{"id":5849,"date":"2022-03-27T15:46:29","date_gmt":"2022-03-27T10:16:29","guid":{"rendered":"https:\/\/ccssmathanswers.com\/?p=5849"},"modified":"2022-04-07T12:57:13","modified_gmt":"2022-04-07T07:27:13","slug":"go-math-grade-7-answer-key-chapter-4-rates-and-proportionality","status":"publish","type":"post","link":"https:\/\/bigideasmathanswers.com\/go-math-grade-7-answer-key-chapter-4-rates-and-proportionality\/","title":{"rendered":"Go Math Grade 7 Answer Key Chapter 4 Rates and Proportionality"},"content":{"rendered":"<p>Students who are in search of the HMH Go Math Chapter 4 Rates and Proportionality Answer Key can get them on this page. With the help of the <a href=\"https:\/\/ccssmathanswers.com\/go-math-grade-7-answer-key\/\" target=\"_blank\" rel=\"noopener noreferrer\">Go Math Grade 7 Answer Key<\/a> 4th Chapter Rates and Proportionality parents can teach simple methods to solve the problems to their children. So, Download Go Math Grade 7 Rates and Proportionality Chapter 4 pdf for free of cost.<\/p>\n<h2>Go Math Grade 7 Answer Key Chapter 4 Rates and Proportionality<\/h2>\n<p>It is important for the students to learn the concepts given in Go Math Grade 7 Chapter 4 Answer Key to score the highest marks in the exams. The quick way of solving the problems will help you to save time in the exam. The topics covered in this chapter are Unit rates, Constant Rates of Change, Proportional Relationships, and Graphs. Click on the below-provided links and go through all the questions and answers.<\/p>\n<p><strong>Chapter 4 &#8211; Unit Rates<\/strong><\/p>\n<ul>\n<li><a href=\"#Unit_Rates_Guided_Practice_Page_No_120\">Unit Rates &#8211; Guided Practice &#8211; Page No. 120<\/a><\/li>\n<li><a href=\"#Unit_Rates_Independent_Practice_Page_No_121\">Unit Rates &#8211; Independent Practice &#8211; Page No. 121<\/a><\/li>\n<li><a href=\"#Unit_Rates_Page_No_122\">Unit Rates &#8211; Page No. 122<\/a><\/li>\n<\/ul>\n<p><strong>Chapter 4 &#8211; Constant Rates of Change<\/strong><\/p>\n<ul>\n<li><a href=\"#Constant_Rates_of_Change_Guided_Practice_Page_No_126\">Constant Rates of Change &#8211; Guided Practice &#8211; Page No. 126<\/a><\/li>\n<li><a href=\"#Constant_Rates_of_Change_Page_No_127\">Constant Rates of Change &#8211; Page No. 127<\/a><\/li>\n<li><a href=\"#Constant_Rates_of_Change_Page_No_128\">Constant Rates of Change &#8211; Page No. 128<\/a><\/li>\n<\/ul>\n<p><strong>Chapter 4 &#8211; Proportional Relationships and Graphs<\/strong><\/p>\n<ul>\n<li><a href=\"#Proportional_Relationships_and_Graphs_Guided_Practice_Page_No_132\">Proportional Relationships and Graphs &#8211; Guided Practice &#8211; Page No. 132<\/a><\/li>\n<li><a href=\"#Proportional_Relationships_and_Graphs_Guided_Practice_Page_No_133\">Proportional Relationships and Graphs &#8211; Guided Practice &#8211; Page No. 133<\/a><\/li>\n<li><a href=\"#Proportional_Relationships_and_Graphs_Page_No_134\">Proportional Relationships and Graphs &#8211; Page No. 134<\/a><\/li>\n<\/ul>\n<p><strong>Chapter 4 &#8211; Module 4<\/strong><\/p>\n<ul>\n<li><a href=\"#MODULE_QUIZ_4.1_Unit_Rates_Page_No_135\">MODULE QUIZ &#8211; 4.1 Unit Rates &#8211; Page No. 135<\/a><\/li>\n<li><a href=\"#MIXED_REVIEW_Selected_Response_Page_No_136\">MIXED REVIEW &#8211; Selected Response &#8211; Page No. 136<\/a><\/li>\n<li><a href=\"#Module_4_Page_No_161\">Module 4 &#8211; Page No. 161<\/a><\/li>\n<\/ul>\n<h3><a id=\"Unit_Rates_Guided_Practice_Page_No_120\"><\/a>Unit Rates &#8211; Guided Practice &#8211; Page No. 120<\/h3>\n<p>Question 1.<br \/>\nBrandon enters bike races. He bikes 8 \\(\\frac{1}{2}\\) miles every \\(\\frac{1}{2}\\) hour. Complete the table to find how far Brandon bikes for each time interval<br \/>\n<img loading=\"lazy\" src=\"https:\/\/ccssmathanswers.com\/wp-content\/uploads\/2020\/08\/Go-Math-Grade-7-Answer-Key-Chapter-4-Rates-and-Proportionality-img-1.jpg\" alt=\"Go Math Grade 7 Answer Key Chapter 4 Rates and Proportionality Lesson 1: Unit Rates img 1\" width=\"398\" height=\"72\" \/><br \/>\nType below:<br \/>\n____________<\/p>\n<p>Answer:<br \/>\n1 hour: 8 \\(\\frac{1}{2}\\) + 8 \\(\\frac{1}{2}\\) = 17<br \/>\n1 \\(\\frac{1}{2}\\) hour: 17 + 8 \\(\\frac{1}{2}\\) = 25 \\(\\frac{1}{2}\\)<br \/>\n2 hour: 25 \\(\\frac{1}{2}\\) + 8 \\(\\frac{1}{2}\\) = 34<br \/>\n2 \\(\\frac{1}{2}\\) hour: 34 + 8 \\(\\frac{1}{2}\\) = 42 \\(\\frac{1}{2}\\)<\/p>\n<p><img loading=\"lazy\" class=\"alignnone size-medium wp-image-7565\" src=\"https:\/\/ccssmathanswers.com\/wp-content\/uploads\/2020\/08\/Go-Math-Grade-7-Answer-Key-Chapter-4-Rates-and-Proportionality-img-1-1-300x54.jpg\" alt=\"Go-Math-Grade-7-Answer-Key-Chapter-4-Rates-and-Proportionality-img-1\" width=\"300\" height=\"54\" srcset=\"https:\/\/bigideasmathanswers.com\/wp-content\/uploads\/2020\/08\/Go-Math-Grade-7-Answer-Key-Chapter-4-Rates-and-Proportionality-img-1-1-300x54.jpg 300w, https:\/\/bigideasmathanswers.com\/wp-content\/uploads\/2020\/08\/Go-Math-Grade-7-Answer-Key-Chapter-4-Rates-and-Proportionality-img-1-1.jpg 398w\" sizes=\"(max-width: 300px) 100vw, 300px\" \/><\/p>\n<p><strong>Find each unit rate.<\/strong><\/p>\n<p>Question 2.<br \/>\nJulio walks 3 \\(\\frac{1}{2}\\) miles in 1 \\(\\frac{1}{4}\\) hours.<br \/>\n________ \\(\\frac{\u25a1}{\u25a1}\\)<\/p>\n<p>Answer: 2 \\(\\frac{4}{5}\\)<\/p>\n<p>Explanation:<br \/>\nDivide the number of miles by the number of hours to find the unit rate in miles per hour.<br \/>\n3 \\(\\frac{1}{2}\\) \u00f7 1 \\(\\frac{1}{4}\\) = \\(\\frac{7}{2}\\)\/\\(\\frac{5}{4}\\)<br \/>\n\\(\\frac{7}{2}\\) \u00d7 \\(\\frac{4}{5}\\) = \\(\\frac{14}{5}\\)<br \/>\nConvert from improper fraction to the mixed fraction.<br \/>\n\\(\\frac{14}{5}\\) = 2 \\(\\frac{4}{5}\\) miles per hour<\/p>\n<p>Question 3.<br \/>\nKenny reads \\(\\frac{5}{8}\\) page in \\(\\frac{2}{3}\\) minute.<br \/>\n________ \\(\\frac{\u25a1}{\u25a1}\\)<\/p>\n<p>Answer: \\(\\frac{15}{16}\\)<\/p>\n<p>Explanation:<br \/>\nDivide the number of pages by the number of minutes to find the unit rate in pages per minute.<br \/>\n\\(\\frac{5}{8}\\) \u00f7 \\(\\frac{2}{3}\\)<br \/>\n= \\(\\frac{5}{8}\\) \u00d7 \\(\\frac{3}{2}\\) = \\(\\frac{15}{16}\\)<br \/>\nThus Kenny read \\(\\frac{15}{16}\\) pages per minute.<\/p>\n<p>Question 4.<br \/>\nA garden snail moves \\(\\frac{1}{6}\\) foot in \\(\\frac{1}{3}\\) hour.<br \/>\n\\(\\frac{\u25a1}{\u25a1}\\)<\/p>\n<p>Answer: \\(\\frac{1}{2}\\)<\/p>\n<p>Explanation:<br \/>\nGiven that,<br \/>\nA garden snail moves \\(\\frac{1}{6}\\) foot in \\(\\frac{1}{3}\\) hour.<br \/>\nDivide the number of feet by the number of hours to find the unit rate in feet per hour.<br \/>\n\\(\\frac{1}{6}\\) \u00f7 \\(\\frac{1}{3}\\)<br \/>\n\\(\\frac{1}{6}\\) \u00d7 \\(\\frac{3}{1}\\) = \\(\\frac{1}{2}\\)<br \/>\nTherefore A garden snail moves \\(\\frac{1}{2}\\) feet per hour.<\/p>\n<p>Question 5.<br \/>\nA fertilizer covers \\(\\frac{5}{8}\\) square foot in \\(\\frac{1}{4}\\) hour.<br \/>\n________ \\(\\frac{\u25a1}{\u25a1}\\)<\/p>\n<p>Answer: 2 \\(\\frac{1}{2}\\) square feet per hour<\/p>\n<p>Explanation:<br \/>\nGiven,<br \/>\nA fertilizer covers \\(\\frac{5}{8}\\) square foot in \\(\\frac{1}{4}\\) hour.<br \/>\nDivide the number of square feet, which is \\(\\frac{5}{8}\\) by the number of hours, which is \\(\\frac{1}{4}\\), to find the unit rate in square feet per hour.<br \/>\n\\(\\frac{5}{8}\\) \u00f7 \\(\\frac{1}{4}\\)<br \/>\n\\(\\frac{5}{8}\\) \u00d7 \\(\\frac{4}{1}\\) =\\(\\frac{5}{2}\\)<br \/>\nConvert from improper fraction to the mixed fraction.<br \/>\n\\(\\frac{5}{2}\\) = 2 \\(\\frac{1}{2}\\) square feet per hour<br \/>\nThus A fertilizer covers 2 \\(\\frac{1}{2}\\) square feet per hour.<\/p>\n<p><strong>Find each unit rate. Determine which is lower.<\/strong><\/p>\n<p>Question 6.<br \/>\nBrand A: 240 mg sodium for \\(\\frac{1}{3}\\) pickle or Brand B: 325 mg sodium for \\(\\frac{1}{2}\\) pickle.<br \/>\n____________<\/p>\n<p>Answer:<br \/>\nFind the unit rates in mg per pickle for each brand by dividing the number of mg by the number of pickles.<br \/>\nBrand A: 240 mg \u00f7 \\(\\frac{1}{3}\\) = 240 \u00d7 3 = 720<br \/>\nBrand B: 325 mg \u00f7 \\(\\frac{1}{2}\\) = 325 \u00d7 2 = 650<br \/>\n650 is less than 720 so Brand B has a lower unit rate.<\/p>\n<p>Question 7.<br \/>\nIngredient C: \\(\\frac{1}{4}\\) cup for \\(\\frac{2}{3}\\) serving or Ingredient D: \\(\\frac{1}{3}\\) cup for \\(\\frac{3}{4}\\) serving.<br \/>\n____________<\/p>\n<p>Answer: Find the unit rates in cups per serving by dividing the number of cups by the number of servings.<br \/>\nIngredient C: \\(\\frac{1}{4}\\) \u00f7 \\(\\frac{2}{3}\\)<br \/>\n\\(\\frac{1}{4}\\) \u00d7 \\(\\frac{3}{2}\\) = \\(\\frac{3}{8}\\)<br \/>\nIngredient D: \\(\\frac{1}{3}\\) \u00f7 \\(\\frac{3}{4}\\)<br \/>\n\\(\\frac{1}{3}\\) \u00d7 \\(\\frac{4}{3}\\) = \\(\\frac{4}{9}\\)<br \/>\n\\(\\frac{3}{8}\\) is less than \\(\\frac{4}{9}\\), ingredient C has a lower unit rate.<\/p>\n<p><strong>Essential Question Check-In<\/strong><\/p>\n<p>Question 8.<br \/>\nHow can you find a unit rate when given a rate?<br \/>\nType below:<br \/>\n____________<\/p>\n<p>Answer: To find a unit rate when given a rate such as 25 miles per 5 minutes, divide the first quantity by the second quantity.<br \/>\nIn the example I gave, this would mean the unit rate is 25 \u00f7 5 = 5 miles per minute.<\/p>\n<h3><a id=\"Unit_Rates_Independent_Practice_Page_No_121\"><\/a>Unit Rates &#8211; Independent Practice &#8211; Page No. 121<\/h3>\n<p><img loading=\"lazy\" src=\"https:\/\/ccssmathanswers.com\/wp-content\/uploads\/2020\/08\/Go-Math-Grade-7-Answer-Key-Chapter-4-Rates-and-Proportionality-img-2.jpg\" alt=\"Go Math Grade 7 Answer Key Chapter 4 Rates and Proportionality Lesson 1: Unit Rates img 2\" width=\"308\" height=\"98\" \/><\/p>\n<p>Question 9.<br \/>\nThe information for two pay-as-you-go cell phone companies is given.<br \/>\na. What is the unit rate in dollars per hour for each company?<br \/>\nOn Call: ____________ dollars per hour<br \/>\nTalk Time: ____________ dollars per hour<\/p>\n<p>Answer:<br \/>\nDivide the cost by the number of hours for each company to find the unit rates.<br \/>\nOn Call: 10 \u00f7 3.5 = 2 \\(\\frac{6}{7}\\) \u2248 2.86<br \/>\nTalk Time: 1.25 \u00f7 \\(\\frac{1}{2}\\) = 2.50<\/p>\n<p>Question 9.<br \/>\nb. Analyze Relationships<br \/>\nWhich company offers the best deal? Explain your answer.<br \/>\n____________<\/p>\n<p>Answer: Talk time has the lowest unit rate so it offers the best deal.<\/p>\n<p>Question 9.<br \/>\nc. What If?<br \/>\nAnother company offers a rate of $0.05 per minute. How would you find the unit rate per hour?<br \/>\n____________ dollars per hour<\/p>\n<p>Answer:<br \/>\nSince there are 60 minutes in 1 hour, $.0.05 per minute is<br \/>\n60 \u00d7 0.05 = $3 per hour.<br \/>\nThus the unit rate per hour is $3.<\/p>\n<p>Question 9.<br \/>\nd. Draw Conclusions<br \/>\nIs the rate in part c a better deal than On Call or Talk Time? Explain.<br \/>\n____________<\/p>\n<p>Answer:<br \/>\nThe unit rate in part c is greater than the unit rates from part a so it is not a better deal than the other two companies.<\/p>\n<p>Question 10.<br \/>\nRepresent Real-World Problems<br \/>\nYour teacher asks you to find a recipe that includes two ingredients with a rate of \\(\\frac{2 \\text { units }}{3 \\text { units }}\\).<br \/>\na. Give an example of two ingredients in a recipe that would meet this requirement.<br \/>\nType below:<br \/>\n____________<\/p>\n<p>Answer: A rate of 2\/3 units means that there need to be 2 units of 1 ingredient for every 3 units of a second ingredient.<br \/>\nOne example could then be 2 eggs per 3 cups of flour.<br \/>\nAnother example could 2 teaspoons of vanilla per 3 teaspoons of sugar.<\/p>\n<p>Question 10.<br \/>\nb. If you needed to triple the recipe, would the rate change? Explain.<br \/>\n____________<\/p>\n<p>Answer: No, the rate would not change. Using the example I gave in<br \/>\npart a) of 2 eggs per 3 cups of flour, tripling the recipe would require using 3(2 eggs) = 6 eggs<br \/>\n3(3 cups of sugar) = 9 cups of flour.<br \/>\nSince 6 eggs\/9 cups of flour = 2 eggs\/3 cups of flour, the rate is still the same.<\/p>\n<p>Question 11.<br \/>\nA radio station requires DJs to play 2 commercials for every 10 songs they play. What is the unit rate of songs to commercials?<br \/>\n____________ songs per commercials<\/p>\n<p>Answer: 10 \u00f7 2 = 5<br \/>\nDivide the number of songs by the number of commercials.<br \/>\nThus the radio requires 5 songs per commercial.<\/p>\n<p>Question 12.<br \/>\nMultistep<br \/>\nTerrance and Jesse are training for a long-distance race. Terrance trains at a rate of 6 miles every half hour and Jesse trains at a rate of 2 miles every 15 minutes.<br \/>\na. What is the unit rate in miles per hour for each runner?<br \/>\nTerrance: ____________ mi per hour<br \/>\nJesse: ____________ mi per hour<\/p>\n<p>Answer:<br \/>\nFind the unit rates for each runner by dividing the number of miles by the number of hours. Remember that 15 minutes is 1\/4 of an hour since there are 60 minutes in an hour<br \/>\n15 \u00f7 60 = 1\/4<br \/>\na) Terrance: 6 \u00f7 1\/2 = 6 \u00d7 2 = 12 miles per hour.<br \/>\nJesse: 2 \u00f7 1\/4 = 2 \u00d7 4 = 8 miles per hour.<\/p>\n<p>Question 12.<br \/>\nb. How long will each person take to run a total of 50 miles at the given rates?<br \/>\nTerrance: ______ \\(\\frac{\u25a1}{\u25a1}\\)<br \/>\nJesse: ______ \\(\\frac{\u25a1}{\u25a1}\\)<\/p>\n<p>Answer:<br \/>\nDivide the number of miles by the unit rates found in part a to find the time.<br \/>\nTerrance: 50 \u00f7 12 = 50\/12 = 4 \\(\\frac{1}{6}\\) hours<br \/>\nJesse: 50 \u00f7 8 = 50\/8 = 6 \\(\\frac{1}{4}\\) hours<\/p>\n<p>Question 12.<br \/>\nc. Sandra runs at a rate of 8 miles in 45 minutes. How does her unit rate compare to Terrance\u2019s and to Jesse\u2019s?<br \/>\n______ \\(\\frac{\u25a1}{\u25a1}\\) mi per hour<\/p>\n<p>Answer:<br \/>\nWe need to find the unit rate for Sandra by dividing the number of miles by the number of hours.<br \/>\nRemember that 45 minutes is 3\/4 of an hour.<br \/>\nSince 45\/60 = 3\/4.<br \/>\nSandra&#8217;s unit rate is smaller than Terrance&#8217;s but larger than Jesse&#8217;s.<\/p>\n<h3><a id=\"Unit_Rates_Page_No_122\"><\/a>Unit Rates &#8211; Page No. 122<\/h3>\n<p>Question 13.<br \/>\nAnalyze Relationships<br \/>\nEli takes a typing test and types all 300 words in \\(\\frac{1}{10}\\) hour. He takes the test a second time and types the words in \\(\\frac{1}{12}\\) hour. Was he faster or slower on the second attempt? Explain.<br \/>\n____________<\/p>\n<p>Answer:<br \/>\nWe need to find the unit rates for each time he took the test.<br \/>\n1st time: 300 \u00f7 1\/10 = 300 \u00d7 10 = 3000<br \/>\n2nd time: 300 \u00f7 1\/12 = 300 \u00d7 12 = 3600<br \/>\nThe second time has a faster unit rate since 3600 &gt; 3000.<\/p>\n<p>Question 14.<br \/>\nJustify Reasoning<br \/>\nAn online retailer sells two packages of protein bars.<br \/>\n<img loading=\"lazy\" src=\"https:\/\/ccssmathanswers.com\/wp-content\/uploads\/2020\/08\/Go-Math-Grade-7-Answer-Key-Chapter-4-Rates-and-Proportionality-img-3.jpg\" alt=\"Go Math Grade 7 Answer Key Chapter 4 Rates and Proportionality Lesson 1: Unit Rates img 3\" width=\"543\" height=\"95\" \/><br \/>\na. Which package has the better price per bar?<br \/>\n____________<\/p>\n<p>Answer:<br \/>\nFind the unit rates per bar by dividing the costs by the number of bars. the 12 pack has the better price per bar.<br \/>\n10-pack: 15.37 \u00f7 10 = 1.537 \u2248 1.54<br \/>\n12-pack: 15.35 \u00f7 12 \u2248 1.30<\/p>\n<p>Question 14.<br \/>\nb. Which package has the better price per ounce?<br \/>\n____________<\/p>\n<p>Answer:<br \/>\nFirst, find the total number of ounces by multiplying the number of bars times the number of ounces per bar. then find the unit rates per ounce by dividing the costs by the total number of ounces the 10-pack has the better price per ounce.<br \/>\n10-pack: 10 \u00d7 2.1 = 21 ounces<br \/>\n12-pack: 12 \u00d7 1.4 = 16.8 ounces<br \/>\n10-pack: 15.37 \u00f7 21 \u2248 0.73<br \/>\n12-pack: 15.35 \u00f7 16.8 \u2248 0.91<\/p>\n<p>Question 14.<br \/>\nc. Which package do you think is a better buy? Justify your reasoning.<br \/>\n____________<\/p>\n<p>Answer:<br \/>\nThe 10-pack is a better deal since the price per ounce is a better measure to use than price per bar. The number of bars doesn&#8217;t tell you how you are actually buying since the bars can be very small meaning the number of ounces you are actually buying is small.<\/p>\n<p>Question 15.<br \/>\nCheck for Reasonableness<br \/>\nA painter painted about half a room in half a day. Coley estimated the painter would paint 7 rooms in 7 days. Is Coley\u2019s estimate reasonable? Explain.<br \/>\n____________<\/p>\n<p>Answer:<br \/>\nIf a painter can paint half a room in a half day, then he can paint 1 room in 1 day.<br \/>\nThis would be equivalent to painting 7 rooms in 7 days so his estimate is reasonable.<br \/>\n7 rooms \u00f7 7 days = 1\/2 room \u00f7 1\/2 days<\/p>\n<p>Question 16.<br \/>\nCommunicate Mathematical<br \/>\nIdeas If you know the rate of a water leak in gallons per hour, how can you find the number of hours it takes for 1 gallon to leak out? Justify your answer.<br \/>\nType below:<br \/>\n____________<\/p>\n<p>Answer: If you know the rate in gallons per hour, then the rate in hours per gallon is the reciprocal of the rate in gallons per hour.<br \/>\nExample:<br \/>\nIf water is leaking at a rate of 5 gallons per hour, then it is leaking at 1\/5 hour per gallon.<\/p>\n<h3><a id=\"Constant_Rates_of_Change_Guided_Practice_Page_No_126\"><\/a>Constant Rates of Change &#8211; Guided Practice &#8211; Page No. 126<\/h3>\n<p>Question 1.<br \/>\nBased on the information in the table, is the relationship between time and the number of words typed a proportional relationship?<br \/>\n<img loading=\"lazy\" src=\"https:\/\/ccssmathanswers.com\/wp-content\/uploads\/2020\/08\/Go-Math-Grade-7-Answer-Key-Chapter-4-Rates-and-Proportionality-img-4.jpg\" alt=\"Go Math Grade 7 Answer Key Chapter 4 Rates and Proportionality Lesson 2: Constant Rates of Change img 4\" width=\"457\" height=\"66\" \/><br \/>\nThe relationship ____________ proportional<\/p>\n<p>Answer: is proportional<\/p>\n<p>Explanation:<br \/>\nSince 45 \u00f7 1 = 45, 90 \u00f7 2 = 45, 135 \u00f7 3 = 45 and 180 \u00f7 4 = 45, the relationship is proportional.<br \/>\nThus the relationship for the above table is proportional.<\/p>\n<p><strong>Find the constant of proportionality k. Then write an equation for the relationship between x and y.<\/strong><\/p>\n<p>Question 2.<br \/>\n<img loading=\"lazy\" src=\"https:\/\/ccssmathanswers.com\/wp-content\/uploads\/2020\/08\/Go-Math-Grade-7-Answer-Key-Chapter-4-Rates-and-Proportionality-img-5.jpg\" alt=\"Go Math Grade 7 Answer Key Chapter 4 Rates and Proportionality Lesson 2: Constant Rates of Change img 5\" width=\"345\" height=\"63\" \/><br \/>\nk = _______<\/p>\n<p>Answer: 5<\/p>\n<p>Explanation:<br \/>\nThe equation is of the form y = kx so k = y\/x.<br \/>\nSubstituting values of x and y from the table gives k = 10\/2 = 5.<br \/>\nPlugging this value into y = kx gives the equation y = 5x.<br \/>\nThe relationship between x and y is y = 5x.<\/p>\n<p>Question 3.<br \/>\n<img loading=\"lazy\" src=\"https:\/\/ccssmathanswers.com\/wp-content\/uploads\/2020\/08\/Go-Math-Grade-7-Answer-Key-Chapter-4-Rates-and-Proportionality-img-6.jpg\" alt=\"Go Math Grade 7 Answer Key Chapter 4 Rates and Proportionality Lesson 2: Constant Rates of Change img 6\" width=\"350\" height=\"64\" \/><br \/>\nk = \\(\\frac{\u25a1}{\u25a1}\\)<\/p>\n<p>Answer: k = \\(\\frac{1}{4}\\)<\/p>\n<p>Explanation:<br \/>\nThe equation is of the form y = kx so k = y\/x.<br \/>\nSubstituting values of x and y from the table gives k = 2\/8 = \\(\\frac{1}{4}\\).<br \/>\nPlugging this value into y = kx gives the equation y = \\(\\frac{1}{4}\\)x.<\/p>\n<p><strong>Essential Question Check-In<\/strong><\/p>\n<p>Question 4.<br \/>\nHow can you represent a proportional relationship using an equation?<br \/>\nType below:<br \/>\n____________<\/p>\n<p>Answer: y = kx<\/p>\n<p>Explanation:<br \/>\nA proportional relationship can always be represented by an equation of the form y = kx<br \/>\nwhere ks is the constant of proportionality and represents the rate of the change in the y quantity in relation to the x quantity.<\/p>\n<h3><a id=\"Constant_Rates_of_Change_Page_No_127\"><\/a>Constant Rates of Change &#8211; Page No. 127<\/h3>\n<p><strong>Information on three car-rental companies is given.<\/strong><br \/>\n<img loading=\"lazy\" src=\"https:\/\/ccssmathanswers.com\/wp-content\/uploads\/2020\/08\/Go-Math-Grade-7-Answer-Key-Chapter-4-Rates-and-Proportionality-img-7.jpg\" alt=\"Go Math Grade 7 Answer Key Chapter 4 Rates and Proportionality Lesson 2: Constant Rates of Change img 7\" width=\"351\" height=\"276\" \/><\/p>\n<p>Question 5.<br \/>\nWrite an equation that gives the cost y of renting a car for x days from Rent-All.<br \/>\ny = _______ x<\/p>\n<p>Answer: 18.50<\/p>\n<p>Explanation:<br \/>\nFind the constant of proportionality by dividing the total costs by the number of days.<br \/>\nk = 55.50\/3 = 18.50<br \/>\nThe equation is y = 18.50x<\/p>\n<p>Question 6.<br \/>\nWhat is the cost per day of renting a car from A-1?<br \/>\n$ _______ per day<\/p>\n<p>Answer: $21.98<\/p>\n<p>Explanation:<br \/>\nSince the cost of each half day is $10.99, the cost for each day is 2 \u00d7 10.99 = 21.98<br \/>\nThe cost per day of renting a car from A-1 is $21.98<\/p>\n<p>Question 7.<br \/>\nAnalyze Relationships<br \/>\nWhich company offers the best deal? Why?<br \/>\nThe company that offers the best deal is ____________<\/p>\n<p>Answer: Rent all<\/p>\n<p>Explanation:<br \/>\nThe costs per day were $18.50 for Rent-All, $21.98 for A-1 Rentals, and $19.25 for Car Town so Reant All offers the best deal since it offers the lowest cost per day.<br \/>\nThus the company that offers the best deal is Rent-All.<\/p>\n<p>Question 8.<br \/>\nCritique Reasoning<br \/>\nA skydiver jumps out of an airplane. After 0.8 second, she has fallen 100 feet. After 3.1 seconds, she has fallen 500 feet. Emtiaz says that the skydiver should fall about 187.5 feet in 1.5 seconds. Is his answer reasonable? Explain.<br \/>\n_______<\/p>\n<p>Answer: No. He assumed the rate of descent was proportional but the rate is increasing as time increases.<\/p>\n<p>Explanation:<br \/>\nSince 100 \u00f7 0.8 = 125 the skydiver fell at a speed of 125 ft per second for the first 0.8 second.<br \/>\nSince 500 \u00f7 3.1 = 161, the skydiver fell at a speed of about 161 ft per second for the first 3.1 seconds.<br \/>\nThe rate of descent is then increased as time increases and is not proportional since 125 \u2260 161.<br \/>\nSince 187.5 \u00f7 1.5 = 125, he assumed the rate of descent was proportional. His estimate is then not reasonable. The actual rate of descent should be between 125 and 161.3 since 1.5 seconds is between 0.8 and 3.1 seconds.<\/p>\n<p><strong>Steven earns extra money babysitting. He charges $31.25 for 5 hours and $50 for 8 hours.<\/strong><\/p>\n<p>Question 9.<br \/>\nExplain why the relationship between how much Steven charges and time is a proportional relationship.<br \/>\nType below:<br \/>\n____________<\/p>\n<p>Answer: The relationship is proportional since the ratios are equal.<\/p>\n<p>Explanation:<br \/>\nSince 31.25 \u00f7 5 = 6.25 and 50 \u2248 8 = 6.25 the relationship is proportional since the ratios are equal.<\/p>\n<p>Question 10.<br \/>\nInterpret the Answer<br \/>\nExplain what the constant rate of change means in the context.<br \/>\nType below:<br \/>\n____________<\/p>\n<p>Answer: The rate of change means he charges $6.25.<\/p>\n<p>Explanation:<br \/>\nThe constant rate of change of 6.25 means he charges $6.25 per hour since the rate was found by dividing the charge by the number of hours.<br \/>\nThe rate of change means he charges $6.25.<\/p>\n<p>Question 11.<br \/>\nWrite an equation to represent the relationship. Tell what the variables represent.<br \/>\nType below:<br \/>\n____________<\/p>\n<p>Answer: The equation is y = 6.25x<br \/>\nwhere x is the number of hours and ys is the total charge.<\/p>\n<p>Explanation:<br \/>\nThe rate of change is 6.25 so k = 6.25.<br \/>\nThis gives an equation of y = 6.25x where x is the number of hours and y is the total charge.<\/p>\n<p>Question 12.<br \/>\nHow much would Steven charge for 3 hours?<br \/>\n$ _______<\/p>\n<p>Answer: $18.75<\/p>\n<p>Explanation:<br \/>\ny = 6.25 \u00d7 3 = 18.75<br \/>\nThus Steve charges $18.75 for 3 hours.<\/p>\n<h3><a id=\"Constant_Rates_of_Change_Page_No_128\"><\/a>Constant Rates of Change &#8211; Page No. 128<\/h3>\n<p><strong>A submarine dives 300 feet every 2 minutes, and 6,750 feet every 45 minutes.<\/strong><\/p>\n<p>Question 13.<br \/>\nFind the constant rate at which the submarine dives. Give your answer in feet per minute and in feet per hour.<br \/>\n____________ feet per minute<br \/>\n____________ feet per hour<\/p>\n<p>Answer: 150 feet per minute, 9000 feet per hour<\/p>\n<p>Explanation:<br \/>\nSince 300 \u00f7 2 = 150, the submarine is diving at 150 feet per minute.<br \/>\nSince 45 minutes = 3\/4 of an hour and 6750 \u00f7 3\/4 = 9000, the submarine is diving at a rate of 9000 feet per hour.<\/p>\n<p>Question 14.<br \/>\nLet x represent the time of the dive. Let y represent the depth of the submarine. Write an equation for the proportional relationship using the rate in feet per minute.<br \/>\nType below:<br \/>\n____________<\/p>\n<p>Answer: y = 150x<\/p>\n<p>Explanation:<br \/>\nThe submarine was diving at a rate of 150 feet per minute so k = 150.<br \/>\nThe equation is then y = 150x.<\/p>\n<p>Question 15.<br \/>\nDraw Conclusions<br \/>\nIf you wanted to find the depth of a submarine during a dive, would it be more reasonable to use an equation with the rate in feet per minute or feet per hour? Explain your reasoning.<br \/>\n____________<\/p>\n<p>Answer: Feet per minute<\/p>\n<p>Explanation:<br \/>\nSince a submarine would only dive for a few minutes at a time and not dive for hours at a time, it is more reasonable to use the rate in feet per minute.<\/p>\n<p><strong>H.O.T.<\/strong><\/p>\n<p><strong>Focus on Higher Order Thinking<\/strong><\/p>\n<p>Question 16.<br \/>\nMake a Conjecture<br \/>\nThere is a proportional relationship between your distance from a thunderstorm and the time from when you see lightning and hear thunder. If there are 9 seconds between lightning and thunder, the storm is about 3 kilometers away. If you double the amount of time between lightning and thunder, do you think the distance in kilometers also double? justify your reasoning.<br \/>\n_______<\/p>\n<p>Answer: Yes the distance will also double. If the relationship is proportional then distance\/time = k<br \/>\nwhere k is the constant of proportionality.<br \/>\nSince the time was 9 seconds for 3km, then for 18 seconds the distance would be 6 km since 3\/9 = 6\/18.<br \/>\n6 is double 3 so the distance doubles when the time doubles.<\/p>\n<p>Question 17.<br \/>\nCommunicate Mathematical Ideas<br \/>\nA store sells 3 ears of corn for $1. They round prices to the nearest cent as shown in the table. Tell whether you would describe the relationship between cost and number of ears of corn as a proportional relationship. Justify your answer.<br \/>\n<img loading=\"lazy\" src=\"https:\/\/ccssmathanswers.com\/wp-content\/uploads\/2020\/08\/Go-Math-Grade-7-Answer-Key-Chapter-4-Rates-and-Proportionality-img-8.jpg\" alt=\"Go Math Grade 7 Answer Key Chapter 4 Rates and Proportionality Lesson 2: Constant Rates of Change img 8\" width=\"536\" height=\"69\" \/><br \/>\n_______<\/p>\n<p>Answer:<br \/>\nSince 0.33 \u00f7 1 = 0.33, 0.67 \u00f7 2 = 0.335, 1.00 \u00f7 3 = 0.33.., 1.34 \u00f7 4 = 0.335, the relationship is approximately proportional since all the ratios are approximately equal. The difference in the ratios com from rounding the amount charged to the nearest cent.<\/p>\n<p>Question 18.<br \/>\nJack is 12 and his sister Sophia is 16. Jack says that the relationship between his age and Sophia&#8217;s age is proportional and the constant of proportionality is \\(\\frac{12}{16}\\) Do you agree? Explain.<br \/>\n____________<\/p>\n<p>Answer:<br \/>\nGiven that current age of Jack = 12 years<br \/>\nGiven that current age of Sophia = 16 years<br \/>\nJack says that the relationship between his age and Sophia\u2018s is proportional<br \/>\nIf Jack&#8217;s age is represented by y and Sophia&#8217;s age by x then we can write y=kx as they are in proportion<br \/>\nwhere k is called constant of proportion<br \/>\nNow let&#8217;s plug given ages of each that is y=12 and x=16 into y=kx to find the constant of proportionality<br \/>\n12=k\u00d716<br \/>\n12\/16=k<br \/>\nWhich is the same as the given value of the constant of proportionality?<br \/>\nHence Jack is right about his statement.<br \/>\nBut if you think about practical life situation then the age of both will not be in proportion<br \/>\nFor example, after 1 year Jack&#8217;s age will be 13 and Sophie&#8217;s age will be 17<br \/>\nthen constant of proportionality using new values will be 13\/17<br \/>\nClearly 12\/16 and 13\/17 are not same.<br \/>\nSo in practical life, the age of both will not in proportion.<\/p>\n<p>Question 19.<br \/>\nLuke&#8217;s turkey chili recipe calls for 1.5 pounds of ground turkey for every 6 servings. How many servings can he make if he has 5 pounds of ground turkey? Show your work.<br \/>\n____________ servings<\/p>\n<p>Answer: 20 servings<\/p>\n<p>Explanation:<br \/>\nGiven,<br \/>\nLuke&#8217;s turkey chili recipe calls for 1.5 pounds of ground turkey for every 6 servings.<br \/>\nSo if 1.5 pounds of turkey can get you 6 servings<br \/>\n1.5 = 6<br \/>\n3 = 12<br \/>\n4.5 = 18<br \/>\n5 =?<br \/>\nto find what 5 pounds are equal to we must do 1.5\/6 to find the unit rate of 0.25. We then add 0.25 to 18.25 servings or if you round you can get about 18 servings.<br \/>\n18 + 0.25 \u00d7 8 = 18 + 2 = 20<\/p>\n<h3><a id=\"Proportional_Relationships_and_Graphs_Guided_Practice_Page_No_132\"><\/a>Proportional Relationships and Graphs &#8211; Guided Practice &#8211; Page No. 132<\/h3>\n<p><strong>Complete each table. Tell whether the relationship is a proportional relationship. Explain why or why not.<\/strong><\/p>\n<p>Question 1.<br \/>\nA student reads 65 pages per hour.<br \/>\n<img loading=\"lazy\" src=\"https:\/\/ccssmathanswers.com\/wp-content\/uploads\/2020\/08\/Go-Math-Grade-7-Answer-Key-Chapter-4-Rates-and-Proportionality-img-9.jpg\" alt=\"Go Math Grade 7 Answer Key Chapter 4 Rates and Proportionality Lesson 3: Proportional Relationships and Graphs img 9\" width=\"349\" height=\"96\" \/><br \/>\n____________<\/p>\n<p>Answer:<br \/>\nGiven that,<br \/>\nA student reads 65 pages per hour.<br \/>\n3 hours: 3 \u00d7 65 = 195 pages<br \/>\n5 hours: 5 \u00d7 65 = 325 pages<br \/>\n10 hours: 10 \u00d7 65 = 650 pages<br \/>\nWe need to find the number of hours for 585 pages by dividing the number of pages by 65 since the students read 65 pages per hour:<br \/>\n585 pages: 585 \u00f7 65 = 9 hours<br \/>\n<img loading=\"lazy\" class=\"alignnone size-medium wp-image-7526\" src=\"https:\/\/ccssmathanswers.com\/wp-content\/uploads\/2020\/08\/Go-Math-Grade-7-Answer-Key-Chapter-4-Rates-and-Proportionality-img-9-1-300x83.jpg\" alt=\"Go-Math-Grade-7-Answer-Key-Chapter-4-Rates-and-Proportionality-img-9\" width=\"300\" height=\"83\" srcset=\"https:\/\/bigideasmathanswers.com\/wp-content\/uploads\/2020\/08\/Go-Math-Grade-7-Answer-Key-Chapter-4-Rates-and-Proportionality-img-9-1-300x83.jpg 300w, https:\/\/bigideasmathanswers.com\/wp-content\/uploads\/2020\/08\/Go-Math-Grade-7-Answer-Key-Chapter-4-Rates-and-Proportionality-img-9-1.jpg 349w\" sizes=\"(max-width: 300px) 100vw, 300px\" \/><br \/>\nA relationship is proportional if the quotient of each ordered pair is constant. Since the student is reading at a constant rate of 65 pages per hour, and the quotient of each ordered pair in the table is 65, the relationship is proportional.<\/p>\n<p>Question 2.<br \/>\nA babysitter makes $7.50 per hour.<br \/>\n<img loading=\"lazy\" src=\"https:\/\/ccssmathanswers.com\/wp-content\/uploads\/2020\/08\/Go-Math-Grade-7-Answer-Key-Chapter-4-Rates-and-Proportionality-img-10.jpg\" alt=\"Go Math Grade 7 Answer Key Chapter 4 Rates and Proportionality Lesson 3: Proportional Relationships and Graphs img 10\" width=\"351\" height=\"94\" \/><br \/>\n____________<\/p>\n<p>Answer:<br \/>\n2 hours = 2 \u00d7 7.50 = 15<br \/>\n22.50 = 22.50 \u00f7 7.50 = 3 hours<br \/>\n5 hours = 5 \u00d7 7.50 = 37.50<br \/>\n6. = 60 \u00f7 7.50 = 8 hours<br \/>\n<img loading=\"lazy\" class=\"alignnone size-medium wp-image-7527\" src=\"https:\/\/ccssmathanswers.com\/wp-content\/uploads\/2020\/08\/Go-Math-Grade-7-Answer-Key-Chapter-4-Rates-and-Proportionality-img-10-1-300x80.jpg\" alt=\"Go-Math-Grade-7-Answer-Key-Chapter-4-Rates-and-Proportionality-img-10\" width=\"300\" height=\"80\" srcset=\"https:\/\/bigideasmathanswers.com\/wp-content\/uploads\/2020\/08\/Go-Math-Grade-7-Answer-Key-Chapter-4-Rates-and-Proportionality-img-10-1-300x80.jpg 300w, https:\/\/bigideasmathanswers.com\/wp-content\/uploads\/2020\/08\/Go-Math-Grade-7-Answer-Key-Chapter-4-Rates-and-Proportionality-img-10-1.jpg 351w\" sizes=\"(max-width: 300px) 100vw, 300px\" \/><\/p>\n<p><strong>Tell whether the relationship is a proportional relationship. Explain why or why not.<\/strong><\/p>\n<p>Question 3.<br \/>\n<img loading=\"lazy\" src=\"https:\/\/ccssmathanswers.com\/wp-content\/uploads\/2020\/08\/Go-Math-Grade-7-Answer-Key-Chapter-4-Rates-and-Proportionality-img-11.jpg\" alt=\"Go Math Grade 7 Answer Key Chapter 4 Rates and Proportionality Lesson 3: Proportional Relationships and Graphs img 11\" width=\"220\" height=\"226\" \/><br \/>\n____________<\/p>\n<p>Answer:<br \/>\nThe relationship has the points (2, 4) and (8, 10).<br \/>\nSince 4 \u00f7 2 = 2 and 10 \u00f7 8 = 1.25, the relationship is not proportional since the ratios are not equal.<\/p>\n<p>Question 4.<br \/>\n<img loading=\"lazy\" src=\"https:\/\/ccssmathanswers.com\/wp-content\/uploads\/2020\/08\/Go-Math-Grade-7-Answer-Key-Chapter-4-Rates-and-Proportionality-img-12.jpg\" alt=\"Go Math Grade 7 Answer Key Chapter 4 Rates and Proportionality Lesson 3: Proportional Relationships and Graphs img 12\" width=\"222\" height=\"232\" \/><br \/>\n____________<\/p>\n<p>Answer:<br \/>\nThe relationship appears to be proportional since the points appear to form a line that goes through the origin. That line would go through the points (1,2), (2, 4), (5, 10), and (8, 16).<br \/>\nSince 2 \u00f7 1 = 2, 4 \u00f7 2 = 2, 10 \u00f7 5 = 2, and 16 \u00f7 8 = 2, the relationship is proportional since all the ratios are equal.<\/p>\n<p><strong>Write an equation of the form y = kx for the relationship shown in each graph.<\/strong><\/p>\n<p>Question 5.<br \/>\n<img loading=\"lazy\" src=\"https:\/\/ccssmathanswers.com\/wp-content\/uploads\/2020\/08\/Go-Math-Grade-7-Answer-Key-Chapter-4-Rates-and-Proportionality-img-13.jpg\" alt=\"Go Math Grade 7 Answer Key Chapter 4 Rates and Proportionality Lesson 3: Proportional Relationships and Graphs img 13\" width=\"224\" height=\"203\" \/><br \/>\ny = ____________ x<\/p>\n<p>Answer: y = 3.5x<\/p>\n<p>Explanation:<br \/>\nOne of the points is (8, 28) so k = 28\/8 = 7\/2. The equation is the y = 7\/2 = 3.5x<\/p>\n<p>Question 6.<br \/>\n<img loading=\"lazy\" src=\"https:\/\/ccssmathanswers.com\/wp-content\/uploads\/2020\/08\/Go-Math-Grade-7-Answer-Key-Chapter-4-Rates-and-Proportionality-img-14.jpg\" alt=\"Go Math Grade 7 Answer Key Chapter 4 Rates and Proportionality Lesson 3: Proportional Relationships and Graphs img 14\" width=\"213\" height=\"209\" \/><br \/>\ny = ____________ x<\/p>\n<p>Answer: y = 0.25x<\/p>\n<p>Explanation:<br \/>\nOne of the points is (8,2) so k = 2\/8 = 1\/4.<br \/>\nThe equation is the ya = 1\/4x = 0.25 x.<\/p>\n<p><strong>Essential Question Check-In<\/strong><\/p>\n<p>Question 7.<br \/>\nHow does a graph show a proportional relationship?<br \/>\nType below:<br \/>\n____________<\/p>\n<p>Answer:<br \/>\nA proportional relationship between two variables, x and y, exists if y = kx.<br \/>\nThis equation is a line that passes through the origin and has a slope of k. The slope can be positive or negative. Therefore is the points lie on a line that goes through the origin, the graph shows a proportional relationship. If the points lie on a line that does not go through the origin, that is, has a non zero y-intercept, then the relationship is not proportional.<\/p>\n<h3><a id=\"Proportional_Relationships_and_Graphs_Guided_Practice_Page_No_133\"><\/a>Proportional Relationships and Graphs &#8211; Guided Practice &#8211; Page No. 133<\/h3>\n<p><strong>For Exercises 8\u201312, the graph shows the relationship between time and distance run by two horses.<\/strong><br \/>\n<img loading=\"lazy\" src=\"https:\/\/ccssmathanswers.com\/wp-content\/uploads\/2020\/08\/Go-Math-Grade-7-Answer-Key-Chapter-4-Rates-and-Proportionality-img-15.jpg\" alt=\"Go Math Grade 7 Answer Key Chapter 4 Rates and Proportionality Lesson 3: Proportional Relationships and Graphs img 15\" width=\"225\" height=\"206\" \/><\/p>\n<p>Question 8.<br \/>\nExplain the meaning of the point (0,0).<br \/>\nType below:<br \/>\n____________<\/p>\n<p>Answer: The point (0, 0) represents a distance of 0 miles in 0 min.<\/p>\n<p>Question 9.<br \/>\nHow long does it take each horse to run a mile?<br \/>\nHorse A runs 1 mile in ____________ minutes<br \/>\nHorse B runs 1 mile in ____________ minutes<\/p>\n<p>Answer: Horse A: 4 min per mile.<br \/>\nHorse B: 2.5 min per mile<\/p>\n<p>Explanation:<br \/>\nLine A goes through the point (8, 2) which gives a rate of 8\/2 = 4 min per mile. Line B goes through the point (10, 4) which gives a rate of 10\/4 = 2.5 min per mile.<\/p>\n<p>Question 10.<br \/>\nMultiple Representations<br \/>\nWrite an equation for the relationship between time and distance for each horse.<br \/>\nFor Horse A : y = ____________ x<br \/>\nFor Horse B : y = ____________ x<\/p>\n<p>Answer: A: y = 1\/4x, B: y = 2\/5x<\/p>\n<p>Explanation:<br \/>\nThe graph has x representing the time in minutes and y representing the distance in miles so the slope of the line has units of miles per minute.<br \/>\nSince horse A runs 4 min per mile, it runs at a rate of 1\/4 mi per min.<br \/>\nThis gives the equation y = 1\/4x.<br \/>\nSince horse B runs at a rate of 2.5 min per mi, it runs at a rate of 1\/2.5 = 2\/5 miles per min.<br \/>\nThe equation is then y = 2\/5x.<\/p>\n<p>Question 11.<br \/>\nDraw Conclusions<br \/>\nAt the given rates, how far would each horse run in 12 minutes?<br \/>\nHorse A will run ____________ miles<br \/>\nHorse B will run ____________ miles<\/p>\n<p>Answer: Horse A will run 3 miles.<br \/>\nHorse B will run 4.8 miles.<\/p>\n<p>Explanation:<br \/>\nMultiply the rates in mi per min from the above problem by the number of minutes.<br \/>\nA: 1\/4 mi per min \u00d7 12 min = 3 miles<br \/>\nB: 2\/5 mi per min \u00d7 12 min = 4.8 miles<\/p>\n<p>Question 12.<br \/>\nAnalyze Relationships<br \/>\nDraw a line on the graph representing a horse than runs faster than horses A and B.<br \/>\nType below:<br \/>\n____________<\/p>\n<p>Answer:<br \/>\nTo have a line representing at the rate of the horse faster than horses A and B, the line should be a little bit steeper than the other two lines. This can be represented in the graph as:<br \/>\n<img loading=\"lazy\" class=\"alignnone size-full wp-image-7550\" src=\"https:\/\/ccssmathanswers.com\/wp-content\/uploads\/2020\/08\/Go-Math-Grade-7-Answer-Key-Chapter-4-img-1.jpg\" alt=\"Go-Math-Grade-7-Answer-Key-Chapter-4-img-1\" width=\"209\" height=\"242\" \/><\/p>\n<p>Question 13.<br \/>\nA bullet train can travel at 170 miles per hour. Will a graph representing the distance in miles compared to the time in hours show a proportional relationship? Explain.<br \/>\n____________<\/p>\n<p>Answer: Yes<br \/>\nSince the train is travelling at a constant rate, a graph representing distance in miles compared to time in hours will show a proportional relationship.<\/p>\n<p>Question 14.<br \/>\nCritical Thinking<br \/>\nWhen would it be more useful to represent a proportional relationship with a graph rather than an equation?<br \/>\nType below:<br \/>\n____________<\/p>\n<p>Answer: It is more useful to represent a proportional relationship with a graph when comparing different and various situations.<\/p>\n<p>Question 15.<br \/>\nMultiple Representations<br \/>\nBargain DVDs cost $5 each at Mega Movie.<br \/>\na. Graph the proportional relationship that gives the cost y in dollars of buying x bargain DVDs.<br \/>\n<img loading=\"lazy\" src=\"https:\/\/ccssmathanswers.com\/wp-content\/uploads\/2020\/08\/Go-Math-Grade-7-Answer-Key-Chapter-4-Rates-and-Proportionality-img-16.jpg\" alt=\"Go Math Grade 7 Answer Key Chapter 4 Rates and Proportionality Lesson 3: Proportional Relationships and Graphs img 16\" width=\"230\" height=\"202\" \/><br \/>\nType below:<br \/>\n____________<\/p>\n<p>Answer:<br \/>\nSince each DVD is $5 each, make sure to graph a line that corresponds to this rate.<br \/>\n<img loading=\"lazy\" class=\"alignnone size-full wp-image-7552\" src=\"https:\/\/ccssmathanswers.com\/wp-content\/uploads\/2020\/08\/Go-Math-Grade-7-Answer-Key-Chapter-4-Rates-and-Proportionality-img-16-1.jpg\" alt=\"Go-Math-Grade-7-Answer-Key-Chapter-4-Rates-and-Proportionality-img-16\" width=\"230\" height=\"202\" \/><\/p>\n<p>Question 15.<br \/>\nb. Give an ordered pair on the graph and explain its meaning in the real world context.<br \/>\nType below:<br \/>\n____________<\/p>\n<p>Answer: An ordered pair in the graph is (3, 15) and this means that three DVDs cost $15.<\/p>\n<h3><a id=\"Proportional_Relationships_and_Graphs_Page_No_134\"><\/a>Proportional Relationships and Graphs &#8211; Page No. 134<\/h3>\n<p><strong>The graph shows the relationship between distance and time as Glenda swims.<\/strong><br \/>\n<img loading=\"lazy\" src=\"https:\/\/ccssmathanswers.com\/wp-content\/uploads\/2020\/08\/Go-Math-Grade-7-Answer-Key-Chapter-4-Rates-and-Proportionality-img-17.jpg\" alt=\"Go Math Grade 7 Answer Key Chapter 4 Rates and Proportionality Lesson 3: Proportional Relationships and Graphs img 17\" width=\"210\" height=\"206\" \/><\/p>\n<p>Question 16.<br \/>\nHow far did Glenda swim in 4 seconds?<br \/>\n______ feet<\/p>\n<p>Answer: 8 ft<\/p>\n<p>Explanation:<br \/>\nThe graph goes through the point (4, 8) so she swam 8 ft in 4 sec.<\/p>\n<p>Question 17.<br \/>\nCommunicate Mathematical Ideas<br \/>\nIs this a proportional relationship? Explain your reasoning.<br \/>\n____________<\/p>\n<p>Answer: The relationship is proportional since the points lie on a line and the line connecting the points goes through the origin.<\/p>\n<p>Question 18.<br \/>\nMultiple Representations<br \/>\nWrite an equation that shows the relationship between time and distance.<br \/>\nType below:<br \/>\n____________<\/p>\n<p>Answer: y = 2x<\/p>\n<p>Explanation:<br \/>\nThe line goes through the point (4, 8) which means k = 8\/4 = 2.<br \/>\nThis give an equation of y = 2x.<\/p>\n<p><strong>H.O.T.<\/strong><\/p>\n<p><strong>Focus on Higher Order Thinking<\/strong><\/p>\n<p>Question 19.<br \/>\nMake a Conjecture<br \/>\nIf you know that a relationship is proportional and are given one ordered pair that is not (0,0), how can you find another pair?<br \/>\nType below:<br \/>\n____________<\/p>\n<p>Answer:<br \/>\nIf you are given a point (a, b) that is not (0, 0) and that the relationship is proportional, then you can find k since k = y\/x = b\/a.<br \/>\nThen you can write the equation as y = b\/ax. From there, you can plug in any value for x to find the corresponding y-coordinate.<\/p>\n<p><strong>The tables show the distance traveled by three cars.<\/strong><br \/>\n<img loading=\"lazy\" src=\"https:\/\/ccssmathanswers.com\/wp-content\/uploads\/2020\/08\/Go-Math-Grade-7-Answer-Key-Chapter-4-Rates-and-Proportionality-img-18.jpg\" alt=\"Go Math Grade 7 Answer Key Chapter 4 Rates and Proportionality Lesson 3: Proportional Relationships and Graphs img 18\" width=\"640\" height=\"213\" \/><\/p>\n<p>Question 20.<br \/>\nCommunicate Mathematical Ideas<br \/>\nWhich car is not traveling at a constant speed? Explain your reasoning.<br \/>\n____________<\/p>\n<p>Answer:<br \/>\nSince 120 \u00f7 2 = 180 \u00f7 3 = 300 \u00f7 5 = 360 \u00f7 6 = 60, Car 1 is travelling at a constant speed.<br \/>\nSince 200 \u00f7 5 = 400 \u00f7 10 = 600 \u00f7 15 = 800 \u00f7 20 = 40, Car 2 is travelling at a constant speed.<br \/>\nSince 65 \u00f7 1 \u2260 85 \u00f7 2, Car 3 is not traveling at a constant speed.<\/p>\n<p>Question 21.<br \/>\nMake a Conjecture<br \/>\nCar 4 is traveling at twice the rate of speed of car 2. How will the table values for car 4 compare to the table values for car 2?<br \/>\nType below:<br \/>\n____________<\/p>\n<p>Answer:<br \/>\nFrom problem 20, car 2 is traveling at 40 miles per hour. If car 4 is traveling twice that rate, then it is traveling at 80 miles per hour. This means all the values for the distances for car 4 will be double the values for the distances for car 2.<\/p>\n<h3><a id=\"MODULE_QUIZ_4.1_Unit_Rates_Page_No_135\"><\/a>MODULE QUIZ &#8211; 4.1 Unit Rates &#8211; Page No. 135<\/h3>\n<p><strong>Find each unit rate. Round to the nearest hundredth, if necessary.<\/strong><\/p>\n<p>Question 1.<br \/>\n$140 for 18 ft<sup>2<\/sup><br \/>\n$ ______<\/p>\n<p>Answer: $7.78 per ft<sup>2<\/sup><\/p>\n<p>Explanation:<br \/>\nDivide the cost of $140 by the number of square feet, 18 sq. ft, using a calculator:<br \/>\n140 \u00f7 18 \u2248 $7.78 per sq. ft.<br \/>\nIf you are required by your teacher to do the division by hand, divide to three decimal points as shown below:<br \/>\nSince the dollar amounts must be rounded to two decimal places, then $7.77.. \u2248 $7.78 so the cost per square foot is $7.78 sq. ft.<\/p>\n<p>Question 1.<br \/>\n14 lb for $2.99<br \/>\n$ ______<\/p>\n<p>Answer: $0.21 per lb<\/p>\n<p>Explanation:<br \/>\nDivide the cost by the number of pounds.<br \/>\n2.99 \u00f7 14 = $0.21<\/p>\n<p><strong>Circle the better deal in each pair. Then give the unit rate for the better deal.<\/strong><\/p>\n<p>Question 3.<br \/>\n\\(\\frac{\\$ 56}{25 \\text { gal }} or \\frac{\\$ 32.05}{15 \\text { gal }}\\)<br \/>\n____________<\/p>\n<p>Answer:<br \/>\nBetter deal: $32.05\/15 gal<br \/>\nUnit rate: $2.14 per gal<\/p>\n<p>Explanation:<br \/>\nFind the unit rates by dividing the cost by the number of gallons:<br \/>\n$56\/25 gal = $2.24 per gal<br \/>\n$32.05\/15 gal \u2248 $2.14 per gal<br \/>\nSince 2.14 &lt; 2.24, then the better deal is $32.25\/15 gal.<\/p>\n<p>Question 4.<br \/>\n\\(\\frac{\\$ 160}{5 \\mathrm{g}} \\text { or } \\frac{\\$ 315}{9 \\mathrm{g}}\\)<br \/>\n____________<\/p>\n<p>Answer:<br \/>\nBetter deal: $160\/5g<br \/>\nUnit rate: $32 per gram<\/p>\n<p>Explanation:<br \/>\nFind the unit rates by dividing the cost by the number of grams:<br \/>\n$160\/5 g = $32 per gram<br \/>\n$315\/9 g = $35 per gram<br \/>\nSince 32 &lt; 35, then the better deal is $160\/5 g.<\/p>\n<p><strong>4.2 Constant Rates of Change<\/strong><\/p>\n<p>Question 5.<br \/>\nThe table shows the amount of money Tyler earns for mowing lawns. Is the relationship a proportional relationship? Why or why not?<br \/>\n<img loading=\"lazy\" src=\"https:\/\/ccssmathanswers.com\/wp-content\/uploads\/2020\/08\/Go-Math-Grade-7-Answer-Key-Chapter-4-Rates-and-Proportionality-img-19.jpg\" alt=\"Go Math Grade 7 Answer Key Chapter 4 Rates and Proportionality MODULE QUIZ img 19\" width=\"307\" height=\"95\" \/><br \/>\n____________<\/p>\n<p>Answer: not proportional<\/p>\n<p>Explanation:<br \/>\nSince 15 \u00f7 1 = 15 but 48 \u00f7 3 = 16, the relationship is not proportional.<\/p>\n<p>Question 6.<br \/>\nOn a recent day, 8 euros were worth $9 and 24 euros were worth $27. Write an equation of the form y = kx to show the relationship between the number of euros and the value in dollars.<br \/>\nType below:<br \/>\n____________<\/p>\n<p>Answer: y = \\(\\frac{9}{8}\\)x<\/p>\n<p>Explanation:<br \/>\nk = \\(\\frac{value in dollars}{number of euros}\\) = \\(\\frac{9}{8}\\)<br \/>\nso, the equation is y = \\(\\frac{9}{8}\\)x<\/p>\n<p><strong>4.3 Proportional Relationships and Graphs<\/strong><\/p>\n<p>Question 7.<br \/>\nThe graph shows the number of servings in different amounts of frozen yogurt listed on a carton. Write an equation that gives the number of servings y in x pints.<br \/>\n<img loading=\"lazy\" src=\"https:\/\/ccssmathanswers.com\/wp-content\/uploads\/2020\/08\/Go-Math-Grade-7-Answer-Key-Chapter-4-Rates-and-Proportionality-img-20.jpg\" alt=\"Go Math Grade 7 Answer Key Chapter 4 Rates and Proportionality MODULE QUIZ img 20\" width=\"207\" height=\"235\" \/><br \/>\nType below:<br \/>\n____________<\/p>\n<p>Answer: y = \\(\\frac{5}{2}\\)x<\/p>\n<p>Explanation:<br \/>\nThe graph goes through the point (2, 5) so k = \\(\\frac{5}{2}\\).<br \/>\nThis gives an equation of y = \\(\\frac{5}{2}\\)x<\/p>\n<p>Question 8.<br \/>\nA refreshment stand makes 2 large servings of frozen yogurt from 3 pints. Add the line to the graph and write its equation.<br \/>\nType below:<br \/>\n____________<\/p>\n<p>Answer: y =\u00a0\\(\\frac{2}{3}\\)x<\/p>\n<p>Explanation:<br \/>\nIf the situation states that 2 servings of frozen yogurt can be made from 3 pints, then we can say that k = \\(\\frac{2}{3}\\), and therefore the equation of the line is y = \\(\\frac{2}{3}\\)x. The graph of the line is shown below.<br \/>\n<img loading=\"lazy\" class=\"alignnone size-full wp-image-7563\" src=\"https:\/\/ccssmathanswers.com\/wp-content\/uploads\/2020\/08\/Go-Math-Grade-7-Answer-Key-Chapter-4-img-2.jpg\" alt=\"Go-Math-Grade-7-Answer-Key-Chapter-4-img-2\" width=\"209\" height=\"242\" \/><\/p>\n<p><strong>Essential Question<\/strong><\/p>\n<p>Question 9.<br \/>\nHow can you use rates to determine whether a situation is a proportional relationship?<br \/>\nType below:<br \/>\n____________<\/p>\n<p>Answer: If the rate is constant, then the situation is a proportional relationship. If the rate is not constant, the situation cannot be a proportional relationship.<\/p>\n<h3><a id=\"MIXED_REVIEW_Selected_Response_Page_No_136\"><\/a>MIXED REVIEW &#8211; Selected Response &#8211; Page No. 136<\/h3>\n<p>Question 1.<br \/>\nKori spent $46.20 on 12 gallons of gasoline. What was the price per gallon?<br \/>\nOptions:<br \/>\na. $8.35<br \/>\nb. $3.85<br \/>\nc. $2.59<br \/>\nd. $0.26<\/p>\n<p>Answer: $3.85<\/p>\n<p>Explanation:<br \/>\nGiven that,<br \/>\nKori spent $46.20 on 12 gallons of gasoline.<br \/>\nDivide the cost by the number of gallons to find the price per gallon.<br \/>\n46.20\/12 = 3.85<br \/>\nThus the correct answer is option B.<\/p>\n<p>Question 2.<br \/>\nA rabbit can run short distances at a rate of 35 miles per hour. A fox can run short distances at a rate of 21 miles per half hour. Which animal is faster, and by how much?<br \/>\nOptions:<br \/>\na. The rabbit; 7 miles per hour<br \/>\nb. The fox; 7 miles per hour<br \/>\nc. The rabbit; 14 miles per hour<br \/>\nd. The fox; 14 miles per hour<\/p>\n<p>Answer: The fox; 7 miles per hour<\/p>\n<p>Explanation:<br \/>\nGiven that,<br \/>\nA rabbit can run short distances at a rate of 35 miles per hour. A fox can run short distances at a rate of 21 miles per half hour.<br \/>\nIf a fox runs 21 miles for half an hour then it can 42 miles per hour.<br \/>\n42 &#8211; 35 = 7 miles per hour<br \/>\nThe fox is faster by 7 miles per hour.<br \/>\nTherefore the correct answer is option B.<\/p>\n<p>Question 3.<br \/>\nA pet survey found that the ratio of dogs to cats is 25. Which proportion shows the number of dogs if the number of cats is 140?<br \/>\nOptions:<br \/>\na. \\(\\frac{2 \\mathrm{dogs}}{5 \\mathrm{cats}}=\\frac{140 \\mathrm{dogs}}{350 \\mathrm{cats}}\\)<br \/>\nb. \\(\\frac{2 \\mathrm{dogs}}{5 \\mathrm{cats}}=\\frac{140 \\mathrm{cats}}{350 \\mathrm{dogs}}\\)<br \/>\nc. \\(\\frac{2 \\mathrm{dogs}}{5 \\mathrm{cats}}=\\frac{28 \\mathrm{dogs}}{140 \\mathrm{cats}}\\)<br \/>\nd. \\(\\frac{2 \\mathrm{dogs}}{5 \\mathrm{cats}}=\\frac{56 \\mathrm{dogs}}{140 \\mathrm{cats}}\\)<\/p>\n<p>Answer: \\(\\frac{2 \\mathrm{dogs}}{5 \\mathrm{cats}}=\\frac{56 \\mathrm{dogs}}{140 \\mathrm{cats}}\\)<\/p>\n<p>Explanation:<br \/>\nGiven,<br \/>\nA pet survey found that the ratio of dogs to cats is 25.<br \/>\nSince 5 \u00d7 25 = 140 and<br \/>\n2 \u00d7 28 = 56<br \/>\n= 56\/140<br \/>\nThus the correct answer is option D.<\/p>\n<p>Question 4.<br \/>\nWhat is the cost of 2 kilograms of flour if 3 kilograms cost $4.86 and the unit price for each package of flour is the same?<br \/>\nOptions:<br \/>\na. $0.81<br \/>\nb. $2.86<br \/>\nc. $3.24<br \/>\nd. $9.72<\/p>\n<p>Answer: $3.24<\/p>\n<p>Explanation:<br \/>\nWe need to find the unit price.<br \/>\n4.86\/3 = 1.62<br \/>\nmultiply the unit price by 2 to find the cost of 2 kg<br \/>\n1.62 \u00d7 2 = 3.24<br \/>\nTherefore the correct answer is option C.<\/p>\n<p>Question 5.<br \/>\nOne gallon of paint covers about 450 square feet. How many square feet will 1.5 gallons of paint cover?<br \/>\nOptions:<br \/>\na. 300ft<sup>2<\/sup><br \/>\nb. 451.5ft<sup>2<\/sup><br \/>\nc. 675ft<sup>2<\/sup><br \/>\nd. 900ft<sup>2<\/sup><\/p>\n<p>Answer: 675ft<sup>2<\/sup><\/p>\n<p>Explanation:<br \/>\nGiven,<br \/>\nOne gallon of paint covers about 450 square feet.<br \/>\nWe need to find how many square feet will 1.5 gallons of paint cover.<br \/>\nFor that, we have to multiply the number of gallons by the number of square feet covered by each gallon.<br \/>\n1.5 \u00d7 450 = 675 sq. ft.<br \/>\nThus the correct answer is option C.<\/p>\n<p>Question 6.<br \/>\nThe graph shows the relationship between the late fines the library charges and the number of days late.<br \/>\n<img loading=\"lazy\" src=\"https:\/\/ccssmathanswers.com\/wp-content\/uploads\/2020\/08\/Go-Math-Grade-7-Answer-Key-Chapter-4-Rates-and-Proportionality-img-21.jpg\" alt=\"Go Math Grade 7 Answer Key Chapter 4 Rates and Proportionality MIXED REVIEW img 21\" width=\"219\" height=\"177\" \/><br \/>\nOptions:<br \/>\na. y = 0.25x<br \/>\nb. y = 0.40x<br \/>\nc. y = 0.50x<br \/>\nd. y = 0.75x<\/p>\n<p>Answer: y = 0.25x<\/p>\n<p>Explanation:<br \/>\nThe graph shows the relationship between the late fines the library charges and the number of days late<br \/>\nOne of the points is (2, 0.5) so k = 0.5\/2 = 0.25.<br \/>\nThis gives an equation of y = 0.25x<br \/>\nThus the correct answer is option A.<\/p>\n<p><strong>Mini-Task<\/strong><\/p>\n<p>Question 7.<br \/>\nSchool is 2 miles from home along a straight road. The table shows your distance from home as you walk home at a constant rate.<br \/>\na. Is the relationship in the table proportional?<br \/>\n<img loading=\"lazy\" src=\"https:\/\/ccssmathanswers.com\/wp-content\/uploads\/2020\/08\/Go-Math-Grade-7-Answer-Key-Chapter-4-Rates-and-Proportionality-img-22.jpg\" alt=\"Go Math Grade 7 Answer Key Chapter 4 Rates and Proportionality MIXED REVIEW img 22\" width=\"286\" height=\"79\" \/><br \/>\n___________<\/p>\n<p>Answer: no<br \/>\nSince 1.5\/10 = 0.15 and 1\/20 = 0.05, the relationship is not proportional since the ratios are not equal.<\/p>\n<p>Question 7.<br \/>\nb. Find your distance from school for each time in the table.<br \/>\nType below:<br \/>\n___________<\/p>\n<p>Answer: Since the distance between school and home is 2 mi, the distance from school when the distance from home is 1.5 mi is 2 &#8211; 1.5 = 0.5 mi, for 1 mi its 2 &#8211; 1 = 1 mi, and for 0.5 mi its 2 &#8211; 0.5 = 1.5 mi.<\/p>\n<p>Question 7.<br \/>\nc. Write an equation representing the relationship between the distance from school and time walking.<br \/>\nType below:<br \/>\n___________<\/p>\n<p>Answer: y = -0.05 x + 2<\/p>\n<p>Explanation:<br \/>\nAt time t = 0, you are 2 mi from home since the distance from home to school is 2 mi. This means the y-intercept, b is 2.<br \/>\nTo find the slope of the line, find the rate of change:<br \/>\nm = (y2 &#8211; y1)\/(x2 &#8211; x1) = (1 &#8211; 1.5)\/(20 &#8211; 10) = -0.5\/10 = -0.05<br \/>\nThe line is then y = mx + b<br \/>\ny = 0.5x\u00a0 + 2.<\/p>\n<h3><a id=\"Module_4_Page_No_161\"><\/a>Module 4 &#8211; Page No. 161<\/h3>\n<p><strong>EXERCISES<\/strong><\/p>\n<p>Question 1.<br \/>\nSteve uses \\(\\frac{8}{9}\\) gallon of paint to paint 4 identical birdhouses. How many gallons of paint does he use for each birdhouse?<br \/>\n\\(\\frac{\u25a1}{\u25a1}\\)<\/p>\n<p>Answer: \\(\\frac{2}{9}\\) gallons<\/p>\n<p>Explanation:<br \/>\nGiven that,<br \/>\nSteve uses \\(\\frac{8}{9}\\) gallon of paint to paint 4 identical birdhouses.<br \/>\nDivide the number of gallons by the number of birdhouses.<br \/>\n\\(\\frac{8}{9}\\) \u00f7 4 = \\(\\frac{8}{9}\\) \u00d7 \\(\\frac{1}{4}\\)<br \/>\n= \\(\\frac{2}{9}\\) gallons<br \/>\nThus Steve uses \\(\\frac{2}{9}\\) gallons of paint for each birdhouse.<\/p>\n<p>Question 2.<br \/>\nRon walks 0.5 mile on the track in 10 minutes. Stevie walks 0.25 mile on the track in 6 minutes. Find the unit rate for each walker in miles per hour. Who is the faster walker?<br \/>\nRon: ___________ miles per hour<br \/>\nStevie: ___________ miles per hour<br \/>\n___________ is the faster walker.<\/p>\n<p>Answer: Ron<\/p>\n<p>Explanation:<br \/>\nGiven,<br \/>\nRon walks 0.5 miles on the track in 10 minutes.<br \/>\nStevie walks 0.25 miles on the track in 6 minutes.<br \/>\nWe can find each unit rate by dividing the number of miles by the number of minutes then multiply by 60 to get the number of miles per hour.<br \/>\nRon: 0.5 \u00f7 10 = 0.05 miles = 3 miles per hour<br \/>\nStevie: 0.25\/6 = 1\/24 mi per min = 2.5 mi per hour<\/p>\n<p>Question 3.<br \/>\nThe table below shows the proportional relationship between Juan\u2019s pay and the hours he works. Complete the table. Plot the data and connect the points with a line.<br \/>\n<img loading=\"lazy\" src=\"https:\/\/ccssmathanswers.com\/wp-content\/uploads\/2020\/08\/Go-Math-Grade-7-Answer-Key-Chapter-4-Rates-and-Proportionality-img-23.jpg\" alt=\"Go Math Grade 7 Answer Key Chapter 4 Rates and Proportionality img 23\" width=\"373\" height=\"84\" \/><br \/>\n<img loading=\"lazy\" src=\"https:\/\/ccssmathanswers.com\/wp-content\/uploads\/2020\/08\/Go-Math-Grade-7-Answer-Key-Chapter-4-Rates-and-Proportionality-img-24.jpg\" alt=\"Go Math Grade 7 Answer Key Chapter 4 Rates and Proportionality img 24\" width=\"228\" height=\"227\" \/><br \/>\nType below:<br \/>\n____________<\/p>\n<p>Answer:<br \/>\nFirst, find the constant of proportionality.<br \/>\nLet y represents pay and x represents the number of hours worked.<br \/>\nThe constant of proportionality = y\/x = 40\/2 = 20<br \/>\nHence, for 1 hour of work, he earns $20.<br \/>\nTo find how many hours he needs to work $80, we divide 80 by the constant of proportionality.<br \/>\n80\/20 = 4<br \/>\nFor 1 hour he earns $20, so for 5 hours he earns 5 \u00d7 20 = $100.<br \/>\nFor 1 hour he earns $20, so for 6 hours he earns 6 \u00d7 20 = $120.<br \/>\n<img loading=\"lazy\" class=\"alignnone size-medium wp-image-7522\" src=\"https:\/\/ccssmathanswers.com\/wp-content\/uploads\/2020\/08\/Go-Math-Grade-7-Answer-Key-Chapter-4-Rates-and-Proportionality-img-23-1-300x68.jpg\" alt=\"Go-Math-Grade-7-Answer-Key-Chapter-4-Rates-and-Proportionality-img-23\" width=\"300\" height=\"68\" srcset=\"https:\/\/bigideasmathanswers.com\/wp-content\/uploads\/2020\/08\/Go-Math-Grade-7-Answer-Key-Chapter-4-Rates-and-Proportionality-img-23-1-300x68.jpg 300w, https:\/\/bigideasmathanswers.com\/wp-content\/uploads\/2020\/08\/Go-Math-Grade-7-Answer-Key-Chapter-4-Rates-and-Proportionality-img-23-1.jpg 373w\" sizes=\"(max-width: 300px) 100vw, 300px\" \/><br \/>\n<img loading=\"lazy\" class=\"alignnone size-full wp-image-7523\" src=\"https:\/\/ccssmathanswers.com\/wp-content\/uploads\/2020\/08\/Go-Math-Grade-7-Answer-Key-Chapter-4-Rates-and-Proportionality-img-24-1.jpg\" alt=\"Go-Math-Grade-7-Answer-Key-Chapter-4-Rates-and-Proportionality-img-24\" width=\"228\" height=\"227\" srcset=\"https:\/\/bigideasmathanswers.com\/wp-content\/uploads\/2020\/08\/Go-Math-Grade-7-Answer-Key-Chapter-4-Rates-and-Proportionality-img-24-1.jpg 228w, https:\/\/bigideasmathanswers.com\/wp-content\/uploads\/2020\/08\/Go-Math-Grade-7-Answer-Key-Chapter-4-Rates-and-Proportionality-img-24-1-150x150.jpg 150w\" sizes=\"(max-width: 228px) 100vw, 228px\" \/><\/p>\n<p><em>Conclusion:<\/em><\/p>\n<p>After the preparation of\u00a0 Go Math Grade 7 Answer Key Chapter 4 Rates and Proportionality, we suggest the students solve the questions given in the Module Quiz. Test yourself by solving the questions given at the end of this chapter. By this, you can enhance your math skills and secure good marks in the exams. If you have any doubts regarding the solutions you can post your comment in the below comment section.<\/p>\n","protected":false},"excerpt":{"rendered":"<p>Students who are in search of the HMH Go Math Chapter 4 Rates and Proportionality Answer Key can get them on this page. With the help of the Go Math Grade 7 Answer Key 4th Chapter Rates and Proportionality parents can teach simple methods to solve the problems to their children. So, Download Go Math &#8230; <a title=\"Go Math Grade 7 Answer Key Chapter 4 Rates and Proportionality\" class=\"read-more\" href=\"https:\/\/bigideasmathanswers.com\/go-math-grade-7-answer-key-chapter-4-rates-and-proportionality\/\" aria-label=\"More on Go Math Grade 7 Answer Key Chapter 4 Rates and Proportionality\">Read more<\/a><\/p>\n","protected":false},"author":2,"featured_media":8802,"comment_status":"open","ping_status":"open","sticky":false,"template":"","format":"standard","meta":{"spay_email":""},"categories":[2],"tags":[],"jetpack_featured_media_url":"https:\/\/bigideasmathanswers.com\/wp-content\/uploads\/2020\/11\/go-math-grade-7-chapter-4-rates-and-proportionality-answer-key.jpeg","_links":{"self":[{"href":"https:\/\/bigideasmathanswers.com\/wp-json\/wp\/v2\/posts\/5849"}],"collection":[{"href":"https:\/\/bigideasmathanswers.com\/wp-json\/wp\/v2\/posts"}],"about":[{"href":"https:\/\/bigideasmathanswers.com\/wp-json\/wp\/v2\/types\/post"}],"author":[{"embeddable":true,"href":"https:\/\/bigideasmathanswers.com\/wp-json\/wp\/v2\/users\/2"}],"replies":[{"embeddable":true,"href":"https:\/\/bigideasmathanswers.com\/wp-json\/wp\/v2\/comments?post=5849"}],"version-history":[{"count":1,"href":"https:\/\/bigideasmathanswers.com\/wp-json\/wp\/v2\/posts\/5849\/revisions"}],"predecessor-version":[{"id":92820,"href":"https:\/\/bigideasmathanswers.com\/wp-json\/wp\/v2\/posts\/5849\/revisions\/92820"}],"wp:featuredmedia":[{"embeddable":true,"href":"https:\/\/bigideasmathanswers.com\/wp-json\/wp\/v2\/media\/8802"}],"wp:attachment":[{"href":"https:\/\/bigideasmathanswers.com\/wp-json\/wp\/v2\/media?parent=5849"}],"wp:term":[{"taxonomy":"category","embeddable":true,"href":"https:\/\/bigideasmathanswers.com\/wp-json\/wp\/v2\/categories?post=5849"},{"taxonomy":"post_tag","embeddable":true,"href":"https:\/\/bigideasmathanswers.com\/wp-json\/wp\/v2\/tags?post=5849"}],"curies":[{"name":"wp","href":"https:\/\/api.w.org\/{rel}","templated":true}]}}