{"id":5833,"date":"2022-03-25T13:26:57","date_gmt":"2022-03-25T07:56:57","guid":{"rendered":"https:\/\/ccssmathanswers.com\/?p=5833"},"modified":"2022-04-07T12:58:20","modified_gmt":"2022-04-07T07:28:20","slug":"go-math-grade-7-answer-key-chapter-3-rational-numbers","status":"publish","type":"post","link":"https:\/\/bigideasmathanswers.com\/go-math-grade-7-answer-key-chapter-3-rational-numbers\/","title":{"rendered":"Go Math Grade 7 Answer Key Chapter 3 Rational Numbers"},"content":{"rendered":"<p>Get expert verified solutions in Go Math Grade 7 Answer Key Chapter 3 Rational Numbers here. So, the students of the 7th class can Download <a href=\"https:\/\/ccssmathanswers.com\/go-math-grade-7-answer-key\/\" target=\"_blank\" rel=\"noopener noreferrer\">Go Math Grade 7 Answer Key<\/a> Chapter 3 Rational Numbers pdf for free. Our Go Math 7th Grade Chapter 3 Rational Numbers helps the students to complete their homework in time and also score the highest marks in the exams.<\/p>\n<h2>Go Math Grade 7 Answer Key Chapter 3 Rational Numbers<\/h2>\n<p>All concepts are covered in one place along with answers for Go Math Grade 7 Chapter 3 Rational Numbers. Follow the steps to Download HMH Go Math Chapter 3 Grade 7 Answer Key pdf to learn simple methods to solve the problems. The quick way of solving problems will help the students to save time. Hence, check the question and find out the complete answers and explanations for every problem.<\/p>\n<p><strong>Chapter 3 &#8211; Rational Numbers and Decimals<\/strong><\/p>\n<ul>\n<li><a href=\"#Rational_Numbers_and_Decimals_Guided Practice_Page_No_64\">Rational Numbers and Decimals &#8211; Guided Practice &#8211; Page No. 64<\/a><\/li>\n<li><a href=\"#Rational_Numbers_and_Decimals_Independent_Practice_Page_No_65\">Rational Numbers and Decimals &#8211; Independent Practice &#8211; Page No. 65<\/a><\/li>\n<li><a href=\"#Rational_Numbers_and_Decimals_Page_No_66\">Rational Numbers and Decimals &#8211; Page No. 66<\/a><\/li>\n<\/ul>\n<p><strong>Chapter 3 &#8211; Adding Rational Numbers<\/strong><\/p>\n<ul>\n<li><a href=\"#Adding_Rational_Numbers_Guided_Practice_Page_No_72\">Adding Rational Numbers &#8211; Guided Practice &#8211; Page No. 72<\/a><\/li>\n<li><a href=\"#Adding_Rational_Numbers_Independent_Practice_Page_No_73\">Adding Rational Numbers &#8211; Independent Practice &#8211; Page No. 73<\/a><\/li>\n<li><a href=\"#Adding_Rational_Numbers_Independent_Practice_Page_No_74\">Adding Rational Numbers &#8211; Independent Practice &#8211; Page No. 74<\/a><\/li>\n<\/ul>\n<p><strong>Chapter 3 &#8211; Subtracting Rational Numbers<\/strong><\/p>\n<ul>\n<li><a href=\"#Subtracting_Rational_Numbers_Guided_Practice_Page_No_79\">Subtracting Rational Numbers &#8211; Guided Practice &#8211; Page No. 79<\/a><\/li>\n<li><a href=\"#Subtracting_Rational_Numbers_Independent_Practice_Page_No_80\">Subtracting Rational Numbers &#8211; Independent Practice &#8211; Page No. 80<\/a><\/li>\n<li><a href=\"#Subtracting_Rational_Numbers_Page_No_81\">Subtracting Rational Numbers &#8211; Page No. 81<\/a><\/li>\n<li><a href=\"#Subtracting_Rational_Numbers_HOT_Page_No_82\">Subtracting Rational Numbers &#8211; H.O.T &#8211; Page No. 82<\/a><\/li>\n<\/ul>\n<p><strong>Chapter 3 &#8211; Multiply Rational Numbers<\/strong><\/p>\n<ul>\n<li><a href=\"#Multiply_Rational_Numbers_Guided_Practice_Page_No_86\">Multiply Rational Numbers &#8211; Guided Practice &#8211; Page No. 86<\/a><\/li>\n<li><a href=\"#Multiply_Rational_Numbers_Independent_Practice_Page_No_87\">Multiply Rational Numbers &#8211; Independent Practice &#8211; Page No. 87<\/a><\/li>\n<li><a href=\"#Multiply_Rational_Numbers_Page_No_88\">Multiply Rational Numbers &#8211; Page No. 88<\/a><\/li>\n<\/ul>\n<p><strong>Chapter 3 &#8211; Divide Rational Numbers<\/strong><\/p>\n<ul>\n<li><a href=\"#Divide_Rational_Numbers_Guided_Practice_Page_No_92\">Divide Rational Numbers &#8211; Guided Practice &#8211; Page No. 92<\/a><\/li>\n<li><a href=\"#Divide_Rational_Numbers_Independent_Practice_Page_No_93\">Divide Rational Numbers &#8211; Independent Practice &#8211; Page No. 93<\/a><\/li>\n<li><a href=\"#Divide_Rational_Numbers_Page_No_94\">Divide Rational Numbers &#8211; Page No. 94<\/a><\/li>\n<\/ul>\n<p><strong>Chapter 3 &#8211; Applying Rational Number Operations<\/strong><\/p>\n<ul>\n<li><a href=\"#Applying_Rational_Numbers_Operations_Guided_Practice_Page_No_98\">Applying Rational Number Operations &#8211; Guided Practice &#8211; Page No. 98<\/a><\/li>\n<li><a href=\"#Applying_Rational_Numbers_Operations_Independent_Practice_Page_No_99\">Applying Rational Number Operations &#8211; Independent Practice &#8211; Page No. 99<\/a><\/li>\n<li><a href=\"#Applying_Rational_Numbers_Operations_Page_No_100\">Applying Rational Number Operations &#8211; Page No. 100<\/a><\/li>\n<\/ul>\n<p><strong>Chapter 3 &#8211; Module Review<\/strong><\/p>\n<ul>\n<li><a href=\"#Module_Quiz_3.1_Rational_Numbers_and_Decimals_Page_No_101\">Module Quiz &#8211; 3.1 Rational Numbers and Decimals &#8211; Page No. 101<\/a><\/li>\n<li><a href=\"#MODULE_3_MIXED_REVIEW_Selected_Response_Page_No_102\">MODULE 3 MIXED REVIEW &#8211; Selected Response &#8211; Page No. 102<\/a><\/li>\n<li><a href=\"#MODULE_3_REVIEW_Rational_Numbers_Page_No_106\">Module 3 Review &#8211; Rational Numbers &#8211; Page No. 106<\/a><\/li>\n<\/ul>\n<p><strong>Chapter 3 &#8211; Performance Tasks<\/strong><\/p>\n<ul>\n<li><a href=\"#Unit_1_Performance_Tasks_Page_No_107\">Unit 1 Performance Tasks &#8211; Page No. 107<\/a><\/li>\n<li><a href=\"#Unit_1_Performance_Tasks_Page_No_108\">Unit 1 Performance Tasks &#8211; Page No. 108<\/a><\/li>\n<\/ul>\n<p><strong>Chapter 3 &#8211; MIXED REVIEW<\/strong><\/p>\n<ul>\n<li><a href=\"#Unit_1_MIXED_REVIEW_Selected_Response_Page_No_109\">Unit 1 MIXED REVIEW &#8211; Selected Response &#8211; Page No. 109<\/a><\/li>\n<li><a href=\"#Unit_1_MIXED_REVIEW_Page_No_110\">Unit 1 MIXED REVIEW &#8211; Page No. 110<\/a><\/li>\n<\/ul>\n<h3><a id=\"Rational_Numbers_and_Decimals_Guided Practice_Page_No_64\"><\/a>Rational Numbers and Decimals &#8211; Guided Practice &#8211; Page No. 64<\/h3>\n<p><strong>Write each rational number as a decimal. Then tell whether each decimal is a terminating or a repeating decimal.<\/strong><\/p>\n<p>Question 1.<br \/>\n\\(\\frac{3}{5}\\) =<br \/>\n___________ decimals<\/p>\n<p>Answer: terminating<\/p>\n<p>Explanation:<br \/>\nTo convert fraction decimals, we have to divide the numerator to the denominator. If the quotient goes on and on, then it is a repeating decimal, and to write this as a decimal, put a bar on top of the repeating digits.<\/p>\n<p>\\(\\frac{3}{5}\\) = 3 \u00f7 5<br \/>\n3\/5 = 0.6<br \/>\nThe decimal is not repeating so it is a terminating decimal which is 0.6<\/p>\n<p>Question 2.<br \/>\n\\(\\frac{89}{100}\\) =<br \/>\n___________ decimals<\/p>\n<p>Answer: terminating<\/p>\n<p>Explanation:<br \/>\nTo convert fraction decimals, we have to divide the numerator to the denominator. If the quotient goes on and on, then it is a repeating decimal, and to write this as a decimal, put a bar on top of the repeating digits.<br \/>\n\\(\\frac{89}{100}\\) = 0.89<br \/>\nThe decimal is not repeating so it is a terminating decimal which is 0.89<\/p>\n<p>Question 3.<br \/>\n\\(\\frac{4}{12}\\) =<br \/>\n___________ decimals<\/p>\n<p>Answer: repeating<\/p>\n<p>Explanation:<br \/>\nTo convert fraction decimals, we have to divide the numerator to the denominator. If the quotient goes on and on, then it is a repeating decimal, and to write this as a decimal, put a bar on top of the repeating digits.<br \/>\n\\(\\frac{4}{12}\\) = 4 \u00f7 12<br \/>\n4\/12 = 0. 333&#8230;.<br \/>\nThe quotient is a repeating decimal which is 0.33&#8230;<\/p>\n<p>Question 4.<br \/>\n\\(\\frac{25}{99}\\) =<br \/>\n___________ decimals<\/p>\n<p>Answer: repeating<\/p>\n<p>Explanation:<br \/>\nTo convert fraction decimals, we have to divide the numerator to the denominator. If the quotient goes on and on, then it is a repeating decimal, and to write this as a decimal, put a bar on top of the repeating digits.<br \/>\n\\(\\frac{25}{99}\\) = 0.2525&#8230;<br \/>\nThe quotient is a repeating decimal which is 0.2525&#8230;<\/p>\n<p>Question 5.<br \/>\n\\(\\frac{7}{9}\\) =<br \/>\n___________ decimals<\/p>\n<p>Answer: repeating<\/p>\n<p>Explanation:<br \/>\nTo convert fraction decimals, we have to divide the numerator to the denominator. If the quotient goes on and on, then it is a repeating decimal, and to write this as a decimal, put a bar on top of the repeating digits.<br \/>\n\\(\\frac{7}{9}\\) = 0.77&#8230;<br \/>\nThe quotient is a repeating decimal which is 0.77&#8230;<\/p>\n<p>Question 6.<br \/>\n\\(\\frac{9}{25}\\) =<br \/>\n___________ decimals<\/p>\n<p>Answer: terminating<\/p>\n<p>Explanation:<br \/>\nTo convert fraction decimals, we have to divide the numerator to the denominator. If the quotient goes on and on, then it is a repeating decimal, and to write this as a decimal, put a bar on top of the repeating digits.<br \/>\n\\(\\frac{9}{25}\\) = 0.36<br \/>\nThe decimal is not repeating so it is a terminating decimal which is 0.36<\/p>\n<p>Question 7.<br \/>\n\\(\\frac{1}{25}\\) =<br \/>\n___________ decimals<\/p>\n<p>Answer: terminating<\/p>\n<p>Explanation:<br \/>\nTo convert fraction decimals, we have to divide the numerator to the denominator. If the quotient goes on and on, then it is a repeating decimal, and to write this as a decimal, put a bar on top of the repeating digits.<br \/>\n\\(\\frac{1}{25}\\) = 0.04<br \/>\nThe decimal is not repeating so it is a terminating decimal which is 0.04<\/p>\n<p>Question 8.<br \/>\n\\(\\frac{25}{176}\\) =<br \/>\n___________ decimals<\/p>\n<p>Answer: repeating<\/p>\n<p>Explanation:<br \/>\nTo convert fraction decimals, we have to divide the numerator to the denominator. If the quotient goes on and on, then it is a repeating decimal, and to write this as a decimal, put a bar on top of the repeating digits.<br \/>\n\\(\\frac{25}{176}\\) = 0.14204545454<br \/>\nThe quotient is a repeating decimal which is 0.14204545454<\/p>\n<p>Question 9.<br \/>\n\\(\\frac{12}{1000}\\) =<br \/>\n___________ decimals<\/p>\n<p>Answer: terminating<\/p>\n<p>Explanation:<br \/>\nTo convert fraction decimals, we have to divide the numerator to the denominator. If the quotient goes on and on, then it is a repeating decimal, and to write this as a decimal, put a bar on top of the repeating digits.<br \/>\n\\(\\frac{12}{1000}\\) =0.012<br \/>\nThe decimal is not repeating so it is a terminating decimal which is 0.012<\/p>\n<p><strong>Write each mixed number as a decimal.<\/strong><\/p>\n<p>Question 10.<br \/>\n11 \\(\\frac{1}{6}\\) =<br \/>\n___________ decimals<\/p>\n<p>Answer: repeating<\/p>\n<p>Explanation:<br \/>\nTo convert fraction decimals, we have to divide the numerator to the denominator. If the quotient goes on and on, then it is a repeating decimal, and to write this as a decimal, put a bar on top of the repeating digits.<br \/>\n11 \\(\\frac{1}{6}\\) = 11.1666666667<br \/>\nThe quotient is a repeating decimal which is 11.1666666667<\/p>\n<p>Question 11.<br \/>\n2 \\(\\frac{9}{10}\\) =<br \/>\n___________ decimals<\/p>\n<p>Answer: terminating<\/p>\n<p>Explanation:<br \/>\nTo convert fraction decimals, we have to divide the numerator to the denominator. If the quotient goes on and on, then it is a repeating decimal, and to write this as a decimal, put a bar on top of the repeating digits.<br \/>\nFirst, convert the mixed fraction to the improper fraction.<br \/>\n2 \\(\\frac{9}{10}\\) = \\(\\frac{29}{10}\\) = 2.9<br \/>\nThus, the decimal is not repeating so it is a terminating decimal which is 2.9<\/p>\n<p>Question 12.<br \/>\n8 \\(\\frac{23}{100}\\) =<br \/>\n___________ decimals<\/p>\n<p>Answer: terminating<\/p>\n<p>Explanation:<br \/>\nTo convert fraction decimals, we have to divide the numerator to the denominator. If the quotient goes on and on, then it is a repeating decimal, and to write this as a decimal, put a bar on top of the repeating digits.<br \/>\nFirst, convert the mixed fraction to the improper fraction.<br \/>\n8 \\(\\frac{23}{100}\\) = \\(\\frac{823}{100}\\) = 8.23<br \/>\nThus, the decimal is not repeating so it is a terminating decimal which is 8.23<\/p>\n<p>Question 13.<br \/>\n7 \\(\\frac{3}{15}\\) =<br \/>\n___________ decimals<\/p>\n<p>Answer: terminating<\/p>\n<p>Explanation:<br \/>\nTo convert fraction decimals, we have to divide the numerator to the denominator. If the quotient goes on and on, then it is a repeating decimal, and to write this as a decimal, put a bar on top of the repeating digits.<br \/>\nFirst, convert the mixed fraction to the improper fraction.<br \/>\n7 \\(\\frac{3}{15}\\) = \\(\\frac{108}{15}\\) = 7.2<br \/>\nThus, the decimal is not repeating so it is a terminating decimal which is 7.2<\/p>\n<p>Question 14.<br \/>\n54 \\(\\frac{3}{11}\\) =<br \/>\n___________ decimals<\/p>\n<p>Answer: repeating<\/p>\n<p>Explanation:<br \/>\nTo convert fraction decimals, we have to divide the numerator to the denominator. If the quotient goes on and on, then it is a repeating decimal, and to write this as a decimal, put a bar on top of the repeating digits.<br \/>\nFirst, convert the mixed fraction to the improper fraction.<br \/>\n54 \\(\\frac{3}{11}\\) = \\(\\frac{597}{11}\\) = 54.2727&#8230;<br \/>\nThe quotient is a repeating decimal which is 54.2727&#8230;<\/p>\n<p>Question 15.<br \/>\n3 \\(\\frac{1}{18}\\) =<br \/>\n___________ decimals<\/p>\n<p>Answer: repeating<\/p>\n<p>Explanation:<br \/>\nTo convert fraction decimals, we have to divide the numerator to the denominator. If the quotient goes on and on, then it is a repeating decimal, and to write this as a decimal, put a bar on top of the repeating digits.<br \/>\nFirst, convert the mixed fraction to the improper fraction.<br \/>\n3 \\(\\frac{1}{18}\\) = \\(\\frac{55}{18}\\) = 3.055..<br \/>\nThe quotient is a repeating decimal which is 3.055..<\/p>\n<p>Question 16.<br \/>\nMaggie bought 3 \\(\\frac{2}{3}\\) lb of apples to make some apple pies. What is the weight of the apples written as a decimal?<br \/>\n3 \\(\\frac{2}{3}\\) =<br \/>\n___________ decimal<\/p>\n<p>Answer: repeating<\/p>\n<p>Explanation:<br \/>\nTo convert fraction decimals, we have to divide the numerator to the denominator. If the quotient goes on and on, then it is a repeating decimal, and to write this as a decimal, put a bar on top of the repeating digits.<br \/>\nFirst, convert the mixed fraction to the improper fraction.<br \/>\n3 \\(\\frac{2}{3}\\) = \\(\\frac{11}{3}\\) = 3.66..<br \/>\nThe quotient is a repeating decimal which is 3.66..<\/p>\n<p>Question 17.<br \/>\nHarry\u2019s dog weighs 12 \\(\\frac{7}{8}\\) pounds. What is the weight of Harry\u2019s dog written as a decimal?<br \/>\n12 \\(\\frac{7}{8}\\) =<br \/>\n___________ decimals<\/p>\n<p>Answer: terminating<\/p>\n<p>Explanation:<br \/>\nGiven that,<br \/>\nHarry\u2019s dog weighs 12 \\(\\frac{7}{8}\\) pounds.<br \/>\nTo convert fraction decimals, we have to divide the numerator to the denominator. If the quotient goes on and on, then it is a repeating decimal, and to write this as a decimal, put a bar on top of the repeating digits.<br \/>\nFirst, convert the mixed fraction to the improper fraction.<br \/>\n12 \\(\\frac{7}{8}\\) = \\(\\frac{103}{8}\\) = 12.875<\/p>\n<p><strong>Essential Question Check-In<\/strong><\/p>\n<p>Question 18.<br \/>\nTom is trying to write \\(\\frac{3}{47}\\) as a decimal. He used long division and divided until he got the quotient 0.0638297872, at which point he stopped. Since the decimal doesn\u2019t seem to terminate or repeat, he concluded that \\(\\frac{3}{47}\\) is not rational. Do you agree or disagree? Why?<br \/>\n___________<\/p>\n<p>Answer: disagree<\/p>\n<p>Explanation:<br \/>\nWe are given the number:<br \/>\n{0, 1, 2, 3, &#8230;&#8230;45, 46}<br \/>\nWhen dividing a number by 47 the possible remainders at each step are:<br \/>\nThis means that after at most 47 steps we get a remainder which repeats. This means that process and which repeats. This means that the process stops and we get a repeating decimal.<\/p>\n<h3><a id=\"Rational_Numbers_and_Decimals_Independent_Practice_Page_No_65\"><\/a>Rational Numbers and Decimals &#8211; Independent Practice &#8211; Page No. 65<\/h3>\n<p><strong>Use the table for 19\u201323. Write each ratio in the form \\(\\frac{a}{b}\\) and then as a decimal. Tell whether each decimal is a terminating or a repeating decimal.<\/strong><br \/>\n<img loading=\"lazy\" src=\"https:\/\/ccssmathanswers.com\/wp-content\/uploads\/2020\/08\/Go-Math-Grade-7-Answer-Key-Chapter-3-Rational-Numbers-img-1.jpg\" alt=\"Go Math Grade 7 Answer Key Chapter 3 Rational Numbers Lesson 1: Rational Numbers and Decimals img 1\" width=\"340\" height=\"495\" \/><\/p>\n<p>Question 19.<br \/>\nBasketball players to football players<br \/>\n___________ decimal<\/p>\n<p>Answer: Repeating<\/p>\n<p>Explanation:<br \/>\nTo convert fraction decimals, we have to divide the numerator to the denominator. If the quotient goes on and on, then it is a repeating decimal, and to write this as a decimal, put a bar on top of the repeating digits.<br \/>\nSince the item is asking us to write basketball players to football players, we write the number of basketball players (5) in the numerator and the number of football players (11) in the denominator.<br \/>\n5\/11 = 0.4545..<br \/>\nThis is a repeating decimal with 45 as the repeating digits.<\/p>\n<p>Question 20.<br \/>\nHockey players to lacrosse players<br \/>\n___________ decimal<\/p>\n<p>Answer: terminating<\/p>\n<p>Explanation:<br \/>\nTo convert fraction decimals, we have to divide the numerator to the denominator. If the quotient goes on and on, then it is a repeating decimal, and to write this as a decimal, put a bar on top of the repeating digits.<br \/>\nSince the item is asking us to write hockey players to lacrosse players, we write the number of hockey players (6) in the numerator and the number of lacrosse players (10) in the denominator.<br \/>\nNow convert the fraction into the decimal<br \/>\n6\/10 = 0.6<br \/>\nThis is a terminating decimal which is 0.6.<\/p>\n<p>Question 21.<br \/>\nPolo players to football players<br \/>\n___________ decimal<\/p>\n<p>Answer: Repeating<\/p>\n<p>Explanation:<br \/>\nTo convert fraction decimals, we have to divide the numerator to the denominator. If the quotient goes on and on, then it is a repeating decimal, and to write this as a decimal, put a bar on top of the repeating digits.<br \/>\nSince the item is asking us to write polo players to football players, we write the number of polo players (4) in the numerator and the number of football players (11) in the denominator.<br \/>\nNow we convert this as a decimal.<br \/>\n4\/11 = 0.36..<br \/>\nThis is a repeating decimal with 36 as the repeating digits.<\/p>\n<p>Question 22.<br \/>\nLacrosse players to rugby players<br \/>\n___________ decimal<\/p>\n<p>Answer: Repeating<\/p>\n<p>Explanation:<br \/>\nTo convert fraction decimals, we have to divide the numerator to the denominator. If the quotient goes on and on, then it is a repeating decimal, and to write this as a decimal, put a bar on top of the repeating digits.<br \/>\nSince the item is asking us to write lacrosse players to rugby players, we write the number of lacrosse players (10) in the numerator and the number of rugby players (15) in the denominator.<br \/>\n10\/15 = 0.66..<br \/>\nThis is a repeating decimal with 6 as the repeating digit.<\/p>\n<p>Question 23.<br \/>\nFootball players to soccer players<br \/>\n___________ decimal<\/p>\n<p>Answer: terminating<\/p>\n<p>Explanation:<br \/>\nTo convert fraction decimals, we have to divide the numerator to the denominator. If the quotient goes on and on, then it is a repeating decimal, and to write this as a decimal, put a bar on top of the repeating digits<br \/>\nSince the item is asking us to write football players to soccer players, we write the number of football players (11) in the numerator and the number of soccer players (11) in the denominator.<br \/>\n11\/11 = 1<br \/>\nThis is a terminating decimal which is 1.<\/p>\n<p>Question 24.<br \/>\nLook for a Pattern Beth said that the ratio of the number of players in any sport to the number of players on a lacrosse team must always be a terminating decimal. Do you agree or disagree? Why?<br \/>\n___________<\/p>\n<p>Answer: agree<\/p>\n<p>Explanation:<br \/>\nThe ratios of the number of players in any sport to the number of players on a lacrosse team are:<br \/>\n{9\/10, 5\/10, 11\/10, 6\/10, 10\/10, 4\/10, 15\/10, 11\/10}<br \/>\nAll these ratios are terminating decimals as all numerators divided by 10 lead to a terminating decimal.<\/p>\n<p>Question 25.<br \/>\nYvonne bought 4 \\(\\frac{7}{8}\\) yards of material to make a dress.<br \/>\na. What is 4 \\(\\frac{7}{8}\\) written as an improper fraction?<br \/>\n\\(\\frac{\u25a1}{\u25a1}\\)<\/p>\n<p>Answer:<br \/>\nTo convert fraction decimals, we have to divide the numerator to the denominator. If the quotient goes on and on, then it is a repeating decimal, and to write this as a decimal, put a bar on top of the repeating digits.<br \/>\nConvert from mixed fraction to the improper fraction.<br \/>\n4 \\(\\frac{7}{8}\\) = (8 \u00d7 4) + 7 = 32 + 7 = 39\/8<\/p>\n<p>Question 25.<br \/>\nb. What is 4 \\(\\frac{7}{8}\\) written as a decimal?<br \/>\n______<\/p>\n<p>Answer:<br \/>\nRemember that we need to add the whole number and just convert the fraction part to decimal.<br \/>\n7\/8 = 0.875<br \/>\nThe fraction is a terminating decimal. Combining the whole number and the decimal part we get,<br \/>\n4 + 0.875 = 4.875<\/p>\n<p>Question 25.<br \/>\nc. Communicate Mathematical Ideas If Yvonne wanted to make 3 dresses that use 4 \\(\\frac{7}{8}\\) yd of fabric each, explain how she could use estimation to make sure she has enough fabric for all of them.<br \/>\nType below:<br \/>\n_____________<\/p>\n<p>Answer:<br \/>\nUsing estimation, we say that 4 \\(\\frac{7}{8}\\) \u2248 5.<br \/>\nWe can now multiply 3 by 5, and therefore, she needs 15 yards of fabric.<\/p>\n<h3><a id=\"Rational_Numbers_and_Decimals_Page_No_66\"><\/a>Rational Numbers and Decimals &#8211; Page No. 66<\/h3>\n<p>Question 26.<br \/>\nVocabulary A rational number can be written as the ratio of one _______ to another and can be represented by a repeating or ______ decimal.<br \/>\nType below:<br \/>\n_____________<\/p>\n<p>Answer: A rational number can be written as the ratio of one integer to another and can be represented by a repeating or terminating decimal.<\/p>\n<p>Question 27.<br \/>\nProblem Solving Marcus is 5 \\(\\frac{7}{24}\\) feet tall. Ben is 5 \\(\\frac{5}{16}\\) feet tall. Which of the two boys is taller? Justify your answer.<br \/>\n_____________<\/p>\n<p>Answer:<br \/>\nExplanation:<br \/>\nTo convert fraction decimals, we have to divide the numerator to the denominator. If the quotient goes on and on, then it is a repeating decimal, and to write this as a decimal, put a bar on top of the repeating digits.<br \/>\nTo determine who is taller, we convert both to decimals. Remember that we need to add the whole number and just convert the fraction part to decimal.<br \/>\nFor Marcus:<br \/>\n7\/24 = 0.29166..<br \/>\nCombine the whole number and the decimal part we get 5.29166..<br \/>\nFor Ben:<br \/>\n5\/16 = 0.3125<br \/>\nCombine the whole number and the decimal part we get 5.1325<br \/>\nHence Ben is taller.<\/p>\n<p>Question 28.<br \/>\nRepresent Real-World Problems If one store is selling \\(\\frac{3}{4}\\) of a bushel of apples for 9 dollars, and another store is selling \\(\\frac{2}{3}\\) of a bushel of apples for 9 dollars, which store has the better deal? Explain your answer.<br \/>\n_____________<\/p>\n<p>Answer:<br \/>\nTo convert fraction decimals, we have to divide the numerator to the denominator. If the quotient goes on and on, then it is a repeating decimal, and to write this as a decimal, put a bar on top of the repeating digits.<br \/>\nTo determine which store has a better deal, we convert both fractions to decimals.<br \/>\nFor the first store:<br \/>\n3\/4 = 0.75<br \/>\nFor the second store:<br \/>\n2\/3 = 0.666..<br \/>\nSince the first store offers 0.75 of a bushel of apples, this store has a better deal.<\/p>\n<p>Question 29.<br \/>\nAnalyze Relationships You are given a fraction in simplest form. The numerator is not zero. When you write the fraction as a decimal, it is a repeating decimal. Which numbers from 1 to 10 could be the denominator?<br \/>\nType below:<br \/>\n_____________<\/p>\n<p>Answer: {3, 6, 7, 9}<\/p>\n<p>Explanation:<br \/>\nSince the only numbers which can be factors of the denominators lead to a terminating decimal are 1, 2, and 5 and combinations of them, it means that if the denominator has at least one of the other numbers at the denominator, the decimal form will be a repeating decimal.<br \/>\nAmong the numbers from 1 to 10, the presence of any of these numbers in the denominator will lead to a repeating decimal:<br \/>\n{3, 6, 7, 9}<\/p>\n<p>Question 30.<br \/>\nCommunicate Mathematical Ideas Julie got 21 of the 23 questions on her math test correct. She got 29 of the 32 questions on her science test correct. On which test did she get a higher score? Can you compare the fractions \\(\\frac{21}{23}\\) and \\(\\frac{29}{32}\\) by comparing 29 and 21? Explain. How can Julie compare her scores?<br \/>\n_____________<\/p>\n<p>Answer:<br \/>\nTo convert fraction decimals, we have to divide the numerator to the denominator. If the quotient goes on and on, then it is a repeating decimal, and to write this as a decimal, put a bar on top of the repeating digits.<br \/>\nFor the math test:<br \/>\n21\/23 = 0.9130<br \/>\nFor the science test:<br \/>\n29\/32 = 0.9063<br \/>\nTherefore she got a higher score in her math test.<br \/>\nJulie got a higher score in her math test. We cannot compare the fractions by comparing the numerators. Instead, we can compare her scores if the denominators of the fractions are the same.<\/p>\n<p>Question 31.<br \/>\nLook for a Pattern Look at the decimal 0.121122111222.\u2026 If the pattern continues, is this a repeating decimal? Explain.<br \/>\n_____________<\/p>\n<p>Answer: The number is not a repeating decimal.<\/p>\n<h3><a id=\"Adding_Rational_Numbers_Guided_Practice_Page_No_72\"><\/a>Adding Rational Numbers &#8211; Guided Practice &#8211; Page No. 72<\/h3>\n<p><strong>Use a number line to find each sum.<\/strong><\/p>\n<p>Question 1.<br \/>\n\u22123 + (\u22121.5) =<br \/>\n______<\/p>\n<p>Answer: -4.5<\/p>\n<p>Explanation:<br \/>\nRemember if the number being added is positive, move the number of units going to the right and if the number being added is negative, move the number of units to the left.<br \/>\nSince we are adding a negative number, starting from -3, we move 1.5 units to the left. This results in -4.5.<\/p>\n<p>Question 2.<br \/>\n1.5 + 3.5 =<br \/>\n______<\/p>\n<p>Answer: 5<\/p>\n<p>Explanation:<br \/>\nRemember if the number being added is positive, move the number of units going to the right and if the number being added is negative, move the number of units to the left.<br \/>\nSince we are adding a positive number, starting from 1.5 we move 3.5 units to the right. This results in 5.<\/p>\n<p>Question 3.<br \/>\n\\(\\frac{1}{4}+\\frac{1}{2}\\) =<br \/>\n\\(\\frac{\u25a1}{\u25a1}\\)<\/p>\n<p>Answer: \\(\\frac{3}{4}\\)<\/p>\n<p>Explanation:<br \/>\nRemember if the number being added is positive, move the number of units going to the right and if the number being added is negative, move the number of units to the left.<br \/>\nSince we are adding a positive number, starting from 1\/4, we move 1\/2 or 2\/4, units to the right. This results in 3\/4.<\/p>\n<p>Question 4.<br \/>\n\u22121 \\(\\frac{1}{2}\\) + (\u22121 \\(\\frac{1}{2}\\)) =<br \/>\n______<\/p>\n<p>Answer: -3<\/p>\n<p>Explanation:<br \/>\nRemember if the number being added is positive, move the number of units going to the right and if the number being added is negative, move the number of units to the left.<br \/>\nSince we are adding a negative number, starting from \u22121 \\(\\frac{1}{2}\\), we move 1 1\/2 units to the left. This is results in -3.<\/p>\n<p>Question 5.<br \/>\n3 + (\u22125) =<br \/>\n______<\/p>\n<p>Answer: -2<\/p>\n<p>Explanation:<br \/>\nRemember if the number being added is positive, move the number of units going to the right and if the number being added is negative, move the number of units to the left.<br \/>\nSince we are adding a negative number, starting from 3 we move 5 units to the left. This results in -2.<\/p>\n<p>Question 6.<br \/>\n(\u22121.5) + 4 =<br \/>\n______<\/p>\n<p>Answer: 2.5<\/p>\n<p>Explanation:<br \/>\nRemember if the number being added is positive, move the number of units going to the right and if the number being added is negative, move the number of units to the left.<br \/>\nSince we are adding a positive number, starting from 1.5 we move 4 units to the left. This results in 2.5<\/p>\n<p>Question 7.<br \/>\nVictor borrowed 21.50 dollars from his mother to go to the theater. A week later, he paid her 21.50 dollars back. How much does he still owe her?<br \/>\n______<\/p>\n<p>Answer: 0<\/p>\n<p>Explanation:<br \/>\nWe use positive numbers for the money he receives and negative numbers for the money he returns.<br \/>\n21.50 &#8211; 21.50 = 0<br \/>\nThe result is zero. This means he doesn&#8217;t owe anything to his mother.<\/p>\n<p>Question 8.<br \/>\nSandra used her debit card to buy lunch for 8.74 on Monday. On Tuesday, she deposited 8.74 back into her account. What is the overall increase or decrease in her bank account?<br \/>\n______<\/p>\n<p>Answer: 0<\/p>\n<p>Explanation:<br \/>\nWe use positive numbers for the money she deposits and negative numbers for the money she spends.<br \/>\n-8.74 + 8.74 = 0<br \/>\nThe result is zero. This means her bank account didn&#8217;t increase or decrease.<\/p>\n<p><strong>Find each sum without using a number line.<\/strong><\/p>\n<p>Question 9.<br \/>\n2.75 + (\u22122) + (\u22125.25) =<br \/>\n______<\/p>\n<p>Answer: -4.50<\/p>\n<p>Explanation:<br \/>\nWe are given the expression:<br \/>\n2.75 + (-2) + (-5.25)<br \/>\nWe group numbers with the same sign using the associative property.<br \/>\n2.75 &#8211; 7.25 = -4.50<\/p>\n<p>Question 10.<br \/>\n\u22123 + (1 \\(\\frac{1}{2}\\)) + (2 \\(\\frac{1}{2}\\)) =<br \/>\n______<\/p>\n<p>Answer: 1<\/p>\n<p>Explanation:<br \/>\nWe are given the expression<br \/>\n-3 + (1 \\(\\frac{1}{2}\\)) + (2 \\(\\frac{1}{2}\\))<br \/>\n-3 + 1.5 + 2.5<br \/>\nWe group numbers with the same sign using the associative property.<br \/>\n-3 + 4 = 1<br \/>\nThe larger number is having a positive sign so the sum is 1.<\/p>\n<p>Question 11.<br \/>\n\u221212.4 + 9.2 + 1 =<br \/>\n______<\/p>\n<p>Answer: -2.2<\/p>\n<p>Explanation:<br \/>\nWe are given the expression<br \/>\n-12.4 + 9.2 + 1<br \/>\nWe group numbers with the same sign using the associative property.<br \/>\n-12.4 + 10.2 = -2.2<br \/>\nThe larger number is having a negative sign so the answer is -2.2.<\/p>\n<p>Question 12.<br \/>\n\u221212 + 8 + 13 =<br \/>\n______<\/p>\n<p>Answer: 9<\/p>\n<p>Explanation:<br \/>\nWe are given the expression|<br \/>\n-12 + 8 + 13<br \/>\nWe group numbers with the same sign using the associative property.<br \/>\n-12 + 21 = 9<br \/>\nThe larger number is having the positive sign so the answer is 9.<\/p>\n<p>Question 13.<br \/>\n4.5 + (\u221212) + (\u22124.5) =<br \/>\n______<\/p>\n<p>Answer: -12<\/p>\n<p>Explanation:<br \/>\nWe are given the expression<br \/>\n4.5 + (-12) + (-4.5)<br \/>\nWe group numbers with the same sign using the associative property.<br \/>\n0 &#8211; 12 = -12<br \/>\nThe larger number is having the negative sign so the answer is -12.<\/p>\n<p>Question 14.<br \/>\n\\(\\frac{1}{4}\\) + (\u2212 \\(\\frac{3}{4}\\)) =<br \/>\n&#8211; \\(\\frac{\u25a1}{\u25a1}\\)<\/p>\n<p>Answer: -0.50<\/p>\n<p>Explanation:<br \/>\nWe are given the expression<br \/>\n\\(\\frac{1}{4}\\) + (\u2212 \\(\\frac{3}{4}\\))<br \/>\nConvert the fraction to Decimal.<br \/>\n0.25 &#8211; 0.75 = -0.50<br \/>\nThe larger number is having the negative sign so the sum is -0.50<\/p>\n<p>Question 15.<br \/>\n\u22124 \\(\\frac{1}{2}\\) + 2 =<br \/>\n&#8211; \\(\\frac{\u25a1}{\u25a1}\\)<\/p>\n<p>Answer: -2.5<\/p>\n<p>Explanation:<br \/>\nWe\u00a0 = are given the expression<br \/>\n\u22124 \\(\\frac{1}{2}\\) + 2<br \/>\nConvert from fraction to decimal.<br \/>\n-4.5 + 2 = -2.5<br \/>\nThe larger number is having the negative sign so the sum is -2.5.<\/p>\n<p>Question 16.<br \/>\n\u22128 + (\u22121 \\(\\frac{1}{8}\\)) =<br \/>\n&#8211; \\(\\frac{\u25a1}{\u25a1}\\)<\/p>\n<p>Answer: -9.125<\/p>\n<p>Explanation:<br \/>\nWe are given the expression<br \/>\n\u22128 + (\u22121 \\(\\frac{1}{8}\\))<br \/>\nConvert from fraction to decimal.<br \/>\n-8 + (-1.125) = &#8211; 9.125<\/p>\n<p>Question 17.<br \/>\nHow can you use a number line to find the sum of -4 and 6?<br \/>\nType below:<br \/>\n____________<\/p>\n<p>Answer: 6<\/p>\n<p>Explanation:<br \/>\nRemember if the number being added is positive, move the number of units going to the right and if the number being added is negative, move the number of units to the left.<br \/>\nSince we are adding a positive number, starting from -4 we move 6 units to the right. This results in 2.<\/p>\n<h3><a id=\"Adding_Rational_Numbers_Independent_Practice_Page_No_73\"><\/a>Adding Rational Numbers &#8211; Independent Practice &#8211; Page No. 73<\/h3>\n<p>Question 18.<br \/>\nSamuel walks forward 19 steps. He represents this movement with a positive 19. How would he represent the opposite of this number?<br \/>\n_______<\/p>\n<p>Answer: -19<br \/>\nHe would represent the opposite of 19 by a negative 19.<\/p>\n<p>Question 19.<br \/>\nJulia spends 2.25 on gas for her lawn mower. She earns 15.00 mowing her neighbor\u2019s yard. What is Julia\u2019s profit?<br \/>\n_______<\/p>\n<p>Answer: $12.75<\/p>\n<p>Explanation:<br \/>\nWe use positive numbers for the money she earns and negative numbers for the money she spends.<br \/>\n-2.25 + 15 = 12.75<br \/>\nThus her profit is $12.75<\/p>\n<p>Question 20.<br \/>\nA submarine submerged at a depth of -35.25 meters dives an additional 8.5 meters. What is the new depth of the submarine?<br \/>\n_______<\/p>\n<p>Answer: In adding two integers with same sign add their absolute value and keep the common sign.<br \/>\nWhen adding two integers with opposite sign subtract the smaller absolute value from the larger and keep the sign of the number with the larger absolute value.<br \/>\nSince the submarine dove 32.25 meters down this can be interrupted as -32.25. And because it dove an additional 8.5 meters down, we can add -8.5 meters to the previous distance.<br \/>\nAdd 32.25 and 8.5 meters<br \/>\n32.25 + 8.5 = 43.75 meters<br \/>\nThus the submarines new depth is 43.75 meters deep or -43.75 meters.<\/p>\n<p>Question 21.<br \/>\nRenee hiked for 4 \\(\\frac{3}{4}\\) miles. After resting, Renee hiked back along the same route for 3 \\(\\frac{1}{4}\\) miles. How many more miles does Renee need to hike to return to the place where she started?<br \/>\n_______ \\(\\frac{\u25a1}{\u25a1}\\)<\/p>\n<p>Answer:<br \/>\nGiven that<br \/>\nRenee hiked for 4 \\(\\frac{3}{4}\\) miles. After resting, Renee hiked back along the same route for 3 \\(\\frac{1}{4}\\) miles.<br \/>\n4 \\(\\frac{3}{4}\\) + (-3 \\(\\frac{1}{4}\\)) = 1 \\(\\frac{1}{2}\\)<br \/>\nThus Renee needs to hike to return to the place where she started is 1 \\(\\frac{1}{2}\\) or 1.5 miles.<\/p>\n<p>Question 22.<br \/>\nGeography<br \/>\nThe average elevation of the city of New Orleans, Louisiana, is 0.5 m below sea level. The highest point in Louisiana is Driskill Mountain at about 163.5 m higher than New Orleans. How high is Driskill Mountain?<br \/>\n_______<\/p>\n<p>Answer: 163 meters<\/p>\n<p>Explanation:<br \/>\nWe use the positive numbers for the elevation above the sea level and negative numbers for the elevation below the sea level.<br \/>\n163.5 &#8211; 0.5 = 163 meters<br \/>\nThus the height of the Driskill mountain is 163 meters.<\/p>\n<p>Question 23.<br \/>\nProblem Solving<br \/>\nA contestant on a game show has 30 points. She answers a question correctly to win 15 points. Then she answers a question incorrectly and loses 25 points. What is the contestant\u2019s final score?<br \/>\n_______<\/p>\n<p>Answer: 20<\/p>\n<p>Explanation:<br \/>\nWe use positive numbers for won points and negative numbers for lost points.<br \/>\n30 + 15 + (-25) = 20<br \/>\nThus the final score is 20.<\/p>\n<p><img loading=\"lazy\" src=\"https:\/\/ccssmathanswers.com\/wp-content\/uploads\/2020\/08\/Go-Math-Grade-7-Answer-Key-Chapter-3-Rational-Numbers-img-2.jpg\" alt=\"Go Math Grade 7 Answer Key Chapter 3 Rational Numbers Lesson 2: Adding Rational Numbers img 2\" width=\"327\" height=\"212\" \/><\/p>\n<p><strong>Financial Literacy<\/strong><\/p>\n<p><strong>Use the table for 24\u201326. Kameh owns a bakery. He recorded the bakery income and expenses in a table.<\/strong><\/p>\n<p>Question 24.<br \/>\nIn which months were the expenses greater than the income? Name the month and find how much money was lost.<br \/>\nType below:<br \/>\n___________<\/p>\n<p>Answer:<br \/>\nWe count the balance for January<br \/>\n1205 + (-1290.60)\u00a0 = -85.60<br \/>\nWe count the balance for February<br \/>\n1183 + (-1345.44) = -162.44<br \/>\nJanuary: $85.60<br \/>\nFebruary: $162.44<\/p>\n<p>Question 25.<br \/>\nIn which months was the income greater than the expenses? Name the months and find how much money was gained.<br \/>\nType below:<br \/>\n___________<\/p>\n<p>Answer:<br \/>\nThe income was greater than the expenses in the months:<br \/>\nWe count the balance for june:<br \/>\n2413 + (-2106.23) = 306.77<br \/>\nWe count the balance for july:<br \/>\n2260 + (-1958.50) = 301.5<br \/>\nWe count the balance for august:<br \/>\n2183 + (-1845.12) = 337.88<br \/>\nJune: $306.77 gained<br \/>\nJuly: $301.5 gained<br \/>\nAugust: $337.88 gained<\/p>\n<p>Question 26.<br \/>\nCommunicate Mathematical Ideas<br \/>\nIf the bakery started with an extra $250 from the profits in December, describe how to use the information in the table to figure out the profit or loss of money at the bakery by the end of August. Then calculate the profit or loss.<br \/>\nBalance: $ _______<\/p>\n<p>Answer: 948.71<\/p>\n<p>Explanation:<br \/>\nIf the bakery started with an extra $250 from the profits in December.<br \/>\nWe will add this amount to January&#8217;s income.<br \/>\n250 + 1205 + 1183 + 1664 + 2413 + 2260 + 2183 = 11,158<br \/>\nWe compute the expenses during the 6 months<br \/>\n(-1290) + (-1345.44) + (-1664) + (-2106.24) + (-1958.50) + (-1845.12) = -10209.29<br \/>\n11158 -10209.29 = 948.71<br \/>\nSince the result is a positive number, the bakery has profit.<\/p>\n<h3><a id=\"Adding_Rational_Numbers_Independent_Practice_Page_No_74\"><\/a>Adding Rational Numbers &#8211; Independent Practice &#8211; Page No. 74<\/h3>\n<p>Question 27.<br \/>\nVocabulary<br \/>\n-2 is the ________ of 2.<br \/>\n__________<\/p>\n<p>Answer: additive inverse<\/p>\n<p>Explanation:<br \/>\nWhen the sum of two numbers with opposite signs is 0, then they are additive inverses of eacj other.<br \/>\nTherefore, -2 is the additive inverse of 2.<\/p>\n<p>Question 28.<br \/>\nThe basketball coach made up a game to play where each player takes 10 shots at the basket. For every basket made, the player gains 10 points. For every basket missed, the player loses 15 points.<br \/>\na. The player with the highest score sank 7 baskets and missed 3. What was the highest score?<br \/>\n_______ points<\/p>\n<p>Answer: 25<\/p>\n<p>Explanation:<br \/>\nWe use the positive numbers for won points and negative numbers for lost points.<br \/>\nWe determine the highest score:<br \/>\n7(10) + 3(-15) = 70 + (-45) = 25<\/p>\n<p>Question 28.<br \/>\nb. The player with the lowest score sank 2 baskets and missed 8. What was the lowest score?<br \/>\n_______ points<\/p>\n<p>Answer: -100<\/p>\n<p>Explanation:<br \/>\nWe determine the lowest score:<br \/>\n2(10) + 8(-15) = 20 + (-120) = -100<\/p>\n<p>Question 28.<br \/>\nc. Write an expression using addition to find out what the score would be if a player sank 5 baskets and missed 5 baskets.<br \/>\nType below:<br \/>\n__________<\/p>\n<p>Answer: -25<\/p>\n<p>Explanation:<br \/>\nWe determine the score for 5 baskets and 5 missed baskets:<br \/>\n5(10) + 5(-15) = 50 + (-75)<br \/>\n50 &#8211; 75 = -25<\/p>\n<p><strong>H.O.T<\/strong><\/p>\n<p><strong>FOCUS ON HIGHER ORDER THINKING<\/strong><\/p>\n<p>Question 29.<br \/>\nCommunicate Mathematical Ideas<br \/>\nExplain the different ways it is possible to add two rational numbers and get a negative number.<br \/>\nType below:<br \/>\n__________<\/p>\n<p>Answer:<br \/>\nThe sum of two rational numbers is negative either if both numbers are negative, or they have different signs, but the negative number is the one with the greater absolute value.<\/p>\n<p>Question 30.<br \/>\nExplain the Error<br \/>\nA student evaluated -4 + x for x = -9 \\(\\frac{1}{2}\\) and got an answer of 5 \\(\\frac{1}{2}\\). What might the student have done wrong?<br \/>\nType below:<br \/>\n__________<\/p>\n<p>Answer:<br \/>\nWe expect about 95% of all possible samples to have a 95% confidence interval that contains the population proportion who favor such an amendment.<\/p>\n<p>Question 31.<br \/>\nDraw Conclusions<br \/>\nCan you find the sum [5.5 + (-2.3)] + (-5.5 + 2.3) without performing any additions?<br \/>\n_______<\/p>\n<p>Answer:<br \/>\nYes, we can find the sum without performing any computation if we notice that the two numbers from each set of brackets are the opposites of the numbers in the other set\u00a0 of bracelets, thus the sum is zero:<br \/>\n[5.5 + (-2.3)] + (-5.5 + 2.3)<br \/>\n5.5 &#8211; 2.3 &#8211; 5.5 + 2.3 = 0<\/p>\n<h3><a id=\"Subtracting_Rational_Numbers_Guided_Practice_Page_No_79\"><\/a>Subtracting Rational Numbers &#8211; Guided Practice &#8211; Page No. 79<\/h3>\n<p><strong>Use a number line to find each difference.<\/strong><\/p>\n<p>Question 1.<br \/>\n5 \u2212 (\u22128) =<br \/>\n_______<\/p>\n<p>Answer: 13<\/p>\n<p>Explanation:<br \/>\nRemember if the number being subtracted is positive, move the number of units going to the left and if the number being subtracted is negative, move the number of units to the right.<br \/>\nSince we are subtracting a negative number, starting from 5, we move 8 units to the right. This results in 13.<\/p>\n<p>Question 2.<br \/>\n\u22123 \\(\\frac{1}{2}\\) \u2212 4 \\(\\frac{1}{2}\\) =<br \/>\n_______<\/p>\n<p>Answer: -8<\/p>\n<p>Explanation:<br \/>\nRemember if the number being subtracted is positive, move the number of units going to the left and if the number being subtracted is negative, move the number of units to the right.<br \/>\nSince we are subtracting a positive number, starting from \u22123 \\(\\frac{1}{2}\\), we move 4 \\(\\frac{1}{2}\\) units to the left. This results in -8.<\/p>\n<p>Question 3.<br \/>\n\u22127 \u2212 4 =<br \/>\n_______<\/p>\n<p>Answer: -11<\/p>\n<p>Explanation:<br \/>\nRemember if the number being subtracted is positive, move the number of units going to the left and if the number being subtracted is negative, move the number of units to the right.<br \/>\nSince we are subtracting a positive number, starting from -7, we move 4 units to the left. This results in -11.<\/p>\n<p>Question 4.<br \/>\n\u22120.5 \u2212 3.5 =<br \/>\n_______<\/p>\n<p>Answer: -4<\/p>\n<p>Explanation:<br \/>\nRemember if the number being subtracted is positive, move the number of units going to the left and if the number being subtracted is negative, move the number of units to the right.<br \/>\nSince we are subtracting a positive number, starting from -0.5, we move 3.5 units to the left. This results in -4<\/p>\n<p><strong>Find each difference.<\/strong><\/p>\n<p>Question 5.<br \/>\n\u221214 \u2212 22 =<br \/>\n_______<\/p>\n<p>Answer: -36<\/p>\n<p>Explanation:<br \/>\nWe have to determine the difference<br \/>\n-14 &#8211; 22 = (-14) + (-22) = -36<br \/>\n\u221214 \u2212 22 = -36<\/p>\n<p>Question 6.<br \/>\n\u221212.5 \u2212 (\u22124.8) =<br \/>\n_______<\/p>\n<p>Answer: -7.7<\/p>\n<p>Explanation:<br \/>\n-12.5 &#8211; (-4.8)<br \/>\nWe convert subtraction into addition with the opposite number<br \/>\n-12.5 &#8211; (-4.8) = -12.5 + 4.8 = -7.7<br \/>\nSo, the answer is -7.7<\/p>\n<p>Question 7.<br \/>\n\\(\\frac{1}{3}\\) \u2212 (\u2212\\(\\frac{2}{3}\\)) =<br \/>\n_______<\/p>\n<p>Answer: 1<\/p>\n<p>Explanation:<br \/>\n\\(\\frac{1}{3}\\) \u2212 (\u2212\\(\\frac{2}{3}\\))<br \/>\n\\(\\frac{1}{3}\\) + \\(\\frac{2}{3}\\) = \\(\\frac{3}{3}\\) = 1<br \/>\nThe result is 1.<\/p>\n<p>Question 8.<br \/>\n65 \u2212 (\u221214) =<br \/>\n_______<\/p>\n<p>Answer: 79<\/p>\n<p>Explanation:<br \/>\nWe convert subtraction into addition with the opposite number<br \/>\n65 \u2212 (\u221214) = 65 + 14 = 79<br \/>\nThe answer is 79.<\/p>\n<p>Question 9.<br \/>\n\u2212 \\(\\frac{2}{9}\\) \u2212 (\u22123) =<br \/>\n_______ \\(\\frac{\u25a1}{\u25a1}\\)<\/p>\n<p>Answer: 2 \\(\\frac{7}{9}\\)<\/p>\n<p>Explanation:<br \/>\nWe convert subtraction into addition with the opposite number<br \/>\n\u2212 \\(\\frac{2}{9}\\) \u2212 (\u22123) = \u2212 \\(\\frac{2}{9}\\) + 3 = 2 \\(\\frac{7}{9}\\)<br \/>\nThe answer is 2 \\(\\frac{7}{9}\\)<\/p>\n<p>Question 10.<br \/>\n24 \\(\\frac{3}{8}\\) \u2212 (\u221254 \\(\\frac{1}{8}\\)) =<br \/>\n_______ \\(\\frac{\u25a1}{\u25a1}\\)<\/p>\n<p>Answer: 78 \\(\\frac{1}{2}\\)<\/p>\n<p>Explanation:<br \/>\nWe convert subtraction into addition with the opposite number.<br \/>\n24 \\(\\frac{3}{8}\\) \u2212 (\u221254 \\(\\frac{1}{8}\\)) = 24 \\(\\frac{3}{8}\\) + 54 \\(\\frac{1}{8}\\) = 78 \\(\\frac{1}{2}\\)<br \/>\nThus the result is 78 \\(\\frac{1}{2}\\).<\/p>\n<p>Question 11.<br \/>\nA girl is snorkeling 1 meter below sea level and then dives down another 0.5 meter. How far below sea level is the girl?<br \/>\n_______<\/p>\n<p>Answer: 1.5 meter<\/p>\n<p>Explanation:<br \/>\n1 m below sea level is represented by the number -14. Since she is diving down 0.5 m, you must subtract -1 &#8211; 0.5 = -1.5 m<br \/>\nThus the girl is 1.5 m long.<\/p>\n<p>Question 12.<br \/>\nThe first play of a football game resulted in a loss of 12 \\(\\frac{1}{2}\\) yards. Then a penalty resulted in another loss of 5 yards. What is the total loss or gain?<br \/>\n_______<\/p>\n<p>Answer: 17 \\(\\frac{1}{2}\\) yards<\/p>\n<p>Explanation:<br \/>\nThe first play of a football game resulted in a loss of 12 \\(\\frac{1}{2}\\) yards. Then a penalty resulted in another loss of 5 yards.<br \/>\n-12 \\(\\frac{1}{2}\\) &#8211; 5 = -17 \\(\\frac{1}{2}\\) yards<br \/>\nIt is a loss of 17 \\(\\frac{1}{2}\\) yards<\/p>\n<p>Question 13.<br \/>\nA climber starts descending from 533 feet above sea level and keeps going until she reaches 10 feet below sea level. How many feet did she descend?<br \/>\n_______<\/p>\n<p>Answer: 543 feet<\/p>\n<p>Explanation:<br \/>\nGiven,<br \/>\nA climber starts descending from 533 feet above sea level and keeps going until she reaches 10 feet below sea level.<br \/>\n533 feet + 10 feet = 543 feet<\/p>\n<p>Question 14.<br \/>\nEleni withdrew 45.00 dollars from her savings account. She then used her debit card to buy groceries for 30.15 dollars. What was the total amount Eleni took out of her account?<br \/>\n_______<\/p>\n<p>Answer: $75.15<\/p>\n<p>Explanation:<br \/>\nGiven that,<br \/>\nEleni withdrew 45.00 dollars from her savings account. She then used her debit card to buy groceries for 30.15 dollars.<br \/>\n$45 + $30.15 = $75.15<br \/>\nThus Eleni took $75.15 out of her account.<\/p>\n<p>Question 15.<br \/>\nMandy is trying to subtract 4 &#8211; 12, and she has asked you for help. How would you explain the process of solving the problem to Mandy, using a number line?<br \/>\nType below:<br \/>\n____________<\/p>\n<p>Answer: Start at 4 on the number line. Then move 12 places to the left since you are subtracting. This gives -8.<\/p>\n<h3><a id=\"Subtracting_Rational_Numbers_Independent_Practice_Page_No_80\"><\/a>Subtracting Rational Numbers &#8211; Independent Practice &#8211; Page No. 80<\/h3>\n<p>Question 16.<br \/>\nScience<br \/>\nAt the beginning of a laboratory experiment, the temperature of a substance is -12.6 \u00b0C. During the experiment, the temperature of the substance decreases 7.5 \u00b0C. What is the final temperature of the substance?<br \/>\n_______<\/p>\n<p>Answer: -20.1\u00b0C<\/p>\n<p>Explanation:<br \/>\nRemember if the number being subtracted is positive, move the number of units going to the left and if the number being subtracted is negative, move the number of units to the right.<br \/>\nSince the temperature of the substance is -12.6 and it decreases further by 7.5, we can create the expression -12.6 &#8211; 7.5.<br \/>\n-12.6 &#8211; 7.5 = -20.1<br \/>\nThus the final temperature is -20.1\u00b0C<\/p>\n<p>Question 17.<br \/>\nA diver went 25.65 feet below the surface of the ocean, and then 16.5 feet further down, he then rose 12.45 feet. Write and solve an expression to find the diver\u2019s new depth.<br \/>\n_______<\/p>\n<p>Answer: -29.7 feet<\/p>\n<p>Explanation:<br \/>\nRemember if the number being subtracted is positive, move the number of units going to the left and if the number being subtracted is negative, move the number of units to the right.<br \/>\nSince the diver went down 25.65 feet then dove again further by 16.5 feet then rose up by 12.45 feet, we can create the expression -25.65 &#8211; 16.5 + 12.45 = -29.7 feet<br \/>\nThe diver&#8217;s new depth is -29.7 feet.<\/p>\n<p>Question 18.<br \/>\nA city known for its temperature extremes started the day at -5 degrees Fahrenheit. The temperature increased by 78 degrees Fahrenheit by midday, and then dropped 32 degrees by nightfall.<br \/>\na. What expression can you write to find the temperature at nightfall?<br \/>\nType below:<br \/>\n____________<\/p>\n<p>Answer:<br \/>\nThe temperature started at -5 degrees then increased 78 degrees and then dropped 32 degrees.<br \/>\nThe expression is -5 + 78 &#8211; 32<\/p>\n<p>Question 18.<br \/>\nb. What expression can you write to describe the overall change in temperature? Hint: Do not include the temperature at the beginning of the day since you only<br \/>\nType below:<br \/>\n____________<\/p>\n<p>Answer: The overall change is the increase and decrease combined.<br \/>\nThe expression is 78 &#8211; 32<\/p>\n<p>Question 18.<br \/>\nc. What is the final temperature at nightfall? What is the overall change in temperature?<br \/>\nType below:<br \/>\n____________<\/p>\n<p>Answer:<br \/>\nUse the first expression -5 + 78 &#8211; 32 = 73 &#8211; 32 = 41 degrees<br \/>\n78 &#8211; 32 = 46 degrees<\/p>\n<p>Question 19.<br \/>\nFinancial Literacy<br \/>\nOn Monday, your bank account balance was -$12.58. Because you didn\u2019t realize this, you wrote a check for $30.72 for groceries.<br \/>\na. What is the new balance in your checking account?<br \/>\n$ _______<\/p>\n<p>Answer:<br \/>\nSubtract the check amount from the initial balance.<br \/>\n-$12.58 &#8211; $30.72 = -$43.30<\/p>\n<p>Question 19.<br \/>\nb. The bank charges a $25 fee for paying a check on a negative balance. What is the balance in your checking account after this fee?<br \/>\n$ _______<\/p>\n<p>Answer:<br \/>\nSubtract 25 from the balance from part a.<br \/>\n-$43.30 &#8211; $25 = -$68.30<\/p>\n<p>Question 19.<br \/>\nc. How much money do you need to deposit to bring your account balance back up to $0 after the fee?<br \/>\n$ _______<\/p>\n<p>Answer:<br \/>\nSince the account balance is -$68.30, a deposit of $68.30 is required to make the balance $0.<\/p>\n<p><strong>Astronomy<\/strong><\/p>\n<p><strong>Use the table for problems 20\u201321.<\/strong><br \/>\n<img loading=\"lazy\" src=\"https:\/\/ccssmathanswers.com\/wp-content\/uploads\/2020\/08\/Go-Math-Grade-7-Answer-Key-Chapter-3-Rational-Numbers-img-3.jpg\" alt=\"Go Math Grade 7 Answer Key Chapter 3 Rational Numbers Lesson 3: Subtracting Rational Numbers img 3\" width=\"354\" height=\"138\" \/><\/p>\n<p>Question 20.<br \/>\nHow much deeper is the deepest canyon on Mars than the deepest canyon on Venus?<br \/>\n_______<\/p>\n<p>Answer: -16,500 feet deper<\/p>\n<p>Explanation:<br \/>\nSubtract the lowest elevations of Mars and Venus.<br \/>\n-26,000 &#8211; (-9500) = -16,500<\/p>\n<p>Question 21.<br \/>\nPersevere in Problem Solving<br \/>\nWhat is the difference between Earth\u2019s highest mountain and its deepest ocean canyon? What is the difference between Mars\u2019 highest mountain and its deepest canyon? Which difference is greater? How much greater is it?<br \/>\nType below:<br \/>\n____________<\/p>\n<p>Answer:<br \/>\nSubtract the highest elevation and the lowest elevation on Earth.<br \/>\n29,035 &#8211; (-36,198) = 65,233<br \/>\nSubtract the highest elevation and the lowest elevation on Mars.<br \/>\n96,000 &#8211; 65,233 = 30,767<br \/>\n96,000 is greater than 65,233 so the difference for Mars is greater. subtract these two numbers to get how much greater.<\/p>\n<h3><a id=\"Subtracting_Rational_Numbers_Page_No_81\"><\/a>Subtracting Rational Numbers &#8211; Page No. 81<\/h3>\n<p>Question 22.<br \/>\nPamela wants to make some friendship bracelets for her friends. Each friendship bracelet needs 5.2 inches of string.<br \/>\na. If Pamela has 20 inches of string, does she have enough to make bracelets for 4 of her friends?<br \/>\na. _______<\/p>\n<p>Answer: no<\/p>\n<p>Explanation:<br \/>\nEach bracelet needs 5.2 inches so multiply 4 and 5.2 inches to see how many total inches she needs this is greater than 20 so she does not have enough.<br \/>\n4 \u00d7 5.2 = 20.8 inches<\/p>\n<p>Question 22.<br \/>\nb. If so, how much string would she had left over? If not, how much more string would she need?<br \/>\n_______ in.<\/p>\n<p>Answer: She needs 0.8 inches more<\/p>\n<p>Question 23.<br \/>\nJeremy is practicing some tricks on his skateboard. One trick takes him forward 5 feet, then he flips around and moves backwards 7.2 feet, then he moves forward again for 2.2 feet.<br \/>\na. What expression could be used to find how far Jeremy is from his starting position when he finishes the trick?<br \/>\nType below:<br \/>\n___________<\/p>\n<p>Answer: 5 &#8211; 7.2 + 2.2<\/p>\n<p>Explanation:<br \/>\nHe moves 5 feet forward, back 7.2 feet, and then forward 2.2 feet.<\/p>\n<p>Question 23.<br \/>\nb. How far from his starting point is he when he finishes the trick? Explain<br \/>\n_______ ft.<\/p>\n<p>Answer: 0 ft<\/p>\n<p>Explanation:<br \/>\nSince the distance just pulls hi back and forth at the same amount of distance.<br \/>\n5 &#8211; 7.2 + 2.2 = 0 ft<\/p>\n<p>Question 24.<br \/>\nEsteban has $20 from his allowance. There is a comic book he wishes to buy that costs $4.25, a cereal bar that costs $0.89, and a small remote control car that costs $10.99.<br \/>\na. Does Esteban have enough to buy everything?<br \/>\na. _______<\/p>\n<p>Answer:<br \/>\nFind the total amount of money he wants to spend this is less than 20 so he has enough<br \/>\n4.25 + 0.89 + 10.99 = 16.13<br \/>\nThus Esteban had enough money.<\/p>\n<p>Question 24.<br \/>\nb. If so, how much will he have left over? If not, how much does he still need?<br \/>\n$ _______<\/p>\n<p>Answer:<br \/>\nSubtract the amount he wants to spend from the amount he has to find how much he has left.<br \/>\n20 &#8211; 16.13 = 3.87<br \/>\nThus $3.87 left.<\/p>\n<h3><a id=\"Subtracting_Rational_Numbers_HOT_Page_No_82\"><\/a>Subtracting Rational Numbers &#8211; H.O.T &#8211; Page No. 82<\/h3>\n<p><strong>Focus on Higher Order Thinking<\/strong><\/p>\n<p>Question 25.<br \/>\nLook for a Pattern<br \/>\nShow how you could use the Commutative Property to simplify the evaluation of the expression \\(-\\frac{7}{16}-\\frac{1}{4}-\\frac{5}{16}\\).<br \/>\n_______<\/p>\n<p>Answer:<br \/>\n\\(-\\frac{7}{16}-\\frac{1}{4}-\\frac{5}{16}\\)<br \/>\n-12\/16 &#8211; 1\/4<br \/>\n= -3\/4 -1\/4<br \/>\n= -4\/4 = -1<\/p>\n<p>Question 26.<br \/>\nProblem Solving<br \/>\nThe temperatures for five days in Kaktovik, Alaska, are given below.<br \/>\n-19.6 \u00b0F, -22.5 \u00b0F, -20.9 \u00b0F, -19.5 \u00b0F, -22.4 \u00b0F<br \/>\nTemperatures for the following week are expected to be twelve degrees lower every day. What are the highest and lowest temperatures expected for the corresponding 5 days next week?<br \/>\nType below:<br \/>\n____________<\/p>\n<p>Answer:<br \/>\nThe highest temperature for the first five days was -19.5 degrees so the highest temperature the following week is 12 degrees less than that. the lowest temperature the first week was -22.9 degree so the lowest temperature the second week is 12 degree below that<br \/>\nhigh: -19.5 &#8211; 12 = -31.5\u00b0F<br \/>\nlow: -22.5 &#8211; 12 = -34.5\u00b0F<\/p>\n<p>Question 27.<br \/>\nMake a Conjecture<br \/>\nMust the difference between two rational numbers be a rational number? Explain.<br \/>\n_______<\/p>\n<p>Answer:<br \/>\nYes, the difference between two rational numbers must be rational. Subtracting two fractions equals a fraction of an integer. Integers are rational numbers so even if the answer isn&#8217;t a fraction, it is still a rational number.<\/p>\n<p>Question 28.<br \/>\nLook for a Pattern<br \/>\nEvan said that the difference between two negative numbers must be negative. Was he right? Use examples to illustrate your answer.<br \/>\n_______<\/p>\n<p>Answer:<br \/>\nHe is not correct. The difference between -2 and -5 is -2- (-5) = -2 + 5 = 3<br \/>\nwhich is not negative.<\/p>\n<h3><a id=\"Multiply_Rational_Numbers_Guided_Practice_Page_No_86\"><\/a>Multiply Rational Numbers &#8211; Guided Practice &#8211; Page No. 86<\/h3>\n<p><strong>Use a number line to find each product.<\/strong><\/p>\n<p>Question 1.<br \/>\n5(\u2212\\(\\frac{2}{3}\\)) =<br \/>\n_______ \\(\\frac{\u25a1}{\u25a1}\\)<\/p>\n<p>Answer: -3 \\(\\frac{1}{3}\\)<\/p>\n<p>Explanation:<br \/>\nRemember if the number being multiplied is positive, starting from zero move the number of units by how many times it is multiplied going to the right and if the number being multiplied is negative, starting from zero, move the number of units by how many times it is multiplied going to the left.<br \/>\nSince we are multiplying \u2212\\(\\frac{2}{3}\\) by 5, starting from 0, we move \\(\\frac{2}{3}\\) units to the left five times. This results in -3 \\(\\frac{1}{3}\\)<\/p>\n<p>Question 2.<br \/>\n3(\u2212\\(\\frac{1}{4}\\)) =<br \/>\n\\(\\frac{\u25a1}{\u25a1}\\)<\/p>\n<p>Answer: &#8211;\\(\\frac{3}{4}\\)<\/p>\n<p>Explanation:<br \/>\nRemember if the number being multiplied is positive, starting from zero move the number of units by how many times it is multiplied going to the right and if the number being multiplied is negative, starting from zero, move the number of units by how many times it is multiplied going to the left.<br \/>\nSince we are multiplying \u2212\\(\\frac{1}{4}\\) by 3, starting from 0, we move \u2212\\(\\frac{1}{4}\\) units to the left three times. This results in &#8211;\\(\\frac{3}{4}\\).<\/p>\n<p>Question 3.<br \/>\n\u22123(\u2212\\(\\frac{4}{7}\\)) =<br \/>\n_______ \\(\\frac{\u25a1}{\u25a1}\\)<\/p>\n<p>Answer: 1 \\(\\frac{5}{7}\\)<\/p>\n<p>Explanation:<br \/>\nRemember if the number being multiplied is positive, starting from zero move the number of units by how many times it is multiplied going to the right and if the number being multiplied is negative, starting from zero, move the number of units by how many times it is multiplied going to the left.<br \/>\nSince we are multiplying \u2212\\(\\frac{4}{7}\\) by -3, let us first multiply \u2212\\(\\frac{4}{7}\\) by 3. Starting from 0, we move \\(\\frac{4}{7}\\) units to the left three times.<br \/>\nThis results in -1 \\(\\frac{5}{7}\\)<br \/>\nTherefore the opposite of this is 1 \\(\\frac{5}{7}\\).<\/p>\n<p>Question 4.<br \/>\n\u2212\\(\\frac{3}{4}\\)(\u22124) =<br \/>\n______<\/p>\n<p>Answer: 3<\/p>\n<p>Explanation:<br \/>\nRemember if the number being multiplied is positive, starting from zero move the number of units by how many times it is multiplied going to the right and if the number being multiplied is negative, starting from zero, move the number of units by how many times it is multiplied going to the left.<br \/>\nSince we are multiplying \u2212\\(\\frac{3}{4}\\) by -4, let us first multiply \u2212\\(\\frac{3}{4}\\) by 4. Starting from 0, we move \\(\\frac{3}{4}\\) units to the left three times. This results in -3. Therefore the opposite of this is 3.<\/p>\n<p>Question 5.<br \/>\n4(\u22123) =<br \/>\n______<\/p>\n<p>Answer: -12<\/p>\n<p>Explanation:<br \/>\nRemember if the number being multiplied is positive, starting from zero move the number of units by how many times it is multiplied going to the right and if the number being multiplied is negative, starting from zero, move the number of units by how many times it is multiplied going to the left.<br \/>\nSince we are multiplying -3 by 4, starting from 0, we move 3 units to the left four times. This results in -12.<\/p>\n<p>Question 6.<br \/>\n(\u22121.8)5 =<br \/>\n______<\/p>\n<p>Answer: -9<\/p>\n<p>Explanation:<br \/>\nRemember if the number being multiplied is positive, starting from zero move the number of units by how many times it is multiplied going to the right and if the number being multiplied is negative, starting from zero, move the number of units by how many times it is multiplied going to the left.<br \/>\nSince we are multiplying -1.8 by 5, starting from 0, we move 1.8 units to the left five times. This results in -9.<\/p>\n<p>Question 7.<br \/>\n\u22122(\u22123.4) =<br \/>\n______<\/p>\n<p>Answer: 6.8<\/p>\n<p>Explanation:<br \/>\nRemember if the number being multiplied is positive, starting from zero move the number of units by how many times it is multiplied going to the right and if the number being multiplied is negative, starting from zero, move the number of units by how many times it is multiplied going to the left.<br \/>\nSince we are multiplying -2 by -3.4, starting from 0, starting from 0, we move 3.4 units to the left two times. This results in -6.8. Therefore, the opposite of this is 6.8.<\/p>\n<p>Question 8.<br \/>\n0.54(8) =<br \/>\n______<\/p>\n<p>Answer: 4.32<\/p>\n<p>Explanation:<br \/>\nRemember if the number being multiplied is positive, starting from zero move the number of units by how many times it is multiplied going to the right and if the number being multiplied is negative, starting from zero, move the number of units by how many times it is multiplied going to the left.<br \/>\nSince we are multiplying 0.54 by 8, starting from 0, we move 0.54 units to the right eight times. This results in 4.32.<\/p>\n<p>Question 9.<br \/>\n\u22125(\u22121.2) =<br \/>\n______<\/p>\n<p>Answer: 6<\/p>\n<p>Explanation:<br \/>\nRemember if the number being multiplied is positive, starting from zero move the number of units by how many times it is multiplied going to the right and if the number being multiplied is negative, starting from zero, move the number of units by how many times it is multiplied going to the left.<br \/>\nSince we are multiplying -1.2 by -5, Starting from 0, we move 1.2 units to the left five times. This results in -6. Therefore the opposite of this is 6.<\/p>\n<p>Question 10.<br \/>\n\u22122.4(3) =<br \/>\n______<\/p>\n<p>Answer: -7.2<\/p>\n<p>Explanation:<br \/>\nRemember if the number being multiplied is positive, starting from zero move the number of units by how many times it is multiplied going to the right and if the number being multiplied is negative, starting from zero, move the number of units by how many times it is multiplied going to the left.<br \/>\nSince we are multiplying -2.4 by 3, starting from 0, we move 2.4 units to the left three times. This results in -7.2<\/p>\n<p><strong>Multiply.<\/strong><\/p>\n<p>Question 11.<br \/>\n\\(\\frac{1}{2} \\times \\frac{2}{3} \\times \\frac{3}{4}\\) = \u25a1 \u00d7 \\(\\frac{3}{4}\\) =<br \/>\n\\(\\frac{\u25a1}{\u25a1}\\)<\/p>\n<p>Answer: \\(\\frac{1}{4}\\)<\/p>\n<p>Explanation:<br \/>\n\\(\\frac{1}{2} \\times \\frac{2}{3} \\times \\frac{3}{4}\\) = \u25a1 \u00d7 \\(\\frac{3}{4}\\)<br \/>\n1\/3 \u00d7 3\/4 = 1\/4<br \/>\n\\(\\frac{1}{2} \\times \\frac{2}{3} \\times \\frac{3}{4}\\) = \u25a1 \u00d7 \\(\\frac{3}{4}\\) = \\(\\frac{1}{4}\\)<\/p>\n<p>Question 12.<br \/>\n\\(-\\frac{4}{7}\\left(-\\frac{3}{5}\\right)\\left(-\\frac{7}{3}\\right)\\) = \u25a1 \u00d7 \\(\\left(-\\frac{7}{3}\\right)\\) =<br \/>\n\\(\\frac{\u25a1}{\u25a1}\\)<\/p>\n<p>Answer: &#8211; \\(\\frac{4}{5}\\)<\/p>\n<p>Explanation:<br \/>\nMultiply the first two fractions by multiplying the top numbers together and multiply the bottom numbers together.<br \/>\nRemember that two negatives make a positive so the product of the first two fractions is positive.<br \/>\n\\(-\\frac{4}{7}\\left(-\\frac{3}{5}\\right)\\left(-\\frac{7}{3}\\right)\\) = \u25a1 \u00d7 \\(\\left(-\\frac{7}{3}\\right)\\)<br \/>\n12\/35 \u00d7 -7\/3 = -4\/5<\/p>\n<p>Question 13.<br \/>\n\\(-\\frac{1}{8} \\times 5 \\times \\frac{2}{3}\\) =<br \/>\n\\(\\frac{\u25a1}{\u25a1}\\)<\/p>\n<p>Answer: &#8211;\\(\\frac{5}{12}\\)<\/p>\n<p>Explanation:<br \/>\nUse the commutative property to switch the order of the first two fractions.<br \/>\n\\(-\\frac{1}{8} \\times 5 \\times \\frac{2}{3}\\) = &#8211;\\(\\frac{1}{8}\\) \u00d7 \\(\\frac{2}{3}\\) \u00d7 5<br \/>\n&#8211;\\(\\frac{1}{12}\\) \u00d7 5 = &#8211;\\(\\frac{5}{12}\\)<\/p>\n<p>Question 14.<br \/>\n\\(-\\frac{2}{3}\\left(\\frac{1}{2}\\right)\\left(-\\frac{6}{7}\\right)\\) =<br \/>\n\\(\\frac{\u25a1}{\u25a1}\\)<\/p>\n<p>Answer: \\(\\frac{2}{7}\\)<\/p>\n<p>Explanation:<br \/>\nMultiply the first two fractions by cancelling the 2s.<br \/>\n\\(-\\frac{2}{3}\\left(\\frac{1}{2}\\right)\\left(-\\frac{6}{7}\\right)\\) = &#8211;\\(\\frac{1}{3}\\)(-\\(\\frac{6}{7}\\))<br \/>\nMultiply by cancelling the 3 and 6 to get a 2 in the numerator two negatives make a positive.<br \/>\nSo the answer is\u00a0\\(\\frac{2}{7}\\)<\/p>\n<p>Question 15.<br \/>\nThe price of one share of Acme Company declined $3.50 per day for 4 days in a row. What is the overall change in price of one share?<br \/>\n$ _______<\/p>\n<p>Answer: -$14<\/p>\n<p>Explanation:<br \/>\nGiven that,<br \/>\nThe price of one share of Acme Company declined $3.50 per day for 4 days in a row.<br \/>\n-$3.50 \u00d7 4 = -$14.00<br \/>\nThus the overall change in the price of one share is -$14.<\/p>\n<p>Question 16.<br \/>\nIn one day, 18 people each withdrew $100 from an ATM machine. What is the overall change in the amount of money in the ATM machine?<br \/>\n$ _______<\/p>\n<p>Answer: The overall change in the amount of money in the ATM machine is the product of the amount people withdrew times the number of people. This gives -100(18) = -1800.<br \/>\nTherefore the overall change in the amount of money in the ATM machine is -$1800.<\/p>\n<p>Question 17.<br \/>\nExplain how you can find the sign of the product of two or more rational numbers.<br \/>\nType below:<br \/>\n____________<\/p>\n<p>Answer: If the product has an even number of negative signs, then the product is positive. If the product has an odd number of negative signs, then the product is negative.<\/p>\n<h3><a id=\"Multiply_Rational_Numbers_Independent_Practice_Page_No_87\"><\/a>Multiply Rational Numbers &#8211; Independent Practice &#8211; Page No. 87<\/h3>\n<p>Question 18.<br \/>\nFinancial Literacy<br \/>\nSandy has $200 in her bank account.<br \/>\na. If she writes 6 checks for exactly $19.98, what expression describes the change in her bank account?<br \/>\n_______<\/p>\n<p>Answer: The change in her bank account is equal to the product of the check amounts and the number of checks.<br \/>\nThis gives the expressions 6(-19.98)<\/p>\n<p>Question 18.<br \/>\nb. What is her account balance after the checks are cashed?<br \/>\n$ _______<\/p>\n<p>Answer: She started with $200 and her account balance changes by 6(-19.98) dollars so her account balance is 200 &#8211; 6(-19.98) = 200 &#8211; 119.88 = 80.12<\/p>\n<p>Question 19.<br \/>\nCommunicating Mathematical Ideas<br \/>\nExplain, in words, how to find the product of -4(-1.5) using a number line. Where do you end up?<br \/>\nType below:<br \/>\n____________<\/p>\n<p>Answer:<br \/>\nFirst, find the value of -4(-1.5) by starting at 0 on the number line and moving 1.5 units left four times.<br \/>\nThis gives a value of 4(-1.5) = -6<br \/>\nSince -4(-1.5) is the opposite of 4(-1.5), the answer is 6.<\/p>\n<p>Question 20.<br \/>\nGreg sets his watch for the correct time on Wednesday. Exactly one week later, he finds that his watch has lost 3 \\(\\frac{1}{4}\\) minutes. If his watch continues to lose time at the same rate, what will be the overall change in time after 8 weeks?<br \/>\n_______ minutes<\/p>\n<p>Answer: 26 minutes<\/p>\n<p>Explanation:<br \/>\nGiven,<br \/>\nGreg sets his watch for the correct time on Wednesday.<br \/>\nExactly one week later, he finds that his watch has lost 3 \\(\\frac{1}{4}\\) minutes.<br \/>\n8(3 \\(\\frac{1}{4}\\)) = 8 \\(\\frac{13}{4}\\)<br \/>\n= 2 \u00d7 13 = 26 minutes.<br \/>\nTherefore the overall change in time after 8 weeks is 26 minutes.<\/p>\n<p>Question 21.<br \/>\nA submarine dives below the surface, heading downward in three moves. If each move downward was 325 feet, where is the submarine after it is finished diving?<br \/>\n_______ feet<\/p>\n<p>Answer: 975<\/p>\n<p>Explanation:<br \/>\nMoving downward is represented by a negative number. Multiply the distance traveled down by the number of moves.<br \/>\n3 \u00d7 -325 feet = -975<br \/>\nThe submarine is 975 feet below the surface.<\/p>\n<p>Question 22.<br \/>\nMultistep<br \/>\nFor Home Economics class, Sandra has 5 cups of flour. She made 3 batches of cookies that each used 1.5 cups of flour. Write and solve an expression to find the amount of flour Sandra has left after making the 3 batches of cookies.<br \/>\n_______ cups<\/p>\n<p>Answer: 0.5 cups<\/p>\n<p>Explanation:<br \/>\nSandra has a total of 5 cups of flour. Since she used 1.5 cups per batch of the cookie, and there are 3 batches, we can subtract the product of the cups and the number of batches<br \/>\n1.5 \u00d7 3 = 4.5<br \/>\nTherefore the expression should be 5 &#8211; 4.5 = 0.5<br \/>\nThus Sandra has 0.5 cups of flour left.<\/p>\n<p>Question 23.<br \/>\nCritique Reasoning<br \/>\nIn class, Matthew stated,\u201cI think that a negative is like the opposite. That is why multiplying a negative times a negative equals a positive. The opposite of negative is positive, so it is just like multiplying the opposite of a negative twice, which is two positives.\u201d<br \/>\nDo you agree or disagree with his reasoning? What would you say in response to him?<br \/>\n_______<\/p>\n<p>Answer: I agree with him. The product of two negatives is positive because the product of two positives is positive and negatives are opposites of positives.<\/p>\n<p>Question 24.<br \/>\nKaitlin is on a long car trip. Every time she stops to buy gas, she loses 15 minutes of travel time. If she has to stop 5 times, how late will she be getting to her destination?<br \/>\n_______ minutes<\/p>\n<p>Answer: 75 minutes<\/p>\n<p>Explanation:<br \/>\nMultiply the number of stops by the length of each stop to find the time she will be late.<br \/>\n5 \u00d7 15 = 75<br \/>\nThus Kaitlin will be 75 minutes late to reach her destination.<\/p>\n<h3><a id=\"Multiply_Rational_Numbers_Page_No_88\"><\/a>Multiply Rational Numbers &#8211; Page No. 88<\/h3>\n<p>Question 25.<br \/>\nThe table shows the scoring system for quarterbacks in Jeremy\u2019s fantasy football league. In one game, Jeremy\u2019s quarterback had 2 touchdown passes, 16 complete passes, 7 incomplete passes, and 2 interceptions. How many total points did Jeremy\u2019s quarterback score?<br \/>\n<img loading=\"lazy\" src=\"https:\/\/ccssmathanswers.com\/wp-content\/uploads\/2020\/08\/Go-Math-Grade-7-Answer-Key-Chapter-3-Rational-Numbers-img-4.jpg\" alt=\"Go Math Grade 7 Answer Key Chapter 3 Rational Numbers Lesson 4: Multiply Rational Numbers img 4\" width=\"279\" height=\"182\" \/><br \/>\n_______ pts<\/p>\n<p>Answer: 13.5 points<\/p>\n<p>Explanation:<br \/>\nWrite the expression for the total number of points<br \/>\n2(6) + 16(0.5) + 7(-0.5) + 2(-1.5)<br \/>\n= 12 + 8 &#8211; 3.5 &#8211; 3<br \/>\n= 20 &#8211; 6.5<br \/>\n= 13.5<br \/>\nThus Jeremy\u2019s quarterback scored 13.5 points.<\/p>\n<p><strong>H.O.T<\/strong><\/p>\n<p><strong>Focus On Higher Order Thinking<\/strong><\/p>\n<p>Question 26.<br \/>\nRepresent Real-World Problems<br \/>\nThe ground temperature at Brigham Airport is 12 \u00b0C. The temperature decreases by 6.8 \u00b0C for every increase of 1 kilometer above the ground. What is the overall change in temperature outside a plane flying at an altitude of 5 kilometers above Brigham Airport?<br \/>\n_______ \u00b0C<\/p>\n<p>Answer: -22\u00b0C<\/p>\n<p>Explanation:<br \/>\nRemember if the number being multiplied is positive, starting from zero moves the number of units by how many times it is multiplied going to the right and if the number being multiplied is negative, starting from zero, move the number of units by how many times it is multiplied going to the left.<br \/>\nNote that the ground temperature is 12\u00b0C. Since the temperature decreases by 6.8\u00b0C for every kilometer above ground, and the given height of the plane is 5 kilometers,<br \/>\nWe can subtract the product of the temperature and the distance 5(6.8) from the ground temperature.<br \/>\nTherefore the expression should be 12 &#8211; 5(6.8)<br \/>\n= 12 &#8211; 34<br \/>\n= -22<br \/>\nThus the temperature outside a plane flying at an altitude of 5 kilometers above Brigham Airport is -22\u00b0C<\/p>\n<p>Question 27.<br \/>\nIdentify Patterns<br \/>\nThe product of four numbers, a, b, c, and d, is a negative number. The table shows one combination of positive and negative signs of the four numbers that could produce a negative product. Complete the table to show the seven other possible combinations.<br \/>\n<img loading=\"lazy\" src=\"https:\/\/ccssmathanswers.com\/wp-content\/uploads\/2020\/08\/Go-Math-Grade-7-Answer-Key-Chapter-3-Rational-Numbers-img-5.jpg\" alt=\"Go Math Grade 7 Answer Key Chapter 3 Rational Numbers Lesson 4: Multiply Rational Numbers img 5\" width=\"378\" height=\"357\" \/><br \/>\nType below:<br \/>\n_____________<\/p>\n<p>Answer:<br \/>\nIn multiplying numbers, an odd number of negative signs produces a negative product.<br \/>\n<img loading=\"lazy\" class=\"alignnone size-medium wp-image-7515\" src=\"https:\/\/ccssmathanswers.com\/wp-content\/uploads\/2020\/08\/Go-Math-Grade-7-Answer-Key-Chapter-3-Rational-Numbers-img-5-1-300x283.jpg\" alt=\"Go-Math-Grade-7-Answer-Key-Chapter-3-Rational-Numbers-img-5\" width=\"300\" height=\"283\" srcset=\"https:\/\/bigideasmathanswers.com\/wp-content\/uploads\/2020\/08\/Go-Math-Grade-7-Answer-Key-Chapter-3-Rational-Numbers-img-5-1-300x283.jpg 300w, https:\/\/bigideasmathanswers.com\/wp-content\/uploads\/2020\/08\/Go-Math-Grade-7-Answer-Key-Chapter-3-Rational-Numbers-img-5-1.jpg 378w\" sizes=\"(max-width: 300px) 100vw, 300px\" \/><\/p>\n<p>Question 28.<br \/>\nReason Abstractly<br \/>\nFind two integers whose sum is -7 and whose product is 12. Explain how you found the numbers.<br \/>\nType below:<br \/>\n_____________<\/p>\n<p>Answer: -3 and -4<\/p>\n<p>Explanation:<br \/>\nLet x and y be the two numbers. Write the equations using the given information<br \/>\nx + y = -7<br \/>\nxy = 12<br \/>\nSince the two numbers multiply to a positive and add to a negative the two numbers must be negative. Find the pairs of negative numbers that multiply to 12.<br \/>\n-1 and -12, -2 and -6 and -3 and -4.<br \/>\nThus the pairs that have a sum as -7 and product as 12 is -3 and -4.<\/p>\n<h3><a id=\"Divide_Rational_Numbers_Guided_Practice_Page_No_92\"><\/a>Divide Rational Numbers &#8211; Guided Practice &#8211; Page No. 92<\/h3>\n<p><strong>Find each quotient.<\/strong><\/p>\n<p>Question 1.<br \/>\n\\(\\frac{0.72}{-0.9}\\) =<br \/>\n_______<\/p>\n<p>Answer: -0.8<\/p>\n<p>Explanation:<br \/>\nWe have to find the quotient:<br \/>\n\\(\\frac{0.72}{-0.9}\\)<br \/>\nWe determine the sign of the quotient.<br \/>\nThe quotient will be negative because the numbers have different signs.<br \/>\n\\(\\frac{0.72}{-0.9}\\) = -0.8<\/p>\n<p>Question 2.<br \/>\n\\(\\left(-\\frac{\\frac{1}{5}}{\\frac{7}{5}}\\right)\\) =<br \/>\n\\(\\frac{\u25a1}{\u25a1}\\)<\/p>\n<p>Answer: &#8211; \\(\\frac{1}{7}\\)<\/p>\n<p>Explanation:<br \/>\nWe have to find the quotient:<br \/>\n\\(\\left(-\\frac{\\frac{1}{5}}{\\frac{7}{5}}\\right)\\)<br \/>\nWe determine the sign of the quotient.<br \/>\nThe quotient will be negative because the numbers have different signs.<br \/>\n\\(\\left(-\\frac{\\frac{1}{5}}{\\frac{7}{5}}\\right)\\) = &#8211; \\(\\frac{5}{35}\\) = &#8211; \\(\\frac{1}{7}\\)<\/p>\n<p>Question 3.<br \/>\n\\(\\frac{56}{-7}\\) =<br \/>\n_______<\/p>\n<p>Answer: -8<\/p>\n<p>Explanation:<br \/>\nWe have to find the quotient:<br \/>\n\\(\\frac{56}{-7}\\)<br \/>\nWe determine the sign of the quotient.<br \/>\nThe quotient will be negative because the numbers have different signs.<br \/>\n7 divides 56 eight times.<br \/>\nThus the quotient of \\(\\frac{56}{-7}\\) = -8<\/p>\n<p>Question 4.<br \/>\n\\(\\frac{251}{4} \\div\\left(-\\frac{3}{8}\\right)\\) =<br \/>\n\\(\\frac{\u25a1}{\u25a1}\\)<\/p>\n<p>Answer: &#8211;\\(\\frac{502}{3}\\)<\/p>\n<p>Explanation:<br \/>\nWe have to find the quotient:<br \/>\n\\(\\frac{251}{4} \\div\\left(-\\frac{3}{8}\\right)\\)<br \/>\nWe determine the sign of the quotient.<br \/>\nThe quotient will be negative because the numbers have different signs.<br \/>\nRewrite using multiplication by multiplying with the reciprocal.<br \/>\n\\(\\frac{251}{4}\\) \u00d7 &#8211;\\( \\frac{8}{3}\\) = &#8211;\\(\\frac{2008}{12}\\)<br \/>\n&#8211;\\(\\frac{2008}{12}\\) = &#8211;\\(\\frac{502}{3}\\)<br \/>\nThe quotient of \\(\\frac{251}{4} \\div\\left(-\\frac{3}{8}\\right)\\) is &#8211;\\(\\frac{502}{3}\\)<\/p>\n<p>Question 5.<br \/>\n\\(\\frac{75}{-\\frac{1}{5}}\\) =<br \/>\n_______<\/p>\n<p>Answer: -375<\/p>\n<p>Explanation:<br \/>\nWe have to find the quotient:<br \/>\n\\(\\frac{75}{-\\frac{1}{5}}\\)<br \/>\nWe determine the sign of the quotient.<br \/>\nThe quotient will be negative because the numbers have different signs.<br \/>\n75 \u00f7 1\/5<br \/>\n75 \u00d7 -5 = -375<br \/>\nThus the quotient of \\(\\frac{75}{-\\frac{1}{5}}\\) is -375.<\/p>\n<p>Question 6.<br \/>\n\\(\\frac{-91}{-13}\\) =<br \/>\n_______<\/p>\n<p>Answer: 7<\/p>\n<p>Explanation:<br \/>\nWe have to find the quotient:<br \/>\n\\(\\frac{-91}{-13}\\)<br \/>\nWe determine the sign of the quotient.<br \/>\nThe quotient will be positive because the numbers have the same signs.<br \/>\n13 divides 91 seven times.<br \/>\n\\(\\frac{-91}{-13}\\) = 7<br \/>\nThus the quotient is 7.<\/p>\n<p>Question 7.<br \/>\n\\(\\frac{-\\frac{3}{7}}{\\frac{9}{4}}\\) =<br \/>\n\\(\\frac{\u25a1}{\u25a1}\\)<\/p>\n<p>Answer: &#8211;\\(\\frac{4}{21}\\)<\/p>\n<p>Explanation:<br \/>\nWe have to find the quotient:<br \/>\n\\(\\frac{-\\frac{3}{7}}{\\frac{9}{4}}\\)<br \/>\nWe determine the sign of the quotient.<br \/>\nThe quotient will be negative because the numbers have different signs.<br \/>\n\\(\\frac{-\\frac{3}{7}}{\\frac{9}{4}}\\) = -3\/7 \u00d7 4\/9 = -12\/63<br \/>\n-12\/63 = -4\/21<br \/>\n\\(\\frac{-\\frac{3}{7}}{\\frac{9}{4}}\\) = &#8211;\\(\\frac{4}{21}\\)<\/p>\n<p>Question 8.<br \/>\n&#8211; \\(\\frac{12}{0.03}\\) =<br \/>\n_______<\/p>\n<p>Answer: -400<\/p>\n<p>Explanation:<br \/>\nWe have to find the quotient:<br \/>\n&#8211; \\(\\frac{12}{0.03}\\)<br \/>\nWe determine the sign of the quotient.<br \/>\nThe quotient will be negative because the numbers have different signs.<br \/>\n&#8211; \\(\\frac{12}{0.03}\\) = -400<br \/>\nSo the quotient is -400.<\/p>\n<p>Question 9.<br \/>\nA water pail in your backyard has a small hole in it. You notice that it has drained a total of 3.5 liters in 4 days. What is the average change in water volume each day?<br \/>\n_______ liters per day<\/p>\n<p>Answer: -0.875 litres\/day<\/p>\n<p>Explanation:<br \/>\nGiven that,<br \/>\nA water pail in your backyard has a small hole in it. You notice that it has drained a total of 3.5 liters in 4 days.<br \/>\nThe average change of water volume each day is the quotient.<br \/>\nSo, divide -3.5 by 4.<br \/>\nThe quotient will be negative because the numbers have different signs.<br \/>\n-3.5\/4 = -0.875<br \/>\nThus the water volume diminishes by 0.875 liters each day.<\/p>\n<p>Question 10.<br \/>\nThe price of one share of ABC Company declined a total of $45.75 in 5 days. What was the average change of the price of one share per day?<br \/>\n$ _______<\/p>\n<p>Answer: -$9.15<\/p>\n<p>Explanation:<br \/>\nThe price of one share of ABC Company declined a total of $45.75 in 5 days.<br \/>\nWe use negative numbers for the price going down.<br \/>\nThe average change in the price of one share per day is the quotient.<br \/>\n-45.75\/5<br \/>\nWe determine the sign of the quotient.<br \/>\nThe quotient will be negative because the numbers have different signs.<br \/>\n-45.75\/5 = -9.15<br \/>\nThus the price of one share diminishes by $9.15 per day.<\/p>\n<p>Question 11.<br \/>\nTo avoid a storm, a passenger-jet pilot descended 0.44 mile in 0.8 minutes. What was the plane\u2019s average change of altitude per minute?<br \/>\n_______<\/p>\n<p>Answer: -0.55 miles\/min<\/p>\n<p>Explanation:<br \/>\nWe use negative numbers for the altitude going down.<br \/>\nThe plane&#8217;s average change of altitude per minute is the quotient:<br \/>\n-0.44\/0.8<br \/>\nWe determine the sign of the quotient<br \/>\nThe quotient will be negative because the numbers have different signs.<br \/>\n-0.44\/0.8 = -0.55<br \/>\nTherefore the plane descends by 0.55 miles per minute.<\/p>\n<p><strong>Essential Question Check-In<\/strong><\/p>\n<p>Question 12.<br \/>\nExplain how you would find the sign of the quotient \\(\\frac{32 \\div(-2)}{-16 \\div 4}\\).<br \/>\nType below:<br \/>\n___________<\/p>\n<p>Answer: positive<\/p>\n<p>Explanation:<br \/>\nGiven,<br \/>\n\\(\\frac{32 \\div(-2)}{-16 \\div 4}\\)<br \/>\nSince all the operations are of multiplication and division, the sign is given by the number of negative signs.<br \/>\nIf the number of negative signs is even, the quotient is positive while if the number of negative signs is odd, the quotient is negative.<br \/>\nIn this case, the number of negative signs is 2, therefore even, so the quotient is positive.<br \/>\n\\(\\frac{32 \\div(-2)}{-16 \\div 4}\\) = -16\/-4 = 4<br \/>\nThus the solution is positive.<\/p>\n<h3><a id=\"Divide_Rational_Numbers_Independent_Practice_Page_No_93\"><\/a>Divide Rational Numbers &#8211; Independent Practice &#8211; Page No. 93<\/h3>\n<p>Question 13.<br \/>\n\\(\\frac{5}{-\\frac{2}{8}}\\) =<br \/>\n_______<\/p>\n<p>Answer: -20<\/p>\n<p>Explanation:<br \/>\nWe are given the expression:<br \/>\n\\(\\frac{5}{-\\frac{2}{8}}\\)<br \/>\nThe quotient will be negative because the numbers have different signs.<br \/>\n\\(\\frac{5}{-\\frac{2}{8}}\\) = 5 \u00f7 (-2\/8)<br \/>\nWe rewrite using the multiplication by multiplying with the reciprocal:<br \/>\n5 \u00d7 -8\/2 = 5 \u00d7 -4 = -20<br \/>\nThus the quotient for \\(\\frac{5}{-\\frac{2}{8}}\\) is -20.<\/p>\n<p>Question 14.<br \/>\n\\(5 \\frac{1}{3} \\div\\left(-1 \\frac{1}{2}\\right)\\) =<br \/>\n\\(\\frac{\u25a1}{\u25a1}\\)<\/p>\n<p>Answer: &#8211; \\(\\frac{32}{9}\\)<\/p>\n<p>Explanation:<br \/>\nWe have to find the quotient:<br \/>\n\\(5 \\frac{1}{3} \\div\\left(-1 \\frac{1}{2}\\right)\\)<br \/>\nWe determine the sign of the quotient.<br \/>\nThe quotient will be negative because the numbers have different signs.<br \/>\n16\/3 \u00f7 -3\/2<br \/>\n16\/3 \u00d7 -2\/3 = -32\/9<br \/>\nThus the quotient for \\(5 \\frac{1}{3} \\div\\left(-1 \\frac{1}{2}\\right)\\) is &#8211; \\(\\frac{32}{9}\\)<\/p>\n<p>Question 15.<br \/>\n\\(\\frac{(-120)}{(-6)}\\) =<br \/>\n_______<\/p>\n<p>Answer: 20<\/p>\n<p>Explanation:<br \/>\nWe have to find the quotient:<br \/>\n\\(\\frac{(-120)}{(-6)}\\)<br \/>\nWe determine the sign of the quotient.<br \/>\nThe quotient will be positive because the numbers have the same signs.<br \/>\n6 divides 120 twenty times.<br \/>\n\\(\\frac{(-120)}{(-6)}\\) = 20<br \/>\nThus the quotient for \\(\\frac{(-120)}{(-6)}\\) is 20.<\/p>\n<p>Question 16.<br \/>\n\\(\\frac{-\\frac{4}{5}}{-\\frac{2}{3}}\\) =<br \/>\n\\(\\frac{\u25a1}{\u25a1}\\)<\/p>\n<p>Answer: \\(\\frac{6}{5}\\)<\/p>\n<p>Explanation:<br \/>\nWe have to find the quotient:<br \/>\n\\(\\frac{-\\frac{4}{5}}{-\\frac{2}{3}}\\)<br \/>\nWe determine the sign of the quotient.<br \/>\nThe quotient will be positive because the numbers have the same signs.<br \/>\n(-4\/5) \u00d7 (-3\/2) = 12\/10 = 6\/5<br \/>\nThus the quotient for \\(\\frac{-\\frac{4}{5}}{-\\frac{2}{3}}\\) is \\(\\frac{6}{5}\\)<\/p>\n<p>Question 17.<br \/>\n1.03 \u00f7 (\u221210.3) =<br \/>\n_______<\/p>\n<p>Answer: -0.1<\/p>\n<p>Explanation:<br \/>\nWe have to find the quotient:<br \/>\n1.03 \u00f7 (\u221210.3)<br \/>\nWe determine the sign of the quotient.<br \/>\nThe quotient will be negative because the numbers have different signs.<br \/>\n1.03 \u00f7 (-10.3) = -0.1<\/p>\n<p>Question 18.<br \/>\n\\(\\frac{(-0.4)}{80}\\) =<br \/>\n_______<\/p>\n<p>Answer: -0.005<\/p>\n<p>Explanation:<br \/>\nWe have to find the quotient:<br \/>\n\\(\\frac{(-0.4)}{80}\\)<br \/>\nWe determine the sign of the quotient.<br \/>\nThe quotient will be negative because the numbers have different signs.<br \/>\n\\(\\frac{(-0.4)}{80}\\) = -0.005<br \/>\nThus the quotient for \\(\\frac{(-0.4)}{80}\\) is -0.005.<\/p>\n<p>Question 19.<br \/>\n\\(1 \\div \\frac{9}{5}\\) =<br \/>\n\\(\\frac{\u25a1}{\u25a1}\\)<\/p>\n<p>Answer: \\(\\frac{5}{9}\\)<\/p>\n<p>Explanation:<br \/>\nWe have to find the quotient:<br \/>\n\\(1 \\div \\frac{9}{5}\\)<br \/>\nWe determine the sign of the quotient.<br \/>\nThe quotient will be positive because the numbers have the same signs<br \/>\n\\(1 \\div \\frac{9}{5}\\) = 1 \u00d7 5\/9 = 5\/9<br \/>\nThus the quotient for \\(1 \\div \\frac{9}{5}\\) is \\(\\frac{5}{9}\\)<\/p>\n<p>Question 20.<br \/>\n\\(\\frac{\\frac{-1}{4}}{\\frac{23}{0.4}}\\) =<br \/>\n\\(\\frac{\u25a1}{\u25a1}\\)<\/p>\n<p>Answer: &#8211;\\(\\frac{6}{23}\\)<\/p>\n<p>Explanation:<br \/>\nWe have to find the quotient:<br \/>\n\\(\\frac{\\frac{-1}{4}}{\\frac{23}{0.4}}\\)<br \/>\nWe determine the sign of the quotient.<br \/>\nThe quotient will be negative because the numbers have different signs.<br \/>\n\\(\\frac{\\frac{-1}{4}}{\\frac{23}{0.4}}\\) = (-1\/4) . (24\/23) = -24\/92<br \/>\n-24\/92 = -6\/23<br \/>\nThus the quotient for \\(\\frac{\\frac{-1}{4}}{\\frac{23}{0.4}}\\) is &#8211;\\(\\frac{6}{23}\\)<\/p>\n<p>Question 21.<br \/>\n\\(\\frac{-10.35}{-2.3}\\) =<br \/>\n_______<\/p>\n<p>Answer: 4.5<\/p>\n<p>Explanation:<br \/>\nWe have to find the quotient:<br \/>\n\\(\\frac{-10.35}{-2.3}\\)<br \/>\nWe determine the sign of the quotient.<br \/>\nThe quotient will be positive because the numbers have the same signs<br \/>\n\\(\\frac{-10.35}{-2.3}\\) = 4.5<br \/>\nSo, the quotient for \\(\\frac{-10.35}{-2.3}\\) is 4.5<\/p>\n<p>Question 22.<br \/>\nAlex usually runs for 21 hours a week, training for a marathon. If he is unable to run for 3 days, describe how to find out how many hours of training time he loses, and write the appropriate integer to describe how it affects his time.<br \/>\n_______ hours<\/p>\n<p>Answer: -9<\/p>\n<p>Explanation:<br \/>\nAlex usually runs for 21 hours a week, training for a marathon.<br \/>\nIf he runs 21 hours a week, he runs 21\/3 = 3 hours.<br \/>\nIf he doesn&#8217;t run for 3 days, then he is losing 3(3) = 9 hours of training time.<br \/>\nSince he is losing hours, the integer is negative so the answer is -9.<\/p>\n<p>Question 23.<br \/>\nThe running back for the Bulldogs football team carried the ball 9 times for a total loss of 15 \\(\\frac{3}{4}\\) yards. Find the average change in field position on each run.<br \/>\n\\(\\frac{\u25a1}{\u25a1}\\) yards per run<\/p>\n<p>Answer: 1 \\(\\frac{3}{4}\\) yards per run<\/p>\n<p>Explanation:<br \/>\nThe running back for the Bulldogs football team carried the ball 9 times for a total loss of 15 \\(\\frac{3}{4}\\) yards<br \/>\nConvert from mixed fractions to the improper fraction.<br \/>\n15 \\(\\frac{3}{4}\\) = \\(\\frac{63}{4}\\)<br \/>\n\\(\\frac{63}{4}\\) \u00d7 \\(\\frac{1}{9}\\)<br \/>\nDivide 63 and 9 by 9 and then multiply the remaining factors.<br \/>\n\\(\\frac{7}{4}\\) \u00d7 1 = \\(\\frac{7}{4}\\)<br \/>\nRewrite as a mixed fraction.<br \/>\n\\(\\frac{7}{4}\\) = 1 \\(\\frac{3}{4}\\) yards per run.<\/p>\n<p>Question 24.<br \/>\nThe 6:00 a.m. temperatures for four consecutive days in the town of Lincoln were -12.1 \u00b0C, -7.8\u00b0C, -14.3\u00b0C, and -7.2\u00b0C. What was the average 6:00 a.m. temperature for the four days?<br \/>\n_______ \u00b0C<\/p>\n<p>Answer: -10.35\u00b0C<\/p>\n<p>Explanation:<br \/>\nThe average is the sum of the temperatures divided by the number of temperatures.<br \/>\n(-12.1 &#8211; 7.8 &#8211; 14.3 &#8211; 7.2)\/4<br \/>\n= 41.4\/4 = -10.35\u00b0C<\/p>\n<p>Question 25.<br \/>\nMultistep<br \/>\nA seafood restaurant claims an increase of $1,750.00 over its average profit during a week where it introduced a special of baked clams.<br \/>\na. If this is true, how much extra profit did it receive per day?<br \/>\n$ _______ per day<\/p>\n<p>Answer:<br \/>\nThere are 7 days in a week so divide the total profit of $1750 by 7 to find the extra profit per day.<br \/>\n1750\/7 = 250<br \/>\nThus he receive $250 extra profit per day.<\/p>\n<p>Question 25.<br \/>\nb. If it had, instead, lost $150 per day, how much money would it have lost for the week?<br \/>\n$ _______<\/p>\n<p>Answer:<br \/>\nMultiply the daily loss of $150 by 7 to get the weekly loss.<br \/>\n150 \u00d7 7 = $1050<\/p>\n<p>Question 25.<br \/>\nc. If its total loss was $490 for the week, what was its average daily change?<br \/>\n$ _______ per day<\/p>\n<p>Answer:<br \/>\nSince the company lost $490, its income changed by -$490.<br \/>\nDivide the change in income by 7 to find the average daily change.<br \/>\n-$490\/7 = -$70<br \/>\nThus the average daily change is -$70 per day.<\/p>\n<p>Question 26.<br \/>\nA hot air balloon descended 99.6 meters in 12 seconds. What was the balloon\u2019s average rate of descent in meters per second?<br \/>\n_______ m\/s<\/p>\n<p>Answer: 8.3 meters per second<\/p>\n<p>Explanation:<br \/>\nGiven that,<br \/>\nA hot air balloon descended 99.6 meters in 12 seconds.<br \/>\n99.6\/12 = 8.3 meters per second.<br \/>\nThus the balloon\u2019s average rate of descent is 8.3 meters per second.<\/p>\n<h3><a id=\"Divide_Rational_Numbers_Page_No_94\"><\/a>Divide Rational Numbers &#8211; Page No. 94<\/h3>\n<p>Question 27.<br \/>\nSanderson is having trouble with his assignment. His shown work is as follows:<br \/>\n\\(\\frac{-\\frac{3}{4}}{\\frac{4}{3}}=-\\frac{3}{4} \\times \\frac{4}{3}=-\\frac{12}{12}=-1\\)<br \/>\nHowever, his answer does not match the answer that his teacher gives him. What is Sanderson\u2019s mistake? Find the correct answer.<br \/>\n\\(\\frac{\u25a1}{\u25a1}\\)<\/p>\n<p>Answer: &#8211; \\(\\frac{9}{16}\\)<\/p>\n<p>Explanation:<br \/>\nSanderson made the mistake of not flipping the bottom fraction when he rewrote the problem as multiplication. The correct work is<br \/>\n\\(\\frac{-\\frac{3}{4}}{\\frac{4}{3}}\\) = -3\/4 \u00d7 4\/3 = &#8211; \\(\\frac{9}{16}\\)<\/p>\n<p>Question 28.<br \/>\nScience<br \/>\nBeginning in 1996, a glacier lost an average of 3.7 meters of thickness each year. Find the total change in its thickness by the end of 2012.<br \/>\n_______ meters<\/p>\n<p>Answer: 59.2 meters<\/p>\n<p>Explanation:<br \/>\nBeginning in 1996, a glacier lost an average of 3.7 meters of thickness each year.<br \/>\n1996 to 2012 is 16 years so the total change in thickness is 16(3.7) = 59.2 meters.<\/p>\n<p><strong>H.O.T<\/strong><\/p>\n<p><strong>Focus On Higher Order Thinking<\/strong><\/p>\n<p>Question 29.<br \/>\nRepresent Real-World Problems<br \/>\nDescribe a real-world situation that can be represented by the quotient -85 \u00f7 15. Then find the quotient and explain what the quotient means in terms of the real-world situation.<br \/>\nQuotient: _______<\/p>\n<p>Answer: -5.67<\/p>\n<p>Explanation:<br \/>\nA possible real-world situation could be:<br \/>\nSam has withdrawn $85 from his bank account over a period of 15 days. Find the average change in his account balance per day.<br \/>\nAnswer: -85\/15 = -5.67<br \/>\nSo, the average rate of change in his account balance is -$5.67 per day.<\/p>\n<p>Question 30.<br \/>\nConstruct an Argument<br \/>\nDivide 5 by 4. Is your answer a rational number? Explain.<br \/>\n_______<\/p>\n<p>Answer: The quotient is a rational number because it is a fraction.<\/p>\n<p>Question 31.<br \/>\nCritical Thinking<br \/>\nShould the quotient of an integer divided by a nonzero integer always be a rational number? Why or why not?<br \/>\n_______<\/p>\n<p>Answer:<br \/>\nRemember that in dividing and simplifying rational numbers, the quotient is positive if the signs of the numbers are the same, and negative if the signs of the numbers are different.<br \/>\nThe quotient should be a rational number. This is because since the integers can be expressed as a quotient of two integers, then it is a rational number.<\/p>\n<h3><a id=\"Applying_Rational_Numbers_Operations_Guided_Practice_Page_No_98\"><\/a>Applying Rational Number Operations &#8211; Guided Practice &#8211; Page No. 98<\/h3>\n<p>Question 1.<br \/>\nMike hiked to Big Bear Lake in 4.5 hours at an average rate of 3 \\(\\frac{1}{5}\\) miles per hour. Pedro hiked the same distance at a rate of 3 \\(\\frac{3}{5}\\) miles per hour. How long did it take Pedro to reach the lake?<br \/>\n_______ hours<\/p>\n<p>Answer: 4 hours<\/p>\n<p>Explanation:<br \/>\nGiven that,<br \/>\nMike hiked to Big Bear Lake in 4.5 hours at an average rate of 3 \\(\\frac{1}{5}\\) miles per hour. Pedro hiked the same distance at a rate of 3 \\(\\frac{3}{5}\\) miles per hour.<br \/>\n4.5h \u00d7 3 \\(\\frac{3}{5}\\) miles per hour = 4.5 \u00d7 3.2 miles = 14.4 miles<br \/>\nPlug in the distance you found in step 1 and the given rate in the problem to find the number of hours for Pedro.<br \/>\n14.4 miles \u00f7 3 \\(\\frac{3}{5}\\) miles per hour = 14.4 \u00f7 3.6 hours = 4 hours<\/p>\n<p>Question 2.<br \/>\nUntil this year, Greenville had averaged 25.68 inches of rainfall per year for more than a century. This year\u2019s total rainfall showed a change of \u22122 \\(\\frac{3}{8}\\)% with respect to the previous average. How much rain fell this year?<br \/>\n_______ inches<\/p>\n<p>Answer: 25.0701 inches<\/p>\n<p>Explanation:<br \/>\nGreenville had averaged 25.68 inches of rainfall per year for more than a century.<br \/>\nThis year\u2019s total rainfall showed a change of \u22122 \\(\\frac{3}{8}\\)% with respect to the previous average.<br \/>\n\u22122 \\(\\frac{3}{8}\\)% = -2.375% = -0.02375<br \/>\n25.68 \u00d7 0.02375 \u2248 0.6099 inches<br \/>\nFind this year&#8217;s total rainfall<br \/>\n25.68 inches &#8211; 0.6099 inches = 25.0701 inches<\/p>\n<p><strong>Essential Question Check-In<\/strong><\/p>\n<p>Question 3.<br \/>\nWhy is it important to consider using tools when you are solving a problem?<br \/>\nType below:<br \/>\n___________<\/p>\n<p>Answer: It is important to consider using tools, such as a calculator, when solving problems because some problems involve multiplying and dividing decimals that are too time consuming to do by hand.<\/p>\n<h3><a id=\"Applying_Rational_Numbers_Operations_Independent_Practice_Page_No_99\"><\/a>Applying Rational Number Operations &#8211; Independent Practice &#8211; Page No. 99<\/h3>\n<p><strong>Solve, using appropriate tools.<\/strong><\/p>\n<p>Question 4.<br \/>\nThree rock climbers started a climb with each person carrying 7.8 kilograms of climbing equipment. A fourth climber with no equipment joined the group. The group divided the total weight of climbing equipment equally among the four climbers. How much did each climber carry?<br \/>\n_______ kilograms<\/p>\n<p>Answer: 5.85 kilograms<\/p>\n<p>Explanation:<br \/>\nGiven,<br \/>\nThree rock climbers started a climb with each person carrying 7.8 kilograms of climbing equipment.<br \/>\nA fourth climber with no equipment joined the group.<br \/>\n3 \u00d7 7.8 = 23.4<br \/>\nThe group divided the total weight of climbing equipment equally among the four climbers.<br \/>\n23.4\/4 = 5.85 kilograms<br \/>\nThus each climber carry 5.85 kilograms<\/p>\n<p>Question 5.<br \/>\nFoster is centering a photo that is 3 \\(\\frac{1}{2}\\) inches wide on a scrapbook page that is 12 inches wide. How far from each side of the page should he put the picture?<br \/>\n________ \\(\\frac{\u25a1}{\u25a1}\\) inches<\/p>\n<p>Answer: 4 \\(\\frac{1}{4}\\) inches<\/p>\n<p>Explanation:<br \/>\nGiven,<br \/>\nFoster is centering a photo that is 3 \\(\\frac{1}{2}\\) inches wide on a scrapbook page that is 12 inches wide.<br \/>\nLet x be how far the photo is from each side of the page.<br \/>\nSince the photo is 3 \\(\\frac{1}{2}\\) inches wide, then the total width of the page is<br \/>\nx + 3 \\(\\frac{1}{2}\\) + x = 2x + 3 \\(\\frac{1}{2}\\)<br \/>\n2x + 3 \\(\\frac{1}{2}\\) = 12<br \/>\n2x + 7\/2 = 12<br \/>\n2x = 17\/2<br \/>\nx = 17\/4<br \/>\nConvert the fraction to the mixed fraction.<br \/>\nx = 4 \\(\\frac{1}{4}\\) inches<\/p>\n<p>Question 6.<br \/>\nDiane serves breakfast to two groups of children at a daycare center. One box of Oaties contains 12 cups of cereal. She needs \\(\\frac{1}{3}\\) cup for each younger child and \\(\\frac{3}{4}\\) cup for each older child. Today\u2019s group includes 11 younger children and 10 older children. Is one box of Oaties enough for everyone? Explain.<br \/>\n________<\/p>\n<p>Answer: Yes<\/p>\n<p>Explanation:<br \/>\n11 \u00d7 \\(\\frac{1}{3}\\) + 10 \u00d7 \\(\\frac{3}{4}\\)<br \/>\n\\(\\frac{11}{3}\\) + \\(\\frac{15}{2}\\)<br \/>\n\\(\\frac{22}{6}\\) + \\(\\frac{45}{6}\\) = \\(\\frac{67}{6}\\)<br \/>\n= 11 \\(\\frac{1}{6}\\)<\/p>\n<p>Question 7.<br \/>\nThe figure shows how the yard lines on a football field are numbered. The goal lines are labeled G. A referee was standing on a certain yard line as the first quarter ended. He walked 41 \\(\\frac{3}{4}\\) yards to a yard line with the same number as the one he had just left. How far was the referee from the nearest goal line?<br \/>\n1<img loading=\"lazy\" src=\"https:\/\/ccssmathanswers.com\/wp-content\/uploads\/2020\/08\/Go-Math-Grade-7-Answer-Key-Chapter-3-Rational-Numbers-img-6.jpg\" alt=\"Go Math Grade 7 Answer Key Chapter 3 Rational Numbers Lesson 6: Applying Rational Number Operations img 6\" width=\"365\" height=\"166\" \/><br \/>\n________ \\(\\frac{\u25a1}{\u25a1}\\)<\/p>\n<p>Answer: 29 \\(\\frac{1}{8}\\)<\/p>\n<p>Explanation:<br \/>\nThe American football field is 100 yds long, 53 1\/3 yards wide, and has 10-yard touchdown zones at each end of the field.<br \/>\nLet x = distance of the referee at the end of the quarter from the nearest goal.<br \/>\nThe distance between the same yard lines on either side of the centerline is<br \/>\n100 &#8211; 2x<br \/>\nThis distance is the 41 3\/4 yards that the referee walked. Therefore<br \/>\n100 &#8211; 2x = 41.75<br \/>\n-2x = 41.75 &#8211; 100 = -58.25<br \/>\nx = 29.125 yd<br \/>\nConvert from decimal to fraction.<br \/>\nx = 29 \\(\\frac{1}{8}\\) yards<\/p>\n<p><strong>In 8\u201310, a teacher gave a test with 50 questions, each worth the same number of points. Donovan got 39 out of 50 questions right. Marci\u2019s score was 10 percentage points higher than Donovan\u2019s.<\/strong><\/p>\n<p>Question 8.<br \/>\nWhat was Marci\u2019s score? Explain.<br \/>\n________ %<\/p>\n<p>Answer: 88 %<\/p>\n<p>Explanation:<br \/>\n39\/50 = 78\/100<br \/>\n78\/100 + 10\/100 = 88\/100 = 44\/50<br \/>\n88\/100 = 88%<\/p>\n<p>Question 9.<br \/>\nHow many more questions did Marci answer correctly? Explain.<br \/>\n________ questions<\/p>\n<p>Answer: 5 questions<\/p>\n<p>Explanation:<br \/>\nMarci got 44 correct and Donovan got 39 correct so she got 44 &#8211; 39 = 5 more questions correct.<\/p>\n<p>Question 10.<br \/>\nExplain how you can check your answers for reasonableness.<br \/>\nType below:<br \/>\n_____________<\/p>\n<p>Answer:<br \/>\nYou can check your answers for reasonableness by using estimates.<br \/>\nDonovan scored 39\/50 which is about 40\/50 = 80\/100 = 80%<br \/>\nTen percentage points higher is then 80% + 10% = 90% = 90\/100 = 45\/50.<br \/>\nSince Marci&#8217;s score was 44\/50, it is a reasonable answer.<\/p>\n<h3><a id=\"Applying_Rational_Numbers_Operations_Page_No_100\"><\/a>Applying Rational Number Operations &#8211; Page No. 100<\/h3>\n<p><strong>For 11\u201313, use the expression 1.43 \u00d7 \\(\\left(-\\frac{19}{37}\\right)\\)<\/strong><\/p>\n<p>Question 11.<br \/>\nCritique Reasoning<br \/>\nJamie says the value of the expression is close to \u22120.75. Does Jamie\u2019s estimate seem reasonable? Explain.<br \/>\n_______<\/p>\n<p>Answer: Yes<\/p>\n<p>Explanation:<br \/>\nJamie is correct. 1.43 is about 1.5 and -19\/37 \u2248 1\/2.<br \/>\nSince 1.5 \u00d7 &#8211; 1\/2 = -0.75<br \/>\nJamie&#8217;s estimation is reasonable.<\/p>\n<p>Question 12.<br \/>\nFind the product. Explain your method.<br \/>\n_______<\/p>\n<p>Answer:<br \/>\nUsing a calculator, you get that 1.43 \u00d7 (-19\/37) \u2248 -0.734<\/p>\n<p>Question 13.<br \/>\nDoes your answer to Exercise 12 justify your answer to Exercise 11?<br \/>\n_______<\/p>\n<p>Answer: Yes<\/p>\n<p>Explanation:<br \/>\n-0.734 is close to the estimate of -0.75 so the answer to Exercise 12 justifies the answer to Exercise 11.<\/p>\n<p><strong>H.O.T<\/strong><\/p>\n<p><strong>Focus On Higher Order Thinking<\/strong><\/p>\n<p>Question 14.<br \/>\nPersevere in Problem Solving<br \/>\nA scuba diver dove from the surface of the ocean to an elevation of \u221279 \\(\\frac{9}{10}\\) feet at a rate of -18.8 feet per minute. After spending 12.75 minutes at that elevation, the diver ascended to an elevation of \u221228 \\(\\frac{9}{10}\\) feet. The total time for the dive so far was 19 \\(\\frac{1}{8}\\) minutes. What was the rate of change in the diver\u2019s elevation during the ascent?<br \/>\n_______ ft\/min<\/p>\n<p>Answer: 24 ft\/min<\/p>\n<p>Explanation:<br \/>\nGiven that,<br \/>\nA scuba diver dove from the surface of the ocean to an elevation of \u221279 \\(\\frac{9}{10}\\) feet at a rate of -18.8 feet per minute.<br \/>\nAfter spending 12.75 minutes at that elevation, the diver ascended to an elevation of \u221228 \\(\\frac{9}{10}\\) feet. The total time for the dive so far was 19 \\(\\frac{1}{8}\\) minutes.<br \/>\n\u221279 \\(\\frac{9}{10}\\) \u00f7 -18.8 = 4.25 minutes<br \/>\nFind the time it took to ascend by subtracting the descent time and time spent at the descent elevation from the total dive time.<br \/>\n19 \\(\\frac{1}{8}\\) &#8211; 4.25 &#8211; 12.75 = 2 1\/8 minutes<br \/>\n-28 \\(\\frac{9}{10}\\) &#8211; (-\u221279 \\(\\frac{9}{10}\\)) = 51 feet<br \/>\nFind the rate of change by dividing the distance in feet divided by the time.<br \/>\n51\/2 1\/8 = 24 feet per minute<\/p>\n<p>Question 15.<br \/>\nAnalyze Relationships<br \/>\nDescribe two ways you could evaluate 37% of the sum of 27 \\(\\frac{3}{5}\\) and 15.9. Tell which method you would use and why<br \/>\nType below:<br \/>\n___________<\/p>\n<p>Answer:<br \/>\nMethod 1:<br \/>\nRewrite numbers in fraction form and evaluate algebraically.<br \/>\n37% (27 \\(\\frac{3}{5}\\) + 15.9)<br \/>\n37\/100 (27 3\/5 + 15 9\/10)<br \/>\n37\/100 (138\/5 + 159\/10)<br \/>\n37\/100 (435\/10)<br \/>\n37\/100 \u00d7 87\/2 = 3219\/200 = 16.095<br \/>\nMethod 2:<br \/>\nRewrite numbers in decimal form and evaluate with a calculator<br \/>\n37% (27 \\(\\frac{3}{5}\\) + 15.9)<br \/>\n0.37(27.6 + 15.9)<br \/>\n0.37 \u00d7 43.5 = 16.095<\/p>\n<p>Question 16.<br \/>\nRepresent Real-World Problems<br \/>\nDescribe a real-world problem you could solve with the help of a yardstick and a calculator.<br \/>\nType below:<br \/>\n___________<\/p>\n<p>Answer:<br \/>\nFinding the perimeter of the table. Using the yardstick you can get the side length of the table and add these measurements to get the perimeter.<\/p>\n<h3><a id=\"Module_Quiz_3.1_Rational_Numbers_and_Decimals_Page_No_101\"><\/a>Module Quiz &#8211; 3.1 Rational Numbers and Decimals &#8211; Page No. 101<\/h3>\n<p><strong>Write each mixed number as a decimal.<\/strong><\/p>\n<p>Question 1.<br \/>\n4 \\(\\frac{1}{5}\\) =<br \/>\n_______<\/p>\n<p>Answer: 4.2<\/p>\n<p>Explanation:<br \/>\nTo convert fractions to decimals, simply divide the numerator to the denominator. If the quotient goes on and on, it is a repeating decimal, and to write this as a decimal, put a bar on top of the repeating digits.<br \/>\n\\(\\frac{1}{5}\\) = 0.2<br \/>\n4 + 0.2 = 4.2<br \/>\n4 \\(\\frac{1}{5}\\) = 4.2<\/p>\n<p>Question 2.<br \/>\n12 \\(\\frac{14}{15}\\) =<br \/>\n_______<\/p>\n<p>Answer: 12.933..<\/p>\n<p>Explanation:<br \/>\nTo convert fractions to decimals, simply divide the numerator to the denominator. If the quotient goes on and on, it is a repeating decimal, and to write this as a decimal, put a bar on top of the repeating digits.<br \/>\n\\(\\frac{14}{15}\\) = 0.933..<br \/>\n12 + 0.933 = 12.933..<br \/>\n12 \\(\\frac{14}{15}\\) = 12.933..<\/p>\n<p>Question 3.<br \/>\n5 \\(\\frac{5}{32}\\) =<br \/>\n_______<\/p>\n<p>Answer: 5.15625<\/p>\n<p>Explanation:<br \/>\nTo convert fractions to decimals, simply divide the numerator to the denominator. If the quotient goes on and on, it is a repeating decimal, and to write this as a decimal, put a bar on top of the repeating digits.<br \/>\n\\(\\frac{5}{32}\\) = 0.15625<br \/>\n5 + 0.15625 = 5.15625<br \/>\n5 \\(\\frac{5}{32}\\) = 5.15625<\/p>\n<p><strong>3.2 Adding Rational Numbers<\/strong><\/p>\n<p><strong>Find each sum.<\/strong><\/p>\n<p>Question 4.<br \/>\n4.5 + 7.1 =<br \/>\n_______<\/p>\n<p>Answer: 11.6<\/p>\n<p>Explanation:<br \/>\nTo add or subtract numbers, make sure to align the digits vertically before doing the operation.<br \/>\nMake sure to align ones, tens, hundreds and thousands digits before adding<br \/>\n4.5<br \/>\n<span style=\"text-decoration: underline\">+7.1<\/span><br \/>\n<span style=\"text-decoration: underline\">\u00a011.6<\/span><\/p>\n<p>Question 5.<br \/>\n\\(5 \\frac{1}{6}+\\left(-3 \\frac{5}{6}\\right)\\) =<br \/>\n_______ \\(\\frac{\u25a1}{\u25a1}\\)<\/p>\n<p>Answer: 1 \\(\\frac{1}{3}\\)<\/p>\n<p>Explanation:<br \/>\n\\(5 \\frac{1}{6}+\\left(-3 \\frac{5}{6}\\right)\\) =<br \/>\n\\(5 \\frac{1}{6}\\) &#8211; [\/latex]3 \\frac{5}{6}\\right)[\/latex] = 4 7\/6 &#8211; 3 5\/6<br \/>\n1 2\/6 = 1 1\/3<br \/>\nThus \\(5 \\frac{1}{6}+\\left(-3 \\frac{5}{6}\\right)\\) = 1 \\(\\frac{1}{3}\\)<\/p>\n<p><strong>3.3 Subtracting Rational Numbers<\/strong><\/p>\n<p><strong>Find each difference.<\/strong><\/p>\n<p>Question 6.<br \/>\n\\(-\\frac{1}{8}-\\left(6 \\frac{7}{8}\\right)\\) =<br \/>\n_______<\/p>\n<p>Answer: -7<\/p>\n<p>Explanation:<br \/>\nBoth numbers are negative. so add the opposites of each number and write the answer as a negative.<br \/>\n\\(-\\frac{1}{8}-\\left(6 \\frac{7}{8}\\right)\\)<br \/>\n-(\\(\\frac{1}{8}+\\left(6 \\frac{7}{8}\\right)\\))<br \/>\n= &#8211; 6 \\(\\frac{8}{8}\\) = -6 &#8211; 1 = -7<\/p>\n<p>Question 7.<br \/>\n14.2 \u2212 (\u22124.9) =<br \/>\n_______<\/p>\n<p>Answer: 19.1<\/p>\n<p>Explanation:<br \/>\n14.2 \u2212 (\u22124.9)<br \/>\n= 14.2 + 4.9 = 19.1<\/p>\n<p><strong>3.4 Multiplying Rational Numbers<\/strong><\/p>\n<p><strong>Multiply.<\/strong><\/p>\n<p>Question 8.<br \/>\n\\(-4\\left(\\frac{7}{10}\\right)\\) =<br \/>\n\\(\\frac{\u25a1}{\u25a1}\\)<\/p>\n<p>Answer: &#8211;\\(\\frac{14}{5}\\)<\/p>\n<p>Explanation:<br \/>\nMultiply the whole number with the numerator. write this product in the numerator and keep the same denominator.<br \/>\n\\(-4\\left(\\frac{7}{10}\\right)\\) = &#8211;\\(\\frac{14}{5}\\)<\/p>\n<p>Question 9.<br \/>\n\u22123.2(\u22125.6)(4) =<br \/>\n_______<\/p>\n<p>Answer: 71.68<\/p>\n<p>Explanation:<br \/>\nMultiply the first two numbers. There are two negative signs so the answer will be positive.<br \/>\n\u22123.2(\u22125.6)(4) = 17.92 \u00d7 4 = 71.68<\/p>\n<p><strong>3.5 Dividing Rational Numbers<\/strong><\/p>\n<p><strong>Find each quotient.<\/strong><\/p>\n<p>Question 10.<br \/>\n\\(-\\frac{19}{2} \\div \\frac{38}{7}\\) =<br \/>\n\\(\\frac{\u25a1}{\u25a1}\\)<\/p>\n<p>Answer: &#8211;\\(\\frac{7}{4}\\)<\/p>\n<p>Explanation:<br \/>\n\\(-\\frac{19}{2} \\div \\frac{38}{7}\\)<br \/>\n-19\/2 \u00d7 7\/38 = -7\/2 \u00d7 1\/2<br \/>\n= &#8211;\\(\\frac{7}{4}\\)<\/p>\n<p>Question 11.<br \/>\n\\(\\frac{-32.01}{-3.3}\\) =<br \/>\n_______<\/p>\n<p>Answer: 9.7<\/p>\n<p>Explanation:<br \/>\nGiven,<br \/>\n\\(\\frac{-32.01}{-3.3}\\)<br \/>\nRemember that dividing two negatives gives a positive answer.<br \/>\n-32.01 \u00f7 -3.3 = 9.7<\/p>\n<p><strong>3.6 Applying Rational Number Operations<\/strong><\/p>\n<p>Question 12.<br \/>\nLuis bought stock at $83.60. The next day, the price increased by 15.35 dollars. This new price changed by \u22124 \\(\\frac{3}{4}\\)% the following day. What was the final stock price? Is your answer reasonable? Explain.<br \/>\n$ _______<\/p>\n<p>Answer: $94.25<\/p>\n<p>Explanation:<br \/>\n83.60 + 15.35 = 98.95<br \/>\n98.95 \u00d7 \u22124 \\(\\frac{3}{4}\\)% = 98.95 \u00d7 -0.0475 = 4.70<br \/>\n98.95 &#8211; 4.70 = $94.25<\/p>\n<p><strong>Essential Question<\/strong><\/p>\n<p>Question 13.<br \/>\nHow can you use negative numbers to represent real-world problems?<br \/>\nType below:<br \/>\n___________<\/p>\n<p>Answer:<br \/>\nNegative numbers can be used in real-world problems to represents decreases or values that are below a level considered to be 0.<\/p>\n<h3><a id=\"MODULE_3_MIXED_REVIEW_Selected_Response_Page_No_102\"><\/a>MODULE 3 MIXED REVIEW &#8211; Selected Response &#8211; Page No. 102<\/h3>\n<p>Question 1.<br \/>\nWhat is \u22127 \\(\\frac{5}{12}\\) written as a decimal?<br \/>\nOptions:<br \/>\na. -7.25<br \/>\nb. -7.333&#8230;<br \/>\nc. -7.41666&#8230;<br \/>\nd. -7.512<\/p>\n<p>Answer: -7.41666&#8230;<\/p>\n<p>Explanation:<br \/>\nGiven,<br \/>\n\u22127 \\(\\frac{5}{12}\\)<br \/>\nConvert from fraction to decimal.<br \/>\n5 \u00f7 12 = 0.4166..<br \/>\n\u22127 \\(\\frac{5}{12}\\) = -7.4166&#8230;.<br \/>\nThus the correct answer is option C.<\/p>\n<p>Question 2.<br \/>\nGlenda began the day with a golf score of -6 and ended with a score of -10. Which statement represents her golf score for that day?<br \/>\nOptions:<br \/>\na. -6 &#8211; (-10) = 4<br \/>\nb. -10 &#8211; (-6) = -4<br \/>\nc. -6 + (-10) = -16<br \/>\nd. -10 + (-6) = -16<\/p>\n<p>Answer: -10 &#8211; (-6) = -4<\/p>\n<p>Explanation:<br \/>\nGiven,<br \/>\nHer golf score for the day can be found by subtracting her ending score and her beginning score which gives<br \/>\n-10 &#8211; (-6) = -10 + 6 = -4<br \/>\nSo, the correct answer is option B.<\/p>\n<p>Question 3.<br \/>\nA submersible vessel at an elevation of -95 feet descends to 5 times that elevation. What is the vessel\u2019s new elevation?<br \/>\nOptions:<br \/>\na. -475 ft<br \/>\nb. -19 ft<br \/>\nc. 19 ft<br \/>\nd. 475 ft<\/p>\n<p>Answer: -475 ft<\/p>\n<p>Explanation:<br \/>\nGiven,<br \/>\nA submersible vessel at an elevation of -95 feet descends to 5 times that elevation.<br \/>\n-95 feet \u00d7 5 = -475 feet<br \/>\nThus the correct answer is option A.<\/p>\n<p>Question 4.<br \/>\nThe temperature at 7 P.M. at a weather station in Minnesota was -5 \u00b0F. The temperature began changing at the rate of -2.5 \u00b0F per hour. What was the temperature at 10 P.M.?<br \/>\nOptions:<br \/>\na. -15 \u00b0F<br \/>\nb. -12.5 \u00b0F<br \/>\nc. 2.5 \u00b0F<br \/>\nd. 5 \u00b0F<\/p>\n<p>Answer: -12.5 \u00b0F<\/p>\n<p>Explanation:<br \/>\nFind the total change in temperature by multiplying the rate of change per hour times the number of hours from 7 pm to 10 pm.<br \/>\n-5 + (-7.5) = -12.5\u00b0F<br \/>\nThus the correct answer is option B.<\/p>\n<p>Question 5.<br \/>\nWhat is the sum of -2.16 and -1.75?<br \/>\nOptions:<br \/>\na. 0.41<br \/>\nb. 3.91<br \/>\nc. -0.41<br \/>\nd. -3.91<\/p>\n<p>Answer: -3.91<\/p>\n<p>Explanation:<br \/>\nBoth numbers are negative so add their opposites and make the answer negative.<br \/>\n-2.16 + (-1.75) = -(2.16 + 1.75) = -3.91<br \/>\nSo, the correct answer is option D.<\/p>\n<p>Question 6.<br \/>\nOn Sunday, the wind chill temperature reached -36 \u00b0F. On Monday, the wind chill temperature only reached \\(\\frac{1}{4}\\) of Sunday\u2019s wind chill temperature. What was the lowest wind chill temperature on Monday?<br \/>\nOptions:<br \/>\na. -9 \u00b0F<br \/>\nb. -36 \\(\\frac{1}{4}\\) \u00b0F<br \/>\nc. -40 \u00b0F<br \/>\nd. -144 \u00b0F<\/p>\n<p>Answer: -9 \u00b0F<\/p>\n<p>Explanation:<br \/>\nGiven that,<br \/>\nOn Sunday, the wind chill temperature reached -36 \u00b0F.<br \/>\nOn Monday, the wind chill temperature only reached \\(\\frac{1}{4}\\) of Sunday\u2019s wind chill temperature.<br \/>\n-36 \u00d7 \\(\\frac{1}{4}\\) = -9\u00b0F<br \/>\nThus the correct answer is option A.<\/p>\n<p>Question 7.<br \/>\nThe level of a lake was 8 inches below normal. It decreased 1 \\(\\frac{1}{4}\\) inches in June and 2 \\(\\frac{3}{8}\\) inches more in July. What was the new level with respect to the normal level?<br \/>\nOptions:<br \/>\na. -11 \\(\\frac{5}{8}\\) in.<br \/>\nb. -10 \\(\\frac{5}{8}\\) in.<br \/>\nc. -9 \\(\\frac{1}{8}\\) in.<br \/>\nd. -5 \\(\\frac{3}{8}\\) in.<\/p>\n<p>Answer: -11 \\(\\frac{5}{8}\\) in.<\/p>\n<p>Explanation:<br \/>\nThe level of a lake was 8 inches below normal. It decreased 1 \\(\\frac{1}{4}\\) inches in June and 2 \\(\\frac{3}{8}\\) inches more in July.<br \/>\nThe initial level is below normal so it is represented by a negative number. The level continued to decrease in June and July so those changes are also represented by negative numbers.<br \/>\nFind the sum of these values to find what the new level was with respect to the normal level.<br \/>\n-8 &#8211; 1 \\(\\frac{1}{4}\\) &#8211; 2 \\(\\frac{3}{8}\\)<br \/>\n= -8 &#8211; \\(\\frac{5}{4}\\) &#8211; \\(\\frac{19}{8}\\)<br \/>\n= &#8211; \\(\\frac{93}{8}\\)<br \/>\n= &#8211; 11 \\(\\frac{5}{8}\\)<br \/>\nThus the correct answer is option A.<\/p>\n<p><strong>Mini-Task<\/strong><\/p>\n<p>Question 8.<br \/>\nThe average annual rainfall for a town is 43.2 inches.<br \/>\na. What is the average monthly rainfall?<br \/>\n________<\/p>\n<p>Answer:<br \/>\nIf the average rainfall us 43.2 inches then the monthly rainfall is 43.2\/12 = 3.6 inches since there are 12 months in a year.<\/p>\n<p>Question 8.<br \/>\n<img loading=\"lazy\" src=\"https:\/\/ccssmathanswers.com\/wp-content\/uploads\/2020\/08\/Go-Math-Grade-7-Answer-Key-Chapter-3-Rational-Numbers-img-7.jpg\" alt=\"Go Math Grade 7 Answer Key Chapter 3 Rational Numbers MODULE 3 MIXED REVIEW img 7\" width=\"295\" height=\"99\" \/><br \/>\nb. The difference of a given month\u2019s rainfall from the average monthly rainfall is called the deviation. What is the deviation for each month shown?<br \/>\nMay: ___________ inch<br \/>\nJune: ___________ inches<br \/>\nJuly: ___________ inches<\/p>\n<p>Answer:<br \/>\nThe deviation for May is 2 3\/5 &#8211; 3.6 = 2.6 &#8211; 3.6 = -1 inches.<br \/>\nThe deviation for June is 7\/8 &#8211; 3.6 = -2.725 inches.<br \/>\nThe deviation for July 4 1\/4 &#8211; 3.6 = 0.65 inches.<\/p>\n<p>Question 8.<br \/>\nc. The average monthly rainfall for the previous 9 months was 4 inches. Did the town exceed its average annual rainfall? If so, by how much?<br \/>\n________<\/p>\n<p>Answer:<br \/>\nIf is rained 4 inches for 9 months, the total amount of rain over the 12 month period is than 9(4) + 2 3\/5 + 7\/8 + 4 1\/4<br \/>\n= 36 + 2.6 + 0.875 + 4.25 = 43.725.<br \/>\nSince this is greater than the average annual rainfall of 43.2, the town did exceed is average annual rainfall.<br \/>\nthe difference of 43.725 and 43.2 is<br \/>\n43.725 &#8211; 43.2 = 0.525<br \/>\nso, it exceeded it by 0.525 inches.<\/p>\n<h3><a id=\"MODULE_3_REVIEW_Rational_Numbers_Page_No_106\"><\/a>Module 3 Review &#8211; Rational Numbers &#8211; Page No. 106<\/h3>\n<p><strong>EXERCISES<\/strong><\/p>\n<p><strong>Write each mixed number as a whole number or decimal. Classify each number according to the group(s) to which it belongs: rational numbers, integers, or whole numbers.<\/strong><\/p>\n<p>Question 1.<br \/>\n\\(\\frac{3}{4}\\)<br \/>\n________<\/p>\n<p>Answer: 0.75, rational<\/p>\n<p>Explanation:<br \/>\nWrite as a decimal by dividing 3 by 4. A shortcut with fourths is to think of the fractions in terms of money. 4 quarters make a dollar and 3 quarters is $0.75 so three-fourths is 0.75 in decimal form.<br \/>\nSince \\(\\frac{3}{4}\\) could not be written as a whole number or integer, it is a rational number.<\/p>\n<p>Question 2.<br \/>\n\\(\\frac{8}{2}\\)<br \/>\n________<\/p>\n<p>Answer: 4<\/p>\n<p>Explanation:<br \/>\n\\(\\frac{8}{2}\\) = 4<br \/>\nSince 4 doesn&#8217;t have a decimal and is positive, it is a whole number. All whole numbers are also integers and rational numbers so 4 is a rational number, integer, and a whole number.<\/p>\n<p>Question 3.<br \/>\n\\(\\frac{11}{3}\\)<br \/>\n________<\/p>\n<p>Answer: 3.66<\/p>\n<p>Explanation:<br \/>\nRewrite as a mixed number and then divide 2 by 3 to get the decimal part of the number.<br \/>\n\\(\\frac{11}{3}\\) = 3 2\/3 = 3.666&#8230;<br \/>\nSince 3.66.. has a decimal, it is not an integer or whole number. Therefore it is a rational number only.<\/p>\n<p>Question 4.<br \/>\n\\(\\frac{5}{2}\\)<br \/>\n________<\/p>\n<p>Answer: 2.5<\/p>\n<p>Explanation:<br \/>\nWrite as a mixed number and then divide 1 by 2 to get the decimal part of the number a shortcut is to think of the fraction in terms of money. Half a dollar is $0.50 so one half equals 0.50 = 0.50<br \/>\nSince 2.5 has a decimal, it is not an integer or whole number. Therefore 2.5 is a rational number only.<\/p>\n<p><strong>Find each sum or difference.<\/strong><\/p>\n<p>Question 5.<br \/>\n\u22125 + 9.5<br \/>\n________<\/p>\n<p>Answer: 4.5<\/p>\n<p>Explanation:<br \/>\nRewrite as subtraction and then subtract.<br \/>\n-5 + 9.5 = 4.5<\/p>\n<p>Question 6.<br \/>\n\\(\\frac{1}{6}\\) + (\u2212\\(\\frac{5}{6}\\))<br \/>\n\\(\\frac{\u25a1}{\u25a1}\\)<\/p>\n<p>Answer: &#8211;\\(\\frac{2}{3}\\)<\/p>\n<p>Explanation:<br \/>\nRewrite as subtraction and then subtract.<br \/>\n\\(\\frac{1}{6}\\) + (\u2212\\(\\frac{5}{6}\\))<br \/>\n\\(\\frac{1}{6}\\) \u2212\\(\\frac{5}{6}\\)<br \/>\n= &#8211;\\(\\frac{4}{6}\\) = &#8211;\\(\\frac{2}{3}\\)<\/p>\n<p>Question 7.<br \/>\n\u22120.5 + (\u22128.5)<br \/>\n________<\/p>\n<p>Answer: -9<\/p>\n<p>Explanation:<br \/>\nBoth numbers are negative so add their opposites and write the answers as a negative.<br \/>\n\u22120.5 + (\u22128.5) = -(0.5 + 8.5) = -9<\/p>\n<p>Question 8.<br \/>\n\u22123 \u2212 (\u22128)<br \/>\n________<\/p>\n<p>Answer: 5<\/p>\n<p>Explanation:<br \/>\nRewrite as addition since subtracting a negative is the same as adding a positive.<br \/>\n\u22123 \u2212 (\u22128) = -3 + 8 = 5<\/p>\n<p>Question 9.<br \/>\n5.6 \u2212 (\u22123.1)<br \/>\n________<\/p>\n<p>Answer: 8.7<\/p>\n<p>Explanation:<br \/>\nRewrite as addition since subtracting a negative is the same as adding a positive.<br \/>\n5.6 \u2212 (\u22123.1) = 5.6 + 3.1 = 8.7<\/p>\n<p>Question 10.<br \/>\n3 \\(\\frac{1}{2}\\) \u2212 2 \\(\\frac{1}{4}\\)<br \/>\n\\(\\frac{\u25a1}{\u25a1}\\)<\/p>\n<p>Answer: 1 \\(\\frac{1}{4}\\)<\/p>\n<p>Explanation:<br \/>\nGet common denominator.<br \/>\n3 \\(\\frac{1}{2}\\) \u2212 2 \\(\\frac{1}{4}\\)<br \/>\n3 \\(\\frac{2}{4}\\) \u2212 2 \\(\\frac{1}{4}\\) = 1 \\(\\frac{1}{4}\\)<\/p>\n<p><strong>Find each product or quotient<\/strong><\/p>\n<p>Question 11.<br \/>\n\u22129 \u00d7 (\u22125)<br \/>\n________<\/p>\n<p>Answer: 45<\/p>\n<p>Explanation:<br \/>\nMultiply two negative numbers make a positive number.<br \/>\n\u22129 \u00d7 (\u22125) = 45<\/p>\n<p>Question 12.<br \/>\n0 \u00d7 (\u22127)<br \/>\n________<\/p>\n<p>Answer: 0<\/p>\n<p>Explanation:<br \/>\nAny number multiplied with 0 will be zero.<br \/>\nSo, the product is 0.<\/p>\n<p>Question 13.<br \/>\n\u22128 \u00d7 8<br \/>\n________<\/p>\n<p>Answer: -64<\/p>\n<p>Explanation:<br \/>\nMultiply since there is only one negative the answer is negative.<br \/>\n-8 \u00d7 8 = -64<\/p>\n<p>Question 14.<br \/>\n\\(\\frac{-56}{8}\\)<br \/>\n________<\/p>\n<p>Answer: -7<\/p>\n<p>Explanation:<br \/>\nDivide since there is only one negative the answer is negative.<br \/>\n8 divides 56 seven times.<br \/>\n\\(\\frac{-56}{8}\\) = -7<\/p>\n<p>Question 15.<br \/>\n\\(\\frac{-130}{-5}\\)<\/p>\n<p>Answer: 26<\/p>\n<p>Explanation:<br \/>\nDivide since there are two negative signs the answer is positive.<br \/>\n\\(\\frac{-130}{-5}\\) = 26<\/p>\n<p>Question 16.<br \/>\n\\(\\frac{34.5}{1.5}\\)<br \/>\n________<\/p>\n<p>Answer: 23<\/p>\n<p>Explanation:<br \/>\nDivide since both the numbers are positive the answer will be positive.<br \/>\n\\(\\frac{34.5}{1.5}\\) = 23<br \/>\n1.5 divides 34.5 23 times.<br \/>\nSo, the quotient is 23.<\/p>\n<p>Question 17.<br \/>\n\\(-\\frac{2}{5}\\left(-\\frac{1}{2}\\right)\\left(-\\frac{5}{6}\\right)\\)<br \/>\n\\(\\frac{\u25a1}{\u25a1}\\)<\/p>\n<p>Answer: &#8211;\\(\\frac{1}{6}\\)<\/p>\n<p>Explanation:<br \/>\nMultiply by cancelling the 2s and 5s an odd number of negatives makes a negative so the answer is negative.<br \/>\n\\(-\\frac{2}{5}\\left(-\\frac{1}{2}\\right)\\left(-\\frac{5}{6}\\right)\\) = &#8211;\\(\\frac{1}{6}\\)<\/p>\n<p>Question 18.<br \/>\n\\(\\frac{1}{5}\\left(-\\frac{5}{7}\\right)\\left(\\frac{3}{4}\\right)\\)<br \/>\n\\(\\frac{\u25a1}{\u25a1}\\)<\/p>\n<p>Answer: &#8211;\\(\\frac{3}{28}\\)<\/p>\n<p>Explanation:<br \/>\n\\(\\frac{1}{5}\\left(-\\frac{5}{7}\\right)\\left(\\frac{3}{4}\\right)\\)<br \/>\nmultiply by cancelling the 5s<br \/>\n\\(\\frac{1}{5}\\left(-\\frac{5}{7}\\right)\\left(\\frac{3}{4}\\right)\\) = &#8211; 3\/7\u00d74 = -3\/28<br \/>\nThus \\(\\frac{1}{5}\\left(-\\frac{5}{7}\\right)\\left(\\frac{3}{4}\\right)\\) = &#8211;\\(\\frac{3}{28}\\)<\/p>\n<p>Question 19.<br \/>\nLei withdrew $50 from her bank account every day for a week. What was the change in her account in that week?<br \/>\n$ ________<\/p>\n<p>Answer: -$350<\/p>\n<p>Explanation:<br \/>\nLei withdrew $50 from her bank account every day for a week.<br \/>\nConvert from week to days<br \/>\n1 week = 7 days<br \/>\n7 \u00d7 -50 = -350<br \/>\nThe change in her account is -$350.<\/p>\n<p>Question 20.<br \/>\nDan is cutting 4.75 foot lengths of twine from a 240 foot spool of twine. He needs to cut 42 lengths, and says that 40.5 feet of twine will remain. Show that this is reasonable.<br \/>\nType below:<br \/>\n__________<\/p>\n<p>Answer:<br \/>\nThe estimation of 4.75 is 5 and 42 is 40.<br \/>\n5 \u00d7 40 = 200<br \/>\nSo he will be using about 200 feet.<br \/>\nHe has 240 feet so he will have about 240-200 = 40 feet remaining.<br \/>\nSince 40 \u2248 40.5<br \/>\nThe answer is reasonable.<\/p>\n<h3><a id=\"Unit_1_Performance_Tasks_Page_No_107\"><\/a>Unit 1 Performance Tasks &#8211; Page No. 107<\/h3>\n<p>Question 1.<br \/>\nArmand is an urban planner, and he has proposed a site for a new town library. The site is between City Hall and the post office on Main Street.<br \/>\n<img loading=\"lazy\" src=\"https:\/\/ccssmathanswers.com\/wp-content\/uploads\/2020\/08\/Go-Math-Grade-7-Answer-Key-Chapter-3-Rational-Numbers-img-8.jpg\" alt=\"Go Math Grade 7 Answer Key Chapter 3 Rational Numbers Unit 1 Performance Tasks img 8\" width=\"566\" height=\"44\" \/><br \/>\nThe distance between City Hall and the post office is 612 miles. City Hall is 114 miles closer to the library site than it is to the post office.<br \/>\na. Write 6 \\(\\frac{1}{2}\\) miles and 1 \\(\\frac{1}{4}\\) miles as decimals<br \/>\n6 \\(\\frac{1}{2}\\) = __________<br \/>\n1 \\(\\frac{1}{4}\\) = __________<\/p>\n<p>Answer:<br \/>\nWrite as decimal by dividing 1 by 2 and dividing 1 by 4 a shortcut is to think about ur in terms of money. Half of a dollae is $0.50 and a quarter is $0.25<br \/>\nSo 1\/2 = 0.50 = 0.5<br \/>\n1\/4 = 0.25<br \/>\n6 1\/2 = 6.5 and 1 1\/4 = 1.25<\/p>\n<p>Question 1.<br \/>\nb. Let d represent the distance from City Hall to the library site. Write an expression for the distance from the library site to the post office.<br \/>\n__________<\/p>\n<p>Answer:<br \/>\nThe library is closer to City Hall than the post office is so d is the difference between the distance from City Hall to the Post Office and the distance between City Hall and the Library Site.<br \/>\nd = 6 1\/2 &#8211; 1 1\/4<\/p>\n<p>Question 1.<br \/>\nc. Write an equation that represents the following statement: The distance from City Hall to the library site plus the distance from the library site to the post office is equal to the distance from City Hall to the post office.<br \/>\nType below:<br \/>\n__________<\/p>\n<p>Answer:<br \/>\nThe distance from the City Hall to the library is d, the distance from the library to the post office is 1 1\/4 since the library is 1 1\/4 miles closer to City Hall than the post office is, the distance from City Hall to the Post Office is 6 1\/4<br \/>\nd + 1 1\/4 = 6 1\/4<\/p>\n<p>Question 1.<br \/>\nd. Solve your equation from part c to determine the distance from City Hall to the library site, and the distance from the post office to the library site.<br \/>\nCity Hall to library site: __________ miles<br \/>\nLibrary site to post office: __________ miles<\/p>\n<p>Answer:<br \/>\nd = 6 1\/2 &#8211; 1 1\/4<br \/>\nd = 6 2\/4 &#8211; 1 1\/4<br \/>\nd = 5 1\/4<br \/>\nThus the distance is 5 1\/4 miles.<\/p>\n<p>Question 2.<br \/>\nSumaya is reading a book with 288 pages. She has already read 90 pages. She plans to read 20 more pages each day until she finishes the book.<br \/>\na. Sumaya writes the equation 378 = -20d to find the number of days she will need to finish the book. Identify the errors that Sumaya made.<br \/>\nType below:<br \/>\n__________<\/p>\n<p>Answer:<br \/>\nShe made the mistake of using -20 in the equation instead of a positive 20. The negative can&#8217;t be used since she is not reading a negative number of pages per day.<br \/>\nShe also made the mistake of adding 90 to 288 instead of subtracting.<br \/>\nSince she has already read 90 pages she has less than 288 pages left to read, not more.<br \/>\n288 &#8211; 90 = 198<br \/>\nThe correct equation is 198 = 20d<\/p>\n<p>Question 2.<br \/>\nb. Write and solve an equation to determine how many days Sumaya will need to finish the book. In your answer, count part of a day as a full day. Show that your answer is reasonable.<br \/>\n______ days<\/p>\n<p>Answer:<\/p>\n<p>198 = 20d is dividing both sides by 20 gives d = 198\/20 = 9.9<br \/>\nRounding this up gives 10 days.<br \/>\nThis answer is reasonable since the books is about 300 pages and she has read about 100 pages of the book leaving about 200 pages left to read.<br \/>\nShe is reading 20 pages per day and 20 \u00d7 10 = 200<br \/>\nSo it would take 10 days to read about 200 pages.<\/p>\n<p>Question 2.<br \/>\nc. Estimate how many days you would need to read a book about the same length as Sumaya\u2019s book. What information did you use to find the estimate?<br \/>\nType below:<br \/>\n__________<\/p>\n<p>Answer:<br \/>\nSumaya&#8217;s book is about 300 pages. Reading 20 pages a day would mean it would take about 300\/20 = 15 days to read the book.<\/p>\n<h3><a id=\"Unit_1_Performance_Tasks_Page_No_108\"><\/a>Unit 1 Performance Tasks &#8211; Page No. 108<\/h3>\n<p>Question 3.<br \/>\nJackson works as a veterinary technician and earns $12.20 per hour.<br \/>\na. Jackson normally works 40 hours a week. In a normal week, what is his total pay before taxes and other deductions?<br \/>\n$ ______<\/p>\n<p>Answer: $488<\/p>\n<p>Explanation:<br \/>\nJackson works as a veterinary technician and earns $12.20 per hour.<br \/>\nJackson normally works 40 hours a week.<br \/>\n40 \u00d7 $12.20 = $488<br \/>\nThus the total pay before taxes and other deductions is $488.<\/p>\n<p>Question 3.<br \/>\nb. Last week, Jackson was ill and missed some work. His total pay before deductions was $372.10. Write and solve an equation to find the number of hours Jackson worked.<br \/>\n______ hours<\/p>\n<p>Answer: 30.5 hours<\/p>\n<p>Explanation:<br \/>\nJackson works as a veterinary technician and earns $12.20 per hour.<br \/>\nHis total pay before deductions was $372.10.<br \/>\n$12.20h = $372.10<br \/>\nh = 372.10\/12.20<br \/>\nh = 30.5 hours<\/p>\n<p>Question 3.<br \/>\nc. Jackson records his hours each day on a time sheet. Last week when he was ill, his time sheet was incomplete. How many hours are missing? Show your work. Then show that your answer is reasonable.<br \/>\n<img loading=\"lazy\" src=\"https:\/\/ccssmathanswers.com\/wp-content\/uploads\/2020\/08\/Go-Math-Grade-7-Answer-Key-Chapter-3-Rational-Numbers-img-9.jpg\" alt=\"Go Math Grade 7 Answer Key Chapter 3 Rational Numbers Unit 1 MIXED REVIEW img 9\" width=\"357\" height=\"69\" \/><br \/>\n______ hours<\/p>\n<p>Answer: 6.75 hours<\/p>\n<p>Explanation:<br \/>\n8 + 7.25 + 8.5 = 23.75<br \/>\n30.5 &#8211; 23.75 = 6.75 hours<\/p>\n<p>Question 3.<br \/>\nd. When Jackson works more than 40 hours in a week, he earns 1.5 times his normal hourly rate for each of the extra hours. Jackson worked 43 hours one week. What was his total pay before deductions? Justify your answer.<br \/>\n$ __________________<\/p>\n<p>Answer: $542.90<\/p>\n<p>Explanation:<br \/>\nWhen Jackson works more than 40 hours in a week, he earns 1.5 times his normal hourly rate for each of the extra hours.<br \/>\nJackson worked 43 hours one week.<br \/>\n40 \u00d7 12.20 + 3 \u00d7 1.5 \u00d7 12.20 = $488 + $54.90 = $542.90<\/p>\n<p>Question 3.<br \/>\ne. What is a reasonable range for Jackson\u2019s expected yearly pay before deductions? Describe any assumptions you made in finding your answer.<br \/>\n$ __________________<\/p>\n<p>Answer:<\/p>\n<p>Assuming he works between 40 and 45 hours per week, his weekly pay range is between 40 \u00d7 12.20 = $488<br \/>\n40 \u00d7 12.20 + 5 \u00d7 1.5 \u00d7 12.20 = 488 + 91.50 = $579.50<br \/>\nSince there are 52 weeks in a year, his yearly pay is between 52 \u00d7 488 \u2248 $25,000<br \/>\nand 52 \u00d7 $579.50 \u2248 $30,000.<\/p>\n<h3><a id=\"Unit_1_MIXED_REVIEW_Selected_Response_Page_No_109\"><\/a>Unit 1 MIXED REVIEW &#8211; Selected Response &#8211; Page No. 109<\/h3>\n<p>Question 1.<br \/>\nWhat is \u22126 \\(\\frac{9}{16}\\) written as a decimal?<br \/>\nOptions:<br \/>\na. -6.625<br \/>\nb. -6.5625<br \/>\nc. -6.4375<br \/>\nd. -6.125<\/p>\n<p>Answer: -6.5625<\/p>\n<p>Explanation:<br \/>\n\u22126 \\(\\frac{9}{16}\\)<br \/>\nDivide 9 by 16 to get 9\/16 = 0.5625.<br \/>\n6 \\(\\frac{9}{16}\\) = 6 + 0.5625 = 6.5625<br \/>\n\u22126 \\(\\frac{9}{16}\\) = -6.5625<br \/>\nThus the correct answer is option B.<\/p>\n<p>Question 2.<br \/>\nWorking together, 6 friends pick 14 \\(\\frac{2}{5}\\) pounds of pecans at a pecan farm. They divide the pecans equally among themselves. How many pounds does each friend get?<br \/>\nOptions:<br \/>\na. 20 \\(\\frac{2}{5}\\) pounds<br \/>\nb. 8 \\(\\frac{2}{5}\\) pounds<br \/>\nc. 2 \\(\\frac{3}{5}\\) pounds<br \/>\nd. 2 \\(\\frac{2}{5}\\) pounds<\/p>\n<p>Answer: \\(\\frac{2}{5}\\) pounds<\/p>\n<p>Explanation:<br \/>\nDivide the number of pounds by the number of friends to get the number of pounds each friend gets.<br \/>\n14 \\(\\frac{2}{5}\\)\/6 = 14.4\/6 = 2.4 pounds.<br \/>\n2.4 = 2 \\(\\frac{2}{5}\\) pounds<br \/>\nThus the correct answer is option D.<\/p>\n<p>Question 3.<br \/>\nWhat is the value of (\u22123.25)(\u22121.56)?<br \/>\nOptions:<br \/>\na. -5.85<br \/>\nb. -5.07<br \/>\nc. 5.07<br \/>\nd. 5.85<\/p>\n<p>Answer: 5.07<\/p>\n<p>Explanation:<br \/>\nMultiply two negatives make a positive.<br \/>\nSo the answer is positive.<br \/>\n(\u22123.25)(\u22121.56) = 5.07<br \/>\nThe answer is option C.<\/p>\n<p>Question 4.<br \/>\nMrs. Rodriguez is going to use 6 \\(\\frac{1}{3}\\) yards of material to make two dresses. The larger dress requires 3 \\(\\frac{2}{3}\\) yards of material. How much material will Mrs. Rodriguez have left to use on the smaller dress?<br \/>\nOptions:<br \/>\na. 1 \\(\\frac{2}{3}\\) yards<br \/>\nb. 2 \\(\\frac{1}{3}\\) yards<br \/>\nc. 2 \\(\\frac{2}{3}\\) yards<br \/>\nd. 3 \\(\\frac{1}{3}\\) yards<\/p>\n<p>Answer: 2 \\(\\frac{2}{3}\\) yards<\/p>\n<p>Explanation:<br \/>\nSubtract the yards of material for the larger dress from the total yards of material.<br \/>\n6 \\(\\frac{1}{3}\\) yards &#8211; 3 \\(\\frac{2}{3}\\) yards = 2 \\(\\frac{2}{3}\\) yards<br \/>\nThus the correct answer is option C.<\/p>\n<p>Question 5.<br \/>\nJaime had $37 in his bank account on Sunday. The table shows his account activity for the next four days. What was the balance in Jaime\u2019s account after his deposit on Thursday?<br \/>\n<img loading=\"lazy\" src=\"https:\/\/ccssmathanswers.com\/wp-content\/uploads\/2020\/08\/Go-Math-Grade-7-Answer-Key-Chapter-3-Rational-Numbers-img-10.jpg\" alt=\"Go Math Grade 7 Answer Key Chapter 3 Rational Numbers Unit 1 MIXED REVIEW img 10\" width=\"358\" height=\"183\" \/><br \/>\nOptions:<br \/>\na. $57.49<br \/>\nb. $59.65<br \/>\nc. $94.49<br \/>\nd. $138.93<\/p>\n<p>Answer: $94.49<\/p>\n<p>Explanation:<br \/>\nAdd up all the deposits and withdrawals to his original balance make sure deposits are represented by positive numbers and withdrawals are represented by negative numbers.<br \/>\n37 + 17.42 &#8211; 12.60 &#8211; 9.62 + 62.29 = 94.49<br \/>\nThus the correct answer is option C.<\/p>\n<p>Question 6.<br \/>\nA used motorcycle is on sale for $3,600. Erik makes an offer equal to \\(\\frac{3}{4}\\) of this price. How much does Erik offer for the motorcycle?<br \/>\nOptions:<br \/>\na. $4800<br \/>\nb. $2700<br \/>\nc. $2400<br \/>\nd. $900<\/p>\n<p>Answer: $2700<\/p>\n<p>Explanation:<br \/>\nGiven that,<br \/>\nA used motorcycle is on sale for $3,600. Erik makes an offer equal to \\(\\frac{3}{4}\\) of this price.<br \/>\n\\(\\frac{3}{4}\\) \u00d7 3600 = 2700<br \/>\nThus the correct answer is option B.<\/p>\n<p>Question 7.<br \/>\nRuby ate \\(\\frac{1}{3}\\) of a pizza, and Angie ate \\(\\frac{1}{5}\\) of the pizza. How much of the pizza did they eat in all?<br \/>\nOptions:<br \/>\na. 1 \\(\\frac{1}{5}\\) of the pizza<br \/>\nb. \\(\\frac{1}{8}\\) of the pizza<br \/>\nc. \\(\\frac{3}{8}\\) of the pizza<br \/>\nd. \\(\\frac{8}{15}\\) of the pizza<\/p>\n<p>Answer: \\(\\frac{8}{15}\\) of the pizza<\/p>\n<p>Explanation:<br \/>\nRuby ate \\(\\frac{1}{3}\\) of a pizza, and Angie ate \\(\\frac{1}{5}\\) of the pizza.<br \/>\n\\(\\frac{1}{3}\\) = \\(\\frac{1}{5}\\) = \\(\\frac{5}{15}\\) + \\(\\frac{3}{15}\\) = \\(\\frac{8}{15}\\)<br \/>\nThus the correct answer is option D.<\/p>\n<h3><a id=\"Unit_1_MIXED_REVIEW_Page_No_110\"><\/a>Unit 1 MIXED REVIEW &#8211; Page No. 110<\/h3>\n<p>Question 8.<br \/>\nWinslow buys 1.2 pounds of bananas. The bananas cost $1.29 per pound. To the nearest cent, how much does Winslow pay for the bananas?<br \/>\nOptions:<br \/>\na. $1.08<br \/>\nb. $1.20<br \/>\nc. $1.55<br \/>\nd. $2.49<\/p>\n<p>Answer: $1.55<\/p>\n<p>Explanation:<br \/>\nWinslow buys 1.2 pounds of bananas. The bananas cost $1.29 per pound.<br \/>\n1.2 \u00d7 $1.29 = $1.548 \u2248 $1.55<br \/>\nThus the correct answer is option C.<\/p>\n<p>Question 9.<br \/>\nThe temperature was -10 \u00b0F and dropped by 16 \u00b0F. Which statement represents the resulting temperature in degrees Fahrenheit?<br \/>\nOptions:<br \/>\na. -10 &#8211; (-16) = -6<br \/>\nb. -10 &#8211; 16 = -26<br \/>\nc. 10 &#8211; (-16) = 26<br \/>\nd. -10 + 16 = 6<\/p>\n<p>Answer: -10 &#8211; 16 = -26<\/p>\n<p>Explanation:<br \/>\nThe temperature was -10 \u00b0F and dropped by 16 \u00b0F.<br \/>\n-10 + (-16) = -26\u00b0F.<br \/>\nSo, the correct answer is option B.<\/p>\n<p>Question 10.<br \/>\nA scuba diver at a depth of -12 ft (12 ft below sea level), dives down to a coral reef that is 3.5 times the diver\u2019s original depth. What is the diver\u2019s new depth?<br \/>\nOptions:<br \/>\na. -420 ft<br \/>\nb. -42 ft<br \/>\nc. 42 ft<br \/>\nd. about 3.4 ft<\/p>\n<p>Answer: -42 ft<\/p>\n<p>A scuba diver at a depth of -12 ft, dives down to a coral reef that is 3.5 times the diver\u2019s original depth.<br \/>\n-12 \u00d7 3.5 = -42 ft<br \/>\nSo, the correct answer is option B.<\/p>\n<p>Question 11.<br \/>\nThe school Spirit Club spent $320.82 on food and took in 643.59 selling the food. How much did the Spirit Club make?<br \/>\nOptions:<br \/>\na. -$322.77<br \/>\nb. -$964.41<br \/>\nc. $322.77<br \/>\nd. $964.41<\/p>\n<p>Answer: $322.77<\/p>\n<p>Explanation:<br \/>\nThe school Spirit Club spent $320.82 on food and took in 643.59 selling the food.<br \/>\n$643.59 &#8211; $320.82 = $322.77<br \/>\nSo, the answer is option C.<\/p>\n<p>Question 12.<br \/>\nLila graphed the points -2 and 2 on a number line. What does the distance between these two points represent?<br \/>\nOptions:<br \/>\na. the sum of -2 and 2<br \/>\nb. the difference of 2 and -2<br \/>\nc. the difference of -2 and 2<br \/>\nd. the product of -2 and 2<\/p>\n<p>Answer: the difference of 2 and -2<\/p>\n<p>Explanation:<br \/>\nDistance is found by subtracting the larger number and the smaller number so it is the difference of 2 and -2.<br \/>\nThus the correct answer is option B.<\/p>\n<p>Question 13.<br \/>\nWhat is a reasonable estimate of \u22123 \\(\\frac{4}{5}\\) + (\u22125.25) and the actual value?<br \/>\nOptions:<br \/>\na. -4 + (-5) = -9; \u22129 \\(\\frac{1}{20}\\)<br \/>\nb. -3 + (-5) = -8; \u22128 \\(\\frac{1}{20}\\)<br \/>\nc. -4 + (-5) = -1; \u22128 \\(\\frac{9}{20}\\)<br \/>\nd. -3 + (-5) = 8; 8 \\(\\frac{1}{20}\\)<\/p>\n<p>Answer: -4 + (-5) = -9; \u22129 \\(\\frac{1}{20}\\)<\/p>\n<p>Explanation:<br \/>\n\u22123 \\(\\frac{4}{5}\\) + (\u22125.25)<br \/>\n\u22123 \\(\\frac{4}{5}\\) \u2248 -4<br \/>\n\u22125.25 \u2248 -5<br \/>\nSo the sum is about -4 + -5 = -9.<br \/>\nThe estimated answer is -9.<\/p>\n<p><strong>Mini-Task<\/strong><\/p>\n<p>Question 14.<br \/>\nJuanita is watering her lawn using the water stored in her rainwater tank. The water level in the tank drops \\(\\frac{1}{3}\\) inch every 10 minutes she waters.<br \/>\na. What is the change in the tank\u2019s water level after 1 hour?<br \/>\n______ inches<\/p>\n<p>Answer: -2 inches<\/p>\n<p>Explanation:<br \/>\nJuanita is watering her lawn using the water stored in her rainwater tank.<br \/>\nThere are six 10 minute intervals in 1 hour so change is<br \/>\n6 \u00d7 &#8211;\\(\\frac{1}{3}\\) = -2 inches<br \/>\nTherefore, the tank&#8217;s water level after 1 hour is -2 inches.<\/p>\n<p>Question 14.<br \/>\nb. What is the expected change in the tank\u2019s water level after 2.25 hours?<br \/>\n______ inches<\/p>\n<p>Answer: -4.5 inches<\/p>\n<p>Explanation:<br \/>\nSince the water level drops 2 inches every hour, in 2.25 hours the water level change will be -2 \u00d7 2.25 = -4.5 inches<br \/>\nThus the expected change in the tank\u2019s water level after 2.25 hours is -4.5 inches.<\/p>\n<p>Question 14.<br \/>\nc. If the tank\u2019s water level is 4 feet, how many days can Juanita water if she waters for 15 minutes each day?<br \/>\n______ days<\/p>\n<p>Answer: 96 days<\/p>\n<p>Explanation:<br \/>\n15 minutes is 1\/4 of an hour so in 15 minutes the water level will have dropped by 2 \u00d7 1\/4 = 1\/2 inches.<br \/>\nSince the water level is initially 4 feet = 48 inches<br \/>\nShe can water for 48\/1\/2 = 48 \u00d7 2 = 96 days<br \/>\nIt takes 96 days if she waters for 15 minutes.<\/p>\n<p><em>Conclusion:<\/em><\/p>\n<p>Hope the info prevailed in this article is beneficial for all the students. Keep in touch with us to get the latest updates regarding Go Math Grade 7 Answer Key Chapter 3 Rational Numbers. Also, the students of 4th grade can get the solutions for all the chapters on Go Math Grade 7 Answer Key page.<\/p>\n","protected":false},"excerpt":{"rendered":"<p>Get expert verified solutions in Go Math Grade 7 Answer Key Chapter 3 Rational Numbers here. 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