\/p>\n<p>Question 6.<br \/>\n\\(\\frac{3}{25}\\)<br \/>\n_____<\/p>\n<p>Answer:<br \/>\n0.12<\/p>\n<p>Explanation:<br \/>\nUse division to rename the fraction part as a decimal.<br \/>\n\\(\\frac{3}{25}\\) = 0.12<br \/>\nThe quotient has 2 decimal places.<br \/>\nAdd the whole number to the decimal.<br \/>\n0 + 0.12 = 0.12.<br \/>\nSo, \\(\\frac{3}{25}\\)= 0.12<\/p>\n<p><strong>On Your Own<\/strong><\/p>\n<p><strong>Write as a fraction or as a mixed number in simplest form.<\/strong><\/p>\n<p>Question 7.<br \/>\n0.27<br \/>\n\\(\\frac{\u25a1}{\u25a1}\\)<\/p>\n<p>Answer:<br \/>\n\\(\\frac{27}{100}\\)<\/p>\n<p>Explanation:<br \/>\n0.27 is 0 ones and 27 hundredths.<br \/>\n27 hundredths = \\(\\frac{27}{100}\\)<br \/>\nSimplify using the GCF.<br \/>\nThe GCF of 27 and 100 is 1.<br \/>\nDivide the numerator and the denominator by 1<br \/>\n\\(\\frac{27 \u00f7 1}{100 \u00f7 1}\\) = \\(\\frac{27}{100}\\)<\/p>\n<p>Question 8.<br \/>\n0.055<br \/>\n\\(\\frac{\u25a1}{\u25a1}\\)<\/p>\n<p>Answer:<br \/>\n\\(\\frac{11}{200}\\)<\/p>\n<p>Explanation:<br \/>\n0.055 is 0 ones and 55 thousandths.<br \/>\n55 thousandths = \\(\\frac{55}{1000}\\)<br \/>\nSimplify using the GCF.<br \/>\nThe GCF of 55 and 1000 is 5.<br \/>\nDivide the numerator and the denominator by 5<br \/>\n\\(\\frac{55 \u00f7 5}{1000 \u00f7 5}\\) = \\(\\frac{11}{200}\\)<\/p>\n<p>Question 9.<br \/>\n2.45<br \/>\n_____ \\(\\frac{\u25a1}{\u25a1}\\)<\/p>\n<p>Answer:<br \/>\n\\(\\frac{9}{20}\\)<\/p>\n<p>Explanation:<br \/>\n2.45 is 2 ones and 45 hundredths.<br \/>\n45 hundredths = \\(\\frac{45}{100}\\)<br \/>\nSimplify using the GCF.<br \/>\nThe GCF of 45 and 100 is 5.<br \/>\nDivide the numerator and the denominator by 1<br \/>\n\\(\\frac{45 \u00f7 5}{100 \u00f7 5}\\) = \\(\\frac{9}{20}\\)<\/p>\n<p><strong>Write as a decimal.<\/strong><\/p>\n<p>Question 10.<br \/>\n\\(\\frac{3}{8}\\)<br \/>\n_____<\/p>\n<p>Answer:<br \/>\n0.375<\/p>\n<p>Explanation:<br \/>\nUse division to rename the fraction part as a decimal.<br \/>\n\\(\\frac{3}{8}\\) = 0.375<br \/>\nThe quotient has 3 decimal places.<br \/>\nAdd the whole number to the decimal.<br \/>\n0 + 0.375 = 0.375.<br \/>\nSo, \\(\\frac{3}{8}\\) = 0.375<\/p>\n<p>Question 11.<br \/>\n3 \\(\\frac{1}{5}\\)<br \/>\n_____<\/p>\n<p>Answer:<br \/>\n3.2<\/p>\n<p>Explanation:<br \/>\nUse division to rename the fraction part as a decimal.<br \/>\n\\(\\frac{1}{5}\\) = 0.2<br \/>\nThe quotient has 1 decimal place.<br \/>\nAdd the whole number to the decimal.<br \/>\n3 + 0.2 = 3.2.<br \/>\nSo, 3 \\(\\frac{1}{5}\\) = 3.2<\/p>\n<p>Question 12.<br \/>\n2 \\(\\frac{11}{20}\\)<br \/>\n_____<\/p>\n<p>Answer:<br \/>\n2.55<\/p>\n<p>Explanation:<br \/>\nUse division to rename the fraction part as a decimal.<br \/>\n\\(\\frac{11}{20}\\) = 0.55<br \/>\nThe quotient has 2 decimal places.<br \/>\nAdd the whole number to the decimal.<br \/>\n2 + 0.55 = 2.55.<br \/>\nSo, 2 \\(\\frac{11}{20}\\) = 2.55<\/p>\n<p><strong>Identify a decimal and a fraction in simplest form for the point.<\/strong><br \/>\n<img loading=\"lazy\" src=\"https:\/\/ccssmathanswers.com\/wp-content\/uploads\/2020\/08\/Go-Math-Grade-6-Answer-Key-Chapter-2-Fractions-and-Decimals-1.jpg\" alt=\"Go Math Grade 6 Answer Key Chapter 2 Fractions and Decimals 1\" width=\"575\" height=\"82\" \/><\/p>\n<p>Question 13.<br \/>\nPoint A<br \/>\nType below:<br \/>\n__________<\/p>\n<p>Answer:<br \/>\n0.2<\/p>\n<p>Question 14.<br \/>\nPoint B<br \/>\nType below:<br \/>\n__________<\/p>\n<p>Answer:<br \/>\n0.9<\/p>\n<p>Explanation:<br \/>\nPoint B is between 0.8 and 1.0. Every point is separated by 0.1. So, Point B is at 0.9<\/p>\n<p>Question 15.<br \/>\nPoint C<br \/>\nType below:<br \/>\n__________<\/p>\n<p>Answer:<br \/>\n0.5<\/p>\n<p>Explanation:<br \/>\nPoint C is between 0.4 and 0.6. Every point is separated by 0.1. So, Point C is at 0.5<\/p>\n<p>Question 16.<br \/>\nPoint D<br \/>\nType below:<br \/>\n__________<\/p>\n<p>Answer:<br \/>\n0.1<\/p>\n<p>Explanation:<br \/>\nPoint D is between 0 and 0.2. Every point is separated by 0.1. So, Point D is at 0.1<\/p>\n<h3><strong><a id=\"Fractions_and_Decimals_-_Page_No._72\"><\/a>Problem Solving + Applications<\/strong> &#8211; Page No. 72<\/h3>\n<p><strong>Use the table for 17 and 18.<\/strong><br \/>\n<img loading=\"lazy\" src=\"https:\/\/ccssmathanswers.com\/wp-content\/uploads\/2020\/08\/Go-Math-Grade-6-Answer-Key-Chapter-2-Fractions-and-Decimals-2.jpg\" alt=\"Go Math Grade 6 Answer Key Chapter 2 Fractions and Decimals 2\" width=\"254\" height=\"235\" \/><\/p>\n<p>Question 17.<br \/>\nMembers of the Ozark Trail Hiking Club hiked a steep section of the trail in June and July. The table shows the distances club members hiked in miles. Write Maria\u2019s July distance as a decimal.<br \/>\n_____ miles<\/p>\n<p>Answer:<br \/>\n2.625 miles<\/p>\n<p>Explanation:<br \/>\nMaria&#8217;s July distance = 2 \\(\\frac{5}{8}\\)<br \/>\nUse division to rename the fraction part as a decimal.<br \/>\n\\(\\frac{5}{8}\\) = 0.625<br \/>\nThe quotient has 3 decimal places.<br \/>\nAdd the whole number to the decimal.<br \/>\n2 + 0.625 = 2.625.<br \/>\n2 \\(\\frac{5}{8}\\) = 2.625<\/p>\n<p>Question 18.<br \/>\nHow much farther did Zoey hike in June and July than Maria hiked in June and July? Explain how you found your answer.<br \/>\n_____ miles<\/p>\n<p>Answer:<br \/>\n0.7 miles<\/p>\n<p>Explanation:<br \/>\nMaria: June = 2.95, July = 2 \\(\\frac{5}{8}\\) = 2.58<br \/>\nZoey: June = 2.85, July = 3 \\(\\frac{3}{8}\\) = 3.38<br \/>\n[2.85 + 3.38] &#8211; [2.95 + 2.58] = 0.7 miles<\/p>\n<p>Question 19.<br \/>\nWhat\u2019s the Error? Tabitha\u2019s hiking distance in July was 2 \\(\\frac{1}{5}\\) miles. She wrote the distance as 2.02 miles. What error did she make?<br \/>\nType below:<br \/>\n__________<\/p>\n<p>Answer:<br \/>\nTabitha\u2019s hiking distance in July was 2 \\(\\frac{1}{5}\\) miles.<br \/>\n2 \\(\\frac{1}{5}\\)<br \/>\nUse division to rename the fraction part as a decimal.<br \/>\n\\(\\frac{1}{5}\\)\u00a0 = 0.2<br \/>\nThe quotient has 1 decimal place.<br \/>\nAdd the whole number to the decimal.<br \/>\n2 + 0.2 = 2.2.<br \/>\n2 \\(\\frac{1}{5}\\) = 2.2<br \/>\nShe wrote the distance as 2.02 miles in mistake.<\/p>\n<p>Question 20.<br \/>\nUse Patterns Write \\(\\frac{3}{8}, \\frac{4}{8}, \\text { and } \\frac{5}{8}\\) as decimals. What pattern do you see? Use the pattern to predict the decimal form of \\(\\frac{6}{8}\\) and \\(\\frac{7}{8}\\).<br \/>\nType below:<br \/>\n__________<\/p>\n<p>Answer:<br \/>\n\\(\\frac{3}{8}, \\frac{4}{8}, \\text { and } \\frac{5}{8}\\) as decimals.<br \/>\n0.375, 0.5, 0.625<br \/>\nEach decimal is separated by 0.125.<br \/>\nSo, 6\/8 = 0.625 + 0.125 = 0.75<br \/>\n7\/8 = 0.75 + 0.125 = 0.875<\/p>\n<p>Question 21.<br \/>\nIdentify a decimal and a fraction in simplest form for the point.<br \/>\n<img loading=\"lazy\" class=\"alignnone size-full wp-image-4784\" src=\"https:\/\/ccssmathanswers.com\/wp-content\/uploads\/2020\/08\/Go-Math-Grade-6-Answer-Key-Chapter-2-Fractions-and-Decimals-3.jpg\" alt=\"Go Math Grade 6 Answer Key Chapter 2 Fractions and Decimals 3\" width=\"355\" height=\"94\" srcset=\"https:\/\/bigideasmathanswers.com\/wp-content\/uploads\/2020\/08\/Go-Math-Grade-6-Answer-Key-Chapter-2-Fractions-and-Decimals-3.jpg 355w, https:\/\/bigideasmathanswers.com\/wp-content\/uploads\/2020\/08\/Go-Math-Grade-6-Answer-Key-Chapter-2-Fractions-and-Decimals-3-300x79.jpg 300w\" sizes=\"(max-width: 355px) 100vw, 355px\" \/><br \/>\nType below:<br \/>\n__________<\/p>\n<p>Answer:<br \/>\nPoint A: 0.5<br \/>\nPoint B: 0.7<br \/>\nPoint C: 0.3<br \/>\nPoint D: 0.8<\/p>\n<p>Explanation:<br \/>\nEvery point is differentiated by 0.1 distance.<br \/>\nThe A is between 0.4 and 0.6 which is 0.5<br \/>\nThe B is between 0.6 and 0.8 which is 0.7<br \/>\nThe C is between 0.1 and 0.6 which is 0.53<\/p>\n<h3><a id=\"Fractions_and_Decimals_Lesson_Check_-_Page_No._73\"><\/a>Fractions and Decimals &#8211; Page No. 73<\/h3>\n<p><strong>Write as a fraction or as a mixed number in simplest form.<\/strong><\/p>\n<p>Question 1.<br \/>\n0.52<br \/>\n\\(\\frac{\u25a1}{\u25a1}\\)<\/p>\n<p>Answer:<br \/>\n\\(\\frac{13}{25}\\)<\/p>\n<p>Explanation:<br \/>\n0.52<br \/>\n0.52 is 52 hundredths.<br \/>\n52 hundredths = \\(\\frac{52}{100}\\)<br \/>\nSimplify using the GCF.<br \/>\nThe GCF of 52 and 100 is 4.<br \/>\nDivide the numerator and the denominator by 4<br \/>\n\\(\\frac{52 \u00f7 4}{100 \u00f7 4}\\) = \\(\\frac{13}{25}\\)<\/p>\n<p>Question 2.<br \/>\n0.02<br \/>\n\\(\\frac{\u25a1}{\u25a1}\\)<\/p>\n<p>Answer:<br \/>\n\\(\\frac{1}{50}\\)<\/p>\n<p>Explanation:<br \/>\n0.02<br \/>\n0.02 is 2 hundredths.<br \/>\n2 hundredths = \\(\\frac{2}{100}\\)<br \/>\nSimplify using the GCF.<br \/>\nThe GCF of 2 and 100 is 2.<br \/>\nDivide the numerator and the denominator by 2<br \/>\n\\(\\frac{2 \u00f7 2}{100 \u00f7 2}\\) = \\(\\frac{1}{50}\\)<\/p>\n<p>Question 3.<br \/>\n4.8<br \/>\n______ \\(\\frac{\u25a1}{\u25a1}\\)<\/p>\n<p>Answer:<br \/>\n\\(\\frac{4}{5}\\)<\/p>\n<p>Explanation:<br \/>\n4.8<br \/>\n4.8 is 4 ones and 8 tenths.<br \/>\n8 tenths = \\(\\frac{8}{10}\\)<br \/>\nSimplify using the GCF.<br \/>\nThe GCF of 8 and 10 is 2.<br \/>\nDivide the numerator and the denominator by 2<br \/>\n\\(\\frac{8 \u00f7 2}{10 \u00f7 2}\\) = \\(\\frac{4}{5}\\)<\/p>\n<p>Question 4.<br \/>\n6.025<br \/>\n______ \\(\\frac{\u25a1}{\u25a1}\\)<\/p>\n<p>Answer:<br \/>\n\\(\\frac{1}{40}\\)<\/p>\n<p>Explanation:<br \/>\n6.025 is 6 ones and 25 thousandths.<br \/>\n25 thousandths = \\(\\frac{25}{1000}\\)<br \/>\nSimplify using the GCF.<br \/>\nThe GCF of 25 and 1000 is 25.<br \/>\nDivide the numerator and the denominator by 25<br \/>\n\\(\\frac{25 \u00f7 25}{1000 \u00f7 25}\\) = \\(\\frac{1}{40}\\)<\/p>\n<p><strong>Write as a decimal.<\/strong><\/p>\n<p>Question 5.<br \/>\n\\(\\frac{17}{25}\\)<br \/>\n______<\/p>\n<p>Answer:<br \/>\n0.68<\/p>\n<p>Explanation:<br \/>\nUse division to rename the fraction part as a decimal.<br \/>\n17\/25 = 0.68<br \/>\nThe quotient has 2 decimal places.<br \/>\nAdd the whole number to the decimal.<br \/>\n0 + 0.68 = 0.68.<br \/>\nSo, \\(\\frac{17}{25}\\) = 0.68<\/p>\n<p>Question 6.<br \/>\n\\(\\frac{11}{20}\\)<br \/>\n______<\/p>\n<p>Answer:<br \/>\n0.55<\/p>\n<p>Explanation:<br \/>\nUse division to rename the fraction part as a decimal.<br \/>\n11\/20 = 0.55<br \/>\nThe quotient has 2 decimal places.<br \/>\nAdd the whole number to the decimal.<br \/>\n0 + 0.55 = 0.55.<br \/>\nSo, \\(\\frac{11}{20}\\) = 0.55<\/p>\n<p>Question 7.<br \/>\n4 \\(\\frac{13}{20}\\)<br \/>\n______<\/p>\n<p>Answer:<br \/>\n4.65<\/p>\n<p>Explanation:<br \/>\nUse division to rename the fraction part as a decimal.<br \/>\n\\(\\frac{13}{20}\\) = 0.65<br \/>\nThe quotient has 2 decimal places.<br \/>\nAdd the whole number to the decimal.<br \/>\n4 + 0.65 = 4.65.<br \/>\nSo, 4 \\(\\frac{13}{20}\\) = 4.65<\/p>\n<p>Question 8.<br \/>\n7 \\(\\frac{3}{8}\\)<br \/>\n______<\/p>\n<p>Answer:<br \/>\n7.375<\/p>\n<p>Explanation:<br \/>\nUse division to rename the fraction part as a decimal.<br \/>\n\\(\\frac{3}{8}\\) = 0.375<br \/>\nThe quotient has 3 decimal places.<br \/>\nAdd the whole number to the decimal.<br \/>\n7 + 0.375 = 7.375.<br \/>\nSo, 7 \\(\\frac{3}{8}\\) = 7.375<\/p>\n<p><strong>Identify a decimal and a fraction or mixed number in simplest form for each point.<\/strong><br \/>\n<img loading=\"lazy\" class=\"alignnone size-full wp-image-4785\" src=\"https:\/\/ccssmathanswers.com\/wp-content\/uploads\/2020\/08\/Go-Math-Grade-6-Answer-Key-Chapter-2-Fractions-and-Decimals-4.jpg\" alt=\"Go Math Grade 6 Answer Key Chapter 2 Fractions and Decimals 4\" width=\"576\" height=\"75\" srcset=\"https:\/\/bigideasmathanswers.com\/wp-content\/uploads\/2020\/08\/Go-Math-Grade-6-Answer-Key-Chapter-2-Fractions-and-Decimals-4.jpg 576w, https:\/\/bigideasmathanswers.com\/wp-content\/uploads\/2020\/08\/Go-Math-Grade-6-Answer-Key-Chapter-2-Fractions-and-Decimals-4-300x39.jpg 300w\" sizes=\"(max-width: 576px) 100vw, 576px\" \/><\/p>\n<p>Question 9.<br \/>\nPoint A<br \/>\nType below:<br \/>\n__________<\/p>\n<p>Answer:<br \/>\n0.4<\/p>\n<p>Explanation:<\/p>\n<p>Point A is between 0 and 0.5. Every point is separated by 0.1. So, Point A is at 0.4<\/p>\n<p>Question 10.<br \/>\nPoint D<br \/>\nType below:<br \/>\n__________<\/p>\n<p>Answer:<br \/>\n1.9<\/p>\n<p>Explanation:<br \/>\nPoint D is between 1.5 and 2. Every point is separated by 0.1. So, Point D is at 1.9<\/p>\n<p>Question 11.<br \/>\nPoint C<br \/>\nType below:<br \/>\n__________<\/p>\n<p>Answer:<br \/>\n1.2<\/p>\n<p>Explanation:<br \/>\nPoint C is between 1 and 1.5. Every point is separated by 0.1. So, Point C is at 1.2<\/p>\n<p>Question 12.<br \/>\nPoint B<br \/>\nType below:<br \/>\n__________<\/p>\n<p>Answer:<br \/>\n0.6<\/p>\n<p>Explanation:<br \/>\nPoint C is between 0.5 and 1. Every point is separated by 0.1. So, Point C is at 0.6<\/p>\n<p><strong>Problem Solving<\/strong><\/p>\n<p>Question 13.<br \/>\nGrace sold \\(\\frac{5}{8}\\) of her stamp collection. What is this amount as a decimal?<br \/>\n______<\/p>\n<p>Answer:<br \/>\n0.625<\/p>\n<p>Explanation:<br \/>\nGrace sold \\(\\frac{5}{8}\\) of her stamp collection.<br \/>\nUse division to rename the fraction part as a decimal.<br \/>\n\\(\\frac{5}{8}\\)\u00a0 = 0.625<br \/>\nThe quotient has 3 decimal places.<br \/>\nAdd the whole number to the decimal.<br \/>\n0 + 0.625 = 0.625.<br \/>\nSo, \\(\\frac{5}{8}\\) = 0.625<\/p>\n<p>Question 14.<br \/>\nWhat if you scored an 0.80 on a test? What fraction of the test, in simplest form, did you answer correctly?<br \/>\n\\(\\frac{\u25a1}{\u25a1}\\)<\/p>\n<p>Answer:<br \/>\n\\(\\frac{4}{5}\\)<\/p>\n<p>Explanation:<br \/>\n0.80 is 0 ones and 8 tenths.<br \/>\n8 tenths = \\(\\frac{8}{10}\\)<br \/>\nSimplify using the GCF.<br \/>\nThe GCF of 8 and 10 is 2.<br \/>\nDivide the numerator and the denominator by 2<br \/>\n\\(\\frac{8 \u00f7 2}{10 \u00f7 2}\\) = \\(\\frac{4}{5}\\)<\/p>\n<p>Question 15.<br \/>\nWhat fraction in simplest form is equivalent to 0.45? What decimal is equivalent to \\(\\frac{17}{20}\\)? Explain how you found your answers.<br \/>\nType below:<br \/>\n__________<\/p>\n<p>Answer:<br \/>\n0.45 is 0 ones and 45 hundredths.<br \/>\n45 hundredths = \\(\\frac{45}{100}\\)<br \/>\nSimplify using the GCF.<br \/>\nThe GCF of 45 and 100 is 5.<br \/>\nDivide the numerator and the denominator by 5<br \/>\n\\(\\frac{45 \u00f7 5}{100 \u00f7 5}\\) = \\(\\frac{9}{20}\\)<br \/>\n\\(\\frac{17}{20}\\)<br \/>\nUse division to rename the fraction part as a decimal.<br \/>\n\\(\\frac{17}{20}\\) = 0.85<br \/>\nThe quotient has 2 decimal places.<br \/>\nAdd the whole number to the decimal.<br \/>\n0 + 0.85 = 0.85.<br \/>\nSo, \\(\\frac{17}{20}\\) = 0.85<\/p>\n<h3><a id=\"Fractions_and_Decimals_Lesson_Check_1_-_Page_No._74\"><\/a>Lesson Check &#8211; Page No. 74<\/h3>\n<p>Question 1.<br \/>\nAfter a storm, Michael measured 6 \\(\\frac{7}{8}\\) inches of snow. What is this amount as a decimal?<br \/>\n______ inches<\/p>\n<p>Answer:<br \/>\n6.875 inches<\/p>\n<p>Explanation:<br \/>\nMichael measured 6 \\(\\frac{7}{8}\\) inches of snow.<br \/>\nUse division to rename the fraction part as a decimal.<br \/>\n\\(\\frac{7}{8}\\) = 0.875<br \/>\nThe quotient has 3 decimal places.<br \/>\nAdd the whole number to the decimal.<br \/>\n6 + 0.875 = 6.875.<br \/>\nSo, 6 \\(\\frac{7}{8}\\) = 6.875.<\/p>\n<p>Question 2.<br \/>\nA recipe calls for 3.75 cups of flour. What is this amount as a mixed number in simplest form?<br \/>\n______ \\(\\frac{\u25a1}{\u25a1}\\) cups<\/p>\n<p>Answer:<br \/>\n3 \\(\\frac{3}{4}\\) cups<\/p>\n<p>Explanation:<br \/>\nA recipe calls for 3.75 cups of flour.<br \/>\n3 + 0.75<br \/>\n0.75 is 0 ones and 75 hundredths.<br \/>\n75 hundredths = \\(\\frac{75}{100}\\)<br \/>\nSimplify using the GCF.<br \/>\nThe GCF of 75 and 100 is 25.<br \/>\nDivide the numerator and the denominator by 25<br \/>\n\\(\\frac{75 \u00f7 25}{100 \u00f7 25}\\) = \\(\\frac{3}{4}\\)<br \/>\n3 \\(\\frac{3}{4}\\)<\/p>\n<p><strong>Spiral Review<\/strong><\/p>\n<p>Question 3.<br \/>\nGina bought 2.3 pounds of red apples and 2.42 pounds of green apples. They were on sale for $0.75 a pound. How much did the apples cost altogether?<br \/>\n$ ______<\/p>\n<p>Answer:<br \/>\n$3.54<\/p>\n<p>Explanation:<br \/>\nGina bought 2.3 pounds of red apples and 2.42 pounds of green apples. They were on sale for $0.75 a pound.<br \/>\n$0.75 x 2.3 = 1.725<br \/>\n$0.75 x 2.42 = 1.815<br \/>\n1.725 + 1.815 = 3.54<br \/>\nSo the apples cost $3.54<\/p>\n<p>Question 4.<br \/>\nKen has 4.66 pounds of walnuts, 2.1 pounds of cashews, and 8 pounds of peanuts. He mixes them together and divides them equally among 18 bags. How many pounds of nuts are in each bag?<br \/>\n______ pounds<\/p>\n<p>Answer:<br \/>\n0.82 pounds<\/p>\n<p>Explanation:<br \/>\nKen has 4.66 pounds of walnuts, 2.1 pounds of cashews, and 8 pounds of peanuts.<br \/>\n4.66 + 2.1 + 8 = 14.76<br \/>\nHe mixes them together and divides them equally among 18 bags.<br \/>\n14.76\/18 = 0.82<\/p>\n<p>Question 5.<br \/>\nMia needs to separate 270 blue pens and 180 red pens into packs. Each pack will have the same number of blue pens and the same number of red pens. What is the greatest number of packs she can make? How many red pens and how many blue pens will be in each pack?<br \/>\nType below:<br \/>\n__________<\/p>\n<p>Answer:<br \/>\nThere are 2 red pens and 3 blue pens in each pack.<\/p>\n<p>Explanation:<br \/>\nMia needs to separate 270 blue pens and 180 red pens into packs.<br \/>\nThe GCF of 270 and 180 is 90<br \/>\nThe greatest number of packs she can make is 90.<br \/>\nDivide the total number of red pens by the total number of packs.<br \/>\n180\/90 = 2<br \/>\nDivide the total number of blue pens by the total number of packs.<br \/>\n270\/90 = 3<br \/>\nThere are 2 red pens and 3 blue pens in each pack.<\/p>\n<p>Question 6.<br \/>\nEvan buys 19 tubes of watercolor paint for $50.35. What is the cost of each tube of paint?<br \/>\n$ ______<\/p>\n<p>Answer:<br \/>\n$2.65<\/p>\n<p>Explanation:<br \/>\nEvan buys 19 tubes of watercolor paint for $50.35.<br \/>\n$50.35\/19 = $2.65<\/p>\n<h3><a id=\"Compare_and_Order_Fractions_and_Decimals_-_Page_No._77\"><\/a>Share and Show &#8211; Page No. 77<\/h3>\n<p><strong>Order from least to greatest.<\/strong><\/p>\n<p>Question 1.<br \/>\n\\(3 \\frac{3}{6}, 3 \\frac{5}{8}, 2 \\frac{9}{10}\\)<br \/>\nType below:<br \/>\n__________<\/p>\n<p>Answer:<br \/>\n2 \\(\\frac{9}{10}\\) &lt; 3 \\(\\frac{3}{6}\\) &lt; 3 \\(\\frac{5}{8}\\)<\/p>\n<p>Explanation:<br \/>\n\\(3 \\frac{3}{6}, 3 \\frac{5}{8}, 2 \\frac{9}{10}\\)<br \/>\nCompare the whole numbers first.<br \/>\n2 &lt; 3<br \/>\nIf the whole numbers are the same, compare the fractions.<br \/>\n3 \\(\\frac{3}{6}\\), 3 \\(\\frac{5}{8}\\)<br \/>\n6 and 8 are multiples of 48.<br \/>\nSo, 48 is a common denominator.<br \/>\n3 \\(\\frac{3 x 8}{6 x 8}\\) = 3 \\(\\frac{24}{48}\\), 3 \\(\\frac{5 x 6}{8 x 6}\\) = 3 \\(\\frac{30}{48}\\)<br \/>\n3 \\(\\frac{24}{48}\\) &lt; 3 \\(\\frac{30}{48}\\)<br \/>\nSo, 3 \\(\\frac{3}{6}\\) &lt; 3 \\(\\frac{5}{8}\\)<br \/>\nOrder the fractions from least to greatest.<br \/>\n2 \\(\\frac{9}{10}\\) &lt; 3 \\(\\frac{3}{6}\\) &lt; 3 \\(\\frac{5}{8}\\)<\/p>\n<p><strong>Write &lt;, &gt;, or =.<\/strong><\/p>\n<p>Question 2.<br \/>\n0.8 _____ \\(\\frac{4}{12}\\)<\/p>\n<p>Answer:<br \/>\n0.8 &lt; latex]\\frac{4}{12}[\/latex]<\/p>\n<p>Explanation:<br \/>\nWrite the decimal form of \\(\\frac{4}{12}\\) = 0.3333<br \/>\n0.8 &gt; 0.333<br \/>\nSo, 0.8 &lt; latex]\\frac{4}{12}[\/latex]<\/p>\n<p>Question 3.<br \/>\n0.22 _____ \\(\\frac{1}{4}\\)<\/p>\n<p>Answer:<br \/>\n0.22 &lt; \\(\\frac{1}{4}\\)<\/p>\n<p>Explanation:<br \/>\nWrite the decimal form of \\(\\frac{1}{4}\\) = 0.25<br \/>\n0.22 &lt; 0.25<br \/>\nSo, 0.22 &lt; \\(\\frac{1}{4}\\)<\/p>\n<p>Question 4.<br \/>\n\\(\\frac{1}{20}\\) _____ 0.06<\/p>\n<p>Answer:<br \/>\n\\(\\frac{1}{20}\\) &lt; 0.06<\/p>\n<p>Explanation:<br \/>\nWrite the decimal form of \\(\\frac{1}{20}\\) = 0.05<br \/>\n0.05 &lt; 0.06<br \/>\nSo, \\(\\frac{1}{20}\\) &lt; 0.06<\/p>\n<p><strong>Use a number line to order from least to greatest.<\/strong><\/p>\n<p>Question 5.<br \/>\n\\(1 \\frac{4}{5}, 1.25, 1 \\frac{1}{10}\\)<br \/>\nType below:<br \/>\n__________<\/p>\n<p>Answer:<br \/>\n1\\(\\frac{1}{10}\\), 1.25, 1\\(\\frac{4}{5}\\)<\/p>\n<p>Explanation:<br \/>\nWrite the decimal form of 1\\(\\frac{4}{5}\\) = 1.8<br \/>\nWrite the decimal form of 1\\(\\frac{1}{10}\\) = 1.1<br \/>\n1.8, 1.25, 1.1<br \/>\nLocate each decimal on a number line.<br \/>\nSo, from least to greatest, the order is 1.1, 1.25, 1.8<br \/>\n1\\(\\frac{1}{10}\\), 1.25, 1\\(\\frac{4}{5}\\)<\/p>\n<p><strong>On Your Own<\/strong><\/p>\n<p><strong>Order from least to greatest.<\/strong><\/p>\n<p>Question 6.<br \/>\n0.6, \\(\\frac{4}{5}\\), 0.75<br \/>\nType below:<br \/>\n__________<\/p>\n<p>Answer:<br \/>\n0.6, 0.75, \\(\\frac{4}{5}\\)<\/p>\n<p>Explanation:<br \/>\nWrite the decimal form of \\(\\frac{4}{5}\\) = 0.8<br \/>\n0.6, 0.8, 0.75<br \/>\nCompare decimals.<br \/>\nAll ones are equal.<br \/>\nCompare tenths: 6 &lt; 7 &lt; 8<br \/>\nSo, from least to greatest, the order is 0.6, 0.75, 0.8<br \/>\nSo, 0.6, 0.75, \\(\\frac{4}{5}\\)<\/p>\n<p>Question 7.<br \/>\n\\(\\frac{1}{2}\\), \\(\\frac{2}{5}\\), \\(\\frac{7}{15}\\)<br \/>\nType below:<br \/>\n__________<\/p>\n<p>Answer:<br \/>\n\\(\\frac{2}{5}\\), \\(\\frac{7}{15}\\), \\(\\frac{1}{2}\\)<\/p>\n<p>Explanation:<br \/>\nWrite the decimal form of \\(\\frac{1}{2}\\) = 0.5<br \/>\nWrite the decimal form of \\(\\frac{2}{5}\\) = 0.4<br \/>\nWrite the decimal form of \\(\\frac{7}{15}\\) = 0.466<br \/>\n0.5, 0.4, 0.466<br \/>\nCompare decimals.<br \/>\nAll ones are equal.<br \/>\nCompare tenths: 4 &lt; 5<br \/>\nCompare hundredths of 0.4 and 0.466; 0 &lt; 6<br \/>\nSo, from least to greatest, the order is 0.4 &lt; 0.466 &lt; 0.5<br \/>\nSo, \\(\\frac{2}{5}\\), \\(\\frac{7}{15}\\), \\(\\frac{1}{2}\\)<\/p>\n<p>Question 8.<br \/>\n5 \\(\\frac{1}{2}\\), 5.05, 5 \\(\\frac{5}{9}\\)<br \/>\nType below:<br \/>\n__________<\/p>\n<p>Answer:<br \/>\n5.05, 5 \\(\\frac{1}{2}\\), 5 \\(\\frac{5}{9}\\)<\/p>\n<p>Explanation:<br \/>\nWrite the decimal form of 5 \\(\\frac{1}{2}\\) = 5.5<br \/>\nWrite the decimal form of 5 \\(\\frac{5}{9}\\) = 5.555<br \/>\n5.5, 5.05, 5.5555<br \/>\nCompare decimals.<br \/>\nAll ones are equal.<br \/>\nCompare tenths: 0 &lt; 5<br \/>\nCompare hundredths of 5.5 and 5.55; 0 &lt; 5<br \/>\nSo, from least to greatest, the order is 5.05 &lt; 5.5 &lt; 5.55<br \/>\nSo, 5.05, 5 \\(\\frac{1}{2}\\), 5 \\(\\frac{5}{9}\\)<\/p>\n<p>Question 9.<br \/>\n\\(\\frac{5}{7}\\), \\(\\frac{5}{6}\\), \\(\\frac{5}{12}\\)<br \/>\nType below:<br \/>\n__________<\/p>\n<p>Answer:<br \/>\n\\(\\frac{5}{12}\\), \\(\\frac{5}{7}\\), \\(\\frac{5}{6}\\)<\/p>\n<p>Explanation:<br \/>\n\\(\\frac{5}{7}\\), \\(\\frac{5}{6}\\), \\(\\frac{5}{12}\\)<br \/>\nTo compare fractions with the same numerators, compare the denominators.<br \/>\nSo, from least to greatest, the order is \\(\\frac{5}{12}\\), \\(\\frac{5}{7}\\), \\(\\frac{5}{6}\\)<\/p>\n<p>Question 10.<br \/>\n\\(\\frac{7}{15}\\) _____ \\(\\frac{7}{10}\\)<\/p>\n<p>Answer:<br \/>\n\\(\\frac{7}{15}\\) &lt; \\(\\frac{7}{10}\\)<\/p>\n<p>Explanation:<br \/>\n\\(\\frac{7}{15}\\) and \\(\\frac{7}{10}\\)<br \/>\nTo compare fractions with the same numerators, compare the denominators.<br \/>\nSo, \\(\\frac{7}{15}\\) &lt; \\(\\frac{7}{10}\\)<\/p>\n<p>Question 11.<br \/>\n\\(\\frac{1}{8}\\) _____ 0.125<\/p>\n<p>Answer:<br \/>\n\\(\\frac{1}{8}\\) = 0.125<\/p>\n<p>Explanation:<br \/>\nWrite the decimal form of \\(\\frac{1}{8}\\) = 0.125<br \/>\n0.125 = 0.125<\/p>\n<p>Question 12.<br \/>\n7 \\(\\frac{1}{3}\\) _____ 6 \\(\\frac{2}{3}\\)<\/p>\n<p>Answer:<br \/>\n7 \\(\\frac{1}{3}\\) &gt; 6 \\(\\frac{2}{3}\\)<\/p>\n<p>Explanation:<br \/>\nCompare the whole numbers first.<br \/>\n7 &gt; 6.<br \/>\nSo, 7 \\(\\frac{1}{3}\\) &gt; 6 \\(\\frac{2}{3}\\)<\/p>\n<p>Question 13.<br \/>\n1 \\(\\frac{2}{5}\\) _____ 1 \\(\\frac{7}{15}\\)<\/p>\n<p>Answer:<br \/>\n1 \\(\\frac{2}{5}\\) &lt; 1 \\(\\frac{7}{15}\\)<\/p>\n<p>Explanation:<br \/>\n1 \\(\\frac{2}{5}\\) _____ 1 \\(\\frac{7}{15}\\)<br \/>\nIf the whole numbers are the same, compare the fractions.<br \/>\nCompare \\(\\frac{2}{5}\\) and \\(\\frac{7}{15}\\)<br \/>\n5 and 15 are multiples of 15.<br \/>\nSo, \\(\\frac{2 x 3}{5 x 3}\\) = \\(\\frac{6}{15}\\)<br \/>\n\\(\\frac{6}{15}\\) &lt; \\(\\frac{7}{15}\\)<br \/>\nUse common denominators to write equivalent fractions.<br \/>\n1 \\(\\frac{2}{5}\\) &lt; 1 \\(\\frac{7}{15}\\)<\/p>\n<p>Question 14.<br \/>\nDarrell spent 3 \\(\\frac{2}{5}\\) hours on a project for school. Jan spent 3 \\(\\frac{1}{4}\\) hours and Maeve spent 3.7 hours on the project. Who spent the least amount of time? Show how you found your answer. Then describe another possible method.<br \/>\nType below:<br \/>\n__________<\/p>\n<p>Answer:<br \/>\nJan spent the least amount of time.<\/p>\n<p>Explanation:<br \/>\nDarrell spent 3 \\(\\frac{2}{5}\\) hours on a project for school. Jan spent 3 \\(\\frac{1}{4}\\) hours and Maeve spent 3.7 hours on the project.<br \/>\nWrite the decimal form of 3 \\(\\frac{2}{5}\\) = 3.4<br \/>\nWrite the decimal form of 3 \\(\\frac{1}{4}\\) = 3.25<br \/>\n3.4, 3.25, 3.7<br \/>\n3.25 is the least one.<br \/>\nSo, Jan spent the least amount of time.<\/p>\n<h3><a id=\"Compare_and_Order_Fractions_and_Decimals_-_Page_No._78\"><\/a>Problem Solving + Applications &#8211; Page No. 78<\/h3>\n<p><strong>Use the table for 15\u201318.<\/strong><br \/>\n<img loading=\"lazy\" class=\"alignnone size-full wp-image-4786\" src=\"https:\/\/ccssmathanswers.com\/wp-content\/uploads\/2020\/08\/Go-Math-Grade-6-Answer-Key-Chapter-2-Fractions-and-Decimals-5.jpg\" alt=\"Go Math Grade 6 Answer Key Chapter 2 Fractions and Decimals 5\" width=\"254\" height=\"306\" srcset=\"https:\/\/bigideasmathanswers.com\/wp-content\/uploads\/2020\/08\/Go-Math-Grade-6-Answer-Key-Chapter-2-Fractions-and-Decimals-5.jpg 254w, https:\/\/bigideasmathanswers.com\/wp-content\/uploads\/2020\/08\/Go-Math-Grade-6-Answer-Key-Chapter-2-Fractions-and-Decimals-5-249x300.jpg 249w\" sizes=\"(max-width: 254px) 100vw, 254px\" \/><\/p>\n<p>Question 15.<br \/>\nIn one week, Altoona, PA, and Bethlehem, PA, received snowfall every day, Monday through Friday. On which days did Altoona receive over 0.1 inch more snow than Bethlehem?<br \/>\nType below:<br \/>\n__________<\/p>\n<p>Answer:<br \/>\nAltoona received over 1 inch more snow than Bethlehem on Friday<\/p>\n<p>Explanation:<br \/>\nAltoona (converted to decimal form): 2.25, 3.25, 2.625, 4.6, 4.75<br \/>\nBethlehem: 2.6, 3.2, 2.5, 4.8, 2.7<br \/>\nAltoona received over 1 inch more snow than Bethlehem on Friday<\/p>\n<p>Question 16.<br \/>\nWhat if Altoona received an additional 0.3 inch of snow on Thursday? How would the total amount of snow in Altoona compare to the amount received in Bethlehem that day?<br \/>\nType below:<br \/>\n__________<\/p>\n<p>Answer:<br \/>\nAltoona received 0.1 inches more snow than Bethlehem on Thursday<\/p>\n<p>Explanation:<br \/>\nAltoona received an additional 0.3 inch of snow on Thursday = 4.6 + 0.3 = 4.9<br \/>\nBethlehem received on Thursday = 4.8<br \/>\nAltoona received 0.1 inches more snow than Bethlehem on Thursday<\/p>\n<p>Question 17.<br \/>\nExplain two ways you could compare the snowfall amounts in Altoona and Bethlehem on Monday.<br \/>\nType below:<br \/>\n__________<\/p>\n<p>Answer:<\/p>\n<p>Explanation:<br \/>\nAltoona received on Monday = 2.25<br \/>\nBethlehem received on Monday = 2.6<br \/>\nBethlehem received 0.35 inches more snow than Altoona on Monday.<br \/>\nAs the whole numbers are equal compare 1\/4 and 0.6.<br \/>\n0.25 &lt; 0.6<br \/>\nSo, Altoona received less snow compared to Bethlehem on Monday.<\/p>\n<p>Question 18.<br \/>\nExplain how you could compare the snowfall amounts in Altoona on Thursday and Friday.<br \/>\nType below:<br \/>\n__________<\/p>\n<p>Answer:<br \/>\nAltoona received on Thursday = 4.6<br \/>\nAltoona received on Friday = 4.75<br \/>\n4.6 &lt; 4.75<br \/>\nAltoona received less snow on Thursday compared to Friday.<\/p>\n<p>Question 19.<br \/>\nWrite the values in order from least to greatest.<br \/>\n<img loading=\"lazy\" class=\"alignnone size-full wp-image-4787\" src=\"https:\/\/ccssmathanswers.com\/wp-content\/uploads\/2020\/08\/Go-Math-Grade-6-Answer-Key-Chapter-2-Fractions-and-Decimals-6.jpg\" alt=\"Go Math Grade 6 Answer Key Chapter 2 Fractions and Decimals 6\" width=\"441\" height=\"41\" srcset=\"https:\/\/bigideasmathanswers.com\/wp-content\/uploads\/2020\/08\/Go-Math-Grade-6-Answer-Key-Chapter-2-Fractions-and-Decimals-6.jpg 441w, https:\/\/bigideasmathanswers.com\/wp-content\/uploads\/2020\/08\/Go-Math-Grade-6-Answer-Key-Chapter-2-Fractions-and-Decimals-6-300x28.jpg 300w\" sizes=\"(max-width: 441px) 100vw, 441px\" \/><br \/>\nType below:<br \/>\n__________<\/p>\n<p>Answer:<br \/>\n1\/3, 0.39, 2\/5, 0.45<\/p>\n<p>Explanation:<br \/>\n1\/3 = 0.333<br \/>\n0.45<br \/>\n0.39<br \/>\n2\/5 = 0.4<br \/>\nCompare tenths: 3 &lt; 4<br \/>\nCompare hundredths:<br \/>\n0.33 &lt; 0.39<br \/>\n0.4 &lt; 0.45<br \/>\nSo, 1\/3, 0.39, 2\/5, 0.45<\/p>\n<h3><a id=\"Compare_and_Order_Fractions_and_Decimals_Lesson_Check_-_Page_No._79\"><\/a>Compare and Order Fractions and Decimals &#8211; Page No. 79<\/h3>\n<p><strong>Write &lt;, &gt;, =.<\/strong><\/p>\n<p>Question 1.<br \/>\n0.64 _____ \\(\\frac{7}{10}\\)<\/p>\n<p>Answer:<br \/>\n0.64 &lt; \\(\\frac{7}{10}\\)<\/p>\n<p>Explanation:<br \/>\nWrite the decimal form of \\(\\frac{7}{10}\\) = 0.7<br \/>\nCompare tenths: 6 &lt; 7<br \/>\nSo, 0.64 &lt; 0.7<br \/>\n0.64 &lt; \\(\\frac{7}{10}\\)<\/p>\n<p>Question 2.<br \/>\n0.48 _____ \\(\\frac{6}{15}\\)<\/p>\n<p>Answer:<br \/>\n0.48 &gt; \\(\\frac{6}{15}\\)<\/p>\n<p>Explanation:<br \/>\nWrite the decimal form of \\(\\frac{6}{15}\\) = 0.4<br \/>\nCompare hundredths:<br \/>\n0.48 &gt; 0.4<br \/>\n0.48 &gt; \\(\\frac{6}{15}\\)<\/p>\n<p>Question 3.<br \/>\n0.75 _____ \\(\\frac{7}{8}\\)<\/p>\n<p>Answer:<br \/>\n0.75 &lt; \\(\\frac{7}{8}\\)<\/p>\n<p>Explanation:<br \/>\nWrite the decimal form of \\(\\frac{7}{8}\\) = 0.875<br \/>\nCompare tenths:<br \/>\n7 &lt; 8<br \/>\n0.75 &lt; \\(\\frac{7}{8}\\)<\/p>\n<p>Question 4.<br \/>\n7 \\(\\frac{1}{8}\\) _____ 7.025<\/p>\n<p>Answer:<br \/>\n7 \\(\\frac{1}{8}\\) &gt; 7.025<\/p>\n<p>Explanation:<br \/>\nWrite the decimal form of 7 \\(\\frac{1}{8}\\) = 7.125<br \/>\nCompare tenths:<br \/>\n1 &gt; 0<br \/>\n7 \\(\\frac{1}{8}\\) &gt; 7.025<\/p>\n<p><strong>Order from least to greatest.<\/strong><\/p>\n<p>Question 5.<br \/>\n\\(\\frac{7}{15}\\), 0.75, \\(\\frac{5}{6}\\)<br \/>\nType below:<br \/>\n__________<\/p>\n<p>Answer:<br \/>\n\\(\\frac{7}{15}\\), 0.75, \\(\\frac{5}{6}\\)<\/p>\n<p>Explanation:<br \/>\nWrite the decimal form of \\(\\frac{7}{15}\\) = 0.466<br \/>\n0.75<br \/>\nWrite the decimal form of \\(\\frac{5}{6}\\) = 0.833<br \/>\nOrder from least to greatest: \\(\\frac{7}{15}\\), 0.75, \\(\\frac{5}{6}\\)<\/p>\n<p>Question 6.<br \/>\n0.5, 0.41, \\(\\frac{3}{5}\\)<br \/>\nType below:<br \/>\n__________<\/p>\n<p>Answer:<br \/>\n0.41, 0.5, \\(\\frac{3}{5}\\)<\/p>\n<p>Explanation:<br \/>\nWrite the decimal form of \\(\\frac{3}{5}\\) = 0.6<br \/>\nCompare tenths:<br \/>\n0.41, 0.5, 0.6<br \/>\nOrder from least to greatest: 0.41, 0.5, \\(\\frac{3}{5}\\)<\/p>\n<p>Question 7.<br \/>\n3.25, 3 \\(\\frac{2}{5}\\), 3 \\(\\frac{3}{8}\\)<br \/>\nType below:<br \/>\n__________<\/p>\n<p>Answer:<br \/>\n3.25, 3 \\(\\frac{2}{5}\\), 3 \\(\\frac{3}{8}\\)<\/p>\n<p>Explanation:<br \/>\nWrite the decimal form of 3 \\(\\frac{2}{5}\\) = 3.4<br \/>\nWrite the decimal form of 3 \\(\\frac{3}{8}\\) = 3.375<br \/>\nCompare tenths:<br \/>\nOrder from least to greatest: 3.25, 3 \\(\\frac{2}{5}\\), 3 \\(\\frac{3}{8}\\)<\/p>\n<p>Question 8.<br \/>\n0.9, \\(\\frac{8}{9}\\), 0.86<br \/>\nType below:<br \/>\n__________<\/p>\n<p>Answer:<br \/>\n0.86, \\(\\frac{8}{9}\\), 0.9<\/p>\n<p>Explanation:<br \/>\nWrite the decimal form of \\(\\frac{8}{9}\\) = 0.88<br \/>\nCompare tenths:<br \/>\n0.86, 0.88, 0.9<br \/>\nOrder from least to greatest: 0.86, \\(\\frac{8}{9}\\), 0.9<\/p>\n<p><strong>Order from greatest to least.<\/strong><\/p>\n<p>Question 9.<br \/>\n0.7, \\(\\frac{7}{9}\\), \\(\\frac{7}{8}\\)<br \/>\nType below:<br \/>\n__________<\/p>\n<p>Answer:<br \/>\n\\(\\frac{7}{8}\\), \\(\\frac{7}{9}\\), 0.7<\/p>\n<p>Explanation:<br \/>\n0.7 = 7\/10<br \/>\nTo compare fractions with the same numerators, compare the denominators.<br \/>\n7\/10, 7\/9, 7\/8<br \/>\nOrder from greatest to least: 7\/8, 7\/9, 7\/10<\/p>\n<p>Question 10.<br \/>\n0.2, 0.19, \\(\\frac{3}{5}\\)<br \/>\nType below:<br \/>\n__________<\/p>\n<p>Answer:<br \/>\n\\(\\frac{3}{5}\\), 0.2, 0.19<\/p>\n<p>Explanation:<br \/>\nWrite the decimal form of \\(\\frac{3}{5}\\) = 0.6<br \/>\nCompare tenths:<br \/>\n0.6, 0.2, 0.19<br \/>\nOrder from greatest to least: \\(\\frac{3}{5}\\), 0.2, 0.19<\/p>\n<p>Question 11.<br \/>\n6\\(\\frac{1}{20}\\), 6.1, 6.07<br \/>\nType below:<br \/>\n__________<\/p>\n<p>Answer:<\/p>\n<p>Explanation:<br \/>\nWrite the decimal form of 6\\(\\frac{1}{20}\\) = 121\/20 = 6.05<br \/>\nCompare tenths:<br \/>\n6.1, 6.07, 6.05<br \/>\nOrder from greatest to least: 6.1, 6.07, 6\\(\\frac{1}{20}\\)<\/p>\n<p>Question 12.<br \/>\n2 \\(\\frac{1}{2}\\), 2.4, 2.35, 2 \\(\\frac{1}{8}\\)<br \/>\nType below:<br \/>\n__________<\/p>\n<p>Answer:<br \/>\n2 \\(\\frac{1}{2}\\), 2.4, 2.35, 2 \\(\\frac{1}{8}\\)<\/p>\n<p>Explanation:<br \/>\nWrite the decimal form of 2 \\(\\frac{1}{2}\\) = 2.5<br \/>\nWrite the decimal form of 2 \\(\\frac{1}{8}\\) = 2.125<br \/>\nCompare tenths: 2.5, 2.4, 2.35, 2.125<br \/>\nOrder from greatest to least: 2 \\(\\frac{1}{2}\\), 2.4, 2.35, 2 \\(\\frac{1}{8}\\)<\/p>\n<p>Question 13.<br \/>\nOne day it snowed 3 \\(\\frac{3}{8}\\) inches in Altoona and 3.45 inches in Bethlehem. Which city received less snow that day?<br \/>\n__________<\/p>\n<p>Answer:<br \/>\nAltoona<\/p>\n<p>Explanation:<br \/>\nOne day it snowed 3 \\(\\frac{3}{8}\\) inches in Altoona and 3.45 inches in Bethlehem.<br \/>\nWrite the decimal form of 3 \\(\\frac{3}{8}\\) = 27\/8 = 3.375<br \/>\n3.375 &lt; 3.45.<br \/>\nAltoona received less snow that day<\/p>\n<p>Question 14.<br \/>\nMalia and John each bought 2 pounds of sunflower seeds. Each ate some seeds. Malia has 1 \\(\\frac{1}{3}\\) pounds left, and John has 1 \\(\\frac{2}{5}\\) pounds left. Who ate more sunflower seeds?<br \/>\n__________<\/p>\n<p>Answer:<br \/>\nMalia<\/p>\n<p>Explanation:<br \/>\nMalia and John each bought 2 pounds of sunflower seeds. Each ate some seeds. Malia has 1 \\(\\frac{1}{3}\\) pounds left, and John has 1 \\(\\frac{2}{5}\\) pounds left.<br \/>\n2 &#8211; 1 \\(\\frac{1}{3}\\) = 0.667<br \/>\n2 &#8211; 1 \\(\\frac{2}{5}\\) = 0.6<br \/>\n0.667 &gt; 0.6<br \/>\nSo, Malia ate more sunflower seeds<\/p>\n<p>Question 15.<br \/>\nExplain how you would compare the numbers 0.4 and \\(\\frac{3}{8}\\).<br \/>\nType below:<br \/>\n__________<\/p>\n<p>Answer:<br \/>\nWrite the decimal form of \\(\\frac{3}{8}\\) = 0.375<br \/>\nCompare tenths:<br \/>\n0.4 &gt; 0.375<\/p>\n<h3><a id=\"Compare_and_Order_Fractions_and_Decimals_Lesson_Check_1_-_Page_No._80\"><\/a>Lesson Check &#8211; Page No. 80<\/h3>\n<p>Question 1.<br \/>\nAndrea has 3 \\(\\frac{7}{8}\\) yards of purple ribbon, 3.7 yards of pink ribbon, and 3 \\(\\frac{4}{5}\\) yards of blue ribbon. List the numbers in order from least to greatest.<br \/>\nType below:<br \/>\n__________<\/p>\n<p>Answer:<br \/>\nAndrea has 3 \\(\\frac{7}{8}\\) yards of purple ribbon, 3.7 yards of pink ribbon, and 3 \\(\\frac{4}{5}\\) yards of blue ribbon.<br \/>\nWrite the decimal form of 3 \\(\\frac{7}{8}\\) = 3.875<br \/>\n3.7<br \/>\nWrite the decimal form of 3 \\(\\frac{4}{5}\\) = 3.8<br \/>\nLeast to greatest : 3.7, 3 \\(\\frac{4}{5}\\), 3 \\(\\frac{7}{8}\\)<\/p>\n<p>Question 2.<br \/>\nNassim completed \\(\\frac{18}{25}\\) of the math homework. Kara completed 0.7 of it. Debbie completed \\(\\frac{5}{8}\\) of it. List the numbers in order from greatest to least.<br \/>\nType below:<br \/>\n__________<\/p>\n<p>Answer:<br \/>\n$1.39, $0.70, $0.63<\/p>\n<p>Explanation:<br \/>\nNassim completed \\(\\frac{18}{25}\\) of the math homework. Kara completed 0.7 of it. Debbie completed \\(\\frac{5}{8}\\) of it.<br \/>\nWrite the decimal form of 18\/25 = 1.39<br \/>\n0.7<br \/>\nWrite the decimal form of 5\/8 = 0.63<br \/>\nThey are now in order from greatest to least.<br \/>\nThink of the amounts as money:<br \/>\n$1.39, $0.70, $0.63<\/p>\n<p><strong>Spiral Review<\/strong><\/p>\n<p>Question 3.<br \/>\nTyler bought 3 \\(\\frac{2}{5}\\) pounds of oranges. Graph 3 \\(\\frac{2}{5}\\) on a number line and write this amount using a decimal.<br \/>\nType below:<br \/>\n__________<\/p>\n<p>Answer:<br \/>\n<img loading=\"lazy\" class=\"alignnone size-medium wp-image-6664\" src=\"https:\/\/ccssmathanswers.com\/wp-content\/uploads\/2020\/08\/grade-6-chapter-2-image-1-300x60.jpg\" alt=\"grade 6 chapter 2 image 1\" width=\"300\" height=\"60\" srcset=\"https:\/\/bigideasmathanswers.com\/wp-content\/uploads\/2020\/08\/grade-6-chapter-2-image-1-300x60.jpg 300w, https:\/\/bigideasmathanswers.com\/wp-content\/uploads\/2020\/08\/grade-6-chapter-2-image-1.jpg 698w\" sizes=\"(max-width: 300px) 100vw, 300px\" \/><br \/>\nTyler bought 3 \\(\\frac{2}{5}\\) pounds of oranges.<br \/>\nDecimal Form: 17\/5 = 3.4<\/p>\n<p>Question 4.<br \/>\nAt the factory, a baseball card is placed in every 9th package of cereal. A football card is placed in every 25th package of the cereal. What is the first package that gets both a baseball card and a football card?<br \/>\nType below:<br \/>\n__________<\/p>\n<p>Answer:<br \/>\n225th package<\/p>\n<p>Explanation:<br \/>\nLook for the first number where both 25 and 9 are a factor of.<br \/>\n25 x 1 = 25 which isn&#8217;t a factor of 9, so it won&#8217;t be 25.<br \/>\n25 x 2 = 50, which isn&#8217;t a factor of 9.<br \/>\n75 is not a factor of 9. (you know because you don&#8217;t get a whole number when you divide 75 into 9.)<br \/>\n100 is not a factor of 9, nor is 125, 150, 175, or 200.<br \/>\nHowever, 225 is a factor of both 25 and 9. This makes sense because 25 x 9 is 225.<br \/>\nThis means that the first package with both will be the 225th package.<\/p>\n<p>Question 5.<br \/>\n$15.30 is divided among 15 students. How much does each student receive?<br \/>\n$ _____<\/p>\n<p>Answer:<br \/>\n$1.02<\/p>\n<p>Explanation:<br \/>\n$15.30 is divided among 15 students.<br \/>\n$15.30\/15 = $1.02<br \/>\neach student receive $1.02<\/p>\n<p>Question 6.<br \/>\nCarrie buys 4.16 pounds of apples for $5.20. How much does 1 pound cost?<br \/>\n$ _____<\/p>\n<p>Answer:<br \/>\n$1.25<\/p>\n<p>Explanation:<br \/>\nCarrie buys 4.16 pounds of apples for $5.20.<br \/>\n$5.20\/4.16 = $1.25<br \/>\n1 pound cost = $1.25<\/p>\n<h3><a id=\"Multiply_Fractions_-_Page_No._83\"><\/a>Share and Show &#8211; Page No. 83<\/h3>\n<p><strong>Find the product. Write it in simplest form.<\/strong><\/p>\n<p>Question 1.<br \/>\n6 \u00d7 \\(\\frac{3}{8}\\)<br \/>\n\\(\\frac{\u25a1}{\u25a1}\\)<\/p>\n<p>Answer:<br \/>\n\\(\\frac{9}{4}\\)<\/p>\n<p>Explanation:<br \/>\n\\(\\frac{6 \u00d7 3}{1 \u00d7 8}\\)<br \/>\n\\(\\frac{18}{8}\\)<br \/>\nSimplify using the GCF.<br \/>\nThe GCF of 18 and 8 is 2.<br \/>\nDivide the numerator and the denominator by 2.<br \/>\n\\(\\frac{18 \u00f7 2}{8 \u00f7 2}\\) = \\(\\frac{9}{4}\\)<\/p>\n<p>Question 2.<br \/>\n\\(\\frac{3}{8}\\) \u00d7 \\(\\frac{8}{9}\\)<br \/>\n\\(\\frac{\u25a1}{\u25a1}\\)<\/p>\n<p>Answer:<br \/>\n\\(\\frac{1}{3}\\)<\/p>\n<p>Explanation:<br \/>\nMultiply the numerators and Multiply the denominators.<br \/>\n\\(\\frac{3 \u00d7 8}{8 \u00d7 9}\\) = \\(\\frac{24}{72}\\)<br \/>\nSimplify using the GCF.<br \/>\nThe GCF of 24 and 72 is 24.<br \/>\nDivide the numerator and the denominator by 24.<br \/>\n\\(\\frac{24 \u00f7 24}{72 \u00f7 24}\\) = \\(\\frac{1}{3}\\)<\/p>\n<p>Question 3.<br \/>\nSam and his friends ate 3 \\(\\frac{3}{4}\\) bags of fruit snacks. If each bag contained 2 \\(\\frac{1}{2}\\) ounces, how many ounces of fruit snacks did Sam and his friends eat?<br \/>\n\\(\\frac{\u25a1}{\u25a1}\\)<\/p>\n<p>Answer:<br \/>\n\\(\\frac{75}{8}\\) ounces<\/p>\n<p>Explanation:<br \/>\nSam and his friends ate 3 \\(\\frac{3}{4}\\) bags of fruit snacks. If each bag contained 2 \\(\\frac{1}{2}\\) ounces<br \/>\n3 \\(\\frac{3}{4}\\) x 2 \\(\\frac{1}{2}\\)<br \/>\n\\(\\frac{15}{4}\\) x \\(\\frac{5}{2}\\)<br \/>\n\\(\\frac{15 x\u00a05}{4 x 2}\\) = \\(\\frac{75}{8}\\)<\/p>\n<p><strong>Attend to Precision Algebra Evaluate using the order of operations.<\/strong><\/p>\n<p><strong>Write the answer in simplest form.<\/strong><\/p>\n<p>Question 4.<br \/>\n\\(\\left(\\frac{3}{4}-\\frac{1}{2}\\right) \\times \\frac{3}{5}\\)<br \/>\n\\(\\frac{\u25a1}{\u25a1}\\)<\/p>\n<p>Answer:<br \/>\n\\(\\frac{3}{20}\\)<\/p>\n<p>Explanation:<br \/>\n\\(\\left(\\frac{3}{4}-\\frac{1}{2}\\right) \\times \\frac{3}{5}\\)<br \/>\nPerform operations in parentheses.<br \/>\n\\(\\frac{3}{4}\\) &#8211; \\(\\frac{1}{2}\\) = \\(\\frac{1}{4}\\)<br \/>\n\\(\\frac{1}{4}\\) x \\(\\frac{3}{5}\\) = \\(\\frac{1 x 3}{4 x 5}\\) = \\(\\frac{3}{20}\\)<\/p>\n<p>Question 5.<br \/>\n\\(\\frac{1}{3}+\\frac{4}{9} \\times 12\\)<br \/>\n\\(\\frac{\u25a1}{\u25a1}\\)<\/p>\n<p>Answer:<br \/>\n\\(\\frac{28}{3}\\)<\/p>\n<p>Explanation:<br \/>\n\\(\\frac{1}{3}\\) + \\(\\frac{4}{9}\\) = \\(\\frac{7}{9}\\)<br \/>\n\\(\\frac{7 x 12}{9 x 1}\\) = \\(\\frac{84}{9}\\)<br \/>\nSimplify using the GCF.<br \/>\nThe GCF of 84 and 9 is 3.<br \/>\nDivide the numerator and the denominator by 3.<br \/>\n\\(\\frac{84 \u00f7 3}{9 \u00f7 3}\\) = \\(\\frac{28}{3}\\)<\/p>\n<p>Question 6.<br \/>\n\\(\\frac{5}{8} \\times \\frac{7}{10}-\\frac{1}{4}\\)<br \/>\n\\(\\frac{\u25a1}{\u25a1}\\)<\/p>\n<p>Answer:<br \/>\n\\(\\frac{11}{16}\\)<\/p>\n<p>Explanation:<br \/>\n\\(\\frac{5 x 7}{8 x 10}\\) = \\(\\frac{35}{80}\\)<br \/>\n\\(\\frac{35}{80}\\) &#8211; \\(\\frac{1}{4}\\) = \\(\\frac{11}{16}\\)<\/p>\n<p>Question 7.<br \/>\n3 \u00d7 (\\(\\frac{5}{18}\\) + \\(\\frac{1}{6}\\)) + \\(\\frac{2}{5}\\)<br \/>\n\\(\\frac{\u25a1}{\u25a1}\\)<\/p>\n<p>Answer:<br \/>\n\\(\\frac{38}{15}\\)<\/p>\n<p>Explanation:<br \/>\n3 x \\(\\frac{4}{9}\\) + \\(\\frac{2}{5}\\)<br \/>\n3 x \\(\\frac{38}{45}\\) = \\(\\frac{38}{15}\\)<\/p>\n<p><strong>On Your Own<\/strong><\/p>\n<p><strong>Practice: Copy and Solve Find the product. Write it in simplest form.<\/strong><\/p>\n<p>Question 8.<br \/>\n\\(1 \\frac{2}{3} \\times 2 \\frac{5}{8}\\)<br \/>\n\\(\\frac{\u25a1}{\u25a1}\\)<\/p>\n<p>Answer:<br \/>\n\\(\\frac{35}{8}\\)<\/p>\n<p>Explanation:<br \/>\n1 \\(\\frac{2}{3}\\) = \\(\\frac{5}{3}\\)<br \/>\n2 \\(\\frac{5}{8}\\) = \\(\\frac{21}{8}\\)<br \/>\n\\(\\frac{5 \u00d7 21}{3 \u00d7 8}\\) = \\(\\frac{105}{24}\\)<br \/>\nSimplify using the GCF<br \/>\nThe GCF of 105 and 24 is 3.<br \/>\nDivide the numerator and the denominator by 3.<br \/>\n\\(\\frac{105 \u00f7 3}{24 \u00f7 3}\\) = \\(\\frac{35}{8}\\)<\/p>\n<p>Question 9.<br \/>\n\\(\\frac{4}{9} \\times \\frac{4}{5}\\)<br \/>\n\\(\\frac{\u25a1}{\u25a1}\\)<\/p>\n<p>Answer:<br \/>\n\\(\\frac{16}{45}\\)<\/p>\n<p>Explanation:<br \/>\n\\(\\frac{4 \u00d7 4}{9 \u00d7 5}\\) = \\(\\frac{16}{45}\\)<\/p>\n<p>Question 10.<br \/>\n\\(\\frac{1}{6} \\times \\frac{2}{3}\\)<br \/>\n\\(\\frac{\u25a1}{\u25a1}\\)<\/p>\n<p>Answer:<br \/>\n\\(\\frac{1}{9}\\)<\/p>\n<p>Explanation:<br \/>\n\\(\\frac{1 \u00d7 2}{6 \u00d7 3}\\) = \\(\\frac{2}{18}\\)<br \/>\nSimplify using the GCF<br \/>\nThe GCF of 2 and 18 is 2.<br \/>\nDivide the numerator and the denominator by 2.<br \/>\n\\(\\frac{2 \u00f7 2}{18 \u00f7 2}\\) = \\(\\frac{1}{9}\\)<\/p>\n<p>Question 11.<br \/>\n\\(4 \\frac{1}{7} \\times 3 \\frac{1}{9}\\)<br \/>\n\\(\\frac{\u25a1}{\u25a1}\\)<\/p>\n<p>Answer:<br \/>\n\\(\\frac{116}{7}\\)<\/p>\n<p>Explanation:<br \/>\n4\\(\\frac{1}{7}\\) = \\(\\frac{29}{7}\\)<br \/>\n3\\(\\frac{1}{9}\\) = \\(\\frac{28}{9}\\)<br \/>\n\\(\\frac{29 \u00d7 28}{7 \u00d7 9}\\) = \\(\\frac{812}{63}\\)<br \/>\nSimplify using the GCF<br \/>\nThe GCF of 812 and 63 is 7.<br \/>\nDivide the numerator and the denominator by 7.<br \/>\n\\(\\frac{812 \u00f7 7}{63 \u00f7 7}\\) = \\(\\frac{116}{7}\\)<\/p>\n<p>Question 12.<br \/>\n\\(\\frac{5}{6}\\) of the 90 pets in the pet show are cats. \\(\\frac{4}{5}\\) of the cats are calico cats. What fraction of the pets are calico cats? How many of the pets are calico cats?<br \/>\nType below:<br \/>\n__________<\/p>\n<p>Answer:<br \/>\n60 calico cats<\/p>\n<p>Explanation:<br \/>\n5\/6 x 90 = 450\/6 = 150\/2<br \/>\n150\/2 x 4\/5 = 60<\/p>\n<p>Question 13.<br \/>\nFive cats each ate \\(\\frac{1}{4}\\) cup of cat food. Four other cats each ate \\(\\frac{1}{3}\\) cup of cat food. How much food did the nine cats eat?<br \/>\nType below:<br \/>\n__________<\/p>\n<p>Answer:<br \/>\n\\(\\frac{31}{12}\\)<\/p>\n<p>Explanation:<br \/>\n5 x 1\/4 = 5\/4<br \/>\n4 x 1\/3 = 4\/3<br \/>\n5\/4 + 4\/3 = 31\/12<\/p>\n<p><strong>Attend to Precision Algebra Evaluate using the order of operations.<\/strong><\/p>\n<p><strong>Write the answer in simplest form.<\/strong><\/p>\n<p>Question 14.<br \/>\n\\(\\frac{1}{4} \\times\\left(\\frac{3}{9}+5\\right)\\)<br \/>\n\\(\\frac{\u25a1}{\u25a1}\\)<\/p>\n<p>Answer:<br \/>\n\\(\\frac{4}{3}\\)<\/p>\n<p>Explanation:<br \/>\n3\/9 + 5 = 16\/3<br \/>\n1\/4 x 16\/3<br \/>\n1 x 16 = 16<br \/>\n4 x 3 = 12<br \/>\n16\/12<br \/>\nSimplify using the GCF<br \/>\nThe GCF of 16 and 12 is 4.<br \/>\nDivide the numerator and the denominator by 4.<br \/>\n\\(\\frac{16 \u00f7 4}{12\u00f7 4}\\) = \\(\\frac{4}{3}\\)<\/p>\n<p>Question 15.<br \/>\n\\(\\frac{9}{10}-\\frac{3}{5} \\times \\frac{1}{2}\\)<br \/>\n\\(\\frac{\u25a1}{\u25a1}\\)<\/p>\n<p>Answer:<br \/>\n\\(\\frac{3}{5}\\)<\/p>\n<p>Explanation:<br \/>\n3\/5 x 1\/2 = 3\/10<br \/>\n9\/10 &#8211; 3\/10 = 6\/10<br \/>\nSimplify using the GCF<br \/>\nThe GCF of 6 and 10 is 2.<br \/>\nDivide the numerator and the denominator by 2.<br \/>\n\\(\\frac{6 \u00f7 2}{10 \u00f7 2}\\) = \\(\\frac{3}{5}\\)<\/p>\n<p>Question 16.<br \/>\n\\(\\frac{4}{5}+\\left(\\frac{1}{2}-\\frac{3}{7}\\right) \\times 2\\)<br \/>\n\\(\\frac{\u25a1}{\u25a1}\\)<\/p>\n<p>Answer:<br \/>\n\\(\\frac{33}{35}\\)<\/p>\n<p>Explanation:<br \/>\n1\/2 &#8211; 3\/7 = 1\/14<br \/>\n1\/14 x 2 = 1\/7<br \/>\n4\/5 + 1\/7 = 33\/35<\/p>\n<p>Question 17.<br \/>\n\\(15 \\times \\frac{3}{10}+\\frac{7}{8}\\)<br \/>\n\\(\\frac{\u25a1}{\u25a1}\\)<\/p>\n<p>Answer:<br \/>\n\\(\\frac{141}{8}\\)<\/p>\n<p>Explanation:<br \/>\n3\/10 + 7\/8 = 47\/40<br \/>\n15 x 47\/40 = 141\/8<br \/>\n\\(\\frac{141}{8}\\)<\/p>\n<h3><a id=\"Multiply_Fractions_-_Page_No._84\"><\/a>Page No. 84<\/h3>\n<p>Question 18.<br \/>\nWrite and solve a word problem for the expression \\(\\frac{1}{4} \\times \\frac{2}{3}\\). Show your work.<br \/>\nType below:<br \/>\n__________<\/p>\n<p>Answer:<br \/>\n\\(\\frac{1}{6}\\)<\/p>\n<p>Explanation:<br \/>\n\\(\\frac{1}{4} \\times \\frac{2}{3}\\) = \\(\\frac{1 X 2}{4 X 3}\\) = \\(\\frac{2}{12}\\)<br \/>\nSimplify using the GCF<br \/>\nThe GCF of 2 and 12 is 2.<br \/>\nDivide the numerator and the denominator by 2.<br \/>\n\\(\\frac{2 \u00f7 2}{12 \u00f7 2}\\) = \\(\\frac{1}{6}\\)<\/p>\n<p>Question 19.<br \/>\nMichelle has a recipe that asks for 2 \\(\\frac{1}{2}\\) cups of vegetable oil. She wants to use \\(\\frac{2}{3}\\) that amount of oil and use applesauce to replace the rest. How much applesauce will she use?<br \/>\nType below:<br \/>\n__________<\/p>\n<p>Answer:<br \/>\n\\(\\frac{10}{6}\\)<\/p>\n<p>Explanation:<br \/>\n2 1\/2 * 2\/3 = 5\/2 * 2\/3 = 10\/6 She will use 10\/6 or 1 2\/3 cups of vegetable oil<\/p>\n<p>Question 20.<br \/>\nCara\u2019s muffin recipe asks for 1 \\(\\frac{1}{2}\\) cups of flour for the muffins and \\(\\frac{1}{4}\\) cup of flour for the topping. If she makes \\(\\frac{1}{2}\\) of the original recipe, how much flour will she use for the muffins and topping?<br \/>\nType below:<br \/>\n__________<\/p>\n<p>Answer:<br \/>\nCara will use 1\\(\\frac{1}{8}\\) cups of flour.<\/p>\n<p>Explanation:<br \/>\nFor first we will find how many cups of flours need to makes the original recipe. Cara uses 1 1\/2 cups of flour for the muffins and 1\/4 cup off flour for the topping.<br \/>\nSo, 1 1\/2 + 1\/4 cups of flour to make the original recipe.<br \/>\n1 1\/2 = 3\/2<br \/>\n3\/2 + 1\/4 = 7\/4<br \/>\nTo make the original recipe Cara needs 7\/4 cups of flour.<br \/>\nIf she makes \\(\\frac{1}{2}\\) of the original recipe, then<br \/>\n7\/4 x 1\/2 = 7\/8 = 1 1\/8<br \/>\nCara will use 1 1\/8 cups of flour.<\/p>\n<h3><a id=\"Multiply_Fractions_Lesson_Check_-_Page_No._85\"><\/a>Multiply Fractions &#8211; Page No. 85<\/h3>\n<p><strong>Find the product. Write it in simplest form.<\/strong><\/p>\n<p>Question 1.<br \/>\n\\(\\frac{4}{5} \\times \\frac{7}{8}\\)<br \/>\n\\(\\frac{\u25a1}{\u25a1}\\)<\/p>\n<p>Answer:<br \/>\n\\(\\frac{7}{10}\\)<\/p>\n<p>Explanation:<br \/>\nMultiply the numerators and Multiply the denominators.<br \/>\n\\(\\frac{4 \u00d7 7}{5 \u00d7 8}\\) = \\(\\frac{28}{40}\\)<br \/>\nSimplify using the GCF.<br \/>\nThe GCF of 28 and 40 is 4.<br \/>\nDivide the numerator and the denominator by 4.<br \/>\n\\(\\frac{28 \u00f7 4}{40 \u00f7 4}\\) = \\(\\frac{7}{10}\\)<\/p>\n<p>Question 2.<br \/>\n\\(\\frac{1}{8} \\times 20\\)<br \/>\n\\(\\frac{\u25a1}{\u25a1}\\)<\/p>\n<p>Answer:<br \/>\n\\(\\frac{5}{2}\\)<\/p>\n<p>Explanation:<br \/>\n\\(\\frac{1 \u00d7 20}{1 \u00d7 8}\\)<br \/>\n\\(\\frac{20}{8}\\)<br \/>\nSimplify using the GCF.<br \/>\nThe GCF of 20 and 8 is 4.<br \/>\nDivide the numerator and the denominator by 4.<br \/>\n\\(\\frac{20 \u00f7 4}{8 \u00f7 4}\\) = \\(\\frac{5}{2}\\)<\/p>\n<p>Question 3.<br \/>\n\\(\\frac{4}{5} \\times \\frac{3}{8}\\)<br \/>\n\\(\\frac{\u25a1}{\u25a1}\\)<\/p>\n<p>Answer:<br \/>\n\\(\\frac{3}{10}\\)<\/p>\n<p>Explanation:<br \/>\nMultiply the numerators and Multiply the denominators.<br \/>\n\\(\\frac{4 \u00d7 3}{5 \u00d7 8}\\) = \\(\\frac{12}{40}\\)<br \/>\nSimplify using the GCF.<br \/>\nThe GCF of 12 and 40 is 4.<br \/>\nDivide the numerator and the denominator by 4.<br \/>\n\\(\\frac{12 \u00f7 4}{40 \u00f7 4}\\) = \\(\\frac{3}{10}\\)<\/p>\n<p>Question 4.<br \/>\n\\(1 \\frac{1}{8} \\times \\frac{1}{9}\\)<br \/>\n\\(\\frac{\u25a1}{\u25a1}\\)<\/p>\n<p>Answer:<br \/>\n\\(\\frac{1}{8}\\)<\/p>\n<p>Explanation:<br \/>\n1\\(\\frac{1}{8}\\) = \\(\\frac{9}{8}\\)<br \/>\nMultiply the numerators and Multiply the denominators.<br \/>\n\\(\\frac{9 \u00d7 1}{8 \u00d7 9}\\) = \\(\\frac{9}{72}\\)<br \/>\nSimplify using the GCF.<br \/>\nThe GCF of 9 and 72 is 9.<br \/>\nDivide the numerator and the denominator by 9.<br \/>\n\\(\\frac{9 \u00f7 9}{72 \u00f7 9}\\) = \\(\\frac{1}{8}\\)<\/p>\n<p>Question 5.<br \/>\n\\(\\frac{3}{4} \\times \\frac{1}{3} \\times \\frac{2}{5}\\)<br \/>\n\\(\\frac{\u25a1}{\u25a1}\\)<\/p>\n<p>Answer:<br \/>\n\\(\\frac{1}{10}\\)<\/p>\n<p>Explanation:<br \/>\nMultiply the numerators and Multiply the denominators.<br \/>\n\\(\\frac{3 \u00d7 1 \u00d7 2}{4 \u00d7 3 \u00d7 5}\\) = \\(\\frac{6}{60}\\)<br \/>\nSimplify using the GCF.<br \/>\nThe GCF of 6 and 60 is 6.<br \/>\nDivide the numerator and the denominator by 6.<br \/>\n\\(\\frac{6 \u00f7 6}{60 \u00f7 6}\\) = \\(\\frac{1}{10}\\)<\/p>\n<p>Question 6.<br \/>\nKaren raked \\(\\frac{3}{5}\\) of the yard. Minni raked \\(\\frac{1}{3}\\) of the amount Karen raked. How much of the yard did Minni rake?<br \/>\n\\(\\frac{\u25a1}{\u25a1}\\)<\/p>\n<p>Answer:<br \/>\n\\(\\frac{1}{3}\\)<\/p>\n<p>Explanation:<br \/>\nMinni raked 1\/5 of the yard.<br \/>\nSo, minni raked 3\/5 of 1\/3 means 3\/5 x 1\/3<br \/>\nMultiply the numerators and Multiply the denominators.<br \/>\n\\(\\frac{3 \u00d7 1}{5 \u00d7 3}\\) = \\(\\frac{3}{15}\\)<br \/>\nSimplify using the GCF.<br \/>\nThe GCF of 3 and 15 is 3.<br \/>\nDivide the numerator and the denominator by 3.<br \/>\n\\(\\frac{3 \u00f7 3}{15 \u00f7 3}\\) = \\(\\frac{1}{3}\\)<\/p>\n<p>Question 7.<br \/>\n\\(\\frac{3}{8}\\) of the pets in the pet show are dogs. \\(\\frac{2}{3}\\) of the dogs have long hair. What fraction of the pets are dogs with long hair?<br \/>\n\\(\\frac{\u25a1}{\u25a1}\\)<\/p>\n<p>Answer:<br \/>\n\\(\\frac{1}{4}\\) are dogs with long hair<\/p>\n<p>Explanation:<br \/>\n\\(\\frac{3}{8}\\) of the pets in the pet show are dogs. \\(\\frac{2}{3}\\) of the dogs have long hair.<br \/>\n\\(\\frac{3}{8}\\) of \\(\\frac{2}{3}\\) = \\(\\frac{3 \u00d7 2}{8 \u00d7 3}\\) = \\(\\frac{6}{24}\\)<br \/>\nThe GCF of 6 and 24 is 6.<br \/>\nDivide the numerator and the denominator by 6.<br \/>\n\\(\\frac{6 \u00f7 6}{24 \u00f7 6}\\) = \\(\\frac{1}{4}\\)<br \/>\n\\(\\frac{1}{4}\\) are dogs with long hair<\/p>\n<p><strong>Evaluate using the order of operations.<\/strong><\/p>\n<p>Question 8.<br \/>\n\\(\\left(\\frac{1}{2}+\\frac{3}{8}\\right) \\times 8\\)<br \/>\n______<\/p>\n<p>Answer:<br \/>\n7<\/p>\n<p>Explanation:<br \/>\n1\/2 + 3\/8 = 7\/8<br \/>\n7\/8 \u00d7 8 = 7<\/p>\n<p>Question 9.<br \/>\n\\(\\frac{3}{4} \\times\\left(1-\\frac{1}{9}\\right)\\)<br \/>\n\\(\\frac{\u25a1}{\u25a1}\\)<\/p>\n<p>Answer:<br \/>\n\\(\\frac{2}{3}\\)<\/p>\n<p>Explanation:<br \/>\n1 &#8211; 1\/9 = 8\/9<br \/>\n3\/4 \u00d7 8\/9 = 24\/36<br \/>\nThe GCF of 24 and 36 is 12.<br \/>\nDivide the numerator and the denominator by 12.<br \/>\n\\(\\frac{24 \u00f7 12}{36 \u00f7 12}\\) = \\(\\frac{2}{3}\\)<\/p>\n<p>Question 10.<br \/>\n\\(4 \\times \\frac{1}{8} \\times \\frac{3}{10}\\)<br \/>\n\\(\\frac{\u25a1}{\u25a1}\\)<\/p>\n<p>Answer:<br \/>\n\\(\\frac{3}{20}\\)<\/p>\n<p>Explanation:<br \/>\nMultiply the numerators and Multiply the denominators.<br \/>\n\\(\\frac{4 \u00d7 1 \u00d7 3}{1 \u00d7 8 \u00d7 10}\\) = \\(\\frac{12}{80}\\)<br \/>\nSimplify using the GCF.<br \/>\nThe GCF of 12 and 80 is 4.<br \/>\nDivide the numerator and the denominator by 4.<br \/>\n\\(\\frac{12 \u00f7 4}{80 \u00f7 4}\\) = \\(\\frac{3}{20}\\)<\/p>\n<p>Question 11.<br \/>\n\\(6 \\times\\left(\\frac{4}{5}+\\frac{2}{10}\\right) \\times \\frac{2}{3}\\)<br \/>\n______<\/p>\n<p>Answer:<br \/>\n4<\/p>\n<p>Explanation:<br \/>\n4\/5 + 2\/10 = 1<br \/>\n6 \u00d7 1 \u00d7 2\/3 = 12\/3<br \/>\nThe GCF of 12 and 3 is 4.<br \/>\nDivide the numerator and the denominator by 3.<br \/>\n\\(\\frac{12 \u00f7 3}{3 \u00f7 3}\\) = \\(\\frac{4}{1}\\) = 4<\/p>\n<p><strong>Problem Solving<\/strong><\/p>\n<p>Question 12.<br \/>\nJason ran \\(\\frac{5}{7}\\) of the distance around the school track. Sara ran \\(\\frac{4}{5}\\) of Jason\u2019s distance. What fraction of the total distance around the track did Sara run?<br \/>\n\\(\\frac{\u25a1}{\u25a1}\\)<\/p>\n<p>Answer:<br \/>\n\\(\\frac{4}{7}\\)<\/p>\n<p>Explanation:<br \/>\nJason ran \\(\\frac{5}{7}\\) of the distance around the school track. Sara ran \\(\\frac{4}{5}\\) of Jason\u2019s distance.<br \/>\n\\(\\frac{5}{7}\\) \u00d7 \\(\\frac{4}{5}\\) = 20\/35<br \/>\nThe GCF of 20 and 35 is 5.<br \/>\nDivide the numerator and the denominator by 5.<br \/>\n\\(\\frac{20 \u00f7 5}{35 \u00f7 5}\\) = \\(\\frac{4}{7}\\)<\/p>\n<p>Question 13.<br \/>\nA group of students attend a math club. Half of the students are boys and \\(\\frac{4}{9}\\) of the boys have brown eyes. What fraction of the group are boys with brown eyes?<br \/>\n\\(\\frac{\u25a1}{\u25a1}\\)<\/p>\n<p>Answer:<br \/>\n\\(\\frac{2}{9}\\) group are boys with brown eyes<\/p>\n<p>Explanation:<br \/>\nA group of students attend a math club. Half of the students are boys and \\(\\frac{4}{9}\\) of the boys have brown eyes.<br \/>\n\\(\\frac{4}{9}\\) \u00d7 \\(\\frac{1}{2}\\) = 4\/18 = 2\/9<br \/>\n2\/9 group are boys with brown eyes<\/p>\n<p>Question 14.<br \/>\nWrite and solve a word problem that involves multiplying by a fraction.<br \/>\nType below:<br \/>\n__________<\/p>\n<p>Answer:<br \/>\nA group of students attends a math club. Half of the students are boys and \\(\\frac{6}{9}\\) of the boys have brown eyes. What fraction of the group are boys with brown eyes?<br \/>\n\\(\\frac{\u25a1}{\u25a1}\\)<br \/>\nAnswer:<br \/>\nA group of students attends a math club. Half of the students are boys and \\(\\frac{6}{9}\\) of the boys have brown eyes.<br \/>\n\\(\\frac{6}{9}\\) \u00d7 \\(\\frac{1}{2}\\) = 6\/18 = 1\/3<br \/>\n1\/3 group are boys with brown eyes.<\/p>\n<h3><a id=\"Multiply_Fractions_Lesson_Check_1_-_Page_No._86\"><\/a>Lesson Check &#8211; Page No. 86<\/h3>\n<p>Question 1.<br \/>\nVeronica\u2019s mom left \\(\\frac{3}{4}\\) of a cake on the table. Her brothers ate \\(\\frac{1}{2}\\) of it. What fraction of the cake did they eat?<br \/>\n\\(\\frac{\u25a1}{\u25a1}\\)<\/p>\n<p>Answer:<br \/>\n\\(\\frac{2}{4}\\)<\/p>\n<p>Explanation:<br \/>\nVeronica\u2019s mom left \\(\\frac{3}{4}\\) of a cake on the table. Her brothers ate \\(\\frac{1}{2}\\) of it.<br \/>\nSince the fraction of the eaten cake is 1\/2, you can multiply the numerator and denominator by and get an equivalent fraction, which is 2\/4.<\/p>\n<p>Question 2.<br \/>\nOne lap around the school track is \\(\\frac{5}{8}\\) mile. Carin ran 3 \\(\\frac{1}{2}\\) laps. How far did she run?<br \/>\n_____ \\(\\frac{\u25a1}{\u25a1}\\)<\/p>\n<p>Answer:<br \/>\n2\\(\\frac{3}{16}\\)<\/p>\n<p>Explanation:<br \/>\nOne lap around the school track is \\(\\frac{5}{8}\\) mile. Carin ran 3 \\(\\frac{1}{2}\\) laps.<br \/>\n3 \\(\\frac{1}{2}\\) = \\(\\frac{7}{2}\\)<br \/>\nTherefore, the total distance covered = 7\/2 \u00d7 5\/8 = 35\/16 = 2 3\/16<\/p>\n<p><strong>Spiral Review<\/strong><\/p>\n<p>Question 3.<br \/>\nTom bought 2 \\(\\frac{5}{16}\\) pounds of peanuts and 2.45 pounds of cashews. Which did he buy more of? Explain.<br \/>\nType below:<br \/>\n__________<\/p>\n<p>Answer:<\/p>\n<p>Explanation:<br \/>\nTom bought 2 \\(\\frac{5}{16}\\) pounds of peanuts and 2.45 pounds of cashews.<br \/>\n2 \\(\\frac{5}{16}\\) = 2.3125<br \/>\n2.3125 &lt; 2.45<br \/>\nHe buys more cashews.<\/p>\n<p>Question 4.<br \/>\nEve has 24 stamps each valued at $24.75. What is the total value of her stamps?<br \/>\n$ _____<\/p>\n<p>Answer:<br \/>\n$594<\/p>\n<p>Explanation:<br \/>\nEve has 24 stamps each valued at $24.75.<br \/>\n24 x $24.75 = $594<\/p>\n<p>Question 5.<br \/>\nNaomi went on a 6.5-mile hike. In the morning, she hiked 1.75 miles, rested, and then hiked 2.4 more miles. She completed the hike in the afternoon. How much farther did she hike in the morning than in the afternoon?<br \/>\n_____ miles<\/p>\n<p>Answer:<br \/>\nNaomi went on a 6.5-mile hike. In the morning, she hiked 1.75 miles, rested, and then hiked 2.4 more miles. She completed the hike in the afternoon.<br \/>\nTo find how many miles she walked in the afternoon you just subtract the morning miles 4.15 from the total miles 6.5.<br \/>\n6.5 &#8211; 4.15\u00a0 = 2.35<br \/>\nTo find how many more miles she walked in the morning you just subtract the morning from the afternoon 4.15 &#8211; 2.35=1.8 miles.<br \/>\nShe hiked 1.8 more miles in the morning<\/p>\n<p>Question 6.<br \/>\nA bookstore owner has 48 science fiction books and 30 mysteries he wants to sell quickly. He will make discount packages with one type of book in each. He wants the most books possible in each package, but all packages must contain the same number of books. How many packages can he make? How many packages of each type of book does he have?<br \/>\nType below:<br \/>\n__________<\/p>\n<p>Answer:<br \/>\n18 packages<\/p>\n<p>Explanation:<br \/>\nThe bookstore owner can make 18 possible packages<br \/>\n48 &#8211; 30 = 18 packages<\/p>\n<h3><a id=\"Simplify_Factors_-_Page_No._89\"><\/a>Share and Show &#8211; Page No. 89<\/h3>\n<p><strong>Find the product. Simplify before multiplying.<\/strong><\/p>\n<p>Question 1.<br \/>\n\\(\\frac{5}{6} \\times \\frac{3}{10}\\)<br \/>\n\\(\\frac{\u25a1}{\u25a1}\\)<\/p>\n<p>Answer:<br \/>\n\\(\\frac{1}{4}\\)<\/p>\n<p>Explanation:<br \/>\n\\(\\frac{5}{6} \\times \\frac{3}{10}\\)<br \/>\nMultiply the numerators and Multiply the denominators.<br \/>\n\\(\\frac{5 \u00d7 3}{6 \u00d7 10}\\) = \\(\\frac{15}{60}\\)<br \/>\nSimplify using the GCF.<br \/>\nThe GCF of 15 and 60 is 15.<br \/>\nDivide the numerator and the denominator by 15.<br \/>\n\\(\\frac{15 \u00f7 15}{60 \u00f7 15}\\) = \\(\\frac{1}{4}\\)<\/p>\n<p>Question 2.<br \/>\n\\(\\frac{3}{4} \\times \\frac{5}{9}\\)<br \/>\n\\(\\frac{\u25a1}{\u25a1}\\)<\/p>\n<p>Answer:<br \/>\n\\(\\frac{5}{12}\\)<\/p>\n<p>Explanation:<br \/>\n\\(\\frac{3}{4} \\times \\frac{5}{9}\\)<br \/>\nMultiply the numerators and Multiply the denominators.<br \/>\n\\(\\frac{3 \u00d7 5}{4 \u00d7 9}\\) = \\(\\frac{15}{36}\\)<br \/>\nSimplify using the GCF.<br \/>\nThe GCF of 15 and 36 is 3.<br \/>\nDivide the numerator and the denominator by 3.<br \/>\n\\(\\frac{15 \u00f7 3}{36 \u00f7 3}\\) = \\(\\frac{5}{12}\\)<\/p>\n<p>Question 3.<br \/>\n\\(\\frac{2}{3} \\times \\frac{9}{10}\\)<br \/>\n\\(\\frac{\u25a1}{\u25a1}\\)<\/p>\n<p>Answer:<br \/>\n\\(\\frac{3}{5}\\)<\/p>\n<p>Explanation:<br \/>\n\\(\\frac{2}{3} \\times \\frac{9}{10}\\)<br \/>\nMultiply the numerators and Multiply the denominators.<br \/>\n\\(\\frac{2 \u00d7 9}{3 \u00d7 10}\\) = \\(\\frac{18}{30}\\)<br \/>\nSimplify using the GCF.<br \/>\nThe GCF of 18 and 30 is 6.<br \/>\nDivide the numerator and the denominator by 6.<br \/>\n\\(\\frac{18 \u00f7 6}{30 \u00f7 6}\\) = \\(\\frac{3}{5}\\)<\/p>\n<p>Question 4.<br \/>\nAfter a picnic, \\(\\frac{5}{12}\\) of the cornbread is left over. Val eats \\(\\frac{3}{5}\\) of the leftover cornbread. What fraction of the cornbread does Val eat?<br \/>\n\\(\\frac{\u25a1}{\u25a1}\\)<\/p>\n<p>Answer:<br \/>\n\\(\\frac{1}{4}\\)<\/p>\n<p>Explanation:<br \/>\nAfter a picnic, \\(\\frac{5}{12}\\) of the cornbread is left over. Val eats \\(\\frac{3}{5}\\) of the leftover cornbread.<br \/>\n\\(\\frac{5}{12} \\times \\frac{3}{5}\\)<br \/>\nMultiply the numerators and Multiply the denominators.<br \/>\n\\(\\frac{5 \u00d7 3}{12 \u00d7 5}\\) = \\(\\frac{15}{60}\\)<br \/>\nSimplify using the GCF.<br \/>\nThe GCF of 15 and 60 is 15.<br \/>\nDivide the numerator and the denominator by 15.<br \/>\n\\(\\frac{15 \u00f7 15}{60 \u00f7 15}\\) = \\(\\frac{1}{4}\\)<\/p>\n<p>Question 5.<br \/>\nThe reptile house at the zoo has an iguana that is \\(\\frac{5}{6}\\) yd long. It has a Gila monster that is \\(\\frac{4}{5}\\) of the length of the iguana. How long is the Gila monster?<br \/>\n\\(\\frac{\u25a1}{\u25a1}\\)<\/p>\n<p>Answer:<br \/>\n\\(\\frac{2}{3}\\)<\/p>\n<p>Explanation:<br \/>\nThe reptile house at the zoo has an iguana that is \\(\\frac{5}{6}\\) yd long. It has a Gila monster that is \\(\\frac{4}{5}\\) of the length of the iguana.<br \/>\n\\(\\frac{5}{6} \\times \\frac{4}{5}\\)<br \/>\nMultiply the numerators and Multiply the denominators.<br \/>\n\\(\\frac{5 \u00d7 4}{6\u00d7 5}\\) = \\(\\frac{20}{30}\\)<br \/>\nSimplify using the GCF.<br \/>\nThe GCF of 20 and 30 is 10.<br \/>\nDivide the numerator and the denominator by 10.<br \/>\n\\(\\frac{20 \u00f7 10}{30 \u00f7 10}\\) = \\(\\frac{2}{3}\\)<\/p>\n<p><strong>On Your Own<\/strong><\/p>\n<p><strong>Find the product. Simplify before multiplying.<\/strong><\/p>\n<p>Question 6.<br \/>\n\\(\\frac{3}{4} \\times \\frac{1}{6}\\)<br \/>\n\\(\\frac{\u25a1}{\u25a1}\\)<\/p>\n<p>Answer:<\/p>\n<p>Explanation:<br \/>\n\\(\\frac{3}{4} \\times \\frac{1}{6}\\)<br \/>\nMultiply the numerators and Multiply the denominators.<br \/>\n\\(\\frac{3 \u00d7 1}{4 \u00d7 6}\\) = \\(\\frac{3}{24}\\)<br \/>\nSimplify using the GCF.<br \/>\nThe GCF of 3 and 24 is 3.<br \/>\nDivide the numerator and the denominator by 3.<br \/>\n\\(\\frac{3 \u00f7 3}{24 \u00f7 3}\\) = \\(\\frac{1}{8}\\)<\/p>\n<p>Question 7.<br \/>\n\\(\\frac{7}{10} \\times \\frac{2}{3}\\)<br \/>\n\\(\\frac{\u25a1}{\u25a1}\\)<\/p>\n<p>Answer:<br \/>\n\\(\\frac{7}{15}\\)<\/p>\n<p>Explanation:<br \/>\n\\(\\frac{7}{10} \\times \\frac{2}{3}\\)<br \/>\nMultiply the numerators and Multiply the denominators.<br \/>\n\\(\\frac{7 \u00d7 2}{10 \u00d7 3}\\) = \\(\\frac{14}{30}\\)<br \/>\nSimplify using the GCF.<br \/>\nThe GCF of 14 and 30 is 2.<br \/>\nDivide the numerator and the denominator by 2.<br \/>\n\\(\\frac{14 \u00f7 2}{30 \u00f7 2}\\) = \\(\\frac{7}{15}\\)<\/p>\n<p>Question 8.<br \/>\n\\(\\frac{5}{8} \\times \\frac{2}{5}\\)<br \/>\n\\(\\frac{\u25a1}{\u25a1}\\)<\/p>\n<p>Answer:<br \/>\n\\(\\frac{1}{4}\\)<\/p>\n<p>Explanation:<br \/>\n\\(\\frac{5}{8} \\times \\frac{2}{5}\\)<br \/>\nMultiply the numerators and Multiply the denominators.<br \/>\n\\(\\frac{5 \u00d7 2}{8 \u00d7 5}\\) = \\(\\frac{10}{40}\\)<br \/>\nSimplify using the GCF.<br \/>\nThe GCF of 10 and 40 is 10.<br \/>\nDivide the numerator and the denominator by 10.<br \/>\n\\(\\frac{10 \u00f7 10}{40 \u00f7 10}\\) = \\(\\frac{1}{4}\\)<\/p>\n<p>Question 9.<br \/>\n\\(\\frac{9}{10} \\times \\frac{5}{6}\\)<br \/>\n\\(\\frac{\u25a1}{\u25a1}\\)<\/p>\n<p>Answer:<br \/>\n\\(\\frac{3}{4}\\)<\/p>\n<p>Explanation:<br \/>\n\\(\\frac{9}{10} \\times \\frac{5}{6}\\)<br \/>\nMultiply the numerators and Multiply the denominators.<br \/>\n\\(\\frac{9 \u00d7 5}{10 \u00d7 6}\\) = \\(\\frac{45}{60}\\)<br \/>\nSimplify using the GCF.<br \/>\nThe GCF of 45 and 60 is 15.<br \/>\nDivide the numerator and the denominator by 15.<br \/>\n\\(\\frac{45 \u00f7 15}{60 \u00f7 15}\\) = \\(\\frac{3}{4}\\)<\/p>\n<p>Question 10.<br \/>\n\\(\\frac{11}{12} \\times \\frac{3}{7}\\)<br \/>\n\\(\\frac{\u25a1}{\u25a1}\\)<\/p>\n<p>Answer:<br \/>\n\\(\\frac{11}{28}\\)<\/p>\n<p>Explanation:<br \/>\n\\(\\frac{11}{12} \\times \\frac{3}{7}\\)<br \/>\nMultiply the numerators and Multiply the denominators.<br \/>\n\\(\\frac{11 \u00d7 3}{12 \u00d7 7}\\) = \\(\\frac{33}{84}\\)<br \/>\nSimplify using the GCF.<br \/>\nThe GCF of 33 and 84 is 3.<br \/>\nDivide the numerator and the denominator by 3.<br \/>\n\\(\\frac{33 \u00f7 3}{84 \u00f7 3}\\) = \\(\\frac{11}{28}\\)<\/p>\n<p>Question 11.<br \/>\nShelley\u2019s basketball team won \\(\\frac{3}{4}\\) of their games last season. In \\(\\frac{1}{6}\\) of the games they won, they outscored their opponents by more than 10 points. What fraction of their games did Shelley\u2019s team win by more than 10 points?<br \/>\n\\(\\frac{\u25a1}{\u25a1}\\)<\/p>\n<p>Answer:<br \/>\n\\(\\frac{1}{8}\\)<\/p>\n<p>Explanation:<br \/>\nLet the total number of games be x.<br \/>\nNumber of games Shelley&#8217;s team won = 3\/4x<br \/>\nNumber of games they outscored their opponents by more than 10 points = 1\/6 X 3\/4x = 1\/8x<br \/>\nHence, 1\/8 of the total games, Shelley&#8217;s team won by 10 points.<\/p>\n<p>Question 12.<br \/>\nMr. Ortiz has \\(\\frac{3}{4}\\) pound of oatmeal. He uses \\(\\frac{2}{3}\\) of the oatmeal to bake muffins. How much oatmeal does Mr. Ortiz have left?<br \/>\n\\(\\frac{\u25a1}{\u25a1}\\)<\/p>\n<p>Answer:<br \/>\n\\(\\frac{1}{2}\\)<\/p>\n<p>Explanation:<br \/>\nMr. Ortiz has \\(\\frac{3}{4}\\) pound of oatmeal. He uses \\(\\frac{2}{3}\\) of the oatmeal to bake muffins.<br \/>\n\\(\\frac{3}{4} \\times \\frac{2}{3}\\)<br \/>\nMultiply the numerators and Multiply the denominators.<br \/>\n\\(\\frac{3 \u00d7 2}{4 \u00d7 3}\\) = \\(\\frac{6}{12}\\)<br \/>\nSimplify using the GCF.<br \/>\nThe GCF of 6 and 12 is 6.<br \/>\nDivide the numerator and the denominator by 6.<br \/>\n\\(\\frac{6 \u00f7 6}{12 \u00f7 6}\\) = \\(\\frac{1}{2}\\)<\/p>\n<p>Question 13.<br \/>\nCompare Strategies To find \\(\\frac{16}{27}\\) \u00d7 \\(\\frac{3}{4}\\), you can multiply the fractions and then simplify the product or you can simplify the fractions and then multiply. Which method do you prefer? Explain.<br \/>\nType below:<br \/>\n__________<\/p>\n<p>Answer:<br \/>\n\\(\\frac{16}{27}\\) \u00d7 \\(\\frac{3}{4}\\)<br \/>\n\\(\\frac{16 \u00d7 3}{27 \u00d7 4}\\) = \\(\\frac{16 \u00d7 3}{4 \u00d7 27}\\)<br \/>\n\\(\\frac{48}{96}\\)<br \/>\nSimplify using the GCF.<br \/>\nThe GCF of 48 and 96 is 48.<br \/>\nDivide the numerator and the denominator by 48.<br \/>\n\\(\\frac{48 \u00f7 48}{96 \u00f7 48}\\) = \\(\\frac{1}{2}\\)<\/p>\n<h3><a id=\"Simplify_Factors_-_Page_No._90\"><\/a>Problem Solving + Applications &#8211; Page No. 90<\/h3>\n<p><img loading=\"lazy\" class=\"alignnone size-full wp-image-4788\" src=\"https:\/\/ccssmathanswers.com\/wp-content\/uploads\/2020\/08\/Go-Math-Grade-6-Answer-Key-Chapter-2-Fractions-and-Decimals-7.jpg\" alt=\"Go Math Grade 6 Answer Key Chapter 2 Fractions and Decimals 7\" width=\"269\" height=\"206\" \/><\/p>\n<p>Question 14.<br \/>\nThree students each popped \\(\\frac{3}{4}\\) cup of popcorn kernels. The table shows the fraction of each student\u2019s kernels that did not pop. Which student had \\(\\frac{1}{16}\\) cup unpopped kernels?<br \/>\n__________<\/p>\n<p>Answer:<br \/>\nMirza<\/p>\n<p>Explanation:<br \/>\nThree students each popped \\(\\frac{3}{4}\\) cup of popcorn kernels. The table shows the fraction of each student\u2019s kernels that did not pop.<br \/>\nKatie = 3\/4 x 1\/10 = 3\/40<br \/>\nMirza = 3\/4 x 1\/12 = 1\/16<\/p>\n<p>Question 15.<br \/>\nThe jogging track at Francine\u2019s school is \\(\\frac{3}{4}\\) mile long. Yesterday Francine completed two laps on the track. If she ran \\(\\frac{1}{3}\\) of the distance and walked the remainder of the way, how far did she walk?<br \/>\n____ mile<\/p>\n<p>Answer:<br \/>\n1 mile<\/p>\n<p>Explanation:<br \/>\nLength of jogging track at Francine\u2019s school = 3\/4 mile<br \/>\nLet the distance covered by running be = x<br \/>\nLet the distance covered by walking be = y<br \/>\nTotal number of laps completed by Francine = 2<br \/>\nTotal distance covered by Francine = number of laps X distance covered in one lap<br \/>\n2 x 3\/4 = 3\/25 mile<br \/>\nNow,<br \/>\ndistance covered by running = 1\/3 of the total distance<br \/>\nx = 1\/3 x 3\/2<br \/>\ndistance covered by walking y = total distance &#8211; distance covered by running<br \/>\n3\/2 &#8211; x = 3\/2 &#8211; 1\/2 = 1 mile<br \/>\nHence, Francine walked for 1 mile.<\/p>\n<p>Question 16.<br \/>\nAt a snack store, \\(\\frac{7}{12}\\) of the customers bought pretzels and \\(\\frac{3}{10}\\) of those customers bought low-salt pretzels. Bill states that \\(\\frac{7}{30}\\) of the customers bought low-salt pretzels. Does Bill\u2019s statement make sense? Explain.<br \/>\nType below:<br \/>\n__________<\/p>\n<p>Answer:<br \/>\nBill&#8217;s statement does not make sense because it is incorrect:<br \/>\n7\/12 customers bought pretzels.<br \/>\n3\/10 Of those customers bought low salt pretzels (x)<br \/>\n3\/10 of 7\/12 = x<br \/>\n21\/120 = x<br \/>\nSimplify: 7\/40<br \/>\nTo be correct, Bill would have to say that 7\/40 of the customers bought low salt pretzels, but instead, he had said 7\/30.<\/p>\n<p>Question 17.<br \/>\nThe table shows Tonya\u2019s homework assignment. Tonya\u2019s teacher instructed the class to simplify each expression by dividing the numerator and denominator by the GCF. Complete the table by simplifying each expression and then finding the value.<br \/>\n<img loading=\"lazy\" class=\"alignnone size-full wp-image-4789\" src=\"https:\/\/ccssmathanswers.com\/wp-content\/uploads\/2020\/08\/Go-Math-Grade-6-Answer-Key-Chapter-2-Fractions-and-Decimals-8.jpg\" alt=\"Go Math Grade 6 Answer Key Chapter 2 Fractions and Decimals 8\" width=\"347\" height=\"232\" srcset=\"https:\/\/bigideasmathanswers.com\/wp-content\/uploads\/2020\/08\/Go-Math-Grade-6-Answer-Key-Chapter-2-Fractions-and-Decimals-8.jpg 347w, https:\/\/bigideasmathanswers.com\/wp-content\/uploads\/2020\/08\/Go-Math-Grade-6-Answer-Key-Chapter-2-Fractions-and-Decimals-8-300x201.jpg 300w\" sizes=\"(max-width: 347px) 100vw, 347px\" \/><br \/>\nType below:<br \/>\n__________<\/p>\n<p>Answer:<br \/>\n<img loading=\"lazy\" class=\"alignnone wp-image-7032\" src=\"https:\/\/ccssmathanswers.com\/wp-content\/uploads\/2020\/08\/Garde-6-chapter-2-image-1-300x205.jpg\" alt=\"Garde 6 chapter 2 image 1\" width=\"316\" height=\"216\" srcset=\"https:\/\/bigideasmathanswers.com\/wp-content\/uploads\/2020\/08\/Garde-6-chapter-2-image-1-300x205.jpg 300w, https:\/\/bigideasmathanswers.com\/wp-content\/uploads\/2020\/08\/Garde-6-chapter-2-image-1.jpg 623w\" sizes=\"(max-width: 316px) 100vw, 316px\" \/><\/p>\n<h3><a id=\"Simplify_Factors_Lesson_Check_-_Page_No._91\"><\/a>Simplify Factors &#8211; Page No. 91<\/h3>\n<p><strong>Find the product. Simplify before multiplying.<\/strong><\/p>\n<p>Question 1.<br \/>\n\\(\\frac{8}{9} \\times \\frac{5}{12}\\)<br \/>\n\\(\\frac{\u25a1}{\u25a1}\\)<\/p>\n<p>Answer:<br \/>\n\\(\\frac{10}{27}\\)<\/p>\n<p>Explanation:<br \/>\n\\(\\frac{8}{9} \\times \\frac{5}{12}\\)<br \/>\nMultiply the numerators and Multiply the denominators.<br \/>\n\\(\\frac{8 \u00d7 5}{9 \u00d7 12}\\) = \\(\\frac{40}{108}\\)<br \/>\nSimplify using the GCF.<br \/>\nThe GCF of 40 and 108 is 4.<br \/>\nDivide the numerator and the denominator by 4.<br \/>\n\\(\\frac{40 \u00f7 4}{108 \u00f7 4}\\) = \\(\\frac{10}{27}\\)<\/p>\n<p>Question 2.<br \/>\n\\(\\frac{3}{4} \\times \\frac{16}{21}\\)<br \/>\n\\(\\frac{\u25a1}{\u25a1}\\)<\/p>\n<p>Answer:<br \/>\n\\(\\frac{4}{7}\\)<\/p>\n<p>Explanation:<br \/>\n\\(\\frac{3}{4} \\times \\frac{16}{21}\\)<br \/>\nMultiply the numerators and Multiply the denominators.<br \/>\n\\(\\frac{3 \u00d7 16}{4 \u00d7 21}\\) = \\(\\frac{48}{84}\\)<br \/>\nSimplify using the GCF.<br \/>\nThe GCF of 48 and 84 is 12.<br \/>\nDivide the numerator and the denominator by 12.<br \/>\n\\(\\frac{48 \u00f7 12}{84 \u00f7 12}\\) = \\(\\frac{4}{7}\\)<\/p>\n<p>Question 3.<br \/>\n\\(\\frac{15}{20} \\times \\frac{2}{5}\\)<br \/>\n\\(\\frac{\u25a1}{\u25a1}\\)<\/p>\n<p>Answer:<br \/>\n\\(\\frac{3}{10}\\)<\/p>\n<p>Explanation:<br \/>\n\\(\\frac{15}{20} \\times \\frac{2}{5}\\)<br \/>\nMultiply the numerators and Multiply the denominators.<br \/>\n\\(\\frac{15 \u00d7 2}{20 \u00d7 5}\\) = \\(\\frac{30}{100}\\)<br \/>\nSimplify using the GCF.<br \/>\nThe GCF of 30 and 100 is 10.<br \/>\nDivide the numerator and the denominator by 10.<br \/>\n\\(\\frac{30 \u00f7 10}{100 \u00f7 10}\\) = \\(\\frac{3}{10}\\)<\/p>\n<p>Question 4.<br \/>\n\\(\\frac{9}{18} \\times \\frac{2}{3}\\)<br \/>\n\\(\\frac{\u25a1}{\u25a1}\\)<\/p>\n<p>Answer:<br \/>\n\\(\\frac{1}{3}\\)<\/p>\n<p>Explanation:<br \/>\n\\(\\frac{9}{18} \\times \\frac{2}{3}\\)<br \/>\nMultiply the numerators and Multiply the denominators.<br \/>\n\\(\\frac{9 \u00d7 2}{18 \u00d7 3}\\) = \\(\\frac{18}{54}\\)<br \/>\nSimplify using the GCF.<br \/>\nThe GCF of 18 and 54 is 18.<br \/>\nDivide the numerator and the denominator by 18.<br \/>\n\\(\\frac{18 \u00f7 18}{54 \u00f7 18}\\) = \\(\\frac{1}{3}\\)<\/p>\n<p>Question 5.<br \/>\n\\(\\frac{3}{4} \\times \\frac{7}{30}\\)<br \/>\n\\(\\frac{\u25a1}{\u25a1}\\)<\/p>\n<p>Answer:<br \/>\n\\(\\frac{7}{40}\\)<\/p>\n<p>Explanation:<br \/>\n\\(\\frac{3}{4} \\times \\frac{7}{30}\\)<br \/>\nMultiply the numerators and Multiply the denominators.<br \/>\n\\(\\frac{3 \u00d7 7}{4 \u00d7 30}\\) = \\(\\frac{21}{120}\\)<br \/>\nSimplify using the GCF.<br \/>\nThe GCF of 21 and 120 is 3.<br \/>\nDivide the numerator and the denominator by 3.<br \/>\n\\(\\frac{21 \u00f7 3}{120 \u00f7 3}\\) = \\(\\frac{7}{40}\\)<\/p>\n<p>Question 6.<br \/>\n\\(\\frac{8}{15} \\times \\frac{15}{32}\\)<br \/>\n\\(\\frac{\u25a1}{\u25a1}\\)<\/p>\n<p>Answer:<br \/>\n\\(\\frac{1}{4}\\)<\/p>\n<p>Explanation:<br \/>\n\\(\\frac{8}{15} \\times \\frac{15}{32}\\)<br \/>\nMultiply the numerators and Multiply the denominators.<br \/>\n\\(\\frac{8 \u00d7 15}{15 \u00d7 32}\\) = \\(\\frac{120}{480}\\)<br \/>\nSimplify using the GCF.<br \/>\nThe GCF of 120 and 480 is 120.<br \/>\nDivide the numerator and the denominator by 120.<br \/>\n\\(\\frac{120 \u00f7 120}{480 \u00f7 120}\\) = \\(\\frac{1}{4}\\)<\/p>\n<p>Question 7.<br \/>\n\\(\\frac{12}{21} \\times \\frac{7}{9}\\)<br \/>\n\\(\\frac{\u25a1}{\u25a1}\\)<\/p>\n<p>Answer:<br \/>\n\\(\\frac{4}{9}\\)<\/p>\n<p>Explanation:<br \/>\n\\(\\frac{12}{21} \\times \\frac{7}{9}\\)<br \/>\nMultiply the numerators and Multiply the denominators.<br \/>\n\\(\\frac{12 \u00d7 7}{21 \u00d7 9}\\) = \\(\\frac{84}{189}\\)<br \/>\nSimplify using the GCF.<br \/>\nThe GCF of 84 and 189 is 21.<br \/>\nDivide the numerator and the denominator by 21.<br \/>\n\\(\\frac{84 \u00f7 21}{189 \u00f7 21}\\) = \\(\\frac{4}{9}\\)<\/p>\n<p>Question 8.<br \/>\n\\(\\frac{18}{22} \\times \\frac{8}{9}\\)<br \/>\n\\(\\frac{\u25a1}{\u25a1}\\)<\/p>\n<p>Answer:<br \/>\n\\(\\frac{8}{11}\\)<\/p>\n<p>Explanation:<br \/>\n\\(\\frac{18}{22} \\times \\frac{8}{9}\\)<br \/>\nMultiply the numerators and Multiply the denominators.<br \/>\n\\(\\frac{18 \u00d7 8}{22 \u00d7 9}\\) = \\(\\frac{144}{198}\\)<br \/>\nSimplify using the GCF.<br \/>\nThe GCF of 144 and 198 is 18.<br \/>\nDivide the numerator and the denominator by 18.<br \/>\n\\(\\frac{144 \u00f7 18}{198 \u00f7 18}\\) = \\(\\frac{8}{11}\\)<\/p>\n<p><strong>Problem Solving<\/strong><\/p>\n<p>Question 9.<br \/>\nAmber has a \\(\\frac{4}{5}\\)-pound bag of colored sand. She uses \\(\\frac{1}{2}\\) of the bag for an art project. How much sand does she use for the project?<br \/>\n\\(\\frac{\u25a1}{\u25a1}\\) pounds<\/p>\n<p>Answer:<br \/>\n\\(\\frac{2}{5}\\) pounds<\/p>\n<p>Explanation:<br \/>\nAmber has a \\(\\frac{4}{5}\\)-pound bag of colored sand. She uses \\(\\frac{1}{2}\\) of the bag for an art project.<br \/>\n4\/5 X 1\/2 = 2\/5<\/p>\n<p>Question 10.<br \/>\nTyler has \\(\\frac{3}{4}\\) month to write a book report. He finished the report in \\(\\frac{2}{3}\\) that time. How much time did it take Tyler to write the report?<br \/>\n\\(\\frac{\u25a1}{\u25a1}\\) month<\/p>\n<p>Answer:<br \/>\n\\(\\frac{1}{2}\\) month<\/p>\n<p>Explanation:<br \/>\nTyler has \\(\\frac{3}{4}\\) month to write a book report. He finished the report in \\(\\frac{2}{3}\\) that time.<br \/>\n3\/4 X 2\/3 = 1\/2<\/p>\n<p>Question 11.<br \/>\nShow two ways to multiply \\(\\frac{2}{15} \\times \\frac{3}{20}\\). Then tell which way is easier and justify your choice.<br \/>\nType below:<br \/>\n__________<\/p>\n<p>Answer:<br \/>\n\\(\\frac{2}{15} \\times \\frac{3}{20}\\)<br \/>\n2\/15 X 3\/20 = 2\/20 X 3\/15 = 1\/10 X 1\/5 = 1\/50<\/p>\n<h3><a id=\"Simplify_Factors_Lesson_Check_1_-_Page_No._92\"><\/a>Lesson Check &#8211; Page No. 92<\/h3>\n<p><strong>Find each product. Simplify before multiplying.<\/strong><\/p>\n<p>Question 1.<br \/>\nAt Susie\u2019s school, \\(\\frac{5}{8}\\) of all students play sports. Of the students who play sports, \\(\\frac{2}{5}\\) play soccer. What fraction of the students in Susie\u2019s school play soccer?<br \/>\n\\(\\frac{\u25a1}{\u25a1}\\)<\/p>\n<p>Answer:<br \/>\n\\(\\frac{1}{4}\\)<\/p>\n<p>Explanation:<br \/>\nAt Susie\u2019s school, \\(\\frac{5}{8}\\) of all students play sports. Of the students who play sports, \\(\\frac{2}{5}\\) play soccer.<br \/>\nMultiply 5\/8 X 2\/5, and the answer is 0.25, which converts to 25\/100 or 1\/4<\/p>\n<p>Question 2.<br \/>\nA box of popcorn weighs \\(\\frac{15}{16}\\) pounds. The box contains \\(\\frac{1}{3}\\) buttered popcorn and \\(\\frac{2}{3}\\) cheesy popcorn. How much does the cheesy popcorn weigh?<br \/>\n\\(\\frac{\u25a1}{\u25a1}\\)<\/p>\n<p>Answer:<br \/>\n\\(\\frac{5}{8}\\)<\/p>\n<p>Explanation:<br \/>\nTotal weight of a box of popcorn =15\/16 pounds.<br \/>\nWe are given two types of popcorns are there, butter popcorns and cheesy popcorns.<br \/>\nButter popcorn is the one-third of the total weight = 1\/3 of the Total weight<br \/>\nPlugging the value of the total weight, we get<br \/>\n= 1\/3 * 15\/16 = 5\/16 pounds.<br \/>\nCheesy popcorn = 2\/3 of Total weight<br \/>\nPlugging the value of total weight, we get<br \/>\n= 2\/3 * 15\/16 = 10\/16 or 5\/8 pounds.<br \/>\nTherefore, cheesy popcorn weighs is 5\/8 pounds.<\/p>\n<p><strong>Spiral Review<\/strong><\/p>\n<p>Question 3.<br \/>\nRam\u00f2n bought a dozen ears of corn for $1.80. What was the cost of each ear of corn?<br \/>\n$ ______<\/p>\n<p>Answer:<br \/>\n$0.15<\/p>\n<p>Explanation:<br \/>\nRam\u00f2n bought a dozen ears of corn for $1.80.<br \/>\nSo, for the cost of each ear of corn, $1.80\/12 = $0.15<\/p>\n<p>Question 4.<br \/>\nA 1.8-ounce jar of cinnamon costs $4.05. What is the cost per ounce?<br \/>\n$ ______<\/p>\n<p>Answer:<br \/>\n$2.25 per ounce<\/p>\n<p>Explanation:<br \/>\nIf a 1.8-ounce jar costs $4.05, do $4.05 divided by 1.8.<br \/>\n$4.05 \/ 1.8 = $2.25 per ounce.<\/p>\n<p>Question 5.<br \/>\nRose bought \\(\\frac{7}{20}\\) kilogram of ginger candy and 0.4 kilogram of cinnamon candy. Which did she buy more of? Explain how you know.<br \/>\nType below:<br \/>\n__________<\/p>\n<p>Answer:<br \/>\nRose bought ginger candy = 7\/20 kilogram = 0.35 Kilogram<br \/>\nShe bought cinnamon candy = 0.4 kilogram<br \/>\n0.4 &gt; 0.35<br \/>\nTherefore, She bought cinnamon candy more.<\/p>\n<p>Question 6.<br \/>\nDon walked 3 \\(\\frac{3}{5}\\) miles on Friday, 3.7 miles on Saturday, and 3 \\(\\frac{5}{8}\\) miles on Sunday. List the distances from least to greatest.<br \/>\nType below:<br \/>\n__________<\/p>\n<p>Answer:<br \/>\n3 \\(\\frac{3}{5}\\), 3 \\(\\frac{5}{8}\\), 3.7<\/p>\n<p>Explanation:<br \/>\n3 \\(\\frac{3}{5}\\) = 18\/5 = 3.6<br \/>\n3 \\(\\frac{5}{8}\\) = 29\/8 = 3.625<br \/>\n3.6 &lt; 3.625 &lt; 3.7<br \/>\n3 \\(\\frac{3}{5}\\), 3 \\(\\frac{5}{8}\\), 3.7<\/p>\n<h3><a id=\"Mid-Chapter_Checkpoint_-_Page_No._93\"><\/a>Mid-Chapter Checkpoint &#8211; Vocabulary &#8211; Page No. 93<\/h3>\n<p><strong>Choose the best term from the box to complete the sentence.<\/strong><br \/>\n<img loading=\"lazy\" class=\"alignnone size-full wp-image-4790\" src=\"https:\/\/ccssmathanswers.com\/wp-content\/uploads\/2020\/08\/Go-Math-Grade-6-Answer-Key-Chapter-2-Fractions-and-Decimals-9.jpg\" alt=\"Go Math Grade 6 Answer Key Chapter 2 Fractions and Decimals 9\" width=\"234\" height=\"161\" \/><\/p>\n<p>Question 1.<br \/>\nThe fractions \\(\\frac{1}{2}\\) and \\(\\frac{5}{10}\\) are _____.<br \/>\nType below:<br \/>\n__________<\/p>\n<p>Answer:<br \/>\nEquivalent fractions<\/p>\n<p>Question 2.<br \/>\nA _____ is a denominator that is the same in two or more fractions.<br \/>\nType below:<br \/>\n__________<\/p>\n<p>Answer:<br \/>\nCommon Denominator<\/p>\n<p><strong>Concepts and Skills<\/strong><\/p>\n<p><strong>Write as a decimal. Tell whether you used division, a number line, or some other method.<\/strong><\/p>\n<p>Question 3.<br \/>\n\\(\\frac{7}{20}\\)<br \/>\n_____<\/p>\n<p>Answer:<br \/>\n0.35<\/p>\n<p>Explanation:<br \/>\nBy using Division,<br \/>\n\\(\\frac{7}{20}\\) = 0.35<\/p>\n<p>Question 4.<br \/>\n8 \\(\\frac{39}{40}\\)<br \/>\n_____<\/p>\n<p>Answer:<br \/>\n8.975<\/p>\n<p>Explanation:<br \/>\nBy using Division,<br \/>\n8 \\(\\frac{39}{40}\\) = 359\/40 = 8.975<\/p>\n<p>Question 5.<br \/>\n1 \\(\\frac{5}{8}\\)<br \/>\n_____<\/p>\n<p>Answer:<br \/>\n1.625<\/p>\n<p>Explanation:<br \/>\nBy using Division,<br \/>\n1 \\(\\frac{5}{8}\\) = 13\/8 = 1.625<\/p>\n<p>Question 6.<br \/>\n\\(\\frac{19}{25}\\)<br \/>\n_____<\/p>\n<p>Answer:<br \/>\n0.76<\/p>\n<p>Explanation:<br \/>\nBy using Division,<br \/>\n\\(\\frac{19}{25}\\) = 0.76<\/p>\n<p><strong>Order from least to greatest.<\/strong><\/p>\n<p>Question 7.<br \/>\n\\(\\frac{4}{5}, \\frac{3}{4}, 0.88\\)<br \/>\nType below:<br \/>\n__________<\/p>\n<p>Answer:<br \/>\n\\(\\frac{3}{4}\\), \\(\\frac{4}{5}\\),0.88<\/p>\n<p>Explanation:<br \/>\nWrite the decimal form of 4\/5 = 0.8<br \/>\nWrite the decimal form of 3\/4 = 0.75<br \/>\n0.88<br \/>\n0.75 &lt; 0.8 &lt; 0.88<\/p>\n<p>Question 8.<br \/>\n0.65, 0.59, \\(\\frac{3}{5}\\)<br \/>\nType below:<br \/>\n__________<\/p>\n<p>Answer:<br \/>\n0.59, \\(\\frac{3}{5}\\), 0.65<\/p>\n<p>Explanation:<br \/>\nWrite the decimal form of 3\/5 = 0.6<br \/>\n0.59 &lt; 0.6 &lt; 0.65<\/p>\n<p>Question 9.<br \/>\n\\(1 \\frac{1}{4}, 1 \\frac{2}{3}, \\frac{11}{12}\\)<br \/>\nType below:<br \/>\n__________<\/p>\n<p>Answer:<br \/>\n\\(\\frac{11}{12}\\), 1\\(\\frac{1}{4}\\), 1\\(\\frac{2}{3}\\)<\/p>\n<p>Explanation:<br \/>\nWrite the decimal form of 1 1\/4 = 5\/4 = 1.25<br \/>\nWrite the decimal form of 1 2\/3 = 5\/3 = 1.66<br \/>\nWrite the decimal form of 11\/12 = 0.916<br \/>\n0.916 &lt; 1.25 &lt; 1.66<\/p>\n<p>Question 10.<br \/>\n0.9, \\(\\frac{7}{8}\\), 0.86<br \/>\nType below:<br \/>\n__________<\/p>\n<p>Answer:<br \/>\n0.86, \\(\\frac{7}{8}\\), 0.9<\/p>\n<p>Explanation:<br \/>\nWrite the decimal form of \\(\\frac{7}{8}\\) = 0.875<br \/>\n0.86 &lt; 0.875 &lt; 0.9<\/p>\n<p><strong>Find the product. Write it in simplest form.<\/strong><\/p>\n<p>Question 11.<br \/>\n\\(\\frac{2}{3} \\times \\frac{1}{8}\\)<br \/>\n\\(\\frac{\u25a1}{\u25a1}\\)<\/p>\n<p>Answer:<br \/>\n\\(\\frac{1}{12}\\)<\/p>\n<p>Explanation:<br \/>\n\\(\\frac{2}{3} \\times \\frac{1}{8}\\)<br \/>\nMultiply the numerators and Multiply the denominators.<br \/>\n\\(\\frac{2 \u00d7 1}{3 \u00d7 8}\\) = \\(\\frac{2}{24}\\)<br \/>\nSimplify using the GCF.<br \/>\nThe GCF of 2 and 24 is 2.<br \/>\nDivide the numerator and the denominator by 2.<br \/>\n\\(\\frac{2 \u00f7 2}{24 \u00f7 2}\\) = \\(\\frac{1}{12}\\)<\/p>\n<p>Question 12.<br \/>\n\\(\\frac{4}{5} \\times \\frac{2}{5}\\)<br \/>\n\\(\\frac{\u25a1}{\u25a1}\\)<\/p>\n<p>Answer:<br \/>\n\\(\\frac{8}{25}\\)<\/p>\n<p>Explanation:<br \/>\n\\(\\frac{4}{5} \\times \\frac{2}{5}\\)<br \/>\nMultiply the numerators and Multiply the denominators.<br \/>\n\\(\\frac{4 \u00d7 2}{5 \u00d7 5}\\) = \\(\\frac{8}{25}\\)<\/p>\n<p>Question 13.<br \/>\n12 \u00d7 \\(\\frac{3}{4}\\)<br \/>\n_____<\/p>\n<p>Answer:<br \/>\n9<\/p>\n<p>Explanation:<br \/>\n12 \u00d7 \\(\\frac{3}{4}\\)<br \/>\nMultiply the numerators and Multiply the denominators.<br \/>\n\\(\\frac{12 \u00d7 3}{1 \u00d7 4}\\) = \\(\\frac{36}{4}\\) = 9<\/p>\n<p>Question 14.<br \/>\nMia climbs \\(\\frac{5}{8}\\) of the height of the rock wall. Lee climbs \\(\\frac{4}{5}\\) of Mia\u2019s distance. What fraction of the wall does Lee climb?<br \/>\n\\(\\frac{\u25a1}{\u25a1}\\)<\/p>\n<p>Answer:<br \/>\n\\(\\frac{7}{40}\\)<\/p>\n<p>Explanation:<br \/>\nfind the LCM (least common denominator) for 5\/8 and 4\/5.<br \/>\n5\/8= 25\/40 and 4\/5= 32\/40.<br \/>\nSubtract and you get 7\/40.<\/p>\n<h3><a id=\"Mid-Chapter_Checkpoint_Lesson_Check_-_Page_No._94\"><\/a>Page No. 94<\/h3>\n<p>Question 15.<br \/>\nIn Zoe\u2019s class, \\(\\frac{4}{5}\\) of the students have pets. Of the students who have pets, \\(\\frac{1}{8}\\) have rodents. What fraction of the students in Zoe\u2019s class have pets that are rodents? What fraction of the students in Zoe\u2019s class have pets that are not rodents?<br \/>\nType below:<br \/>\n__________<\/p>\n<p>Answer:<br \/>\n\\(\\frac{1}{10}\\) of the students in Zoe\u2019s class have pets that are rodents<br \/>\n\\(\\frac{7}{10}\\) of the students in Zoe\u2019s class have pets that are not rodents<\/p>\n<p>Explanation:<br \/>\nIn Zoe\u2019s class, \\(\\frac{4}{5}\\) of the students have pets. Of the students who have pets, \\(\\frac{1}{8}\\) have rodents.<br \/>\n4\/5 X 1\/8 = 1\/10<br \/>\n4\/5 &#8211; 1\/10 = 7\/10<\/p>\n<p>Question 16.<br \/>\nA recipe calls for 2 \\(\\frac{2}{3}\\) cups of flour. Terell wants to make \\(\\frac{3}{4}\\) of the recipe. How much flour should he use?<br \/>\n_____ cups<\/p>\n<p>Answer:<br \/>\n2 cups<\/p>\n<p>Explanation:<br \/>\n2 \\(\\frac{2}{3}\\) = 8\/3<br \/>\n8\/3 * 3\/4 = 2<\/p>\n<p>Question 17.<br \/>\nFollowing the Baltimore Running Festival in 2009, volunteers collected and recycled 3.75 tons of trash. Graph 3.75 on a number line and write the weight as a mixed number.<br \/>\nType below:<br \/>\n__________<\/p>\n<p>Answer:<br \/>\nVolunteers collected and recycled 3.75 tons of trash.<br \/>\nWe need to convert 3.75 as a mixed number.<br \/>\nThe mixed number consists of a whole number and a proper fraction.<br \/>\nIn the given number 3.75, 3 as the whole number and convert 0.75 to a fraction.<br \/>\n3.75 = 3 + 0.75 = 3 + 75\/100<br \/>\nWe can reduce the fraction 75\/ 100 = 3+ 3\/4 = 3 3\/4<\/p>\n<p>Question 18.<br \/>\nFour students took an exam. The fraction of the total possible points that each received is given. Which student had the highest score? If students receive a whole number of points on every exam item, can the exam be worth a total of 80 points? Explain.<br \/>\n<img loading=\"lazy\" class=\"alignnone size-full wp-image-4791\" src=\"https:\/\/ccssmathanswers.com\/wp-content\/uploads\/2020\/08\/Go-Math-Grade-6-Answer-Key-Chapter-2-Fractions-and-Decimals-10.jpg\" alt=\"Go Math Grade 6 Answer Key Chapter 2 Fractions and Decimals 10\" width=\"172\" height=\"171\" srcset=\"https:\/\/bigideasmathanswers.com\/wp-content\/uploads\/2020\/08\/Go-Math-Grade-6-Answer-Key-Chapter-2-Fractions-and-Decimals-10.jpg 172w, https:\/\/bigideasmathanswers.com\/wp-content\/uploads\/2020\/08\/Go-Math-Grade-6-Answer-Key-Chapter-2-Fractions-and-Decimals-10-150x150.jpg 150w\" sizes=\"(max-width: 172px) 100vw, 172px\" \/><br \/>\nType below:<br \/>\n__________<\/p>\n<p>Answer:<br \/>\n22\/25 = 0.88<br \/>\n17\/20 = 0.85<br \/>\n4\/5 = 0.8<br \/>\n3\/4 = 0.75<br \/>\nMonica had the highest score<br \/>\nLet x be the total number of points:<br \/>\n(22\/25 + 17\/20 + 4\/5 + 3\/4)x = 80<br \/>\nx = 24.39<br \/>\nThat is not a whole number of points.<\/p>\n<h3><a id=\"Model_Fraction_Division_\u2013_Page_No._97\"><\/a>Share and Show &#8211; Page No. 97<\/h3>\n<p><strong>Use the model to find the quotient.<\/strong><\/p>\n<p>Question 1.<br \/>\n\\(\\frac{1}{2}\\) \u00f7 3<br \/>\n<img loading=\"lazy\" class=\"alignnone size-full wp-image-4792\" src=\"https:\/\/ccssmathanswers.com\/wp-content\/uploads\/2020\/08\/Go-Math-Grade-6-Answer-Key-Chapter-2-Fractions-and-Decimals-11.jpg\" alt=\"Go Math Grade 6 Answer Key Chapter 2 Fractions and Decimals 11\" width=\"109\" height=\"77\" \/><br \/>\n\\(\\frac{\u25a1}{\u25a1}\\)<\/p>\n<p>Answer:<br \/>\n\\(\\frac{1}{6}\\)<\/p>\n<p>Explanation:<br \/>\n1\/2 groups of 3<br \/>\n\\(\\frac{1}{2}\\) \u00f7 3<br \/>\n1\/2 \u00d7 1\/3 = 1\/6<\/p>\n<p>Question 2.<br \/>\n\\(\\frac{3}{4} \\div \\frac{3}{8}\\)<br \/>\n<img loading=\"lazy\" class=\"alignnone size-full wp-image-4793\" src=\"https:\/\/ccssmathanswers.com\/wp-content\/uploads\/2020\/08\/Go-Math-Grade-6-Answer-Key-Chapter-2-Fractions-and-Decimals-12.jpg\" alt=\"Go Math Grade 6 Answer Key Chapter 2 Fractions and Decimals 12\" width=\"162\" height=\"77\" \/><br \/>\n______<\/p>\n<p>Answer:<br \/>\n2<\/p>\n<p>Explanation:<br \/>\n3\/4 groups of 3\/8<br \/>\n3\/4 \u00d7 8\/3 = 2<\/p>\n<p><strong>Use fraction strips to find the quotient. Then draw the model.<\/strong><\/p>\n<p>Question 3.<br \/>\n\\(\\frac{1}{3}\\) \u00f7 4<br \/>\n\\(\\frac{\u25a1}{\u25a1}\\)<\/p>\n<p>Answer:<br \/>\n\\(\\frac{1}{12}\\)<br \/>\n<img loading=\"lazy\" class=\"alignnone size-medium wp-image-7038\" src=\"https:\/\/ccssmathanswers.com\/wp-content\/uploads\/2020\/08\/Garde-6-chapter-2-image-2-300x181.jpg\" alt=\"Garde 6 chapter 2 image 2\" width=\"300\" height=\"181\" srcset=\"https:\/\/bigideasmathanswers.com\/wp-content\/uploads\/2020\/08\/Garde-6-chapter-2-image-2-300x181.jpg 300w, https:\/\/bigideasmathanswers.com\/wp-content\/uploads\/2020\/08\/Garde-6-chapter-2-image-2.jpg 415w\" sizes=\"(max-width: 300px) 100vw, 300px\" \/><\/p>\n<p>Explanation:<br \/>\n\\(\\frac{1}{3}\\) \u00f7 4<br \/>\n\\(\\frac{1}{3}\\) \u00d7 \\(\\frac{1}{4}\\)<br \/>\n\\(\\frac{1}{12}\\)<\/p>\n<p>Question 4.<br \/>\n\\(\\frac{3}{5} \\div \\frac{3}{10}\\)<br \/>\n______<\/p>\n<p>Answer:<br \/>\n2<\/p>\n<p>Explanation:<br \/>\n\\(\\frac{3}{5} \\div \\frac{3}{10}\\)<br \/>\n\\(\\frac{3}{5}\\) \u00d7 \\(\\frac{10}{3}\\)<br \/>\n2<\/p>\n<p><strong>Draw a model to solve. Then write an equation for the model. Interpret the result.<\/strong><\/p>\n<p>Question 5.<br \/>\nHow many \\(\\frac{1}{4}\\) cup servings of raisins are in \\(\\frac{3}{8}\\) cup of raisins?<br \/>\nType below:<br \/>\n__________<\/p>\n<p>Answer:<br \/>\n1.5<\/p>\n<p>Explanation:<br \/>\n3\/8 \u00d7 1\/4 = 1.5<\/p>\n<p>Question 6.<br \/>\nHow many \\(\\frac{1}{3}\\) lb bags of trail mix can Josh make from \\(\\frac{5}{6}\\) lb of trail mix?<br \/>\nType below:<br \/>\n__________<\/p>\n<p>Answer:<br \/>\n2<\/p>\n<p>Explanation:<br \/>\nMultiply 1\/3 with 2<br \/>\n1\/3 \u00d7 2 = 2\/6. 2\/6 can go into 5\/6 twice so the answer is two bags.<\/p>\n<p>Question 7.<br \/>\nPose a Problem Write and solve a problem for \\(\\frac{3}{4}\\) \u00f7 3 that represents how much in each of 3 groups.<br \/>\nType below:<br \/>\n__________<\/p>\n<p>Answer:<br \/>\n\\(\\frac{1}{4}\\)<\/p>\n<p>Explanation:<br \/>\n\\(\\frac{3}{4}\\) \u00f7 3<br \/>\n\\(\\frac{3}{4}\\) \u00d7 \\(\\frac{1}{3}\\) = 1\/4<\/p>\n<h3><a id=\"Model_Fraction_Division_\u2013_Page_No._98\"><\/a>Problem Solving + Applications &#8211; Page No. 98<\/h3>\n<p><strong>The table shows the amount of each material that students in a sewing class need for one purse.<\/strong><\/p>\n<p><strong>Use the table for 8\u201310. Use models to solve.<\/strong><br \/>\n<img loading=\"lazy\" class=\"alignnone size-full wp-image-4794\" src=\"https:\/\/ccssmathanswers.com\/wp-content\/uploads\/2020\/08\/Go-Math-Grade-6-Answer-Key-Chapter-2-Fractions-and-Decimals-13.jpg\" alt=\"Go Math Grade 6 Answer Key Chapter 2 Fractions and Decimals 13\" width=\"250\" height=\"153\" \/><\/p>\n<p>Question 8.<br \/>\nMrs. Brown has \\(\\frac{1}{3}\\) yd of blue denim and \\(\\frac{1}{2}\\) yd of black denim. How many purses can be made using denim as the main fabric?<br \/>\n_____ purses<\/p>\n<p>Answer:<br \/>\n5 purses<\/p>\n<p>Explanation:<br \/>\nMrs. Brown has \\(\\frac{1}{3}\\) yd of blue denim and \\(\\frac{1}{2}\\) yd of black denim.<br \/>\n3 + 2 = 5<\/p>\n<p>Question 9.<br \/>\nOne student brings \\(\\frac{1}{2}\\) yd of ribbon. If 3 students receive an equal length of the ribbon, how much ribbon will each student receive? Will each of them have enough ribbon for a purse? Explain.<br \/>\nType below:<br \/>\n__________<\/p>\n<p>Answer:<br \/>\nOne student brings \\(\\frac{1}{2}\\) yd of ribbon. If 3 students receive an equal length of the ribbon,<br \/>\n\\(\\frac{1}{2}\\) \u00f7 3<br \/>\n1\/2 \u00d7 1\/3 = 1\/6<br \/>\nThey don&#8217;t have enough ribbon for a purse<\/p>\n<p>Question 10.<br \/>\nMake Arguments There was \\(\\frac{1}{2}\\) yd of purple and pink striped fabric. Jessie said she could only make \\(\\frac{1}{24}\\) of a purse using that fabric as the trim. Is she correct? Use what you know about the meanings of multiplication and division to defend your answer.<br \/>\nType below:<br \/>\n__________<\/p>\n<p>Answer:<br \/>\nThere was \\(\\frac{1}{2}\\) yd of purple and pink striped fabric. Jessie said she could only make \\(\\frac{1}{24}\\) of a purse using that fabric as the trim.<br \/>\n1\/2 \u00d7 12 = 1\/24<br \/>\nSo, 12 is the answer<\/p>\n<p>Question 11.<br \/>\nDraw a model to find the quotient.<br \/>\n\\(\\frac{1}{2}\\) \u00f7 4 =<br \/>\nType below:<br \/>\n__________<\/p>\n<p>Answer:<br \/>\n<img loading=\"lazy\" class=\"alignnone size-medium wp-image-7041\" src=\"https:\/\/ccssmathanswers.com\/wp-content\/uploads\/2020\/08\/Garde-6-chapter-2-image-3-300x169.jpg\" alt=\"Garde 6 chapter 2 image 3\" width=\"300\" height=\"169\" srcset=\"https:\/\/bigideasmathanswers.com\/wp-content\/uploads\/2020\/08\/Garde-6-chapter-2-image-3-300x169.jpg 300w, https:\/\/bigideasmathanswers.com\/wp-content\/uploads\/2020\/08\/Garde-6-chapter-2-image-3.jpg 464w\" sizes=\"(max-width: 300px) 100vw, 300px\" \/><\/p>\n<p>Explanation:<br \/>\n1\/2 \u00d7 1\/4 = 1\/8<\/p>\n<h3><a id=\"Model_Fraction_Division_Lesson_Check_\u2013_Page_No._99\"><\/a>Model Fraction Division &#8211; Page No. 99<\/h3>\n<p><strong>Use the model to find the quotient<\/strong><\/p>\n<p>Question 1.<br \/>\n\\(\\frac{1}{4}\\) \u00f7 3 =<br \/>\n<img loading=\"lazy\" class=\"alignnone size-full wp-image-4795\" src=\"https:\/\/ccssmathanswers.com\/wp-content\/uploads\/2020\/08\/Go-Math-Grade-6-Answer-Key-Chapter-2-Fractions-and-Decimals-14.jpg\" alt=\"Go Math Grade 6 Answer Key Chapter 2 Fractions and Decimals 14\" width=\"59\" height=\"79\" \/><br \/>\n\\(\\frac{\u25a1}{\u25a1}\\)<\/p>\n<p>Answer:<br \/>\n\\(\\frac{1}{12}\\)<\/p>\n<p>Explanation:<br \/>\n\\(\\frac{1}{4}\\) \u00f7 3<br \/>\n\\(\\frac{1}{4}\\) \u00d7 \\(\\frac{1}{3}\\) = \\(\\frac{1}{12}\\)<\/p>\n<p>Question 2.<br \/>\n\\(\\frac{1}{2} \\div \\frac{2}{12}=\\)<br \/>\n<img loading=\"lazy\" class=\"alignnone size-full wp-image-4796\" src=\"https:\/\/ccssmathanswers.com\/wp-content\/uploads\/2020\/08\/Go-Math-Grade-6-Answer-Key-Chapter-2-Fractions-and-Decimals-15.jpg\" alt=\"Go Math Grade 6 Answer Key Chapter 2 Fractions and Decimals 15\" width=\"121\" height=\"80\" \/><br \/>\n______<\/p>\n<p>Answer:<br \/>\n3<\/p>\n<p>Explanation:<br \/>\n\\(\\frac{1}{2} \\div \\frac{2}{12}=\\)<br \/>\n\\(\\frac{1}{2}\\) \u00d7 \\(\\frac{12}{2}\\) = \\(\\frac{12}{4}\\) = 3<\/p>\n<p><strong>Use fraction strips to find the quotient.<\/strong><\/p>\n<p>Question 3.<br \/>\n\\(\\frac{5}{6} \\div \\frac{1}{2}=\\)<br \/>\n______ \\(\\frac{\u25a1}{\u25a1}\\)<\/p>\n<p>Answer:<br \/>\n\\(\\frac{5}{3}\\)<\/p>\n<p>Explanation:<br \/>\n\\(\\frac{5}{6} \\div \\frac{1}{2}=\\)<br \/>\n\\(\\frac{5}{6}\\) \u00d7 \\(\\frac{2}{1}\\) = \\(\\frac{5}{3}\\)<\/p>\n<p>Question 4.<br \/>\n\\(\\frac{2}{3}\\) \u00f7 4 =<br \/>\n\\(\\frac{\u25a1}{\u25a1}\\)<\/p>\n<p>Answer:<br \/>\n\\(\\frac{1}{6}\\)<\/p>\n<p>Explanation:<br \/>\n\\(\\frac{2}{3}\\) \u00f7 4<br \/>\n\\(\\frac{2}{3}\\) \u00d7 \\(\\frac{1}{4}\\) = \\(\\frac{2}{12}\\) = 1\/6<\/p>\n<p>Question 5.<br \/>\n\\(\\frac{1}{2}\\) \u00f7 6 =<br \/>\n\\(\\frac{\u25a1}{\u25a1}\\)<\/p>\n<p>Answer:<br \/>\n\\(\\frac{1}{12}\\)<\/p>\n<p>Explanation:<br \/>\n\\(\\frac{1}{2}\\) \u00f7 6<br \/>\n\\(\\frac{1}{2}\\) \u00d7 \\(\\frac{1}{6}\\) = \\(\\frac{1}{12}\\)<\/p>\n<p>Question 6.<br \/>\n\\(\\frac{1}{3} \\div \\frac{1}{12}\\)<br \/>\n______<\/p>\n<p>Answer:<br \/>\n4<\/p>\n<p>Explanation:<br \/>\n\\(\\frac{1}{3} \\div \\frac{1}{12}\\)<br \/>\n\\(\\frac{1}{3}\\) \u00d7 \\(\\frac{12}{1}\\) = \\(\\frac{12}{3}\\) = 4<\/p>\n<p><strong>Draw a model to solve. Then write an equation for the model. Interpret the result.<\/strong><\/p>\n<p>Question 7.<br \/>\nIf Jerry runs \\(\\frac{1}{10}\\) mile each day, how many days will it take for him to run \\(\\frac{4}{5}\\) mile?<br \/>\n______ days<\/p>\n<p>Answer:<br \/>\n8 days<\/p>\n<p>Explanation:<br \/>\nIf Jerry runs \\(\\frac{1}{10}\\) mile each day,<br \/>\n\\(\\frac{4}{5}\\) \u00f7 \\(\\frac{1}{10}\\)<br \/>\n\\(\\frac{4}{5}\\) \u00d7 \\(\\frac{10}{1}\\) = \\(\\frac{40}{5}\\) = 8<\/p>\n<p><strong>Problem Solving<\/strong><\/p>\n<p>Question 8.<br \/>\nMrs. Jennings has \\(\\frac{3}{4}\\) gallon of paint for an art project. She plans to divide the paint equally into jars. If she puts \\(\\frac{1}{8}\\) gallon of paint into each jar, how many jars will she use?<br \/>\n______ jars<\/p>\n<p>Answer:<br \/>\n6 jars<\/p>\n<p>Explanation:<br \/>\nMrs. Jennings has 3\/4 Gallons of paint for an art project.<br \/>\nIn 1 jar she puts 1\/8 gallon of paint.<br \/>\nThe number of jars in which she plans to to divide the paint equally is given by,<br \/>\nn= 3\/4 \u00f7 1\/8<br \/>\nn = \\(\\frac{3}{4}\\) \u00d7 \\(\\frac{8}{1}\\) = \\(\\frac{24}{4}\\) = 6<\/p>\n<p>Question 9.<br \/>\nIf one jar of glue weighs \\(\\frac{1}{12}\\) pound, how many jars can Rickie get from \\(\\frac{2}{3}\\) pound of glue?<br \/>\n______ jars<\/p>\n<p>Answer:<br \/>\n8 jars<\/p>\n<p>Explanation:<br \/>\nThe weight of glue in one jar = 1\/12 pound<br \/>\nTo get 2\/3 pound of glue Rickie can get the number of jars<br \/>\n2\/3 \u00f7 1\/12<br \/>\n2\/3 \u00d7 12\/1 = 24\/3 = 8<\/p>\n<p>Question 10.<br \/>\nExplain how to use a model to show \\(\\frac{2}{6} \\div \\frac{1}{12}\\) and \\(\\frac{2}{6}\\) \u00f7 4.<br \/>\nType below:<br \/>\n__________<\/p>\n<p>Answer:<br \/>\n<img loading=\"lazy\" class=\"alignnone size-medium wp-image-7043\" src=\"https:\/\/ccssmathanswers.com\/wp-content\/uploads\/2020\/08\/Garde-6-chapter-2-image-4-300x169.jpg\" alt=\"Garde 6 chapter 2 image 4\" width=\"300\" height=\"169\" srcset=\"https:\/\/bigideasmathanswers.com\/wp-content\/uploads\/2020\/08\/Garde-6-chapter-2-image-4-300x169.jpg 300w, https:\/\/bigideasmathanswers.com\/wp-content\/uploads\/2020\/08\/Garde-6-chapter-2-image-4.jpg 462w\" sizes=\"(max-width: 300px) 100vw, 300px\" \/><br \/>\n<img loading=\"lazy\" class=\"alignnone size-medium wp-image-7038\" src=\"https:\/\/ccssmathanswers.com\/wp-content\/uploads\/2020\/08\/Garde-6-chapter-2-image-2-300x181.jpg\" alt=\"Garde 6 chapter 2 image 2\" width=\"300\" height=\"181\" srcset=\"https:\/\/bigideasmathanswers.com\/wp-content\/uploads\/2020\/08\/Garde-6-chapter-2-image-2-300x181.jpg 300w, https:\/\/bigideasmathanswers.com\/wp-content\/uploads\/2020\/08\/Garde-6-chapter-2-image-2.jpg 415w\" sizes=\"(max-width: 300px) 100vw, 300px\" \/><\/p>\n<p>Explanation:<br \/>\n\\(\\frac{2}{6} \\div \\frac{1}{12}\\)<br \/>\n2\/6 = 1\/3<br \/>\n1\/3 x 12\/1 = 4<br \/>\n\\(\\frac{2}{6}\\) \u00f7 4<br \/>\n1\/3 x 1\/4 = 1\/12<\/p>\n<h3><a id=\"Model_Fraction_Division_Lesson_Check_1_\u2013_Page_No._100\"><\/a>Lesson Check &#8211; Page No. 100<\/h3>\n<p>Question 1.<br \/>\nDarcy needs \\(\\frac{1}{4}\\) yard of fabric to make a banner. She has 2 yards of fabric. How many banners can she make?<br \/>\n______ banners<\/p>\n<p>Answer:<br \/>\n8 banners<\/p>\n<p>Explanation:<br \/>\nDarcy needs \\(\\frac{1}{4}\\) yard of fabric to make a banner. She has 2 yards of fabric.<br \/>\n2 \u00f7 \\(\\frac{1}{4}\\) = 2 x 4 = 8<\/p>\n<p>Question 2.<br \/>\nLorenzo bought \\(\\frac{15}{16}\\) pounds of ground beef. He wants to make hamburgers that weigh \\(\\frac{3}{16}\\) pound each. How many hamburgers can he make?<br \/>\n______ hamburgers<\/p>\n<p>Answer:<br \/>\n5 hamburgers<\/p>\n<p>Explanation:<br \/>\nLorenzo bought \\(\\frac{15}{16}\\) pounds of ground beef. He wants to make hamburgers that weigh \\(\\frac{3}{16}\\) pound each.<br \/>\n\\(\\frac{15}{16}\\) \u00f7 \\(\\frac{3}{16}\\)<br \/>\n15\/3 = 5<\/p>\n<p><strong>Spiral Review<\/strong><\/p>\n<p>Question 3.<br \/>\nLetisha wants to read 22 pages a night. At that rate, how long will it take her to read a book with 300 pages?<br \/>\n______ nights<\/p>\n<p>Answer:<br \/>\n14 nights<\/p>\n<p>Explanation:<br \/>\nLetisha wants to read 22 pages a night. It takes her to read a book with 300 pages<br \/>\n300\/22 = 13.6<br \/>\n13.6 is near to 14<br \/>\nSo, it is for 2 weeks.<\/p>\n<p>Question 4.<br \/>\nA principal wants to order enough notebooks for 624 students. The notebooks come in boxes of 28. How many boxes should he order?<br \/>\n______ boxes<\/p>\n<p>Answer:<br \/>\n22 boxes<\/p>\n<p>Explanation:<br \/>\nA principal wants to order enough notebooks for 624 students. The notebooks come in boxes of 28.<br \/>\n624\/28 = 22.2857<br \/>\n22.2857 is closer to 22<br \/>\n22 boxes.<\/p>\n<p>Question 5.<br \/>\nEach block in Ton\u2019s neighborhood is \\(\\frac{2}{3}\\) mile long. If he walks 4 \\(\\frac{1}{2}\\) blocks, how far does he walk?<br \/>\n______ miles<\/p>\n<p>Answer:<br \/>\n3 miles<\/p>\n<p>Explanation:<br \/>\nIf each block is 2\/3 miles long, and he walks 4 1\/2 blocks, we can simply multiply to two. It looks like this:<br \/>\n(2\/3)(4 1\/2)<br \/>\nto multiply, make 4 1\/2 into an improper fraction and multiply normally<br \/>\n(2\/3)(9\/4)<br \/>\nTon walks 3 miles total.<\/p>\n<p>Question 6.<br \/>\nIn Cathy\u2019s garden, \\(\\frac{5}{6}\\) of the area is planted with flowers. Of the flowers, \\(\\frac{3}{10}\\) of them are red. What fraction of Cathy\u2019s garden is planted with red flowers?<br \/>\n\\(\\frac{\u25a1}{\u25a1}\\)<\/p>\n<p>Answer:<br \/>\n\\(\\frac{1}{4}\\)<\/p>\n<p>Explanation:<br \/>\nIn Cathy\u2019s garden, \\(\\frac{5}{6}\\) of the area is planted with flowers. Of the flowers, \\(\\frac{3}{10}\\) of them are red.<br \/>\n5\/6 x 3\/10 = 1\/4<\/p>\n<h3><a id=\"Estimate_Quotients_\u2013_Page_No._103\"><\/a>Share and Show &#8211; Page No. 103<\/h3>\n<p><strong>Estimate using compatible numbers.<\/strong><\/p>\n<p>Question 1.<br \/>\n\\(22 \\frac{4}{5} \\div 6 \\frac{1}{4}\\)<br \/>\n_______<\/p>\n<p>Answer:<br \/>\n4<\/p>\n<p>Explanation:<br \/>\n22 \\(\\frac{4}{5}\\) = 114\/5 = 22.8<br \/>\n6 \\(\\frac{1}{4}\\) = 25\/4 = 6.25<br \/>\n22.8 is closer to 24<br \/>\n6.25 is closer to 6<br \/>\n24\/6 = 4<\/p>\n<p>Question 2.<br \/>\n\\(12 \\div 3 \\frac{3}{4}\\)<br \/>\n_______<\/p>\n<p>Answer:<br \/>\n3<\/p>\n<p>Explanation:<br \/>\n3 \\(\\frac{3}{4}\\) = 15\/4 = 3.75<br \/>\n3.75 is closer to 4<br \/>\n12\/4 = 3<\/p>\n<p>Question 3.<br \/>\n\\(33 \\frac{7}{8} \\div 5 \\frac{1}{3}\\)<br \/>\n_______<\/p>\n<p>Answer:<br \/>\n7<\/p>\n<p>Explanation:<br \/>\n33 \\(\\frac{7}{8}\\) = 271\/8 = 33.875<br \/>\n5 \\(\\frac{1}{3}\\) = 16\/3 = 5.333<br \/>\n33.875 is closer to 35<br \/>\n5.333 is closer to 5<br \/>\n35\/5 = 7<\/p>\n<p>Question 4.<br \/>\n\\(3 \\frac{7}{8} \\div \\frac{5}{9}\\)<br \/>\n_______<\/p>\n<p>Answer:<br \/>\n4<\/p>\n<p>Explanation:<br \/>\n3 \\(\\frac{7}{8}\\) = 31\/8 = 3.875<br \/>\n\\(\\frac{5}{9}\\) = 0.555<br \/>\n3.875 is closer to 4<br \/>\n0.555 is closer to 1<br \/>\n4\/1 = 4<\/p>\n<p>Question 5.<br \/>\n\\(34 \\frac{7}{12} \\div 7 \\frac{3}{8}\\)<br \/>\n_______<\/p>\n<p>Answer:<br \/>\n5<\/p>\n<p>Explanation:<br \/>\n34 \\(\\frac{7}{12}\\) = 415\/12 = 34.583<br \/>\n7 \\(\\frac{3}{8}\\) = 59\/8 = 7.375<br \/>\n34.583 is closer to 35<br \/>\n7.375 is closer to 7<br \/>\n35\/7 = 5<\/p>\n<p>Question 6.<br \/>\n\\(1 \\frac{2}{9} \\div \\frac{1}{6}\\)<br \/>\n_______<\/p>\n<p>Answer:<br \/>\n5<\/p>\n<p>Explanation:<br \/>\n1 \\(\\frac{2}{9}\\) = 11\/9 = 1.222<br \/>\n\\(\\frac{1}{6}\\) = 0.1666<br \/>\n1.222 is closer to 1<br \/>\n0.1666 is closer to 0.2<br \/>\n1\/0.2 = 5<\/p>\n<p><strong>On Your Own<\/strong><\/p>\n<p><strong>Estimate using compatible numbers.<\/strong><\/p>\n<p>Question 7.<br \/>\n\\(44 \\frac{1}{4} \\div 11 \\frac{7}{9}\\)<br \/>\n_______<\/p>\n<p>Answer:<br \/>\n4<\/p>\n<p>Explanation:<br \/>\n44 \\(\\frac{1}{4}\\) = 177\/4 = 44.25<br \/>\n11 \\(\\frac{7}{9}\\) = 106\/9 = 11.77<br \/>\n44.25 is closer to 44<br \/>\n11.77 is closer to 11<br \/>\n44\/11 = 4<\/p>\n<p>Question 8.<br \/>\n\\(71 \\frac{11}{12} \\div 8 \\frac{3}{4}\\)<br \/>\n_______<\/p>\n<p>Answer:<br \/>\n8<\/p>\n<p>Explanation:<br \/>\n71 \\(\\frac{11}{12}\\) = 863\/12 = 71.916<br \/>\n8 \\(\\frac{3}{4}\\) = 35\/4 = 8.75<br \/>\n71.916 is closer to 72<br \/>\n8.75 is closer to 9<br \/>\n72\/9 = 8<\/p>\n<p>Question 9.<br \/>\n\\(1 \\frac{1}{6} \\div \\frac{1}{8}\\)<br \/>\n_______<\/p>\n<p>Answer:<br \/>\n12<\/p>\n<p>Explanation:<br \/>\n1 \\(\\frac{1}{6}\\) = 7\/6 = 1.166<br \/>\n\\(\\frac{1}{8}\\) = 0.125<br \/>\n1.166 is closer to 1.2<br \/>\n0.125 is closer to 0.1<br \/>\n1.2\/0.1 = 12<\/p>\n<p><strong>Estimate to compare. Write &lt;, &gt;, or =.<\/strong><\/p>\n<p>Question 10.<br \/>\n\\(21 \\frac{3}{10} \\div 2 \\frac{5}{6}\\) _______ \\(35 \\frac{7}{9} \\div 3 \\frac{2}{3}\\)<\/p>\n<p>Answer:<br \/>\n\\(21 \\frac{3}{10} \\div 2 \\frac{5}{6}\\) &lt; \\(35 \\frac{7}{9} \\div 3 \\frac{2}{3}\\)<\/p>\n<p>Explanation:<br \/>\n21 \\(\\frac{3}{10}\\) = 213\/10 = 21.3<br \/>\n2 \\(\\frac{5}{6}\\) = 17\/6 = 2.833<br \/>\n21.3 is closer to 21<br \/>\n2.833 is closer to 3<br \/>\n21\/3 = 7<br \/>\n35 \\(\\frac{7}{9}\\) = 322\/9 = 35.777<br \/>\n3 \\(\\frac{2}{3}\\) = 11\/3 = 3.666<br \/>\n35.777 is closer to 36<br \/>\n3.666 is closer to 4<br \/>\n36\/4 = 9<br \/>\n7 &lt; 9<br \/>\nSo, \\(21 \\frac{3}{10} \\div 2 \\frac{5}{6}\\) &lt; \\(35 \\frac{7}{9} \\div 3 \\frac{2}{3}\\)<\/p>\n<p>Question 11.<br \/>\n\\(29 \\frac{4}{5} \\div 5 \\frac{1}{6}\\) _______ \\(27 \\frac{8}{9} \\div 6 \\frac{5}{8}\\)<\/p>\n<p>Answer:<br \/>\n\\(29 \\frac{4}{5} \\div 5 \\frac{1}{6}\\) &gt; \\(27 \\frac{8}{9} \\div 6 \\frac{5}{8}\\)<\/p>\n<p>Explanation:<br \/>\n29 \\(\\frac{4}{5}\\) = 149\/5 = 29.8<br \/>\n5 \\(\\frac{1}{6}\\) = 31\/6 = 5.1666<br \/>\n29.8 is closer to 30<br \/>\n5.1666 is closer to 5<br \/>\n30\/5 = 6<br \/>\n27 \\(\\frac{8}{9}\\) = 251\/9 = 27.888<br \/>\n6 \\(\\frac{5}{8}\\) = 53\/8 = 6.625<br \/>\n27.888 is closer to 30<br \/>\n6.625 is closer 7<br \/>\n30\/7 = 5<br \/>\n6 &gt; 5<br \/>\n\\(29 \\frac{4}{5} \\div 5 \\frac{1}{6}\\) &gt; \\(27 \\frac{8}{9} \\div 6 \\frac{5}{8}\\)<\/p>\n<p>Question 12.<br \/>\n\\(55 \\frac{5}{6} \\div 6 \\frac{7}{10}\\) _______ \\(11 \\frac{5}{7} \\div \\frac{5}{8}\\)<\/p>\n<p>Answer:<br \/>\n\\(55 \\frac{5}{6} \\div 6 \\frac{7}{10}\\) &lt; \\(11 \\frac{5}{7} \\div \\frac{5}{8}\\)<\/p>\n<p>Explanation:<br \/>\n55 \\(\\frac{5}{6}\\) = 335\/6 = 55.833<br \/>\n6 \\(\\frac{7}{10}\\) = 67\/10 = 6.7<br \/>\n55.833 is closer to 56<br \/>\n6.7 is closer to 7<br \/>\n56\/7 = 8<br \/>\n11 \\(\\frac{5}{7}\\) = 82\/7 = 11.714<br \/>\n\\(\\frac{5}{8}\\) = 0.625<br \/>\n11.714 is closer to 12<br \/>\n0.625 is closer to 1<br \/>\n12\/1 = 12<br \/>\n8 &lt; 12<\/p>\n<p>Question 13.<br \/>\nMarion is making school flags. Each flag uses 2 \\(\\frac{3}{4}\\) yards of felt. Marion has 24 \\(\\frac{1}{8}\\) yards of felt. About how many flags can he make?<br \/>\nAbout _______ flags<\/p>\n<p>Answer:<br \/>\nAbout 8 flags<\/p>\n<p>Explanation:<br \/>\nMarion is making school flags. Each flag uses 2 \\(\\frac{3}{4}\\) yards of felt. Marion has 24 \\(\\frac{1}{8}\\) yards of felt.<br \/>\n2 \\(\\frac{3}{4}\\) = 11\/4<br \/>\n24 \\(\\frac{1}{8}\\) = 193\/8<br \/>\n193\/8 \u00f7 11\/4<br \/>\n193\/8 x 4\/11 = 8.77<br \/>\nAbout 8 flags<\/p>\n<p>Question 14.<br \/>\nA garden snail travels about 2 \\(\\frac{3}{5}\\) feet in 1 minute. At that speed, about how many hours would it take the snail to travel 350 feet?<br \/>\nAbout _______ hours<\/p>\n<p>Answer:<br \/>\nAbout 2 hours<\/p>\n<p>Explanation:<br \/>\n2 \\(\\frac{3}{5}\\) = 2.6<br \/>\nThat&#8217;s how long he travels in one minute. There are 60 minutes in an hour so multiply it by 60 and see if that gets you close to 350.<br \/>\n60 x 2.6 = 156<br \/>\nNow let&#8217;s add one more hour.<br \/>\n156 + 156 = 312<br \/>\n14 x 2.6 = 36.4<br \/>\n312 + 36.4 = 348.4<br \/>\n348.4 + 2.6 = 351<br \/>\nSo two hours and fourteen minutes<\/p>\n<h3><a id=\"Estimate_Quotients_\u2013_Page_No._104\"><\/a>Problem Solving + Applications &#8211; Page No. 104<\/h3>\n<p><strong>What\u2019s the Error?<\/strong><\/p>\n<p>Question 15.<br \/>\nMegan is making pennants from a piece of butcher paper that is 10 \\(\\frac{3}{8}\\) yards long. Each pennant requires \\(\\frac{3}{8}\\) yard of paper. To estimate the number of pennants she could make, Megan estimated the quotient 10 \\(\\frac{3}{8}\\) \u00f7 \\(\\frac{3}{8}\\).<br \/>\nLook at how Megan solved the problem. Find her error<br \/>\nEstimate:<br \/>\n10 \\(\\frac{3}{8}\\) \u00f7 \\(\\frac{3}{8}\\)<br \/>\n10 \u00f7 \\(\\frac{1}{2}\\) = 5<br \/>\nCorrect the error. Estimate the quotient.<br \/>\nSo, Megan can make about _____ pennants.<br \/>\nDescribe the error that Megan made<br \/>\nExplain Tell which compatible numbers you used to estimate 10 \\(\\frac{3}{8}\\) \u00f7 \\(\\frac{3}{8}\\). Explain why you chose those numbers.<br \/>\nType below:<br \/>\n__________<\/p>\n<p>Answer:<br \/>\n10 \\(\\frac{3}{8}\\) \u00f7 \\(\\frac{3}{8}\\)<br \/>\n10 \\(\\frac{3}{8}\\) = 83\/8 = 10.375<br \/>\n\\(\\frac{3}{8}\\) = 0.375<br \/>\nShe had written 10 \u00f7 \\(\\frac{1}{2}\\) = 5<br \/>\n10.375 is closer to 10<br \/>\n0.375 is closer to 0.5<br \/>\n10\/0.5 = 20<br \/>\nBut she has written 5 instead of 20.<br \/>\nMegan can make about 20 pennants.<\/p>\n<p><strong>For numbers 16a\u201316c, estimate to compare. Choose &lt;, &gt;, or =.<\/strong><\/p>\n<p>Question 16.<br \/>\n16a. 18 \\(\\frac{3}{10} \\div 2 \\frac{5}{6}\\) ? \\(30 \\frac{7}{9} \\div 3 \\frac{1}{3}\\)<br \/>\n_____<\/p>\n<p>Answer:<br \/>\n16a. 18 \\(\\frac{3}{10} \\div 2 \\frac{5}{6}\\) &lt; \\(30 \\frac{7}{9} \\div 3 \\frac{1}{3}\\)<\/p>\n<p>Explanation:<br \/>\n18 \\(\\frac{3}{10}\\) = 183\/10 = 18.3<br \/>\n2 \\(\\frac{5}{6}\\) = 17\/6 = 2.833<br \/>\n18.3 is closer to 18<br \/>\n2.833 is closer to 3<br \/>\n18\/3 = 6<br \/>\n30 \\(\\frac{7}{9}\\) = 277\/9 = 30.777<br \/>\n3 \\(\\frac{1}{3}\\) = 10\/3 = 3.333<br \/>\n30.777 is closer to 30<br \/>\n3.333 is closer to 3<br \/>\n30\/3 = 10<br \/>\n6 &lt; 10<\/p>\n<p>Question 16.<br \/>\n16b. 17 \\(\\frac{4}{5} \\div 6 \\frac{1}{6}\\) ? \\(19 \\frac{8}{9} \\div 4 \\frac{5}{8}\\)<br \/>\n_____<\/p>\n<p>Answer:<br \/>\n17 \\(\\frac{4}{5} \\div 6 \\frac{1}{6}\\) &lt; \\(19 \\frac{8}{9} \\div 4 \\frac{5}{8}\\)<\/p>\n<p>Explanation:<br \/>\n17 \\(\\frac{4}{5}\\) = 89\/5 = 17.8<br \/>\n6 \\(\\frac{1}{6}\\) = 37\/6 = 6.1666<br \/>\n17.8 is closer to 18<br \/>\n6.1666 is closer to 6<br \/>\n18\/6 = 3<br \/>\n19 \\(\\frac{8}{9}\\) = 179\/9 = 19.888<br \/>\n4 \\(\\frac{5}{8}\\) = 37\/8 = 4.625<br \/>\n19.888 is closer to 20<br \/>\n4.625 is closer to 5<br \/>\n20\/5 = 4<br \/>\n3 &lt; 4<br \/>\n17 \\(\\frac{4}{5} \\div 6 \\frac{1}{6}\\) &lt; \\(19 \\frac{8}{9} \\div 4 \\frac{5}{8}\\)<\/p>\n<p>Question 16.<br \/>\n16c. 17 \\(\\frac{5}{6} \\div 6 \\frac{1}{4}\\) ? \\(11 \\frac{5}{7} \\div 2 \\frac{3}{4}\\)<br \/>\n_____<\/p>\n<p>Answer:<br \/>\n17 \\(\\frac{5}{6} \\div 6 \\frac{1}{4}\\) &lt; \\(11 \\frac{5}{7} \\div 2 \\frac{3}{4}\\)<\/p>\n<p>Explanation:<br \/>\n17 \\(\\frac{5}{6}\\) = 107\/6 = 17.833<br \/>\n6 \\(\\frac{1}{4}\\) = 25\/4 = 6.25<br \/>\n17.833 is closer to 18<br \/>\n6.25 is closer to 6<br \/>\n18\/6 = 3<br \/>\n11 \\(\\frac{5}{7}\\) = 82\/7 = 11.714<br \/>\n2 \\(\\frac{3}{4}\\) = 11\/4 = 2.75<br \/>\n11.714 is closer to 12<br \/>\n2.75 is closer to 3<br \/>\n12\/3 = 4<br \/>\n3 &lt; 4<br \/>\n17 \\(\\frac{5}{6} \\div 6 \\frac{1}{4}\\) &lt; \\(11 \\frac{5}{7} \\div 2 \\frac{3}{4}\\)<\/p>\n<h3><a id=\"Estimate_Quotients_Lesson_Check_\u2013_Page_No._105\"><\/a>Estimate Quotients &#8211; Page No. 105<\/h3>\n<p><strong>Estimate using compatible numbers.<\/strong><\/p>\n<p>Question 1.<br \/>\n\\(12 \\frac{3}{16} \\div 3 \\frac{9}{10}\\)<br \/>\n______<\/p>\n<p>Answer:<br \/>\n3<\/p>\n<p>Explanation:<br \/>\n12 \\(\\frac{3}{16}\\) = 195\/16 = 12.1875<br \/>\n3 \\(\\frac{9}{10}\\) = 39\/10 = 3.9<br \/>\n12.1875 is closer to 12<br \/>\n3.9 is closer to 4<br \/>\n12\/4 = 3<\/p>\n<p>Question 2.<br \/>\n\\(15 \\frac{3}{8} \\div \\frac{1}{2}\\)<br \/>\n______<\/p>\n<p>Answer:<br \/>\n30<\/p>\n<p>Explanation:<br \/>\n15 \\(\\frac{3}{8}\\) = 123\/8 = 15.375<br \/>\n\\(\\frac{1}{2}\\) = 0.5<br \/>\n15.375 is closer to 15<br \/>\n0.5 is closer to 0.5<br \/>\n15\/0.5 = 30<\/p>\n<p>Question 3.<br \/>\n\\(22 \\frac{1}{5} \\div 1 \\frac{5}{6}\\)<br \/>\n______<\/p>\n<p>Answer:<br \/>\n11<\/p>\n<p>Explanation:<br \/>\n22 \\(\\frac{1}{5}\\) = 111\/5 = 22.2<br \/>\n1 \\(\\frac{5}{6}\\) = 11\/6 = 1.8333<br \/>\n22.2 is closer to 22<br \/>\n1.8333 is closer to 2<br \/>\n22\/2 = 11<\/p>\n<p>Question 4.<br \/>\n\\(7 \\frac{7}{9} \\div \\frac{4}{7}\\)<br \/>\n______<\/p>\n<p>Answer:<br \/>\n16<\/p>\n<p>Explanation:<br \/>\n7 \\(\\frac{7}{9}\\) = 70\/9 = 7.777<br \/>\n\\(\\frac{4}{7}\\) = 0.571<br \/>\n7.777 is closer to 8<br \/>\n0.571 is closer to 0.5<br \/>\n8\/0.5 = 16<\/p>\n<p>Question 5.<br \/>\n\\(18 \\frac{1}{4} \\div 2 \\frac{4}{5}\\)<br \/>\n______<\/p>\n<p>Answer:<br \/>\n6<\/p>\n<p>Explanation:<br \/>\n18 \\(\\frac{1}{4}\\) = 73\/4 = 18.25<br \/>\n2 \\(\\frac{4}{5}\\) = 14\/5 = 2.8<br \/>\n18.25 is closer to 18<br \/>\n2.8 is closer to 3<br \/>\n18\/3 = 6<\/p>\n<p>Question 6.<br \/>\n\\(\\frac{15}{16} \\div \\frac{1}{7}\\)<br \/>\n______<\/p>\n<p>Answer:<br \/>\n10<\/p>\n<p>Explanation:<br \/>\n\\(\\frac{15}{16}\\) = 0.9375<br \/>\n\\(\\frac{1}{7}\\) = 0.1428<br \/>\n0.9375 is closer to 1<br \/>\n0.1428 is closer to 0.1<br \/>\n1\/0.1 = 10<\/p>\n<p>Question 7.<br \/>\n\\(14 \\frac{7}{8} \\div \\frac{5}{11}\\)<br \/>\n______<\/p>\n<p>Answer:<br \/>\n30<\/p>\n<p>Explanation:<br \/>\n14 \\(\\frac{7}{8}\\) = 119\/8 = 14.875<br \/>\n\\(\\frac{5}{11}\\) = 0.4545<br \/>\n14.875 is closer to 15<br \/>\n0.4545 is closer to 0.5<br \/>\n15\/0.5 = 30<\/p>\n<p>Question 8.<br \/>\n\\(53 \\frac{7}{12} \\div 8 \\frac{11}{12}\\)<br \/>\n______<\/p>\n<p>Answer:<br \/>\n6<\/p>\n<p>Explanation:<br \/>\n53 \\(\\frac{7}{12}\\) = 643\/12 = 53.58<br \/>\n8 \\(\\frac{11}{12}\\) = 107\/12 = 8.916<br \/>\n53.58 is closer to 54<br \/>\n8.916 is closer to 9<br \/>\n54\/9 = 6<\/p>\n<p>Question 9.<br \/>\n\\(1 \\frac{1}{6} \\div \\frac{1}{9}\\)<br \/>\n______<\/p>\n<p>Answer:<br \/>\n10<\/p>\n<p>Explanation:<br \/>\n1 \\(\\frac{1}{6}\\) = 7\/6 = 1.166<br \/>\n\\(\\frac{1}{9}\\) = 0.111<br \/>\n1.166 is closer to 1<br \/>\n0.111 is closer to 0.1<br \/>\n1\/0.1 = 10<\/p>\n<p><strong>Problem Solving<\/strong><\/p>\n<p>Question 10.<br \/>\nEstimate the number of pieces Sharon will have if she divides 15 \\(\\frac{1}{3}\\) yards of fabric into 4 \\(\\frac{4}{5}\\) yard lengths.<br \/>\nAbout ______ pieces<\/p>\n<p>Answer:<br \/>\nAbout 3 pieces<\/p>\n<p>Explanation:<br \/>\nSharon will have if she divides 15 \\(\\frac{1}{3}\\) yards of fabric into 4 \\(\\frac{4}{5}\\) yard lengths.<br \/>\n3 7\/36 is the answer.<br \/>\nSo, about 3 pieces<\/p>\n<p>Question 11.<br \/>\nEstimate the number of \\(\\frac{1}{2}\\) quart containers Ethan can fill from a container with 8 \\(\\frac{7}{8}\\) quarts of water.<br \/>\nAbout ______ containers<\/p>\n<p>Answer:<br \/>\nAbout 18 containers<\/p>\n<p>Question 12.<br \/>\nHow is estimating quotients different from estimating products?<br \/>\nType below:<br \/>\n__________<\/p>\n<p>Answer:<br \/>\nTo estimate products and quotients, you need to first round the numbers. To round to the nearest whole number, look at the digit in the tenths place. If it is less than 5, round down. If it is 5 or greater, round up. Remember that an estimate is an answer that is not exact, but is approximate and reasonable.<br \/>\nLet\u2019s look at an example of estimating a product.<br \/>\nEstimate the product: 11.256\u00d76.81<br \/>\nFirst, round the first number. Since there is a 2 in the tenths place, 11.256 rounds down to 11.<br \/>\nNext, round the second number. Since there is an 8 in the tenths place, 6.81 rounds up to 7.<br \/>\nThen, multiply the rounded numbers. 11\u00d77=77<br \/>\nThe answer is 77.<br \/>\nLet\u2019s look at an example of estimating a quotient.<br \/>\nEstimate the quotient: 91.93\u00f74.39<br \/>\nFirst, round the first number. Since there is a 9 in the tenths place, 91.93 rounds up to 92.<br \/>\nNext, round the second number. Since there is a 3 in the tenths place, 4.39 rounds down to 4.<br \/>\nThen, divide the rounded numbers.<br \/>\n92\u00f74=23<br \/>\nThe answer is 23.<\/p>\n<h3><a id=\"Estimate_Quotients_Lesson_Check_1_\u2013_Page_No._106\"><\/a>Lesson Check &#8211; Page No. 106<\/h3>\n<p>Question 1.<br \/>\nEach loaf of pumpkin bread calls for 1 \\(\\frac{3}{4}\\) cups of raisins. About how many loaves can be made from 10 cups of raisins?<br \/>\nAbout ______ loaves<\/p>\n<p>Answer:<br \/>\nAbout 5 loaves<\/p>\n<p>Explanation:<br \/>\nDivide 10 by 1 3\/4.<br \/>\nThe answer is 5.714285<br \/>\nSo you can make about 5 loaves of bread with 10 cups of raisins if each loaf needs 1 3\/4 cups of raisins.<\/p>\n<p>Question 2.<br \/>\nPerry\u2019s goal is to run 2 \\(\\frac{1}{4}\\) miles each day. One lap around the school track is \\(\\frac{1}{3}\\) mile. About how many laps must he run to reach his goal?<br \/>\nAbout ______ laps<\/p>\n<p>Answer:<br \/>\nAbout 9 laps<\/p>\n<p>Explanation:<br \/>\nPerry\u2019s goal is to run 2 \\(\\frac{1}{4}\\) miles each day. One lap around the school track is \\(\\frac{1}{3}\\) mile.<br \/>\n2 \\(\\frac{1}{4}\\) = 9\/4 = 2.25<br \/>\n\\(\\frac{1}{3}\\) = 0.333<br \/>\nPerry will have to run 9 laps to reach his goal.<\/p>\n<p><strong>Spiral Review<\/strong><\/p>\n<p>Question 3.<br \/>\nA recipe calls for \\(\\frac{3}{4}\\) teaspoon of red pepper. Uri wants to use \\(\\frac{1}{3}\\) of that amount. How much red pepper should he use?<br \/>\n\\(\\frac{\u25a1}{\u25a1}\\) teaspoon<\/p>\n<p>Answer:<br \/>\n\\(\\frac{1}{4}\\) teaspoon<\/p>\n<p>Explanation:<br \/>\nA recipe calls for \\(\\frac{3}{4}\\) teaspoon of red pepper. Uri wants to use \\(\\frac{1}{3}\\) of that amount.<br \/>\n\\(\\frac{1}{3}\\) of \\(\\frac{3}{4}\\) = \\(\\frac{1}{4}\\)<\/p>\n<p>Question 4.<br \/>\nA recipe calls for 2 \\(\\frac{2}{3}\\) cups of apple slices. Zoe wants to use 1 \\(\\frac{1}{2}\\) times this amount. How many cups of apples should Zoe use?<br \/>\n______ cups<\/p>\n<p>Answer:<br \/>\n4 cups<\/p>\n<p>Explanation:<br \/>\nA recipe calls for 2 2\/3 cups of apple slices.<br \/>\nZoe wants to use 1 1\/2 times this amount.<br \/>\nWe will multiply the number of apple slices to 1 1\/2<br \/>\n2 2\/3 X 1 1\/2<br \/>\n8\/3 X3\/2 = 24\/6 = 4 cups<br \/>\nZoe will use 4 cups of apple slices.<\/p>\n<p>Question 5.<br \/>\nEdgar has 2.8 meters of rope. If he cuts it into 7 equal parts, how long will each piece be?<br \/>\n______ meters<\/p>\n<p>Answer:<br \/>\n0.4 meters<\/p>\n<p>Explanation:<br \/>\n2.8\/7 = 0.4 meters<\/p>\n<p>Question 6.<br \/>\nKami has 7 liters of water to fill water bottles that each hold 2.8 liters. How many bottles can she fill?<br \/>\n______ bottles<\/p>\n<p>Answer:<br \/>\n2 bottles<\/p>\n<p>Explanation:<br \/>\n7\/2.8 = 2.5<br \/>\nshe can only fill 2 because anything over that would 8.4 liters of water<\/p>\n<h3><a id=\"Divide_Fractions_\u2013_Page_No._109\"><\/a>Share and Show &#8211; Page No. 109<\/h3>\n<p><strong>Estimate. Then find the quotient.<\/strong><\/p>\n<p>Question 1.<br \/>\n\\(\\frac{5}{6}\\) \u00f7 3<br \/>\n\\(\\frac{\u25a1}{\u25a1}\\)<\/p>\n<p>Answer:<br \/>\n\\(\\frac{3}{10}\\)<\/p>\n<p>Explanation:<br \/>\n5\/6 = 0.8333 is closer to 0.9<br \/>\n0.9\/3 = 0.3 = 3\/10<\/p>\n<p><strong>Use a number line to find the quotient.<\/strong><\/p>\n<p>Question 2.<br \/>\n\\(\\frac{3}{4} \\div \\frac{1}{8}\\)<br \/>\n_______<\/p>\n<p>Answer:<br \/>\n<img loading=\"lazy\" class=\"alignnone size-medium wp-image-8324\" src=\"https:\/\/ccssmathanswers.com\/wp-content\/uploads\/2020\/08\/grade-6-chapter-2-image-7-300x108.jpg\" alt=\"grade 6 chapter 2 image 7\" width=\"300\" height=\"108\" srcset=\"https:\/\/bigideasmathanswers.com\/wp-content\/uploads\/2020\/08\/grade-6-chapter-2-image-7-300x108.jpg 300w, https:\/\/bigideasmathanswers.com\/wp-content\/uploads\/2020\/08\/grade-6-chapter-2-image-7.jpg 390w\" sizes=\"(max-width: 300px) 100vw, 300px\" \/><\/p>\n<p>Explanation:<br \/>\n3\/4 x 8 = 3 x 2 = 6<\/p>\n<p>Question 3.<br \/>\n\\(\\frac{3}{5} \\div \\frac{3}{10}\\)<br \/>\n_______<\/p>\n<p>Answer:<\/p>\n<p>Explanation:<br \/>\n3\/5 x 10\/3 = 2<\/p>\n<p><strong>Estimate. Then write the quotient in simplest form.<\/strong><\/p>\n<p>Question 4.<br \/>\n\\(\\frac{3}{4} \\div \\frac{5}{6}\\)<br \/>\n\\(\\frac{\u25a1}{\u25a1}\\)<\/p>\n<p>Answer:<br \/>\n\\(\\frac{1}{1}\\)<\/p>\n<p>Explanation:<br \/>\n3\/4 = 0.75 is closer to 0.8<br \/>\n5\/6 = 0.8333 is closer to 0.8<br \/>\n0.8\/0.8 = 1<\/p>\n<p>Question 5.<br \/>\n\\(3 \\div \\frac{3}{4}\\)<br \/>\n_______<\/p>\n<p>Answer:<br \/>\n4<\/p>\n<p>Explanation:<br \/>\n3\/4 = 0.75<br \/>\n3\/0.75 = 4<\/p>\n<p>Question 6.<br \/>\n\\(\\frac{1}{2} \\div \\frac{3}{4}\\)<br \/>\n\\(\\frac{\u25a1}{\u25a1}\\)<\/p>\n<p>Answer:<br \/>\n\\(\\frac{625}{1000}\\)<\/p>\n<p>Explanation:<br \/>\n1\/2 = 0.5<br \/>\n3\/4 = 0.75 is closer to 0.8<br \/>\n0.5\/0.8 = 0.625 = 625\/1000<\/p>\n<p>Question 7.<br \/>\n\\(\\frac{5}{12} \\div 3\\)<br \/>\n\\(\\frac{\u25a1}{\u25a1}\\)<\/p>\n<p>Answer:<br \/>\n\\(\\frac{2}{10}\\)<\/p>\n<p>Explanation:<br \/>\n5\/12 = 0.4166 is closer to 0.6<br \/>\n0.6\/3 = 0.2 = 2\/10<\/p>\n<p><strong>On Your Own<\/strong><\/p>\n<p><strong>Practice: Copy and Solve Estimate. Then write the quotient in simplest form<\/strong><\/p>\n<p>Question 8.<br \/>\n\\(2 \\div \\frac{1}{8}\\)<br \/>\n_______<\/p>\n<p>Answer:<br \/>\n20<\/p>\n<p>Explanation:<br \/>\n1\/8 = 0.125 is closer to 0.1<br \/>\n2\/0.1 = 20<\/p>\n<p>Question 9.<br \/>\n\\(\\frac{3}{4} \\div \\frac{3}{5}\\)<br \/>\n\\(\\frac{\u25a1}{\u25a1}\\)<\/p>\n<p>Answer:<br \/>\n\\(\\frac{1}{1}\\)<\/p>\n<p>Explanation:<br \/>\n3\/4 = 0.75 is closer to 0.8<br \/>\n3\/5 = is 0.6 closer to 0.8<br \/>\n0.8\/0.8 = 1<\/p>\n<p>Question 10.<br \/>\n\\(\\frac{2}{5} \\div 5\\)<br \/>\n\\(\\frac{\u25a1}{\u25a1}\\)<\/p>\n<p>Answer:<br \/>\n\\(\\frac{1}{10}\\)<\/p>\n<p>Explanation:<br \/>\n2\/5 = 0.4 is closer to 0.5<br \/>\n0.5\/5 = 0.1 = 1\/10<\/p>\n<p>Question 11.<br \/>\n\\(4 \\div \\frac{1}{7}\\)<br \/>\n_______<\/p>\n<p>Answer:<br \/>\n40<\/p>\n<p>Explanation:<br \/>\n1\/7 = 0.1428 is closer to 0.1<br \/>\n4\/0.1 = 40<\/p>\n<p><strong>Practice: Copy and Solve Evaluate using the order of operations.<\/strong><\/p>\n<p><strong>Write the answer in simplest form.<\/strong><\/p>\n<p>Question 12.<br \/>\n\\(\\left(\\frac{3}{5}+\\frac{1}{10}\\right) \\div 2\\)<br \/>\n\\(\\frac{\u25a1}{\u25a1}\\)<\/p>\n<p>Answer:<br \/>\n\\(\\frac{7}{20}\\)<\/p>\n<p>Explanation:<br \/>\n3\/5 + 1\/10 = 7\/10 = 0.7<br \/>\n0.7\/2 = 7\/20<\/p>\n<p>Question 13.<br \/>\n\\(\\frac{3}{5}+\\frac{1}{10} \\div 2\\)<br \/>\n\\(\\frac{\u25a1}{\u25a1}\\)<\/p>\n<p>Answer:<br \/>\n\\(\\frac{13}{20}\\)<\/p>\n<p>Explanation:<br \/>\n\\(\\frac{3}{5}+\\frac{1}{10} \\div 2\\)<br \/>\n(1\/10)\/2 = 1\/20<br \/>\n3\/5 + 1\/20 = 0.65 = 13\/20<\/p>\n<p>Question 14.<br \/>\n\\(\\frac{3}{5}+2 \\div \\frac{1}{10}\\)<br \/>\n_______ \\(\\frac{\u25a1}{\u25a1}\\)<\/p>\n<p>Answer:<\/p>\n<p>Explanation:<br \/>\n2\/(1\/10) = 1\/5<br \/>\n3\/5 + 1\/5 = 4\/5<\/p>\n<p>Question 15.<br \/>\nGeneralize Suppose the divisor and the dividend of a division problem are both fractions between 0 and 1, and the divisor is greater than the dividend. Is the quotient less than, equal to, or greater than 1?<br \/>\nType below:<br \/>\n__________<\/p>\n<p>Answer:<br \/>\nDivisor and Dividend are fractions lying between 0 and 1<br \/>\nAlso, Divisor &gt; Dividend<br \/>\nA smaller number is being divided by a larger number<br \/>\nWhenever a smaller number is divided by a larger number, the quotient is less than 1<br \/>\nExample:<br \/>\n0,5\/0,6 Here, they are both numbers between 0 and 1, and the divisor is greater than the dividend.<br \/>\nThe result is 0,8333, LESS THAN 1<br \/>\nHence, the answer is that the quotient will be less than 1<\/p>\n<h3><a id=\"Divide_Fractions_\u2013_Page_No._110\"><\/a>Problem Solving + Applications &#8211; Page No. 110<\/h3>\n<p><strong>Use the table for 16\u201319.<\/strong><br \/>\n<img loading=\"lazy\" class=\"alignnone size-full wp-image-4798\" src=\"https:\/\/ccssmathanswers.com\/wp-content\/uploads\/2020\/08\/Go-Math-Grade-6-Answer-Key-Chapter-2-Fractions-and-Decimals-16.jpg\" alt=\"Go Math Grade 6 Answer Key Chapter 2 Fractions and Decimals 16\" width=\"288\" height=\"181\" \/><\/p>\n<p>Question 16.<br \/>\nKristen wants to cut ladder rungs from a 6 ft board. How many ladder rungs can she cut?<br \/>\n_______ ladder rungs<\/p>\n<p>Answer:<br \/>\n8 ladder rungs<\/p>\n<p>Explanation:<br \/>\nKristen wants to cut ladder rungs from a 6 ft board.<br \/>\nladder rungs = 3\/4 ft<br \/>\n6\/(3\/4) = 8 rungs<\/p>\n<p>Question 17.<br \/>\nPose a Problem Look back at Problem 16. Write and solve a new problem by changing the length of the board Kristen is cutting for ladder rungs.<br \/>\nType below:<br \/>\n__________<\/p>\n<p>Answer:<br \/>\nKristen wants to cut ladder rungs from a 9 ft board. How many ladder rungs can she cut?<br \/>\nKristen wants to cut ladder rungs from a 9 ft board.<br \/>\nladder rungs = 3\/4 ft<br \/>\n9\/(3\/4) = 12 rungs<\/p>\n<p>Question 18.<br \/>\nDan paints a design that has 8 equal parts along the entire length of the windowsill. How long is each part of the design?<br \/>\n\\(\\frac{\u25a1}{\u25a1}\\) yards<\/p>\n<p>Answer:<br \/>\n\\(\\frac{1}{16}\\) yards<\/p>\n<p>Explanation:<br \/>\nDan paints a design that has 8 equal parts along the entire length of the windowsill.<br \/>\n(1\/2)\/8 = 1\/2 x 1\/8 = 1\/16 yards<\/p>\n<p>Question 19.<br \/>\nDan has a board that is \\(\\frac{15}{16}\\) yd. How many \u201cKeep Out\u201d signs can he make if the length of the sign is changed to half of the original length?<br \/>\n_______ signs<\/p>\n<p>Answer:<br \/>\n3 signs<\/p>\n<p>Explanation:<br \/>\nDan has a board that is \\(\\frac{15}{16}\\) yd.<br \/>\nIf the length of the sign is changed to half of the original length, (5\/8)\/2 = 5\/16<br \/>\n(15\/16) \u00f7 5\/16 = 15\/16 x 16\/5 = 3<\/p>\n<p>Question 20.<br \/>\nLauren has \\(\\frac{3}{4}\\) cup of dried fruit. She puts the dried fruit into bags, each holding \\(\\frac{1}{8}\\) cup. How many bags will Lauren use? Explain your answer using words and numbers.<br \/>\nType below:<br \/>\n__________<\/p>\n<p>Answer:<br \/>\n6<\/p>\n<p>Explanation:<br \/>\nLauren has \\(\\frac{3}{4}\\) cup of dried fruit. She puts the dried fruit into bags, each holding \\(\\frac{1}{8}\\) cup.<br \/>\n3\/4 \u00f7 1\/8 = 3\/4 x 8 = 6<br \/>\nLauren has 3\/4 and in 1\/4 there are 2 1\/8s. That 3 fourths times two = 6 so 6 one eights<\/p>\n<h3><a id=\"Divide_Fractions_Lesson_Check_\u2013_Page_No._111\"><\/a>Divide Fractions &#8211; Page No. 111<\/h3>\n<p><strong>Estimate. Then write the quotient in simplest form.<\/strong><\/p>\n<p>Question 1.<br \/>\n\\(5 \\div \\frac{1}{6}\\)<br \/>\n_____<\/p>\n<p>Answer:<br \/>\n25<\/p>\n<p>Explanation:<br \/>\n1\/6 = 0.166 is closer to 0.2<br \/>\n5\/0.2 = 25<\/p>\n<p>Question 2.<br \/>\n\\(\\frac{1}{2} \\div \\frac{1}{4}\\)<br \/>\n_____<\/p>\n<p>Answer:<br \/>\n5<\/p>\n<p>Explanation:<br \/>\n1\/2 = 0.5 is closer to 1<br \/>\n1\/4 = 0.25 is closer to 0.2<br \/>\n1\/0.2 = 5<\/p>\n<p>Question 3.<br \/>\n\\(\\frac{4}{5} \\div \\frac{2}{3}\\)<br \/>\n_____ \\(\\frac{\u25a1}{\u25a1}\\)<\/p>\n<p>Answer:<br \/>\n1 \\(\\frac{1}{5}\\)<\/p>\n<p>Explanation:<br \/>\n4\/5 = 0.8 is closer to 0.8<br \/>\n2\/3 = 0.66 is closer to 0.6<br \/>\n0.8\/0.6 = 1 1\/5<\/p>\n<p>Question 4.<br \/>\n\\(\\frac{14}{15} \\div 7\\)<br \/>\n\\(\\frac{\u25a1}{\u25a1}\\)<\/p>\n<p>Answer:<br \/>\n\\(\\frac{2}{15}\\)<\/p>\n<p>Explanation:<br \/>\n14\/15 = 0.9333<br \/>\n0.9\/7 = 2\/15<\/p>\n<p>Question 5.<br \/>\n\\(8 \\div \\frac{1}{3}\\)<br \/>\n_____<\/p>\n<p>Answer:<br \/>\n20<\/p>\n<p>Explanation:<br \/>\n1\/3 = 0.33 is closer to 0.4<br \/>\n8\/0.4 = 20<\/p>\n<p>Question 6.<br \/>\n\\(\\frac{12}{21} \\div \\frac{2}{3}\\)<br \/>\n\\(\\frac{\u25a1}{\u25a1}\\)<\/p>\n<p>Answer:<br \/>\n\\(\\frac{1}{1}\\)<\/p>\n<p>Explanation:<br \/>\n12\/21 = 0.571 is closer to 0.6<br \/>\n2\/3 = 0.666 is closer to 0.6<br \/>\n0.6\/0.6 = 1<\/p>\n<p>Question 7.<br \/>\n\\(\\frac{5}{6} \\div \\frac{5}{12}\\)<br \/>\n_____<\/p>\n<p>Answer:<br \/>\n2<\/p>\n<p>Explanation:<br \/>\n5\/6 = 0.833 is closer to 0.8<br \/>\n5\/12 = 0.416 is closer to 0.4<br \/>\n0.8\/0.4 = 2<\/p>\n<p>Question 8.<br \/>\n\\(\\frac{5}{8} \\div \\frac{1}{2}\\)<br \/>\n_____ \\(\\frac{\u25a1}{\u25a1}\\)<\/p>\n<p>Answer:<br \/>\n1 \\(\\frac{2}{10}\\)<\/p>\n<p>Explanation:<br \/>\n5\/8 = 0.625 is closer to 0.6<br \/>\n1\/2 = 0.5 is closer to 0.5<br \/>\n0.6\/0.5 = 1.2 = 1 2\/10<\/p>\n<p>Question 9.<br \/>\nJoy ate \\(\\frac{1}{4}\\) of a pizza. If she divides the rest of the pizza into pieces equal to \\(\\frac{1}{8}\\) pizza for her family, how many pieces will her family get?<br \/>\n_____ pieces<\/p>\n<p>Answer:<br \/>\n6 pieces<\/p>\n<p>Explanation:<br \/>\nThe pizza is divided into 4 pieces, Joy ate 1\/4.<br \/>\nSo, the left pices are 1 &#8211; 1\/4 = 3\/4<br \/>\nnow, 3\/4 of a pizza and Joy will divide this rest of the pizza in pieces equal to 1\/8, so we need to make a division<br \/>\n(3\/4) \u00f7 (1\/8) = 24\/4 = 6 pieces.<\/p>\n<p>Question 10.<br \/>\nHideko has \\(\\frac{3}{5}\\) yard of ribbon to tie on balloons for the festival. Each balloon will need \\(\\frac{3}{10}\\) yard of ribbon. How many balloons can Hideko tie with ribbon?<br \/>\n_____ balloons<\/p>\n<p>Answer:<br \/>\n2 balloons<\/p>\n<p>Explanation:<br \/>\n3\/10 yard of ribbon required to tie = 1 balloon<br \/>\n3\/5 yard of ribber can tie = (3\/5) \u00f7 (3\/10) = 2 ballons<br \/>\nWith 3\/5 yard, Hideko can tie 2 balloons<\/p>\n<p><strong>Problem Solving<\/strong><\/p>\n<p>Question 11.<br \/>\nRick knows that 1 cup of glue weighs \\(\\frac{1}{18}\\) pound. He has \\(\\frac{2}{3}\\) pound of glue. How many cups of glue does he have?<br \/>\n_____ cups<\/p>\n<p>Answer:<br \/>\n12 cups<\/p>\n<p>Explanation:<br \/>\nFor 1\/18lb, 1 cup<br \/>\nFor 2\/3lb, x cups.<br \/>\n1\/8x = 1 x 2\/3<br \/>\n1\/8x = 2\/3<br \/>\nx = 2\/3 x 18<br \/>\nx = 2 x 6 = 12 cups<\/p>\n<p>Question 12.<br \/>\nMrs. Jennings had \\(\\frac{5}{7}\\) gallon of paint. She gave \\(\\frac{1}{7}\\) gallon each to some students. How many students received paint if Mrs. Jennings gave away all the paint?<br \/>\n_____ students<\/p>\n<p>Answer:<br \/>\n4 students<\/p>\n<p>Explanation:<br \/>\nMrs. Jennings had \\(\\frac{5}{7}\\) gallon of paint. She gave \\(\\frac{1}{7}\\) gallon each to some students.<br \/>\n\\(\\frac{5}{7}\\) \u00f7 \\(\\frac{1}{7}\\) = 25\/7 = 3.571 is closer to 4<\/p>\n<p>Question 13.<br \/>\nWrite a word problem that involves two fractions. Include the solution.<br \/>\nType below:<br \/>\n__________<\/p>\n<p>Answer:<br \/>\nMrs. Jennings had \\(\\frac{5}{7}\\) gallon of paint. She gave \\(\\frac{1}{7}\\) gallon each to some students. How many students received paint if Mrs. Jennings gave away all the paint?<br \/>\nAnswer:<br \/>\nMrs. Jennings had \\(\\frac{5}{7}\\) gallon of paint. She gave \\(\\frac{1}{7}\\) gallon each to some students.<br \/>\n\\(\\frac{5}{7}\\) \u00f7 \\(\\frac{1}{7}\\) = 25\/7 = 3.571 is closer to 4<\/p>\n<h3><a id=\"Divide_Fractions_Lesson_Check_1_\u2013_Page_No._112\"><\/a>Lesson Check &#8211; Page No. 112<\/h3>\n<p>Question 1.<br \/>\nThere was \\(\\frac{2}{3}\\) of a pizza for 6 friends to share equally. What fraction of the pizza did each person get?<br \/>\n\\(\\frac{\u25a1}{\u25a1}\\)<\/p>\n<p>Answer:<br \/>\n\\(\\frac{1}{9}\\)<\/p>\n<p>Explanation:<br \/>\nThere was \\(\\frac{2}{3}\\) of a pizza for 6 friends to share equally.<br \/>\n\\(\\frac{2}{3}\\) \u00f7 6 = 2\/3 x 1\/6 = 2\/18 = 1\/9<\/p>\n<p>Question 2.<br \/>\nRashad needs \\(\\frac{2}{3}\\) pound of wax to make a candle. How many candles can he make with 6 pounds of wax?<br \/>\n_____ candles<\/p>\n<p>Answer:<br \/>\n9 candles<\/p>\n<p>Explanation:<br \/>\nRashad needs 2\/3 pound a wax to make candles.<br \/>\n1 Candle = 2\/3 pounds.<br \/>\nSo, for 2 pounds,<br \/>\n3 x 2\/3 = 3 candles<br \/>\n2 pounds = 3 candles<br \/>\n1 pound = 3\/2 candles<br \/>\nSo, for 6 pounds,<br \/>\n6 x 3\/2 = 9 candles<\/p>\n<p><strong>Spiral Review<\/strong><\/p>\n<p>Question 3.<br \/>\nJeremy had \\(\\frac{3}{4}\\) of a submarine sandwich and gave his friend \\(\\frac{1}{3}\\) of it. What fraction of the sandwich did the friend receive?<br \/>\n\\(\\frac{\u25a1}{\u25a1}\\)<\/p>\n<p>Answer:<br \/>\n\\(\\frac{1}{4}\\)<\/p>\n<p>Explanation:<br \/>\nJeremy had \\(\\frac{3}{4}\\) of a submarine sandwich and gave his friend \\(\\frac{1}{3}\\) of it.<br \/>\n1\/3 x 3\/4 = 1\/4<\/p>\n<p>Question 4.<br \/>\nEbony walked at a rate of 3 \\(\\frac{1}{2}\\) miles per hour for 1 \\(\\frac{1}{3}\\) hours. How far did she walk?<br \/>\n_____ \\(\\frac{\u25a1}{\u25a1}\\)<\/p>\n<p>Answer:<br \/>\n4 \\(\\frac{2}{3}\\)<\/p>\n<p>Explanation:<br \/>\nEbony walked at a rate of 3 \\(\\frac{1}{2}\\) miles per hour for 1 \\(\\frac{1}{3}\\) hours.<br \/>\n3 1\/2 miles = 7\/2 miles &#8230; 1 hour<br \/>\nx miles = ? &#8230; 1 1\/3 hours = 4\/3 hours<br \/>\n7\/2 x 4\/3 = 1 x x<br \/>\nx = 7\/2 x 4\/3<br \/>\nx = 14\/3 = 4 2\/3 miles<br \/>\nThe correct result would be 4 2\/3 miles.<\/p>\n<p>Question 5.<br \/>\nPenny uses \\(\\frac{3}{4}\\) yard of fabric for each pillow she makes. How many pillows can she make using 6 yards of fabric?<br \/>\n_____ pillows<\/p>\n<p>Answer:<br \/>\n8 pillows<\/p>\n<p>Explanation:<br \/>\nPenny uses \\(\\frac{3}{4}\\) yard of fabric for each pillow she makes.<br \/>\nUsing 6 yards of fabric 6\/(3\/4) = 24\/3 = 8<\/p>\n<p>Question 6.<br \/>\nDuring track practice, Chris ran 2.5 laps in 81 seconds. What was his average time per lap?<br \/>\n_____ seconds<\/p>\n<p>Answer:<br \/>\n32.4 seconds<\/p>\n<p>Explanation:<br \/>\nDuring track practice, Chris ran 2.5 laps in 81 seconds.<br \/>\n81\/2.5 = 32.4 seconds<\/p>\n<h3><a id=\"Model_Mixed_Number_Division_\u2013_Page_No._115\"><\/a>Share and Show &#8211; Page No. 115<\/h3>\n<p><strong>Use the model to find the quotient.<\/strong><\/p>\n<p>Question 1.<br \/>\n\\(3 \\frac{1}{3} \\div \\frac{1}{3}\\)<br \/>\n<img loading=\"lazy\" class=\"alignnone size-full wp-image-4799\" src=\"https:\/\/ccssmathanswers.com\/wp-content\/uploads\/2020\/08\/Go-Math-Grade-6-Answer-Key-Chapter-2-Fractions-and-Decimals-17.jpg\" alt=\"Go Math Grade 6 Answer Key Chapter 2 Fractions and Decimals 17\" width=\"303\" height=\"94\" srcset=\"https:\/\/bigideasmathanswers.com\/wp-content\/uploads\/2020\/08\/Go-Math-Grade-6-Answer-Key-Chapter-2-Fractions-and-Decimals-17.jpg 303w, https:\/\/bigideasmathanswers.com\/wp-content\/uploads\/2020\/08\/Go-Math-Grade-6-Answer-Key-Chapter-2-Fractions-and-Decimals-17-300x93.jpg 300w\" sizes=\"(max-width: 303px) 100vw, 303px\" \/><br \/>\n_____<\/p>\n<p>Answer:<br \/>\n21<\/p>\n<p>Explanation:<br \/>\nModel 3 with 3 hexagonal blocks.<br \/>\nModel 1\/2 with 1 trapezoid block.<br \/>\nFor 1\/6,<br \/>\n6 triangle blocks are equal to 1 hexagon.<br \/>\nSo, a triangle block shows 1\/6.<br \/>\nCount the triangles.<br \/>\nThere are 21 triangle blocks.<br \/>\nSo, 3 1\/2 \u00f7 1\/6 = 21.<\/p>\n<p>Question 2.<br \/>\n\\(2 \\frac{1}{2} \\div \\frac{1}{6}\\)<br \/>\n<img loading=\"lazy\" class=\"alignnone size-full wp-image-4800\" src=\"https:\/\/ccssmathanswers.com\/wp-content\/uploads\/2020\/08\/Go-Math-Grade-6-Answer-Key-Chapter-2-Fractions-and-Decimals-18.jpg\" alt=\"Go Math Grade 6 Answer Key Chapter 2 Fractions and Decimals 18\" width=\"265\" height=\"87\" \/><br \/>\n_____<\/p>\n<p>Answer:<br \/>\n15<\/p>\n<p>Explanation:<br \/>\nModel 2 with 2 hexagonal blocks.<br \/>\nModel 1\/2 with 1 trapezoid block.<br \/>\nFor 1\/6,<br \/>\n6 triangle blocks are equal to 1 hexagon.<br \/>\nSo, a triangle block shows 1\/6.<br \/>\nCount the triangles.<br \/>\nThere are 15 triangle blocks.<br \/>\nSo, \\(2 \\frac{1}{2} \\div \\frac{1}{6}\\) = 15.<\/p>\n<p><strong>Use pattern blocks to find the quotient. Then draw the model.<\/strong><\/p>\n<p>Question 3.<br \/>\n\\(2 \\frac{2}{3} \\div \\frac{1}{6}\\)<br \/>\n_____<\/p>\n<p>Answer:<br \/>\n<img loading=\"lazy\" class=\"alignnone size-full wp-image-8241\" src=\"https:\/\/ccssmathanswers.com\/wp-content\/uploads\/2020\/08\/grade-6-chapter-2-image-1-1.jpg\" alt=\"grade 6 chapter 2 image 1\" width=\"275\" height=\"91\" \/><\/p>\n<p>Explanation:<br \/>\n2 2\/3 = 8\/3<br \/>\n8\/3 \u00f7 1\/6 = 16<\/p>\n<p>Question 4.<br \/>\n\\(3 \\frac{1}{2} \\div \\frac{1}{2}\\)<br \/>\n_____<\/p>\n<p>Answer:<br \/>\n<img loading=\"lazy\" class=\"alignnone size-medium wp-image-8242\" src=\"https:\/\/ccssmathanswers.com\/wp-content\/uploads\/2020\/08\/grade-6-chapter-2-image-2-300x71.jpg\" alt=\"grade 6 chapter 2 image 2\" width=\"300\" height=\"71\" srcset=\"https:\/\/bigideasmathanswers.com\/wp-content\/uploads\/2020\/08\/grade-6-chapter-2-image-2-300x71.jpg 300w, https:\/\/bigideasmathanswers.com\/wp-content\/uploads\/2020\/08\/grade-6-chapter-2-image-2.jpg 368w\" sizes=\"(max-width: 300px) 100vw, 300px\" \/><\/p>\n<p>Explanation:<br \/>\n3 1\/2 = 7\/2<br \/>\n7\/2 \u00f7 1\/2 = 7<\/p>\n<p><strong>Draw a model to find the quotient.<\/strong><\/p>\n<p>Question 5.<br \/>\n\\(3 \\frac{1}{2} \\div 3\\)<br \/>\n_____ \\(\\frac{\u25a1}{\u25a1}\\)<\/p>\n<p>Answer:<br \/>\n<img loading=\"lazy\" class=\"alignnone size-medium wp-image-8244\" src=\"https:\/\/ccssmathanswers.com\/wp-content\/uploads\/2020\/08\/grade-6-chapter-2-image-3-300x51.jpg\" alt=\"grade 6 chapter 2 image 3\" width=\"300\" height=\"51\" srcset=\"https:\/\/bigideasmathanswers.com\/wp-content\/uploads\/2020\/08\/grade-6-chapter-2-image-3-300x51.jpg 300w, https:\/\/bigideasmathanswers.com\/wp-content\/uploads\/2020\/08\/grade-6-chapter-2-image-3.jpg 572w\" sizes=\"(max-width: 300px) 100vw, 300px\" \/><\/p>\n<p>Explanation:<br \/>\n3 1\/2 = 7\/2<br \/>\n7\/2 \u00f7 3 = 21\/2<\/p>\n<p>Question 6.<br \/>\n\\(1 \\frac{1}{4} \\div 2\\)<br \/>\n\\(\\frac{\u25a1}{\u25a1}\\)<\/p>\n<p>Answer:<br \/>\n<img loading=\"lazy\" class=\"alignnone size-medium wp-image-8245\" src=\"https:\/\/ccssmathanswers.com\/wp-content\/uploads\/2020\/08\/grade-6-chapter-2-image-4-300x53.jpg\" alt=\"grade 6 chapter 2 image 4\" width=\"300\" height=\"53\" srcset=\"https:\/\/bigideasmathanswers.com\/wp-content\/uploads\/2020\/08\/grade-6-chapter-2-image-4-300x53.jpg 300w, https:\/\/bigideasmathanswers.com\/wp-content\/uploads\/2020\/08\/grade-6-chapter-2-image-4.jpg 572w\" sizes=\"(max-width: 300px) 100vw, 300px\" \/><\/p>\n<p>Explanation:<br \/>\n1\/4 \u00f7 2 = 1\/2<\/p>\n<p>Question 7.<br \/>\nUse Appropriate Tools Explain how models can be used to divide mixed numbers by fractions or whole numbers<br \/>\nType below:<br \/>\n__________<\/p>\n<p>Answer:<br \/>\nMultiply the whole number part by the fraction&#8217;s denominator. Add that to the numerator. Then write the result on top of the denominator.<\/p>\n<h3><a id=\"Model_Mixed_Number_Division_\u2013_Page_No._116\"><\/a>Problem Solving + Applications &#8211; Page No. 116<\/h3>\n<p><strong>Use a model to solve. Then write an equation for the model.<\/strong><\/p>\n<p>Question 8.<br \/>\nUse Models Eliza opens a box of bead kits. The box weighs 2 \\(\\frac{2}{3}\\) lb. Each bead kit weighs \\(\\frac{1}{6}\\) lb. How many kits are in the box? What does the answer mean?<br \/>\nType below:<br \/>\n__________<\/p>\n<p>Answer:<br \/>\n<img loading=\"lazy\" class=\"alignnone size-medium wp-image-8323\" src=\"https:\/\/ccssmathanswers.com\/wp-content\/uploads\/2020\/08\/grade-6-chapter-2-image-6-1-300x95.jpg\" alt=\"grade 6 chapter 2 image 6\" width=\"300\" height=\"95\" srcset=\"https:\/\/bigideasmathanswers.com\/wp-content\/uploads\/2020\/08\/grade-6-chapter-2-image-6-1-300x95.jpg 300w, https:\/\/bigideasmathanswers.com\/wp-content\/uploads\/2020\/08\/grade-6-chapter-2-image-6-1.jpg 568w\" sizes=\"(max-width: 300px) 100vw, 300px\" \/><br \/>\n16 kits are in the box<\/p>\n<p>Explanation:<br \/>\nEliza opens a box of bead kits. The box weighs 2 \\(\\frac{2}{3}\\) lb. Each bead kit weighs \\(\\frac{1}{6}\\) lb, 2 \\(\\frac{2}{3}\\) \u00f7 \\(\\frac{1}{6}\\) = 8\/3 \u00f7 1\/6 = 16.<br \/>\n16 kits are in the box<\/p>\n<p>Question 9.<br \/>\nHassan has two boxes of trail mix. Each box holds 1 \\(\\frac{2}{3}\\) lb of trail mix. He eats \\(\\frac{1}{3}\\) lb of trail mix each day. How many days can Hassan eat trail mix before he runs out?<br \/>\n_____ days<\/p>\n<p>Answer:<br \/>\n10 days<\/p>\n<p>Explanation:<br \/>\nHassan has two boxes of trail mix. Each box holds 1 \\(\\frac{2}{3}\\) lb of trail mix.<br \/>\n1 \\(\\frac{2}{3}\\) = 5\/3<br \/>\n2 x (5\/3) = 10\/3<br \/>\nHe eats \\(\\frac{1}{3}\\) lb of trail mix each day.<br \/>\n10\/3 \u00f7 1\/3 = 10<br \/>\nHassan eats trail mix for 10 days before he runs out.<\/p>\n<p>Question 10.<br \/>\nSense or Nonsense? Steve made this model to show \\(2 \\frac{1}{3} \\div \\frac{1}{6}\\). He says that the quotient is 7. Is his answer sense or nonsense? Explain your reasoning<br \/>\n<img loading=\"lazy\" class=\"alignnone size-full wp-image-4801\" src=\"https:\/\/ccssmathanswers.com\/wp-content\/uploads\/2020\/08\/Go-Math-Grade-6-Answer-Key-Chapter-2-Fractions-and-Decimals-19.jpg\" alt=\"Go Math Grade 6 Answer Key Chapter 2 Fractions and Decimals 19\" width=\"361\" height=\"122\" srcset=\"https:\/\/bigideasmathanswers.com\/wp-content\/uploads\/2020\/08\/Go-Math-Grade-6-Answer-Key-Chapter-2-Fractions-and-Decimals-19.jpg 361w, https:\/\/bigideasmathanswers.com\/wp-content\/uploads\/2020\/08\/Go-Math-Grade-6-Answer-Key-Chapter-2-Fractions-and-Decimals-19-300x101.jpg 300w\" sizes=\"(max-width: 361px) 100vw, 361px\" \/><br \/>\nType below:<br \/>\n__________<\/p>\n<p>Answer:<br \/>\n\\(2 \\frac{1}{3} \\div \\frac{1}{6}\\) = 7\/3 \u00f7 1\/6 = 14.<br \/>\nHe said the quotient is 7.<br \/>\nHis answer is Nonsense.<\/p>\n<p>Question 11.<br \/>\nEva is making muffins to sell at a fundraiser. She has 2 \\(\\frac{1}{4}\\) cups of flour, and the recipe calls for \\(\\frac{3}{4}\\) cup of flour for each batch of muffins. Explain how to use a model to find the number of batches of muffins Eva can make.<br \/>\nType below:<br \/>\n__________<\/p>\n<p>Answer:<br \/>\n3<\/p>\n<p>Explanation:<br \/>\nEva is making muffins to sell at a fundraiser. She has 2 \\(\\frac{1}{4}\\) cups of flour, and the recipe calls for \\(\\frac{3}{4}\\) cup of flour for each batch of muffins.<br \/>\n2 \\(\\frac{1}{4}\\) \u00f7 \\(\\frac{3}{4}\\) = 9\/4 \u00f7 3\/4 = 3<\/p>\n<h3><a id=\"Model_Mixed_Number_Division_Lesson_Check_\u2013_Page_No._117\"><\/a>Model Mixed Number Division &#8211; Page No. 117<\/h3>\n<p><strong>Use the model to find the quotient.<\/strong><\/p>\n<p>Question 1.<br \/>\n\\(4 \\frac{1}{2} \\div \\frac{1}{2}\\)<br \/>\n<img loading=\"lazy\" class=\"alignnone size-full wp-image-4802\" src=\"https:\/\/ccssmathanswers.com\/wp-content\/uploads\/2020\/08\/Go-Math-Grade-6-Answer-Key-Chapter-2-Fractions-and-Decimals-20.jpg\" alt=\"Go Math Grade 6 Answer Key Chapter 2 Fractions and Decimals 20\" width=\"302\" height=\"179\" srcset=\"https:\/\/bigideasmathanswers.com\/wp-content\/uploads\/2020\/08\/Go-Math-Grade-6-Answer-Key-Chapter-2-Fractions-and-Decimals-20.jpg 302w, https:\/\/bigideasmathanswers.com\/wp-content\/uploads\/2020\/08\/Go-Math-Grade-6-Answer-Key-Chapter-2-Fractions-and-Decimals-20-300x178.jpg 300w\" sizes=\"(max-width: 302px) 100vw, 302px\" \/><br \/>\n_____<\/p>\n<p>Answer:<br \/>\n9<\/p>\n<p>Explanation:<br \/>\nCount the number of trapezoids to find the answer.<\/p>\n<p>Question 2.<br \/>\n\\(3 \\frac{1}{3} \\div \\frac{1}{6}\\)<br \/>\n<img loading=\"lazy\" class=\"alignnone size-full wp-image-4803\" src=\"https:\/\/ccssmathanswers.com\/wp-content\/uploads\/2020\/08\/Go-Math-Grade-6-Answer-Key-Chapter-2-Fractions-and-Decimals-21.jpg\" alt=\"Go Math Grade 6 Answer Key Chapter 2 Fractions and Decimals 21\" width=\"379\" height=\"91\" srcset=\"https:\/\/bigideasmathanswers.com\/wp-content\/uploads\/2020\/08\/Go-Math-Grade-6-Answer-Key-Chapter-2-Fractions-and-Decimals-21.jpg 379w, https:\/\/bigideasmathanswers.com\/wp-content\/uploads\/2020\/08\/Go-Math-Grade-6-Answer-Key-Chapter-2-Fractions-and-Decimals-21-300x72.jpg 300w\" sizes=\"(max-width: 379px) 100vw, 379px\" \/><br \/>\n_____<\/p>\n<p>Answer:<br \/>\n20<\/p>\n<p><strong>Use pattern blocks or another model to find the quotient. Then draw the model.<\/strong><\/p>\n<p>Question 3.<br \/>\n\\(2 \\frac{1}{2} \\div \\frac{1}{6}\\)<br \/>\n_____<\/p>\n<p>Answer:<br \/>\n<img loading=\"lazy\" class=\"alignnone size-full wp-image-7125\" src=\"https:\/\/ccssmathanswers.com\/wp-content\/uploads\/2020\/08\/grade-6-chapter-2-image-5.jpg\" alt=\"grade 6 chapter 2 image 5\" width=\"290\" height=\"96\" \/><\/p>\n<p>Explanation:<br \/>\nModel 2 with 2 hexagonal blocks.<br \/>\nModel 1\/2 with 1 trapezoid block.<br \/>\nFor 1\/6,<br \/>\n6 triangle blocks are equal to 1 hexagon.<br \/>\nSo, a triangle block shows 1\/6.<br \/>\nCount the triangles.<br \/>\nThere are 15 triangle blocks.<br \/>\nSo, 212\u00f716 = 15.<\/p>\n<p>Question 4.<br \/>\n\\(2 \\frac{3}{4} \\div 2\\)<br \/>\n_____<\/p>\n<p>Answer:<br \/>\n<img loading=\"lazy\" class=\"alignnone size-medium wp-image-7126\" src=\"https:\/\/ccssmathanswers.com\/wp-content\/uploads\/2020\/08\/grade-6-chapter-2-image-6-300x121.jpg\" alt=\"grade 6 chapter 2 image 6\" width=\"300\" height=\"121\" srcset=\"https:\/\/bigideasmathanswers.com\/wp-content\/uploads\/2020\/08\/grade-6-chapter-2-image-6-300x121.jpg 300w, https:\/\/bigideasmathanswers.com\/wp-content\/uploads\/2020\/08\/grade-6-chapter-2-image-6.jpg 327w\" sizes=\"(max-width: 300px) 100vw, 300px\" \/><\/p>\n<p>Explanation:<br \/>\n2 3\/4 \u00f7 2 = 11\/2<\/p>\n<p><strong>Problem Solving<\/strong><\/p>\n<p>Question 5.<br \/>\nMarty has 2 \\(\\frac{4}{5}\\) quarts of juice. He pours the same amount of juice into 2 bottles. How much does he pour into each bottle?<br \/>\n_____ \\(\\frac{\u25a1}{\u25a1}\\) quarts<\/p>\n<p>Answer:<br \/>\n1\\(\\frac{2}{5}\\) quarts<\/p>\n<p>Explanation:<br \/>\nMarty has 2 \\(\\frac{4}{5}\\) quarts of juice. He pours the same amount of juice into 2 bottles.<br \/>\n2 \\(\\frac{4}{5}\\) = 14\/5 = 2.8<br \/>\n2.8\/2 = 1.4 = 1 2\/5<\/p>\n<p>Question 6.<br \/>\nHow many \\(\\frac{1}{3}\\) pound servings are in 4 \\(\\frac{2}{3}\\) pounds of cheese?<br \/>\n_____ pounds<\/p>\n<p>Answer:<br \/>\n14 pounds<\/p>\n<p>Explanation:<br \/>\n4 2\/3 = 14\/3<br \/>\n(14\/3)\/(1\/3) = 14<\/p>\n<p>Question 7.<br \/>\nWrite a word problem that involves dividing a mixed number by a whole number. Solve the problem and describe how you found the answer.<br \/>\nType below:<br \/>\n__________<\/p>\n<p>Answer:<br \/>\nHow many \\(\\frac{1}{3}\\) pound servings are in 4 \\(\\frac{2}{3}\\) pounds of cheese?<br \/>\nExplanation:<br \/>\n4 2\/3 = 14\/3<br \/>\n(14\/3)\/(1\/3) = 14<\/p>\n<h3><a id=\"Model_Mixed_Number_Division_Lesson_Check_1_\u2013_Page_No._118\"><\/a>Lesson Check &#8211; Page No. 118<\/h3>\n<p><strong>Sketch a model to find the quotient.<\/strong><\/p>\n<p>Question 1.<br \/>\nEmma has 4 \\(\\frac{1}{2}\\) pounds of birdseed. She wants to divide it evenly among 3 bird feeders. How much birdseed should she put in each?<br \/>\n_____ \\(\\frac{\u25a1}{\u25a1}\\) pounds<\/p>\n<p>Answer:<br \/>\n1\\(\\frac{1}{2}\\) pounds<\/p>\n<p>Explanation:<br \/>\nEmma has 4 1\/2 pounds of birdseed.<br \/>\nConvert this to an improper fraction.<br \/>\n4 1\/2 = 9\/2<br \/>\nEmma wants to divide it evenly among 3 bird feeders.<br \/>\nSo, she should put (9\/2)\/3 = 3\/2 = 1 1\/2<\/p>\n<p>Question 2.<br \/>\nA box of crackers weighs 11 \\(\\frac{1}{4}\\) ounces. Kaden estimates that one serving is \\(\\frac{3}{4}\\) ounce. How many servings are in the box?<br \/>\n_____ servings<\/p>\n<p>Answer:<br \/>\n15 servings<\/p>\n<p>Explanation:<br \/>\n11 1\/4 by 3\/4<br \/>\n11 1\/4 = 45\/4<br \/>\n45\/4 \/ 3\/4 = 45\/4 \u00d7 4\/3 = 180\/12 = 15<br \/>\nthere are 15 servings<\/p>\n<p><strong>Spiral Review<\/strong><\/p>\n<p>Question 3.<br \/>\nThe Ecology Club has volunteered to clean up 4.8 kilometers of highway. The members are organized into 16 teams. Each team will clean the same amount of highway. How much highway will each team clean?<br \/>\n_____ kilometers<\/p>\n<p>Answer:<br \/>\n0.3 kilometers<\/p>\n<p>Explanation:<br \/>\nThe Ecology Club has volunteered to clean up 4.8 kilometers of highway. The members are organized into 16 teams.<br \/>\nThe total length of the highway is given to clean = 4.8 kilometers<br \/>\nIf the members are organized into 16 teams.<br \/>\n4.8\/16 = 0.3<br \/>\nHence, each team will clean 0.3 kilometers of the highway.<\/p>\n<p>Question 4.<br \/>\nTyrone has $8.06. How many bagels can he buy if each bagel costs $0.65?<br \/>\n_____ bagels<\/p>\n<p>Answer:<br \/>\n12 bagels<\/p>\n<p>Explanation:<br \/>\n$8.06\/$0.65 = 12.4<br \/>\n12 bagels<\/p>\n<p>Question 5.<br \/>\nA nail is 0.1875 inch thick. What is its thickness as a fraction? Is 0.1875 inch closer to \\(\\frac{1}{8}\\) inch or \\(\\frac{1}{4}\\) inch on a number line?<br \/>\nType below:<br \/>\n__________<\/p>\n<p>Answer:<br \/>\n0.1875 = 3\/16 which is at the same distance to 1\/4 and 1\/8<br \/>\nIt is the same distance apart.<\/p>\n<p>Question 6.<br \/>\nMaria wants to find the product of 5 \\(\\frac{3}{20}\\) \u00d7 3 \\(\\frac{4}{25}\\) using decimals instead of fractions. How can she rewrite the problem using decimals?<br \/>\nType below:<br \/>\n__________<\/p>\n<p>Answer:<br \/>\n16.274<\/p>\n<p>Explanation:<br \/>\nThe decimal for 5 3\/20 is 5.15<br \/>\nThe decimal for 3 4\/25 is 3.16<br \/>\n5.15 \u00d7 3.16 = 16.274<\/p>\n<h3><a id=\"Divide_Mixed_Numbers_\u2013_Page_No._121\"><\/a>Share and Show &#8211; Page No. 121<\/h3>\n<p><strong>Estimate. Then write the quotient in simplest form.<\/strong><\/p>\n<p>Question 1.<br \/>\n\\(4 \\frac{1}{3} \\div \\frac{3}{4}\\)<br \/>\n______ \\(\\frac{\u25a1}{\u25a1}\\)<\/p>\n<p>Answer:<br \/>\n5\\(\\frac{375}{1000}\\)<\/p>\n<p>Explanation:<br \/>\n4 1\/3 = 13\/3 = 4.333 is closer to 4.3<br \/>\n3\/4 = 0.75 is closer to 0.8<br \/>\n4.3\/0.8 = 5.375 = 5 375\/1000<\/p>\n<p>Question 2.<br \/>\nSix hikers shared 4 \\(\\frac{1}{2}\\) lb of trail mix. How much trail mix did each hiker receive?<br \/>\n\\(\\frac{\u25a1}{\u25a1}\\)<\/p>\n<p>Answer:<br \/>\n\\(\\frac{75}{100}\\)<\/p>\n<p>Explanation:<br \/>\n6 hikers = 4.5 lbs of trail mix<br \/>\n4.5\/6= .75 lbs each hiker.<\/p>\n<p>Question 3.<br \/>\n\\(5 \\frac{2}{3} \\div 3\\)<br \/>\n______ \\(\\frac{\u25a1}{\u25a1}\\)<\/p>\n<p>Answer:<br \/>\n2\\(\\frac{947}{1000}\\)<\/p>\n<p>Explanation:<br \/>\n5 2\/3 = 17\/3 = 5.666 is closer to 5.6<br \/>\n5.6\/3 = 1.866 is closer to 1.9<br \/>\n5.6\/1.9 = 2.947 = 2 947\/1000<\/p>\n<p>Question 4.<br \/>\n\\(7 \\frac{1}{2} \\div 2 \\frac{1}{2}\\)<br \/>\n______<\/p>\n<p>Answer:<br \/>\n3<\/p>\n<p>Explanation:<br \/>\n7 1\/2 = 15\/2 = 7.5<br \/>\n2 1\/2 = 5\/2 = 2.5<br \/>\n7.5\/2.5 = 3<\/p>\n<p><strong>On Your Own<\/strong><\/p>\n<p><strong>Estimate. Then write the quotient in simplest form.<\/strong><\/p>\n<p>Question 5.<br \/>\n\\(5 \\frac{3}{4} \\div 4 \\frac{1}{2}\\)<br \/>\n______ \\(\\frac{\u25a1}{\u25a1}\\)<\/p>\n<p>Answer:<br \/>\n1\\(\\frac{27}{100}\\)<\/p>\n<p>Explanation:<br \/>\n5 3\/4 = 23\/4 = 5.75<br \/>\n4 1\/2 = 9\/2 = 4.5<br \/>\n5.75\/4.5 = 1.27 = 1 27\/100<\/p>\n<p>Question 6.<br \/>\n\\(5 \\div 1 \\frac{1}{3}\\)<br \/>\n______ \\(\\frac{\u25a1}{\u25a1}\\)<\/p>\n<p>Answer:<br \/>\n3\\(\\frac{84}{100}\\)<\/p>\n<p>Explanation:<br \/>\n1 1\/3 = 4\/3 = 1.33 is closer to 1.3<br \/>\n5\/1.3 = 3.84 = 3 84\/100<\/p>\n<p>Question 7.<br \/>\n\\(6 \\frac{3}{4} \\div 2\\)<br \/>\n______ \\(\\frac{\u25a1}{\u25a1}\\)<\/p>\n<p>Answer:<br \/>\n3\\(\\frac{2}{5}\\)<\/p>\n<p>Explanation:<br \/>\n6 3\/4 = 27\/4 = 6.75 is closer to 6.8<br \/>\n6.8\/2 = 3.4 = 3 2\/5<\/p>\n<p>Question 8.<br \/>\n\\(2 \\frac{2}{9} \\div 1 \\frac{3}{7}\\)<br \/>\n______ \\(\\frac{\u25a1}{\u25a1}\\)<\/p>\n<p>Answer:<br \/>\n1\\(\\frac{571}{1000}\\)<\/p>\n<p>Explanation:<br \/>\n2 2\/9 = 20\/9 = 2.22 is closer to 2.2<br \/>\n1 3\/7 = 10\/7 = 1.428 is closer to 1.4<br \/>\n2.2\/1.4 = 1.571 = 1 571\/1000<\/p>\n<p>Question 9.<br \/>\nHow many 3 \\(\\frac{1}{3}\\) yd pieces can Amanda get from a 3 \\(\\frac{1}{3}\\) yd ribbon?<br \/>\n______<\/p>\n<p>Answer:<br \/>\n1<\/p>\n<p>Explanation:<br \/>\n(3 1\/3) \u00f7 (3 1\/3) = 1<\/p>\n<p>Question 10.<br \/>\nSamantha cut 6 \\(\\frac{3}{4}\\) yd of yarn into 3 equal pieces. Explain how she could use mental math to find the length of each piece<br \/>\nType below:<br \/>\n__________<\/p>\n<p>Answer:<br \/>\n27\/12<\/p>\n<p>Explanation:<br \/>\nSamantha cut 6 \\(\\frac{3}{4}\\) yd of yarn into 3 equal pieces.<br \/>\n6 3\/4 = 27\/4<br \/>\n(27\/4)\/3<br \/>\n(27\/4)(1\/3) = 27\/12<\/p>\n<p><strong>Evaluate Algebra Evaluate using the order of operations. Write the answer in simplest form.<\/strong><\/p>\n<p>Question 11.<br \/>\n\\(1 \\frac{1}{2} \\times 2 \\div 1 \\frac{1}{3}\\)<br \/>\n_____ \\(\\frac{\u25a1}{\u25a1}\\)<\/p>\n<p>Answer:<br \/>\n2\\(\\frac{1}{4}\\)<\/p>\n<p>Explanation:<br \/>\n(1 1\/2) \u00d7 2 = 3\/2 \u00d7 2 = 3<br \/>\n1 1\/3 = 4\/3<br \/>\n3\/(4\/3) = 9\/4 = 2.25 = 2 1\/4<\/p>\n<p>Question 12.<br \/>\n\\(1 \\frac{2}{5} \\div 1 \\frac{13}{15}+\\frac{5}{8}\\)<br \/>\n_____ \\(\\frac{\u25a1}{\u25a1}\\)<\/p>\n<p>Answer:<br \/>\n1\\(\\frac{3}{8}\\)<\/p>\n<p>Explanation:<br \/>\n(1 2\/5)\/(1 13\/15) = (7\/5)\/(28\/15) = 3\/4 = 0.75<br \/>\n0.75 + 0.625 = 1.375 = 1 3\/8<\/p>\n<p>Question 13.<br \/>\n\\(3 \\frac{1}{2}-1 \\frac{5}{6} \\div 1 \\frac{2}{9}\\)<br \/>\n_____<\/p>\n<p>Answer:<br \/>\n2<\/p>\n<p>Explanation:<br \/>\n(1 5\/6)\/(1 2\/9) = (11\/6)\/11\/9 = 3\/2 = 1 1\/2 = 1.5<br \/>\n3 1\/2 = 7\/2 = 3.5<br \/>\n3.5 &#8211; 1.5 = 2<\/p>\n<p>Question 14.<br \/>\nLook for a Pattern Find these quotients: \\(20 \\div 4 \\frac{4}{5}\\), \\(10 \\div 4 \\frac{4}{5}\\), \\(5 \\div 4 \\frac{4}{5}\\). Describe a pattern you see.<br \/>\nType below:<br \/>\n__________<\/p>\n<p>Answer:<br \/>\n20 \u00f7 4 4\/5 = 20 \u00f7 24\/5 = 20\/4.8 = 4.1666<br \/>\n10 \u00f7 4 4\/5 = 10 \u00f7 24\/5 = 10\/4.8 = 2.08333<br \/>\n5 \u00f7 4 4\/5 = 5 \u00f7 24\/5 = 5\/4.8 = 1.04166<br \/>\nThe pattern is multiplied by 2 every time.<\/p>\n<h3><a id=\"Divide_Mixed_Numbers_\u2013_Page_No._122\"><\/a>Page No. 122<\/h3>\n<p>Question 15.<br \/>\nDina hikes \\(\\frac{1}{2}\\) of the easy trail and stops for a break every 3 \\(\\frac{1}{4}\\) miles. How many breaks will she take?<br \/>\n<img loading=\"lazy\" class=\"alignnone size-full wp-image-4804\" src=\"https:\/\/ccssmathanswers.com\/wp-content\/uploads\/2020\/08\/Go-Math-Grade-6-Answer-Key-Chapter-2-Fractions-and-Decimals-22.jpg\" alt=\"Go Math Grade 6 Answer Key Chapter 2 Fractions and Decimals 22\" width=\"460\" height=\"226\" srcset=\"https:\/\/bigideasmathanswers.com\/wp-content\/uploads\/2020\/08\/Go-Math-Grade-6-Answer-Key-Chapter-2-Fractions-and-Decimals-22.jpg 460w, https:\/\/bigideasmathanswers.com\/wp-content\/uploads\/2020\/08\/Go-Math-Grade-6-Answer-Key-Chapter-2-Fractions-and-Decimals-22-300x147.jpg 300w\" sizes=\"(max-width: 460px) 100vw, 460px\" \/><br \/>\na. What problem are you asked to solve?<br \/>\nType below:<br \/>\n__________<\/p>\n<p>Answer:<br \/>\nHow many breaks Dina will take when hikes \\(\\frac{1}{2}\\) of the easy trail and stops for a break every 3 \\(\\frac{1}{4}\\) mile.<\/p>\n<p>Question 15.<br \/>\nb. How will you use the information in the table to solve the problem?<br \/>\nType below:<br \/>\n__________<\/p>\n<p>Answer:<br \/>\nDina easy trail length, break time<\/p>\n<p>Question 15.<br \/>\nc. How can you find the distance Dina hikes? How far does she hike?<br \/>\n______ \\(\\frac{\u25a1}{\u25a1}\\) miles<\/p>\n<p>Answer:<br \/>\n9\\(\\frac{3}{4}\\) miles<\/p>\n<p>Explanation:<br \/>\n19 1\/2 \u00d7 1\/2 = 39\/2 \u00d7 1\/2 = 39\/4 = 9 3\/4<\/p>\n<p>Question 15.<br \/>\nd. What operation will you use to find how many breaks Dina takes?<br \/>\nType below:<br \/>\n__________<\/p>\n<p>Answer:<br \/>\nDivision<\/p>\n<p>Question 15.<br \/>\ne. How many breaks will Dina take?<br \/>\n______ breaks<\/p>\n<p>Answer:<br \/>\n3 breaks<\/p>\n<p>Explanation:<br \/>\n39\/4 \u00f7 13\/4 = 3<\/p>\n<p>Question 16.<br \/>\nCarlo packs 15 \\(\\frac{3}{4}\\) lb of books in 2 boxes. Each book weighs 1 \\(\\frac{1}{8}\\) lb. There are 4 more books in Box A than in Box B. How many books are in Box A? Explain your work.<br \/>\n______ books<\/p>\n<p>Answer:<br \/>\nCarlo packs 15 \\(\\frac{3}{4}\\) lb of books in 2 boxes. Each book weighs 1 \\(\\frac{1}{8}\\) lb.<br \/>\n15 \\(\\frac{3}{4}\\) \u00f7 1 \\(\\frac{1}{8}\\) = 63\/4 \u00f7 9\/8 = 14<br \/>\n14 books available in 2 boxes.<br \/>\nThere are 4 more books in Box A than in Box B.<br \/>\nBox A contains 5 + 4 = 9 books<br \/>\nBox B contains 5 books<\/p>\n<p>Question 17.<br \/>\nRex\u2019s goal is to run 13 \\(\\frac{3}{4}\\) miles over 5 days. He wants to run the same distance each day. Jordan said that Rex would have to run 3 \\(\\frac{3}{4}\\) miles each day to reach his goal. Do you agree with Jordan? Explain your answer using words and numbers.<br \/>\nType below:<br \/>\n__________<\/p>\n<p>Answer:<br \/>\nRex\u2019s goal is to run 13 \\(\\frac{3}{4}\\) miles over 5 days. He wants to run the same distance each day.<br \/>\n13 \\(\\frac{3}{4}\\) \u00f7 5 = 55\/4 \u00f7 5 = 11\/4 or 2 3\/4.<br \/>\nJordan answer is wrong<\/p>\n<h3><a id=\"Divide_Mixed_Numbers_Lesson_Check_\u2013_Page_No._123\"><\/a>Divide Mixed Numbers &#8211; Page No. 123<\/h3>\n<p><strong>Estimate. Then write the quotient in simplest form.<\/strong><\/p>\n<p>Question 1.<br \/>\n\\(2 \\frac{1}{2} \\div 2 \\frac{1}{3}\\)<br \/>\n______ \\(\\frac{\u25a1}{\u25a1}\\)<\/p>\n<p>Answer:<br \/>\n1\\(\\frac{1}{2}\\)<\/p>\n<p>Explanation:<br \/>\n2 1\/2 = 5\/2 = 2.5 is closer to 3<br \/>\n2 1\/3 = 7\/3 = 2.333 is closer to 2<br \/>\n3\/2 = 1.5 = 1 1\/2<\/p>\n<p>Question 2.<br \/>\n\\(2 \\frac{2}{3} \\div 1 \\frac{1}{3}\\)<br \/>\n______<\/p>\n<p>Answer:<br \/>\n2<\/p>\n<p>Explanation:<br \/>\n2 2\/3 = 8\/3 = 2.666 is closer to 2.6<br \/>\n1 1\/3 = 4\/3 = 1.333 is closer to 1.3<br \/>\n2.6\/1.3 = 2<\/p>\n<p>Question 3.<br \/>\n\\(2 \\div 3 \\frac{5}{8}\\)<br \/>\n\\(\\frac{\u25a1}{\u25a1}\\)<\/p>\n<p>Answer:<br \/>\n\\(\\frac{1}{2}\\)<\/p>\n<p>Explanation:<br \/>\n3 5\/8 = 29\/8 = 3.625 is closer to 3.6<br \/>\n2\/3.6 = 0.5 = 1\/2<\/p>\n<p>Question 4.<br \/>\n\\(1 \\frac{13}{15} \\div 1 \\frac{2}{5}\\)<br \/>\n\\(\\frac{\u25a1}{\u25a1}\\)<\/p>\n<p>Answer:<br \/>\n\\(\\frac{126}{100}\\)<\/p>\n<p>Explanation:<br \/>\n1 13\/15 = 28\/15 = 1.8666 is closer to 1.9<br \/>\n1 2\/5 = 7\/5 = 1.4 is closer to 1.5<br \/>\n1.9\/1.5 = 1.266<br \/>\n126\/100<\/p>\n<p>Question 5.<br \/>\n\\(10 \\div 6 \\frac{2}{3}\\)<br \/>\n______ \\(\\frac{\u25a1}{\u25a1}\\)<\/p>\n<p>Answer:<br \/>\n1\\(\\frac{1}{2}\\)<\/p>\n<p>Explanation:<br \/>\n6 2\/3 = 20\/3 = 6.666 is closer to 6.7<br \/>\n10\/6.7 = 3\/2 = 1 1\/2<\/p>\n<p>Question 6.<br \/>\n\\(2 \\frac{3}{5} \\div 1 \\frac{1}{25}\\)<br \/>\n______ \\(\\frac{\u25a1}{\u25a1}\\)<\/p>\n<p>Answer:<br \/>\n2\\(\\frac{3}{5}\\)<\/p>\n<p>Explanation:<br \/>\n2 3\/5 = 13\/5 = 2.6<br \/>\n1 1\/25 = 26\/25 = 1.04 is closer to 1<br \/>\n2.6\/1 = 13\/5 or 2 3\/5<\/p>\n<p>Question 7.<br \/>\n\\(2 \\frac{1}{5} \\div 2\\)<br \/>\n______ \\(\\frac{\u25a1}{\u25a1}\\)<\/p>\n<p>Answer:<br \/>\n1\\(\\frac{1}{10}\\)<\/p>\n<p>Explanation:<br \/>\n2 1\/5 = 11\/5 = 2.2 is closer to 2.2<br \/>\n2.2\/2 = 1.1 = 11\/10 = 1 1\/10<\/p>\n<p>Question 8.<br \/>\nSid and Jill hiked 4 \\(\\frac{1}{8}\\) miles in the morning and 1 \\(\\frac{7}{8}\\) miles in the afternoon. How many times as far did they hike in the morning as in the afternoon?<br \/>\n______ \\(\\frac{\u25a1}{\u25a1}\\) times<\/p>\n<p>Answer:<br \/>\n2\\(\\frac{1}{5}\\) times<\/p>\n<p>Explanation:<br \/>\nSid and Jill hiked 4 \\(\\frac{1}{8}\\) miles in the morning and 1 \\(\\frac{7}{8}\\) miles in the afternoon.<br \/>\n4 \\(\\frac{1}{8}\\) = 33\/8<br \/>\n1 \\(\\frac{7}{8}\\) = 15\/8<br \/>\n(33\/8) \u00f7 (15\/8) = 33\/15 = 11\/5 or 2 1\/5<\/p>\n<p><strong>Problem Solving<\/strong><\/p>\n<p>Question 9.<br \/>\nIt takes Nim 2 \\(\\frac{2}{3}\\) hours to weave a basket. He worked Monday through Friday, 8 hours a day. How many baskets did he make?<br \/>\n______ baskets<\/p>\n<p>Answer:<br \/>\n15 baskets<\/p>\n<p>Explanation:<br \/>\nhe worked (Mon &#8211; Fri) 5 days at 8 hrs per day = 5 \u00d7 8= 40 hrs<br \/>\n40\/ (2 2\/3) = 40 \/ (8\/3) = 40 \u00d7 3\/8 = 120\/8 = 15 baskets<\/p>\n<p>Question 10.<br \/>\nA tree grows 1 \\(\\frac{3}{4}\\) feet per year. How long will it take the tree to grow from a height of 21 \\(\\frac{1}{4}\\) feet to a height of 37 feet?<br \/>\n______ years<\/p>\n<p>Answer:<br \/>\n9 years<\/p>\n<p>Explanation:<br \/>\nA tree grows 1 3\/4 = 7\/4 feet per year.<br \/>\nIf you would like to know how long will it take the tree to grow from a height of 21 1\/4 = 85\/4 feet to a height of 37 feet,<br \/>\n37 &#8211; 21 1\/4 = 37 &#8211; 85\/4 = 148\/4 &#8211; 85\/4 = 63\/4 = 15 3\/4<br \/>\n15 3\/4 \/ 1 3\/4 = 63\/4 \/ 7\/4 = 63\/4 \u00d7 4\/7 = 9 years<\/p>\n<p>Question 11.<br \/>\nExplain how you would find how many 1 \\(\\frac{1}{2}\\) cup servings there are in a pot that contains 22 \\(\\frac{1}{2}\\) cups of soup.<br \/>\nType below:<br \/>\n__________<\/p>\n<p>Answer:<br \/>\nGiven that, Total number of cups = 22 1\/2<br \/>\nThe number of cups required for each serving = 1 1\/2<br \/>\nThe number of servings = 22 1\/2 \u00f7 1 1\/2<br \/>\n= 45\/2 \u00f7 3\/2 = 45\/3 = 15<\/p>\n<h3><a id=\"Divide_Mixed_Numbers_Lesson_Check_1\u2013_Page_No._124\"><\/a>Lesson Check &#8211; Page No. 124<\/h3>\n<p>Question 1.<br \/>\nTom has a can of paint that covers 37 \\(\\frac{1}{2}\\) square meters. Each board on the fence has an area of \\(\\frac{3}{16}\\) square meters. How many boards can he paint?<br \/>\n______ boards<\/p>\n<p>Answer:<br \/>\n200 boards<\/p>\n<p>Explanation:<br \/>\nTom has a can of paint that covers 37 \\(\\frac{1}{2}\\) square meters. Each board on the fence has an area of \\(\\frac{3}{16}\\) square meters.<br \/>\n37 \\(\\frac{1}{2}\\) \u00f7 \\(\\frac{3}{16}\\) = 200 square meters<\/p>\n<p>Question 2.<br \/>\nA baker wants to put 3 \\(\\frac{3}{4}\\) pounds of apples in each pie she makes. She purchased 52 \\(\\frac{1}{2}\\) pounds of apples. How many pies can she make?<br \/>\n______ pies<\/p>\n<p>Answer:<br \/>\n14 pies<\/p>\n<p>Explanation:<br \/>\nA baker wants to put 3 \\(\\frac{3}{4}\\) pounds of apples in each pie she makes. She purchased 52 \\(\\frac{1}{2}\\) pounds of apples.<br \/>\n52 \\(\\frac{1}{2}\\) \u00f7 3 \\(\\frac{3}{4}\\) = 14 pies<\/p>\n<p><strong>Spiral Review<\/strong><\/p>\n<p>Question 3.<br \/>\nThe three sides of a triangle measure 9.97 meters, 10.1 meters, and 0.53 meter. What is the distance around the triangle?<br \/>\n______ meters<\/p>\n<p>Answer:<br \/>\n20.6 meters<\/p>\n<p>Explanation:<br \/>\nThe distance around the triangle is call perimeter, to get it we must add the 3 sides.<br \/>\nSo, 9.97 + 10.1 + 0.53 = 20.6 meters<\/p>\n<p>Question 4.<br \/>\nSelena bought 3.75 pounds of meat for $4.64 per pound. What was the total cost of the meat?<br \/>\n$ ______<\/p>\n<p>Answer:<br \/>\n$17.40<\/p>\n<p>Explanation:<br \/>\nSelena bought 3.75 pounds of meat.<br \/>\nThe cost of meat of one pound = $4.64<br \/>\nThe total cost of the meat = 4.64 \u00d7 3.75 = $17.40<br \/>\nThe total cost of 3.75 lb of meat was $17.40.<\/p>\n<p>Question 5.<br \/>\nMelanie prepared 7 \\(\\frac{1}{2}\\) tablespoons of a spice mixture. She uses \\(\\frac{1}{4}\\) tablespoon to make a batch of barbecue sauce. Estimate the number of batches of barbecue sauce she can make using the spice mixture.<br \/>\nType below:<br \/>\n__________<\/p>\n<p>Answer:<br \/>\n30 batches of sauce<\/p>\n<p>Explanation:<br \/>\nMelanie prepared 7 \\(\\frac{1}{2}\\) tablespoons of a spice mixture. She uses \\(\\frac{1}{4}\\) tablespoon to make a batch of barbecue sauce.<br \/>\n4 X 1\/4 tbsp = 1 tbsp.<br \/>\n4 X 7 1\/2 = 30.<br \/>\nshe can make 30 batches of sauce<\/p>\n<p>Question 6.<br \/>\nArturo mixed together 1.24 pounds of pretzels, 0.78 pounds of nuts, 0.3 pounds of candy, and 2 pounds of popcorn. He then packaged it in bags that each contained 0.27 pounds. How many bags could he fill?<br \/>\n______ bags<\/p>\n<p>Answer:<br \/>\n16 bags<\/p>\n<p>Explanation:<br \/>\nArturo mixed together 1.24 pounds of pretzels, 0.78 pounds of nuts, 0.3 pounds of candy, and 2 pounds of popcorn.<br \/>\n1.24 + 0.78 + 0.3 + 2 = 4.32<br \/>\n4.32\/0.27 = 16<\/p>\n<h3><a id=\"Fraction_Operations_\u2013_Page_No._127\"><\/a>Page No. 127<\/h3>\n<p>Question 1.<br \/>\nThere is \\(\\frac{4}{5}\\) lb of sand in the class science supplies. If one scoop of sand weighs \\(\\frac{1}{20}\\) lb, how many scoops of sand can Maria get from the class supplies and still leave \\(\\frac{1}{2}\\) lb in the supplies?<br \/>\nType below:<br \/>\n__________<\/p>\n<p>Answer:<br \/>\n16 scoops<\/p>\n<p>Explanation:<br \/>\nThere is \\(\\frac{4}{5}\\) lb of sand in the class science supplies. If one scoop of sand weighs \\(\\frac{1}{20}\\) lb,<br \/>\n\\(\\frac{4}{5}\\) \u00f7 \\(\\frac{1}{20}\\) = 4\/5 \u00d7 1\/20 = 16 scoops<\/p>\n<p>Question 2.<br \/>\nWhat if Maria leaves \\(\\frac{2}{5}\\) lb of sand in the supplies? How many scoops of sand can she get?<br \/>\n______ scoops<\/p>\n<p>Answer:<br \/>\n8 scoops<\/p>\n<p>Explanation:<br \/>\nThere is \\(\\frac{2}{5}\\) lb of sand in the class science supplies. If one scoop of sand weighs \\(\\frac{1}{20}\\) lb,<br \/>\n\\(\\frac{2}{5}\\) \u00f7 \\(\\frac{1}{20}\\) = 2\/5 \u00d7 20 = 8<\/p>\n<p>Question 3.<br \/>\nThere are 6 gallons of distilled water in the science supplies. If 10 students each use an equal amount of the distilled water and there is 1 gal left in the supplies, how much will each student get?<br \/>\n\\(\\frac{\u25a1}{\u25a1}\\) gallon<\/p>\n<p>Answer:<br \/>\n\\(\\frac{1}{2}\\) gallon<\/p>\n<p>Explanation:<br \/>\nThere are 6 gallons of distilled water in the science supplies.<br \/>\nThere is 1 gal left in the supplies, 6 &#8211; 1 = 5<br \/>\n10 students each use an equal amount of the distilled water = 5\/10 = 1\/2<br \/>\n.5 gal for each student<\/p>\n<h3><a id=\"Fraction_Operations_\u2013_Page_No._128\"><\/a>On Your Own &#8211; Page No. 128<\/h3>\n<p>Question 4.<br \/>\nThe total weight of the fish in a tank of tropical fish at Fish \u2018n\u2019 Fur was \\(\\frac{7}{8}\\) lb. Each fish weighed \\(\\frac{1}{64}\\) lb. After Eric bought some fish, the total weight of the fish remaining in the tank was \\(\\frac{1}{2}\\) lb. How many fish did Eric buy?<br \/>\n______ fish<\/p>\n<p>Answer:<br \/>\n386 fish<\/p>\n<p>Explanation:<br \/>\nThe total weight of the fish in a tank of tropical fish at Fish \u2018n\u2019 Fur was \\(\\frac{7}{8}\\) lb. Each fish weighed \\(\\frac{1}{64}\\) lb. After Eric bought some fish, the total weight of the fish remaining in the tank was \\(\\frac{1}{2}\\) lb.<br \/>\n386 is the answer<\/p>\n<p>Question 5.<br \/>\nFish \u2018n\u2019 Fur had a bin containing 2 \\(\\frac{1}{2}\\) lb of gerbil food. After selling bags of gerbil food that each held \\(\\frac{3}{4}\\) lb, \\(\\frac{1}{4}\\) lb of food was left in the bin. If each bag of gerbil food sold for $3.25, how much did the store earn?<br \/>\n$ ______<\/p>\n<p>Answer:<br \/>\n$9.75<\/p>\n<p>Explanation:<br \/>\nThe store would earn 9.75$ because 3 bags of gerbil food is sold. Then you would multiply 3 by 3.25.<\/p>\n<p>Question 6.<br \/>\nDescribe Niko bought 2 lb of dog treats. He gave his dog \\(\\frac{3}{5}\\) lb of treats one week and \\(\\frac{7}{10}\\) lb of treats the next week. Describe how Niko can find how much is left.<br \/>\nType below:<br \/>\n__________<\/p>\n<p>Answer:<br \/>\nNiko bought 2 lb of dog treats. He gave his dog \\(\\frac{3}{5}\\) lb of treats one week and \\(\\frac{7}{10}\\) lb of treats the next week.<br \/>\nLet us find the amount of dog-food eaten by dogs in two months.<br \/>\n3\/5 + 7\/10 = 13\/10<br \/>\nNow we will subtract the amount of food eaten by the dog from the amount of food initially to find the remaining amount of dog food.<br \/>\n2 &#8211; 13\/10 = 7\/10<br \/>\nTherefore, 7\/10 pounds of food was remaining in the bag at the end of the two months.<\/p>\n<p>Question 7.<br \/>\nThere were 14 \\(\\frac{1}{4}\\) cups of apple juice in a container. Each day, Elise drank 1 \\(\\frac{1}{2}\\) cups of apple juice. Today, there is \\(\\frac{3}{4}\\) cup of apple juice left. Derek said that Elise drank apple juice on nine days. Do you agree with Derek? Use words and numbers to explain your answer.<br \/>\nType below:<br \/>\n__________<\/p>\n<p>Answer:<br \/>\nDerek is correct.<\/p>\n<p>Explanation:<br \/>\nAn apple juice the container had 14 1\/2 =14.25<br \/>\nShe drank per day 1 1\/2= 1.5<br \/>\nThe left part in the container 3\/4= .75<br \/>\n14.25 cups &#8211; .75 cup = 13.5 cups<br \/>\n13.5 cups \u00f7 1.5 cups per day= 9 days<\/p>\n<h3><a id=\"Fraction_Operations_Lesson_Check_\u2013_Page_No._129\"><\/a>Problem Solving Fraction Operations &#8211; Page No. 129<\/h3>\n<p><strong>Read each problem and solve.<\/strong><\/p>\n<p>Question 1.<br \/>\n\\(\\frac{2}{3}\\) of a pizza was left over. A group of friends divided the leftover pizza into pieces each equal to \\(\\frac{1}{18}\\) of the original pizza. After each friend took one piece, \\(\\frac{1}{6}\\) of the original pizza remained. How many friends were in the group?<br \/>\n<img loading=\"lazy\" class=\"alignnone size-full wp-image-4805\" src=\"https:\/\/ccssmathanswers.com\/wp-content\/uploads\/2020\/08\/Go-Math-Grade-6-Answer-Key-Chapter-2-Fractions-and-Decimals-23.jpg\" alt=\"Go Math Grade 6 Answer Key Chapter 2 Fractions and Decimals 23\" width=\"259\" height=\"224\" \/><br \/>\n______ friends<\/p>\n<p>Answer:<br \/>\n9 friends<\/p>\n<p>Explanation:<br \/>\nLet us say that there are x friends.<br \/>\nEach one gets 1\/18 of the original pizza: but this in turn leaves 1\/6 of the 2\/3 leftover.<br \/>\n1x\/18 = 2\/3 &#8211; 1\/6<br \/>\nx = 12 &#8211; 3 = 9<\/p>\n<p>Question 2.<br \/>\nSarah\u2019s craft project uses pieces of yarn that are \\(\\frac{1}{8}\\) yard long. She has a piece of yarn that is 3 yards long. How many \\(\\frac{1}{8}\\) -yard pieces can she cut and still have 1 \\(\\frac{1}{4}\\) yards left?<br \/>\n______ pieces<\/p>\n<p>Answer:<br \/>\n14 pieces<\/p>\n<p>Explanation:<br \/>\nSarah\u2019s craft project uses pieces of yarn that are \\(\\frac{1}{8}\\) yard long. She has a piece of yarn that is 3 yards long.<br \/>\nIf she left 1 \\(\\frac{1}{4}\\) yards left, 3 &#8211; 1 \\(\\frac{1}{4}\\) = 7\/4<br \/>\n7\/4 \u00f7 \\(\\frac{1}{8}\\) = 14<\/p>\n<p>Question 3.<br \/>\nAlex opens a 1-pint container of orange butter. He spreads \\(\\frac{1}{16}\\) of the butter on his bread. Then he divides the rest of the butter into \\(\\frac{3}{4}\\) -pint containers. How many \\(\\frac{3}{4}\\) -pint containers is he able to fill?<br \/>\n______ \\(\\frac{\u25a1}{\u25a1}\\) containers<\/p>\n<p>Answer:<br \/>\n1\\(\\frac{1}{4}\\) containers<\/p>\n<p>Explanation:<br \/>\nAlex opens a 1-pint container of orange butter. He spreads \\(\\frac{1}{16}\\) of the butter on his bread.<br \/>\n1 &#8211; 1\/16 = 15\/16<br \/>\nThen he divides the rest of the butter into \\(\\frac{3}{4}\\) -pint containers.<br \/>\n(15\/16) \u00f7 (3\/4) = 5\/4 = 1 1\/4<\/p>\n<p>Question 4.<br \/>\nKaitlin buys \\(\\frac{9}{10}\\) a pound of orange slices. She eats \\(\\frac{1}{3}\\) of them and divides the rest equally into 3 bags. How much is in each bag?<br \/>\n______ lb<\/p>\n<p>Answer:<br \/>\n17\/90 lb<\/p>\n<p>Explanation:<br \/>\nKaitlin buys \\(\\frac{9}{10}\\) a pound of orange slices. She eats \\(\\frac{1}{3}\\) of them and divides the rest equally into 3 bags.<br \/>\nIf she starts with 9\/10 pounds and has eaten 1\/3 of them, 9\/10 &#8211; 1\/3 = 17\/30<br \/>\nThis is the amount she has left. Let&#8217;s divide this value by 3 to see how many pounds are in one bag.<br \/>\n(17\/30)\/3 = 17\/90<br \/>\nThere are 17\/90 pounds in one bag.<\/p>\n<p>Question 5.<br \/>\nExplain how to draw a model that represents \\(\\left(1 \\frac{1}{4}-\\frac{1}{2}\\right) \\div \\frac{1}{8}\\).<br \/>\nType below:<br \/>\n__________<\/p>\n<p>Answer:<br \/>\nDivide 2 bars into 8 quarters.<br \/>\nBelow that draw 1 1\/4 or 5 quarters.<br \/>\nRemove 1\/2 or 2 quarters<br \/>\nDivide each of the 3 quarters left into 2 eighths<\/p>\n<p>Explanation:<br \/>\n\\(\\left(1 \\frac{1}{4}-\\frac{1}{2}\\right) \\div \\frac{1}{8}\\)<br \/>\n1 1\/4 -1\/2 = 5\/4 &#8211; 1\/2 = 3\/4<br \/>\n3\/4 \u00f7 1\/8 = 6<\/p>\n<h3><a id=\"Fraction_Operations_Lesson_Check_1\u2013_Page_No._130\"><\/a>Lesson Check &#8211; Page No. 130<\/h3>\n<p>Question 1.<br \/>\nEva wanted to fill bags with \\(\\frac{3}{4}\\) pounds of trail mix. She started with 11 \\(\\frac{3}{8}\\) pounds but ate \\(\\frac{1}{8}\\) pound before she started filling the bags. How many bags could she fill?<br \/>\n______ bags<\/p>\n<p>Answer:<br \/>\n15 bags<\/p>\n<p>Explanation:<br \/>\n11 and 3\/8-1\/8=11 and 2\/8=11 and 1\/4<br \/>\n3\/4 times x bags=11 and 1\/4<br \/>\nconvert 11 and 1\/4 to improper fraction<br \/>\n11 and 1\/4 = 11 + 1\/4 = 44\/4 + 1\/4 = 45\/4<br \/>\n3\/4 times x bags=45\/4<br \/>\nx bags = 45\/4 \u00d7 4\/3 = 15 bags<br \/>\nshe could fill 15 bags<\/p>\n<p>Question 2.<br \/>\nJohn has a roll containing 24 \\(\\frac{2}{3}\\) feet of wrapping paper. He wants to divide it into 11 pieces. First, though, he must cut off \\(\\frac{5}{6}\\) foot because it was torn. How long will each piece be?<br \/>\n______ \\(\\frac{\u25a1}{\u25a1}\\) feet<\/p>\n<p>Answer:<br \/>\n2\\(\\frac{4}{25}\\) feet<\/p>\n<p>Explanation:<br \/>\nJohn had a roll containing wrapping paper = 24 2\/3 = 74\/3<br \/>\nFirst, he must cut off 5\/6 foot because it was torn.<br \/>\nHe wants to divide it into 11 pieces.<br \/>\n74\/3 &#8211; 5\/6<br \/>\nTaking the L.C.M of 3 and 6 is 6<br \/>\n(148-5)\/6 = 143\/6 = 23.83 feet<br \/>\nHe wants to divide it into 11 pieces. length of the each piece = 23.83\/11 = 2.16 feet<\/p>\n<p><strong>Spiral Review<\/strong><\/p>\n<p>Question 3.<br \/>\nAlexis has 32 \\(\\frac{2}{5}\\) ounces of beads. How many necklaces can she make if each uses 2 \\(\\frac{7}{10}\\) ounces of beads?<br \/>\n______ necklaces<\/p>\n<p>Answer:<br \/>\n12 necklaces<\/p>\n<p>Explanation:<br \/>\nAlexis has 32 \\(\\frac{2}{5}\\) ounces of beads.<br \/>\nIf each uses 2 \\(\\frac{7}{10}\\) ounces of beads, 32 \\(\\frac{2}{5}\\) \u00d7 2 \\(\\frac{7}{10}\\)<br \/>\n32 \\(\\frac{2}{5}\\) = 162\/5<br \/>\n2 \\(\\frac{7}{10}\\) = 27\/10<br \/>\n162\/5 \u00d7 27\/10 = 12 necklaces<\/p>\n<p>Question 4.<br \/>\nJoseph has $32.40. He wants to buy several comic books that each cost $2.70. How many comic books can he buy?<br \/>\n______ comic books<\/p>\n<p>Answer:<br \/>\n12 comic books<\/p>\n<p>Explanation:<br \/>\nJoseph has $32.40. He wants to buy several comic books that each cost $2.70.<br \/>\n$32.40\/$2.70 = 12 comic books<\/p>\n<p>Question 5.<br \/>\nA rectangle is 2 \\(\\frac{4}{5}\\) meters wide and 3 \\(\\frac{1}{2}\\) meters long. What is its area?<br \/>\n______ \\(\\frac{\u25a1}{\u25a1}\\) m<sup>2<\/sup><\/p>\n<p>Answer:<br \/>\n9\\(\\frac{4}{5}\\) m2<\/p>\n<p>Explanation:<br \/>\n2 \\(\\frac{4}{5}\\) = 14\/5<br \/>\n3 \\(\\frac{1}{2}\\) = 7\/2<br \/>\n14\/5 \u00d7 7\/2 = 9 4\/5<\/p>\n<p>Question 6.<br \/>\nA rectangle is 2.8 meters wide and 3.5 meters long. What is its area?<br \/>\n______ m<sup>2<\/sup><\/p>\n<p>Answer:<br \/>\n9.8 m<sup>2<\/sup><\/p>\n<p>Explanation:<br \/>\nA rectangle is 2.8 meters wide and 3.5 meters long.<br \/>\n2.8 \u00d7 3.5 = 9.8<\/p>\n<h3><a id=\"Review\/Test_-_Page_No._131\"><\/a>Chapter 2 Review\/Test &#8211; Page No. 131<\/h3>\n<p>Question 1.<br \/>\nWrite the values in order from least to greatest.<br \/>\n<img loading=\"lazy\" class=\"alignnone size-full wp-image-4806\" src=\"https:\/\/ccssmathanswers.com\/wp-content\/uploads\/2020\/08\/Go-Math-Grade-6-Answer-Key-Chapter-2-Fractions-and-Decimals-24.jpg\" alt=\"Go Math Grade 6 Answer Key Chapter 2 Fractions and Decimals 24\" width=\"518\" height=\"67\" srcset=\"https:\/\/bigideasmathanswers.com\/wp-content\/uploads\/2020\/08\/Go-Math-Grade-6-Answer-Key-Chapter-2-Fractions-and-Decimals-24.jpg 518w, https:\/\/bigideasmathanswers.com\/wp-content\/uploads\/2020\/08\/Go-Math-Grade-6-Answer-Key-Chapter-2-Fractions-and-Decimals-24-300x39.jpg 300w\" sizes=\"(max-width: 518px) 100vw, 518px\" \/><br \/>\nType below:<br \/>\n__________<\/p>\n<p>Answer:<br \/>\n0.45, 0.5, 5\/8, 3\/4<\/p>\n<p>Explanation:<br \/>\n3\/4 = 0.75<br \/>\n5\/8 = 0.625<br \/>\n0.45, 0.5<br \/>\n0.45 &lt; 0.5 &lt; 0.625 &lt; 0.75<\/p>\n<p>Question 2.<br \/>\nFor numbers 2a\u20132d, compare. Choose &lt;, &gt;, or =.<br \/>\n2a. 0.75 _____ \\(\\frac{3}{4}\\)<br \/>\n2b. \\(\\frac{4}{5}\\) _____ 0.325<br \/>\n2c. 1 \\(\\frac{3}{5}\\) _____ 1.9<br \/>\n2d. 7.4 _____ 7 \\(\\frac{2}{5}\\)<\/p>\n<p>Answer:<br \/>\n2a. 0.75 = \\(\\frac{3}{4}\\)<br \/>\n2b. \\(\\frac{4}{5}\\) &gt; 0.325<br \/>\n2c. 1 \\(\\frac{3}{5}\\) &lt; 1.9<br \/>\n2d. 7.4 = 7 \\(\\frac{2}{5}\\)<\/p>\n<p>Explanation:<br \/>\n2a. 3\/4 = 0.75<br \/>\n0.75 = 0.75<br \/>\n2b. \\(\\frac{4}{5}\\) = 0.8<br \/>\n0.8 &gt; 0.325<br \/>\n2c. 1 \\(\\frac{3}{5}\\) = 8\/5 = 1.6<br \/>\n1.6 &lt; 1.9<br \/>\n2d. 7 \\(\\frac{2}{5}\\) = 37\/5 = 7.4<br \/>\n7.4 = 7.4<\/p>\n<p>Question 3.<br \/>\nThe table lists the heights of 4 trees.<br \/>\n<img loading=\"lazy\" class=\"alignnone size-full wp-image-4807\" src=\"https:\/\/ccssmathanswers.com\/wp-content\/uploads\/2020\/08\/Go-Math-Grade-6-Answer-Key-Chapter-2-Fractions-and-Decimals-25.jpg\" alt=\"Go Math Grade 6 Answer Key Chapter 2 Fractions and Decimals 25\" width=\"284\" height=\"195\" \/><br \/>\nFor numbers 3a\u20133d, select True or False for each statement.<br \/>\n3a. The oak tree is the shortest. True False<br \/>\n3b. The birch tree is the tallest. True False<br \/>\n3c. Two of the trees are the same height. True False<br \/>\n3d. The sycamore tree is taller than the maple tree. True False<br \/>\nType below:<br \/>\n__________<\/p>\n<p>Answer:<br \/>\n3a. The oak tree is the shortest. True<br \/>\n3b. The birch tree is the tallest. False<br \/>\n3c. Two of the trees are the same height. False<br \/>\n3d. The sycamore tree is taller than the maple tree. False<\/p>\n<p>Explanation:<br \/>\nSycamore = 15 2\/3 = 47\/3 = 15.666<br \/>\nOak = 14 3\/4 = 59\/4 = 14.75<br \/>\nMaple = 15 3\/4 = 63\/4 = 15.75<br \/>\nBirch = 15.72<\/p>\n<h3><a id=\"Review\/Test_-_Page_No._132\"><\/a>Page No. 132<\/h3>\n<p>Question 4.<br \/>\nFor numbers 4a\u20134d, choose Yes or No to indicate whether the statement is correct.<br \/>\n<img loading=\"lazy\" class=\"alignnone size-full wp-image-4808\" src=\"https:\/\/ccssmathanswers.com\/wp-content\/uploads\/2020\/08\/Go-Math-Grade-6-Answer-Key-Chapter-2-Fractions-and-Decimals-26.jpg\" alt=\"Go Math Grade 6 Answer Key Chapter 2 Fractions and Decimals 26\" width=\"359\" height=\"117\" srcset=\"https:\/\/bigideasmathanswers.com\/wp-content\/uploads\/2020\/08\/Go-Math-Grade-6-Answer-Key-Chapter-2-Fractions-and-Decimals-26.jpg 359w, https:\/\/bigideasmathanswers.com\/wp-content\/uploads\/2020\/08\/Go-Math-Grade-6-Answer-Key-Chapter-2-Fractions-and-Decimals-26-300x98.jpg 300w\" sizes=\"(max-width: 359px) 100vw, 359px\" \/><br \/>\n4a. Point A represents 1.0. Yes No<br \/>\n4b. Point B represents \\(\\frac{3}{10}\\). Yes No<br \/>\n4c. Point C represents 6.5. Yes No<br \/>\n4d. Point D represents \\(\\frac{4}{5}\\). Yes No<br \/>\nType below:<br \/>\n__________<\/p>\n<p>Answer:<br \/>\n4a. Point A represents 1.0. Yes<br \/>\n4b. Point B represents \\(\\frac{3}{10}\\). Yes<br \/>\n4c. Point C represents 6.5. No<br \/>\n4d. Point D represents \\(\\frac{4}{5}\\). Yes<\/p>\n<p>Question 5.<br \/>\nSelect the values that are equivalent to one twenty-fifth. Mark all that apply.<br \/>\nOptions:<br \/>\na. 125<br \/>\nb. 25<br \/>\nc. 0.04<br \/>\nd. 0.025<\/p>\n<p>Answer:<br \/>\nc. 0.04<\/p>\n<p>Explanation:<br \/>\none twenty-fifth = 1\/25 = 0.04<\/p>\n<p>Question 6.<br \/>\nThe table shows Lily\u2019s homework assignment. Lily\u2019s teacher instructed the class to simplify each expression by dividing the numerator and denominator by the GCF. Complete the table by simplifying each expression and then finding the product.<br \/>\n<img loading=\"lazy\" class=\"alignnone size-full wp-image-4809\" src=\"https:\/\/ccssmathanswers.com\/wp-content\/uploads\/2020\/08\/Go-Math-Grade-6-Answer-Key-Chapter-2-Fractions-and-Decimals-27.jpg\" alt=\"Go Math Grade 6 Answer Key Chapter 2 Fractions and Decimals 27\" width=\"560\" height=\"254\" srcset=\"https:\/\/bigideasmathanswers.com\/wp-content\/uploads\/2020\/08\/Go-Math-Grade-6-Answer-Key-Chapter-2-Fractions-and-Decimals-27.jpg 560w, https:\/\/bigideasmathanswers.com\/wp-content\/uploads\/2020\/08\/Go-Math-Grade-6-Answer-Key-Chapter-2-Fractions-and-Decimals-27-300x136.jpg 300w\" sizes=\"(max-width: 560px) 100vw, 560px\" \/><br \/>\nType below:<br \/>\n___________<\/p>\n<p>Answer:<br \/>\na. Simplified Expression: 1\/10<br \/>\nProduct: 0.1<br \/>\nb. Simplified Expression: 1\/2<br \/>\nProduct: 0.5<br \/>\nc. Simplified Expression: 15\/56<br \/>\nProduct: 0.267<br \/>\nd. Simplified Expression: 1\/12<br \/>\nProduct: 0.083<\/p>\n<p>Explanation:<br \/>\na. 2\/5 \u00d7 1\/4 = 2\/20<br \/>\nSimplify using the GCF.<br \/>\nThe GCF of 2 and 20 is 2.<br \/>\nDivide the numerator and the denominator by 2.<br \/>\nSo, 1\/10 is the answer.<br \/>\nProduct: 0.1<br \/>\nb. 4\/5 \u00d7 5\/8 = 1\/2<br \/>\nProduct: 0.5<br \/>\nc. 3\/7 \u00d7 5\/8 = 15\/ 56<br \/>\nProduct: 0.267<br \/>\nd. 4\/9 \u00d7 3\/16 = 1\/12<br \/>\nProduct: 0.083<\/p>\n<h3><a id=\"Review\/Test_-_Page_No._133\"><\/a>Page No. 133<\/h3>\n<p>Question 7.<br \/>\nTwo-fifths of the fish in Gary\u2019s fish tank are guppies. One fourth of the guppies are red. What fraction of the fish in Gary\u2019s tank are red guppies? What fraction of the fish in Gary&#8217;s tank are not red guppies? Show your work.<br \/>\nType below:<br \/>\n___________<\/p>\n<p>Answer:<br \/>\n1\/10 of the fish are red guppies.<br \/>\nand 9\/10 of the fish are not red guppies.<\/p>\n<p>Explanation:<br \/>\ntwo-fifths of the fish in Gary&#8217;s fish tank are guppies.<br \/>\nOne-fourth of the guppies are red.<br \/>\nLet the total number of fish in Gary&#8217;s fish tank be x.<br \/>\nIt is given that two-fifths of the fish in Gary&#8217;s fish tank are guppies.<br \/>\nSo, the number of guppies in Gary&#8217;s fish tank is 2\/5 \u00d7 x<br \/>\nGiven that One-fourth of the guppies are red.<br \/>\nnumber of red guppies = 1\/4 \u00d7 2x\/5 = x\/10<br \/>\nSo, 1\/10 of the fish are red guppies.<br \/>\n1 &#8211; 1\/10 = 9\/10 of the fish are not red guppies.<\/p>\n<p>Question 8.<br \/>\nOne-third of the students at Finley High School play sports. Two-fifths of the students who play sports are girls. What fraction of all students are girls who play sports? Use numbers and words to explain your answer.<br \/>\nType below:<br \/>\n___________<\/p>\n<p>Answer:<br \/>\nOne-third of the students at Finley High School play sports. Two-fifths of the students who play sports are girls.<br \/>\n1\/3 \u00d7 2\/5 = 2\/15 of the girls in the school play sports.<\/p>\n<p>Question 9.<br \/>\nDraw a model to find the quotient.<br \/>\n\\(\\frac{3}{4}\\) \u00f7 2 =<br \/>\n\\(\\frac{3}{4}\\) \u00f7 \\(\\frac{3}{8}\\) =<br \/>\nHow are your models alike? How are they different?<br \/>\nType below:<br \/>\n___________<\/p>\n<p>Answer:<br \/>\n<img loading=\"lazy\" class=\"alignnone size-medium wp-image-8322\" src=\"https:\/\/ccssmathanswers.com\/wp-content\/uploads\/2020\/08\/grade-6-chapter-2-image-5-1-300x104.jpg\" alt=\"grade 6 chapter 2 image 5\" width=\"300\" height=\"104\" srcset=\"https:\/\/bigideasmathanswers.com\/wp-content\/uploads\/2020\/08\/grade-6-chapter-2-image-5-1-300x104.jpg 300w, https:\/\/bigideasmathanswers.com\/wp-content\/uploads\/2020\/08\/grade-6-chapter-2-image-5-1.jpg 370w\" sizes=\"(max-width: 300px) 100vw, 300px\" \/><\/p>\n<p>Explanation:<br \/>\n\\(\\frac{3}{4}\\) \u00f7 2 = 3\/4 \u00d7 1\/2 = 3\/8<br \/>\n\\(\\frac{3}{4}\\) \u00f7 \\(\\frac{3}{8}\\) = 3\/4 \u00d7 8\/3 = 2<br \/>\nBoth models are multiplying with the 3\/4.<br \/>\nThe number line model shows how many groups of 3\/8 are in 3\/4.<\/p>\n<p>Question 10.<br \/>\nExplain how to use a model to find the quotient.<br \/>\n2 \\(\\frac{1}{2}\\) \u00f7 2 =<br \/>\nType below:<br \/>\n___________<\/p>\n<p>Answer:<br \/>\n5\/4<\/p>\n<p>Explanation:<br \/>\n2 1\/2 = 5\/2<br \/>\n5\/2 groups of 2<br \/>\n5\/2 \u00f7 2 = 5\/2 \u00d7 1\/2 = 5\/4<\/p>\n<h3><a id=\"Review\/Test_-_Page_No._134\"><\/a>Page No. 134<\/h3>\n<p><strong>Divide. Show your work.<\/strong><\/p>\n<p>Question 11.<br \/>\n\\(\\frac{7}{8}\\) \u00f7 \\(\\frac{3}{5}\\) =<br \/>\n_______ \\(\\frac{\u25a1}{\u25a1}\\)<\/p>\n<p>Answer:<br \/>\n1 \\(\\frac{11}{24}\\)<\/p>\n<p>Explanation:<br \/>\n\\(\\frac{7}{8}\\) \u00f7 \\(\\frac{3}{5}\\)<br \/>\n\\(\\frac{7}{8}\\) \u00d7 \\(\\frac{5}{3}\\) = 35\/24 = 1 \\(\\frac{11}{24}\\)<\/p>\n<p>Question 12.<br \/>\n\\(2 \\frac{1}{10} \\div 1 \\frac{1}{5}=\\) =<br \/>\n_______ \\(\\frac{\u25a1}{\u25a1}\\)<\/p>\n<p>Answer:<br \/>\n1 \\(\\frac{3}{4}\\)<\/p>\n<p>Explanation:<br \/>\n2 \\(\\frac{1}{10}\\) = 21\/10<br \/>\n1 \\(\\frac{1}{5}\\) = 6\/5<br \/>\n(21\/10) \u00f7 (6\/5) = 7\/4 or 1 3\/4<\/p>\n<p>Question 13.<br \/>\nSophie has \\(\\frac{3}{4}\\) quart of lemonade. If she divides the lemonade into glasses that hold \\(\\frac{1}{16}\\) quart, how many glasses can Sophie fill? Show your work<br \/>\n_______ glasses<\/p>\n<p>Answer:<br \/>\n12 glasses<\/p>\n<p>Explanation:<br \/>\nLet x be the number of glasses<br \/>\n1\/16x = 3\/4<br \/>\nx = 3\/4 \u00d7 16 = 3 \u00d7 4 = 12 glasses<\/p>\n<p>Question 14.<br \/>\nInk cartridges weigh \\(\\frac{1}{8}\\) pound. The total weight of the cartridges in a box is 4 \\(\\frac{1}{2}\\) pounds. How many cartridges does the box contain? Show your work and explain why you chose the operation you did.<br \/>\n_______ cartridges<\/p>\n<p>Answer:<br \/>\n36 cartridges<\/p>\n<p>Explanation:<br \/>\nWeight of ink cartridges = 1\/8 pounds<br \/>\nTotal weight of the cartridges in a box = 4 1\/2 = 9\/2 pounds<br \/>\nso, the Number of cartridges that box contain is given by<br \/>\n9\/2 \u00f7 1\/8 = 36<br \/>\nHence, there are 36 cartridges that box contain.<\/p>\n<p>Question 15.<br \/>\nBeth had 1 yard of ribbon. She used \\(\\frac{1}{3}\\) yard for a project. She wants to divide the rest of the ribbon into pieces \\(\\frac{1}{6}\\) yard long. How many \\(\\frac{1}{6}\\) yard pieces of ribbon can she make? Explain your solution.<br \/>\n_______ pieces<\/p>\n<p>Answer:<br \/>\n4 pieces<\/p>\n<p>Explanation:<br \/>\nBeth had 1 yard of ribbon. She used \\(\\frac{1}{3}\\) yard for a project.<br \/>\n1 &#8211; \\(\\frac{1}{3}\\) = 2\/3 yard left<br \/>\nShe wants to divide the rest of the ribbon into pieces \\(\\frac{1}{6}\\) yard long.<br \/>\n2\/3 \u00f7 1\/6 = 4<\/p>\n<h3><a id=\"Review\/Test_-_Page_No._135\"><\/a>Page No. 135<\/h3>\n<p>Question 16.<br \/>\nComplete the table by finding the products. Then answer the questions in Part A and Part B.<br \/>\n<img loading=\"lazy\" class=\"alignnone size-full wp-image-4810\" src=\"https:\/\/ccssmathanswers.com\/wp-content\/uploads\/2020\/08\/Go-Math-Grade-6-Answer-Key-Chapter-2-Fractions-and-Decimals-28.jpg\" alt=\"Go Math Grade 6 Answer Key Chapter 2 Fractions and Decimals 28\" width=\"285\" height=\"238\" \/><br \/>\nPart A<br \/>\nExplain how each pair of division and multiplication problems are the same, and how they are different.<br \/>\nType below:<br \/>\n___________<\/p>\n<p>Answer:<br \/>\n1\/5 \u00f7 3\/4 = 4\/15; 1\/5 \u00d7 4\/3 = 4\/15<br \/>\n2\/13 \u00f7 1\/5 = 10\/13; 2\/13 \u00d7 5\/1 = 10\/13<br \/>\n4\/5 \u00f7 3\/5 = 4\/3; 4\/5 \u00d7 5\/3 = 4\/3<br \/>\nthe product of the each pair of division and multiplication problems are the same.<br \/>\nThey are different from the operation performed.<\/p>\n<p>Question 16.<br \/>\nPart B<br \/>\nExplain how to use the pattern in the table to rewrite a division problem involving fractions as a multiplication problem.<br \/>\nType below:<br \/>\n___________<\/p>\n<p>Answer:<br \/>\nFirst, since it&#8217;s the division you have to change the second fraction which is called the reciprocal. That means the second fraction has to be flipped before you can multiple the fractions.<\/p>\n<h3><a id=\"Review\/Test_-_Page_No._136\"><\/a>Page No. 136<\/h3>\n<p>Question 17.<br \/>\nMargie hiked a 17 \\(\\frac{7}{8}\\) mile trail. She stopped every 3 \\(\\frac{2}{5}\\) miles to take a picture. Martin and Tina estimated how many times Margie stopped.<br \/>\n<img loading=\"lazy\" class=\"alignnone size-full wp-image-4811\" src=\"https:\/\/ccssmathanswers.com\/wp-content\/uploads\/2020\/08\/Go-Math-Grade-6-Answer-Key-Chapter-2-Fractions-and-Decimals-29.jpg\" alt=\"Go Math Grade 6 Answer Key Chapter 2 Fractions and Decimals 29\" width=\"384\" height=\"149\" srcset=\"https:\/\/bigideasmathanswers.com\/wp-content\/uploads\/2020\/08\/Go-Math-Grade-6-Answer-Key-Chapter-2-Fractions-and-Decimals-29.jpg 384w, https:\/\/bigideasmathanswers.com\/wp-content\/uploads\/2020\/08\/Go-Math-Grade-6-Answer-Key-Chapter-2-Fractions-and-Decimals-29-300x116.jpg 300w\" sizes=\"(max-width: 384px) 100vw, 384px\" \/><br \/>\nWho made the better estimate? Use numbers and words to explain your answer.<br \/>\nType below:<br \/>\n___________<\/p>\n<p>Answer:<br \/>\nMargie hiked a 17 7\/8 mile trail.<br \/>\nDistance hiked by Margie = 17 7\/8 = 143\/8 mile.<br \/>\nShe stopped every 3 2\/5 miles to take a picture = 17\/5 mile<br \/>\nNumber of pictures = (143\/8) \u00f7 (17\/5) = 715\/136 = 5.28<br \/>\nSo she can take a maximum of 6 pictures and a minimum of 5 pictures.<br \/>\nB is the correct answer.<\/p>\n<p>Question 18.<br \/>\nBrad and Wes are building a tree house. They cut a 12 \\(\\frac{1}{2}\\) foot piece of wood into 5 of the same length pieces. How long is each piece of wood? Show your work.<br \/>\n_______ \\(\\frac{\u25a1}{\u25a1}\\) foot<\/p>\n<p>Answer:<br \/>\n2 \\(\\frac{1}{2}\\) foot<\/p>\n<p>Explanation:<br \/>\nBrad and Wes cut a 12 1\/2foot piece of wood into 5 of the same length.<br \/>\nLet the length of 1 piece be x<br \/>\nSo, Length of 5 pieces = 5x<br \/>\nThe total length of wood = 25\/2<br \/>\n5x = 25\/2<br \/>\nx = 5\/2 = 2 1\/2<\/p>\n<h3>Free Grade 6 HMH Go Math Answer Key PDF Download<\/h3>\n<p>In addition, to the exercise problems students of grade 6 can get the solutions for mid-chapter checkpoint and review test also. So, start solving the problems which are at the end of the chapter and check the solutions from here. Hope the information regarding Go Math 6th Grade Answer Key Chapter 2 Fractions and Decimals is helpful for you to overcome the issues in maths. Check out the links and start solving all the questions.<\/p>\n","protected":false},"excerpt":{"rendered":"<p>Are you looking for the best material to score top in the exams? Then, you are in the right place. HMH Go Math Grade 6 Answer Key Chapter 2 Fractions and Decimals is the best material for the 6th standard students. Here you can find the explanations for each and every question in different methods. &#8230; <a title=\"Go Math Grade 6 Answer Key Chapter 2 Fractions and Decimals\" class=\"read-more\" href=\"https:\/\/bigideasmathanswers.com\/go-math-grade-6-answer-key-chapter-2-fractions-and-decimals\/\" aria-label=\"More on Go Math Grade 6 Answer Key Chapter 2 Fractions and Decimals\">Read more<\/a><\/p>\n","protected":false},"author":5,"featured_media":8819,"comment_status":"open","ping_status":"open","sticky":false,"template":"","format":"standard","meta":{"spay_email":""},"categories":[2],"tags":[],"jetpack_featured_media_url":"https:\/\/bigideasmathanswers.com\/wp-content\/uploads\/2020\/10\/go-math-grade-6-chapter-2-fractions-and-decimals-answer-key.jpeg","_links":{"self":[{"href":"https:\/\/bigideasmathanswers.com\/wp-json\/wp\/v2\/posts\/4780"}],"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\/5"}],"replies":[{"embeddable":true,"href":"https:\/\/bigideasmathanswers.com\/wp-json\/wp\/v2\/comments?post=4780"}],"version-history":[{"count":1,"href":"https:\/\/bigideasmathanswers.com\/wp-json\/wp\/v2\/posts\/4780\/revisions"}],"predecessor-version":[{"id":92760,"href":"https:\/\/bigideasmathanswers.com\/wp-json\/wp\/v2\/posts\/4780\/revisions\/92760"}],"wp:featuredmedia":[{"embeddable":true,"href":"https:\/\/bigideasmathanswers.com\/wp-json\/wp\/v2\/media\/8819"}],"wp:attachment":[{"href":"https:\/\/bigideasmathanswers.com\/wp-json\/wp\/v2\/media?parent=4780"}],"wp:term":[{"taxonomy":"category","embeddable":true,"href":"https:\/\/bigideasmathanswers.com\/wp-json\/wp\/v2\/categories?post=4780"},{"taxonomy":"post_tag","embeddable":true,"href":"https:\/\/bigideasmathanswers.com\/wp-json\/wp\/v2\/tags?post=4780"}],"curies":[{"name":"wp","href":"https:\/\/api.w.org\/{rel}","templated":true}]}}