{"id":30345,"date":"2022-04-02T16:20:55","date_gmt":"2022-04-02T10:50:55","guid":{"rendered":"https:\/\/ccssmathanswers.com\/?p=30345"},"modified":"2022-04-07T10:57:18","modified_gmt":"2022-04-07T05:27:18","slug":"big-ideas-math-answers-grade-7-chapter-5","status":"publish","type":"post","link":"https:\/\/bigideasmathanswers.com\/big-ideas-math-answers-grade-7-chapter-5\/","title":{"rendered":"Big Ideas Math Answers Grade 7 Chapter 5 Ratios and Proportions"},"content":{"rendered":"<p>For the best practice, the<strong> Big Ideas Math Grade 7 Chapter 5 Ratios and Proportions Answer Sheet<\/strong> is given here. A detailed explanation of solutions prepared by great math experts which are included in the below sections. Click on the Big Ideas Math Book Grade 7 Answer Key Chapter 5 Ratios and Proportions link on our website and start your preparation. Get the free pdfs here in the following sections.<\/p>\n<p><a href=\"https:\/\/bigideasmathanswers.com\/big-ideas-math-answers-grade-7\/\">Big Ideas Math Answers Grade 7 <\/a>Chapter 5 Ratios and Proportions preparation material is here. Candidates can quickly get this material without much search because we are giving the lesson-wise information in detail here. This will act as a guide for your complete preparation. Get a clear idea of ratios and their tables. Follow the below sections and know more about Ratios and Proportions.<\/p>\n<p><span style=\"font-size: 1.7em; font-weight: bold;\">Big Ideas Math Book 7th Grade Answer Key Chapter 5 Ratios and Proportions<\/span><\/p>\n<p>Feeling difficult to get the best solutions for all the math problems? If you get a guide with clear explanations and short solutions, then you will feel it easy and fun learning. Therefore, check out <em>Big Ideas Math Book 7th Grade Answer Key Chapter 5 Ratios and Proportions Pdf<\/em> here which is given with a clear explanation. Know the various topics involved in ratios and proportions.<\/p>\n<p>Various topics like graphs of proportional relationships, rates, and unit rates, identifying proportional relationships, writing and solving proportions, ratios, and ratio tables, scale drawings, and so on. Check <strong>Big Ideas Math Answers Grade 7 Chapter 5 Ratios and Proportions<\/strong> solved examples in the next sections.<\/p>\n<p><strong>Performance Task<\/strong><\/p>\n<ul>\n<li><a href=\"#Ratios_and_Proportions_STEAM_Video\/_Performance_Task\">Ratios and Proportions STEAM Video\/ Performance Task<\/a><\/li>\n<li><a href=\"#Ratios_and_Proportions_Getting_Ready_for_Chapter_5\">Ratios and Proportions Getting Ready for Chapter 5<\/a><\/li>\n<\/ul>\n<p><strong>Lesson: 1 Ratios and Ratio Tables<\/strong><\/p>\n<ul>\n<li><a href=\"#Lesson_5.1_Ratios_and_Ratio_Tables\">Lesson 5.1 Ratios and Ratio Tables<\/a><\/li>\n<li><a href=\"#Ratios_and_Ratio_Tables_Homework_&amp;_Practice_5.1\">Ratios and Ratio Tables Homework &amp; Practice 5.1<\/a><\/li>\n<\/ul>\n<p><strong>Lesson: 2 Rates and Unit Rates<\/strong><\/p>\n<ul>\n<li><a href=\"#Lesson_5.2_Rates_and_Unit_Rates\">Lesson 5.2 Rates and Unit Rates<\/a><\/li>\n<li><a href=\"#Rates_and_Unit_Rates_Homework_&amp;_Practice_5.2\">Rates and Unit Rates Homework &amp; Practice 5.2<\/a><\/li>\n<\/ul>\n<p><strong>Lesson: 3 Identifying Proportional Relationships<\/strong><\/p>\n<ul>\n<li><a href=\"#Lesson_5.3_Identifying_Proportional_Relationships\">Lesson 5.3 Identifying Proportional Relationships<\/a><\/li>\n<li><a href=\"#Identifying_Proportional_Relationships_Homework_&amp;_Practice_5.3\">Identifying Proportional Relationships Homework &amp; Practice 5.3<\/a><\/li>\n<\/ul>\n<p><strong>Lesson: 4 Writing and Solving Proportions<\/strong><\/p>\n<ul>\n<li><a href=\"#Lesson_5.4_Writing_and_Solving_Proportions\">Lesson 5.4 Writing and Solving Proportions<\/a><\/li>\n<li><a href=\"#Writing_and_Solving_Proportions_Homework_&amp;_Practice_5.4\">Writing and Solving Proportions Homework &amp; Practice 5.4<\/a><\/li>\n<\/ul>\n<p><strong>Lesson: 5 Graphs of Proportional Relationships<\/strong><\/p>\n<ul>\n<li><a href=\"#Lesson_5.5_Graphs_of_Proportional_Relationships\">Lesson 5.5 Graphs of Proportional Relationships<\/a><\/li>\n<li><a href=\"#Graphs_of_Proportional_Relationships_Homework_&amp;_Practice_5.5\">Graphs of Proportional Relationships Homework &amp; Practice 5.5<\/a><\/li>\n<\/ul>\n<p><strong>Lesson: 6 Scale Drawings<\/strong><\/p>\n<ul>\n<li><a href=\"#Lesson_5.6_Scale_Drawings\">Lesson 5.6 Scale Drawings<\/a><\/li>\n<li><a href=\"#Scale_Drawings_Homework_&amp;_Practice_5.6\">Scale Drawings Homework &amp; Practice 5.6<\/a><\/li>\n<\/ul>\n<p><strong>Chapter: 5 &#8211; Ratios and Proportions<\/strong><\/p>\n<ul>\n<li><a href=\"#Ratios_and_Proportions_Connecting_Concepts\">Ratios and Proportions Connecting Concepts<\/a><\/li>\n<li><a href=\"#Ratios_and_Proportions_Chapter_Review\">Ratios and Proportions Chapter Review<\/a><\/li>\n<li><a href=\"#Ratios_and_Proportions_Practice_Test\">Ratios and Proportions Practice Test<\/a><\/li>\n<li><a href=\"#Ratios_and_Proportions_Cumulative_Practice\">Ratios and Proportions Cumulative Practice<\/a><\/li>\n<\/ul>\n<h3><a id=\"Ratios_and_Proportions_STEAM_Video\/_Performance_Task\"><\/a>Ratios and Proportions STEAM Video\/ Performance Task<\/h3>\n<p><strong>STEAM Video<\/strong><\/p>\n<p>Painting a Large Room<br \/>\nShades of paint can be made by mixing other paints. What colors of paints can you mix to make green paint?<br \/>\n<img loading=\"lazy\" class=\"alignnone size-full wp-image-30347\" src=\"https:\/\/ccssmathanswers.com\/wp-content\/uploads\/2021\/01\/Big-Ideas-Math-Answer-Key-Grade-7-Chapter-5-Ratios-and-Proportions-1.png\" alt=\"Big Ideas Math Answer Key Grade 7 Chapter 5 Ratios and Proportions 1\" width=\"139\" height=\"384\" srcset=\"https:\/\/bigideasmathanswers.com\/wp-content\/uploads\/2021\/01\/Big-Ideas-Math-Answer-Key-Grade-7-Chapter-5-Ratios-and-Proportions-1.png 139w, https:\/\/bigideasmathanswers.com\/wp-content\/uploads\/2021\/01\/Big-Ideas-Math-Answer-Key-Grade-7-Chapter-5-Ratios-and-Proportions-1-109x300.png 109w\" sizes=\"(max-width: 139px) 100vw, 139px\" \/><br \/>\nWatch the STEAM Video \u201cPainting a Large Room.\u201d Then answer the following questions.<br \/>\n1. Enid estimates that they need 2 gallons of paint to apply two coats to the wall shown. How many square feet does she expect \\(\\frac{1}{2}\\) gallon of paint will cover?<br \/>\n<img loading=\"lazy\" class=\"alignnone size-full wp-image-30348\" src=\"https:\/\/ccssmathanswers.com\/wp-content\/uploads\/2021\/01\/Big-Ideas-Math-Answer-Key-Grade-7-Chapter-5-Ratios-and-Proportions-2.png\" alt=\"Big Ideas Math Answer Key Grade 7 Chapter 5 Ratios and Proportions 2\" width=\"302\" height=\"132\" srcset=\"https:\/\/bigideasmathanswers.com\/wp-content\/uploads\/2021\/01\/Big-Ideas-Math-Answer-Key-Grade-7-Chapter-5-Ratios-and-Proportions-2.png 302w, https:\/\/bigideasmathanswers.com\/wp-content\/uploads\/2021\/01\/Big-Ideas-Math-Answer-Key-Grade-7-Chapter-5-Ratios-and-Proportions-2-300x131.png 300w\" sizes=\"(max-width: 302px) 100vw, 302px\" \/><\/p>\n<p>Answer:<br \/>\n1\/2 gallon of paint will cover 60 sq feet.<\/p>\n<p>Explanation:<br \/>\nEnid estimates that they need 2 gallons of paint to apply two coats to the wall of 240 sq ft<br \/>\nThe area of the shown figure = 24 x 10<br \/>\n= 240 square feet<br \/>\nTo know how many sq feet does 1\/2 gallon of paint will cover (240 . 1\/2) . 1\/2<br \/>\n= 240 . 1\/4<br \/>\n= 60<br \/>\nSo, 1\/2 gallon of paint will cover 60 sq feet.<\/p>\n<p>2. Describe a room that requires 5\\(\\frac{1}{2}\\) gallons of paint to apply one coat of paint to each of the four walls.<\/p>\n<p>Answer:<br \/>\nThe room has 4 walls each wall is 330 sq feet.<\/p>\n<p>Explanation:<br \/>\nA room requires 5(1\/2) gallons of paint to apply one coat of paint to each of the four walls.<br \/>\nEnid estimates that they need 2 gallons of paint to apply two coats to the wall of 240 sq ft<br \/>\nIf they coat only once, she would require 1 gallon of paint for a wall of 240 sq feet.<br \/>\nIf she wants to use 5(1\/2) = 11\/2 gallons of paint, then the area of walls will be<br \/>\n= 240 . (11\/2)<br \/>\n= 120 . 11 = 1320 Square feet<br \/>\nEach wall = 1320\/4 =330 sq feet<br \/>\nThe room has 4 walls each wall is 330 sq feet.<\/p>\n<p><strong>Performance Task<\/strong><\/p>\n<p>Mixing Paint<br \/>\nAfter completing this chapter, you will be able to use the concepts you learned to answer the questions in the STEAM Video Performance Task. You will be given the amounts of each tint used to make different colors of paint. For example:<br \/>\n<img loading=\"lazy\" class=\"alignnone size-full wp-image-30349\" src=\"https:\/\/ccssmathanswers.com\/wp-content\/uploads\/2021\/01\/Big-Ideas-Math-Answer-Key-Grade-7-Chapter-5-Ratios-and-Proportions-3.png\" alt=\"Big Ideas Math Answer Key Grade 7 Chapter 5 Ratios and Proportions 3\" width=\"530\" height=\"323\" srcset=\"https:\/\/bigideasmathanswers.com\/wp-content\/uploads\/2021\/01\/Big-Ideas-Math-Answer-Key-Grade-7-Chapter-5-Ratios-and-Proportions-3.png 530w, https:\/\/bigideasmathanswers.com\/wp-content\/uploads\/2021\/01\/Big-Ideas-Math-Answer-Key-Grade-7-Chapter-5-Ratios-and-Proportions-3-300x183.png 300w\" sizes=\"(max-width: 530px) 100vw, 530px\" \/><br \/>\nYou will be asked to solve various ratio problems about mixing paint. Given any color of paint, how can you make the paint slightly lighter in color?<\/p>\n<h3><a id=\"Ratios_and_Proportions_Getting_Ready_for_Chapter_5\"><\/a>Ratios and Proportions Getting Ready for Chapter 5<\/h3>\n<p><strong>Chapter Exploration<\/strong><\/p>\n<p>The Meaning of a Word Rate<br \/>\nWhen you rent snorkel gear at the beach, rate you should pay attention to the rental. The rental rate is in dollars per hour.<br \/>\n<img loading=\"lazy\" class=\"alignnone size-full wp-image-30350\" src=\"https:\/\/ccssmathanswers.com\/wp-content\/uploads\/2021\/01\/Big-Ideas-Math-Answer-Key-Grade-7-Chapter-5-Ratios-and-Proportions-4.png\" alt=\"Big Ideas Math Answer Key Grade 7 Chapter 5 Ratios and Proportions 4\" width=\"302\" height=\"164\" srcset=\"https:\/\/bigideasmathanswers.com\/wp-content\/uploads\/2021\/01\/Big-Ideas-Math-Answer-Key-Grade-7-Chapter-5-Ratios-and-Proportions-4.png 302w, https:\/\/bigideasmathanswers.com\/wp-content\/uploads\/2021\/01\/Big-Ideas-Math-Answer-Key-Grade-7-Chapter-5-Ratios-and-Proportions-4-300x163.png 300w\" sizes=\"(max-width: 302px) 100vw, 302px\" \/><br \/>\n1. Work with a partner. Complete each step.<br \/>\n\u2022 Match each description with a rate.<br \/>\n\u2022 Match each rate with a fraction.<br \/>\n\u2022 Give a reasonable value for each fraction. Then give an unreasonable value.<br \/>\n<img loading=\"lazy\" class=\"alignnone size-full wp-image-30370\" src=\"https:\/\/ccssmathanswers.com\/wp-content\/uploads\/2021\/01\/Big-Ideas-Math-Answer-Key-Grade-7-Chapter-5-Ratios-and-Proportions-5.png\" alt=\"Big Ideas Math Answer Key Grade 7 Chapter 5 Ratios and Proportions 5\" width=\"554\" height=\"223\" srcset=\"https:\/\/bigideasmathanswers.com\/wp-content\/uploads\/2021\/01\/Big-Ideas-Math-Answer-Key-Grade-7-Chapter-5-Ratios-and-Proportions-5.png 554w, https:\/\/bigideasmathanswers.com\/wp-content\/uploads\/2021\/01\/Big-Ideas-Math-Answer-Key-Grade-7-Chapter-5-Ratios-and-Proportions-5-300x121.png 300w\" sizes=\"(max-width: 554px) 100vw, 554px\" \/><br \/>\n2. Work with a partner Describe a situation to which the given fraction can apply. Show how to rewrite each expression as a division problem. Then simplify and interpret your result.<br \/>\n<img loading=\"lazy\" class=\"alignnone size-full wp-image-30371\" src=\"https:\/\/ccssmathanswers.com\/wp-content\/uploads\/2021\/01\/Big-Ideas-Math-Answer-Key-Grade-7-Chapter-5-Ratios-and-Proportions-6.png\" alt=\"Big Ideas Math Answer Key Grade 7 Chapter 5 Ratios and Proportions 6\" width=\"484\" height=\"71\" srcset=\"https:\/\/bigideasmathanswers.com\/wp-content\/uploads\/2021\/01\/Big-Ideas-Math-Answer-Key-Grade-7-Chapter-5-Ratios-and-Proportions-6.png 484w, https:\/\/bigideasmathanswers.com\/wp-content\/uploads\/2021\/01\/Big-Ideas-Math-Answer-Key-Grade-7-Chapter-5-Ratios-and-Proportions-6-300x44.png 300w\" sizes=\"(max-width: 484px) 100vw, 484px\" \/><br \/>\n<strong>Vocabulary<\/strong><br \/>\nThe following vocabulary terms are defined in this chapter. Think about what each term might mean and record your thoughts.<br \/>\nproportional<br \/>\nconstant of proportionality<br \/>\nscale drawing<\/p>\n<h3><a id=\"Lesson_5.1_Ratios_and_Ratio_Tables\"><\/a>Lesson 5.1 Ratios and Ratio Tables<\/h3>\n<p><strong>EXPLORATION 1<\/strong><\/p>\n<p>Describing Ratio Relationships<br \/>\nWork with a partner. Use the recipe shown.<br \/>\n<img loading=\"lazy\" class=\"alignnone size-full wp-image-30351\" src=\"https:\/\/ccssmathanswers.com\/wp-content\/uploads\/2021\/01\/Big-Ideas-Math-Answer-Key-Grade-7-Chapter-5-Ratios-and-Proportions-5.1-1.png\" alt=\"Big Ideas Math Answer Key Grade 7 Chapter 5 Ratios and Proportions 5.1 1\" width=\"645\" height=\"155\" srcset=\"https:\/\/bigideasmathanswers.com\/wp-content\/uploads\/2021\/01\/Big-Ideas-Math-Answer-Key-Grade-7-Chapter-5-Ratios-and-Proportions-5.1-1.png 645w, https:\/\/bigideasmathanswers.com\/wp-content\/uploads\/2021\/01\/Big-Ideas-Math-Answer-Key-Grade-7-Chapter-5-Ratios-and-Proportions-5.1-1-300x72.png 300w\" sizes=\"(max-width: 645px) 100vw, 645px\" \/><br \/>\na. Identify several ratios in the recipe.<br \/>\nb. You halve the recipe. Describe your ratio relationships in part (a) using the new quantities. Is the relationship between the ingredients the same as in part(a)? Explain.<\/p>\n<p>Answer:<br \/>\na. Stewed tomatoes : chicken broth = 9 ounces : 15 ounces<br \/>\nStewed tomatoes : Chopped Spinach = 9 ounces : 9 ounces = 1 : 1<br \/>\nChopped Spinach : chicken broth = 9 ounces : 15 ounces<br \/>\nChopped Chicken : grated parmesan = 1 cup : 5 tablespoons<br \/>\nChicken broth : Chopped Chicken = 15 ounces : 1 cup<br \/>\nStewed tomatoes : chopped chicken = 9 ounces : 1 cup = Chopped Spinach : chopped chicken<br \/>\nStewed tomatoes : grated parmesan = 9 ounces : 5 tablespoons = Chopped Spinach : grated parmesan<br \/>\nchicken broth : grated parmesan = 15 ounces : 5 tablespoons = 5 ounces : 1 tablespoon<br \/>\nb. The relationship between the ingredients the same as in part(a).<\/p>\n<p>Explanation:<br \/>\na. The several ratios of the recipe are Stewed tomatoes : chicken broth = 9 ounces : 15 ounces<br \/>\nStewed tomatoes : Chopped Spinach = 9 ounces : 9 ounces = 1 : 1<br \/>\nChopped Spinach : chicken broth = 9 ounces : 15 ounces<br \/>\nChopped Chicken : grated parmesan = 1 cup : 5 tablespoons<br \/>\nChicken broth : Chopped Chicken = 15 ounces : 1 cup<br \/>\nStewed tomatoes : chopped chicken = 9 ounces : 1 cup = Chopped Spinach : chopped chicken<br \/>\nStewed tomatoes : grated parmesan = 9 ounces : 5 tablespoons = Chopped Spinach : grated parmesan<br \/>\nchicken broth : grated parmesan = 15 ounces : 5 tablespoons = 5 ounces : 1 tablespoon<br \/>\nb. The relationship between the ingredients the same as in part(a).<\/p>\n<p><strong>EXPLORATION 2<\/strong><\/p>\n<p>Completing Ratio Tables<br \/>\nWork with a partner. Use the ratio tables shown.<br \/>\n<img loading=\"lazy\" class=\"alignnone size-full wp-image-30352\" src=\"https:\/\/ccssmathanswers.com\/wp-content\/uploads\/2021\/01\/Big-Ideas-Math-Answer-Key-Grade-7-Chapter-5-Ratios-and-Proportions-5.1-2.png\" alt=\"Big Ideas Math Answer Key Grade 7 Chapter 5 Ratios and Proportions 5.1 2\" width=\"544\" height=\"161\" srcset=\"https:\/\/bigideasmathanswers.com\/wp-content\/uploads\/2021\/01\/Big-Ideas-Math-Answer-Key-Grade-7-Chapter-5-Ratios-and-Proportions-5.1-2.png 544w, https:\/\/bigideasmathanswers.com\/wp-content\/uploads\/2021\/01\/Big-Ideas-Math-Answer-Key-Grade-7-Chapter-5-Ratios-and-Proportions-5.1-2-300x89.png 300w\" sizes=\"(max-width: 544px) 100vw, 544px\" \/><br \/>\na. Complete the first ratio table using multiple operations. Use the same operations to complete the second ratio table.<br \/>\nb. Are the ratios in the first table equivalent? the second table? Explain.<br \/>\nc. Do the strategies for completing ratio tables of whole numbers work for completing ratio tables of fractions? Explain your reasoning.<\/p>\n<p>Answer:<br \/>\na. <img loading=\"lazy\" class=\"alignnone size-full wp-image-44101\" src=\"https:\/\/ccssmathanswers.com\/wp-content\/uploads\/2021\/01\/big-ideas-math-answer-key-grade-7-chapter-5-ratios-and-proportions-5.1-2.jpg\" alt=\"Big Ideas Math Answer Key Grade 7 Chapter 5 Ratios and Proportions 5.1 2\" width=\"395\" height=\"118\" srcset=\"https:\/\/bigideasmathanswers.com\/wp-content\/uploads\/2021\/01\/big-ideas-math-answer-key-grade-7-chapter-5-ratios-and-proportions-5.1-2.jpg 395w, https:\/\/bigideasmathanswers.com\/wp-content\/uploads\/2021\/01\/big-ideas-math-answer-key-grade-7-chapter-5-ratios-and-proportions-5.1-2-300x90.jpg 300w\" sizes=\"(max-width: 395px) 100vw, 395px\" \/><br \/>\nb. Yes<\/p>\n<p>Explanation:<br \/>\na. 5 x 2 = 10, 1 x 2 = 2, 1\/4 x 2 = 1\/2, 1\/2 x 2 = 1<br \/>\n5 x 1.5 = 7.5, 1 x 1.5 = 1.5, 1\/4 x 3\/2 = 3\/8, 1\/2 x 3\/2 = 3\/4<br \/>\n5 x 4 = 20, 1 x 4 = 4, 1\/4 x 4 = 1, 1\/2 x 4= 2<br \/>\nb. Yes the ratios in the first table are equivalent to the second table.<\/p>\n<p><img loading=\"lazy\" class=\"alignnone size-full wp-image-30353\" src=\"https:\/\/ccssmathanswers.com\/wp-content\/uploads\/2021\/01\/Big-Ideas-Math-Answer-Key-Grade-7-Chapter-5-Ratios-and-Proportions-5.1-3.png\" alt=\"Big Ideas Math Answer Key Grade 7 Chapter 5 Ratios and Proportions 5.1 3\" width=\"189\" height=\"121\" \/><\/p>\n<p><strong>Try It<\/strong><\/p>\n<p>Question 1.<br \/>\nYou mix \\(\\frac{2}{3}\\) teaspoon of baking soda with 3 teaspoons of salt. Find and interpret the value of the ratio of baking soda to salt.<\/p>\n<p>Answer:<br \/>\nThe ratio of baking soda to salt is 2 : 1.<\/p>\n<p>Explanation:<br \/>\nGiven that,<br \/>\nYou mix \\(\\frac{2}{3}\\) teaspoon of baking soda with 3 teaspoons of salt.<br \/>\nThe ratio of baking soda to salt = 2\/3 to 3 = 2\/3 : 3<br \/>\n= 2\/3 \/ 3 = 2\/3 . 3\/1 = 2\/1 = 2 : 1<br \/>\nThe ratio of baking soda to salt is 2 : 1.<\/p>\n<p><strong>Find the missing values in the ratio table. Then write the equivalent ratios.<\/strong><br \/>\nQuestion 2.<br \/>\n<img loading=\"lazy\" class=\"alignnone size-full wp-image-30354\" src=\"https:\/\/ccssmathanswers.com\/wp-content\/uploads\/2021\/01\/Big-Ideas-Math-Answer-Key-Grade-7-Chapter-5-Ratios-and-Proportions-5.1-4.png\" alt=\"Big Ideas Math Answer Key Grade 7 Chapter 5 Ratios and Proportions 5.1 4\" width=\"204\" height=\"82\" \/><\/p>\n<p>Answer:<br \/>\n<img loading=\"lazy\" class=\"alignnone size-full wp-image-44125\" src=\"https:\/\/ccssmathanswers.com\/wp-content\/uploads\/2021\/01\/big-ideas-math-answer-key-grade-7-chapter-5-ratios-and-proportions-5.1-3.jpg\" alt=\"Big Ideas Math Answer Key Grade 7 Chapter 5 Ratios and Proportions 5.1 3\" width=\"199\" height=\"83\" \/><\/p>\n<p>Explanation:<br \/>\nThe missing values in the ratio table are<br \/>\n4 x 4 = 16. So, 5\/2 x 4 = 10<br \/>\n5\/2 . x = 5<br \/>\nx = 2<br \/>\nSo, 4 . 2 = 8<br \/>\nThe equivalent ratios are 5\/2 : 4, 10 : 16, 5 : 8.<\/p>\n<p>Question 3.<br \/>\n<img loading=\"lazy\" class=\"alignnone size-full wp-image-30355\" src=\"https:\/\/ccssmathanswers.com\/wp-content\/uploads\/2021\/01\/Big-Ideas-Math-Answer-Key-Grade-7-Chapter-5-Ratios-and-Proportions-5.1-5.png\" alt=\"Big Ideas Math Answer Key Grade 7 Chapter 5 Ratios and Proportions 5.1 5\" width=\"213\" height=\"73\" \/><\/p>\n<p>Answer:<br \/>\n<img loading=\"lazy\" class=\"alignnone size-full wp-image-44128\" src=\"https:\/\/ccssmathanswers.com\/wp-content\/uploads\/2021\/01\/big-ideas-math-answer-key-grade-7-chapter-5-ratios-and-proportions-5.1-4.jpg\" alt=\"Big Ideas Math Answer Key Grade 7 Chapter 5 Ratios and Proportions 5.1 4\" width=\"217\" height=\"78\" \/><\/p>\n<p>Explanation:<br \/>\n0.4 . x = 1.2<br \/>\nx = 1.2\/0.4 = 3<br \/>\nSo, 0.75 . 3 = 2.25<br \/>\n0.4 . y = 1.6<br \/>\ny = 1.6\/0.4 = 4<br \/>\nSo, 0.75 . 4 = 3<br \/>\nThe equivalent ratios are 0.4 : 0.75, 1.2 : 2.25, 1.6 : 3<\/p>\n<p><strong>Self-Assessment for Concepts &amp; Skills<\/strong><br \/>\nSolve each exercise. Then rate your understanding of the success criteria in your journal.<\/p>\n<p>Question 4.<br \/>\n<strong>WRITING AND INTERPRETING RATIOS<\/strong><br \/>\nYou include \\(\\frac{1}{2}\\) tablespoon of essential oils in a solution for every 12 tablespoons of jojoba oil. Find and interpret the value of the ratio of jojoba oil to essential oils.<br \/>\n<img loading=\"lazy\" class=\"alignnone size-full wp-image-30356\" src=\"https:\/\/ccssmathanswers.com\/wp-content\/uploads\/2021\/01\/Big-Ideas-Math-Answer-Key-Grade-7-Chapter-5-Ratios-and-Proportions-5.1-6.png\" alt=\"Big Ideas Math Answer Key Grade 7 Chapter 5 Ratios and Proportions 5.1 6\" width=\"170\" height=\"76\" \/><\/p>\n<p>Answer:<br \/>\nThe amount of jojoba oil in the solution is the 24th amount of essential oil.<\/p>\n<p>Explanation:<br \/>\nYou include \\(\\frac{1}{2}\\) tablespoon of essential oils in a solution for every 12 tablespoons of jojoba oil<br \/>\nThe ratio of jojoba oil to essential oil = 12 : 1\/2<br \/>\n= 12 \u00f7 1\/2<br \/>\n= 12 . 2\/1<br \/>\n= 24<br \/>\nThe amount of jojoba oil in the solution is the 24th amount of essential oil.<\/p>\n<p>Question 5.<br \/>\n<strong>NUMBER SENSE<\/strong><br \/>\nFind the missing values in the ratio table. Then write the equivalent ratios.<br \/>\n<img loading=\"lazy\" class=\"alignnone size-full wp-image-30357\" src=\"https:\/\/ccssmathanswers.com\/wp-content\/uploads\/2021\/01\/Big-Ideas-Math-Answer-Key-Grade-7-Chapter-5-Ratios-and-Proportions-5.1-7.png\" alt=\"Big Ideas Math Answer Key Grade 7 Chapter 5 Ratios and Proportions 5.1 7\" width=\"176\" height=\"99\" \/><\/p>\n<p>Answer:<br \/>\n<img loading=\"lazy\" class=\"alignnone size-full wp-image-44136\" src=\"https:\/\/ccssmathanswers.com\/wp-content\/uploads\/2021\/01\/big-ideas-math-answer-key-grade-7-chapter-5-ratios-and-proportions-5.1-5.jpg\" alt=\"Big Ideas Math Answer Key Grade 7 Chapter 5 Ratios and Proportions 5.1 5\" width=\"219\" height=\"116\" \/><\/p>\n<p>Explanation:<br \/>\n1\/12 . x = 2\/3<br \/>\nx = 2\/3 . 12<br \/>\nx = 8<br \/>\nSo, Pounds = 3\/2 . 8 = 12<br \/>\n3\/2 . 7 = 21\/2<br \/>\n1\/12 . 7 = 7\/12<br \/>\nThe equivalent ratios are 3\/2 : 1\/12, 12 : 2\/3, 21\/2 : 7\/12<\/p>\n<p><strong>Self-Assessment for Problem Solving<\/strong><br \/>\nSolve each exercise. Then rate your understanding of the success criteria in your journal.<\/p>\n<p>Question 6.<br \/>\n<strong>DIG DEEPER!<\/strong><br \/>\nA satellite orbiting Earth travels 14\\(\\frac{1}{2}\\) miles every 3 seconds. How far does the satellite travel in \\(\\frac{3}{4}\\) minute?<br \/>\n<img loading=\"lazy\" class=\"alignnone size-full wp-image-30358\" src=\"https:\/\/ccssmathanswers.com\/wp-content\/uploads\/2021\/01\/Big-Ideas-Math-Answer-Key-Grade-7-Chapter-5-Ratios-and-Proportions-5.1-8.png\" alt=\"Big Ideas Math Answer Key Grade 7 Chapter 5 Ratios and Proportions 5.1 8\" width=\"115\" height=\"195\" \/><\/p>\n<p>Answer:<br \/>\nThe satellite travels 217(1\/2) miles in 3\/4 minutes.<\/p>\n<p>Explanation:<br \/>\nA satellite orbiting Earth travels 14\\(\\frac{1}{2}\\) miles every 3 seconds.<br \/>\nSo, it travels 14.5\/3 miles = 29\/6 miles in every 1 second<br \/>\n3\/4 minutes = 3\/4 . 60<br \/>\n= 45 seconds<br \/>\nTherefore, it travels 45 . 29\/6 miles in 3\/4 minutes<br \/>\n= 217(1\/2) miles in 3\/4 minutes.<br \/>\nHence, the satellite travels 217(1\/2) miles in 3\/4 minutes.<\/p>\n<p>Question 7.<br \/>\nAn engine runs on a mixture of 0.1 quart of oil for every 3.5 quarts of gasoline. You make 3 quarts of the mixture. How much oil and how much gasoline do you use?<\/p>\n<p>Answer:<br \/>\nWe use 0.083 quarts of oil and 2.917 quarts of gasoline.<\/p>\n<p>Explanation:<br \/>\nThe ratio of oil to gasoline = 0.1 : 3.5 = 1 : 35<br \/>\nuse the ratio table to find an equivalent ratio in which the total mixture is 3 quarts.<br \/>\nFor 3 quarts mixture<br \/>\nOil required is 1\/36 * 3 = 3\/36<br \/>\n= 1\/12 = 0.083 quarts<br \/>\nGasoline required is<br \/>\n35\/36 * 3 = 35\/12 = 2.917 quarts<br \/>\nWe use 0.083 quarts of oil and 2.917 quarts of gasoline.<\/p>\n<h3><a id=\"Ratios_and_Ratio_Tables_Homework_&amp;_Practice_5.1\"><\/a>Ratios and Ratio Tables Homework &amp; Practice 5.1<\/h3>\n<p><strong>Review &amp; Refresh<\/strong><\/p>\n<p><strong>Solve the inequality. Graph the solution.<\/strong><br \/>\nQuestion 1.<br \/>\n4p + 7 \u2265 19<\/p>\n<p>Answer:<br \/>\np \u2265 3<br \/>\n<img loading=\"lazy\" class=\"alignnone size-full wp-image-44293\" src=\"https:\/\/ccssmathanswers.com\/wp-content\/uploads\/2021\/01\/big-ideas-math-answer-key-grade-7-chapter-5-ratios-and-proportions-5.1-6.jpg\" alt=\"Big Ideas Math Answer Key Grade 7 Chapter 5 Ratios and Proportions 5.1 6\" width=\"740\" height=\"86\" srcset=\"https:\/\/bigideasmathanswers.com\/wp-content\/uploads\/2021\/01\/big-ideas-math-answer-key-grade-7-chapter-5-ratios-and-proportions-5.1-6.jpg 740w, https:\/\/bigideasmathanswers.com\/wp-content\/uploads\/2021\/01\/big-ideas-math-answer-key-grade-7-chapter-5-ratios-and-proportions-5.1-6-300x35.jpg 300w\" sizes=\"(max-width: 740px) 100vw, 740px\" \/><\/p>\n<p>Explanation:<br \/>\nGiven that,<br \/>\n4p + 7 \u2265 19<br \/>\nSubtract 7 from both sides<br \/>\n4p + 7 &#8211; 7 \u2265 19 &#8211; 7<br \/>\n4p \u2265 12<br \/>\nDivide both sides by 4<br \/>\n4p\/4 \u2265 12\/4<br \/>\np \u2265 3<\/p>\n<p>Question 2.<br \/>\n14 &lt; &#8211; 6n &#8211; 10<\/p>\n<p>Answer:<br \/>\n-4 &gt; n<br \/>\n<img loading=\"lazy\" class=\"alignnone size-full wp-image-44399\" src=\"https:\/\/ccssmathanswers.com\/wp-content\/uploads\/2021\/01\/big-ideas-math-answer-key-grade-7-chapter-5-ratios-and-proportions-5.1-7.jpg\" alt=\"Big Ideas Math Answer Key Grade 7 Chapter 5 Ratios and Proportions 5.1 7\" width=\"757\" height=\"108\" srcset=\"https:\/\/bigideasmathanswers.com\/wp-content\/uploads\/2021\/01\/big-ideas-math-answer-key-grade-7-chapter-5-ratios-and-proportions-5.1-7.jpg 757w, https:\/\/bigideasmathanswers.com\/wp-content\/uploads\/2021\/01\/big-ideas-math-answer-key-grade-7-chapter-5-ratios-and-proportions-5.1-7-300x43.jpg 300w\" sizes=\"(max-width: 757px) 100vw, 757px\" \/><\/p>\n<p>Explanation:<br \/>\nGiven that,<br \/>\n14 &lt; &#8211; 6n &#8211; 10<br \/>\nAdd 10 to both sides<br \/>\n14 + 10 &lt; -6n &#8211; 10 + 10<br \/>\n24 &lt; -6n<br \/>\nDivide both sides by -6<br \/>\n24\/-6 &gt; -6n\/-6<br \/>\n-4 &gt; n<\/p>\n<p>Question 3.<br \/>\n&#8211; 3(2 + d) \u2264 15<\/p>\n<p>Answer:<br \/>\nd \u2265 -7<br \/>\n<img loading=\"lazy\" class=\"alignnone size-full wp-image-44403\" src=\"https:\/\/ccssmathanswers.com\/wp-content\/uploads\/2021\/01\/big-ideas-math-answer-key-grade-7-chapter-5-ratios-and-proportions-5.1-8.jpg\" alt=\"Big Ideas Math Answer Key Grade 7 Chapter 5 Ratios and Proportions 5.1 8\" width=\"778\" height=\"93\" srcset=\"https:\/\/bigideasmathanswers.com\/wp-content\/uploads\/2021\/01\/big-ideas-math-answer-key-grade-7-chapter-5-ratios-and-proportions-5.1-8.jpg 778w, https:\/\/bigideasmathanswers.com\/wp-content\/uploads\/2021\/01\/big-ideas-math-answer-key-grade-7-chapter-5-ratios-and-proportions-5.1-8-300x36.jpg 300w, https:\/\/bigideasmathanswers.com\/wp-content\/uploads\/2021\/01\/big-ideas-math-answer-key-grade-7-chapter-5-ratios-and-proportions-5.1-8-768x92.jpg 768w\" sizes=\"(max-width: 778px) 100vw, 778px\" \/><\/p>\n<p>Explanation:<br \/>\nGiven that,<br \/>\n&#8211; 3(2 + d) \u2264 15<br \/>\nDivide both sides by -3<br \/>\n&#8211; 3(2 + d)\/-3 \u2265\u00a015\/-3<br \/>\n2 + d \u2265\u00a0-5<br \/>\nd \u2265 -5 &#8211; 2<br \/>\nd \u2265 -7<\/p>\n<p><strong>Find the quotient. Write fractions in simplest form.<\/strong><br \/>\nQuestion 4.<br \/>\n\\(\\frac{2}{9}\\) \u00f7 \\(\\frac{4}{3}\\)<\/p>\n<p>Answer:<br \/>\n\\(\\frac{2}{9}\\) \u00f7 \\(\\frac{4}{3}\\) = 1\/6 = 0.166<\/p>\n<p>Explanation:<br \/>\n\\(\\frac{2}{9}\\) \u00f7 \\(\\frac{4}{3}\\) = 2\/9 . 3\/4<br \/>\n= (2 . 3) \/ (9 . 4)<br \/>\n= 1\/6<br \/>\n<img loading=\"lazy\" class=\"alignnone size-full wp-image-44404\" src=\"https:\/\/ccssmathanswers.com\/wp-content\/uploads\/2021\/01\/big-ideas-math-answer-key-grade-7-chapter-5-ratios-and-proportions-5.1-9.jpg\" alt=\"Big Ideas Math Answer Key Grade 7 Chapter 5 Ratios and Proportions 5.1 9\" width=\"170\" height=\"421\" srcset=\"https:\/\/bigideasmathanswers.com\/wp-content\/uploads\/2021\/01\/big-ideas-math-answer-key-grade-7-chapter-5-ratios-and-proportions-5.1-9.jpg 170w, https:\/\/bigideasmathanswers.com\/wp-content\/uploads\/2021\/01\/big-ideas-math-answer-key-grade-7-chapter-5-ratios-and-proportions-5.1-9-121x300.jpg 121w\" sizes=\"(max-width: 170px) 100vw, 170px\" \/><\/p>\n<p>Question 5.<br \/>\n10.08 \u00f7 12<\/p>\n<p>Answer:<br \/>\n10.08 \u00f7 12 = 3024\/25 = 120.96<\/p>\n<p>Explanation:<br \/>\n10.08 \u00f7 12 = 1008\/100 \u00f7 12<br \/>\n= 1008\/100 . 12\/1<br \/>\n= (1008 . 12)\/100<br \/>\n= (100.8 . 3)\/25<br \/>\n= 3024\/25 = 120.96<br \/>\n<img loading=\"lazy\" class=\"alignnone size-full wp-image-44500\" src=\"https:\/\/ccssmathanswers.com\/wp-content\/uploads\/2021\/01\/big-ideas-math-answer-key-grade-7-chapter-5-ratios-and-proportions-5.1-10.jpg\" alt=\"Big Ideas Math Answer Key Grade 7 Chapter 5 Ratios and Proportions 5.1 10\" width=\"259\" height=\"585\" srcset=\"https:\/\/bigideasmathanswers.com\/wp-content\/uploads\/2021\/01\/big-ideas-math-answer-key-grade-7-chapter-5-ratios-and-proportions-5.1-10.jpg 259w, https:\/\/bigideasmathanswers.com\/wp-content\/uploads\/2021\/01\/big-ideas-math-answer-key-grade-7-chapter-5-ratios-and-proportions-5.1-10-133x300.jpg 133w\" sizes=\"(max-width: 259px) 100vw, 259px\" \/><\/p>\n<p>Question 6.<br \/>\n&#8211; \\(\\frac{5}{6}\\) \u00f7 \\(\\frac{3}{10}\\) = -25\/9 = -2.7777<\/p>\n<p>Answer:<br \/>\n&#8211; \\(\\frac{5}{6}\\) \u00f7 \\(\\frac{3}{10}\\)<\/p>\n<p>Explanation:<br \/>\n&#8211; \\(\\frac{5}{6}\\) \u00f7 \\(\\frac{3}{10}\\) = -5\/6 . 10\/3<br \/>\n= (-5 . 10)\/(3 . 6)<br \/>\n= -25\/9 = -2.7777<br \/>\n<img loading=\"lazy\" class=\"alignnone size-full wp-image-44514\" src=\"https:\/\/ccssmathanswers.com\/wp-content\/uploads\/2021\/01\/big-ideas-math-answer-key-grade-7-chapter-5-ratios-and-proportions-5.1-11.jpg\" alt=\"Big Ideas Math Answer Key Grade 7 Chapter 5 Ratios and Proportions 5.1 11\" width=\"242\" height=\"435\" srcset=\"https:\/\/bigideasmathanswers.com\/wp-content\/uploads\/2021\/01\/big-ideas-math-answer-key-grade-7-chapter-5-ratios-and-proportions-5.1-11.jpg 242w, https:\/\/bigideasmathanswers.com\/wp-content\/uploads\/2021\/01\/big-ideas-math-answer-key-grade-7-chapter-5-ratios-and-proportions-5.1-11-167x300.jpg 167w\" sizes=\"(max-width: 242px) 100vw, 242px\" \/><\/p>\n<p>Question 7.<br \/>\nWhich ratio can be represented by the tape diagram?<br \/>\n<img loading=\"lazy\" class=\"alignnone size-full wp-image-30359\" src=\"https:\/\/ccssmathanswers.com\/wp-content\/uploads\/2021\/01\/Big-Ideas-Math-Answer-Key-Grade-7-Chapter-5-Ratios-and-Proportions-5.1-9.png\" alt=\"Big Ideas Math Answer Key Grade 7 Chapter 5 Ratios and Proportions 5.1 9\" width=\"249\" height=\"76\" \/><br \/>\nA. 3 : 4<br \/>\nB. 4 : 5<br \/>\nC. 4 : 9<br \/>\nD. 8 : 12<\/p>\n<p>Answer:<br \/>\nD. 8 : 12<\/p>\n<p>Explanation:<br \/>\nQuantity 1 has 2 boxes, quantity 2 has 3 boxes.<br \/>\nOut of all given ratios, 8 : 12 satisfy the condition<br \/>\nThe ratio of given quantity = 2 : 3<br \/>\n2 * 4 : 3 * 4 = 8 : 12<\/p>\n<p><strong>Concepts, Skills, &amp; Problem Solving<\/strong><\/p>\n<p><strong>OPEN-ENDED<\/strong> Complete the ratio table using multiple operations. Are the ratios in the table equivalent? Explain. (See Exploration 2, p. 183.)<br \/>\nQuestion 8.<br \/>\n<img loading=\"lazy\" class=\"alignnone size-full wp-image-30360\" src=\"https:\/\/ccssmathanswers.com\/wp-content\/uploads\/2021\/01\/Big-Ideas-Math-Answer-Key-Grade-7-Chapter-5-Ratios-and-Proportions-5.1-10.png\" alt=\"Big Ideas Math Answer Key Grade 7 Chapter 5 Ratios and Proportions 5.1 10\" width=\"173\" height=\"70\" \/><\/p>\n<p>Answer:<br \/>\n<img loading=\"lazy\" class=\"alignnone size-full wp-image-44518\" src=\"https:\/\/ccssmathanswers.com\/wp-content\/uploads\/2021\/01\/big-ideas-math-answer-key-grade-7-chapter-5-ratios-and-proportions-5.1-12.jpg\" alt=\"Big Ideas Math Answer Key Grade 7 Chapter 5 Ratios and Proportions 5.1 12\" width=\"394\" height=\"161\" srcset=\"https:\/\/bigideasmathanswers.com\/wp-content\/uploads\/2021\/01\/big-ideas-math-answer-key-grade-7-chapter-5-ratios-and-proportions-5.1-12.jpg 394w, https:\/\/bigideasmathanswers.com\/wp-content\/uploads\/2021\/01\/big-ideas-math-answer-key-grade-7-chapter-5-ratios-and-proportions-5.1-12-300x123.jpg 300w\" sizes=\"(max-width: 394px) 100vw, 394px\" \/><\/p>\n<p>Explanation:<br \/>\n4 x 2 = 8, 10\u00a0 2 = 20<br \/>\n8 x 2 = 16, 20 x 2 = 40<br \/>\n16\/8 = 2, 40\/8 = 5<br \/>\nThe equivalent ratios are 4:10, 8:20, 16:40, 2:5.<\/p>\n<p>Question 9.<br \/>\n<img loading=\"lazy\" class=\"alignnone size-full wp-image-30361\" src=\"https:\/\/ccssmathanswers.com\/wp-content\/uploads\/2021\/01\/Big-Ideas-Math-Answer-Key-Grade-7-Chapter-5-Ratios-and-Proportions-5.1-11.png\" alt=\"Big Ideas Math Answer Key Grade 7 Chapter 5 Ratios and Proportions 5.1 11\" width=\"179\" height=\"96\" \/><\/p>\n<p>Answer:<br \/>\n<img loading=\"lazy\" class=\"alignnone size-full wp-image-44526\" src=\"https:\/\/ccssmathanswers.com\/wp-content\/uploads\/2021\/01\/big-ideas-math-answer-key-grade-7-chapter-5-ratios-and-proportions-5.1-14.jpg\" alt=\"Big Ideas Math Answer Key Grade 7 Chapter 5 Ratios and Proportions 5.1 14\" width=\"298\" height=\"160\" \/><\/p>\n<p>Explanation:<br \/>\n4\/5 x 10 = 8, 1\/2 x 10 = 5<br \/>\n4\/5 x 5 = 4, 1\/2 x 5 = 5\/2<br \/>\n4 x 1\/25 = 4\/25, 5\/2 x 1\/25 = 1\/10<\/p>\n<p><strong>WRITING AND INTERPRETING RATIOS<\/strong> Find the ratio. Then find and interpret the value of the ratio.<br \/>\n<img loading=\"lazy\" class=\"alignnone size-full wp-image-30362\" src=\"https:\/\/ccssmathanswers.com\/wp-content\/uploads\/2021\/01\/Big-Ideas-Math-Answer-Key-Grade-7-Chapter-5-Ratios-and-Proportions-5.1-12.png\" alt=\"Big Ideas Math Answer Key Grade 7 Chapter 5 Ratios and Proportions 5.1 12\" width=\"373\" height=\"203\" srcset=\"https:\/\/bigideasmathanswers.com\/wp-content\/uploads\/2021\/01\/Big-Ideas-Math-Answer-Key-Grade-7-Chapter-5-Ratios-and-Proportions-5.1-12.png 373w, https:\/\/bigideasmathanswers.com\/wp-content\/uploads\/2021\/01\/Big-Ideas-Math-Answer-Key-Grade-7-Chapter-5-Ratios-and-Proportions-5.1-12-300x163.png 300w\" sizes=\"(max-width: 373px) 100vw, 373px\" \/><br \/>\nQuestion 10.<br \/>\nclub soda : white grape juice<\/p>\n<p>Answer:<br \/>\nclub soda : white grape juice = 2 : 1<\/p>\n<p>Explanation:<br \/>\nClub soda = 4 cups<br \/>\nwhite grape juice = 2 cups<br \/>\nclub soda : white grape juice = 4 : 2<br \/>\n= 2 : 1<\/p>\n<p>Question 11.<br \/>\nmint leaves : chopped watermelon<\/p>\n<p>Answer:<br \/>\nmint leaves : chopped watermelon = 1 : 6<\/p>\n<p>Explanation:<br \/>\nmint leaves = 1\/2 cup<br \/>\nchopped watermelon = 3 cups<br \/>\nmint leaves : chopped watermelon = 1\/2 : 3<br \/>\n= 1 : 3 x 2<br \/>\n= 1 : 6<\/p>\n<p>Question 12.<br \/>\nwhite grape juice to sugar<\/p>\n<p>Answer:<br \/>\nwhite grape juice : sugar = 8 : 3<\/p>\n<p>Explanation:<br \/>\nwhite grape juice = 2 cups<br \/>\nsugar=3\/4 cup<br \/>\nwhite grape juice : sugar = 2 : 3\/4<br \/>\n= 2 x 4: 3<br \/>\n= 8 : 3<\/p>\n<p>Question 13.<br \/>\nlime juice to mint leaves<\/p>\n<p>Answer:<br \/>\nlime juice to mint leaves is 3 : 2<\/p>\n<p>Explanation:<br \/>\nlime juice = 3\/4 cup<br \/>\nmint leaves = 1\/2 cup<br \/>\nlime juice to mint leaves = 3\/4 : 1\/2<br \/>\n= 3\/2 : 1<br \/>\n= 3 : 2<\/p>\n<p>Question 14.<br \/>\nYou have blue ribbon and red ribbon in the ratio \\(\\frac{1}{2}\\) : \\(\\frac{1}{5}\\) . Your friend finds the value of the ratio. Is your friend correct? Explain your reasoning.<br \/>\n<img loading=\"lazy\" class=\"alignnone size-full wp-image-30363\" src=\"https:\/\/ccssmathanswers.com\/wp-content\/uploads\/2021\/01\/Big-Ideas-Math-Answer-Key-Grade-7-Chapter-5-Ratios-and-Proportions-5.1-13.png\" alt=\"Big Ideas Math Answer Key Grade 7 Chapter 5 Ratios and Proportions 5.1 13\" width=\"209\" height=\"144\" \/><\/p>\n<p>Answer:<br \/>\nWrong.<\/p>\n<p>Explanation:<br \/>\n1\/2 : 1\/5 = 1\/2 \u00f7 1\/5<br \/>\n= 1\/2 . 5\/1 = 5\/2<\/p>\n<p><strong>COMPLETING A RATIO TABLE<\/strong> Find the missing values in the ratio table. Then write the equivalent ratios.<br \/>\nQuestion 15.<br \/>\n<img loading=\"lazy\" class=\"alignnone size-full wp-image-30364\" src=\"https:\/\/ccssmathanswers.com\/wp-content\/uploads\/2021\/01\/Big-Ideas-Math-Answer-Key-Grade-7-Chapter-5-Ratios-and-Proportions-5.1-14.png\" alt=\"Big Ideas Math Answer Key Grade 7 Chapter 5 Ratios and Proportions 5.1 14\" width=\"214\" height=\"75\" \/><\/p>\n<p>Answer:<br \/>\n<img loading=\"lazy\" class=\"alignnone size-full wp-image-44539\" src=\"https:\/\/ccssmathanswers.com\/wp-content\/uploads\/2021\/01\/big-ideas-math-answer-key-grade-7-chapter-5-ratios-and-proportions-5.1-15.jpg\" alt=\"Big Ideas Math Answer Key Grade 7 Chapter 5 Ratios and Proportions 5.1 15\" width=\"515\" height=\"182\" srcset=\"https:\/\/bigideasmathanswers.com\/wp-content\/uploads\/2021\/01\/big-ideas-math-answer-key-grade-7-chapter-5-ratios-and-proportions-5.1-15.jpg 515w, https:\/\/bigideasmathanswers.com\/wp-content\/uploads\/2021\/01\/big-ideas-math-answer-key-grade-7-chapter-5-ratios-and-proportions-5.1-15-300x106.jpg 300w\" sizes=\"(max-width: 515px) 100vw, 515px\" \/><\/p>\n<p>Explanation:<br \/>\nTo find the missing values,<br \/>\n1\/6 . x = 2\/3<br \/>\nx = 2\/3 . 6<br \/>\nx = 4<br \/>\nSo, calories = 20 . 4 = 80<br \/>\n20 . y = 10<br \/>\ny = 10\/20 = 1\/2<br \/>\nMiles = 1\/6 . 1\/2 = 1\/12<br \/>\n10 . z = 90<br \/>\nz = 90\/10<br \/>\nz = 9<br \/>\nMiles = 1\/12 . 9 = 3\/4<br \/>\nThe equivalent ratios are 20 : 1\/6, 80 : 2\/3, 10 : 1\/12, 90 : 3\/4<\/p>\n<p>Question 16.<br \/>\n<img loading=\"lazy\" class=\"alignnone size-full wp-image-30365\" src=\"https:\/\/ccssmathanswers.com\/wp-content\/uploads\/2021\/01\/Big-Ideas-Math-Answer-Key-Grade-7-Chapter-5-Ratios-and-Proportions-5.1-15.png\" alt=\"Big Ideas Math Answer Key Grade 7 Chapter 5 Ratios and Proportions 5.1 15\" width=\"217\" height=\"76\" \/><\/p>\n<p>Answer:<br \/>\n<img loading=\"lazy\" class=\"alignnone size-full wp-image-44581\" src=\"https:\/\/ccssmathanswers.com\/wp-content\/uploads\/2021\/01\/big-ideas-math-answer-key-grade-7-chapter-5-ratios-and-proportions-5.1-16.jpg\" alt=\"Big Ideas Math Answer Key Grade 7 Chapter 5 Ratios and Proportions 5.1 16\" width=\"376\" height=\"132\" srcset=\"https:\/\/bigideasmathanswers.com\/wp-content\/uploads\/2021\/01\/big-ideas-math-answer-key-grade-7-chapter-5-ratios-and-proportions-5.1-16.jpg 376w, https:\/\/bigideasmathanswers.com\/wp-content\/uploads\/2021\/01\/big-ideas-math-answer-key-grade-7-chapter-5-ratios-and-proportions-5.1-16-300x105.jpg 300w\" sizes=\"(max-width: 376px) 100vw, 376px\" \/><\/p>\n<p>Explanation:<br \/>\nTo find the missing values,<br \/>\n8\/2 = 4<br \/>\nMinutes = 1\/3\/2 = 1\/3 . 2 = 1\/6<br \/>\n1\/3 . x = 1\/4<br \/>\nx = 1\/4 . 3 = 3\/4<br \/>\nMeters = 8 . 3\/4 = 6<br \/>\n1\/3 . y = 5\/12<br \/>\ny = 5\/12 . 3 = 5\/4<br \/>\nMeters = 8 . 5\/4 = 10<br \/>\nThe equivalent ratios are 8 : 1\/3, 4 : 2\/3, 6 : 1\/4, 10 : 5\/12<\/p>\n<p>Question 17.<br \/>\n<img loading=\"lazy\" class=\"alignnone size-full wp-image-30366\" src=\"https:\/\/ccssmathanswers.com\/wp-content\/uploads\/2021\/01\/Big-Ideas-Math-Answer-Key-Grade-7-Chapter-5-Ratios-and-Proportions-5.1-16.png\" alt=\"Big Ideas Math Answer Key Grade 7 Chapter 5 Ratios and Proportions 5.1 16\" width=\"207\" height=\"91\" \/><\/p>\n<p>Answer:<br \/>\n<img loading=\"lazy\" class=\"alignnone size-full wp-image-44597\" src=\"https:\/\/ccssmathanswers.com\/wp-content\/uploads\/2021\/01\/big-ideas-math-answer-key-grade-7-chapter-5-ratios-and-proportions-5.1-17.jpg\" alt=\"Big Ideas Math Answer Key Grade 7 Chapter 5 Ratios and Proportions 5.1 17\" width=\"309\" height=\"128\" srcset=\"https:\/\/bigideasmathanswers.com\/wp-content\/uploads\/2021\/01\/big-ideas-math-answer-key-grade-7-chapter-5-ratios-and-proportions-5.1-17.jpg 309w, https:\/\/bigideasmathanswers.com\/wp-content\/uploads\/2021\/01\/big-ideas-math-answer-key-grade-7-chapter-5-ratios-and-proportions-5.1-17-300x124.jpg 300w\" sizes=\"(max-width: 309px) 100vw, 309px\" \/><\/p>\n<p>Explanation:<br \/>\nTo find the missing values,<br \/>\n1\/2 . x = 1<br \/>\nx = 2<br \/>\n1\/24 . 2 = 1\/12 = Feet<br \/>\n1\/24 . y = 1\/8<br \/>\ny = 1\/8 . 24 = 3<br \/>\nInches = 1\/2 . 3 = 3\/2<br \/>\n1\/2 . z = 1\/4<br \/>\nz = 1\/4 . 2 = 1\/2<br \/>\nFeet = 1\/24 . 1\/2 = 1\/48<br \/>\nThe equivalent ratios are 1\/24 : 1\/2, 1\/12 : 1, 1\/8 : 3, 1\/48 : 1\/4<\/p>\n<p>Question 18.<br \/>\n<img loading=\"lazy\" class=\"alignnone size-full wp-image-30367\" src=\"https:\/\/ccssmathanswers.com\/wp-content\/uploads\/2021\/01\/Big-Ideas-Math-Answer-Key-Grade-7-Chapter-5-Ratios-and-Proportions-5.1-17.png\" alt=\"Big Ideas Math Answer Key Grade 7 Chapter 5 Ratios and Proportions 5.1 17\" width=\"233\" height=\"69\" \/><\/p>\n<p>Answer:<br \/>\n<img loading=\"lazy\" class=\"alignnone size-full wp-image-44600\" src=\"https:\/\/ccssmathanswers.com\/wp-content\/uploads\/2021\/01\/big-ideas-math-answer-key-grade-7-chapter-5-ratios-and-proportions-5.1-18.jpg\" alt=\"Big Ideas Math Answer Key Grade 7 Chapter 5 Ratios and Proportions 5.1 18\" width=\"430\" height=\"130\" srcset=\"https:\/\/bigideasmathanswers.com\/wp-content\/uploads\/2021\/01\/big-ideas-math-answer-key-grade-7-chapter-5-ratios-and-proportions-5.1-18.jpg 430w, https:\/\/bigideasmathanswers.com\/wp-content\/uploads\/2021\/01\/big-ideas-math-answer-key-grade-7-chapter-5-ratios-and-proportions-5.1-18-300x91.jpg 300w\" sizes=\"(max-width: 430px) 100vw, 430px\" \/><\/p>\n<p>Explanation:<br \/>\nTo find missing values,<br \/>\n1.5 . x = 1<br \/>\nx = 1\/1.5 = 2\/3<br \/>\nTea = 3.75 . 2\/3 = 2.5<br \/>\n1.5 . y = 3.5<br \/>\ny = 35\/15 = 7\/3<br \/>\nTea = 3.75 . 7\/3 = 8.75<br \/>\n1.5 . z = 2.5<br \/>\nz = 5\/3<br \/>\n3.75 . 5\/3 = 6.25<\/p>\n<p>Question 19.<br \/>\n<strong>CRITICAL THINKING<\/strong><br \/>\nAre the two statements equivalent? Explain your reasoning.<br \/>\nThe ratio of boys to girls is 2 to 3.<br \/>\nThe ratio of girls to boys is 3 to 2.<\/p>\n<p>Answer:<br \/>\nYes, both the statements are equivalent.<\/p>\n<p>Explanation:<br \/>\nThe ratio of boys to girls is 2 to 3.<br \/>\nboys : girls = 2 : 3<br \/>\nThe ratio of girls to boys is 3 to 2.<br \/>\ngirls : boys = 3 : 2<\/p>\n<p>Question 20.<br \/>\n<strong>MODELING REAL LIFE<\/strong><br \/>\nA city dumps plastic shade balls into a reservoir to prevent water from evaporating during a drought. It costs $5760 for 16,000 shade balls. How much does it cost for 12,000 shade balls?<br \/>\n<img loading=\"lazy\" class=\"alignnone size-full wp-image-30368\" src=\"https:\/\/ccssmathanswers.com\/wp-content\/uploads\/2021\/01\/Big-Ideas-Math-Answer-Key-Grade-7-Chapter-5-Ratios-and-Proportions-5.1-18.png\" alt=\"Big Ideas Math Answer Key Grade 7 Chapter 5 Ratios and Proportions 5.1 18\" width=\"256\" height=\"162\" \/><\/p>\n<p>Answer:<br \/>\nThe cost for 12,000 shade balls is $4320<\/p>\n<p>Explanation:<br \/>\nIt costs $5760 for 16,000 shade balls.<br \/>\nThe cost for 12,000 shade balls = (5760 x 12,000)\/16000<br \/>\n= 69120\/16<br \/>\n= 4320<br \/>\nSo, the The cost for 12,000 shade balls is $4320<\/p>\n<p>Question 21.<br \/>\n<strong>MODELING REAL LIFE<\/strong><br \/>\nAn oil spill spreads 25 square meters every \\(\\frac{1}{6}\\) hour. What is the area of the oil spill after 2 hours?<\/p>\n<p>Answer:<br \/>\nThe area that the oil spill covers after 2 hours is 300 sq meters.<\/p>\n<p>Explanation:<br \/>\nAn oil spill spreads 25 square meters every 1\/6 hour<br \/>\nThe unit rate = 25 \u00f7 1\/6<br \/>\n= 25 x 6 = 150 square meters per hour<br \/>\nEvery 1 hour spreads 150 square meters<br \/>\nThe area that the oil spill covers after 2 hours = 2 x 150 = 300 sq meters<\/p>\n<p>Question 22.<br \/>\n<strong>MODELING REAL LIFE<\/strong><br \/>\nYou mix 0.25 cup of juice concentrate for every 2 cups of water to make 18 cups of juice. How much juice concentrate do you use? How much water do you use?<br \/>\n<img loading=\"lazy\" class=\"alignnone size-full wp-image-30369\" src=\"https:\/\/ccssmathanswers.com\/wp-content\/uploads\/2021\/01\/Big-Ideas-Math-Answer-Key-Grade-7-Chapter-5-Ratios-and-Proportions-5.1-19.png\" alt=\"Big Ideas Math Answer Key Grade 7 Chapter 5 Ratios and Proportions 5.1 19\" width=\"197\" height=\"274\" \/><\/p>\n<p>Answer:<br \/>\nTo make 18 cups of juice we use 16 cups of water and 2 cups of juice concentrate<\/p>\n<p>Explanation:<br \/>\nThe ratio between cups of water and cups of juice concentration is 2 to 1\/4<br \/>\nThe unit rate = 2 \/ 1\/4<br \/>\n= 2 x 4 = 8 cups of water per cup of juice concentrate<br \/>\nSo, to make 9 cups of juice we use 8 cups of water and 1 cup of juice concentrate<br \/>\nTo make 18 cups of juice we use 16 cups of water and 2 cups of juice concentrate<\/p>\n<p>Question 23.<br \/>\nA store sells 2\\(\\frac{1}{4}\\) pounds of mulch for every 1\\(\\frac{1}{2}\\) pounds of gravel sold. The store sells 180 pounds of mulch and gravel combined. How many pounds of each item does the store sell?<\/p>\n<p>Answer:<br \/>\nMulch = 108 pounds, gravel = 72 pounds<\/p>\n<p>Explanation:<br \/>\nLet 2(1\/4)x = 9\/4 x be the amount of mulch so that 1(1\/2)x = 3x\/2 is the amount of gravel the store sell, both in pounds.<br \/>\nGiven that thestore sells a total of 180 pounds of mulch and gravel, we can write<br \/>\n9x\/4 + 3x\/2 = 180<br \/>\n9x + 6x = 180 x 4<br \/>\n15x = 720<br \/>\nx = 720\/15<br \/>\nx = 48<br \/>\nSo, the store sells 9\/4(48) = 108 pounds of mulch and 3\/2(48) = 72 pounds of gravel.<\/p>\n<p>Question 24.<br \/>\n<strong>DIG DEEPER!<\/strong><br \/>\nYou mix \\(\\frac{1}{4}\\) cup of red paint for every \\(\\frac{1}{2}\\) cup of blue paint to make 3 gallons of purple paint.<br \/>\na. How much red paint do you use? How much blue paint do you use?<br \/>\nb. You decide that you want to make a lighter purple paint. You make the new mixture by adding \\(\\frac{1}{4}\\) cup of white paint for every \\(\\frac{1}{4}\\) cup of red paint and \\(\\frac{1}{2}\\) cup of blue paint. How much red paint, blue paint, and white paint do you use to make 1\\(\\frac{1}{2}\\) gallons of the lighter purple paint?<\/p>\n<p>Answer:<br \/>\na. We use 12 cups of red paint, 24 cups of blue paint<br \/>\nb. white paint = 6 cups, red paint = 6 cups, blue paint = 12 cups.<\/p>\n<p>Explanation:<br \/>\nYou mix \\(\\frac{1}{4}\\) cup of red paint for every \\(\\frac{1}{2}\\) cup of blue paint to make 3 gallons of purple paint.<br \/>\na. The ratio of red paint to blue paint = 1\/4 : 1\/2<br \/>\n1\/4x + 1\/2x = (x + 2x)\/4 = 3x\/4<br \/>\n3x\/4 = 3<br \/>\nx = 3 . 4\/3<br \/>\nx = 4 cups<br \/>\n1 cup = 1\/16 gallons<br \/>\nSo, 4 cups = 4\/16 = 1\/4 gallons<br \/>\n12 . 4 = 48 cups = 1\/4 . 12 = 3 gallons<br \/>\nSo, 1\/4(48) = 12 cups of red paint and 1\/2(48) = 24 cups of blue paint is required to make 3 gallons<br \/>\nb. You make the new mixture by adding \\(\\frac{1}{4}\\) cup of white paint for every \\(\\frac{1}{4}\\) cup of red paint and \\(\\frac{1}{2}\\) cup of blue paint.<br \/>\n(1\/4 + 1\/4 +1\/2) = 1<br \/>\n1 cup = 1\/16 gallons<br \/>\nThe total lighter purple paint = 1(1\/2) = 3\/2 gallons<br \/>\nTotal number of cups = (3\/2) 16<br \/>\n= 24<br \/>\nwhite paint = 1\/4 (24) = 6 cups<br \/>\nred paint = 1\/4 (24) = 6 cups<br \/>\nblue paint = 1\/2 (24) = 12 cups<\/p>\n<h3><a id=\"Lesson_5.2_Rates_and_Unit_Rates\"><\/a>Lesson 5.2 Rates and Unit Rates<\/h3>\n<p><strong>EXPLORATION 1<\/strong><\/p>\n<p>Writing Rates<br \/>\nWork with a partner.<br \/>\na. How many degrees does the minute hand on a clock move every 15 minutes? Write a rate that compares the number of degrees moved by the minute hand to the number of hours elapsed.<br \/>\n<img loading=\"lazy\" class=\"alignnone size-full wp-image-30372\" src=\"https:\/\/ccssmathanswers.com\/wp-content\/uploads\/2021\/01\/Big-Ideas-Math-Answers-7th-Grade-Chapter-5-Ratios-and-Proportions-5.2-1.png\" alt=\"Big Ideas Math Answers 7th Grade Chapter 5 Ratios and Proportions 5.2 1\" width=\"396\" height=\"160\" srcset=\"https:\/\/bigideasmathanswers.com\/wp-content\/uploads\/2021\/01\/Big-Ideas-Math-Answers-7th-Grade-Chapter-5-Ratios-and-Proportions-5.2-1.png 396w, https:\/\/bigideasmathanswers.com\/wp-content\/uploads\/2021\/01\/Big-Ideas-Math-Answers-7th-Grade-Chapter-5-Ratios-and-Proportions-5.2-1-300x121.png 300w\" sizes=\"(max-width: 396px) 100vw, 396px\" \/><br \/>\nb. Can you use the rate in part(a) to determine how many degrees the minute hand moves in \\(\\frac{1}{2}\\) hour? Explain your reasoning.<br \/>\nc. Write a rate that represents the number of degrees moved by the minute hand every hour. How can you use this rate to find the number of degrees moved by the minute hand in 2\\(\\frac{1}{2}\\) hours?<br \/>\nd. Draw a clock with hour and minute hands. Draw another clock that shows the time after the minute hand moves 900\u00b0. How many degrees does the hour hand move in this time? in one hour? Explain your reasoning.<br \/>\n<img loading=\"lazy\" class=\"alignnone size-full wp-image-30373\" src=\"https:\/\/ccssmathanswers.com\/wp-content\/uploads\/2021\/01\/Big-Ideas-Math-Answers-7th-Grade-Chapter-5-Ratios-and-Proportions-5.2-2.png\" alt=\"Big Ideas Math Answers 7th Grade Chapter 5 Ratios and Proportions 5.2 2\" width=\"391\" height=\"236\" srcset=\"https:\/\/bigideasmathanswers.com\/wp-content\/uploads\/2021\/01\/Big-Ideas-Math-Answers-7th-Grade-Chapter-5-Ratios-and-Proportions-5.2-2.png 391w, https:\/\/bigideasmathanswers.com\/wp-content\/uploads\/2021\/01\/Big-Ideas-Math-Answers-7th-Grade-Chapter-5-Ratios-and-Proportions-5.2-2-300x181.png 300w\" sizes=\"(max-width: 391px) 100vw, 391px\" \/><\/p>\n<p><img loading=\"lazy\" class=\"alignnone size-full wp-image-30374\" src=\"https:\/\/ccssmathanswers.com\/wp-content\/uploads\/2021\/01\/Big-Ideas-Math-Answers-7th-Grade-Chapter-5-Ratios-and-Proportions-5.2-3.png\" alt=\"Big Ideas Math Answers 7th Grade Chapter 5 Ratios and Proportions 5.2 3\" width=\"190\" height=\"101\" \/><\/p>\n<p><strong>Try It<\/strong><\/p>\n<p>Question 1.<br \/>\nThere is \\(\\frac{1}{4}\\) gram of fat for every \\(\\frac{1}{3}\\) tablespoon of powdered peanut butter. How many grams of fat are there for every tablespoon of the powder?<\/p>\n<p>Answer:<br \/>\nWe have 3\/4 grams of fat for every tablespoon of the powder.<\/p>\n<p>Explanation:<br \/>\nThere is \\(\\frac{1}{4}\\) gram of fat for every \\(\\frac{1}{3}\\) tablespoon of powdered peanut butter.<br \/>\nThere are 1\/4 \/ 1\/3 = 1\/4. 3 = 3\/4 grams of fat for every tablespoon of the powder.<\/p>\n<p>Question 2.<br \/>\n<strong>WHAT IF?<\/strong><br \/>\nThe scientist later states that the iron travels 3 feet every 10 minutes. Does this change your answer in Example 2? Explain.<\/p>\n<p>Answer:<br \/>\nThe liquid iron travels about 432 feet in 1 day.<\/p>\n<p>Explanation:<br \/>\nThe iron travels 3 feet for every 10 minutes<br \/>\nThe ratio of feet to minutes is 3 : 10<br \/>\nDivide the quantity by 10 to get the unit rate per minute. Then multiply each quantity by 1440 to find the distance traveled in 24 hours.<br \/>\n<img loading=\"lazy\" class=\"alignnone size-full wp-image-45045\" src=\"https:\/\/ccssmathanswers.com\/wp-content\/uploads\/2021\/01\/big-ideas-math-answer-key-grade-7-chapter-5-ratios-and-proportions-5.1-19.jpg\" alt=\"Big Ideas Math Answer Key Grade 7 Chapter 5 Ratios and Proportions 5.1 19\" width=\"703\" height=\"99\" srcset=\"https:\/\/bigideasmathanswers.com\/wp-content\/uploads\/2021\/01\/big-ideas-math-answer-key-grade-7-chapter-5-ratios-and-proportions-5.1-19.jpg 703w, https:\/\/bigideasmathanswers.com\/wp-content\/uploads\/2021\/01\/big-ideas-math-answer-key-grade-7-chapter-5-ratios-and-proportions-5.1-19-300x42.jpg 300w\" sizes=\"(max-width: 703px) 100vw, 703px\" \/><br \/>\nSo, the liquid iron travels about 432 feet in 1 day.<\/p>\n<p><strong>Self-Assessment for Concepts &amp; Skills<\/strong><br \/>\nSolve each exercise. Then rate your understanding of the success criteria in your journal.<\/p>\n<p>Question 3.<br \/>\n<strong>VOCABULARY<\/strong><br \/>\nHow can you tell when a rate is a unit rate?<\/p>\n<p>Answer:<br \/>\nA unit rate is described as hoe many units of the first type of quantity corresponds to one unit of the second type of quantity. When the denominator is 1, then you can say that that rate is a unit rate. Few examples of unit rate are m\/sec, feet\/hour.<\/p>\n<p>Question 4.<br \/>\n<strong>WRITING<\/strong><br \/>\nExplain why rates are usually written as unit rates.<\/p>\n<p>Answer:<br \/>\nGenerally, a rate is a ratio of two quantities. Rates are usually written as unit rates because they are easier to read, easier to understand and easier to compare.<\/p>\n<p><strong>Find the unit rate.<\/strong><br \/>\nQuestion 5.<br \/>\n$1.32 for 12 ounces<\/p>\n<p>Answer:<br \/>\n$0.11 for 1 ounce<\/p>\n<p>Explanation:<br \/>\n$1.32 for 12 ounces = 1.32 : 12<br \/>\n= 1.32\/12 : 12\/12<br \/>\n= 0.11 : 1<\/p>\n<p>Question 6.<br \/>\n\\(\\frac{1}{4}\\) gallon for every \\(\\frac{3}{10}\\) mile<\/p>\n<p>Answer:<br \/>\n5\/6 gallon for every 1 mile<\/p>\n<p>Explanation:<br \/>\n\\(\\frac{1}{4}\\) gallon for every \\(\\frac{3}{10}\\) mile = 1\/4 : 3\/10<br \/>\n= 1\/4 x 10\/3 : 3\/10 x 10\/3<br \/>\n= 5\/6 : 1<\/p>\n<p>Question 7.<br \/>\n<strong>USING TOOLS<\/strong><br \/>\nFind the missing values in the ratio table. Then write the unit rate of grams per cup and the unit rate of cups per gram.<br \/>\n<img loading=\"lazy\" class=\"alignnone size-full wp-image-30375\" src=\"https:\/\/ccssmathanswers.com\/wp-content\/uploads\/2021\/01\/Big-Ideas-Math-Answers-7th-Grade-Chapter-5-Ratios-and-Proportions-5.2-4.png\" alt=\"Big Ideas Math Answers 7th Grade Chapter 5 Ratios and Proportions 5.2 4\" width=\"240\" height=\"89\" \/><\/p>\n<p>Answer:<br \/>\n<img loading=\"lazy\" class=\"alignnone size-full wp-image-45065\" src=\"https:\/\/ccssmathanswers.com\/wp-content\/uploads\/2021\/01\/big-ideas-math-answer-key-grade-7-chapter-5-ratios-and-proportions-5.2-1.jpg\" alt=\"Big Ideas Math Answer Key Grade 7 Chapter 5 Ratios and Proportions 5.2 1\" width=\"321\" height=\"131\" srcset=\"https:\/\/bigideasmathanswers.com\/wp-content\/uploads\/2021\/01\/big-ideas-math-answer-key-grade-7-chapter-5-ratios-and-proportions-5.2-1.jpg 321w, https:\/\/bigideasmathanswers.com\/wp-content\/uploads\/2021\/01\/big-ideas-math-answer-key-grade-7-chapter-5-ratios-and-proportions-5.2-1-300x122.jpg 300w\" sizes=\"(max-width: 321px) 100vw, 321px\" \/><br \/>\nThe unit rate of grams per cup = 15\/4 : 1<br \/>\nThe unit rate of cups per gram = 1 : 4\/15<\/p>\n<p>Explanation:<br \/>\n2\/3 . x = 1\/6<br \/>\nx = 1\/6 . 3\/2 = 1\/4<br \/>\n1\/4 . 5\/2 = 5\/8 = grams<br \/>\n5\/2 . y = 1<br \/>\ny = 1 . 2\/5 = 2\/5<br \/>\n2\/3 . 2\/5 = 4\/15 = cups<br \/>\n5\/2 . 3\/2 = 15\/4<br \/>\nSo, 2\/3 . 3\/2 = 1 = cups<br \/>\n2\/3 . z = 4<br \/>\nz = 4 . 3\/2 = 6<br \/>\nSo, 5\/2 . 6 = 15<br \/>\ngrams: cups = 5\/2 : 2\/3<br \/>\nThe unit rate of grams per cup = 5\/2 . 3\/2 : 1 = 15\/4 : 1<br \/>\ncups : grams = 4\/15 : 1<\/p>\n<p><strong>Self-Assessment for Problem Solving<\/strong><br \/>\nSolve each exercise. Then rate your understanding of the success criteria in your journal.<\/p>\n<p>Question 8.<br \/>\nTwo people compete in a five-mile go-kart race. Person A travels \\(\\frac{1}{10}\\) mile every 15 seconds. Person B travels \\(\\frac{3}{8}\\) mile every 48 seconds. Who wins the race? What is the difference of the finish times of the competitors?<br \/>\n<img loading=\"lazy\" class=\"alignnone size-full wp-image-30376\" src=\"https:\/\/ccssmathanswers.com\/wp-content\/uploads\/2021\/01\/Big-Ideas-Math-Answers-7th-Grade-Chapter-5-Ratios-and-Proportions-5.2-5.png\" alt=\"Big Ideas Math Answers 7th Grade Chapter 5 Ratios and Proportions 5.2 5\" width=\"204\" height=\"131\" \/><\/p>\n<p>Answer:<br \/>\nPerson B wins the race.<br \/>\nThe difference of the finish times of the competitors = 1.833 minutes<\/p>\n<p>Explanation:<br \/>\nTwo people compete in a five-mile go-kart race.<br \/>\nPerson A travels 1\/10 miles for 15 seconds = 1\/10 : 15<br \/>\nPerson A unit rate = 1\/150 : 1<br \/>\nIt means, A travels 1\/150 miles per1 second<br \/>\nSo, person A completes the race in 5 x 150 = 750 seconds = 750\/60 = 12.5 minutes<br \/>\nPerson B travels 3\/8 mile for 48 seconds = 3\/8 : 48<br \/>\nPerson B unit rate = 3\/384 : 1<br \/>\nIt means B travels 3\/384 miles in 1 second.<br \/>\nSo, person B completes the race in 5 . (384\/3) = 1920\/3 = 640<br \/>\n= 640\/60 = 10.666 minutes<br \/>\nHence, person B wins the race.<br \/>\nThe difference of the finish times of the competitors = 12.5 &#8211; 10.66 = 1.8333 minutes<\/p>\n<p>Question 9.<br \/>\n<strong>DIG DEEPER!<\/strong><br \/>\nA bus travels 0.8 mile east every 45 seconds. A second bus travels 0.55 mile west every 30 seconds. The buses start at the same location. Use two methods to determine how far apart the buses are after 15 minutes. Explain your reasoning.<\/p>\n<p>Answer:<br \/>\nTwo buses are 1\/2 mile apart after 15 minutes.<\/p>\n<p>Explanation:<br \/>\nA bus travels 0.8 mile east every 45 seconds = 0.8 : 45<br \/>\nThe unit rate = 0.8\/45 : 1<br \/>\nA second bus travels 0.55 mile west every 30 seconds = 0.55 : 30<br \/>\nThe unit rate = 0.55\/30 : 1<br \/>\nFind how much distance, busses travelled after 15 minutes = 15 x 60 = 900 seconds<br \/>\nFirst bus travels (0.8\/45) x 900 = 16 miles<br \/>\nSecond bus travels (0.55\/30) x 900 = 16.5 miles<br \/>\nThe difference in their distances = 16.5 &#8211; 16 = 1\/2 mile<\/p>\n<h3><a id=\"Rates_and_Unit_Rates_Homework_&amp;_Practice_5.2\"><\/a>Rates and Unit Rates Homework &amp; Practice 5.2<\/h3>\n<p><strong>Review &amp; Refresh<\/strong><\/p>\n<p><strong>Find the missing values in the ratio table. Then write the equivalent ratios.<\/strong><br \/>\nQuestion 1.<br \/>\n<img loading=\"lazy\" class=\"alignnone size-full wp-image-30377\" src=\"https:\/\/ccssmathanswers.com\/wp-content\/uploads\/2021\/01\/Big-Ideas-Math-Answers-7th-Grade-Chapter-5-Ratios-and-Proportions-5.2-6.png\" alt=\"Big Ideas Math Answers 7th Grade Chapter 5 Ratios and Proportions 5.2 6\" width=\"237\" height=\"86\" \/><\/p>\n<p>Answer:<br \/>\n<img loading=\"lazy\" class=\"alignnone size-full wp-image-45229\" src=\"https:\/\/ccssmathanswers.com\/wp-content\/uploads\/2021\/01\/big-ideas-math-answer-key-grade-7-chapter-5-ratios-and-proportions-5.2-2.jpg\" alt=\"Big Ideas Math Answer Key Grade 7 Chapter 5 Ratios and Proportions 5.2 2\" width=\"323\" height=\"120\" srcset=\"https:\/\/bigideasmathanswers.com\/wp-content\/uploads\/2021\/01\/big-ideas-math-answer-key-grade-7-chapter-5-ratios-and-proportions-5.2-2.jpg 323w, https:\/\/bigideasmathanswers.com\/wp-content\/uploads\/2021\/01\/big-ideas-math-answer-key-grade-7-chapter-5-ratios-and-proportions-5.2-2-300x111.jpg 300w\" sizes=\"(max-width: 323px) 100vw, 323px\" \/><br \/>\nThe equivalent ratios are 3\/4 : 1\/3, 3\/2 : 2\/3, 3 : 3\/4, 1 : 4\/9<\/p>\n<p>Explanation:<br \/>\nTo find the missing values,<br \/>\n1\/3 . x = 2\/3<br \/>\nx = 2<br \/>\n3\/4 . 2 = 3\/2 = flour<br \/>\n3\/4 . y = 3<br \/>\ny = 4<br \/>\n1\/3 . 4 = 4\/3 = oats1<br \/>\n3\/4 . z = 1<br \/>\nz = 4\/3<br \/>\n4\/3 . 1\/3 = 4\/9 = oats2<br \/>\nThe equivalent ratios are 3\/4 : 1\/3, 3\/2 : 2\/3, 3 : 3\/4, 1 : 4\/9<\/p>\n<p>Question 2.<br \/>\n<img loading=\"lazy\" class=\"alignnone size-full wp-image-30378\" src=\"https:\/\/ccssmathanswers.com\/wp-content\/uploads\/2021\/01\/Big-Ideas-Math-Answers-7th-Grade-Chapter-5-Ratios-and-Proportions-5.2-7.png\" alt=\"Big Ideas Math Answers 7th Grade Chapter 5 Ratios and Proportions 5.2 7\" width=\"221\" height=\"83\" \/><\/p>\n<p>Answer:<br \/>\n<img loading=\"lazy\" class=\"alignnone size-full wp-image-45306\" src=\"https:\/\/ccssmathanswers.com\/wp-content\/uploads\/2021\/01\/big-ideas-math-answer-key-grade-7-chapter-5-ratios-and-proportions-5.2-3.jpg\" alt=\"Big Ideas Math Answer Key Grade 7 Chapter 5 Ratios and Proportions 5.2 3\" width=\"348\" height=\"133\" srcset=\"https:\/\/bigideasmathanswers.com\/wp-content\/uploads\/2021\/01\/big-ideas-math-answer-key-grade-7-chapter-5-ratios-and-proportions-5.2-3.jpg 348w, https:\/\/bigideasmathanswers.com\/wp-content\/uploads\/2021\/01\/big-ideas-math-answer-key-grade-7-chapter-5-ratios-and-proportions-5.2-3-300x115.jpg 300w\" sizes=\"(max-width: 348px) 100vw, 348px\" \/><br \/>\nThe equivalent ratios are 1\/4 : 1\/2, 3\/4 : 3\/2, 3\/2 : 3, 5 : 10<\/p>\n<p>Explanation:<br \/>\nTo find the missing values,<br \/>\n1\/4 . x = 3\/4<br \/>\nx = 3<br \/>\n1\/2 . 3 = 3\/2 = minutes1<br \/>\n1\/2 . y = 3<br \/>\ny = 6<br \/>\n1\/4 . 6 = 3\/2 = pages<br \/>\n1\/4 . z = 5<br \/>\nz = 20<br \/>\n1\/2 . 20 = 10 = minutes 2<br \/>\nThe equivalent ratios are 1\/4 : 1\/2, 3\/4 : 3\/2, 3\/2 : 3, 5 : 10<\/p>\n<p><strong>Copy and complete the statement using &lt;, &gt;, or =.<\/strong><br \/>\nQuestion 3.<br \/>\n<img loading=\"lazy\" class=\"alignnone size-full wp-image-30379\" src=\"https:\/\/ccssmathanswers.com\/wp-content\/uploads\/2021\/01\/Big-Ideas-Math-Answers-7th-Grade-Chapter-5-Ratios-and-Proportions-5.2-8.png\" alt=\"Big Ideas Math Answers 7th Grade Chapter 5 Ratios and Proportions 5.2 8\" width=\"93\" height=\"46\" \/><\/p>\n<p>Answer:<br \/>\n9\/2 &gt; 8\/3<\/p>\n<p>Explanation:<br \/>\n9\/2 = 4.5<br \/>\n8\/3 = 2.6666<br \/>\nSo, 9\/2 &gt; 8\/3<\/p>\n<p>Question 4.<br \/>\n<img loading=\"lazy\" class=\"alignnone size-full wp-image-30380\" src=\"https:\/\/ccssmathanswers.com\/wp-content\/uploads\/2021\/01\/Big-Ideas-Math-Answers-7th-Grade-Chapter-5-Ratios-and-Proportions-5.2-9.png\" alt=\"Big Ideas Math Answers 7th Grade Chapter 5 Ratios and Proportions 5.2 9\" width=\"116\" height=\"62\" \/><\/p>\n<p>Answer:<br \/>\n-8\/15 &lt; 10\/18<\/p>\n<p>Explanation:<br \/>\n-8\/15 = -0.5333<br \/>\n10\/18 = 0.555<br \/>\nSo, -8\/15 &lt; 10\/18<\/p>\n<p>Question 5.<br \/>\n<img loading=\"lazy\" class=\"alignnone size-full wp-image-30381\" src=\"https:\/\/ccssmathanswers.com\/wp-content\/uploads\/2021\/01\/Big-Ideas-Math-Answers-7th-Grade-Chapter-5-Ratios-and-Proportions-5.2-10.png\" alt=\"Big Ideas Math Answers 7th Grade Chapter 5 Ratios and Proportions 5.2 10\" width=\"130\" height=\"81\" \/><\/p>\n<p>Answer:<br \/>\n-6\/24 = -2\/8<\/p>\n<p>Explanation:<br \/>\n-6\/24 = -0.25<br \/>\n-2\/8 = -0.25<br \/>\nSo, -6\/24 = -2\/8<\/p>\n<p><strong>Concepts, Skills, &amp; Problem Solving<\/strong><\/p>\n<p><strong>WRITING RATES<\/strong> Find the number of degrees moved by the minute hand of a clock in the given amount of time. Explain your reasoning. (See Exploration 1, p. 189.)<br \/>\nQuestion 6.<br \/>\n\\(\\frac{2}{3}\\) hour<\/p>\n<p>Answer:<br \/>\n240 degrees.<\/p>\n<p>Explanation:<br \/>\nThe minute hand passes through 60 minutes ( = 360 degrees) in 1 hour.<br \/>\nIn 2\/3 hours it passes through 2\/3 * 360 = 240 degrees.<\/p>\n<p>Question 7.<br \/>\n\\(\\frac{7}{12}\\) hour<\/p>\n<p>Answer:<br \/>\n210 degrees<\/p>\n<p>Explanation:<br \/>\nThe minute hand passes through 60 minutes ( = 360 degrees) in 1 hour.<br \/>\nIn 7\/12 hours it passes through 7\/12 * 360 = 210 degrees<\/p>\n<p>Question 8.<br \/>\n1\\(\\frac{1}{4}\\) hours<\/p>\n<p>Answer:<br \/>\n450 degrees = (360 + 90) degrees<\/p>\n<p>Explanation:<br \/>\nThe minute hand passes through 60 minutes ( = 360 degrees) in 1 hour.<br \/>\nIn 1(1\/4) = 5\/4 hours it passes through 5\/4 * 360 = 450 degrees<\/p>\n<p><strong>FINDING UNIT RATES<\/strong> Find the unit rate.<br \/>\nQuestion 9.<br \/>\n180 miles in 3 hours<\/p>\n<p>Answer:<br \/>\n6 miles per 1 hour<\/p>\n<p>Explanation:<br \/>\n180 miles in 3 hours = 18 : 3<br \/>\nThe unit rate is 18\/3 : 1 = 6 : 1<\/p>\n<p>Question 10.<br \/>\n256 miles per 8 gallons<\/p>\n<p>Answer:<br \/>\n32 miles per 1 gallon<\/p>\n<p>Explanation:<br \/>\n256 miles per 8 gallons = 256 : 8<br \/>\nThe unit rate is 256\/8 : 1 = 32 : 1<\/p>\n<p>Question 11.<br \/>\n\\(\\frac{1}{2}\\) pound : 5 days<\/p>\n<p>Answer:<br \/>\n1\/10 pounds for 1 day<\/p>\n<p>Explanation:<br \/>\n\\(\\frac{1}{2}\\) pound : 5 days = 1\/2 : 5<br \/>\nThe unit rate is 1\/2\/5 : 1<br \/>\n= 1\/10 : 1<\/p>\n<p>Question 12.<br \/>\n4 grams for every \\(\\frac{3}{4}\\) serving<\/p>\n<p>Answer:<br \/>\n16\/3 grams per serving<\/p>\n<p>Explanation:<br \/>\n4 grams for every \\(\\frac{3}{4}\\) serving = 4 : 3\/4<br \/>\nThe unit rate is = 4 x (4\/3) : 1<br \/>\n= 16\/3 : 1<\/p>\n<p>Question 13.<br \/>\n$9.60 for 4 pounds<\/p>\n<p>Answer:<br \/>\n$2.4 per 1 pound<\/p>\n<p>Explanation:<br \/>\n$9.60 for 4 pounds = 9.60 : 4<br \/>\nThe unit rate is 9.60\/4 : 1<br \/>\n= 2.4 : 1<\/p>\n<p>Question 14.<br \/>\n$4.80 for 6 cans<\/p>\n<p>Answer:<br \/>\n$0.8 per 1 can<\/p>\n<p>Explanation:<br \/>\n$4.80 for 6 cans = 4.80 : 6<br \/>\nThe unit rate is 4.80\/6 : 1<br \/>\n= 0.8 : 1<\/p>\n<p>Question 15.<br \/>\n297 words in 5.5 minutes<\/p>\n<p>Answer:<br \/>\n54 words in 1 minute<\/p>\n<p>Explanation:<br \/>\n297 words in 5.5 minutes = 297 : 5.5<br \/>\nThe unit rate is 297\/5.5 : 1<br \/>\n= 54 : 1<\/p>\n<p>Question 16.<br \/>\n\\(\\frac{1}{3}\\) kilogram: \\(\\frac{2}{3}\\) foot<\/p>\n<p>Answer:<br \/>\n1\/2 kilogram per 1 foot<\/p>\n<p>Explanation:<br \/>\n\\(\\frac{1}{3}\\) kilogram: \\(\\frac{2}{3}\\) foot = 1\/3 : 2\/3<br \/>\nThe unit rate is 1\/3 x (3\/2) : 1<br \/>\n= 1\/2 : 1<\/p>\n<p>Question 17.<br \/>\n\\(\\frac{5}{8}\\) ounce per \\(\\frac{1}{4}\\) pint<\/p>\n<p>Answer:<br \/>\n5\/2 ounce per 1 pint<\/p>\n<p>Explanation:<br \/>\n\\(\\frac{5}{8}\\) ounce per \\(\\frac{1}{4}\\) pint = 5\/8 : 1\/4<br \/>\nThe unit rate is 5\/8 x 4 : 1<br \/>\n= 5\/2 : 1<\/p>\n<p>Question 18.<br \/>\n21\\(\\frac{3}{4}\\) meters in 2\\(\\frac{1}{2}\\) hours<\/p>\n<p>Answer:<br \/>\n87 meters in 1 hour<\/p>\n<p>Explanation:<br \/>\n21\\(\\frac{3}{4}\\) meters in 2\\(\\frac{1}{2}\\) hours = 21(3\/4) : 2(1\/2)<br \/>\n= 87\/4 : 5\/2<br \/>\nThe unit rate is 87\/4 x (2\/5) : 1<br \/>\n= 87\/10 : 1<\/p>\n<p><strong>USING TOOLS<\/strong> Find the missing values in the ratio table. Then write the equivalent ratios.<br \/>\nQuestion 19.<br \/>\n<img loading=\"lazy\" class=\"alignnone size-full wp-image-30382\" src=\"https:\/\/ccssmathanswers.com\/wp-content\/uploads\/2021\/01\/Big-Ideas-Math-Answers-7th-Grade-Chapter-5-Ratios-and-Proportions-5.2-11.png\" alt=\"Big Ideas Math Answers 7th Grade Chapter 5 Ratios and Proportions 5.2 11\" width=\"205\" height=\"85\" \/><\/p>\n<p>Answer:<br \/>\n<img loading=\"lazy\" class=\"alignnone size-full wp-image-45444\" src=\"https:\/\/ccssmathanswers.com\/wp-content\/uploads\/2021\/01\/big-ideas-math-answer-key-grade-7-chapter-5-ratios-and-proportions-5.2-5.jpg\" alt=\"Big Ideas Math Answer Key Grade 7 Chapter 5 Ratios and Proportions 5.2 5\" width=\"323\" height=\"130\" srcset=\"https:\/\/bigideasmathanswers.com\/wp-content\/uploads\/2021\/01\/big-ideas-math-answer-key-grade-7-chapter-5-ratios-and-proportions-5.2-5.jpg 323w, https:\/\/bigideasmathanswers.com\/wp-content\/uploads\/2021\/01\/big-ideas-math-answer-key-grade-7-chapter-5-ratios-and-proportions-5.2-5-300x121.jpg 300w\" sizes=\"(max-width: 323px) 100vw, 323px\" \/><br \/>\nThe equivalent ratios are 25 : 1\/3, 50 : 2\/3, 75 : 1, 100 : 4\/3<\/p>\n<p>Explanation:<br \/>\nTo find the missing values,<br \/>\n25 . x = 50<br \/>\nx = 50\/25 = 2<br \/>\n1\/3 . 2 = 2\/3 = servings<br \/>\n1\/3 . y = 1<br \/>\ny = 3<br \/>\n25 . 3 = 75 = calories1<br \/>\n1\/3 . z = 4\/3<br \/>\nz = 4<br \/>\n25 . 4 = 100 = calories2<br \/>\nThe equivalent ratios are 25 : 1\/3, 50 : 2\/3, 75 : 1, 100 : 4\/3<\/p>\n<p>Question 20.<br \/>\n<img loading=\"lazy\" class=\"alignnone size-full wp-image-30383\" src=\"https:\/\/ccssmathanswers.com\/wp-content\/uploads\/2021\/01\/Big-Ideas-Math-Answers-7th-Grade-Chapter-5-Ratios-and-Proportions-5.2-12.png\" alt=\"Big Ideas Math Answers 7th Grade Chapter 5 Ratios and Proportions 5.2 12\" width=\"256\" height=\"82\" \/><\/p>\n<p>Answer:<br \/>\n<img loading=\"lazy\" class=\"alignnone size-full wp-image-45439\" src=\"https:\/\/ccssmathanswers.com\/wp-content\/uploads\/2021\/01\/big-ideas-math-answer-key-grade-7-chapter-5-ratios-and-proportions-5.2-4.jpg\" alt=\"Big Ideas Math Answer Key Grade 7 Chapter 5 Ratios and Proportions 5.2 4\" width=\"397\" height=\"130\" srcset=\"https:\/\/bigideasmathanswers.com\/wp-content\/uploads\/2021\/01\/big-ideas-math-answer-key-grade-7-chapter-5-ratios-and-proportions-5.2-4.jpg 397w, https:\/\/bigideasmathanswers.com\/wp-content\/uploads\/2021\/01\/big-ideas-math-answer-key-grade-7-chapter-5-ratios-and-proportions-5.2-4-300x98.jpg 300w\" sizes=\"(max-width: 397px) 100vw, 397px\" \/><br \/>\nThe equivalent ratios are 4 : 3\/4, 4\/3 : 1\/4, 16\/3 : 1, 16 : 3<\/p>\n<p>Explanation:<br \/>\nTo find the missing values,<br \/>\n4x = 4\/3<br \/>\nx = 1\/3<br \/>\n3\/4 . 1\/3 = 1\/4 = time1<br \/>\n3\/4 y = 1<br \/>\ny = 4\/3<br \/>\n4 . 4\/3 = 16\/3 = oxygen<br \/>\n4z = 16<br \/>\nz = 16\/4 = 4<br \/>\n3\/4 . 4 = 3 = time2<br \/>\nThe equivalent ratios are 4 : 3\/4, 4\/3 : 1\/4, 16\/3 : 1, 16 : 3<\/p>\n<p>Question 21.<br \/>\n<strong>PROBLEM SOLVING<\/strong><br \/>\nIn January 2012, the U.S.population was about 313 million people. In January 2017, it was about 324 million. What was the average rate of population change per year?<\/p>\n<p>Answer:<br \/>\nThe average rate of population change per year = 2.2 million<\/p>\n<p>Explanation:<br \/>\nIn January 2012, the U.S.population was about 313 million people<br \/>\nIn January 2017, it was about 324 million<br \/>\nAfter 5 years, the population change = 324 &#8211; 313 = 11 million<br \/>\nThe average rate of population change per year = 11\/5 = 2.2 million<\/p>\n<p>Question 22.<br \/>\n<strong>MODELING REAL LIFE<\/strong><br \/>\nYou can sand \\(\\frac{4}{9}\\) square yard of wood in \\(\\frac{1}{2}\\) hour. How many square yards can you sand in 3.2 hours? Justify your answer.<\/p>\n<p>Answer:<br \/>\n128\/45 square yards can you sand in 3.2 hours.<\/p>\n<p>Explanation:<br \/>\nYou can sand \\(\\frac{4}{9}\\) square yard of wood in \\(\\frac{1}{2}\\) hour<br \/>\nIn 3.2 hours, you can sand 4\/9 x 3.2 x 2 sq yads<br \/>\n= 25.6\/9 = 128\/45<br \/>\nSo, 128\/45 square yards can you sand in 3.2 hours.<\/p>\n<p>Question 23.<br \/>\n<strong>REASONING<\/strong><br \/>\nTell whether the rates are equivalent. Justify your answer.<br \/>\nQuestion 23.<br \/>\n75 pounds per 1.5 years<br \/>\n38.4 ounces per 0.75 year<\/p>\n<p>Answer:<br \/>\nRates are not equivalent.<\/p>\n<p>Explanation:<br \/>\n75 pounds per 1.5 years = 75 : 1.5<br \/>\n= 750\/15 = 50<br \/>\n38.4 ounces per 0.75 year = 38.4 : 0.75<br \/>\n= 384 : 7.5 = 51.2<br \/>\nSo, rates are not equivalent<\/p>\n<p>Question 24.<br \/>\n7\\(\\frac{1}{2}\\) miles for every \\(\\frac{3}{4}\\) hour<br \/>\n\\(\\frac{1}{2}\\) mile for every 3 minutes<\/p>\n<p>Answer:<br \/>\nRates are not equivalent.<\/p>\n<p>Explanation:<br \/>\n7\\(\\frac{1}{2}\\) miles for every \\(\\frac{3}{4}\\) hour = 7(1\/2) : 3\/4<br \/>\n= 15\/2 : 3\/4<br \/>\n= 15\/2 . 4\/3 = 10<br \/>\n\\(\\frac{1}{2}\\) mile for every 3 minutes = 1\/2 : 3<br \/>\n= 1 : 6<br \/>\nSo, rates are not equivalent<\/p>\n<p>Question 25.<br \/>\n<strong>PROBLEM SOLVING<\/strong><br \/>\nThe table shows nutritional information for three beverages.<br \/>\n<img loading=\"lazy\" class=\"alignnone size-full wp-image-30385\" src=\"https:\/\/ccssmathanswers.com\/wp-content\/uploads\/2021\/01\/Big-Ideas-Math-Answers-7th-Grade-Chapter-5-Ratios-and-Proportions-5.2-13.png\" alt=\"Big Ideas Math Answers 7th Grade Chapter 5 Ratios and Proportions 5.2 13\" width=\"322\" height=\"140\" srcset=\"https:\/\/bigideasmathanswers.com\/wp-content\/uploads\/2021\/01\/Big-Ideas-Math-Answers-7th-Grade-Chapter-5-Ratios-and-Proportions-5.2-13.png 322w, https:\/\/bigideasmathanswers.com\/wp-content\/uploads\/2021\/01\/Big-Ideas-Math-Answers-7th-Grade-Chapter-5-Ratios-and-Proportions-5.2-13-300x130.png 300w\" sizes=\"(max-width: 322px) 100vw, 322px\" \/><br \/>\na. Which has the most calories per fluid ounce?<br \/>\nb. Which has the least sodium per fluid ounce?<\/p>\n<p>Answer:<br \/>\na. whole milk has the most calories per fluid ounce<br \/>\nb. Oange juice has the least sodium per fluid ounce.<\/p>\n<p>Explanation:<br \/>\na.<br \/>\nConvert serving size to fluid ounce<br \/>\nWhole Milk = 1 c = 8 fl oz<br \/>\nOrange juice = 1 pt = 16 fl oz<br \/>\nWhole milk = 146 : 8 = 146\/8 : 1<br \/>\n= 18.25<br \/>\nThere are 18.25 calories in 1 fluid ounce of Whole Milk.<br \/>\nOrange juice = 210 : 16 = 210\/16 : 1<br \/>\n= 13.125<br \/>\nThere are 13.125 calories in 1 fluid ounce of Orange Juice.<br \/>\nApple juice = 351 : 24<br \/>\n= 351\/24 : 1<br \/>\nThere are 14.625 calories in 1 fluid ounce of Apple Juice.<br \/>\nSo, whole milk has the most calories per fluid ounce<br \/>\nb. Whole milk = 98 : 8<br \/>\n= 98\/8 : 1<br \/>\n= 12.25<br \/>\nOrange juice = 10 : 16<br \/>\n= 10\/16 : 1<br \/>\n= 0.625<br \/>\nApple juice = 21 : 24<br \/>\n= 21\/24 : 1<br \/>\n= 0.875<br \/>\nSo, orange juice has the least sodium per fluid ounce.<\/p>\n<p>Question 26.<br \/>\n<strong>MODELING REAL LIFE<\/strong><br \/>\nA shuttle leaving Earth\u2019s atmosphere travels 15 miles every 2 seconds. When entering the Earth\u2019s atmosphere, the shuttle travels 2\\(\\frac{3}{8}\\) miles per \\(\\frac{1}{2}\\) second. Find the difference in the distances traveled after 15 seconds when leaving and entering the atmosphere.<\/p>\n<p>Answer:<br \/>\nThe difference in the distances traveled is 2503 miles.<\/p>\n<p>Explanation:<br \/>\nA shuttle leaving Earth\u2019s atmosphere travels 15 miles every 2 seconds. = 15 : 2<br \/>\n= 15\/2 : 1<br \/>\n= 7.5 miles for every second<br \/>\nWhen entering the Earth\u2019s atmosphere, the shuttle travels 2\\(\\frac{3}{8}\\) miles per \\(\\frac{1}{2}\\) second = 2(3\/8) : \/2<br \/>\n= 19\/8 : 1\/2<br \/>\n= 19\/8 . 2 = 19\/4<br \/>\n= 4.75 miles per second<br \/>\nAfter 15 minutes = 15 x 60 = 900 seconds,<br \/>\nA shuttle leaving Earth\u2019s atmosphere travels = 7.5 x 900<br \/>\n= 6750 miles<br \/>\nWhen entering the Earth\u2019s atmosphere, the shuttle travels = 4.75 x 900<br \/>\n= 4247 miles<br \/>\nThe difference in the distances traveled = 6750 &#8211; 4247<br \/>\n= 2503 miles<\/p>\n<p>Question 27.<br \/>\n<strong>RESEARCH<\/strong><br \/>\nFire hydrants are one of four different colors to indicate the rate at which water comes from the hydrant.<br \/>\n<img loading=\"lazy\" class=\"alignnone size-full wp-image-30386\" src=\"https:\/\/ccssmathanswers.com\/wp-content\/uploads\/2021\/01\/Big-Ideas-Math-Answers-7th-Grade-Chapter-5-Ratios-and-Proportions-5.2-14.png\" alt=\"Big Ideas Math Answers 7th Grade Chapter 5 Ratios and Proportions 5.2 14\" width=\"310\" height=\"110\" srcset=\"https:\/\/bigideasmathanswers.com\/wp-content\/uploads\/2021\/01\/Big-Ideas-Math-Answers-7th-Grade-Chapter-5-Ratios-and-Proportions-5.2-14.png 310w, https:\/\/bigideasmathanswers.com\/wp-content\/uploads\/2021\/01\/Big-Ideas-Math-Answers-7th-Grade-Chapter-5-Ratios-and-Proportions-5.2-14-300x106.png 300w\" sizes=\"(max-width: 310px) 100vw, 310px\" \/><br \/>\na. Use the Internet to find the ranges of rates indicated by each color.<br \/>\nb. Research why a fire fighter needs to know the rate at which water comes out of a hydrant.<\/p>\n<p>Answer:<br \/>\na. Blue &#8211; 1500 or more gallons per minute<br \/>\nGreen &#8211; 1000 to 1499 gallons per minute<br \/>\nRed &#8211; Less than 500 gallons per minute<br \/>\nOrange &#8211; 500 to 999 gallons per minute<br \/>\nb. Fire hydrants are flow-tested at a residual pressure of 20 psi. Therefore, firefighters should understand the typical flow rates of fire hydrants at a pressure. They should not expect that the fire hydrant will be supplied at an increased pressure, resulting in a greater flow rate.<\/p>\n<p>Explanation:<br \/>\na. Blue &#8211; 1500 or more gallons per minute<br \/>\nGreen &#8211; 1000 to 1499 gallons per minute<br \/>\nRed &#8211; Less than 500 gallons per minute<br \/>\nOrange &#8211; 500 to 999 gallons per minute<\/p>\n<p>Question 28.<br \/>\n<strong>DIG DEEPER!<\/strong><br \/>\nYou and a friend start riding bikes toward each other from opposite ends of a 24-mile biking route. You ride 2\\(\\frac{1}{6}\\) miles every \\(\\frac{1}{4}\\) hour. Your friend rides 7\\(\\frac{1}{3}\\) miles per hour.<br \/>\n<img loading=\"lazy\" class=\"alignnone size-full wp-image-30387\" src=\"https:\/\/ccssmathanswers.com\/wp-content\/uploads\/2021\/01\/Big-Ideas-Math-Answers-7th-Grade-Chapter-5-Ratios-and-Proportions-5.2-15.png\" alt=\"Big Ideas Math Answers 7th Grade Chapter 5 Ratios and Proportions 5.2 15\" width=\"131\" height=\"247\" \/><br \/>\na. After how many hours do you meet?<br \/>\nb. When you meet, who has traveled farther? How much farther?<\/p>\n<p>Answer:<br \/>\na. They meet after 1(1\/2) hour.<br \/>\nb. You have traveled farther 2 miles.<\/p>\n<p>Explanation:<br \/>\nYou ride 2\\(\\frac{1}{6}\\) miles every \\(\\frac{1}{4}\\) hour.<br \/>\n= 2(1\/6) : 1\/4<br \/>\n= 13\/6 : 1\/4<br \/>\n= 13\/6 . 4 = (13 . 2)\/3 = 26\/3 : 1<br \/>\nYour friend rides 7\\(\\frac{1}{3}\\) miles per hour.<br \/>\n= 7(1\/3) : 1<br \/>\n= 22\/3 : 1<br \/>\nAfter 1 hour, you traveled = 26\/3 miles, your friend traveled 22\/3 miles<br \/>\n= 26\/3 + 22\/3 = 48\/3<br \/>\n= 16 miles<br \/>\nSince you and your friend moving towards each other at 16 miles per hour<br \/>\nwe can write 24\/16 = 3\/2 = 1.5 hours.<br \/>\nSo, they meet after 1(1\/2) hour.<br \/>\nb. You have traveled 26\/3 (1.5) = 13 miles at the time of the meeting<br \/>\nYour friend has traveled 22\/3 (1.5) = 11 miles at the time of the meeting.<br \/>\nYou have traveled farther 2 miles.<\/p>\n<h3><a id=\"Lesson_5.3_Identifying_Proportional_Relationships\"><\/a>Lesson 5.3 Identifying Proportional Relationships<\/h3>\n<p><strong>EXPLORATION 1<\/strong><\/p>\n<p>Determining Proportional Relationships<br \/>\nWork with a partner.<br \/>\na. You can paint 50 square feet of a surface every 40 minutes. How long does it take you to paint the mural shown? Explain how you found your answer.<br \/>\n<img loading=\"lazy\" class=\"alignnone size-full wp-image-30388\" src=\"https:\/\/ccssmathanswers.com\/wp-content\/uploads\/2021\/01\/Big-Ideas-Math-Answers-Grade-7-Chapter-5-Ratios-and-Proportions-5.3-1.png\" alt=\"Big Ideas Math Answers Grade 7 Chapter 5 Ratios and Proportions 5.3 1\" width=\"431\" height=\"240\" srcset=\"https:\/\/bigideasmathanswers.com\/wp-content\/uploads\/2021\/01\/Big-Ideas-Math-Answers-Grade-7-Chapter-5-Ratios-and-Proportions-5.3-1.png 431w, https:\/\/bigideasmathanswers.com\/wp-content\/uploads\/2021\/01\/Big-Ideas-Math-Answers-Grade-7-Chapter-5-Ratios-and-Proportions-5.3-1-300x167.png 300w\" sizes=\"(max-width: 431px) 100vw, 431px\" \/><br \/>\nb. The number of square feet you paint is proportional to the number of minutes it takes you. What do you think it means for a quantity to be proportional to another quantity?<br \/>\nc. Assume your friends paint at the same rate as you. The table shows how long it takes you and different numbers of friends to paint a fence. Is x proportional to y in the table? Explain.<br \/>\n<img loading=\"lazy\" class=\"alignnone size-full wp-image-30392\" src=\"https:\/\/ccssmathanswers.com\/wp-content\/uploads\/2021\/01\/Big-Ideas-Math-Answers-Grade-7-Chapter-5-Ratios-and-Proportions-5.3-2.png\" alt=\"Big Ideas Math Answers Grade 7 Chapter 5 Ratios and Proportions 5.3 2\" width=\"451\" height=\"142\" srcset=\"https:\/\/bigideasmathanswers.com\/wp-content\/uploads\/2021\/01\/Big-Ideas-Math-Answers-Grade-7-Chapter-5-Ratios-and-Proportions-5.3-2.png 451w, https:\/\/bigideasmathanswers.com\/wp-content\/uploads\/2021\/01\/Big-Ideas-Math-Answers-Grade-7-Chapter-5-Ratios-and-Proportions-5.3-2-300x94.png 300w\" sizes=\"(max-width: 451px) 100vw, 451px\" \/><br \/>\nd. How long will it take you and four friends to paint the fence? Explain how you found your answer.<\/p>\n<p>Answer:<br \/>\na. It takes 3 hours to paint the mural.<br \/>\nb. It means if the number of squares feet increases or decreases then the number of minutes to paint also increases or decreases respectively.<br \/>\nc. x is not proportional to y.<\/p>\n<p>Explanation:<br \/>\na. The area of mural = 25 x 9 = 225 sq ft<br \/>\nYou can paint 50 square feet of a surface every 40 minutes<br \/>\nTo paint the given mural it takes (40 x 225)\/50 = 180 minutes = 3 hours<br \/>\nb. The number of square feet you paint is proportional to the number of minutes it takes you.<br \/>\nIt means if the number of squares feet increases or decreases then the number of minutes to paint also increases or decreases respectively.<br \/>\nc. x : y = 1 : 4, 2 : 2 = 1 : 1<br \/>\n3 : 4\/3 = 9 : 4, 4 : 1<br \/>\nAll those are not equa so, x is not proportional to y.<\/p>\n<p><img loading=\"lazy\" class=\"alignnone size-full wp-image-30393\" src=\"https:\/\/ccssmathanswers.com\/wp-content\/uploads\/2021\/01\/Big-Ideas-Math-Answers-Grade-7-Chapter-5-Ratios-and-Proportions-5.3-3.png\" alt=\"Big Ideas Math Answers Grade 7 Chapter 5 Ratios and Proportions 5.3 3\" width=\"190\" height=\"119\" \/><\/p>\n<p><strong>Try It<\/strong><\/p>\n<p><strong>Tell whether the ratios form a proportion.<\/strong><br \/>\nQuestion 1.<br \/>\n1 : 2 and 5 : 10<\/p>\n<p>Answer:<br \/>\n1 : 2 and 5 : 10 form a proportion.<\/p>\n<p>Explanation:<br \/>\nCompare the values of the ratios<br \/>\n1\/2<br \/>\n5\/10 = (5 \u00f7 5) \/ (10 \u00f7 5) = 1\/2<br \/>\nThe values of the ratios are equivalent<br \/>\nSo, 1 : 2 and 5 : 10 form a proportion.<\/p>\n<p>Question 2.<br \/>\n4 : 6 and 18 : 24<\/p>\n<p>Answer:<br \/>\n4 : 6 and 18 : 24 do not form a proportion.<\/p>\n<p>Explanation:<br \/>\nCompare the values of the ratios<br \/>\n4\/6 = (4 \u00f7 2)\/(6 \u00f7 2) = 2\/3<br \/>\n18\/24 = (18 \u00f7 6)\/(24 \u00f7 6) = 3\/4<br \/>\nThe values of the ratios are not equivalent<br \/>\nSo, 4 : 6 and 18 : 24 do not form a proportion.<\/p>\n<p>Question 3.<br \/>\n4.5 to 3 and 6 to 9<\/p>\n<p>Answer:<br \/>\n4.5 to 3 and 6 to 9 do not form a proportion.<\/p>\n<p>Explanation:<br \/>\nCompare the values of the ratios<br \/>\n4.5\/3 = 45\/30<br \/>\n= (45 \u00f7 15) \/ (30 \u00f7 15) =3\/2<br \/>\n6\/9 = (6 \u00f7 3) \/ (9 \u00f7 3)<br \/>\n= 2\/3<br \/>\nThe values of the ratios are not equivalent<br \/>\nSo, 4.5 to 3 and 6 to 9 do not form a proportion.<\/p>\n<p>Question 4.<br \/>\n\\(\\frac{1}{2}\\) to \\(\\frac{1}{4}\\) and 8 to 4<\/p>\n<p>Answer:<br \/>\n\\(\\frac{1}{2}\\) to \\(\\frac{1}{4}\\) and 8 to 4 form a proportion<\/p>\n<p>Explanation:<br \/>\nCompare the values of the ratios<br \/>\n1\/2 : 1\/4 = (1\/2) \/ (1\/4)<br \/>\n= 1\/2 . 4 = 2 : 1<br \/>\n8 : 4 = (8 \u00f7 4) \/ (4 \u00f7 4) = 2 : 1<br \/>\nThe values of the ratios are equivalent<br \/>\nSo, \\(\\frac{1}{2}\\) to \\(\\frac{1}{4}\\) and 8 to 4 form a proportion<\/p>\n<p><strong>Tell whether the ratios form a proportion.<\/strong><br \/>\nQuestion 5.<br \/>\n6 : 2 and 12 : 1<\/p>\n<p>Answer:<br \/>\n6 : 2 and 12 : 1 do not form a proportion.<\/p>\n<p>Explanation:<br \/>\nCompare the values of the ratios<br \/>\n6 : 2 = (6 \u00f7 2) : (2 \u00f7 2) = 3 : 1<br \/>\n12 : 1 = (12 \u00f7 1) : (1 \u00f7 1) = 12 : 1<br \/>\nThe values of the ratios are not equivalent<br \/>\nSo, 6 : 2 and 12 : 1 do not form a proportion.<\/p>\n<p>Question 6.<br \/>\n8 : 12 and \\(\\frac{2}{3}\\) : 1<\/p>\n<p>Answer:<br \/>\n8 : 12 and \\(\\frac{2}{3}\\) : 1 form a proportion<\/p>\n<p>Explanation:<br \/>\nUse the cross product property to determine whether the ratios form a proportion.<br \/>\n8\/12 = 2\/3 : 1<br \/>\n8\/12 = 2\/3<br \/>\n8 . 3 = 12 . 2<br \/>\n24 = 24<br \/>\nThe cross productsare equal.<br \/>\nSo, 8 : 12 and \\(\\frac{2}{3}\\) : 1 form a proportion<\/p>\n<p><strong>Tell whether x and y are proportional.<\/strong><br \/>\nQuestion 7.<br \/>\n<img loading=\"lazy\" class=\"alignnone size-full wp-image-30394\" src=\"https:\/\/ccssmathanswers.com\/wp-content\/uploads\/2021\/01\/Big-Ideas-Math-Answers-Grade-7-Chapter-5-Ratios-and-Proportions-5.3-4.png\" alt=\"Big Ideas Math Answers Grade 7 Chapter 5 Ratios and Proportions 5.3 4\" width=\"217\" height=\"66\" \/><\/p>\n<p>Answer:<br \/>\nx and y are proportional.<\/p>\n<p>Explanation:<br \/>\nCompare the values of ratios x to y<br \/>\n1\/2, 2\/4 = 1\/2, 3\/6 = 1\/2, 4\/8 = 1\/2<br \/>\nThe values of the ratios are equivalent.<br \/>\nSo, x and y are proportional.<\/p>\n<p>Question 8.<br \/>\n<img loading=\"lazy\" class=\"alignnone size-full wp-image-30395\" src=\"https:\/\/ccssmathanswers.com\/wp-content\/uploads\/2021\/01\/Big-Ideas-Math-Answers-Grade-7-Chapter-5-Ratios-and-Proportions-5.3-5.png\" alt=\"Big Ideas Math Answers Grade 7 Chapter 5 Ratios and Proportions 5.3 5\" width=\"254\" height=\"81\" \/><\/p>\n<p>Answer:<br \/>\nx and y are not proportional.<\/p>\n<p>Explanation:<br \/>\nCompare the values of ratios x to y<br \/>\n2\/4 = 1\/2, 4\/2 = 2, 6\/1 = 6, 8\/1\/2 = 16, 10\/1\/4 = 40<br \/>\nThe values of the ratios are not equivalent.<br \/>\nSo, x and y are not proportional.<\/p>\n<p><strong>Self-Assessment for Concepts &amp; Skills<\/strong><br \/>\nSolve each exercise. Then rate your understanding of the success criteria in your journal.<\/p>\n<p><strong>PROPORTIONS<\/strong> Tell whether the ratios form a proportion.<br \/>\nQuestion 9.<br \/>\n4 : 14 and 12 : 40<\/p>\n<p>Answer:<br \/>\n4 : 14 and 12 : 40 do not form a proportion.<\/p>\n<p>Explanation:<br \/>\nUse the cross product property to determine whether the ratios form a proportion.<br \/>\n4\/14 = 12\/40<br \/>\nCross multiply<br \/>\n4 . 40 = 12 . 14<br \/>\n160 \u2260 168<br \/>\nThe cross products are not equal<br \/>\nSo, 4 : 14 and 12 : 40 do not form a proportion<\/p>\n<p>Question 10.<br \/>\n9 : 3 and 45 : 15<\/p>\n<p>Answer:<br \/>\n9 : 3 and 45 : 15 form a proportion.<\/p>\n<p>Explanation:<br \/>\nCompare the values of the ratios<br \/>\n9\/3 = (9 \u00f7 3) \/ (3 \u00f7 3) = 3\/1<br \/>\n45\/15 = (45 \u00f7 15) \/ (15 \u00f7 15) = 3\/1<br \/>\nThe ratios are equivalent<br \/>\nSo, 9 : 3 and 45 : 15 form a proportion<\/p>\n<p>Question 11.<br \/>\n<strong>VOCABULARY<\/strong><br \/>\nExplain how to determine whether two quantities are proportional.<\/p>\n<p>Answer:<br \/>\nThe two quantities are proportional means they are having equivalent ratios.<\/p>\n<p>Question 12.<br \/>\n<strong>WHICH ONE DOESN\u2019T BELONG?<\/strong><br \/>\nWhich ratio does not belong with the other three? Explain your reasoning.<br \/>\n<img loading=\"lazy\" class=\"alignnone size-full wp-image-30396\" src=\"https:\/\/ccssmathanswers.com\/wp-content\/uploads\/2021\/01\/Big-Ideas-Math-Answers-Grade-7-Chapter-5-Ratios-and-Proportions-5.3-6.png\" alt=\"Big Ideas Math Answers Grade 7 Chapter 5 Ratios and Proportions 5.3 6\" width=\"182\" height=\"98\" \/><\/p>\n<p>Answer:<br \/>\n3\/5 does not belong with the other three.<\/p>\n<p>Explanation:<br \/>\n4\/10 = 2\/5<br \/>\n2\/5<br \/>\n3\/5<br \/>\n6\/15 = 2\/5<br \/>\nSo, 3\/5 does not belong with the other three.<\/p>\n<p><strong>Self-Assessment for Problem Solving<\/strong><br \/>\nSolve each exercise. Then rate your understanding of the success criteria in your journal.<\/p>\n<p>Question 13.<br \/>\nAfter making 20 servings of pasta, a chef has used 30 cloves of garlic. The chef used 6 cloves to make the first 4 servings. How many cloves of garlic are used to make 10 servings? Justify your answer.<br \/>\n<img loading=\"lazy\" class=\"alignnone size-full wp-image-30397\" src=\"https:\/\/ccssmathanswers.com\/wp-content\/uploads\/2021\/01\/Big-Ideas-Math-Answers-Grade-7-Chapter-5-Ratios-and-Proportions-5.3-7.png\" alt=\"Big Ideas Math Answers Grade 7 Chapter 5 Ratios and Proportions 5.3 7\" width=\"186\" height=\"255\" \/><\/p>\n<p>Answer:<br \/>\n15 cloves of garlic are used to make 10 servings?<\/p>\n<p>Explanation:<br \/>\nAfter making 20 servings of pasta, a chef has used 30 cloves of garlic.<br \/>\nThe ratio of garlic cloves to serving of pasta = 30 : 20<br \/>\n= 30\/20 : 1<br \/>\n= 3\/2 : 1<br \/>\nThe chef used 6 cloves to make the first 4 servings<br \/>\nThe ratio of garlic cloves to serving of pasta = 6 : 4<br \/>\n= 6\/4 : 1<br \/>\n= 3\/2 : 1<br \/>\nIt means 1.5 garlic cloves are used to make 1 serving.<br \/>\nThe ratios are proportional<br \/>\nSo, to make 10 servings, multiply 1.5 by 10<br \/>\n= 1.5 x 10 = 15 cloves<br \/>\nTherefore, 15 cloves of garlic are used to make 10 servings.<\/p>\n<p>Question 14.<br \/>\n<strong>DIG DEEPER!<\/strong><br \/>\nA runner completes a 25-mile race in 5 hours. The runner completes the first 7.5 miles in 1.5 hours.<br \/>\na. Do these rates form a proportion? Justify your answer.<br \/>\nb. Can you determine, with certainty, the time it took the runner to complete 10 miles? Explain your reasoning.<\/p>\n<p>Answer:<br \/>\na. Yes, these form a proportion<br \/>\nb. It takes 2 hours for the runner to complete 10 miles.<\/p>\n<p>Explanation:<br \/>\na. A runner completes a 25-mile race in 5 hours.<br \/>\nThe ratio of miles to hours = 25 : 5<br \/>\n= 25\/5 : 1<br \/>\n= 5 : 1<br \/>\nThe runner completes the first 7.5 miles in 1.5 hours.<br \/>\nThe ratio of miles to hours = 7.5\/1.5<br \/>\n= 75\/15 : 1<br \/>\n= 5 : 1<br \/>\nIt means the runner completes 5 miles in 1 hour<br \/>\nThe ratios are proportional<br \/>\nb. So, it takes 10\/5 = 2 hours for the runner to complete 10 miles.<\/p>\n<h3><a id=\"Identifying_Proportional_Relationships_Homework_&amp;_Practice_5.3\"><\/a>Identifying Proportional Relationships Homework &amp; Practice 5.3<\/h3>\n<p><strong>Review &amp; Refresh<\/strong><\/p>\n<p><strong>Find the unit rate.<\/strong><br \/>\nQuestion 1.<br \/>\n30 inches per 5 years<\/p>\n<p>Answer:<br \/>\n6 inches per 1 year<\/p>\n<p>Explanation:<br \/>\n30 inches per 5 years = 30 : 5<br \/>\n= 30\/5 : 1<br \/>\n= 6 : 1<br \/>\n6 inches per 1 year<\/p>\n<p>Question 2.<br \/>\n486 games every 3 seasons<\/p>\n<p>Answer:<br \/>\n162 games every season<\/p>\n<p>Explanation:<br \/>\n486 games every 3 seasons = 486 : 3<br \/>\n= 486\/3 : 1<br \/>\n= 162 : 1<br \/>\n162 games every season<\/p>\n<p>Question 3.<br \/>\n8750 steps every 1.25 hours<\/p>\n<p>Answer:<br \/>\n7000 steps every hour<\/p>\n<p>Explanation:<br \/>\n8750 steps every 1.25 hours = 8750 : 1.25<br \/>\n= 8750\/1.25 : 1<br \/>\n= 7000 : 1<br \/>\n7000 steps every hour<\/p>\n<p>Question 4.<br \/>\n3.75 pints out of every 5 gallons<\/p>\n<p>Answer:<br \/>\n0.75 prints out of every gallon<\/p>\n<p>Explanation:<br \/>\n3.75 pints out of every 5 gallons = 3.75 : 5<br \/>\n= 3.75\/5 : 1<br \/>\n= 3\/4 : 1<br \/>\n0.75 prints out of every gallon<\/p>\n<p><strong>Add or subtract.<\/strong><br \/>\nQuestion 5.<br \/>\n&#8211; 28 + 15<\/p>\n<p>Answer:<br \/>\n&#8211; 28 + 15 = -13<\/p>\n<p>Explanation:<br \/>\n&#8211; 28 + 15 = -13<\/p>\n<p>Question 6.<br \/>\n&#8211; 6 + (- 11)<\/p>\n<p>Answer:<br \/>\n&#8211; 6 + (- 11) = -17<\/p>\n<p>Explanation:<br \/>\n&#8211; 6 + (- 11) = -6 &#8211; 11<br \/>\n= -17<\/p>\n<p>Question 7.<br \/>\n&#8211; 10 &#8211; 8<\/p>\n<p>Answer:<br \/>\n&#8211; 10 &#8211; 8 = -18<\/p>\n<p>Explanation:<br \/>\n&#8211; 10 &#8211; 8 = -18<\/p>\n<p>Question 8.<br \/>\n&#8211; 17 &#8211; (- 14)<\/p>\n<p>Answer:<br \/>\n&#8211; 17 &#8211; (- 14) = -3<\/p>\n<p>Explanation:<br \/>\n&#8211; 17 &#8211; (- 14) = -17 + 14<br \/>\n= -3<\/p>\n<p><strong>Solve the equation.<\/strong><br \/>\nQuestion 9.<br \/>\n\\(\\frac{x}{6}\\) = 25<\/p>\n<p>Answer:<br \/>\nx = 150<\/p>\n<p>Explanation:<br \/>\n\\(\\frac{x}{6}\\) = 25<br \/>\nMultiply both sides by 6<br \/>\nx\/6 \u2022 6 = 25 \u2022 6<br \/>\nx = 150<\/p>\n<p>Question 10.<br \/>\n8x = 72<\/p>\n<p>Answer:<br \/>\nx = 9<\/p>\n<p>Explanation:<br \/>\n8x = 72<br \/>\nDivide both sides by 8<br \/>\n8x\/8 = 72\/8<br \/>\nx = 9<\/p>\n<p>Question 11.<br \/>\n150 = 2x<\/p>\n<p>Answer:<br \/>\nx = 75<\/p>\n<p>Explanation:<br \/>\n150 = 2x<br \/>\nDivide both sides by 2<br \/>\n150\/2 = 2x\/2<br \/>\n75 = x<\/p>\n<p>Question 12.<br \/>\n35 = \\(\\frac{x}{4}\\)<\/p>\n<p>Answer:<br \/>\nx = 140<\/p>\n<p>Explanation:<br \/>\n35 = \\(\\frac{x}{4}\\)<br \/>\nMultiply both sides by 4<br \/>\n35 \u2022 4 = x\/4 \u2022 4<br \/>\n140 = x<\/p>\n<p><strong>Concepts, Skills, &amp; Problem Solving<\/strong><\/p>\n<p><strong>REASONING<\/strong> You can paint 75 square feet of a surface every 45 minutes. Determine how long it takes you to paint a wall with the given dimensions. (See Exploration 1, p. 195.)<br \/>\nQuestion 13.<br \/>\n8 ft \u00d7 5 ft<\/p>\n<p>Answer:<br \/>\n24 minutes<\/p>\n<p>Explanation:<br \/>\nYou can paint 75 square feet of a surface every 45 minutes<br \/>\n= 75 : 45<br \/>\n= 75\/45 : 1<br \/>\n= 5\/3 : 1<br \/>\nSo, you can paint 5\/3 sq feet of a surface in 1 minute.<br \/>\nThe given area is 8 ft \u00d7 5 ft = 40 sq ft<br \/>\nDivide 40 by 5\/3<br \/>\n= 40 \/ 5\/3<br \/>\n= 40 . 3\/5<br \/>\n= 24 minutes<\/p>\n<p>Question 14.<br \/>\n7 ft \u00d7 6 ft<\/p>\n<p>Answer:<br \/>\n25 minutes 12 seconds<\/p>\n<p>Explanation:<br \/>\nThe given area is 7 ft \u00d7 6 ft = 42 sq ft<br \/>\nDivide 42 by 5\/3<br \/>\n= 42\/5\/3<br \/>\n= 42 . 3\/5<br \/>\n= 126\/5<br \/>\n= 25(1\/5)<br \/>\n= 25 minutes 12 seconds<\/p>\n<p>Question 15.<br \/>\n9 ft \u00d7 9 ft<\/p>\n<p>Answer:<br \/>\n48 minutes 36 seconds<\/p>\n<p>Explanation:<br \/>\nThe given area is 9 ft \u00d7 9 ft = 81 sq ft<br \/>\nDivide 81 by 5\/3<br \/>\n= 81\/5\/3<br \/>\n= 81 . 3\/5<br \/>\n= 243\/5<br \/>\n= 48(3\/5)<br \/>\n= 48 minutes 36 seconds<\/p>\n<p><strong>PROPORTIONS<\/strong> Tell whether the ratios form a proportion.<br \/>\nQuestion 16.<br \/>\n1 to 3 and 7 to 21<\/p>\n<p>Answer:<br \/>\n1 to 3 and 7 to 21 form a proportion.<\/p>\n<p>Explanation:<br \/>\nCompare the values of the ratios<br \/>\n1 to 3 = 1 : 3<br \/>\n7 to 21 = 7 : 21<br \/>\n= (7 \u00f7 7) : (21 \u00f7 7)<br \/>\n= 1 : 3<br \/>\nThe ratios are equivalent<br \/>\nSo, 1 to 3 and 7 to 21 form a proportion.<\/p>\n<p>Question 17.<br \/>\n1 : 5 and 6 : 30<\/p>\n<p>Answer:<br \/>\n1 : 5 and 6 : 30 form a proportion<\/p>\n<p>Explanation:<br \/>\nCompare the values of the ratios<br \/>\n1 : 5 = 1\/5<br \/>\n6 : 30 = (6 \u00f7 6) : (30 \u00f7 6)<br \/>\n= 1\/5<br \/>\nThe ratios are equivalent<br \/>\nSo, 1 : 5 and 6 : 30 form a proportion<\/p>\n<p>Question 18.<br \/>\n3 to 4 and 24 to 18<\/p>\n<p>Answer:<br \/>\n3 to 4 and 24 to 18 do not form a proportion<\/p>\n<p>Explanation:<br \/>\nCompare the values of the ratios<br \/>\n3 to 24 = 3 : 24<br \/>\n= (3 \u00f7 3) : (24 \u00f7 3)<br \/>\n= 1 : 8<br \/>\n24 to 18 = 24 : 18<br \/>\n= (24 \u00f7 6) : (18 \u00f7 6)<br \/>\n= 4 : 3<br \/>\nThe ratios are not equivalent<br \/>\nSo, 3 to 4 and 24 to 18 do not form a proportion<\/p>\n<p>Question 19.<br \/>\n3.5 : 2 and 14 : 8<\/p>\n<p>Answer:<br \/>\n3.5 : 2 and 14 : 8 do not form a proportion<\/p>\n<p>Explanation:<br \/>\nCompare the values of the ratios<br \/>\n35 : 2 = 35\/2<br \/>\n14 : 8 = (14 \u00f7 2) : (8 \u00f7 2)<br \/>\n= 7 : 4 = 7\/4<br \/>\nThe ratios are not equivalent<br \/>\nSo, 3.5 : 2 and 14 : 8 do not form a proportion<\/p>\n<p>Question 20.<br \/>\n24: 30 and 3 : \\(\\frac{7}{2}\\)<\/p>\n<p>Answer:<br \/>\n24: 30 and 3 : \\(\\frac{7}{2}\\) do not form a proportion.<\/p>\n<p>Explanation:<br \/>\nCompare the values of the ratios<br \/>\n24 : 30 = 24\/30<br \/>\n= (24 \u00f7 2)\/(30 \u00f7 2)<br \/>\n= 12\/15<br \/>\n3 : 7\/2 = 6 : 7<br \/>\n= 6\/7<br \/>\nThe ratios are not equivalent<br \/>\nSo, 24: 30 and 3 : \\(\\frac{7}{2}\\) do not form a proportion.<\/p>\n<p>Question 21.<br \/>\n\\(\\frac{21}{2}\\) : 3 and 16 : 6<\/p>\n<p>Answer:<br \/>\n\\(\\frac{21}{2}\\) : 3 and 16 : 6 do not form a proportion.<\/p>\n<p>Explanation:<\/p>\n<p>21\/2 : 3 = 21 : 6<br \/>\n= (21 \u00f7 3) : (6 \u00f7 3)<br \/>\n= 7 : 2<br \/>\n16 : 6 = (16 \u00f7 2) : (6 \u00f7 2)<br \/>\n= 8 : 3<br \/>\nThe ratios are not equivalent<br \/>\nSo, \\(\\frac{21}{2}\\) : 3 and 16 : 6 do not form a proportion.<\/p>\n<p>Question 22.<br \/>\n0.6 : 0.5 and 12 : 10<\/p>\n<p>Answer:<br \/>\n0.6 : 0.5 and 12 : 10 form a proportion<\/p>\n<p>Explanation:<br \/>\nCompare the values of the ratios<br \/>\n0.6 : 0.5 = 6\/5<br \/>\n12 : 10 = (12 \u00f7 2) : (10 \u00f7 2)<br \/>\n= 6 : 5<br \/>\nThe ratios are equivalent<br \/>\nSo, 0.6 : 0.5 and 12 : 10 form a proportion<\/p>\n<p>Question 23.<br \/>\n2 to 4 and 11 to \\(\\frac{11}{2}\\)<\/p>\n<p>Answer:<br \/>\n2 to 4 and 11 to \\(\\frac{11}{2}\\) do not form a proportion.<\/p>\n<p>Explanation:<br \/>\nCompare the values of the ratios<br \/>\n2 to 4 = 2 : 4<br \/>\n= (2 \u00f7 2) : (4 \u00f7 2)<br \/>\n= 1 : 2<br \/>\n11 to \\(\\frac{11}{2}\\) = 11 : 11\/2<br \/>\n= 22 : 11<br \/>\n= (22 \u00f7 11) : (11 \u00f7 11)<br \/>\n= 2 : 1<br \/>\nThe ratios are not equivalent<br \/>\nSo, 2 to 4 and 11 to \\(\\frac{11}{2}\\) do not form a proportion.<\/p>\n<p>Question 24<br \/>\n\\(\\frac{5}{8}\\) : \\(\\frac{2}{3}\\) and \\(\\frac{1}{4}\\) : \\(\\frac{1}{3}\\)<\/p>\n<p>Answer:<br \/>\n\\(\\frac{5}{8}\\) : \\(\\frac{2}{3}\\) and \\(\\frac{1}{4}\\) : \\(\\frac{1}{3}\\) do not form a proportion.<\/p>\n<p>Explanation:<br \/>\nCompare the values of the ratios<br \/>\n\\(\\frac{5}{8}\\) : \\(\\frac{2}{3}\\) = 5\/8 \/ 2\/3<br \/>\n= 5\/8 . 3\/2<br \/>\n= 15\/16<br \/>\n\\(\\frac{1}{4}\\) : \\(\\frac{1}{3}\\) = 1\/4 \/ 1\/3<br \/>\n= 1\/4 . 3 = 3\/4<br \/>\nThe ratios are not equivalent<br \/>\nSo, \\(\\frac{5}{8}\\) : \\(\\frac{2}{3}\\) and \\(\\frac{1}{4}\\) : \\(\\frac{1}{3}\\) do not form proportion<\/p>\n<p><strong>IDENTIFYING PROPORTIONAL RELATIONSHIPS<\/strong> Tell whether x and y are proportional.<br \/>\nQuestion 25.<br \/>\n<img loading=\"lazy\" class=\"alignnone size-full wp-image-30398\" src=\"https:\/\/ccssmathanswers.com\/wp-content\/uploads\/2021\/01\/Big-Ideas-Math-Answers-Grade-7-Chapter-5-Ratios-and-Proportions-5.3-8.png\" alt=\"Big Ideas Math Answers Grade 7 Chapter 5 Ratios and Proportions 5.3 8\" width=\"208\" height=\"58\" \/><\/p>\n<p>Answer:<br \/>\nx and y are not proportional.<\/p>\n<p>Explanation:<br \/>\nCompare the values of the ratios x to y.<br \/>\n1\/7, 2\/8 = 1\/4, 3\/9 = 1\/3<br \/>\nThe values of the ratios are not equivalent.<br \/>\nSo, x and y are not proportional.<\/p>\n<p>Question 26.<br \/>\n<img loading=\"lazy\" class=\"alignnone size-full wp-image-30399\" src=\"https:\/\/ccssmathanswers.com\/wp-content\/uploads\/2021\/01\/Big-Ideas-Math-Answers-Grade-7-Chapter-5-Ratios-and-Proportions-5.3-9.png\" alt=\"Big Ideas Math Answers Grade 7 Chapter 5 Ratios and Proportions 5.3 9\" width=\"209\" height=\"74\" \/><\/p>\n<p>Answer:<br \/>\nx and y are proportional.<\/p>\n<p>Explanation:<br \/>\nCompare the values of the ratios x to y.<br \/>\n2\/5, 4\/10 = 2\/5, 6\/15 = 2\/5<br \/>\nThe values of the ratios are equivalent<br \/>\nSo, x and y are proportional.<\/p>\n<p>Question 27.<br \/>\n<img loading=\"lazy\" class=\"alignnone size-full wp-image-30400\" src=\"https:\/\/ccssmathanswers.com\/wp-content\/uploads\/2021\/01\/Big-Ideas-Math-Answers-Grade-7-Chapter-5-Ratios-and-Proportions-5.3-10.png\" alt=\"Big Ideas Math Answers Grade 7 Chapter 5 Ratios and Proportions 5.3 10\" width=\"210\" height=\"69\" \/><\/p>\n<p>Answer:<br \/>\nx and y are proportional.<\/p>\n<p>Explanation:<br \/>\nCompare the values of the ratios x to y.<br \/>\n0.25\/4 = 1\/16, 0.5\/8 = 1\/6, 0.75\/12 = 1\/16<br \/>\nThe values of the ratios are equivalent<br \/>\nSo, x and y are proportional.<\/p>\n<p>Question 28.<br \/>\n<img loading=\"lazy\" class=\"alignnone size-full wp-image-30401\" src=\"https:\/\/ccssmathanswers.com\/wp-content\/uploads\/2021\/01\/Big-Ideas-Math-Answers-Grade-7-Chapter-5-Ratios-and-Proportions-5.3-11.png\" alt=\"Big Ideas Math Answers Grade 7 Chapter 5 Ratios and Proportions 5.3 11\" width=\"201\" height=\"82\" \/><\/p>\n<p>Answer:<br \/>\nx and y are not proportional.<\/p>\n<p>Explanation:<br \/>\nCompare the values of the ratios x to y.<br \/>\n2\/3 \/ 7\/10 = 2\/3 . 10\/7 = 20\/21, 1\/3\/5 = 1\/3 . 5 = 5\/3<br \/>\n4\/3 \/ 1\/2 = 4\/3 . 2 = 8\/3<br \/>\nThe values of the ratios are not equivalent<br \/>\nSo, x and y are not proportional.<\/p>\n<p><strong>YOU BE THE TEACHER<\/strong> Your friend determines whether x and y are proportional. Is your friend correct? Explain your reasoning.<br \/>\nQuestion 29.<br \/>\n<img loading=\"lazy\" class=\"alignnone size-full wp-image-30402\" src=\"https:\/\/ccssmathanswers.com\/wp-content\/uploads\/2021\/01\/Big-Ideas-Math-Answers-Grade-7-Chapter-5-Ratios-and-Proportions-5.3-12.png\" alt=\"Big Ideas Math Answers Grade 7 Chapter 5 Ratios and Proportions 5.3 12\" width=\"238\" height=\"161\" \/><\/p>\n<p>Answer:<br \/>\nCorrect.<\/p>\n<p>Explanation:<br \/>\nCompare the values of the ratios x to y.<br \/>\n8 + 1 = 9<br \/>\n3 + 1 = 4<br \/>\nThe values of the ratios x to y are equal.<br \/>\nSo, x and y are proportional.<\/p>\n<p>Question 30.<br \/>\n<img loading=\"lazy\" class=\"alignnone size-full wp-image-30403\" src=\"https:\/\/ccssmathanswers.com\/wp-content\/uploads\/2021\/01\/Big-Ideas-Math-Answers-Grade-7-Chapter-5-Ratios-and-Proportions-5.3-13.png\" alt=\"Big Ideas Math Answers Grade 7 Chapter 5 Ratios and Proportions 5.3 13\" width=\"247\" height=\"168\" \/><\/p>\n<p>Answer:<br \/>\nWrong<\/p>\n<p>Explanation:<br \/>\nCompare the values of the ratios x to y.<br \/>\n2\/6 = 1\/3<br \/>\n4\/12 = 1\/3<br \/>\n8\/18 = 4\/9<br \/>\nThe values of the ratios x to y are not equal.<br \/>\nSo, x and y are not proportional.<\/p>\n<p><strong>PROPORTIONS<\/strong> Tell whether the rates form a proportion.<br \/>\nQuestion 31.<br \/>\n7 inches in 9 hours;<br \/>\n42 inches in 54 hours<\/p>\n<p>Answer:<br \/>\nRatios form a proportion.<\/p>\n<p>Explanation:<br \/>\n7 inches in 9 hours = 7 : 9<br \/>\n42 inches in 54 hours = 42 : 54<br \/>\n= (42 \u00f7 6) : (54 \u00f7 6)<br \/>\n= 7 : 9<br \/>\nThe ratios are equivalent<br \/>\nSo, ratios form a proportion.<\/p>\n<p>Question 32.<br \/>\n12 players from 21 teams;<br \/>\n15 players from 24 teams<\/p>\n<p>Answer:<br \/>\nThe ratios do not form a proportion.<\/p>\n<p>Explanation:<br \/>\n12 players from 21 teams; = 12 : 21<br \/>\n= (12 \u00f7 3) : (21 \u00f7 3)<br \/>\n= 4 : 7<br \/>\n15 players from 24 teams = 15 : 24<br \/>\n= (15 \u00f7 3) : (24 \u00f7 3)<br \/>\n= 5 : 8<br \/>\nThe ratios are not equivalent<br \/>\nSo, ratios do not form a proportion.<\/p>\n<p>Question 33.<br \/>\n385 calories in 3.5 servings; 300 calories in 3 servings<\/p>\n<p>Answer:<br \/>\n385 calories in 3.5 servings; 300 calories in 3 servings do not form a proportion.<\/p>\n<p>Explanation:<br \/>\n385 calories in 3.5 servings = 385 : 3.5<br \/>\n= 110<br \/>\n300 calories in 3 servings = 300 : 3<br \/>\n= 100<br \/>\nThe ratios are not equivalent<br \/>\nSo, 385 calories in 3.5 servings; 300 calories in 3 servings do not form a proportion.<\/p>\n<p>Question 34.<br \/>\n4.8 laps every 8 minutes; 3.6 laps every 6 minutes<\/p>\n<p>Answer:<br \/>\n4.8 laps every 8 minutes; 3.6 laps every 6 minutes form a proportion.<\/p>\n<p>Explanation:<br \/>\n4.8 laps every 8 minutes = 4.8 : 8<br \/>\n= (4.8 \u00f7 8) : (8 \u00f7 8)<br \/>\n= 3\/5 : 1<br \/>\n3.6 laps every 6 minutes = 3.6 : 6<br \/>\n= (3.6 \u00f7 6) : (6 \u00f7 6)<br \/>\n= 3\/5 : 1<br \/>\nThe ratios are equivalent<br \/>\nSo, 4.8 laps every 8 minutes; 3.6 laps every 6 minutes form a proportion.<\/p>\n<p>Question 35.<br \/>\n\\(\\frac{3}{4}\\) pound for every 5 gallons; \\(\\frac{4}{5}\\) pound for every 5\\(\\frac{1}{3}\\) gallons<\/p>\n<p>Answer:<br \/>\n\\(\\frac{3}{4}\\) pound for every 5 gallons; \\(\\frac{4}{5}\\) pound for every 5\\(\\frac{1}{3}\\) gallons do not form a proportion.<\/p>\n<p>Explanation:<br \/>\n\\(\\frac{3}{4}\\) pound for every 5 gallons = 3\/4 : 5<br \/>\n= 3 : 20<br \/>\n\\(\\frac{4}{5}\\) pound for every 5\\(\\frac{1}{3}\\) gallons = 4\/5 : 5(1\/3)<br \/>\n= 4\/5 : 16\/3<br \/>\n= 4\/5 . 3\/16<br \/>\n= 15\/16<br \/>\nThe ratios are not equivalent<br \/>\nSo, \\(\\frac{3}{4}\\) pound for every 5 gallons; \\(\\frac{4}{5}\\) pound for every 5\\(\\frac{1}{3}\\) gallons do not form a proportion.<\/p>\n<p>Question 36.<br \/>\n<strong>MODELING REAL LIFE<\/strong><br \/>\nYou do 90 sit-ups in 2 minutes. Your friend does 126 sit-ups in 2.8 minutes. Do these rates form a proportion? Explain.<br \/>\n<img loading=\"lazy\" class=\"alignnone size-full wp-image-30404\" src=\"https:\/\/ccssmathanswers.com\/wp-content\/uploads\/2021\/01\/Big-Ideas-Math-Answers-Grade-7-Chapter-5-Ratios-and-Proportions-5.3-14.png\" alt=\"Big Ideas Math Answers Grade 7 Chapter 5 Ratios and Proportions 5.3 14\" width=\"223\" height=\"117\" \/><\/p>\n<p>Answer:<br \/>\nThe rates form a proportion<\/p>\n<p>Explanation:<br \/>\nYou do 90 sit-ups in 2 minutes = 90\/2<br \/>\n= 45 sit-ups in 1 minute<br \/>\nYour friend does 126 sit-ups in 2.8 minutes = 126\/2.8<br \/>\n= 45 sit-ups in 1 minute<br \/>\nThey are equivalent.<br \/>\nSo, the rates form a proportion<\/p>\n<p>Question 37.<br \/>\n<strong>MODELING REAL LIFE<\/strong><br \/>\nFind the heart rates of you and your friend. Do these rates form a proportion? Explain.<br \/>\n<img loading=\"lazy\" class=\"alignnone size-full wp-image-30405\" src=\"https:\/\/ccssmathanswers.com\/wp-content\/uploads\/2021\/01\/Big-Ideas-Math-Answers-Grade-7-Chapter-5-Ratios-and-Proportions-5.3-15.png\" alt=\"Big Ideas Math Answers Grade 7 Chapter 5 Ratios and Proportions 5.3 15\" width=\"247\" height=\"86\" \/><\/p>\n<p>Answer:<br \/>\nThe rates do not form a proportion<\/p>\n<p>Explanation:<br \/>\nYour heart rate = 22\/20<br \/>\n= 11\/10<br \/>\nYour friend heat rate = 18\/15 = 6\/5<br \/>\nThe ratios are not equivalent<br \/>\nSo, the rates do not form a proportion<\/p>\n<p>Question 38.<br \/>\n<strong>PROBLEM SOLVING<\/strong><br \/>\nYou earn $56 walking your neighbor\u2019s dog for 8 hours. Your friend earns $36 painting your neighbor\u2019s fence for 4 hours. Are the pay rates equivalent? Explain.<\/p>\n<p>Answer:<br \/>\nThe pay rates are not equivalent.<\/p>\n<p>Explanation:<br \/>\nYou earn $56 walking your neighbor\u2019s dog for 8 hours.<br \/>\n= 56 : 8<br \/>\n= 7<br \/>\nYour friend earns $36 painting your neighbor\u2019s fence for 4 hours<br \/>\n= 36 : 4<br \/>\n= 9<br \/>\nSo, the pay rates are not equivalent.<\/p>\n<p>Question 39.<br \/>\n<strong>GEOMETRY<\/strong><br \/>\nAre the heights and bases of the two triangles proportional? Explain.<br \/>\n<img loading=\"lazy\" class=\"alignnone size-full wp-image-30406\" src=\"https:\/\/ccssmathanswers.com\/wp-content\/uploads\/2021\/01\/Big-Ideas-Math-Answers-Grade-7-Chapter-5-Ratios-and-Proportions-5.3-16.png\" alt=\"Big Ideas Math Answers Grade 7 Chapter 5 Ratios and Proportions 5.3 16\" width=\"236\" height=\"110\" \/><\/p>\n<p>Answer:<br \/>\nThe heights and bases of the two triangles proportional<\/p>\n<p>Explanation:<br \/>\nHeight to base of first triangle = 12 : 15<br \/>\n= (12 \u00f7 3) : (15 \u00f7 3)<br \/>\n= 4 : 5<br \/>\nHeight to base of second triangle = 8 : 10<br \/>\n= (8 \u00f7 2) : (10 \u00f7 5)<br \/>\n= 4 : 5<br \/>\nThe ratios are equivalent<br \/>\nSo, the heights and bases of the two triangles proportional<\/p>\n<p>Question 40.<br \/>\n<strong>REASONING<\/strong><br \/>\nA pitcher coming back from an injury limits the number of pitches thrown in bullpen sessions as shown.<br \/>\n<img loading=\"lazy\" class=\"alignnone size-full wp-image-30407\" src=\"https:\/\/ccssmathanswers.com\/wp-content\/uploads\/2021\/01\/Big-Ideas-Math-Answers-Grade-7-Chapter-5-Ratios-and-Proportions-5.3-17.png\" alt=\"Big Ideas Math Answers Grade 7 Chapter 5 Ratios and Proportions 5.3 17\" width=\"259\" height=\"142\" \/><br \/>\na. Which quantities are proportional?<br \/>\nb. How many pitches that are not curveballs will the pitcher likely throw in Session 5?<\/p>\n<p>Answer:<br \/>\na. None of the quantities are proportional.<br \/>\nb. Curveballs are 20, pitches are 50.<\/p>\n<p>Explanation:<br \/>\na. By observing the table we can say that,<br \/>\nNone of the quantities are proportional.<br \/>\nb. In session 5, the pitches are 5 . 10 = 50<br \/>\ncurveballs are 5 . 4 = 20<\/p>\n<p>Question 41.<br \/>\n<strong>STRUCTURE<\/strong><br \/>\nYou add the same numbers of pennies and dimes to the coins shown. Is the new ratio of pennies to dimes proportional to the original ratio of pennies to dimes? If so, illustrate your answer with an example. If not, show why with a counterexample.<br \/>\n<img loading=\"lazy\" class=\"alignnone size-full wp-image-30408\" src=\"https:\/\/ccssmathanswers.com\/wp-content\/uploads\/2021\/01\/Big-Ideas-Math-Answers-Grade-7-Chapter-5-Ratios-and-Proportions-5.3-18.png\" alt=\"Big Ideas Math Answers Grade 7 Chapter 5 Ratios and Proportions 5.3 18\" width=\"500\" height=\"124\" srcset=\"https:\/\/bigideasmathanswers.com\/wp-content\/uploads\/2021\/01\/Big-Ideas-Math-Answers-Grade-7-Chapter-5-Ratios-and-Proportions-5.3-18.png 500w, https:\/\/bigideasmathanswers.com\/wp-content\/uploads\/2021\/01\/Big-Ideas-Math-Answers-Grade-7-Chapter-5-Ratios-and-Proportions-5.3-18-300x74.png 300w\" sizes=\"(max-width: 500px) 100vw, 500px\" \/><\/p>\n<p>Answer:<br \/>\nThe new ratio of pennies to dimes is not proportional to the original ratio of pennies to dimes.<\/p>\n<p>Explanation:<br \/>\nNumber of pennies to dimes in image a = 3 : 2<br \/>\nNumber of pennies to dimes in image b = 4 : 4<br \/>\n= 1 : 1<br \/>\nThe ratios are not equivalent<br \/>\nSo, the new ratio of pennies to dimes is not proportional to the original ratio of pennies to dimes.<\/p>\n<p>Question 42.<br \/>\n<strong>REASONING<\/strong><br \/>\nYou are 13 years old, and your cousin is 19 years old. As you grow older, is your age proportional to your cousin\u2019s age? Explain your reasoning.<\/p>\n<p>Answer:<br \/>\nYour age is not proportional to your cousin\u2019s age<\/p>\n<p>Explanation:<br \/>\nYou are 13 years old, and your cousin is 19 years old.<br \/>\n= 13 : 19<br \/>\nAs you grow older<br \/>\nSuppose after 3 years the ratio is (13 + 3) \/ (19 + 3) = 16\/21<br \/>\n13\/19\u2260 16\/21<br \/>\nSo, your age is not proportional to your cousin\u2019s age<\/p>\n<p>Question 43.<br \/>\n<strong>MODELING REAL LIFE<\/strong><br \/>\nThe shadow of the moon during a solar eclipse travels 2300 miles in 1 hour. In the first 20 minutes, the shadow traveled 766\\(\\frac{2}{3}\\) miles. How long does it take for the shadow to travel 1150 miles? Justify your answer.<br \/>\n<img loading=\"lazy\" class=\"alignnone size-full wp-image-30409\" src=\"https:\/\/ccssmathanswers.com\/wp-content\/uploads\/2021\/01\/Big-Ideas-Math-Answers-Grade-7-Chapter-5-Ratios-and-Proportions-5.3-19.png\" alt=\"Big Ideas Math Answers Grade 7 Chapter 5 Ratios and Proportions 5.3 19\" width=\"191\" height=\"209\" \/><\/p>\n<p>Answer:<br \/>\nIt takes 30 minutes for the shadow to travel 1150 miles<\/p>\n<p>Explanation:<br \/>\nThe shadow of the moon during a solar eclipse travels 2300 miles in 1 hour<br \/>\n= 2300 : 1<br \/>\nIn the first 20 minutes, the shadow traveled 766\\(\\frac{2}{3}\\) miles.<br \/>\n= 766(2\/3) : 20<br \/>\n= 2300\/3 : 20<br \/>\nSo, it travels 2300\/3 miles in 20 minutes<br \/>\nThe time taken for the shadow to travel 1150 miles is 1150 . 20 x (3\/2300)<br \/>\n= 69000\/2300<br \/>\n= 30<br \/>\nTherefore, The time taken for the shadow to travel 1150 miles is 30 minutes<\/p>\n<p>Question 44.<br \/>\n<strong>MODELING REAL LIFE<\/strong><br \/>\nIn 60 seconds, a car in a parade travels 0.2 mile. The car traveled the last 0.05 mile in 12 seconds. How long did it take for the car to travel 0.1 mile? Justify your answer.<\/p>\n<p>Answer:<br \/>\nIt takes 32 seconds for the car to travel 0.1 mile.<\/p>\n<p>Explanation:<br \/>\nIn 60 seconds, a car in a parade travels 0.2 mile.<br \/>\nCar travels to time = 0.2 : 60<br \/>\nThe car traveled the last 0.05 mile in 12 seconds<br \/>\n= 0.05 : 12<br \/>\nSo, the car travels (0.2 &#8211; 0.05 = 0.15 miles) in (60 &#8211; 12 = 48 seconds)<br \/>\nThe time taken to travel 0.1 mile = (48 x 0.1)\/0.15 = 32 seconds.<\/p>\n<p>Question 45.<br \/>\n<strong>OPEN-ENDED<\/strong><br \/>\nDescribe (a) a real-life situation where you expect two quantities to be proportional and (b) a real-life situation where you do not expect two quantities to be proportional. Explain your reasoning.<\/p>\n<p>Answer:<br \/>\n(a) We will the real-life situation as the relationship between the number of gallons of fuel that we put in the tank and the amount of money we have to pay.<br \/>\n(b) The real-life situation is 2 persons buy different items at a store and pay amount.<\/p>\n<p>Explanation:<br \/>\n(a) Let us take two people to put fuel their cars. Person 1 puts 5 gallons of fuel and pays 20 dollars.<br \/>\nPerson 2 puts 8 gallons of fuel pays 32 dollars.<br \/>\nThe ratio to the number of gallons to dollars is 5 : 20, 8 : 32<br \/>\n= 1 : 4, 1 : 4<br \/>\nSo, the ratios are proportional.<br \/>\n(b) Let us assume 2 persons buy different products at the store and pays the bill.<br \/>\nPerson 1 buys 2 items per 15 dollars and person 2 buys 4 items for 32 dollars.<\/p>\n<p>Question 46.<br \/>\n<strong>PROBLEM SOLVING<\/strong><br \/>\nA specific shade of red nail polish requires 7 parts red to 2 parts yellow. A mixture contains 35 quarts of red and 8 quarts of yellow. Is the mixture the correct shade? If so, justify your answer. If not, explain how you can fix the mixture to make the correct shade of red.<br \/>\n<img loading=\"lazy\" class=\"alignnone size-full wp-image-30410\" src=\"https:\/\/ccssmathanswers.com\/wp-content\/uploads\/2021\/01\/Big-Ideas-Math-Answers-Grade-7-Chapter-5-Ratios-and-Proportions-5.3-20.png\" alt=\"Big Ideas Math Answers Grade 7 Chapter 5 Ratios and Proportions 5.3 20\" width=\"180\" height=\"287\" \/><\/p>\n<p>Answer:<br \/>\nTo fix the mixture add 2 more quarts of yellow.<\/p>\n<p>Explanation:<br \/>\nThe ratio of nail polish = 7\/2 = (7 . 5) \/ (2 . 5) = 35\/10 red\/yellow<br \/>\nThe ratio of mixture = 35\/8 red\/yellow<br \/>\nTo fix the mixture make the two ratios 35\/10 and 35\/8 equivalent<br \/>\nAdd 2 more quarts of yellow to the mixture<br \/>\n35\/10 = 35\/(8 + 2)<br \/>\nTo fix the mixture add 2 more quarts of yellow.<\/p>\n<p>Question 47.<br \/>\nLOGIC<br \/>\nThe quantities x and y are proportional. Use each of the integers 1\u20135 to complete the table. Justify your answer.<br \/>\n<img loading=\"lazy\" class=\"alignnone size-full wp-image-30411\" src=\"https:\/\/ccssmathanswers.com\/wp-content\/uploads\/2021\/01\/Big-Ideas-Math-Answers-Grade-7-Chapter-5-Ratios-and-Proportions-5.3-21.png\" alt=\"Big Ideas Math Answers Grade 7 Chapter 5 Ratios and Proportions 5.3 21\" width=\"263\" height=\"70\" \/><\/p>\n<p>Answer:<br \/>\n<img loading=\"lazy\" class=\"alignnone size-full wp-image-46298\" src=\"https:\/\/ccssmathanswers.com\/wp-content\/uploads\/2021\/01\/big-ideas-math-answer-key-grade-7-chapter-5-ratios-and-proportions-5.3.jpg\" alt=\"Big Ideas Math Answer Key Grade 7 Chapter 5 Ratios and Proportions 5.3 1\" width=\"362\" height=\"93\" srcset=\"https:\/\/bigideasmathanswers.com\/wp-content\/uploads\/2021\/01\/big-ideas-math-answer-key-grade-7-chapter-5-ratios-and-proportions-5.3.jpg 362w, https:\/\/bigideasmathanswers.com\/wp-content\/uploads\/2021\/01\/big-ideas-math-answer-key-grade-7-chapter-5-ratios-and-proportions-5.3-300x77.jpg 300w\" sizes=\"(max-width: 362px) 100vw, 362px\" \/><\/p>\n<p>Explanation:<br \/>\nThe quantities x and y are proportional.<br \/>\nLet us take x\/2 = y<br \/>\nSo, 10\/2 = 5<br \/>\n6\/2 = 3<br \/>\n0.5 x 2 = 1<br \/>\n4\/2 = 2<\/p>\n<p>Question 48.<br \/>\n<strong>CRITICAL THINKING<\/strong><br \/>\nRatio A and Ratio B form a proportion. Ratio B and Ratio C also form a proportion. Do Ratio A and Ratio C form a proportion? Justify your answer.<\/p>\n<p>Answer:<br \/>\nRatio A and Ratio C form a proportion.<\/p>\n<p>Explanation:<br \/>\nRatio A and Ratio B form a proportion<br \/>\nRatio B and Ratio C also form a proportion<br \/>\nSo, Ratio A : Ratio B = Ratio B : Ratio C<br \/>\nRatio A = (Ratio B)\/Ratio C x Ratio B<br \/>\nRatio C = (Ratio B x Ratio B)\/Ratio A<br \/>\nRatio A : Ratio C = [(Ratio B)\/Ratio C x Ratio B] : [(Ratio B x Ratio B)\/Ratio A]<br \/>\n= 1\/Ratio C : 1\/Ratio A<br \/>\n= Ratio A : Ratio C<br \/>\nSo, Ratio A and Ratio C form a proportion<\/p>\n<h3><a id=\"Lesson_5.4_Writing_and_Solving_Proportions\"><\/a>Lesson 5.4 Writing and Solving Proportions<\/h3>\n<p><strong>EXPLORATION 1<\/strong><\/p>\n<p>Solving a Ratio Problem<br \/>\nWork with a partner. A train travels 50 miles every 40 minutes. To determine the number of miles the train travels in 90 minutes, your friend creates the following table.<br \/>\n<img loading=\"lazy\" class=\"alignnone size-full wp-image-30412\" src=\"https:\/\/ccssmathanswers.com\/wp-content\/uploads\/2021\/01\/Big-Ideas-Math-Solutions-Grade-7-Chapter-5-Ratios-and-Proportions-5.4-1.png\" alt=\"Big Ideas Math Solutions Grade 7 Chapter 5 Ratios and Proportions 5.4 1\" width=\"178\" height=\"73\" \/><br \/>\na. Explain how you can find the value of x.<br \/>\nb. Can you use the information in the table to write a proportion? If so, explain how you can use the proportion to find the value of x. If not, explain why not.<br \/>\nc. How far does the train below travel in 2 hours?<br \/>\n<img loading=\"lazy\" class=\"alignnone size-full wp-image-30413\" src=\"https:\/\/ccssmathanswers.com\/wp-content\/uploads\/2021\/01\/Big-Ideas-Math-Solutions-Grade-7-Chapter-5-Ratios-and-Proportions-5.4-2.png\" alt=\"Big Ideas Math Solutions Grade 7 Chapter 5 Ratios and Proportions 5.4 2\" width=\"672\" height=\"285\" srcset=\"https:\/\/bigideasmathanswers.com\/wp-content\/uploads\/2021\/01\/Big-Ideas-Math-Solutions-Grade-7-Chapter-5-Ratios-and-Proportions-5.4-2.png 672w, https:\/\/bigideasmathanswers.com\/wp-content\/uploads\/2021\/01\/Big-Ideas-Math-Solutions-Grade-7-Chapter-5-Ratios-and-Proportions-5.4-2-300x127.png 300w\" sizes=\"(max-width: 672px) 100vw, 672px\" \/><br \/>\nd. Share your results in part(c) with other groups. Compare and contrast methods used to solve the problem.<\/p>\n<p>Answer:<br \/>\na. x = 112.5<br \/>\nb. yes<br \/>\nc. 120 miles<\/p>\n<p>Explanation:<br \/>\na. 50\/40 = x\/90<br \/>\n(50\/40) . 90 = x<br \/>\n4500\/40 = x<br \/>\nx = 112.5<br \/>\nb. We can use information in the table to write a proportion.<br \/>\nc. The train travels 30 miles in 1\/2 hour.<br \/>\nThe distance traveled in 2 hours is 30. 2 . 2 = 120 miles<\/p>\n<p><strong>Try It<\/strong><\/p>\n<p><strong>Solve the proportion.<\/strong><br \/>\nQuestion 1.<br \/>\n\\(\\frac{5}{8}=\\frac{20}{d}\\)<\/p>\n<p>Answer:<br \/>\nd = 32<\/p>\n<p>Explanation:<br \/>\n\\(\\frac{5}{8}=\\frac{20}{d}\\)<br \/>\ncross multiply the fractions<br \/>\n5d = 20 . 8<br \/>\n5d = 160<br \/>\nd = 160\/5<br \/>\nd = 32<\/p>\n<p>Question 2.<br \/>\n\\(\\frac{7}{z}=\\frac{14}{10}\\)<\/p>\n<p>Answer:<br \/>\nz = 5<\/p>\n<p>Explanation:<br \/>\n\\(\\frac{7}{z}=\\frac{14}{10}\\)<br \/>\ncross multiply the fractions<br \/>\n7 . 10 = 14 . z<br \/>\n70 = 14z<br \/>\n70\/14 = z<br \/>\n5 = z<\/p>\n<p>Question 3.<br \/>\n\\(\\frac{21}{24}=\\frac{x}{8}\\)<\/p>\n<p>Answer:<br \/>\nx = 7<\/p>\n<p>Explanation:<br \/>\n\\(\\frac{21}{24}=\\frac{x}{8}\\)<br \/>\ncross multiply the fractions<br \/>\n21 . 8 = 24x<br \/>\n168 = 24x<br \/>\n168\/24 = x<br \/>\nx = 7<\/p>\n<p>Solve the proportion.<br \/>\nQuestion 4.<br \/>\n\\(\\frac{w}{6}=\\frac{6}{9}\\)<\/p>\n<p>Answer:<br \/>\nw = 4<\/p>\n<p>Explanation:<br \/>\n\\(\\frac{w}{6}=\\frac{6}{9}\\)<br \/>\ncross multiply the fractions<br \/>\n9w = 6 . 6<br \/>\n9w = 36<br \/>\nw = 36\/9<br \/>\nw = 4<\/p>\n<p>Question 5.<br \/>\n\\(\\frac{12}{10}=\\frac{a}{15}\\)<\/p>\n<p>Answer:<br \/>\na = 18<\/p>\n<p>Explanation:<br \/>\n\\(\\frac{12}{10}=\\frac{a}{15}\\)<br \/>\ncross multiply the fractions<br \/>\n12 . 15 = 10a<br \/>\n180 = 10a<br \/>\na = 180\/10<br \/>\na = 18<\/p>\n<p>Question 6.<br \/>\n\\(\\frac{y}{10}=\\frac{3}{5}\\)<\/p>\n<p>Answer:<br \/>\ny = 6<\/p>\n<p>Explanation:<br \/>\n\\(\\frac{y}{10}=\\frac{3}{5}\\)<br \/>\ncross multiply the fractions<br \/>\n5y = 3 . 10<br \/>\n5y = 30<br \/>\ny = 30\/5<br \/>\ny = 6<\/p>\n<p><strong>Solve the proportion.<br \/>\n<\/strong>Question 7.<br \/>\n\\(\\frac{2}{7}=\\frac{x}{28}\\)<\/p>\n<p>Answer:<br \/>\nx = 8<\/p>\n<p>Explanation:<br \/>\n\\(\\frac{2}{7}=\\frac{x}{28}\\)<br \/>\ncross multiply the fractions<br \/>\n2 . 28 = 7x<br \/>\n56 = 7x<br \/>\nx = 56\/7<br \/>\nx = 8<\/p>\n<p>Question 8.<br \/>\n\\(\\frac{12}{5}=\\frac{6}{y}\\)<\/p>\n<p>Answer:<br \/>\ny = 5\/2<\/p>\n<p>Explanation:<br \/>\n\\(\\frac{12}{5}=\\frac{6}{y}\\)<br \/>\ncross multiply the fractions<br \/>\n12y = 6 . 5<br \/>\n12y = 30<br \/>\ny = 30\/12<br \/>\ny = 5\/2<\/p>\n<p>Question 9.<br \/>\n\\(\\frac{40}{z+1}=\\frac{15}{6}\\)<\/p>\n<p>Answer:<br \/>\nz = 15<\/p>\n<p>Explanation:<br \/>\n\\(\\frac{40}{z+1}=\\frac{15}{6}\\)<br \/>\ncross multiply the fractions<br \/>\n40 . 6 = 15(z + 1)<br \/>\n240 = 15z + 15<br \/>\n240 &#8211; 15 = 15z<br \/>\n225 = 15z<br \/>\nz = 225\/15<br \/>\nz = 15<\/p>\n<p><strong>Find the value of x so that the ratios are equivalent.<\/strong><br \/>\nQuestion 10.<br \/>\n2 : 4 and x : 6<\/p>\n<p>Answer:<br \/>\nx = 3<\/p>\n<p>Explanation:<br \/>\n2\/4 = x\/6<br \/>\ncross multiply the fractions<br \/>\n2 . 6 = 4x<br \/>\n12 = 4x<br \/>\nx = 12\/4<br \/>\nx = 3<\/p>\n<p>Question 11.<br \/>\nx : 5 and 8 : 2<\/p>\n<p>Answer:<br \/>\nx = 20<\/p>\n<p>Explanation:<br \/>\nx\/5 = 8\/2<br \/>\nx\/5 = 4<br \/>\nx = 4 . 5<br \/>\nx = 20<\/p>\n<p>Question 12.<br \/>\n4 to 3 and 10 to x<\/p>\n<p>Answer:<br \/>\nx = 15\/2<\/p>\n<p>Explanation:<br \/>\n4\/3 = 10\/x<br \/>\ncross multiply the fractions<br \/>\n4x = 3 . 10<br \/>\n4x = 30<br \/>\nx = 30\/4<br \/>\nx = 15\/2<\/p>\n<p>Question 13.<br \/>\nWrite a proportion that can be used to find the number of tomatoes in the new recipe.<\/p>\n<p>Answer:<br \/>\nThe number of tomatoes in the new recipe are 4.<\/p>\n<p>Explanation:<br \/>\nIn the original recipe, the ratio of the black beans to the number of tomatoes is 1.5 : 1<br \/>\nFor the new recipe to be proportional to the original recipe, these ratios must be equivalent.<br \/>\nSo the vales of the ratios must be equal<br \/>\n1.5\/1 = 6\/x<br \/>\n1.5 = 6\/x<br \/>\n1.5x = 6<br \/>\nx = 6\/1.5<br \/>\nx = 4<\/p>\n<p><strong>Self-Assessment for Concepts &amp; Skills<\/strong><br \/>\nSolve each exercise. Then rate your understanding of the success criteria in your journal.<\/p>\n<p><strong>SOLVING A PROPORTION<\/strong> Solve the proportion.<br \/>\nQuestion 14.<br \/>\n\\(\\frac{5}{12}=\\frac{b}{36}\\)<\/p>\n<p>Answer:<br \/>\nb = 15<\/p>\n<p>Explanation:<br \/>\n\\(\\frac{5}{12}=\\frac{b}{36}\\)<br \/>\nCross multiply the fractions<br \/>\n(5 x 36) = 12b<br \/>\n180 = 12b<br \/>\nb = 180\/12<br \/>\nb = 15<\/p>\n<p>Question 15.<br \/>\n\\(\\frac{6}{p}=\\frac{42}{35}\\)<\/p>\n<p>Answer:<br \/>\np = 5<\/p>\n<p>Explanation:<br \/>\n\\(\\frac{6}{p}=\\frac{42}{35}\\)<br \/>\nCross multiply the fractions<br \/>\n6 x 35 = 42p<br \/>\n210 = 42p<br \/>\np = 210\/42<br \/>\np = 5<\/p>\n<p>Question 16.<br \/>\n<strong>WRITING AND SOLVING A PROPORTION<\/strong><br \/>\nFind the value of x so that the ratios x : 9 and 5 : 6 are equivalent.<\/p>\n<p>Answer:<br \/>\nx = 15\/2<\/p>\n<p>Explanation:<br \/>\nThe ratios x : 9 and 5 : 6 are equivalent.<br \/>\nx\/9 = 5\/6<br \/>\nCross multiply the fractionsx<br \/>\n6x = 9 . 5<br \/>\n6x = 45<br \/>\nx = 45\/6<br \/>\nx = 15\/2<\/p>\n<p>Question 17.<br \/>\n<strong>DIFFERENT WORDS, SAME QUESTION<\/strong><br \/>\nWhich is different? Find \u201cboth\u201d answers.<br \/>\n<img loading=\"lazy\" class=\"alignnone size-full wp-image-30414\" src=\"https:\/\/ccssmathanswers.com\/wp-content\/uploads\/2021\/01\/Big-Ideas-Math-Solutions-Grade-7-Chapter-5-Ratios-and-Proportions-5.4-3.png\" alt=\"Big Ideas Math Solutions Grade 7 Chapter 5 Ratios and Proportions 5.4 3\" width=\"427\" height=\"104\" srcset=\"https:\/\/bigideasmathanswers.com\/wp-content\/uploads\/2021\/01\/Big-Ideas-Math-Solutions-Grade-7-Chapter-5-Ratios-and-Proportions-5.4-3.png 427w, https:\/\/bigideasmathanswers.com\/wp-content\/uploads\/2021\/01\/Big-Ideas-Math-Solutions-Grade-7-Chapter-5-Ratios-and-Proportions-5.4-3-300x73.png 300w\" sizes=\"(max-width: 427px) 100vw, 427px\" \/><\/p>\n<p>Answer:<br \/>\nSolve 12\/x = 3\/8 is different, x = 32<br \/>\nFor remaining x = 2<\/p>\n<p>Explanation:<br \/>\n3\/x = 12\/8<br \/>\n3 \u2022 8 = 12x<br \/>\n24 = 12x<br \/>\nx = 2<br \/>\n3 : x and 12 : 8 are equivalent<br \/>\n3\/x = 12\/8<br \/>\nSo, x = 2<br \/>\n3 : 12 and x : 8 are equivalent<br \/>\n3\/12 = x\/8<br \/>\n3 \u2022 8 = 12x<br \/>\nx = 2<br \/>\n12\/x = 3\/8<br \/>\n12 \u2022 8 = 3x<br \/>\n3x= 96<br \/>\nx = 96\/3 = 32<\/p>\n<p><strong>Self-Assessment for Problem Solving<\/strong><br \/>\nSolve each exercise. Then rate your understanding of the success criteria in your journal.<\/p>\n<p>Question 18.<br \/>\nYou burn 35 calories every 3 minutes running on a treadmill. You want to run for at least 15 minutes, but no more than 30 minutes. What are the possible numbers of calories that you will burn? Justify your answer.<\/p>\n<p>Answer:<br \/>\nThe possible number of calories burned in between 560\/3 and 350.<\/p>\n<p>Explanation:<br \/>\nYou burn 35 calories every 3 minutes running on a treadmill.<br \/>\n35 : 3<br \/>\n= 35\/3 : 1<br \/>\nYou want to run for at least 15 minutes, but no more than 30 minutes means you want to run in between 16 and 30 minutes<br \/>\nIf you run for 16 minutes then, the number of calories burn = (35\/3) x 16<br \/>\n= 560\/3<br \/>\nIf you run for 30 minutes, then the number of calories burn = (35\/3) x 30<br \/>\n= 1050\/3 = 350<br \/>\nSo, the possible number of calories burned in between 560\/3 and 350.<\/p>\n<p>Question 19.<br \/>\n<strong>DIG DEEPER!<\/strong><br \/>\nTwo boats travel at the same speed to different destinations. Boat A reaches its destination in 12 minutes. Boat B reaches its destination in 18 minutes. Boat B travels 3 miles farther than Boat A. How fast do the boats travel? Justify your answer.<br \/>\n<img loading=\"lazy\" class=\"alignnone size-full wp-image-30415\" src=\"https:\/\/ccssmathanswers.com\/wp-content\/uploads\/2021\/01\/Big-Ideas-Math-Solutions-Grade-7-Chapter-5-Ratios-and-Proportions-5.4-4.png\" alt=\"Big Ideas Math Solutions Grade 7 Chapter 5 Ratios and Proportions 5.4 4\" width=\"185\" height=\"163\" \/><\/p>\n<p>Answer:<br \/>\nThe boat travels with 1\/2 mile\/hr.<\/p>\n<p>Explanation:<br \/>\nBoat A reaches its destination in 12 minutes<br \/>\nBoat B reaches its destination in 18 minutes<br \/>\nLet us take the speed as x miles\/minute<br \/>\nSo, Boat A travels 12x miles<br \/>\nBoat B travels 18x miles<br \/>\nBoat B travels 3 miles farther than Boat A<br \/>\n18x + 3 = 12x<br \/>\n18x &#8211; 12x = -3<br \/>\n6x = -3<br \/>\nx = 3\/6<br \/>\nx = 1\/2 mile\/hr<br \/>\nSo, the boat travels with 1\/2 mile\/hr<\/p>\n<h3><a id=\"Writing_and_Solving_Proportions_Homework_&amp;_Practice_5.4\"><\/a>Writing and Solving Proportions Homework &amp; Practice 5.4<\/h3>\n<p><strong>Review &amp; Refresh<\/strong><\/p>\n<p><strong>Tell whether and are proportional.<\/strong><br \/>\nQuestion 1.<br \/>\n<img loading=\"lazy\" class=\"alignnone size-full wp-image-30416\" src=\"https:\/\/ccssmathanswers.com\/wp-content\/uploads\/2021\/01\/Big-Ideas-Math-Solutions-Grade-7-Chapter-5-Ratios-and-Proportions-5.4-5.png\" alt=\"Big Ideas Math Solutions Grade 7 Chapter 5 Ratios and Proportions 5.4 5\" width=\"164\" height=\"59\" \/><\/p>\n<p>Answer:<br \/>\nx and y are not proportional.<\/p>\n<p>Explanation:<br \/>\nCompare the values of the ratios x to y<br \/>\n4\/6 = 2\/3<br \/>\n6\/8 = 3\/4<br \/>\n8\/10 = 4\/5<br \/>\nThe values of the ratios are not equivalent<br \/>\nSo, x and y are not proportional.<\/p>\n<p>Question 2.<br \/>\n<img loading=\"lazy\" class=\"alignnone size-full wp-image-30417\" src=\"https:\/\/ccssmathanswers.com\/wp-content\/uploads\/2021\/01\/Big-Ideas-Math-Solutions-Grade-7-Chapter-5-Ratios-and-Proportions-5.4-6.png\" alt=\"Big Ideas Math Solutions Grade 7 Chapter 5 Ratios and Proportions 5.4 6\" width=\"194\" height=\"72\" \/><\/p>\n<p>Answer:<br \/>\nx and y are proportional.<\/p>\n<p>Explanation:<br \/>\nCompare the values of the ratios x to y<br \/>\n2\/5\/3 = 2\/15<br \/>\n4\/5\/6 = 2\/15<br \/>\n4\/30 = 2\/15<br \/>\nThe values of the ratios are equivalent<br \/>\nSo, x and y are proportional.<\/p>\n<p><strong>Plot the ordered pair in a coordinate plane.<\/strong><br \/>\nQuestion 3.<br \/>\nA (- 5, &#8211; 2)<\/p>\n<p>Answer:<br \/>\n<img loading=\"lazy\" class=\"alignnone size-full wp-image-46782\" src=\"https:\/\/ccssmathanswers.com\/wp-content\/uploads\/2021\/01\/big-ideas-math-answer-key-grade-7-chapter-5-ratios-and-proportions-5.5-1.jpg\" alt=\"Big Ideas Math Answer Key Grade 7 Chapter 5 Ratios and Proportions 5.5 1\" width=\"960\" height=\"712\" srcset=\"https:\/\/bigideasmathanswers.com\/wp-content\/uploads\/2021\/01\/big-ideas-math-answer-key-grade-7-chapter-5-ratios-and-proportions-5.5-1.jpg 960w, https:\/\/bigideasmathanswers.com\/wp-content\/uploads\/2021\/01\/big-ideas-math-answer-key-grade-7-chapter-5-ratios-and-proportions-5.5-1-300x223.jpg 300w, https:\/\/bigideasmathanswers.com\/wp-content\/uploads\/2021\/01\/big-ideas-math-answer-key-grade-7-chapter-5-ratios-and-proportions-5.5-1-768x570.jpg 768w\" sizes=\"(max-width: 960px) 100vw, 960px\" \/><\/p>\n<p>Explanation:<br \/>\nIn point A (- 5, &#8211; 2)<br \/>\nThe x coordinate and y coordinate values are negative.<br \/>\nso, the point lies in 3rd quadrant.<br \/>\nTake 5 units on the x-axis, 2 units on the y-axis, and locate the point.<\/p>\n<p>Question 4.<br \/>\nB (- 3, 0)<\/p>\n<p>Answer:<br \/>\n<img loading=\"lazy\" class=\"alignnone size-full wp-image-46798\" src=\"https:\/\/ccssmathanswers.com\/wp-content\/uploads\/2021\/01\/big-ideas-math-answer-key-grade-7-chapter-5-ratios-and-proportions-5.5-2.jpg\" alt=\"Big Ideas Math Answer Key Grade 7 Chapter 5 Ratios and Proportions 5.5 2\" width=\"960\" height=\"714\" srcset=\"https:\/\/bigideasmathanswers.com\/wp-content\/uploads\/2021\/01\/big-ideas-math-answer-key-grade-7-chapter-5-ratios-and-proportions-5.5-2.jpg 960w, https:\/\/bigideasmathanswers.com\/wp-content\/uploads\/2021\/01\/big-ideas-math-answer-key-grade-7-chapter-5-ratios-and-proportions-5.5-2-300x223.jpg 300w, https:\/\/bigideasmathanswers.com\/wp-content\/uploads\/2021\/01\/big-ideas-math-answer-key-grade-7-chapter-5-ratios-and-proportions-5.5-2-768x571.jpg 768w\" sizes=\"(max-width: 960px) 100vw, 960px\" \/><\/p>\n<p>Explanation:<br \/>\nIn the point B (- 3, 0)<br \/>\nThe x coordinate, y coordinates are negative and zero.<br \/>\nSo, the point lies in the x-axis.<\/p>\n<p>Question 5.<br \/>\nC (- 1, 2)<\/p>\n<p>Answer:<br \/>\n<img loading=\"lazy\" class=\"alignnone size-full wp-image-46800\" src=\"https:\/\/ccssmathanswers.com\/wp-content\/uploads\/2021\/01\/big-ideas-math-answer-key-grade-7-chapter-5-ratios-and-proportions-5.5-3.jpg\" alt=\"Big Ideas Math Answer Key Grade 7 Chapter 5 Ratios and Proportions 5.5 3\" width=\"961\" height=\"721\" srcset=\"https:\/\/bigideasmathanswers.com\/wp-content\/uploads\/2021\/01\/big-ideas-math-answer-key-grade-7-chapter-5-ratios-and-proportions-5.5-3.jpg 961w, https:\/\/bigideasmathanswers.com\/wp-content\/uploads\/2021\/01\/big-ideas-math-answer-key-grade-7-chapter-5-ratios-and-proportions-5.5-3-300x225.jpg 300w, https:\/\/bigideasmathanswers.com\/wp-content\/uploads\/2021\/01\/big-ideas-math-answer-key-grade-7-chapter-5-ratios-and-proportions-5.5-3-768x576.jpg 768w\" sizes=\"(max-width: 961px) 100vw, 961px\" \/><\/p>\n<p>Explanation:<br \/>\nIn point C (- 1, 2) has x coordinate negative value and y coordinate positive value.<br \/>\nso, the point lies in the 2nd quadrant.<br \/>\nTake -1 units on the x-axis, 2 units on the y-axis, and mark the point.<\/p>\n<p>Question 6.<br \/>\nD (1, 4)<\/p>\n<p>Answer:<br \/>\n<img loading=\"lazy\" class=\"alignnone size-full wp-image-46803\" src=\"https:\/\/ccssmathanswers.com\/wp-content\/uploads\/2021\/01\/big-ideas-math-answer-key-grade-7-chapter-5-ratios-and-proportions-5.5-4.jpg\" alt=\"Big Ideas Math Answer Key Grade 7 Chapter 5 Ratios and Proportions 5.5 4\" width=\"965\" height=\"721\" srcset=\"https:\/\/bigideasmathanswers.com\/wp-content\/uploads\/2021\/01\/big-ideas-math-answer-key-grade-7-chapter-5-ratios-and-proportions-5.5-4.jpg 965w, https:\/\/bigideasmathanswers.com\/wp-content\/uploads\/2021\/01\/big-ideas-math-answer-key-grade-7-chapter-5-ratios-and-proportions-5.5-4-300x224.jpg 300w, https:\/\/bigideasmathanswers.com\/wp-content\/uploads\/2021\/01\/big-ideas-math-answer-key-grade-7-chapter-5-ratios-and-proportions-5.5-4-768x574.jpg 768w\" sizes=\"(max-width: 965px) 100vw, 965px\" \/><\/p>\n<p>Explanation:<br \/>\nIn point D (1, 4) the x, y coordinates are positive.<br \/>\nSo, the point lies in quadrant 1.<br \/>\nTake 1 unit on the x-axis, 4 units on the y-axis, and mark the point.<\/p>\n<p>Question 7.<br \/>\nWhich expression is equivalent to (3w &#8211; 8) &#8211; 4(2w + 3)?<br \/>\nA. 11w + 4<br \/>\nB. &#8211; 5w &#8211; 5<br \/>\nC. &#8211; 5w + 4<br \/>\nD. &#8211; 5w &#8211; 20<\/p>\n<p>Answer:<br \/>\nD. &#8211; 5w &#8211; 20<\/p>\n<p>Explanation:<br \/>\n(3w &#8211; 8) &#8211; 4(2w + 3) = 3w &#8211; 8 &#8211; 8w &#8211; 12<br \/>\n= -5w -20<\/p>\n<p><strong>Concepts, Skills, &amp; Problem Solving<\/strong><\/p>\n<p><strong>SOLVING A RATIO PROBLEM<\/strong> Determine how far the vehicle travels in 3 hours. (See Exploration 1, p. 203.)<br \/>\nQuestion 8.<br \/>\nA helicopter travels 240 miles every 2 hours.<\/p>\n<p>Answer:<br \/>\nThe helicopter travels 360 miles in 3 hours.<\/p>\n<p>Explanation:<br \/>\nA helicopter travels 240 miles every 2 hours = 240 : 2<br \/>\n= 240\/2 : 1<br \/>\n= 120 : 1<br \/>\nThe helicopter travels 120 miles in 1 hour<br \/>\nThe distance traveled by the vehicle in 3 hours = 120 * 3<br \/>\n= 360 miles<\/p>\n<p>Question 9.<br \/>\nA motorcycle travels 25 miles every 0.5 hour.<\/p>\n<p>Answer:<br \/>\nA motorcycle travels 150 miles in 3 hours.<\/p>\n<p>Explanation:<br \/>\nA motorcycle travels 25 miles every 0.5 hour = 25 : 0.5<br \/>\n= 25\/0.5 : 1<br \/>\n= 50 : 1<br \/>\nThe motorcycle travels 50 miles in 1 hour<br \/>\nSo, the distance traveled by the vehicle in 3 hours = 50 * 3 = 150 miles<\/p>\n<p>Question 10.<br \/>\nA train travels 10 miles every \\(\\frac{1}{4}\\) hour.<\/p>\n<p>Answer:<br \/>\nA train travels 120 miles in 3 hours.<\/p>\n<p>Explanation:<br \/>\nA train travels 10 miles every \\(\\frac{1}{4}\\) hour = 10 : 1\/4<br \/>\n= 4 * 10 : 1<br \/>\n= 40 : 1<br \/>\nA train travels 40 miles in 1 hour<br \/>\nSo, the distance traveled by the vehicle in 3 hours = 40 * 3 = 120 miles<\/p>\n<p>Question 11.<br \/>\nA ferry travels 45 miles every 1\\(\\frac{1}{2}\\) hours.<\/p>\n<p>Answer:<br \/>\nA ferry travels 90 miles in 3 hours<\/p>\n<p>Explanation:<br \/>\nA ferry travels 45 miles every 1\\(\\frac{1}{2}\\) hours = 45 : 1(1\/2)<br \/>\n= 45 : 3\/2<br \/>\n= 45 * 2 : 3<br \/>\n= 90 : 3<br \/>\n= 30 : 1<br \/>\nA ferry travels 30 miles in 1 hour<br \/>\nSo, the distance traveled by the vehicle in 3 hours = 30 * 3 = 90<\/p>\n<p><strong>SOLVING A PROPORTION<\/strong> Solve the proportion. Explain your choice of method.<br \/>\nQuestion 12.<br \/>\n\\(\\frac{1}{4}=\\frac{z}{20}\\)<\/p>\n<p>Answer:<br \/>\nz = 5<\/p>\n<p>Explanation:<br \/>\n\\(\\frac{1}{4}=\\frac{z}{20}\\)<br \/>\nCross multiply the fractions<br \/>\n20 = 4z<br \/>\nz = 20\/4<br \/>\nz = 5<\/p>\n<p>Question 13.<br \/>\n\\(\\frac{3}{4}=\\frac{12}{y}\\)<\/p>\n<p>Answer:<br \/>\ny = 16<\/p>\n<p>Explanation:<br \/>\n\\(\\frac{3}{4}=\\frac{12}{y}\\)<br \/>\nThe product of 3 and waht number is 12?<br \/>\nBecause the product pf 3 and 4 is 12, multiply the denominator by 4 to find y<br \/>\n4 * 4 = 16<br \/>\nSo, y = 16<\/p>\n<p>Question 14.<br \/>\n\\(\\frac{35}{k}=\\frac{7}{3}\\)<\/p>\n<p>Answer:<br \/>\nk = 15<\/p>\n<p>Explanation:<br \/>\n\\(\\frac{35}{k}=\\frac{7}{3}\\)<br \/>\nDivide both sides by 35<br \/>\n(35\/k)\/35 = (7\/3)\/35<br \/>\n1\/k = 1\/15<br \/>\nk = 15<\/p>\n<p>Question 15.<br \/>\n\\(\\frac{b}{36}=\\frac{5}{9}\\)<\/p>\n<p>Answer:<br \/>\nb = 20<\/p>\n<p>Explanation:<br \/>\n\\(\\frac{b}{36}=\\frac{5}{9}\\)<br \/>\nCross multiply the proportions<br \/>\n9b = 5 * 36<br \/>\n9b = 180<br \/>\nb = 180\/9<br \/>\nb = 20<\/p>\n<p>Question 16.<br \/>\n\\(\\frac{x}{8}=\\frac{3}{12}\\)<\/p>\n<p>Answer:<br \/>\nx = 2<\/p>\n<p>Explanation:<br \/>\n\\(\\frac{x}{8}=\\frac{3}{12}\\)<br \/>\nCross multiply the fractions<br \/>\n12x = 3 * 8<br \/>\n12x = 24<br \/>\nx = 24\/12<br \/>\nx = 2<\/p>\n<p>Question 17.<br \/>\n\\(\\frac{3}{4}=\\frac{v}{14}\\)<\/p>\n<p>Answer:<br \/>\nv = 21\/2<\/p>\n<p>Explanation:<br \/>\n\\(\\frac{3}{4}=\\frac{v}{14}\\)<br \/>\nCross multiply the fractions<br \/>\n3 * 14 = 4v<br \/>\n42 = 4v<br \/>\nv = 42\/4<br \/>\nv = 21\/2<\/p>\n<p>Question 18.<br \/>\n\\(\\frac{15}{8}=\\frac{45}{c}\\)<\/p>\n<p>Answer:<br \/>\nc = 24<\/p>\n<p>Explanation:<br \/>\n\\(\\frac{15}{8}=\\frac{45}{c}\\)<br \/>\nCross multiply the fractions<br \/>\n15c = 45 * 8<br \/>\n15c = 360<br \/>\nc = 360\/15<br \/>\nc = 24<\/p>\n<p>Question 19.<br \/>\n\\(\\frac{35}{28}=\\frac{n}{12}\\)<\/p>\n<p>Answer:<br \/>\nn = 15<\/p>\n<p>Explanation:<br \/>\n\\(\\frac{35}{28}=\\frac{n}{12}\\)<br \/>\nCross multiply the fractions<br \/>\n35 * 12 = 28n<br \/>\n420 = 28n<br \/>\nn = 420\/28<br \/>\nn = 15<\/p>\n<p>Question 20.<br \/>\n\\(\\frac{a}{6}=\\frac{15}{2}\\)<\/p>\n<p>Answer:<br \/>\na = 45<\/p>\n<p>Explanation:<br \/>\n\\(\\frac{a}{6}=\\frac{15}{2}\\)<br \/>\nCross multiply the fractions<br \/>\n2a = 15 * 6<br \/>\n2a = 90<br \/>\na = 90\/2<br \/>\na = 45<\/p>\n<p>Question 21.<br \/>\n\\(\\frac{y}{9}=\\frac{44}{54}\\)<\/p>\n<p>Answer:<br \/>\ny = 22\/3<\/p>\n<p>Explanation:<br \/>\n\\(\\frac{y}{9}=\\frac{44}{54}\\)<br \/>\nCross multiply the fractions<br \/>\n54y = 44 * 9<br \/>\n54y = 396<br \/>\ny = 396\/54<br \/>\ny = 22\/3<\/p>\n<p>Question 22.<br \/>\n\\(\\frac{4}{24}=\\frac{c}{36}\\)<\/p>\n<p>Answer:<br \/>\nc = 6<\/p>\n<p>Explanation:<br \/>\n\\(\\frac{4}{24}=\\frac{c}{36}\\)<br \/>\nCross multiply the fractions<br \/>\n4 * 36 = 24c<br \/>\n144 = 24c<br \/>\nc = 144\/24<br \/>\nc = 6<\/p>\n<p>Question 23.<br \/>\n\\(\\frac{20}{16}=\\frac{d}{12}\\)<\/p>\n<p>Answer:<br \/>\nd = 15<\/p>\n<p>Explanation:<br \/>\n\\(\\frac{20}{16}=\\frac{d}{12}\\)<br \/>\nCross multiply the fractions<br \/>\n20 * 12 = 16d<br \/>\n240 = 16d<br \/>\nd = 240\/16<br \/>\nd = 15<\/p>\n<p>Question 24.<br \/>\n\\(\\frac{10}{7}=\\frac{8}{k}\\)<\/p>\n<p>Answer:<br \/>\nk = 5.6<\/p>\n<p>Explanation:<br \/>\nCross multiply the fractions<br \/>\n10k = 8 * 7<br \/>\n10k = 56<br \/>\nk = 56\/10<br \/>\nk = 5.6<\/p>\n<p>Question 25.<br \/>\n\\(\\frac{5}{n}=\\frac{16}{32}\\)<\/p>\n<p>Answer:<br \/>\nn = 10<\/p>\n<p>Explanation:<br \/>\n\\(\\frac{5}{n}=\\frac{16}{32}\\)<br \/>\nCross multiply the fractions<br \/>\n5 * 32 = 16n<br \/>\n160 = 16n<br \/>\nn = 160\/16<br \/>\nn = 10<\/p>\n<p>Question 26.<br \/>\n\\(\\frac{9}{10}=\\frac{d}{6.4}\\)<\/p>\n<p>Answer:<br \/>\nd = 5.76<\/p>\n<p>Explanation:<br \/>\n\\(\\frac{9}{10}=\\frac{d}{6.4}\\)<br \/>\nCross multiply the fractions<br \/>\n10d = 6.4 * 9<br \/>\n10d = 57.6<br \/>\nd = 57.6\/10<br \/>\nd = 5.76<\/p>\n<p>Question 27.<br \/>\n\\(\\frac{2.4}{1.8}=\\frac{7.2}{k}\\)<\/p>\n<p>Answer:<br \/>\nk = 5.4<\/p>\n<p>Explanation:<br \/>\n\\(\\frac{2.4}{1.8}=\\frac{7.2}{k}\\)<br \/>\nCross multiply the fractions<br \/>\n2.4k = 7.2 * 1.8<br \/>\n2.4k = 12.96<br \/>\nk = 12.96\/2.4<br \/>\nk = 5.4<\/p>\n<p>Question 28.<br \/>\n<strong>YOU BE THE TEACHER<\/strong><br \/>\nYour friend solves the proportion \\(\\frac{m}{8}=\\frac{15}{24}\\). Is your friend correct? Explain your reasoning.<br \/>\n<img loading=\"lazy\" class=\"alignnone size-full wp-image-30418\" src=\"https:\/\/ccssmathanswers.com\/wp-content\/uploads\/2021\/01\/Big-Ideas-Math-Solutions-Grade-7-Chapter-5-Ratios-and-Proportions-5.4-7.png\" alt=\"Big Ideas Math Solutions Grade 7 Chapter 5 Ratios and Proportions 5.4 7\" width=\"173\" height=\"111\" \/><\/p>\n<p>Answer:<br \/>\nCorrect<\/p>\n<p>Explanation:<br \/>\nm\/8 = 15\/24<br \/>\nCross multiply the fractions<br \/>\n24m = 15 * 8<br \/>\n24m = 120<br \/>\nm = 120\/24<br \/>\nm = 5<\/p>\n<p>Question 29.<br \/>\n<strong>NUMBER SENSE<\/strong><br \/>\nWithout solving, determine whether \\(\\frac{x}{4}=\\frac{15}{3}\\) and \\(\\frac{x}{15}=\\frac{4}{3}\\) have the same solution. Explain your reasoning.<\/p>\n<p>Answer:<br \/>\nBoth have same solution.<\/p>\n<p>Explanation:<br \/>\n\\(\\frac{x}{4}=\\frac{15}{3}[\/latex<br \/>\nCross multiply the fractions<br \/>\n3x = 15 * 4<br \/>\n[latex]\\frac{x}{15}=\\frac{4}{3}\\)<br \/>\nCross multiply the fractions<br \/>\n3x = 4 * 15<br \/>\nWe got same equation<br \/>\nSo, both have same solution.<\/p>\n<p><strong>WRITING A PROPORTION<\/strong> Use the table to write a proportion.<br \/>\nQuestion 30.<br \/>\n<img loading=\"lazy\" class=\"alignnone size-full wp-image-30419\" src=\"https:\/\/ccssmathanswers.com\/wp-content\/uploads\/2021\/01\/Big-Ideas-Math-Solutions-Grade-7-Chapter-5-Ratios-and-Proportions-5.4-8.png\" alt=\"Big Ideas Math Solutions Grade 7 Chapter 5 Ratios and Proportions 5.4 8\" width=\"248\" height=\"87\" \/><\/p>\n<p>Answer:<br \/>\n6\/7 = 18\/w, w = 6<\/p>\n<p>Explanation:<br \/>\n12\/14 = 18\/w<br \/>\nCross multiply the fractions<br \/>\n12w = 18 * 4<br \/>\nw = 72\/12<br \/>\nw = 6<br \/>\n12\/14 = 18\/w<br \/>\n6\/7 = 18\/w<\/p>\n<p>Question 31.<br \/>\n<img loading=\"lazy\" class=\"alignnone size-full wp-image-30420\" src=\"https:\/\/ccssmathanswers.com\/wp-content\/uploads\/2021\/01\/Big-Ideas-Math-Solutions-Grade-7-Chapter-5-Ratios-and-Proportions-5.4-9.png\" alt=\"Big Ideas Math Solutions Grade 7 Chapter 5 Ratios and Proportions 5.4 9\" width=\"241\" height=\"87\" \/><\/p>\n<p>Answer:<br \/>\nn\/85 = 1\/5, n = 17<\/p>\n<p>Explanation:<br \/>\nn\/85 = 34\/170<br \/>\nn\/85 = 1\/5<br \/>\nCross multiply the fractions<br \/>\n5n = 85<br \/>\nn = 85\/5<br \/>\nn = 17<\/p>\n<p>Question 32.<br \/>\n<img loading=\"lazy\" class=\"alignnone size-full wp-image-30421\" src=\"https:\/\/ccssmathanswers.com\/wp-content\/uploads\/2021\/01\/Big-Ideas-Math-Solutions-Grade-7-Chapter-5-Ratios-and-Proportions-5.4-10.png\" alt=\"Big Ideas Math Solutions Grade 7 Chapter 5 Ratios and Proportions 5.4 10\" width=\"230\" height=\"93\" \/><\/p>\n<p>Answer:<br \/>\n15\/2.5 = m\/4, m = 24<\/p>\n<p>Explanation:<br \/>\n15\/2.5 = m\/4<br \/>\nCross multiply the fractions<br \/>\n15 * 4 = 2.5m<br \/>\n60 = 2.5m<br \/>\nm = 60\/2.5<br \/>\nm = 24<\/p>\n<p>Question 33.<br \/>\n<img loading=\"lazy\" class=\"alignnone size-full wp-image-30422\" src=\"https:\/\/ccssmathanswers.com\/wp-content\/uploads\/2021\/01\/Big-Ideas-Math-Solutions-Grade-7-Chapter-5-Ratios-and-Proportions-5.4-11.png\" alt=\"Big Ideas Math Solutions Grade 7 Chapter 5 Ratios and Proportions 5.4 11\" width=\"242\" height=\"92\" \/><\/p>\n<p>Answer:<br \/>\nx = 11.2<\/p>\n<p>Explanation:<br \/>\n100\/x = 200\/22.4<br \/>\nCross multiply the fractions<br \/>\n100 * 22.4 = 200x<br \/>\n2240 = 200x<br \/>\nx = 2240\/200<br \/>\nx = 11.2<\/p>\n<p><strong>WRITING AND SOLVING A PROPORTION<\/strong> Find the value of x so that the ratios are equivalent.<br \/>\nQuestion 34.<br \/>\n1 : 8 and 4 : x<\/p>\n<p>Answer:<br \/>\nx = 32<\/p>\n<p>Explanation:<br \/>\n1\/8 = 4\/x<br \/>\nCross multiply the fractions<br \/>\nx = 8 * 4<br \/>\nx = 32<\/p>\n<p>Question 35.<br \/>\n4 to 5 and x to 20<\/p>\n<p>Answer:<br \/>\nx = 16<\/p>\n<p>Explanation:<br \/>\n4\/5 = x\/20<br \/>\nCross multiply the fractions<br \/>\n20 * 4 = 5x<br \/>\n80 = 5x<br \/>\nx = 80\/5<br \/>\nx = 16<\/p>\n<p>Question 36.<br \/>\n3 : x and 12 : 40<\/p>\n<p>Answer:<br \/>\nx = 10<\/p>\n<p>Explanation:<br \/>\n3\/x = 12\/40<br \/>\nCross multiply the fractions<br \/>\n3 * 40 = 12x<br \/>\n120 = 12x<br \/>\nx = 120\/12<br \/>\nx = 10<\/p>\n<p>Question 37.<br \/>\nx to 0.25 and 6 to 1.5<\/p>\n<p>Answer:<br \/>\nx = 1<\/p>\n<p>Explanation:<br \/>\nx\/0.25 = 6\/1.5<br \/>\nCross multiply the fractions<br \/>\n1.5x = 6 * 0.25<br \/>\n1.5x = 1.5<br \/>\nx = 1.5\/1.5<br \/>\nx = 1<\/p>\n<p>Question 38.<br \/>\nx : \\(\\frac{5}{2}\\) and 8 : 10<\/p>\n<p>Answer:<br \/>\nx = 2<\/p>\n<p>Explanation:<br \/>\nx : 5\/2 = 8 : 10<br \/>\nCross multiply the fractions<br \/>\n10x = 8 * 5\/2<br \/>\n10x = 20<br \/>\nx = 20\/10<br \/>\nx = 2<\/p>\n<p>Question 39.<br \/>\n\\(\\frac{7}{4}\\) to 14 and x to 32<\/p>\n<p>Answer:<br \/>\nx = 4<\/p>\n<p>Explanation:<br \/>\n7\/4 : 14 = x : 32<br \/>\nCross multiply the fractions<br \/>\n14x = 32 * (7\/4)<br \/>\n14x = 56<br \/>\nx = 56\/14<br \/>\nx = 4<\/p>\n<p>Question 40.<br \/>\n<strong>WRITING A PROPORTION<\/strong><br \/>\nYour science teacher has a photograph of the space shuttle Atlantis. Every 1 centimeter in the photograph represents 200 centimeters on the actual shuttle. Which of the proportions can you use to find the actual length x of Atlantis? Explain.<br \/>\n<img loading=\"lazy\" class=\"alignnone size-full wp-image-30423\" src=\"https:\/\/ccssmathanswers.com\/wp-content\/uploads\/2021\/01\/Big-Ideas-Math-Solutions-Grade-7-Chapter-5-Ratios-and-Proportions-5.4-12.png\" alt=\"Big Ideas Math Solutions Grade 7 Chapter 5 Ratios and Proportions 5.4 12\" width=\"552\" height=\"237\" srcset=\"https:\/\/bigideasmathanswers.com\/wp-content\/uploads\/2021\/01\/Big-Ideas-Math-Solutions-Grade-7-Chapter-5-Ratios-and-Proportions-5.4-12.png 552w, https:\/\/bigideasmathanswers.com\/wp-content\/uploads\/2021\/01\/Big-Ideas-Math-Solutions-Grade-7-Chapter-5-Ratios-and-Proportions-5.4-12-300x129.png 300w\" sizes=\"(max-width: 552px) 100vw, 552px\" \/><\/p>\n<p>Answer:<br \/>\n1\/200 = x\/19.5<\/p>\n<p>Explanation:<br \/>\nEvery 1 centimeter in the photograph represents 200 centimeters on the actual shuttle<br \/>\n= 1 : 200<br \/>\nLength of atlantis on model = 19.5<br \/>\nThe actual length on Atlantis = x<br \/>\nScale 1:200<br \/>\nWhen length on model = 1<br \/>\nActual length = 200<br \/>\nWhen actual length = x<br \/>\nLength on model = 19.5<br \/>\nScale = x : 19.5<br \/>\nEquating both scales<br \/>\n1\/200 = x\/19.5<\/p>\n<p>Question 41.<br \/>\n<strong>MODELING REAL LIFE<\/strong><br \/>\nIn an orchestra, the ratio of trombones to violas is 1 to 3. There are 9 violas. How many trombones are in the orchestra?<\/p>\n<p>Answer:<br \/>\nThere are 3 trombones in the orchestra.<\/p>\n<p>Explanation:<br \/>\nt\/9 = 1\/3<br \/>\n3t = 9<br \/>\nt = 9\/3<br \/>\nt = 3<br \/>\nThere are 3 trombones in the orchestra.<\/p>\n<p>Question 42.<br \/>\n<strong>MODELING REAL LIFE<\/strong><br \/>\nA dance team has 80 dancers. The ratio of seventh-grade dancers to all dancers is 5:16. Find the number of seventh-grade dancers on the team.<\/p>\n<p>Answer:<br \/>\nThe number of seventh-grade dancers on the team is 25.<\/p>\n<p>Explanation:<br \/>\nA dance team has 80 dancers<br \/>\nLet us take the seventh-grade dancers as x<br \/>\nThe ratio of seventh-grade dancers to all dancers is 5:16<br \/>\nx : 80 = 5 : 16<br \/>\nx\/80 = 5\/16<br \/>\nCross multiply the fractions<br \/>\n16x = 5 *80<br \/>\n16x = 400<br \/>\nx = 400\/16<br \/>\nx = 25<br \/>\nThe number of seventh-grade dancers on the team is 25.<\/p>\n<p>Question 43.<br \/>\n<strong>MODELING REAL LIFE<\/strong><br \/>\nThere are 144 people in an audience. The ratio of adults to children is 5 to 3. How many are adults?<\/p>\n<p>Answer:<br \/>\nThe number of adults in the audience are 18.<\/p>\n<p>Explanation:<br \/>\nThe ratio of adults to children is 5 to 3<br \/>\nadults : children = 5 : 3<br \/>\nThere are 144 people in an audience.<br \/>\n5x + 3x = 144<br \/>\n8x = 144<br \/>\nx = 144\/8<br \/>\nx = 18<br \/>\nSo, the number of adults in the audience are 18.<\/p>\n<p>Question 44.<br \/>\n<strong>PROBLEM SOLVING<\/strong><br \/>\nYou have $50 to buy T-shirts. You can buy 3 T-shirts for $24. Do you have enough money to buy 7 T-shirts? Justify your answer.<\/p>\n<p>Answer:<br \/>\nNo.<\/p>\n<p>Explanation:<br \/>\nYou can buy 3 T-shirts for $24<br \/>\n= 24 : 3<br \/>\n= 24\/3 : 1<br \/>\n= 8 : 1<br \/>\nSo, you can buy 1 T-shirt per $8.<br \/>\nThe money required to buy 7 T-shirts = 7 * 8 = $56<br \/>\nThe remaining money after buying 3 T-shirts is 50 &#8211; 24 = $26<br \/>\n$26 is not enough to buy 7 T-shirts.<\/p>\n<p>Question 45.<br \/>\n<strong>PROBLEM SOLVING<\/strong><br \/>\nYou buy 10 vegetarian pizzas and pay with $100. How much change do you receive?<br \/>\n<img loading=\"lazy\" class=\"alignnone size-full wp-image-30424\" src=\"https:\/\/ccssmathanswers.com\/wp-content\/uploads\/2021\/01\/Big-Ideas-Math-Solutions-Grade-7-Chapter-5-Ratios-and-Proportions-5.4-13.png\" alt=\"Big Ideas Math Solutions Grade 7 Chapter 5 Ratios and Proportions 5.4 13\" width=\"538\" height=\"88\" srcset=\"https:\/\/bigideasmathanswers.com\/wp-content\/uploads\/2021\/01\/Big-Ideas-Math-Solutions-Grade-7-Chapter-5-Ratios-and-Proportions-5.4-13.png 538w, https:\/\/bigideasmathanswers.com\/wp-content\/uploads\/2021\/01\/Big-Ideas-Math-Solutions-Grade-7-Chapter-5-Ratios-and-Proportions-5.4-13-300x49.png 300w\" sizes=\"(max-width: 538px) 100vw, 538px\" \/><\/p>\n<p>Answer:<br \/>\nThe change you receive = $15<\/p>\n<p>Explanation:<br \/>\n3 vegetarian pizzas for $25.50 = 25.50 : 3<br \/>\n= 25.50\/3 : 1<br \/>\n= 8.5 : 1<br \/>\nSo, you have to pay $8.5 for 1 vegetarian pizza<br \/>\nIf you buy 10 vegetarian pizzas, then amount is 10 * 8.5 = $85<br \/>\nThe change you receive = 100 &#8211; 85 = 15<\/p>\n<p>Question 46.<br \/>\n<strong>MODELING REAL LIFE<\/strong><br \/>\nA person who weighs 120 pounds on Earth weighs 20 pounds on the Moon. How much does a 93-pound person weigh on the Moon?<\/p>\n<p>Answer:<br \/>\nThe weight of a 93-pound person weigh on the Moon is 15.5 pounds<\/p>\n<p>Explanation:<br \/>\nThe ratio of a person weight on earth to moon = 120 : 20<br \/>\n= 120\/20 : 1<br \/>\n= 6 : 1<br \/>\nThe weight of a 93-pound person weigh on the Moon is 93\/6 = 31\/2 = 15.5 pounds.<\/p>\n<p>Question 47.<br \/>\n<strong>PROBLEM SOLVING<\/strong><br \/>\nThree pounds of lawn seed covers 1800 square feet. How many bags are needed to cover 8400 square feet?<br \/>\n<img loading=\"lazy\" class=\"alignnone size-full wp-image-30425\" src=\"https:\/\/ccssmathanswers.com\/wp-content\/uploads\/2021\/01\/Big-Ideas-Math-Solutions-Grade-7-Chapter-5-Ratios-and-Proportions-5.4-14.png\" alt=\"Big Ideas Math Solutions Grade 7 Chapter 5 Ratios and Proportions 5.4 14\" width=\"164\" height=\"197\" \/><\/p>\n<p>Answer:<br \/>\nThe number of bags required to cover 8400 sq ft is 14.<\/p>\n<p>Explanation:<br \/>\nThree pounds of lawn seed covers 1800 square feet.<br \/>\nThe ratio of lawn to seed cover = 1800 : 3<br \/>\n= 1800\/3 : 1<br \/>\n= 600 : 1<br \/>\nSo, 1 seed bag covers 600 sq ft<br \/>\nThe number of bags required to cover 8400 sq ft is 8400\/600<br \/>\n= 14 bags<\/p>\n<p>Question 48.<br \/>\n<strong>MODELING REAL LIFE<\/strong><br \/>\nThere are 180 white lockers in a school. There are 3 white lockers for every 5 blue lockers. How many lockers are in the school?<\/p>\n<p>Answer:<br \/>\nThere are 480 lockers in the school.<\/p>\n<p>Explanation:<br \/>\nThere are 3 white lockers for every 5 blue lockers<br \/>\n= 3 : 5<br \/>\nLet b be the number of blue lockers<br \/>\n3\/5 = 180\/b<br \/>\n3b = 180 * 5<br \/>\n3b = 900<br \/>\nb = 900\/3<br \/>\nb = 300<br \/>\n300 + 180 = 400<br \/>\nSo, there are 480 lockers in the school.<\/p>\n<p><strong>CONVERTING MEASURES<\/strong> Use a proportion to complete the statement. Round to the nearest hundredth if necessary.<br \/>\nQuestion 49.<br \/>\n<img loading=\"lazy\" class=\"alignnone size-full wp-image-30426\" src=\"https:\/\/ccssmathanswers.com\/wp-content\/uploads\/2021\/01\/Big-Ideas-Math-Solutions-Grade-7-Chapter-5-Ratios-and-Proportions-5.4-15.png\" alt=\"Big Ideas Math Solutions Grade 7 Chapter 5 Ratios and Proportions 5.4 15\" width=\"138\" height=\"41\" \/><\/p>\n<p>Answer:<br \/>\n3.73 miles<\/p>\n<p>Explanation:<br \/>\n1 km = 0.621371<br \/>\n6 km = 6 * 0.621371<br \/>\n= 3.72823 miles<br \/>\n= 3.73 miles<\/p>\n<p>Question 50.<br \/>\n<img loading=\"lazy\" class=\"alignnone size-full wp-image-30427\" src=\"https:\/\/ccssmathanswers.com\/wp-content\/uploads\/2021\/01\/Big-Ideas-Math-Solutions-Grade-7-Chapter-5-Ratios-and-Proportions-5.4-16.png\" alt=\"Big Ideas Math Solutions Grade 7 Chapter 5 Ratios and Proportions 5.4 16\" width=\"141\" height=\"57\" \/><\/p>\n<p>Answer:<br \/>\n0.66 gal<\/p>\n<p>Explanation:<br \/>\n1 L = 0.264172 gal<br \/>\n2.5 L = 0.264172 * 2.5<br \/>\n= 0.66043<br \/>\n2.5 L = 0.66 gal<\/p>\n<p>Question 51.<br \/>\n<img loading=\"lazy\" class=\"alignnone size-full wp-image-30429\" src=\"https:\/\/ccssmathanswers.com\/wp-content\/uploads\/2021\/01\/Big-Ideas-Math-Solutions-Grade-7-Chapter-5-Ratios-and-Proportions-5.4-17.png\" alt=\"Big Ideas Math Solutions Grade 7 Chapter 5 Ratios and Proportions 5.4 17\" width=\"136\" height=\"52\" \/><\/p>\n<p>Answer:<br \/>\n40.82 kg<\/p>\n<p>Explanation:<br \/>\n1 lb = 0.453592 kgs<br \/>\n90 lb = 0.453592 * 90<br \/>\n= 40.8233<br \/>\n90 lb = 40.82 kg<\/p>\n<p><strong>SOLVING A PROPORTION<\/strong> Solve the proportion.<br \/>\nQuestion 52.<br \/>\n<img loading=\"lazy\" class=\"alignnone size-full wp-image-30430\" src=\"https:\/\/ccssmathanswers.com\/wp-content\/uploads\/2021\/01\/Big-Ideas-Math-Solutions-Grade-7-Chapter-5-Ratios-and-Proportions-5.4-18.png\" alt=\"Big Ideas Math Solutions Grade 7 Chapter 5 Ratios and Proportions 5.4 18\" width=\"78\" height=\"45\" \/><\/p>\n<p>Answer:<br \/>\nx = 3\/2<\/p>\n<p>Explanation:<br \/>\n2x\/5 = 9\/15<br \/>\nCross-multiply the fractions<br \/>\n15 * 2x = 9 * 5<br \/>\n30x = 45<br \/>\nx = 45\/30<br \/>\nx = 3\/2<\/p>\n<p>Question 53.<br \/>\n<img loading=\"lazy\" class=\"alignnone size-full wp-image-30431\" src=\"https:\/\/ccssmathanswers.com\/wp-content\/uploads\/2021\/01\/Big-Ideas-Math-Solutions-Grade-7-Chapter-5-Ratios-and-Proportions-5.4-19.png\" alt=\"Big Ideas Math Solutions Grade 7 Chapter 5 Ratios and Proportions 5.4 19\" width=\"83\" height=\"49\" \/><\/p>\n<p>Answer:<br \/>\nd = 12<\/p>\n<p>Explanation:<br \/>\n5\/2 = (d &#8211; 2)\/4<br \/>\nCross-multiply the fractions<br \/>\n20 = 2(d &#8211; 2)<br \/>\n20 = 2d &#8211; 4<br \/>\n20 + 4 = 2d<br \/>\n24 = 2d<br \/>\nd = 24\/2<br \/>\nd = 12<\/p>\n<p>Question 54.<br \/>\n<img loading=\"lazy\" class=\"alignnone size-full wp-image-30432\" src=\"https:\/\/ccssmathanswers.com\/wp-content\/uploads\/2021\/01\/Big-Ideas-Math-Solutions-Grade-7-Chapter-5-Ratios-and-Proportions-5.4-20.png\" alt=\"Big Ideas Math Solutions Grade 7 Chapter 5 Ratios and Proportions 5.4 20\" width=\"86\" height=\"55\" \/><\/p>\n<p>Answer:<br \/>\nk = 4<\/p>\n<p>Explanation:<br \/>\n4\/(k + 3) = 8\/14<br \/>\nCross-multiply the fractions<br \/>\n14 * 4 = 8(k + 3)<br \/>\n56 = 8k + 24<br \/>\n56 &#8211; 24 = 8k<br \/>\n32 = 8k<br \/>\nk = 32\/8<br \/>\nk = 4<\/p>\n<p>Question 55.<br \/>\n<strong>LOGIC<\/strong><br \/>\nIt takes 6 hours for 2 people to build a swing set. Can you use the proportion \\(\\frac{2}{6}=\\frac{5}{h}\\) to determine the number of hours h it will take 5 people h6to build the swing set? Explain.<\/p>\n<p>Answer:<br \/>\nIt will take 15 hours for 5 people to build the swing set.<\/p>\n<p>Explanation:<br \/>\nIt takes 6 hours for 2 people to build a swing set<br \/>\n2 people &#8211; 6 hours<br \/>\n5 people &#8211; ?<br \/>\nWe have a proportion,<br \/>\n2\/6 = 5\/h<br \/>\n2h = 6 * 5<br \/>\n2h = 30<br \/>\nh = 30\/2<br \/>\nh = 15<br \/>\nIt will take 15 hours for 5 people to build the swing set.<\/p>\n<p>Question 56.<br \/>\n<strong>STRUCTURE<\/strong><br \/>\nThe ratios a : b and c : d are equivalent. Which of the following equations are proportions? Explain your reasoning.<br \/>\n<img loading=\"lazy\" class=\"alignnone size-full wp-image-30433\" src=\"https:\/\/ccssmathanswers.com\/wp-content\/uploads\/2021\/01\/Big-Ideas-Math-Solutions-Grade-7-Chapter-5-Ratios-and-Proportions-5.4-21.png\" alt=\"Big Ideas Math Solutions Grade 7 Chapter 5 Ratios and Proportions 5.4 21\" width=\"425\" height=\"73\" srcset=\"https:\/\/bigideasmathanswers.com\/wp-content\/uploads\/2021\/01\/Big-Ideas-Math-Solutions-Grade-7-Chapter-5-Ratios-and-Proportions-5.4-21.png 425w, https:\/\/bigideasmathanswers.com\/wp-content\/uploads\/2021\/01\/Big-Ideas-Math-Solutions-Grade-7-Chapter-5-Ratios-and-Proportions-5.4-21-300x52.png 300w\" sizes=\"(max-width: 425px) 100vw, 425px\" \/><\/p>\n<p>Answer:<br \/>\na\/d = c\/b is not equivalent proportion.<\/p>\n<p>Explanation:<br \/>\na\/b = c\/d<br \/>\nad = bc<br \/>\nb\/a = d\/c<br \/>\nbc = ad<br \/>\na\/c = b\/d<br \/>\nad = bc<br \/>\na\/d = c\/b<br \/>\nab = cd<br \/>\nc\/a = d\/b<br \/>\nbc = ad<br \/>\nSo, a\/d = c\/b is not equivalent proportion.<\/p>\n<p>Question 57.<br \/>\n<strong>CRITICAL THINKING<\/strong><br \/>\nConsider the proportions \\(\\frac{m}{n}=\\frac{1}{2}\\) and \\(\\frac{n}{k}=\\frac{2}{5}\\). What is \\(\\frac{m}{k}\\) ? Explain your reasoning.<\/p>\n<p>Answer:<br \/>\nm\/k = 1\/5<\/p>\n<p>Explanation:<br \/>\nm\/n = 1\/2<br \/>\nSo m = x, n = 2x<br \/>\nn\/k = 2\/5<br \/>\nn = 2x, k = 5x<br \/>\nSo, m\/k = x\/5x<br \/>\n= 1\/5<\/p>\n<h3><a id=\"Lesson_5.5_Graphs_of_Proportional_Relationships\"><\/a>Lesson 5.5 Graphs of Proportional Relationships<\/h3>\n<p><strong>EXPLORATION 1<\/strong><\/p>\n<p>Representing Relationships Graphically<\/p>\n<p>Work with a partner. The tables represent two different ways that red and blue food coloring are mixed.<br \/>\n<img loading=\"lazy\" class=\"alignnone size-full wp-image-30434\" src=\"https:\/\/ccssmathanswers.com\/wp-content\/uploads\/2021\/01\/Big-Ideas-Math-Answer-Key-Grade-7-Chapter-5-Ratios-and-Proportions-5.5-1.png\" alt=\"Big Ideas Math Answer Key Grade 7 Chapter 5 Ratios and Proportions 5.5 1\" width=\"413\" height=\"198\" srcset=\"https:\/\/bigideasmathanswers.com\/wp-content\/uploads\/2021\/01\/Big-Ideas-Math-Answer-Key-Grade-7-Chapter-5-Ratios-and-Proportions-5.5-1.png 413w, https:\/\/bigideasmathanswers.com\/wp-content\/uploads\/2021\/01\/Big-Ideas-Math-Answer-Key-Grade-7-Chapter-5-Ratios-and-Proportions-5.5-1-300x144.png 300w\" sizes=\"(max-width: 413px) 100vw, 413px\" \/><br \/>\na. Represent each table in the same coordinate plane. Which graph represents a proportional relationship? How do you know?<br \/>\n<img loading=\"lazy\" class=\"alignnone size-full wp-image-30435\" src=\"https:\/\/ccssmathanswers.com\/wp-content\/uploads\/2021\/01\/Big-Ideas-Math-Answer-Key-Grade-7-Chapter-5-Ratios-and-Proportions-5.5-2.png\" alt=\"Big Ideas Math Answer Key Grade 7 Chapter 5 Ratios and Proportions 5.5 2\" width=\"540\" height=\"197\" srcset=\"https:\/\/bigideasmathanswers.com\/wp-content\/uploads\/2021\/01\/Big-Ideas-Math-Answer-Key-Grade-7-Chapter-5-Ratios-and-Proportions-5.5-2.png 540w, https:\/\/bigideasmathanswers.com\/wp-content\/uploads\/2021\/01\/Big-Ideas-Math-Answer-Key-Grade-7-Chapter-5-Ratios-and-Proportions-5.5-2-300x109.png 300w\" sizes=\"(max-width: 540px) 100vw, 540px\" \/><br \/>\nb. Find the unit rate of the proportional relationship. How is the unit rate shown on the graph?<br \/>\nc. What is the multiplicative relationship between x and y for the proportional relationship? How can you use this value to write an equation that relates y and x?<\/p>\n<p>Answer:<br \/>\nMixture 1<br \/>\na. <img loading=\"lazy\" class=\"alignnone size-full wp-image-46924\" src=\"https:\/\/ccssmathanswers.com\/wp-content\/uploads\/2021\/01\/big-ideas-math-answer-key-grade-7-chapter-5-ratios-and-proportions-5.5-5.jpg\" alt=\"Big Ideas Math Answer Key Grade 7 Chapter 5 Ratios and Proportions 5.5 5\" width=\"967\" height=\"723\" srcset=\"https:\/\/bigideasmathanswers.com\/wp-content\/uploads\/2021\/01\/big-ideas-math-answer-key-grade-7-chapter-5-ratios-and-proportions-5.5-5.jpg 967w, https:\/\/bigideasmathanswers.com\/wp-content\/uploads\/2021\/01\/big-ideas-math-answer-key-grade-7-chapter-5-ratios-and-proportions-5.5-5-300x224.jpg 300w, https:\/\/bigideasmathanswers.com\/wp-content\/uploads\/2021\/01\/big-ideas-math-answer-key-grade-7-chapter-5-ratios-and-proportions-5.5-5-768x574.jpg 768w\" sizes=\"(max-width: 967px) 100vw, 967px\" \/><br \/>\nMixture 2<br \/>\n<img loading=\"lazy\" class=\"alignnone size-full wp-image-46928\" src=\"https:\/\/ccssmathanswers.com\/wp-content\/uploads\/2021\/01\/big-ideas-math-answer-key-grade-7-chapter-5-ratios-and-proportions-5.5-6.jpg\" alt=\"Big Ideas Math Answer Key Grade 7 Chapter 5 Ratios and Proportions 5.5 6\" width=\"956\" height=\"713\" srcset=\"https:\/\/bigideasmathanswers.com\/wp-content\/uploads\/2021\/01\/big-ideas-math-answer-key-grade-7-chapter-5-ratios-and-proportions-5.5-6.jpg 956w, https:\/\/bigideasmathanswers.com\/wp-content\/uploads\/2021\/01\/big-ideas-math-answer-key-grade-7-chapter-5-ratios-and-proportions-5.5-6-300x224.jpg 300w, https:\/\/bigideasmathanswers.com\/wp-content\/uploads\/2021\/01\/big-ideas-math-answer-key-grade-7-chapter-5-ratios-and-proportions-5.5-6-768x573.jpg 768w\" sizes=\"(max-width: 956px) 100vw, 956px\" \/><br \/>\nb. If the line passes through the origin, then x and y are proportional.<\/p>\n<p>Explanation:<br \/>\na.The points in mixture 1 are A (1, 2), B (2, 4), C (3, 6), D (4, 8)<br \/>\nThe points in mixture 2 are E (0, 2), F (2, 4), G (4, 6), H (6, 8)<br \/>\nb. If the line passes through the origin, then x and y are proportional.<\/p>\n<p><img loading=\"lazy\" class=\"alignnone size-full wp-image-30436\" src=\"https:\/\/ccssmathanswers.com\/wp-content\/uploads\/2021\/01\/Big-Ideas-Math-Answer-Key-Grade-7-Chapter-5-Ratios-and-Proportions-5.5-3.png\" alt=\"Big Ideas Math Answer Key Grade 7 Chapter 5 Ratios and Proportions 5.5 3\" width=\"185\" height=\"96\" \/><\/p>\n<p><strong>Try It<\/strong><\/p>\n<p><strong>Tell whether x and y are proportional. Explain your reasoning.<\/strong><\/p>\n<p>Question 1.<br \/>\n<img loading=\"lazy\" class=\"alignnone size-full wp-image-30437\" src=\"https:\/\/ccssmathanswers.com\/wp-content\/uploads\/2021\/01\/Big-Ideas-Math-Answer-Key-Grade-7-Chapter-5-Ratios-and-Proportions-5.5-4.png\" alt=\"Big Ideas Math Answer Key Grade 7 Chapter 5 Ratios and Proportions 5.5 4\" width=\"105\" height=\"126\" \/><\/p>\n<p>Answer:<br \/>\nThe line does not pass through the origin. So, x and y are not proportional.<\/p>\n<p>Explanation:<br \/>\n<img loading=\"lazy\" class=\"alignnone size-full wp-image-46932\" src=\"https:\/\/ccssmathanswers.com\/wp-content\/uploads\/2021\/01\/big-ideas-math-answer-key-grade-7-chapter-5-ratios-and-proportions-5.5-7.jpg\" alt=\"Big Ideas Math Answer Key Grade 7 Chapter 5 Ratios and Proportions 5.5 7\" width=\"966\" height=\"722\" srcset=\"https:\/\/bigideasmathanswers.com\/wp-content\/uploads\/2021\/01\/big-ideas-math-answer-key-grade-7-chapter-5-ratios-and-proportions-5.5-7.jpg 966w, https:\/\/bigideasmathanswers.com\/wp-content\/uploads\/2021\/01\/big-ideas-math-answer-key-grade-7-chapter-5-ratios-and-proportions-5.5-7-300x224.jpg 300w, https:\/\/bigideasmathanswers.com\/wp-content\/uploads\/2021\/01\/big-ideas-math-answer-key-grade-7-chapter-5-ratios-and-proportions-5.5-7-768x574.jpg 768w\" sizes=\"(max-width: 966px) 100vw, 966px\" \/><br \/>\nThe line does not pass through the origin. So, x and y are not proportional.<\/p>\n<p>Question 2.<br \/>\n<img loading=\"lazy\" class=\"alignnone size-full wp-image-30438\" src=\"https:\/\/ccssmathanswers.com\/wp-content\/uploads\/2021\/01\/Big-Ideas-Math-Answer-Key-Grade-7-Chapter-5-Ratios-and-Proportions-5.5-5.png\" alt=\"Big Ideas Math Answer Key Grade 7 Chapter 5 Ratios and Proportions 5.5 5\" width=\"105\" height=\"120\" \/><\/p>\n<p>Answer:<br \/>\nx and y are not proportional.<\/p>\n<p>Explanation:<br \/>\n<img loading=\"lazy\" class=\"alignnone size-full wp-image-46935\" src=\"https:\/\/ccssmathanswers.com\/wp-content\/uploads\/2021\/01\/big-ideas-math-answer-key-grade-7-chapter-5-ratios-and-proportions-5.5-8.jpg\" alt=\"Big Ideas Math Answer Key Grade 7 Chapter 5 Ratios and Proportions 5.5 8\" width=\"948\" height=\"703\" srcset=\"https:\/\/bigideasmathanswers.com\/wp-content\/uploads\/2021\/01\/big-ideas-math-answer-key-grade-7-chapter-5-ratios-and-proportions-5.5-8.jpg 948w, https:\/\/bigideasmathanswers.com\/wp-content\/uploads\/2021\/01\/big-ideas-math-answer-key-grade-7-chapter-5-ratios-and-proportions-5.5-8-300x222.jpg 300w, https:\/\/bigideasmathanswers.com\/wp-content\/uploads\/2021\/01\/big-ideas-math-answer-key-grade-7-chapter-5-ratios-and-proportions-5.5-8-768x570.jpg 768w\" sizes=\"(max-width: 948px) 100vw, 948px\" \/><br \/>\nThe line pass through the origin. So, x and y are not proportional.<\/p>\n<p>Question 3.<br \/>\n<img loading=\"lazy\" class=\"alignnone size-full wp-image-30439\" src=\"https:\/\/ccssmathanswers.com\/wp-content\/uploads\/2021\/01\/Big-Ideas-Math-Answer-Key-Grade-7-Chapter-5-Ratios-and-Proportions-5.5-6.png\" alt=\"Big Ideas Math Answer Key Grade 7 Chapter 5 Ratios and Proportions 5.5 6\" width=\"110\" height=\"120\" \/><\/p>\n<p>Answer:<br \/>\nx and y are not proportional.<\/p>\n<p>Explanation:<br \/>\n<img loading=\"lazy\" class=\"alignnone size-full wp-image-46936\" src=\"https:\/\/ccssmathanswers.com\/wp-content\/uploads\/2021\/01\/big-ideas-math-answer-key-grade-7-chapter-5-ratios-and-proportions-5.5-9.jpg\" alt=\"Big Ideas Math Answer Key Grade 7 Chapter 5 Ratios and Proportions 5.5 9\" width=\"965\" height=\"722\" srcset=\"https:\/\/bigideasmathanswers.com\/wp-content\/uploads\/2021\/01\/big-ideas-math-answer-key-grade-7-chapter-5-ratios-and-proportions-5.5-9.jpg 965w, https:\/\/bigideasmathanswers.com\/wp-content\/uploads\/2021\/01\/big-ideas-math-answer-key-grade-7-chapter-5-ratios-and-proportions-5.5-9-300x224.jpg 300w, https:\/\/bigideasmathanswers.com\/wp-content\/uploads\/2021\/01\/big-ideas-math-answer-key-grade-7-chapter-5-ratios-and-proportions-5.5-9-768x575.jpg 768w\" sizes=\"(max-width: 965px) 100vw, 965px\" \/><br \/>\nThe line pass through the origin. So, x and y are not proportional.<\/p>\n<p>Question 4.<br \/>\n<strong>WHAT IF<\/strong><br \/>\nDoes your answer change when you use the point (\\(\\frac{1}{2}\\), \\(\\frac{1}{4}\\))to find the speed of the subway car? Explain your reasoning.<\/p>\n<p>Answer:<br \/>\nNo.<\/p>\n<p>Explanation:<br \/>\nThe point (1\/2, 1\/4) indicates that the subway car travels 1\/4 mile every 1\/2 minutes.<br \/>\n1\/4 : 1\/2<br \/>\n= 2\/4 : 1<br \/>\n= 1\/2 : 1<br \/>\nSo, the unit rate is 1\/2 mile per minute<br \/>\nThe speed of the subway car is 1\/2 mile per minute.<\/p>\n<p><strong>Self-Assessment for Concepts &amp; Skills<\/strong><br \/>\nSolve each exercise. Then rate your understanding of the success criteria in your journal.<\/p>\n<p><img loading=\"lazy\" class=\"alignnone size-full wp-image-30440\" src=\"https:\/\/ccssmathanswers.com\/wp-content\/uploads\/2021\/01\/Big-Ideas-Math-Answer-Key-Grade-7-Chapter-5-Ratios-and-Proportions-5.5-7.png\" alt=\"Big Ideas Math Answer Key Grade 7 Chapter 5 Ratios and Proportions 5.5 7\" width=\"190\" height=\"192\" \/><br \/>\nQuestion 5.<br \/>\n<strong>IDENTIFYING A PROPORTIONAL RELATIONSHIP<\/strong> Use the graph shown to tell whether x and y are proportional. Explain your reasoning.<\/p>\n<p>Answer:<br \/>\nx and y are proportional.<\/p>\n<p>Explanation:<br \/>\nx\/y = 0\/0<br \/>\n1.5\/1 = 15\/10 = 3\/2<br \/>\n4.5\/3 = 45\/30 = 3\/2<br \/>\nAs the line pass through the origin, so, x and y are proportional.<\/p>\n<p>Question 6.<br \/>\n<strong>FINDING A UNIT RATE<\/strong><br \/>\nInterpret each plotted point in the graph. Then identify the unit rate, if possible.<\/p>\n<p>Answer:<br \/>\nThe unit rate is 1.5<\/p>\n<p>Explanation:<br \/>\ntime : distance = 1.5\/1<br \/>\n= 15\/10 = 3\/2<br \/>\nThe unit rate is 1.5<\/p>\n<p><strong>Self-Assessment for Problem Solving<\/strong><br \/>\nSolve each exercise. Then rate your understanding of the success criteria in your journal.<\/p>\n<p>Question 7.<br \/>\nThe table shows the temperature (in degrees Fahrenheit), hours after midnight.<br \/>\n<img loading=\"lazy\" class=\"alignnone size-full wp-image-30441\" src=\"https:\/\/ccssmathanswers.com\/wp-content\/uploads\/2021\/01\/Big-Ideas-Math-Answer-Key-Grade-7-Chapter-5-Ratios-and-Proportions-5.5-8.png\" alt=\"Big Ideas Math Answer Key Grade 7 Chapter 5 Ratios and Proportions 5.5 8\" width=\"371\" height=\"70\" srcset=\"https:\/\/bigideasmathanswers.com\/wp-content\/uploads\/2021\/01\/Big-Ideas-Math-Answer-Key-Grade-7-Chapter-5-Ratios-and-Proportions-5.5-8.png 371w, https:\/\/bigideasmathanswers.com\/wp-content\/uploads\/2021\/01\/Big-Ideas-Math-Answer-Key-Grade-7-Chapter-5-Ratios-and-Proportions-5.5-8-300x57.png 300w\" sizes=\"(max-width: 371px) 100vw, 371px\" \/><br \/>\na. Describe a proportional relationship between time and temperature shown by the table. Explain your reasoning.<br \/>\nb. Find the temperature 3.5 hours after midnight.<\/p>\n<p>Answer:<br \/>\nb. 161 degrees Fahrenheit<\/p>\n<p>Explanation:<br \/>\na. The table shows the proportional relationship between hours and temperature.<br \/>\n0.5\/44 = 1\/88<br \/>\n1\/46<br \/>\n1.5\/48 = 1\/32<br \/>\nThe temperature after 3.5 hours, is 3.5 * 46 = 161 degrees Fahrenheit<\/p>\n<p>Question 8.<br \/>\n<strong>DIG DEEPER!<\/strong><br \/>\nShow how you can use a proportional relationship to plan the heights of the vertical supports of a waterskiing ramp. Then explain how increasing the steepness of the ramp affects the proportional relationship.<br \/>\n<img loading=\"lazy\" class=\"alignnone size-full wp-image-30442\" src=\"https:\/\/ccssmathanswers.com\/wp-content\/uploads\/2021\/01\/Big-Ideas-Math-Answer-Key-Grade-7-Chapter-5-Ratios-and-Proportions-5.5-9.png\" alt=\"Big Ideas Math Answer Key Grade 7 Chapter 5 Ratios and Proportions 5.5 9\" width=\"218\" height=\"92\" \/><\/p>\n<p>Answer:<br \/>\nThe vertical supports tell the height of the ramp. As the height of the ramp increases the distance from the ramp is increases.<\/p>\n<h3><a id=\"Graphs_of_Proportional_Relationships_Homework_&amp;_Practice_5.5\"><\/a>Graphs of Proportional Relationships Homework &amp; Practice 5.5<\/h3>\n<p><strong>Review &amp; Refresh<\/strong><\/p>\n<p><strong>Find the value of x so that the ratios are equivalent.<\/strong><br \/>\nQuestion 1.<br \/>\n2 : 7 and 8 : x<\/p>\n<p>Answer:<br \/>\nx = 28<\/p>\n<p>Explanation:<br \/>\n2\/7 = 8\/x<br \/>\nCross multiply the fractions<br \/>\n2x = 8 * 7<br \/>\n2x = 56<br \/>\nx = 56\/2<br \/>\nx = 28<\/p>\n<p>Question 2.<br \/>\n3 to 2 and x to 18<\/p>\n<p>Answer:<br \/>\nx = 27<\/p>\n<p>Explanation:<br \/>\n3\/2 = x\/18<br \/>\nCross multiply the fractions<br \/>\n3 * 18 = 2x<br \/>\n54 = 2x<br \/>\nx = 54\/2<br \/>\nx = 27<\/p>\n<p>Question 3.<br \/>\n9 : x and 54 : 8<\/p>\n<p>Answer:<br \/>\nx = 4\/3<\/p>\n<p>Explanation:<br \/>\n9\/x = 54\/8<br \/>\nCross multiply the fractions<br \/>\n54x = 9 * 8<br \/>\n54x = 72<br \/>\nx = 72\/54<br \/>\nx = 4\/3<\/p>\n<p><strong>Find the quotient, if possible.<\/strong><br \/>\nQuestion 4.<br \/>\n36 \u00f7 4<\/p>\n<p>Answer:<br \/>\n36 \u00f7 4 = 9<\/p>\n<p>Explanation:<br \/>\nThe quotient of two integers of the same sign is positive.<br \/>\n36 \u00f7 4 = 9<\/p>\n<p>Question 5.<br \/>\n42 \u00f7 (- 6)<\/p>\n<p>Answer:<br \/>\n42 \u00f7 (- 6) = -7<\/p>\n<p>Explanation:<br \/>\nThe quotient of two integers of the different signs is negative.<br \/>\n42 \u00f7 (- 6) = -7<\/p>\n<p>Question 6.<br \/>\n&#8211; 39 \u00f7 3<\/p>\n<p>Answer:<br \/>\n&#8211; 39 \u00f7 3 = -13<\/p>\n<p>Explanation:<br \/>\nThe quotient of two integers of the different signs is negative.<br \/>\n&#8211; 39 \u00f7 3 = -13<\/p>\n<p>Question 7.<br \/>\n&#8211; 44 \u00f7 (- 4)<\/p>\n<p>Answer:<br \/>\n&#8211; 44 \u00f7 (- 4) = 11<\/p>\n<p>Explanation:<br \/>\nThe quotient of two integers of the same sign is positive.<br \/>\n&#8211; 44 \u00f7 (- 4) = 11<\/p>\n<p><strong>Solve the inequality. Graph the solution.<\/strong><br \/>\nQuestion 8.<br \/>\n&#8211; \\(\\frac{x}{3}\\) &lt; 2<\/p>\n<p>Answer:<br \/>\nx &gt; -6<br \/>\n<img loading=\"lazy\" class=\"alignnone size-full wp-image-47884\" src=\"https:\/\/ccssmathanswers.com\/wp-content\/uploads\/2021\/01\/big-ideas-math-answer-key-grade-7-chapter-5-ratios-and-proportions-5.5-10.jpg\" alt=\"Big Ideas Math Answer Key Grade 7 Chapter 5 Ratios and Proportions 5.5 10\" width=\"767\" height=\"77\" srcset=\"https:\/\/bigideasmathanswers.com\/wp-content\/uploads\/2021\/01\/big-ideas-math-answer-key-grade-7-chapter-5-ratios-and-proportions-5.5-10.jpg 767w, https:\/\/bigideasmathanswers.com\/wp-content\/uploads\/2021\/01\/big-ideas-math-answer-key-grade-7-chapter-5-ratios-and-proportions-5.5-10-300x30.jpg 300w\" sizes=\"(max-width: 767px) 100vw, 767px\" \/><\/p>\n<p>Explanation:<br \/>\n&#8211; \\(\\frac{x}{3}\\) &lt; 2<br \/>\nMultiply each side by 3<br \/>\n-x\/3 . 3 &lt; 2 . 3<br \/>\n-x &lt; 6<br \/>\nx &gt; -6<\/p>\n<p>Question 9.<br \/>\n\\(\\frac{1}{3}\\)p \u2265 4<\/p>\n<p>Answer:<br \/>\np \u2265 12<br \/>\n<img loading=\"lazy\" class=\"alignnone size-full wp-image-47885\" src=\"https:\/\/ccssmathanswers.com\/wp-content\/uploads\/2021\/01\/big-ideas-math-answer-key-grade-7-chapter-5-ratios-and-proportions-5.5-11.jpg\" alt=\"Big Ideas Math Answer Key Grade 7 Chapter 5 Ratios and Proportions 5.5 11\" width=\"776\" height=\"114\" srcset=\"https:\/\/bigideasmathanswers.com\/wp-content\/uploads\/2021\/01\/big-ideas-math-answer-key-grade-7-chapter-5-ratios-and-proportions-5.5-11.jpg 776w, https:\/\/bigideasmathanswers.com\/wp-content\/uploads\/2021\/01\/big-ideas-math-answer-key-grade-7-chapter-5-ratios-and-proportions-5.5-11-300x44.jpg 300w, https:\/\/bigideasmathanswers.com\/wp-content\/uploads\/2021\/01\/big-ideas-math-answer-key-grade-7-chapter-5-ratios-and-proportions-5.5-11-768x113.jpg 768w\" sizes=\"(max-width: 776px) 100vw, 776px\" \/><\/p>\n<p>Explanation:<br \/>\n\\(\\frac{1}{3}\\)p \u2265 4<br \/>\nMultiply each side by 3<br \/>\n\\(\\frac{1}{3}\\)3p \u2265 4 . 3<br \/>\np \u2265 12<\/p>\n<p>Question 10.<br \/>\n&#8211; 8 &lt; \\(\\frac{2}{3}\\)n<\/p>\n<p>Answer:<br \/>\n-24 &lt; n<br \/>\n<img loading=\"lazy\" class=\"alignnone size-full wp-image-47889\" src=\"https:\/\/ccssmathanswers.com\/wp-content\/uploads\/2021\/01\/big-ideas-math-answer-key-grade-7-chapter-5-ratios-and-proportions-5.5-12.jpg\" alt=\"Big Ideas Math Answer Key Grade 7 Chapter 5 Ratios and Proportions 5.5 12\" width=\"760\" height=\"86\" srcset=\"https:\/\/bigideasmathanswers.com\/wp-content\/uploads\/2021\/01\/big-ideas-math-answer-key-grade-7-chapter-5-ratios-and-proportions-5.5-12.jpg 760w, https:\/\/bigideasmathanswers.com\/wp-content\/uploads\/2021\/01\/big-ideas-math-answer-key-grade-7-chapter-5-ratios-and-proportions-5.5-12-300x34.jpg 300w\" sizes=\"(max-width: 760px) 100vw, 760px\" \/><\/p>\n<p>Explanation:<br \/>\n&#8211; 8 &lt; \\(\\frac{2}{3}\\)n<br \/>\nMultiply each side by 3\/2<br \/>\n-8 x (3\/2) &lt; 2n\/3 x (3\/2)<br \/>\n-24 &lt; n<\/p>\n<p>Question 11.<br \/>\n&#8211; 2w \u2264 10<\/p>\n<p>Answer:<br \/>\nw \u2265 5<br \/>\n<img loading=\"lazy\" class=\"alignnone size-full wp-image-47891\" src=\"https:\/\/ccssmathanswers.com\/wp-content\/uploads\/2021\/01\/big-ideas-math-answer-key-grade-7-chapter-5-ratios-and-proportions-5.5-13.jpg\" alt=\"Big Ideas Math Answer Key Grade 7 Chapter 5 Ratios and Proportions 5.5 13\" width=\"776\" height=\"77\" srcset=\"https:\/\/bigideasmathanswers.com\/wp-content\/uploads\/2021\/01\/big-ideas-math-answer-key-grade-7-chapter-5-ratios-and-proportions-5.5-13.jpg 776w, https:\/\/bigideasmathanswers.com\/wp-content\/uploads\/2021\/01\/big-ideas-math-answer-key-grade-7-chapter-5-ratios-and-proportions-5.5-13-300x30.jpg 300w, https:\/\/bigideasmathanswers.com\/wp-content\/uploads\/2021\/01\/big-ideas-math-answer-key-grade-7-chapter-5-ratios-and-proportions-5.5-13-768x76.jpg 768w\" sizes=\"(max-width: 776px) 100vw, 776px\" \/><\/p>\n<p>Explanation:<br \/>\n&#8211; 2w \u2264 10<br \/>\nDivide each side by 2<br \/>\n&#8211; 2w\/2 \u2264 10\/2<br \/>\n-w \u2264 5<br \/>\nw \u2265 5<\/p>\n<p><strong>Concepts, Skills, &amp; Problem Solving<\/strong><\/p>\n<p><strong>REPRESENTING RELATIONSHIPS GRAPHICALLY<\/strong> Represent the table graphically. Does the graph represent a proportional relationship? How do you know? (See Exploration 1, p. 211.)<br \/>\nQuestion 12.<br \/>\n<img loading=\"lazy\" class=\"alignnone size-full wp-image-30443\" src=\"https:\/\/ccssmathanswers.com\/wp-content\/uploads\/2021\/01\/Big-Ideas-Math-Answer-Key-Grade-7-Chapter-5-Ratios-and-Proportions-5.5-10.png\" alt=\"Big Ideas Math Answer Key Grade 7 Chapter 5 Ratios and Proportions 5.5 10\" width=\"184\" height=\"118\" \/><\/p>\n<p>Answer:<br \/>\nx and y are not proportional.<\/p>\n<p>Explanation:<br \/>\n<img loading=\"lazy\" class=\"alignnone size-full wp-image-47893\" src=\"https:\/\/ccssmathanswers.com\/wp-content\/uploads\/2021\/01\/big-ideas-math-answer-key-grade-7-chapter-5-ratios-and-proportions-5.5-14.jpg\" alt=\"Big Ideas Math Answer Key Grade 7 Chapter 5 Ratios and Proportions 5.5 14\" width=\"962\" height=\"715\" srcset=\"https:\/\/bigideasmathanswers.com\/wp-content\/uploads\/2021\/01\/big-ideas-math-answer-key-grade-7-chapter-5-ratios-and-proportions-5.5-14.jpg 962w, https:\/\/bigideasmathanswers.com\/wp-content\/uploads\/2021\/01\/big-ideas-math-answer-key-grade-7-chapter-5-ratios-and-proportions-5.5-14-300x223.jpg 300w, https:\/\/bigideasmathanswers.com\/wp-content\/uploads\/2021\/01\/big-ideas-math-answer-key-grade-7-chapter-5-ratios-and-proportions-5.5-14-768x571.jpg 768w\" sizes=\"(max-width: 962px) 100vw, 962px\" \/><br \/>\nThe line does not pass through the origin.<br \/>\nSo, x and y are not proportional.<\/p>\n<p>Question 13.<br \/>\n<img loading=\"lazy\" class=\"alignnone size-full wp-image-30444\" src=\"https:\/\/ccssmathanswers.com\/wp-content\/uploads\/2021\/01\/Big-Ideas-Math-Answer-Key-Grade-7-Chapter-5-Ratios-and-Proportions-5.5-11.png\" alt=\"Big Ideas Math Answer Key Grade 7 Chapter 5 Ratios and Proportions 5.5 11\" width=\"224\" height=\"121\" \/><\/p>\n<p>Answer:<br \/>\nx and y are proportional.<\/p>\n<p>Explanation:<br \/>\n<img loading=\"lazy\" class=\"alignnone size-full wp-image-47895\" src=\"https:\/\/ccssmathanswers.com\/wp-content\/uploads\/2021\/01\/big-ideas-math-answer-key-grade-7-chapter-5-ratios-and-proportions-5.5-15.jpg\" alt=\"Big Ideas Math Answer Key Grade 7 Chapter 5 Ratios and Proportions 5.5 15\" width=\"965\" height=\"719\" srcset=\"https:\/\/bigideasmathanswers.com\/wp-content\/uploads\/2021\/01\/big-ideas-math-answer-key-grade-7-chapter-5-ratios-and-proportions-5.5-15.jpg 965w, https:\/\/bigideasmathanswers.com\/wp-content\/uploads\/2021\/01\/big-ideas-math-answer-key-grade-7-chapter-5-ratios-and-proportions-5.5-15-300x224.jpg 300w, https:\/\/bigideasmathanswers.com\/wp-content\/uploads\/2021\/01\/big-ideas-math-answer-key-grade-7-chapter-5-ratios-and-proportions-5.5-15-768x572.jpg 768w\" sizes=\"(max-width: 965px) 100vw, 965px\" \/><br \/>\nThe line pass through the origin.<br \/>\nSo, x and y are proportional.<\/p>\n<p><strong>IDENTIFYING A PROPORTIONAL RELATIONSHIP<\/strong> Tell whether x and y are proportional. Explain your reasoning.<br \/>\nQuestion 14.<br \/>\n<img loading=\"lazy\" class=\"alignnone size-full wp-image-30445\" src=\"https:\/\/ccssmathanswers.com\/wp-content\/uploads\/2021\/01\/Big-Ideas-Math-Answer-Key-Grade-7-Chapter-5-Ratios-and-Proportions-5.5-12.png\" alt=\"Big Ideas Math Answer Key Grade 7 Chapter 5 Ratios and Proportions 5.5 12\" width=\"177\" height=\"58\" \/><\/p>\n<p>Answer:<br \/>\nx and y are proportional.<\/p>\n<p>Explanation:<br \/>\nCompare the values of ratios x to y<br \/>\nx\/y = 1\/2<br \/>\n2\/4 = 1\/2<br \/>\n3\/6 = 1\/2<br \/>\n4\/8 = 1\/2<br \/>\nThe ratios are equivalent.<br \/>\nSo, x and y are proportional.<\/p>\n<p>Question 15.<br \/>\n<img loading=\"lazy\" class=\"alignnone size-full wp-image-30446\" src=\"https:\/\/ccssmathanswers.com\/wp-content\/uploads\/2021\/01\/Big-Ideas-Math-Answer-Key-Grade-7-Chapter-5-Ratios-and-Proportions-5.5-13.png\" alt=\"Big Ideas Math Answer Key Grade 7 Chapter 5 Ratios and Proportions 5.5 13\" width=\"177\" height=\"61\" \/><\/p>\n<p>Answer:<br \/>\nx and y are not proportional.<\/p>\n<p>Explanation:<br \/>\nCompare the values of ratios x to y<br \/>\nx\/y = -2\/0 = 0<br \/>\n-1\/2<br \/>\n0\/4 = 0<br \/>\n1\/6<br \/>\nThe ratios are not equivalent<br \/>\nSo, x and y are not proportional.<\/p>\n<p>Question 16.<br \/>\n<img loading=\"lazy\" class=\"alignnone size-full wp-image-30447\" src=\"https:\/\/ccssmathanswers.com\/wp-content\/uploads\/2021\/01\/Big-Ideas-Math-Answer-Key-Grade-7-Chapter-5-Ratios-and-Proportions-5.5-14.png\" alt=\"Big Ideas Math Answer Key Grade 7 Chapter 5 Ratios and Proportions 5.5 14\" width=\"171\" height=\"61\" \/><\/p>\n<p>Answer:<br \/>\nx and y are not proportional.<\/p>\n<p>Explanation:<br \/>\nCompare the values of ratios x to y<br \/>\nx\/y = -1\/-2 = 1\/2<br \/>\n0\/-1 = 0<br \/>\n1\/0 = 0<br \/>\n2\/1<br \/>\nAll the ratios are not equivalent<br \/>\nSo, x and y are not proportional.<\/p>\n<p>Question 17.<br \/>\n<img loading=\"lazy\" class=\"alignnone size-full wp-image-30448\" src=\"https:\/\/ccssmathanswers.com\/wp-content\/uploads\/2021\/01\/Big-Ideas-Math-Answer-Key-Grade-7-Chapter-5-Ratios-and-Proportions-5.5-15.png\" alt=\"Big Ideas Math Answer Key Grade 7 Chapter 5 Ratios and Proportions 5.5 15\" width=\"181\" height=\"62\" \/><\/p>\n<p>Answer:<br \/>\nx and y are proportional.<\/p>\n<p>Explanation:<br \/>\nCompare the values of ratios x to y<br \/>\nx\/y = 3\/2<br \/>\n6\/4 = 3\/2<br \/>\n9\/6 = 3\/2<br \/>\n12\/8 = 3\/2<br \/>\nAll the ratios are equivalent<br \/>\nSo, x and y are proportional.<\/p>\n<p>Question 18.<br \/>\n<img loading=\"lazy\" class=\"alignnone size-full wp-image-30449\" src=\"https:\/\/ccssmathanswers.com\/wp-content\/uploads\/2021\/01\/Big-Ideas-Math-Answer-Key-Grade-7-Chapter-5-Ratios-and-Proportions-5.5-16.png\" alt=\"Big Ideas Math Answer Key Grade 7 Chapter 5 Ratios and Proportions 5.5 16\" width=\"180\" height=\"58\" \/><\/p>\n<p>Answer:<br \/>\nx and y are not proportional.<\/p>\n<p>Explanation:<br \/>\nCompare the values of ratios x to y<br \/>\nx\/y = 1\/3<br \/>\n2\/4 = 1\/2<br \/>\n3\/5<br \/>\n4\/6 = 2\/3<br \/>\nAll the ratios are not equivalent<br \/>\nSo, x and y are not proportional.<\/p>\n<p>Question 19.<br \/>\n<img loading=\"lazy\" class=\"alignnone size-full wp-image-30450\" src=\"https:\/\/ccssmathanswers.com\/wp-content\/uploads\/2021\/01\/Big-Ideas-Math-Answer-Key-Grade-7-Chapter-5-Ratios-and-Proportions-5.5-17.png\" alt=\"Big Ideas Math Answer Key Grade 7 Chapter 5 Ratios and Proportions 5.5 17\" width=\"182\" height=\"63\" \/><\/p>\n<p>Answer:<br \/>\nx and y are proportional.<\/p>\n<p>Explanation:<br \/>\nCompare the values of ratios x to y<br \/>\nx\/y = 1\/0.5 = 2<br \/>\n3\/1.5 = 2<br \/>\n5\/2.5 = 2<br \/>\n7\/3.5 = 2<br \/>\nThe ratios are equivalent<br \/>\nSo, x and y are proportional.<\/p>\n<p>Question 20.<br \/>\n<strong>YOU BE THE TEACHER<\/strong><br \/>\nYour friend uses the graph to determine whether x and y are proportional. Is your friend correct? Explain your reasoning.<br \/>\n<img loading=\"lazy\" class=\"alignnone size-full wp-image-30451\" src=\"https:\/\/ccssmathanswers.com\/wp-content\/uploads\/2021\/01\/Big-Ideas-Math-Answer-Key-Grade-7-Chapter-5-Ratios-and-Proportions-5.5-18.png\" alt=\"Big Ideas Math Answer Key Grade 7 Chapter 5 Ratios and Proportions 5.5 18\" width=\"346\" height=\"112\" srcset=\"https:\/\/bigideasmathanswers.com\/wp-content\/uploads\/2021\/01\/Big-Ideas-Math-Answer-Key-Grade-7-Chapter-5-Ratios-and-Proportions-5.5-18.png 346w, https:\/\/bigideasmathanswers.com\/wp-content\/uploads\/2021\/01\/Big-Ideas-Math-Answer-Key-Grade-7-Chapter-5-Ratios-and-Proportions-5.5-18-300x97.png 300w\" sizes=\"(max-width: 346px) 100vw, 346px\" \/><\/p>\n<p>Answer:<br \/>\nThe line does not pass through the origin.<br \/>\nso, x and y are not proportional.<\/p>\n<p><strong>FINDING A UNIT RATE<\/strong> Interpret each plotted point in the graph. Then identify the unit rate.<br \/>\nQuestion 21.<br \/>\n<img loading=\"lazy\" class=\"alignnone size-full wp-image-30452\" src=\"https:\/\/ccssmathanswers.com\/wp-content\/uploads\/2021\/01\/Big-Ideas-Math-Answer-Key-Grade-7-Chapter-5-Ratios-and-Proportions-5.5-19.png\" alt=\"Big Ideas Math Answer Key Grade 7 Chapter 5 Ratios and Proportions 5.5 19\" width=\"194\" height=\"225\" \/><\/p>\n<p>Answer:<br \/>\nTnit rate is 1\/15<\/p>\n<p>Explanation:<br \/>\nThe points are (1, 15), (4, 60)<br \/>\nx\/y = 1\/15<br \/>\n4\/60 = (4 \u00f7 4)\/(60 \u00f7 4)<br \/>\n= 1\/15<br \/>\nSo, unit rate is 1\/15<\/p>\n<p>Question 22.<br \/>\n<img loading=\"lazy\" class=\"alignnone size-full wp-image-30453\" src=\"https:\/\/ccssmathanswers.com\/wp-content\/uploads\/2021\/01\/Big-Ideas-Math-Answer-Key-Grade-7-Chapter-5-Ratios-and-Proportions-5.5-20.png\" alt=\"Big Ideas Math Answer Key Grade 7 Chapter 5 Ratios and Proportions 5.5 20\" width=\"195\" height=\"226\" \/><\/p>\n<p>Answer:<br \/>\nThe unit rate is 0.2 seconds per feet.<\/p>\n<p>Explanation:<br \/>\nThe points are (1, 5), (6, 30)<br \/>\nx\/y = 1\/5<br \/>\n6\/30 = 1\/5<br \/>\nThe unit rate is 0.2 seconds per feet.<\/p>\n<p><strong>IDENTIFYING A PROPORTIONAL RELATIONSHIP<\/strong> Tell whether x and y are proportional. If so, identify the constant of proportionality. Explain your reasoning.<br \/>\nQuestion 23.<br \/>\nx &#8211; y = 0<\/p>\n<p>Answer:<br \/>\nx and y are proportional.<\/p>\n<p>Explanation:<br \/>\nx &#8211; y = 0<br \/>\nx = 0 + y<br \/>\nx = y<br \/>\n<img loading=\"lazy\" class=\"alignnone size-full wp-image-47919\" src=\"https:\/\/ccssmathanswers.com\/wp-content\/uploads\/2021\/01\/big-ideas-math-answer-key-grade-7-chapter-5-ratios-and-proportions-5.5-16.jpg\" alt=\"Big Ideas Math Answer Key Grade 7 Chapter 5 Ratios and Proportions 5.5 16\" width=\"653\" height=\"90\" srcset=\"https:\/\/bigideasmathanswers.com\/wp-content\/uploads\/2021\/01\/big-ideas-math-answer-key-grade-7-chapter-5-ratios-and-proportions-5.5-16.jpg 653w, https:\/\/bigideasmathanswers.com\/wp-content\/uploads\/2021\/01\/big-ideas-math-answer-key-grade-7-chapter-5-ratios-and-proportions-5.5-16-300x41.jpg 300w\" sizes=\"(max-width: 653px) 100vw, 653px\" \/><br \/>\nSo, x and y are proportional.<\/p>\n<p>Question 24.<br \/>\n\\(\\frac{x}{y}\\) = 2<\/p>\n<p>Answer:<br \/>\nx and y are proportional.<\/p>\n<p>Explanation:<br \/>\n\\(\\frac{x}{y}\\) = 2<br \/>\nx = 2y<br \/>\nIf y = 0, then x = 2(0) = 0<br \/>\nIf y = 1, then x = 2(1) = 2<br \/>\nIf y = 2, then x = 2(2) = 4<br \/>\n<img loading=\"lazy\" class=\"alignnone size-full wp-image-47923\" src=\"https:\/\/ccssmathanswers.com\/wp-content\/uploads\/2021\/01\/big-ideas-math-answer-key-grade-7-chapter-5-ratios-and-proportions-5.5-17.jpg\" alt=\"Big Ideas Math Answer Key Grade 7 Chapter 5 Ratios and Proportions 5.5 17\" width=\"524\" height=\"88\" srcset=\"https:\/\/bigideasmathanswers.com\/wp-content\/uploads\/2021\/01\/big-ideas-math-answer-key-grade-7-chapter-5-ratios-and-proportions-5.5-17.jpg 524w, https:\/\/bigideasmathanswers.com\/wp-content\/uploads\/2021\/01\/big-ideas-math-answer-key-grade-7-chapter-5-ratios-and-proportions-5.5-17-300x50.jpg 300w\" sizes=\"(max-width: 524px) 100vw, 524px\" \/><br \/>\nSo, x and y are proportional.<\/p>\n<p>Question 25.<br \/>\n8 = xy<\/p>\n<p>Answer:<br \/>\nx and y are proportional.<\/p>\n<p>Explanation:<br \/>\n8 = xy<br \/>\ny = 8\/x<br \/>\nIf x = 0, then y = 8\/0 = 0<br \/>\nIf x = 1, then y = 8\/1 = 8<br \/>\nIf x = 2, then y = 8\/2 = 4<br \/>\n<img loading=\"lazy\" class=\"alignnone size-full wp-image-47924\" src=\"https:\/\/ccssmathanswers.com\/wp-content\/uploads\/2021\/01\/big-ideas-math-answer-key-grade-7-chapter-5-ratios-and-proportions-5.5-18.jpg\" alt=\"Big Ideas Math Answer Key Grade 7 Chapter 5 Ratios and Proportions 5.5 18\" width=\"527\" height=\"96\" srcset=\"https:\/\/bigideasmathanswers.com\/wp-content\/uploads\/2021\/01\/big-ideas-math-answer-key-grade-7-chapter-5-ratios-and-proportions-5.5-18.jpg 527w, https:\/\/bigideasmathanswers.com\/wp-content\/uploads\/2021\/01\/big-ideas-math-answer-key-grade-7-chapter-5-ratios-and-proportions-5.5-18-300x55.jpg 300w\" sizes=\"(max-width: 527px) 100vw, 527px\" \/><br \/>\nSo, x and y are proportional.<\/p>\n<p>Question 26.<br \/>\nx<sup>2<\/sup> = y<\/p>\n<p>Answer:<br \/>\nx and y are proportional.<\/p>\n<p>Explanation:<br \/>\nx<sup>2<\/sup> = y<br \/>\nIf x = 0, then y = 0<br \/>\nIf x = 1, then y = 1<br \/>\nIf x = 2, then y = 4<br \/>\n<img loading=\"lazy\" class=\"alignnone size-full wp-image-47949\" src=\"https:\/\/ccssmathanswers.com\/wp-content\/uploads\/2021\/01\/big-ideas-math-answer-key-grade-7-chapter-5-ratios-and-proportions-5.5-19.jpg\" alt=\"Big Ideas Math Answer Key Grade 7 Chapter 5 Ratios and Proportions 5.5 19\" width=\"524\" height=\"90\" srcset=\"https:\/\/bigideasmathanswers.com\/wp-content\/uploads\/2021\/01\/big-ideas-math-answer-key-grade-7-chapter-5-ratios-and-proportions-5.5-19.jpg 524w, https:\/\/bigideasmathanswers.com\/wp-content\/uploads\/2021\/01\/big-ideas-math-answer-key-grade-7-chapter-5-ratios-and-proportions-5.5-19-300x52.jpg 300w\" sizes=\"(max-width: 524px) 100vw, 524px\" \/><br \/>\nSo, x and y are proportional.<\/p>\n<p><strong>WRITING AN EQUATION<\/strong> The variables and are proportional. Use the values to find the constant of proportionality. Then write an equation that relates x and y.<br \/>\nQuestion 27.<br \/>\nWhen y = 72, x = 3.<\/p>\n<p>Answer:<br \/>\ny = 24x<\/p>\n<p>Explanation:<br \/>\ny\/x = 72\/3<br \/>\ny\/x = 24<br \/>\ny = 24x<\/p>\n<p>Question 28.<br \/>\nWhen y = 20, x = 12.<\/p>\n<p>Answer:<br \/>\n5x = 3y<\/p>\n<p>Explanation:<br \/>\ny\/x = 20\/12<br \/>\ny\/x = 5\/3<br \/>\nCross multiply the fractions<br \/>\n3y = 5x<\/p>\n<p>Question 29.<br \/>\nWhen y = 45, x = 40.<\/p>\n<p>Answer:<br \/>\n9x = 8y<\/p>\n<p>Explanation:<br \/>\ny\/x = 45\/40<br \/>\ny\/x = 9\/8<br \/>\nCross multiply the fractions<br \/>\n8y = 9x<\/p>\n<p>Question 30.<br \/>\n<strong>MODELING REAL LIFE<\/strong><br \/>\nThe table shows the profit y for recycling x pounds of aluminum. Find the profit for recycling 75 pounds of aluminum.<br \/>\n<img loading=\"lazy\" class=\"alignnone size-full wp-image-30454\" src=\"https:\/\/ccssmathanswers.com\/wp-content\/uploads\/2021\/01\/Big-Ideas-Math-Answer-Key-Grade-7-Chapter-5-Ratios-and-Proportions-5.5-21.png\" alt=\"Big Ideas Math Answer Key Grade 7 Chapter 5 Ratios and Proportions 5.5 21\" width=\"341\" height=\"75\" srcset=\"https:\/\/bigideasmathanswers.com\/wp-content\/uploads\/2021\/01\/Big-Ideas-Math-Answer-Key-Grade-7-Chapter-5-Ratios-and-Proportions-5.5-21.png 341w, https:\/\/bigideasmathanswers.com\/wp-content\/uploads\/2021\/01\/Big-Ideas-Math-Answer-Key-Grade-7-Chapter-5-Ratios-and-Proportions-5.5-21-300x66.png 300w\" sizes=\"(max-width: 341px) 100vw, 341px\" \/><\/p>\n<p>Answer:<br \/>\nThe profit for recycling 75 pounds of aluminum is $33.75<\/p>\n<p>Explanation:<br \/>\nThe profit is $4.50 for recycling 10 pounds of aluminum<br \/>\n= 4.50 : 10<br \/>\n= 4.50\/10 : 1<br \/>\n= 0.45 : 1<br \/>\nThe profit is 40.45 for recycling 1 pound of aluminum.<br \/>\nThe profit for recycling 75 pounds of aluminum is $135\/4<\/p>\n<p>Question 31.<br \/>\n<strong>MODELING REAL LIFE<\/strong><br \/>\nThe graph shows the cost of buying concert tickets. Tell whether x and y are proportional. If so, find and interpret the constant of proportionality. Then find the cost of 14 tickets.<br \/>\n<img loading=\"lazy\" class=\"alignnone size-full wp-image-30455\" src=\"https:\/\/ccssmathanswers.com\/wp-content\/uploads\/2021\/01\/Big-Ideas-Math-Answer-Key-Grade-7-Chapter-5-Ratios-and-Proportions-5.5-22.png\" alt=\"Big Ideas Math Answer Key Grade 7 Chapter 5 Ratios and Proportions 5.5 22\" width=\"242\" height=\"196\" \/><\/p>\n<p>Answer:<br \/>\nx and y are proportional.<br \/>\nThe cost for buying 14 tickets is $182<br \/>\n13x = y<\/p>\n<p>Explanation:<br \/>\nThe line in the graph passes through the origin. so, x and y are proportional.<br \/>\nThe cost for buying 2 tickets is 26<br \/>\n= 26 : 2<br \/>\n=13 : 1<br \/>\nThe cost for buying 1 ticket is $13.<br \/>\nSo, the cost for buying 14 tickets is 14 * 13 = $182<br \/>\nx\/y = 2\/26<br \/>\nx\/y = 1\/13<br \/>\nCross multiply the fractions<br \/>\n13x = y<\/p>\n<p>Question 32.<br \/>\n<strong>REASONING<\/strong><br \/>\nThe graph of a proportional relationship passes through (12, 16) and (1, y) Find y.<\/p>\n<p>Answer:<br \/>\ny = 4\/3<\/p>\n<p>Explanation:<br \/>\n12\/16 = 1\/y<br \/>\n3\/4 = 1\/y<br \/>\nCross multiply the fractions<br \/>\n3y = 4<br \/>\ny = 4\/3<\/p>\n<p>Question 33.<br \/>\n<strong>PROBLEM SOLVING<\/strong><br \/>\nThe amount of chlorine in a swimming pool is proportional to the volume of water. The pool has 2.5 milligrams of chlorine per liter of water. How much chlorine is in the pool?<br \/>\n<img loading=\"lazy\" class=\"alignnone size-full wp-image-30456\" src=\"https:\/\/ccssmathanswers.com\/wp-content\/uploads\/2021\/01\/Big-Ideas-Math-Answer-Key-Grade-7-Chapter-5-Ratios-and-Proportions-5.5-23.png\" alt=\"Big Ideas Math Answer Key Grade 7 Chapter 5 Ratios and Proportions 5.5 23\" width=\"237\" height=\"141\" \/><\/p>\n<p>Answer:<br \/>\nThe amount of chlorine in the pool is 75708.225 milligrams.<\/p>\n<p>Explanation:<br \/>\nThe amount of chlorine in a swimming pool varies directly with the volume of water. The pool has 2.5 milligrams of chlorine per liter of water.<br \/>\n1 gallon = 3.78541 litre<br \/>\n8000 gallons = 8000 * 3.78541 = 30283.29 litres<br \/>\nThe amount of chlorine in the pool = 30283.29 * 2.5<br \/>\n= 75708.225 milligrams.<\/p>\n<p>Question 34.<br \/>\n<strong>DIG DEEPER!<\/strong><br \/>\nA vehicle travels 250 feet every 3 seconds. Find the value of the ratio, the unit rate, and the constant of proportionality. How are they related?<\/p>\n<p>Answer:<br \/>\nThe ratio is 250 : 3<br \/>\nThe unit rate is 250\/3 : 1<br \/>\n3x = 250y<\/p>\n<p>Explanation:<br \/>\nA vehicle travels 250 feet every 3 seconds<br \/>\n= 250 : 3<br \/>\n= 250\/3 : 1<br \/>\nThe unit rate is 250\/3 : 1<br \/>\nx\/y = 250\/3<br \/>\nCross multiply the proportions<br \/>\n3x = 250y<\/p>\n<h3><a id=\"Lesson_5.6_Scale_Drawings\"><\/a>Lesson 5.6 Scale Drawings<\/h3>\n<p><strong>EXPLORATION 1<\/strong><\/p>\n<p>Creating a Scale Drawing<\/p>\n<p>Work with a partner. Several sections in a zoo are drawn on 1-centimeter grid paper as shown. Each centimeter in the drawing represents 4 meters.<br \/>\n<img loading=\"lazy\" class=\"alignnone size-full wp-image-30457\" src=\"https:\/\/ccssmathanswers.com\/wp-content\/uploads\/2021\/01\/Big-Ideas-Math-Answers-7th-Grade-Chapter-5-Ratios-and-Proportions-5.6-1.png\" alt=\"Big Ideas Math Answers 7th Grade Chapter 5 Ratios and Proportions 5.6 1\" width=\"569\" height=\"292\" srcset=\"https:\/\/bigideasmathanswers.com\/wp-content\/uploads\/2021\/01\/Big-Ideas-Math-Answers-7th-Grade-Chapter-5-Ratios-and-Proportions-5.6-1.png 569w, https:\/\/bigideasmathanswers.com\/wp-content\/uploads\/2021\/01\/Big-Ideas-Math-Answers-7th-Grade-Chapter-5-Ratios-and-Proportions-5.6-1-300x154.png 300w\" sizes=\"(max-width: 569px) 100vw, 569px\" \/><br \/>\na. Describe the relationship between the lengths of the fences in the drawing and the actual side lengths of the fences.<br \/>\nb. Describe the relationship between the areas of the sections in the drawing and the actual areas of the sections.<br \/>\nc. Are the relationships in parts (a) and (b) the same? Explain your reasoning.<br \/>\nd. Choose a different distance to represent each centimeter on a piece of 1-centimeter grid paper. Then create a new drawing of the sections in the zoo using the distance you chose. Describe any similarities or differences in the drawings.<\/p>\n<p><img loading=\"lazy\" class=\"alignnone size-full wp-image-30458\" src=\"https:\/\/ccssmathanswers.com\/wp-content\/uploads\/2021\/01\/Big-Ideas-Math-Answers-7th-Grade-Chapter-5-Ratios-and-Proportions-5.6-2.png\" alt=\"Big Ideas Math Answers 7th Grade Chapter 5 Ratios and Proportions 5.6 2\" width=\"186\" height=\"121\" \/><\/p>\n<p><strong>Try It<\/strong><\/p>\n<p>Question 1.<br \/>\nWhat is the actual distance between Traverse City and Marquette?<\/p>\n<p>Answer:<br \/>\nThe distance between Traverse City and Marquette is 150 miles<\/p>\n<p>Explanation:<br \/>\nUse the centimeter ruler to find the distance on the map between traverse city and Marquette.<br \/>\nthe map distance is about 3 centimeters<br \/>\nUse the scale 1 cm : 50 mi and the ratio 3 cm : d mi to write and solve a proportion<br \/>\n1\/50 = 3\/d<br \/>\nd = 50 * 3<br \/>\nd = 150<br \/>\nSo, the distance between Traverse City and Marquette is 150 miles<\/p>\n<p>Question 2.<br \/>\nA drawing has a scale of 1 mm : 20 cm. What is the scale factor of the drawing?<\/p>\n<p>Answer:<br \/>\nThe scale factor is 1\/200<\/p>\n<p>Explanation:<br \/>\nWrite the scale with the same units. Use the factor 1 cm = 10 mm<br \/>\n1 mm : 20 cm = 1 mm : (20 \u2022 10) mm<br \/>\n= 1 : 200<br \/>\nSo, the scale factor is 1\/200<\/p>\n<p><strong>Self-Assessment for Concepts &amp; Skills<\/strong><br \/>\nSolve each exercise. Then rate your understanding of the success criteria in your journal.<\/p>\n<p>Question 3.<br \/>\n<strong>VOCABULARY<\/strong><br \/>\nIn your own words, explain the meaning of the scale and scale factor of a drawing or model.<\/p>\n<p>Answer:<br \/>\nA scale factor is a number that multiplies times a given quantity to produce a smaller or longer version of the original number. It is also defined as the ratio of a drawing or blueprint to the actual object or distance.<br \/>\nThe measurements in scale drawings are proportional to the measurements of the actual object. The scale is the ratio that compares the measurements of the drawings with the actual measurements.<\/p>\n<p>Question 4.<br \/>\n<strong>FINDING AN ACTUAL DISTANCE<\/strong><br \/>\nConsider the scale drawing of Balanced Rock in Arches National Park. What is the actual height of the structure?<br \/>\n<img loading=\"lazy\" class=\"alignnone size-full wp-image-30459\" src=\"https:\/\/ccssmathanswers.com\/wp-content\/uploads\/2021\/01\/Big-Ideas-Math-Answers-7th-Grade-Chapter-5-Ratios-and-Proportions-5.6-3.png\" alt=\"Big Ideas Math Answers 7th Grade Chapter 5 Ratios and Proportions 5.6 3\" width=\"132\" height=\"219\" \/><\/p>\n<p>Answer:<br \/>\nh = 1\/975.36<\/p>\n<p>Explanation:<br \/>\nscale drawing is 1 cm : 32 ft<br \/>\n1 foot = 30.48 cm<br \/>\nSo, 32 ft = 975.36 cm<br \/>\n1 cm : 32 ft = 1 : 975.36<br \/>\nh = 1\/975.36<\/p>\n<p>Question 5.<br \/>\n<strong>FINDING A SCALE FACTOR<\/strong><br \/>\nA drawing has a scale of 3 in. : 2 ft. What is the scale factor of the drawing?<\/p>\n<p>Answer:<br \/>\nThe scale factor is 1\/8<\/p>\n<p>Explanation:<br \/>\n3 in. : 2 ft<br \/>\n1 foot = 12 inches<br \/>\n2 ft = 24 inches<br \/>\nThe scale is 3 : 24 inches = 1\/8<\/p>\n<p>Question 6.<br \/>\n<strong>REASONING<\/strong><br \/>\nDescribe the scale factor of a model that is (a) larger than the actual object and (b) smaller than the actual object.<\/p>\n<p>Answer:<br \/>\nIf the scale of the factor is larger than the actual object, then every point is considered larger in the image. It means we represent a lion in a smaller box.<br \/>\nIf the scale of the factor is less than the actual object, it means we represent the pen as a larger box.<\/p>\n<p><strong>Self-Assessment for Problem Solving<\/strong><br \/>\nSolve each exercise. Then rate your understanding of the success criteria in your journal.<\/p>\n<p>Question 7.<br \/>\nA scale drawing of the Parthenon is shown. Find the actual perimeter and area of the rectangular face of the Parthenon. Then recreate the scale drawing with a scale factor of 0.2. Find the perimeter and area of the rectangular face in your drawing.<br \/>\n<img loading=\"lazy\" class=\"alignnone size-full wp-image-30460\" src=\"https:\/\/ccssmathanswers.com\/wp-content\/uploads\/2021\/01\/Big-Ideas-Math-Answers-7th-Grade-Chapter-5-Ratios-and-Proportions-5.6-4.png\" alt=\"Big Ideas Math Answers 7th Grade Chapter 5 Ratios and Proportions 5.6 4\" width=\"231\" height=\"179\" \/><\/p>\n<p>Answer:<br \/>\nThe actual perimeter of the rectangular face of the Parthenon is 26 ft<br \/>\nThe actual area of the rectangular face of the Parthenon is 36 sq ft<br \/>\nthe perimeter of the rectangular face in your drawing is 5.2 ft<br \/>\narea of the rectangular face in your drawing is 1.44 sq ft.<\/p>\n<p>Explanation:<br \/>\nPerimeter of the rectangular face of the Parthenon = 2(l + b)<br \/>\n= 2(4 + 9) = 13 * 2<br \/>\n= 26 ft<br \/>\nArea of the rectangular face of the Parthenon = l * b<br \/>\n= 4 * 9<br \/>\n= 36 sq ft<br \/>\nScale factor = 0.2<br \/>\nThe length of the rectangular face in your drawing = 0.2 * 9<br \/>\n= 1.8<br \/>\nThe breadth of the rectangular face in your drawing = 4 * 0.2<br \/>\n= 0.8<br \/>\nPerimeter is 2(1.8 + 0.8) = 5.2<br \/>\nArea is 0.8 * 1.8 = 1.44<\/p>\n<p>Question 8.<br \/>\n<strong>DIG DEEPER!<\/strong><br \/>\nYou are in charge of creating a billboard advertisement that is 16 feet long and 8 feet tall. Choose a product. Create a scale drawing of the billboard using words and a picture. What is the scale factor of your design?<\/p>\n<p>Answer:<br \/>\nThe scale factor is 2<\/p>\n<p>Explanation:<br \/>\nThe details of the billboard advertisement is 16 : 8<br \/>\n= 2 : 1<br \/>\n1 unit is 4 units on the scale<br \/>\nSo, the billboard advertisement is 16 * 4 : 8 * 4<br \/>\n= 64 : 32<br \/>\n= 2 : 1<br \/>\nSo, the scale factor is 2<\/p>\n<h3><a id=\"Scale_Drawings_Homework_&amp;_Practice_5.6\"><\/a>Scale Drawings Homework &amp; Practice 5.6<\/h3>\n<p><strong>Review &amp; Refresh<\/strong><\/p>\n<p><strong>Tell whether x and y are proportional. Explain your reasoning.<\/strong><br \/>\nQuestion 1.<br \/>\n<img loading=\"lazy\" class=\"alignnone size-full wp-image-30461\" src=\"https:\/\/ccssmathanswers.com\/wp-content\/uploads\/2021\/01\/Big-Ideas-Math-Answers-7th-Grade-Chapter-5-Ratios-and-Proportions-5.6-5.png\" alt=\"Big Ideas Math Answers 7th Grade Chapter 5 Ratios and Proportions 5.6 5\" width=\"186\" height=\"59\" \/><\/p>\n<p>Answer:<br \/>\nx and y are not proportional<\/p>\n<p>Explanation:<br \/>\nCompare the values of ratios x to y<br \/>\n10\/5 = 2<br \/>\n9\/4 = 2.25<br \/>\n8\/3 = 2.6666<br \/>\n7\/2 = 3.5<br \/>\nThe ratios are not equivalent<br \/>\nSo, x and y are not proportional<\/p>\n<p>Question 2.<br \/>\n<img loading=\"lazy\" class=\"alignnone size-full wp-image-30462\" src=\"https:\/\/ccssmathanswers.com\/wp-content\/uploads\/2021\/01\/Big-Ideas-Math-Answers-7th-Grade-Chapter-5-Ratios-and-Proportions-5.6-6.png\" alt=\"Big Ideas Math Answers 7th Grade Chapter 5 Ratios and Proportions 5.6 6\" width=\"180\" height=\"65\" \/><\/p>\n<p>Answer:<br \/>\nx and y are proportional<\/p>\n<p>Explanation:<br \/>\nCompare the values of ratios x to y<br \/>\n6\/7<br \/>\n12\/14 = 6\/7<br \/>\n18\/21 = 6\/7<br \/>\n24\/28 = 6\/7<br \/>\nThe ratios are equivalent<br \/>\nSo, x and y are proportional<\/p>\n<p><strong>Simplify the expression.<\/strong><br \/>\nQuestion 3.<br \/>\n7p + 6p<\/p>\n<p>Answer:<br \/>\n7p + 6p = 13p<\/p>\n<p>Explanation:<br \/>\nThe given expression is 7p + 6p<br \/>\n= 13p<\/p>\n<p>Question 4.<br \/>\n8 + 3d &#8211; 17<\/p>\n<p>Answer:<br \/>\n8 + 3d &#8211; 17 = 3d &#8211; 9<\/p>\n<p>Explanation:<br \/>\nThe given expression is 8 + 3d &#8211; 17<br \/>\n= 3d &#8211; 9<\/p>\n<p>Question 5.<br \/>\n&#8211; 2 + \\(\\frac{2}{5}\\)b &#8211; \\(\\frac{1}{4}\\)b + 6<\/p>\n<p>Answer:<br \/>\n&#8211; 2 + \\(\\frac{2}{5}\\)b &#8211; \\(\\frac{1}{4}\\)b + 6 = 4 + 3b\/20<\/p>\n<p>Explanation:<br \/>\nThe given expression is &#8211; 2 + \\(\\frac{2}{5}\\)b &#8211; \\(\\frac{1}{4}\\)b + 6<br \/>\n= 4 + (8b &#8211; 5b)\/20<br \/>\n= 4 + 3b\/20<\/p>\n<p><strong>Write the word sentence as an inequality.<\/strong><br \/>\nQuestion 6.<br \/>\nA number is less than &#8211; 3.<\/p>\n<p>Answer:<br \/>\nn &lt; -3<\/p>\n<p>Explanation:<br \/>\nLet us the number as n<br \/>\nn &lt; -3<\/p>\n<p>Question 7.<br \/>\n7 plus a number z is more than 5.<\/p>\n<p>Answer:<br \/>\n7 + z &gt; 5, z &gt; -2<\/p>\n<p>Explanation:<br \/>\nmore than means &gt; symbol<br \/>\n7 + z &gt; 5<br \/>\nz &gt; 5 &#8211; 7<br \/>\nz &gt; -2<\/p>\n<p>Question 8.<br \/>\nThe product of a number m and 6 is no less than 30.<\/p>\n<p>Answer:<br \/>\n6m &gt; 30<\/p>\n<p>Explanation:<br \/>\nNo less than means &gt;<br \/>\nm . 6 &gt; 30<br \/>\n6m &gt; 30<br \/>\nDivide both sides by 6<br \/>\n6m\/6 &gt; 30\/6<br \/>\nm &gt; 30\/6<\/p>\n<p><strong>Concepts, Skills, &amp; Problem Solving<\/strong><\/p>\n<p><strong>CREATING A SCALE DRAWING<\/strong> Each centimeter on the 1-centimeter grid paper represents 8 inches. Create a proportional drawing of the figure that is larger or smaller than the figure shown. (See Exploration 1, p. 217.)<br \/>\nQuestion 9.<br \/>\n<img loading=\"lazy\" class=\"alignnone size-full wp-image-30463\" src=\"https:\/\/ccssmathanswers.com\/wp-content\/uploads\/2021\/01\/Big-Ideas-Math-Answers-7th-Grade-Chapter-5-Ratios-and-Proportions-5.6-7.png\" alt=\"Big Ideas Math Answers 7th Grade Chapter 5 Ratios and Proportions 5.6 7\" width=\"202\" height=\"128\" \/><\/p>\n<p>Answer:<br \/>\nThe base of the traingle is 16 inches<\/p>\n<p>Explanation:<br \/>\n1 cm = 8 inches<br \/>\nThe base of triangle = 2 cm<br \/>\n= 2 * 8 = 16 inches<br \/>\nActually, 1 cm = 0.393701 inches<br \/>\nThe size of drawing\/real size = 1\/8<br \/>\n2\/real size = 1\/8<br \/>\n16 = real size<\/p>\n<p>Question 10.<br \/>\n<img loading=\"lazy\" class=\"alignnone size-full wp-image-30464\" src=\"https:\/\/ccssmathanswers.com\/wp-content\/uploads\/2021\/01\/Big-Ideas-Math-Answers-7th-Grade-Chapter-5-Ratios-and-Proportions-5.6-8.png\" alt=\"Big Ideas Math Answers 7th Grade Chapter 5 Ratios and Proportions 5.6 8\" width=\"201\" height=\"133\" \/><\/p>\n<p>Answer:<br \/>\nThe bottom surface is 24 inches, the height is 24 inches, the top surface is 8 inches.<\/p>\n<p>Explanation:<br \/>\n1 cm = 8 inches<br \/>\nBottom surface is 3 cm<br \/>\n= 3 * 8 = 24 inches<br \/>\nHeight is 3 cm<br \/>\n= 3 * 8 = 24 inches<br \/>\nTop surface = 1 cm<br \/>\n= 1 * 8 = 8 inches<\/p>\n<p><strong>FINDING AN ACTUAL DISTANCE<\/strong> Use the map in Example 1 to find the actual distance between the cities.<br \/>\nQuestion 11.<br \/>\nKalamazoo and Ann Arbor<\/p>\n<p>Answer:<br \/>\nThe distance between Kalamazoo and Ann Arbor is 100 miles.<\/p>\n<p>Explanation:<br \/>\nUse the centimeter ruler to find the distance on the map between Kalamazoo and Ann Arbor<br \/>\nThe map distance is about 2 cm<br \/>\nUse the scale 1 cm : 50 mi and the ratio 2 cm : d mi to write and solve a proportion<br \/>\n1\/50 = 2\/d<br \/>\nd = 50 * 2<br \/>\nd = 100<br \/>\nSo, the distance between Kalamazoo and Ann Arbor is 100 miles.<\/p>\n<p>Question 12.<br \/>\nLansing and Flint<\/p>\n<p>Answer:<br \/>\nThe distance between Lansing and Flint is 50 miles.<\/p>\n<p>Explanation:<br \/>\nUse the centimeter ruler to find the distance on the map between Lansing and Flint<br \/>\nThe map distance is about 1 cm<br \/>\nUse the scale 1 cm : 50 mi and the ratio 1 cm : d mi to write and solve a proportion<br \/>\n1\/50 = 1\/d<br \/>\nd = 50 * 1<br \/>\nd = 50<br \/>\nSo, the distance between Lansing and Flint is 50 miles.<\/p>\n<p>Question 13.<br \/>\nGrand Rapids and Escanaba<\/p>\n<p>Answer:<br \/>\nThe distance between Grand Rapids and Escanaba is 200 miles.<\/p>\n<p>Explanation:<br \/>\nUse the centimeter ruler to find the distance on the map between Grand Rapids and Escanaba<br \/>\nThe map distance is about 4 cm<br \/>\nUse the scale 1 cm : 50 mi and the ratio 4 cm : d mi to write and solve a proportion<br \/>\n1\/50 = 1\/d<br \/>\nd = 50 * 4<br \/>\nd = 200<br \/>\nSo, the distance between Grand Rapids and Escanaba is 200 miles.<\/p>\n<p>Question 14.<br \/>\nSaginaw and Alpena<\/p>\n<p>Answer:<br \/>\nThe distance between Saginaw and Alpena is 150 miles.<\/p>\n<p>Explanation:<br \/>\nUse the centimeter ruler to find the distance on the map between Saginaw and Alpena<br \/>\nThe map distance is about 3 cm<br \/>\nUse the scale 1 cm : 50 mi and the ratio 4 cm : d mi to write and solve a proportion<br \/>\n1\/50 = 1\/d<br \/>\nd = 50 * 3<br \/>\nd = 150<br \/>\nSo, the distance between Saginaw and Alpena is 150 miles.<\/p>\n<p><strong>USING A SCALE<\/strong> Find the missing dimension. Use the scale 1 : 12.<br \/>\n<img loading=\"lazy\" class=\"alignnone size-full wp-image-30465\" src=\"https:\/\/ccssmathanswers.com\/wp-content\/uploads\/2021\/01\/Big-Ideas-Math-Answers-7th-Grade-Chapter-5-Ratios-and-Proportions-5.6-9.png\" alt=\"Big Ideas Math Answers 7th Grade Chapter 5 Ratios and Proportions 5.6 9\" width=\"497\" height=\"179\" srcset=\"https:\/\/bigideasmathanswers.com\/wp-content\/uploads\/2021\/01\/Big-Ideas-Math-Answers-7th-Grade-Chapter-5-Ratios-and-Proportions-5.6-9.png 497w, https:\/\/bigideasmathanswers.com\/wp-content\/uploads\/2021\/01\/Big-Ideas-Math-Answers-7th-Grade-Chapter-5-Ratios-and-Proportions-5.6-9-300x108.png 300w\" sizes=\"(max-width: 497px) 100vw, 497px\" \/><\/p>\n<p>Answer:<br \/>\n<img loading=\"lazy\" class=\"alignnone size-full wp-image-49107\" src=\"https:\/\/ccssmathanswers.com\/wp-content\/uploads\/2021\/01\/big-ideas-math-answer-key-grade-7-chapter-5-ratios-and-proportions-5.6-1.jpg\" alt=\"Big Ideas Math Answer Key Grade 7 Chapter 5 Ratios and Proportions 5.6 1\" width=\"678\" height=\"248\" srcset=\"https:\/\/bigideasmathanswers.com\/wp-content\/uploads\/2021\/01\/big-ideas-math-answer-key-grade-7-chapter-5-ratios-and-proportions-5.6-1.jpg 678w, https:\/\/bigideasmathanswers.com\/wp-content\/uploads\/2021\/01\/big-ideas-math-answer-key-grade-7-chapter-5-ratios-and-proportions-5.6-1-300x110.jpg 300w\" sizes=\"(max-width: 678px) 100vw, 678px\" \/><\/p>\n<p>Explanation:<br \/>\n15. 1 inch = 12 inches<br \/>\nSo, 6.25 x 12 = 75 inches<br \/>\n16. 1 ft = 12 inches<br \/>\nx in = 15 * 12<br \/>\nx in = 180 inches<br \/>\n17. 1 m = 100 cm<br \/>\n32 cm = 0.32 m<br \/>\n32 * 1 = .32 * 12<br \/>\n= 3.84 m<br \/>\n18. 1 ft = 0.333333 yard<br \/>\n5.4 ft = 5.4 * 0.333333<br \/>\n= 1.8 yard * 12 = 21.6 yard<br \/>\n19. 1 cm = 10 mm<br \/>\n21 cm = 210 mm<br \/>\n210 * 12 = 2520 mm<\/p>\n<p><strong>FINDING A SCALE FACTOR<\/strong> Use a centimeter ruler to find the scale and the scale factor of the drawing.<br \/>\nQuestion 20.<br \/>\n<img loading=\"lazy\" class=\"alignnone size-full wp-image-30466\" src=\"https:\/\/ccssmathanswers.com\/wp-content\/uploads\/2021\/01\/Big-Ideas-Math-Answers-7th-Grade-Chapter-5-Ratios-and-Proportions-5.6-10.png\" alt=\"Big Ideas Math Answers 7th Grade Chapter 5 Ratios and Proportions 5.6 10\" width=\"197\" height=\"148\" \/><\/p>\n<p>Answer:<br \/>\n1 cm = 30 m<\/p>\n<p>Explanation:<br \/>\nUsing the centimeter ruler, the length is 4 cm<br \/>\nSo, 4 cm = 120 m<br \/>\n1 cm = 120\/4<br \/>\n1 cm = 30 m<\/p>\n<p>Question 21.<br \/>\n<img loading=\"lazy\" class=\"alignnone size-full wp-image-30467\" src=\"https:\/\/ccssmathanswers.com\/wp-content\/uploads\/2021\/01\/Big-Ideas-Math-Answers-7th-Grade-Chapter-5-Ratios-and-Proportions-5.6-11.png\" alt=\"Big Ideas Math Answers 7th Grade Chapter 5 Ratios and Proportions 5.6 11\" width=\"195\" height=\"141\" \/><\/p>\n<p>Answer:<br \/>\n1 cm = 8 mm<\/p>\n<p>Explanation:<br \/>\nUsing the centimeter ruler, the length is 3 cm<br \/>\nSo, 3 cm = 24 mm<br \/>\n1 cm = 24\/3<br \/>\n= 8 mm<\/p>\n<p>Question 22.<br \/>\n<strong>CRITICAL THINKING<\/strong><br \/>\nYou know the length and the width of a scale model. What additional information do you need to know to find the scale of the model? Explain.<\/p>\n<p>Answer:<br \/>\nYou need to know the scale factor to know the scale of the model.<\/p>\n<p>Question 23.<br \/>\n<strong>MODELING REAL LIFE<\/strong><br \/>\nCentral Park is a rectangular park in New YorkCity.<br \/>\n<img loading=\"lazy\" class=\"alignnone size-full wp-image-30468\" src=\"https:\/\/ccssmathanswers.com\/wp-content\/uploads\/2021\/01\/Big-Ideas-Math-Answers-7th-Grade-Chapter-5-Ratios-and-Proportions-5.6-12.png\" alt=\"Big Ideas Math Answers 7th Grade Chapter 5 Ratios and Proportions 5.6 12\" width=\"531\" height=\"140\" srcset=\"https:\/\/bigideasmathanswers.com\/wp-content\/uploads\/2021\/01\/Big-Ideas-Math-Answers-7th-Grade-Chapter-5-Ratios-and-Proportions-5.6-12.png 531w, https:\/\/bigideasmathanswers.com\/wp-content\/uploads\/2021\/01\/Big-Ideas-Math-Answers-7th-Grade-Chapter-5-Ratios-and-Proportions-5.6-12-300x79.png 300w\" sizes=\"(max-width: 531px) 100vw, 531px\" \/><br \/>\na. Find the perimeter and the area of the scale drawing of Central Park.<br \/>\nb. Find the actual perimeter and area of Central Park.<\/p>\n<p>Answer:<br \/>\na. The perimeter of the scale drawing of Central Park = 26 cm<br \/>\nThe area of the scale drawing of Central Park = 30 sq cm<br \/>\nb. The perimeter of the scale drawing of Central Park = 8320 cm<br \/>\nThe area of the scale drawing of Central Park = 3072000 sq cm<\/p>\n<p>Explanation:<br \/>\na. The length of the central park is 10 cm<br \/>\nThe breadth of the central park is 3 cm<br \/>\nThe perimeter of the scale drawing of Central Park = 2(10 + 3)<br \/>\n= 2(13)<br \/>\n= 26 cm<br \/>\nThe area of the scale drawing of Central Park = 10 * 3<br \/>\n= 30 sq cm<br \/>\nb. 1 cm = 320 m<br \/>\nThe length of the central park is 10 * 320 = 3200<br \/>\nThe breadth of the central park is 3 * 320 = 960<br \/>\nThe perimeter of the scale drawing of Central Park = 2(3200 + 960)<br \/>\n= 8320 cm<br \/>\nThe area of the scale drawing of Central Park = 3200 * 960<br \/>\n= 3072000 sq cm<\/p>\n<p>Question 24.<br \/>\n<strong>PROBLEM SOLVING<\/strong><br \/>\nIn a blueprint,each square has a side length of \\(\\frac{1}{4}\\) inch.<br \/>\n<img loading=\"lazy\" class=\"alignnone size-full wp-image-30469\" src=\"https:\/\/ccssmathanswers.com\/wp-content\/uploads\/2021\/01\/Big-Ideas-Math-Answers-7th-Grade-Chapter-5-Ratios-and-Proportions-5.6-13.png\" alt=\"Big Ideas Math Answers 7th Grade Chapter 5 Ratios and Proportions 5.6 13\" width=\"185\" height=\"201\" \/><br \/>\na. Ceramic tile costs $5 per square foot. How much does it cost to tile the bathroom?<br \/>\nb. Carpet costs $18 per square yard. How much does it cost to carpet the bedroom and living room?<\/p>\n<p>Answer:<br \/>\na. The cost to the bathroom = $0.06075<br \/>\nb. The cost to carpet the bedroom and living room = $0.02430<\/p>\n<p>Explanation:<br \/>\nSquare side length = 1\/4 inch<br \/>\n1 feet = 12 inch<br \/>\n1 inch : 16 ft = 1 : 16 * 12 = 1 : 192<br \/>\na. one square side length is 1\/4<br \/>\n1 foot = 12 inch<br \/>\nSo, the length of the bathroom = 4(1\/4) = 1 = 1 * 0.0833333<br \/>\n= 0.0833333<br \/>\nThe breadth of the bathroom = 7(1\/4) = 7\/4<br \/>\n= (7 * 0.0833333)\/4<br \/>\n= 0.583333\/4<br \/>\n= 0.14583325<br \/>\nThe area of bathroom = 0.0833333 * 0.14583325<br \/>\n= 0.01215 sq in<br \/>\nCeramic tile costs $5 per square foot<br \/>\nThe cost to the bathroom = 0.01215 * 5 = $0.06075<br \/>\nb. 1 inch = 0.0277778 yard<br \/>\nlength of bathroom + living room = 1 * 0.0277778 = 0.0277778<br \/>\nbreadth of bathroom + living room = 7\/4 (0.0277778)<br \/>\n= 0.04861115<br \/>\nThe area of bathroom + living room = 0.0277778 * 0.04861115<br \/>\n= 0.00135031080247<br \/>\nCarpet costs $18 per square yard.<br \/>\nThe cost to carpet the bedroom and living room = 0.00135031080247 * 18 = $0.02430<\/p>\n<p><strong>REPRODUCING A SCALE DRAWING<\/strong> Recreate the scale drawing so that it has a scale of 1 cm : 4 m.<br \/>\nQuestion 25.<br \/>\n<img loading=\"lazy\" class=\"alignnone size-full wp-image-30470\" src=\"https:\/\/ccssmathanswers.com\/wp-content\/uploads\/2021\/01\/Big-Ideas-Math-Answers-7th-Grade-Chapter-5-Ratios-and-Proportions-5.6-14.png\" alt=\"Big Ideas Math Answers 7th Grade Chapter 5 Ratios and Proportions 5.6 14\" width=\"199\" height=\"127\" \/><\/p>\n<p>Answer:<br \/>\n<img loading=\"lazy\" class=\"alignnone size-full wp-image-49318\" src=\"https:\/\/ccssmathanswers.com\/wp-content\/uploads\/2021\/01\/big-ideas-math-answer-key-grade-7-chapter-5-ratios-and-proportions-5.6-2.jpg\" alt=\"Big Ideas Math Answer Key Grade 7 Chapter 5 Ratios and Proportions 5.6 2\" width=\"413\" height=\"507\" srcset=\"https:\/\/bigideasmathanswers.com\/wp-content\/uploads\/2021\/01\/big-ideas-math-answer-key-grade-7-chapter-5-ratios-and-proportions-5.6-2.jpg 413w, https:\/\/bigideasmathanswers.com\/wp-content\/uploads\/2021\/01\/big-ideas-math-answer-key-grade-7-chapter-5-ratios-and-proportions-5.6-2-244x300.jpg 244w\" sizes=\"(max-width: 413px) 100vw, 413px\" \/><\/p>\n<p>Explanation:<br \/>\n1 m = 100 cm<br \/>\nActual length = 1 cm * (1 cm \/ 400 cm)<br \/>\n= 1\/400 cm<br \/>\nActual breadth = 8 m * (1 cm \/ 4 m)<br \/>\n= 2 cm<\/p>\n<p>Question 26.<br \/>\n<img loading=\"lazy\" class=\"alignnone wp-image-30471\" src=\"https:\/\/ccssmathanswers.com\/wp-content\/uploads\/2021\/01\/Big-Ideas-Math-Answers-7th-Grade-Chapter-5-Ratios-and-Proportions-5.6-15.png\" alt=\"Big Ideas Math Answers 7th Grade Chapter 5 Ratios and Proportions 5.6 15\" width=\"172\" height=\"109\" \/><\/p>\n<p>Answer:<br \/>\n<img loading=\"lazy\" class=\"alignnone size-full wp-image-49321\" src=\"https:\/\/ccssmathanswers.com\/wp-content\/uploads\/2021\/01\/big-ideas-math-answer-key-grade-7-chapter-5-ratios-and-proportions-5.6-3.jpg\" alt=\"Big Ideas Math Answer Key Grade 7 Chapter 5 Ratios and Proportions 5.6 3\" width=\"168\" height=\"184\" \/><\/p>\n<p>Explanation:<br \/>\n1 cm = 100 m<br \/>\nActual length = 1 cm * (1 cm \/ 400 cm)<br \/>\n= 1\/400 cm<br \/>\nActual breadth = 2 m * ( 1 cm \/ 4 m)<br \/>\n= 1\/2 cm<\/p>\n<p>Question 27.<br \/>\n<strong>DIG DEEPER!<\/strong><br \/>\nMake a conjecture about the relationship between the scale factor of a drawing and the quotients <img loading=\"lazy\" class=\"alignnone size-full wp-image-30472\" src=\"https:\/\/ccssmathanswers.com\/wp-content\/uploads\/2021\/01\/Big-Ideas-Math-Answers-7th-Grade-Chapter-5-Ratios-and-Proportions-5.6-16.png\" alt=\"Big Ideas Math Answers 7th Grade Chapter 5 Ratios and Proportions 5.6 16\" width=\"206\" height=\"43\" \/>. Explain your reasoning.<\/p>\n<p>Answer:<br \/>\ndrawing perimeter\/ actual perimeter = scale factor<br \/>\ndrawing area\/actual area = scale factor<\/p>\n<h3><a id=\"Ratios_and_Proportions_Connecting_Concepts\"><\/a>Ratios and Proportions Connecting Concepts<\/h3>\n<p><strong>Using the Problem-Solving Plan<\/strong><br \/>\nQuestion 1.<br \/>\nThe table shows the toll y(in dollars) for traveling x miles on a turnpike. You have $8.25 to pay your toll. How far can you travel on the turnpike?<br \/>\n<img loading=\"lazy\" class=\"alignnone size-full wp-image-30473\" src=\"https:\/\/ccssmathanswers.com\/wp-content\/uploads\/2021\/01\/Big-Ideas-Math-Answers-Grade-7-Chapter-5-Ratios-and-Proportions-cc-1.png\" alt=\"Big Ideas Math Answers Grade 7 Chapter 5 Ratios and Proportions cc 1\" width=\"576\" height=\"190\" srcset=\"https:\/\/bigideasmathanswers.com\/wp-content\/uploads\/2021\/01\/Big-Ideas-Math-Answers-Grade-7-Chapter-5-Ratios-and-Proportions-cc-1.png 576w, https:\/\/bigideasmathanswers.com\/wp-content\/uploads\/2021\/01\/Big-Ideas-Math-Answers-Grade-7-Chapter-5-Ratios-and-Proportions-cc-1-300x99.png 300w\" sizes=\"(max-width: 576px) 100vw, 576px\" \/><br \/>\nUnderstand the problem.<br \/>\nThe table shows the tolls for traveling several different distances on a turnpike. You have $8.25 to pay the toll. You are asked to find how far you can travel on the turnpike with $8.25 for tolls.<\/p>\n<p>Make a plan.<br \/>\nFirst, determine the relationship between x and y and write an equation to represent the relationship. Then use the equation to determine the distance you can travel.<\/p>\n<p>Solve and check.<br \/>\nUse the plan to solve the problem. Then check your solution.<\/p>\n<p>Answer:<br \/>\nYou can travel 55 miles with $8.25 for tolls.<\/p>\n<p>Explanation:<br \/>\nx : y = 40 : 6<br \/>\n= 40\/6 : 1<br \/>\n= 20\/3 : 1<br \/>\nYou need to pay $1 for 20\/3 miles<br \/>\nSo, 20\/3 : 1 = x : 8.25<br \/>\n8.25 (20\/3) = x<br \/>\n55 = x<br \/>\nSo, you can travel 55 miles with $8.25 for tolls.<\/p>\n<p>Question 2.<br \/>\nA company uses a silo in the shape of a rectangular prism to store bird seed. The base of the silo is a square with side lengths of 20 feet. Are the height and the volume of the silo proportional? Justify your answer.<\/p>\n<p>Answer:<br \/>\nThe height and the volume of the silo proportional<\/p>\n<p>Explanation:<br \/>\nThe base of the silo is a square with side lengths of 20 feet.<br \/>\nThe area of silo = side\u00b2 = 20\u00b2<br \/>\n= 400 sq ft<br \/>\nHeight = h<br \/>\nVolume = lwh<br \/>\n= 400h<br \/>\nh : 400h = 1 : 400<br \/>\nThe height and the volume of the silo proportional<\/p>\n<p>Question 3.<br \/>\nA rectangle is drawn in a coordinate plane as shown. In the same coordinate plane, create a scale drawing of the rectangle that has a vertex at (0, 0) and a scale factor of 3.<br \/>\n<img loading=\"lazy\" class=\"alignnone size-full wp-image-30474\" src=\"https:\/\/ccssmathanswers.com\/wp-content\/uploads\/2021\/01\/Big-Ideas-Math-Answers-Grade-7-Chapter-5-Ratios-and-Proportions-cc-2.png\" alt=\"Big Ideas Math Answers Grade 7 Chapter 5 Ratios and Proportions cc 2\" width=\"148\" height=\"135\" \/><\/p>\n<p>Answer:<br \/>\nThe length of rectangle = 2\/3<br \/>\nBreadth = 1\/3<\/p>\n<p>Explanation:<br \/>\nThe length of rectangle = 2 units<br \/>\nThe breadth of rectangle = 1 unit<br \/>\nlength : breadth = 2 : 1<br \/>\nlength = 2breadth<br \/>\nThe scale factor = 3<br \/>\nThe length of rectangle = 2\/3<br \/>\nBreadth = 1\/3<\/p>\n<p><strong>Performance Task<\/strong><\/p>\n<p>Mixing Paint<br \/>\nAt the beginning of this chapter, you watched a STEAM Video called \u201cPainting a Large Room.\u201d You are now ready to complete the performance task related to this video, available at BigIdeasMath.com. Be sure to use the problem-solving plan as you work through the performance task.<br \/>\n<img loading=\"lazy\" class=\"alignnone size-full wp-image-30475\" src=\"https:\/\/ccssmathanswers.com\/wp-content\/uploads\/2021\/01\/Big-Ideas-Math-Answers-Grade-7-Chapter-5-Ratios-and-Proportions-cc-3.png\" alt=\"Big Ideas Math Answers Grade 7 Chapter 5 Ratios and Proportions cc 3\" width=\"351\" height=\"176\" srcset=\"https:\/\/bigideasmathanswers.com\/wp-content\/uploads\/2021\/01\/Big-Ideas-Math-Answers-Grade-7-Chapter-5-Ratios-and-Proportions-cc-3.png 351w, https:\/\/bigideasmathanswers.com\/wp-content\/uploads\/2021\/01\/Big-Ideas-Math-Answers-Grade-7-Chapter-5-Ratios-and-Proportions-cc-3-300x150.png 300w\" sizes=\"(max-width: 351px) 100vw, 351px\" \/><\/p>\n<h3><a id=\"Ratios_and_Proportions_Chapter_Review\"><\/a>Ratios and Proportions Chapter Review<\/h3>\n<p><strong>Review Vocabulary<\/strong><\/p>\n<p>Write the definition and give an example of each vocabulary term.<br \/>\n<img loading=\"lazy\" class=\"alignnone size-full wp-image-30476\" src=\"https:\/\/ccssmathanswers.com\/wp-content\/uploads\/2021\/01\/Big-Ideas-Math-Answers-Grade-7-Chapter-5-Ratios-and-Proportions-cr-1.png\" alt=\"Big Ideas Math Answers Grade 7 Chapter 5 Ratios and Proportions cr 1\" width=\"540\" height=\"117\" srcset=\"https:\/\/bigideasmathanswers.com\/wp-content\/uploads\/2021\/01\/Big-Ideas-Math-Answers-Grade-7-Chapter-5-Ratios-and-Proportions-cr-1.png 540w, https:\/\/bigideasmathanswers.com\/wp-content\/uploads\/2021\/01\/Big-Ideas-Math-Answers-Grade-7-Chapter-5-Ratios-and-Proportions-cr-1-300x65.png 300w\" sizes=\"(max-width: 540px) 100vw, 540px\" \/><\/p>\n<p><strong>Graphic Organizers<\/strong><\/p>\n<p>You can use an Example and Non-Example Chart to list examples and non-examples of a concept. Here is an Example and Non-Example Chart for scale factor.<br \/>\n<img loading=\"lazy\" class=\"alignnone size-full wp-image-30477\" src=\"https:\/\/ccssmathanswers.com\/wp-content\/uploads\/2021\/01\/Big-Ideas-Math-Answers-Grade-7-Chapter-5-Ratios-and-Proportions-cr-2.png\" alt=\"Big Ideas Math Answers Grade 7 Chapter 5 Ratios and Proportions cr 2\" width=\"378\" height=\"210\" srcset=\"https:\/\/bigideasmathanswers.com\/wp-content\/uploads\/2021\/01\/Big-Ideas-Math-Answers-Grade-7-Chapter-5-Ratios-and-Proportions-cr-2.png 378w, https:\/\/bigideasmathanswers.com\/wp-content\/uploads\/2021\/01\/Big-Ideas-Math-Answers-Grade-7-Chapter-5-Ratios-and-Proportions-cr-2-300x167.png 300w\" sizes=\"(max-width: 378px) 100vw, 378px\" \/><\/p>\n<p>Choose and complete a graphic organizer to help you study the concept.<br \/>\n<img loading=\"lazy\" class=\"alignnone size-full wp-image-30478\" src=\"https:\/\/ccssmathanswers.com\/wp-content\/uploads\/2021\/01\/Big-Ideas-Math-Answers-Grade-7-Chapter-5-Ratios-and-Proportions-cr-3.png\" alt=\"Big Ideas Math Answers Grade 7 Chapter 5 Ratios and Proportions cr 3\" width=\"304\" height=\"305\" srcset=\"https:\/\/bigideasmathanswers.com\/wp-content\/uploads\/2021\/01\/Big-Ideas-Math-Answers-Grade-7-Chapter-5-Ratios-and-Proportions-cr-3.png 304w, https:\/\/bigideasmathanswers.com\/wp-content\/uploads\/2021\/01\/Big-Ideas-Math-Answers-Grade-7-Chapter-5-Ratios-and-Proportions-cr-3-300x300.png 300w, https:\/\/bigideasmathanswers.com\/wp-content\/uploads\/2021\/01\/Big-Ideas-Math-Answers-Grade-7-Chapter-5-Ratios-and-Proportions-cr-3-150x150.png 150w\" sizes=\"(max-width: 304px) 100vw, 304px\" \/><br \/>\n1. ratio<br \/>\n2. equivalent ratios<br \/>\n3. rate<br \/>\n4. unit rate<br \/>\n5. equivalent rates<br \/>\n6. proportion<br \/>\n7. cross products<br \/>\n8. proportional<br \/>\n9. scale<\/p>\n<p><strong>Chapter Self-Assessment<\/strong><\/p>\n<p>As you complete the exercises, use the scale below to rate your understanding of the success criteria in your journal.<br \/>\n<img loading=\"lazy\" class=\"alignnone size-full wp-image-30479\" src=\"https:\/\/ccssmathanswers.com\/wp-content\/uploads\/2021\/01\/Big-Ideas-Math-Answers-Grade-7-Chapter-5-Ratios-and-Proportions-cr-4.png\" alt=\"Big Ideas Math Answers Grade 7 Chapter 5 Ratios and Proportions cr 4\" width=\"600\" height=\"72\" srcset=\"https:\/\/bigideasmathanswers.com\/wp-content\/uploads\/2021\/01\/Big-Ideas-Math-Answers-Grade-7-Chapter-5-Ratios-and-Proportions-cr-4.png 600w, https:\/\/bigideasmathanswers.com\/wp-content\/uploads\/2021\/01\/Big-Ideas-Math-Answers-Grade-7-Chapter-5-Ratios-and-Proportions-cr-4-300x36.png 300w\" sizes=\"(max-width: 600px) 100vw, 600px\" \/><\/p>\n<p><strong>5.1 Ratios and Ratio Tables (pp. 183\u2013188)<\/strong><br \/>\nLearning Target: Understand ratios of rational numbers and use ratio tables to represent equivalent ratios.<\/p>\n<p>Write the ratio. Then find and interpret the value of the ratio.<br \/>\n<img loading=\"lazy\" class=\"alignnone size-full wp-image-30480\" src=\"https:\/\/ccssmathanswers.com\/wp-content\/uploads\/2021\/01\/Big-Ideas-Math-Answers-Grade-7-Chapter-5-Ratios-and-Proportions-cr-5.png\" alt=\"Big Ideas Math Answers Grade 7 Chapter 5 Ratios and Proportions cr 5\" width=\"306\" height=\"106\" srcset=\"https:\/\/bigideasmathanswers.com\/wp-content\/uploads\/2021\/01\/Big-Ideas-Math-Answers-Grade-7-Chapter-5-Ratios-and-Proportions-cr-5.png 306w, https:\/\/bigideasmathanswers.com\/wp-content\/uploads\/2021\/01\/Big-Ideas-Math-Answers-Grade-7-Chapter-5-Ratios-and-Proportions-cr-5-300x104.png 300w\" sizes=\"(max-width: 306px) 100vw, 306px\" \/><br \/>\nQuestion 1.<br \/>\nsalt: flour<\/p>\n<p>Answer:<br \/>\n1\/2 : 2<\/p>\n<p>Explanation:<br \/>\nsalt : flour = 1\/2 cup : 2 cups<\/p>\n<p>Question 2.<br \/>\nwater to flour<\/p>\n<p>Answer:<br \/>\n3\/4 cup : 2 cups<\/p>\n<p>Explanation:<br \/>\nwater to flour = 3\/4 : 2<\/p>\n<p>Question 3.<br \/>\nsalt to water<\/p>\n<p>Answer:<br \/>\n1\/2 cup : 3\/4 cup<\/p>\n<p>Explanation:<br \/>\nsalt to water = 1\/2 cup : 3\/4 cup<\/p>\n<p><strong>Find the missing values in the ratio table. Then write the equivalent ratios.<\/strong><br \/>\nQuestion 4.<br \/>\n<img loading=\"lazy\" class=\"alignnone size-full wp-image-30481\" src=\"https:\/\/ccssmathanswers.com\/wp-content\/uploads\/2021\/01\/Big-Ideas-Math-Answers-Grade-7-Chapter-5-Ratios-and-Proportions-cr-6.png\" alt=\"Big Ideas Math Answers Grade 7 Chapter 5 Ratios and Proportions cr 6\" width=\"232\" height=\"94\" \/><\/p>\n<p>Answer:<br \/>\n<img loading=\"lazy\" class=\"alignnone size-full wp-image-49370\" src=\"https:\/\/ccssmathanswers.com\/wp-content\/uploads\/2021\/01\/big-ideas-math-answer-key-grade-7-chapter-5-ratios-and-proportions-5.1-21.jpg\" alt=\"Big Ideas Math Answer Key Grade 7 Chapter 5 Ratios and Proportions 5.1 21\" width=\"294\" height=\"108\" \/><br \/>\nThe equivalent ratios are 3\/2 : 1\/2, 3 : 1, 9\/2 : 3\/2, 6 : 2<\/p>\n<p>Explanation:<br \/>\nThe missing values in the ratio table are<br \/>\n3\/2 \u2022 x = 3<br \/>\nx = 3 \u2022 2\/3<br \/>\nx = 2<br \/>\nMilk1 = 2 \u2022 1\/2 = 1<br \/>\n1\/2 \u2022 y = 3\/2<br \/>\ny = 3<br \/>\nFlour1 = 3\/2 \u2022 3<br \/>\n= 9\/2<br \/>\n1\/2 \u2022 z = 2<br \/>\nz = 4<br \/>\nFlour2 = 3\/2 \u2022 4<br \/>\n= 6<br \/>\nThe equivalent ratios are 3\/2 : 1\/2, 3 : 1, 9\/2 : 3\/2, 6 : 2<\/p>\n<p>Question 5.<br \/>\n<img loading=\"lazy\" class=\"alignnone size-full wp-image-30482\" src=\"https:\/\/ccssmathanswers.com\/wp-content\/uploads\/2021\/01\/Big-Ideas-Math-Answers-Grade-7-Chapter-5-Ratios-and-Proportions-cr-7.png\" alt=\"Big Ideas Math Answers Grade 7 Chapter 5 Ratios and Proportions cr 7\" width=\"224\" height=\"71\" \/><\/p>\n<p>Answer:<br \/>\n<img loading=\"lazy\" class=\"alignnone size-full wp-image-49371\" src=\"https:\/\/ccssmathanswers.com\/wp-content\/uploads\/2021\/01\/big-ideas-math-answer-key-grade-7-chapter-5-ratios-and-proportions-5.1-22.jpg\" alt=\"Big Ideas Math Answer Key Grade 7 Chapter 5 Ratios and Proportions 5.1 22\" width=\"470\" height=\"150\" srcset=\"https:\/\/bigideasmathanswers.com\/wp-content\/uploads\/2021\/01\/big-ideas-math-answer-key-grade-7-chapter-5-ratios-and-proportions-5.1-22.jpg 470w, https:\/\/bigideasmathanswers.com\/wp-content\/uploads\/2021\/01\/big-ideas-math-answer-key-grade-7-chapter-5-ratios-and-proportions-5.1-22-300x96.jpg 300w\" sizes=\"(max-width: 470px) 100vw, 470px\" \/><br \/>\nThe equivalent ratios are 45 : 0.75, 135 : 2.25, 180 : 3, 90 : 1.5<\/p>\n<p>Explanation:<br \/>\nThe missing values in the ratio table are<br \/>\n45 \u2022 x = 135<br \/>\nx = 135\/45<br \/>\nx = 3<br \/>\nHours1 = 0.75 \u2022 3<br \/>\n= 2.25<br \/>\n0.75 \u2022 y = 3<br \/>\ny = 3\/0.75<br \/>\ny = 4<br \/>\nMiles1 = 45 \u2022 4 = 180<br \/>\n45 \u2022 z = 90<br \/>\nz = 90\/45 = 2<br \/>\nHours2 = 0.75 \u2022 2 = 1.5<br \/>\nThe equivalent ratios are 45 : 0.75, 135 : 2.25, 180 : 3, 90 : 1.5<\/p>\n<p>Question 6.<br \/>\nThe cost for 16 ounces of cheese is $3.20. What is the cost for 20 ounces of cheese?<\/p>\n<p>Answer:<br \/>\nThe cost for 20 ounces of cheese is $3.95<\/p>\n<p>Explanation:<br \/>\nThe cost for 16 ounces of cheese is $3.20<br \/>\nThe cost for 1 ounce of cheese is 3.20\/16<br \/>\nThe cost for 20 ounces of cheese is 20(3.20\/16)<br \/>\n= 63.2\/16<br \/>\n= 3.95<\/p>\n<p><strong>5.2 Rates and Unit Rates (pp. 189\u2013194)<\/strong><br \/>\nLearning Target: Understand rates involving fractions and use unit rates to solve problems.<\/p>\n<p><strong>Find the unit rate.<\/strong><br \/>\nQuestion 7.<br \/>\n289 miles on 10 gallons<\/p>\n<p>Answer:<br \/>\n28.9 miles per 1 gallon<\/p>\n<p>Explanation:<br \/>\n289 miles on 10 gallons<br \/>\n= 289 : 10<br \/>\n= 289\/10 : 1<br \/>\n= 28.9 : 1<\/p>\n<p>Question 8.<br \/>\n6 \\(\\frac{2}{5}\\) revolutions in 2\\(\\frac{2}{3}\\) seconds<\/p>\n<p>Answer:<br \/>\n2.4 revolutions in 1 second<\/p>\n<p>Explanation:<br \/>\n6 \\(\\frac{2}{5}\\) revolutions in 2\\(\\frac{2}{3}\\) seconds = 32\/5 : 8\/3<br \/>\n= 32\/5 \u2022 3\/8 : 1<br \/>\n= 12\/5 : 1<\/p>\n<p>Question 9.<br \/>\nYou can mow 23,760 square feet in \\(\\frac{1}{2}\\) hour. How many square feet can you mow in 2 hours? Justify your answer.<\/p>\n<p>Answer:<br \/>\n95040 sq ft you can mow in 2 hours.<\/p>\n<p>Explanation:<br \/>\nYou can mow 23,760 square feet in \\(\\frac{1}{2}\\) hour<br \/>\n= 23760 : 1\/2<br \/>\n= 23760 \u2022 2 : 1<br \/>\n= 47520 : 1<br \/>\nSo you can mow 47520 sq ft in 1 hour<br \/>\nThe number of sq ft you can mow in 2 hours = 47520 \u2022 2<br \/>\n= 95040<\/p>\n<p><strong>Tell whether the rates are equivalent. Justify your answer.<\/strong><br \/>\nQuestion 10.<br \/>\n60 centimeters every 2.5 years<br \/>\n30 centimeters every 15 months<\/p>\n<p>Answer:<br \/>\nThe rates are equivalent.<\/p>\n<p>Explanation:<br \/>\n60 centimeters every 2.5 years = 60 : 2.5<br \/>\n= 600 : 25<br \/>\n= 24 : 1<br \/>\n24 cm every year<br \/>\n= 24 : 12<br \/>\n= 2 : 1<br \/>\n2 cm every month<br \/>\n30 centimeters every 15 months = 30 : 15<br \/>\n= 2 : 1<br \/>\nSo, The rates are equivalent.<\/p>\n<p>Question 11.<br \/>\n2.56 per \\(\\frac{1}{2}\\) pound<br \/>\n$0.48 per 6 ounces<\/p>\n<p>Answer:<br \/>\nThe ratios are not equivalent.<\/p>\n<p>Explanation:<br \/>\n2.56 per \\(\\frac{1}{2}\\) pound = 2.56 : 1\/2<br \/>\n= 2.56 * 2 : 1<br \/>\n= 5.12 : 1<br \/>\n1 pound = 16 ounces<br \/>\n$0.48 per 6 ounces = 0.48 : 6<br \/>\n= 0.48 : 6 * 16<br \/>\n= 0.48 : 96<br \/>\n= 1 : 200<br \/>\nSo, the ratios are not equivalent.<\/p>\n<p><strong>5.3 Identifying Proportional Relationships (pp. 195\u2013202)<\/strong><br \/>\nLearning Target: Determine whether two quantities are in a proportional relationship.<\/p>\n<p><strong>Tell whether the ratios form a proportion.<\/strong><br \/>\nQuestion 12.<br \/>\n4 to 9 and 2 to 3<\/p>\n<p>Answer:<br \/>\nThe rates do not form a proportion.<\/p>\n<p>Explanation:<br \/>\n4 to 9 = 4 : 9<br \/>\n2 to 3 = 2 : 3<br \/>\nSo, the rates do not form a proportion.<\/p>\n<p>Question 13.<br \/>\n12 : 22 and 18 : 33<\/p>\n<p>Answer:<br \/>\nThe rates form a proportion.<\/p>\n<p>Explanation:<br \/>\n12 : 22 = 12 : 22<br \/>\n= 6 : 11<br \/>\n18 : 33 = 18 : 33<br \/>\n= 6 : 11<br \/>\nSo, the rates form a proportion.<\/p>\n<p>Question 14.<br \/>\n\\(\\frac{1}{2}\\) : 2 and \\(\\frac{1}{4}\\) : \\(\\frac{1}{10}\\)<\/p>\n<p>Answer:<br \/>\nThe rates do not form a proportion<\/p>\n<p>Explanation:<br \/>\n\\(\\frac{1}{2}\\) : 2 = 1 : 4<br \/>\n\\(\\frac{1}{4}\\) : \\(\\frac{1}{10}\\) = 1\/4 : 1\/10<br \/>\n= 10 : 4<br \/>\n= 5 : 2<br \/>\nSo, the rates do not form a proportion.<\/p>\n<p>Question 15.<br \/>\n3.2 to 8 and 1.2 to 3<\/p>\n<p>Answer:<br \/>\nThe ratios are equivalent.<\/p>\n<p>Explanation:<br \/>\n3.2 to 8 = 3.2 : 8<br \/>\n= 2\/5<br \/>\n1.2 to 3 = 1.2 : 3<br \/>\n= 2\/5<br \/>\nSo, the ratios are equivalent.<\/p>\n<p>Question 16.<br \/>\nTell whether x and y are proportional.<br \/>\n<img loading=\"lazy\" class=\"alignnone size-full wp-image-30483\" src=\"https:\/\/ccssmathanswers.com\/wp-content\/uploads\/2021\/01\/Big-Ideas-Math-Answers-Grade-7-Chapter-5-Ratios-and-Proportions-cr-16.png\" alt=\"Big Ideas Math Answers Grade 7 Chapter 5 Ratios and Proportions cr 16\" width=\"209\" height=\"65\" \/><\/p>\n<p>Answer:<br \/>\nThe x and y are proportional<\/p>\n<p>Explanation:<br \/>\nx\/y = 1\/4<br \/>\n3\/12 = (3 \u2022 1)\/(4 \u2022 3) = 1\/4<br \/>\n6\/24 = (6 \u2022 1)\/(6 \u2022 4) = 1\/4<br \/>\n8\/32 = (8 \u2022 1)\/(8 \u2022 4) = 1\/4<br \/>\nSo, the x and y are proportional.<\/p>\n<p>Question 17.<br \/>\nYou can type 250 characters in 60 seconds. Your friend can type 375 characters in 90 seconds. Do these rates form a proportion? Explain.<\/p>\n<p>Answer:<br \/>\nThe rates form a proportion.<\/p>\n<p>Explanation:<br \/>\nYou can type 250 characters in 60 seconds = 250 : 60<br \/>\n= (25 \u2022 10) : (6 \u2022 10) = 25 : 6<br \/>\nYour friend can type 375 characters in 90 seconds = 375 : 90<br \/>\n= (25 \u2022 15) : (6 \u2022 15)<br \/>\n= 25 : 6<br \/>\nSo, the rates form a proportion.<\/p>\n<p><strong>5.4 Writing and Solving Proportions (pp. 203\u2013210)<\/strong><br \/>\nLearning Target: Use proportions to solve ratio problems.<\/p>\n<p><strong>Solve the proportion. Explain your choice of method.<\/strong><br \/>\nQuestion 18.<br \/>\n\\(\\frac{3}{8}=\\frac{9}{x}\\)<\/p>\n<p>Answer:<br \/>\nx = 24<\/p>\n<p>Explanation:<br \/>\n\\(\\frac{3}{8}=\\frac{9}{x}\\)<br \/>\nCross multiply the fractions<br \/>\n3x = 9 * 8<br \/>\nx = 3 * 8<br \/>\nx = 24<\/p>\n<p>Question 19.<br \/>\n\\(\\frac{x}{4}=\\frac{2}{5}\\)<\/p>\n<p>Answer:<br \/>\nx = 8\/5<\/p>\n<p>Explanation:<br \/>\n\\(\\frac{x}{4}=\\frac{2}{5}\\)<br \/>\nCross multiply the fractions<br \/>\n5x = 2 * 4<br \/>\n5x = 8<br \/>\nx = 8\/5<\/p>\n<p>Question 20.<br \/>\n\\(\\frac{5}{12}=\\frac{y}{15}\\)<\/p>\n<p>Answer:<br \/>\ny = 75\/12<\/p>\n<p>Explanation:<br \/>\n\\(\\frac{5}{12}=\\frac{y}{15}\\)<br \/>\nCross multiply the fractions<br \/>\n15 * 5 = 12y<br \/>\n75 = 12y<br \/>\ny = 75\/12<\/p>\n<p>Question 21.<br \/>\n\\(\\frac{s+1}{4}=\\frac{4}{8}\\)<\/p>\n<p>Answer:<br \/>\ns = 1<\/p>\n<p>Explanation:<br \/>\n\\(\\frac{s+1}{4}=\\frac{4}{8}\\)<br \/>\nCross multiply the fractions<br \/>\n8(s + 1) = 4 * 4<br \/>\n8s + 8 = 16<br \/>\n8s = 16 &#8211; 8<br \/>\n8s = 8<br \/>\ns = 1<\/p>\n<p><strong>Use the table to write a proportion.<\/strong><br \/>\nQuestion 22.<br \/>\n<img loading=\"lazy\" class=\"alignnone size-full wp-image-30484\" src=\"https:\/\/ccssmathanswers.com\/wp-content\/uploads\/2021\/01\/Big-Ideas-Math-Answers-Grade-7-Chapter-5-Ratios-and-Proportions-cr-22.png\" alt=\"Big Ideas Math Answers Grade 7 Chapter 5 Ratios and Proportions cr 22\" width=\"220\" height=\"110\" \/><\/p>\n<p>Answer:<br \/>\n6\/12 = 8\/m, m = 12<\/p>\n<p>Explanation:<br \/>\nThe ratios are proportional.<br \/>\n6\/12 = 8\/m<br \/>\nCross multiply the fractions<br \/>\n6m = 8 * 12<br \/>\n6m = 96<br \/>\nm = 96\/8<br \/>\nm = 12<\/p>\n<p>Question 23.<br \/>\n<img loading=\"lazy\" class=\"alignnone size-full wp-image-30485\" src=\"https:\/\/ccssmathanswers.com\/wp-content\/uploads\/2021\/01\/Big-Ideas-Math-Answers-Grade-7-Chapter-5-Ratios-and-Proportions-cr-23.png\" alt=\"Big Ideas Math Answers Grade 7 Chapter 5 Ratios and Proportions cr 23\" width=\"236\" height=\"101\" \/><\/p>\n<p>Answer:<br \/>\n15\/h = 18\/2.5<\/p>\n<p>Explanation:<br \/>\nThe ratios are proportional.<br \/>\nSo, 15\/h = 18\/2.5<\/p>\n<p>Question 24.<br \/>\nFind the value of x so that the ratios 8 : 20 and 6 : x are equivalent.<\/p>\n<p>Answer:<br \/>\nx = 15<\/p>\n<p>Explanation:<br \/>\n8\/20 = 6\/x<br \/>\nCross multiply the fractions<br \/>\n8x = 6 * 20<br \/>\n8x = 120<br \/>\nx = 120\/8<br \/>\nx = 15<\/p>\n<p>Question 25.<br \/>\nSwamp gas consists primarily of methane, a chemical compound consisting of a 1 : 4 ratio of carbon to hydrogen atoms. If a sample of methane contains 1564 hydrogen atoms, how many carbon atoms are present in the sample?<br \/>\n<img loading=\"lazy\" class=\"alignnone size-full wp-image-30486\" src=\"https:\/\/ccssmathanswers.com\/wp-content\/uploads\/2021\/01\/Big-Ideas-Math-Answers-Grade-7-Chapter-5-Ratios-and-Proportions-cr-25.png\" alt=\"Big Ideas Math Answers Grade 7 Chapter 5 Ratios and Proportions cr 25\" width=\"240\" height=\"173\" \/><\/p>\n<p>Answer:<br \/>\nThe number of carbon atoms present in the sample is 391.<\/p>\n<p>Explanation:<br \/>\nSwamp gas consists primarily of methane, a chemical compound consisting of a 1 : 4 ratio of carbon to hydrogen atoms<br \/>\nThe number of carbon atoms present in the sample is 1564\/4<br \/>\n= 391<\/p>\n<p><strong>5.5 Graphs of Proportional Relationships (pp. 211\u2013216)<\/strong><br \/>\nLearning Target: Represent proportional relationships using graphs and equations.<\/p>\n<p>Question 26.<br \/>\nTell whether x and y are proportional. Explain your reasoning.<br \/>\n<img loading=\"lazy\" class=\"alignnone size-full wp-image-30487\" src=\"https:\/\/ccssmathanswers.com\/wp-content\/uploads\/2021\/01\/Big-Ideas-Math-Answers-Grade-7-Chapter-5-Ratios-and-Proportions-cr-26.png\" alt=\"Big Ideas Math Answers Grade 7 Chapter 5 Ratios and Proportions cr 26\" width=\"210\" height=\"60\" \/><\/p>\n<p>Answer:<br \/>\nx and y are proportional<\/p>\n<p>Explanation:<br \/>\n<img loading=\"lazy\" class=\"alignnone wp-image-49407 size-medium\" src=\"https:\/\/ccssmathanswers.com\/wp-content\/uploads\/2021\/01\/big-ideas-math-answer-key-grade-7-chapter-5-ratios-and-proportions-5.5-20-300x226.jpg\" alt=\"Big Ideas Math Answer Key Grade 7 Chapter 5 Ratios and Proportions 5.5 20\" width=\"300\" height=\"226\" srcset=\"https:\/\/bigideasmathanswers.com\/wp-content\/uploads\/2021\/01\/big-ideas-math-answer-key-grade-7-chapter-5-ratios-and-proportions-5.5-20-300x226.jpg 300w, https:\/\/bigideasmathanswers.com\/wp-content\/uploads\/2021\/01\/big-ideas-math-answer-key-grade-7-chapter-5-ratios-and-proportions-5.5-20-768x578.jpg 768w, https:\/\/bigideasmathanswers.com\/wp-content\/uploads\/2021\/01\/big-ideas-math-answer-key-grade-7-chapter-5-ratios-and-proportions-5.5-20.jpg 971w\" sizes=\"(max-width: 300px) 100vw, 300px\" \/><br \/>\nThe line passes through origin.<br \/>\nSo, x and y are proportional<\/p>\n<p>Question 27.<br \/>\nThe graph shows the number of visits your website received over the past 6 months. Interpret each plotted point in the graph. Then identify the unit rate.<br \/>\n<img loading=\"lazy\" class=\"alignnone size-full wp-image-30488\" src=\"https:\/\/ccssmathanswers.com\/wp-content\/uploads\/2021\/01\/Big-Ideas-Math-Answers-Grade-7-Chapter-5-Ratios-and-Proportions-cr-27.png\" alt=\"Big Ideas Math Answers Grade 7 Chapter 5 Ratios and Proportions cr 27\" width=\"184\" height=\"202\" \/><\/p>\n<p>Answer:<br \/>\n50 : 1<\/p>\n<p>Explanation:<br \/>\nNumber of visitors : months = 150 : 3<br \/>\n= 150\/3 : 1<br \/>\n= 50 : 1<\/p>\n<p>Tell whether x and y are proportional. If so, identify the constant of proportionality. Explain your reasoning.<br \/>\nQuestion 28.<br \/>\nx + y = 6<\/p>\n<p>Answer:<br \/>\nx and y are not proportional.<\/p>\n<p>Explanation:<br \/>\nx + y = 6<br \/>\ny = 6 &#8211; x<br \/>\nIf x = 1, then y = 6 &#8211; 1 = 5<br \/>\nIf x = 2, then y = 6 &#8211; 2 = 4<br \/>\nIf x = 3, y = 6 &#8211; 3 = 3<br \/>\n1\/5, 2\/4, 3\/3 are not equivalent ratios<br \/>\nSo, x and y are not proportional.<\/p>\n<p>Question 29.<br \/>\ny &#8211; x = 0<\/p>\n<p>Answer:<br \/>\nx and y are proportional.<\/p>\n<p>Explanation:<br \/>\ny &#8211; x = 0<br \/>\ny = x<br \/>\nIf x = 1, then y = 1<br \/>\nIf x = 2, then y = 2<br \/>\nIf x = 3, then y = 3<br \/>\n1\/2, 2\/2, 3\/3 are equivalent ratios<br \/>\nSo, x and y are proportional.<\/p>\n<p>Question 30.<br \/>\n\\(\\frac{x}{y}\\) = 20<\/p>\n<p>Answer:<br \/>\nx and y are proportional.<\/p>\n<p>Explanation:<br \/>\n\\(\\frac{x}{y}\\) = 20<br \/>\nx = 20y<br \/>\nIf y = 1, then x = 20(1) = 20<br \/>\nIf y = 2, then x = 20(2) = 40<br \/>\nIf y = 3, then x = 20(3) = 60<br \/>\n20\/1, 40\/2, 60\/3 are equivalent ratios<br \/>\nSo, x and y are proportional.<\/p>\n<p>Question 31.<br \/>\nx = y + 2<\/p>\n<p>Answer:<br \/>\nx and are not proportional.<\/p>\n<p>Explanation:<br \/>\nx = y + 2<br \/>\nIf y = 1, then x = 1 + 2 = 3<br \/>\nIf y = 2, then x = 2 + 2 = 4<br \/>\nIf y = 3, then x = 3 + 2 = 6<br \/>\n3\/1, 4\/2, 6\/3 are not equivalent<br \/>\nSo, x and are not proportional.<\/p>\n<p>Question 32.<br \/>\nThe variables x and y are proportional. When y = 4, x = \\(\\frac{1}{2}\\). Find the constant of proportionality. Then write an equation that relates x and y.<\/p>\n<p>Answer:<br \/>\nx = 8y<\/p>\n<p>Explanation:<br \/>\nx\/y = k<br \/>\n(1\/2)\/4 = k<br \/>\nk = 1\/8<br \/>\nx\/y = 8<br \/>\nx = 8y<\/p>\n<p><strong>5.6 Scale Drawings (pp. 217\u2013222)<\/strong><br \/>\nLearning Target: Solve problems involving scale drawings.<\/p>\n<p><strong>Find the missing dimension. Use the scale factor 1 : 20.<\/strong><br \/>\n<img loading=\"lazy\" class=\"alignnone size-full wp-image-30489\" src=\"https:\/\/ccssmathanswers.com\/wp-content\/uploads\/2021\/01\/Big-Ideas-Math-Answers-Grade-7-Chapter-5-Ratios-and-Proportions-cr-33.png\" alt=\"Big Ideas Math Answers Grade 7 Chapter 5 Ratios and Proportions cr 33\" width=\"423\" height=\"108\" srcset=\"https:\/\/bigideasmathanswers.com\/wp-content\/uploads\/2021\/01\/Big-Ideas-Math-Answers-Grade-7-Chapter-5-Ratios-and-Proportions-cr-33.png 423w, https:\/\/bigideasmathanswers.com\/wp-content\/uploads\/2021\/01\/Big-Ideas-Math-Answers-Grade-7-Chapter-5-Ratios-and-Proportions-cr-33-300x77.png 300w\" sizes=\"(max-width: 423px) 100vw, 423px\" \/><\/p>\n<p>Answer:<br \/>\n<img loading=\"lazy\" class=\"alignnone size-full wp-image-49413\" src=\"https:\/\/ccssmathanswers.com\/wp-content\/uploads\/2021\/01\/big-ideas-math-answer-key-grade-7-chapter-5-ratios-and-proportions-5.6-4.jpg\" alt=\"Big Ideas Math Answer Key Grade 7 Chapter 5 Ratios and Proportions 5.6 4\" width=\"639\" height=\"166\" srcset=\"https:\/\/bigideasmathanswers.com\/wp-content\/uploads\/2021\/01\/big-ideas-math-answer-key-grade-7-chapter-5-ratios-and-proportions-5.6-4.jpg 639w, https:\/\/bigideasmathanswers.com\/wp-content\/uploads\/2021\/01\/big-ideas-math-answer-key-grade-7-chapter-5-ratios-and-proportions-5.6-4-300x78.jpg 300w\" sizes=\"(max-width: 639px) 100vw, 639px\" \/><\/p>\n<p>Explanation:<br \/>\n33. Scale factor = 1\/20<br \/>\nUse the scale 1 : 20<br \/>\n90(1\/20) = 9\/2 = 4.5<br \/>\n34. x\/20 = 3.75<br \/>\nx = 3.75 * 20<br \/>\nx = 75<br \/>\nActual legth = 75 ft<\/p>\n<p><strong>Use a centimeter ruler to find the scale and the scale factor of the drawing.<\/strong><br \/>\nQuestion 35.<br \/>\n<img loading=\"lazy\" class=\"alignnone size-full wp-image-30490\" src=\"https:\/\/ccssmathanswers.com\/wp-content\/uploads\/2021\/01\/Big-Ideas-Math-Answers-Grade-7-Chapter-5-Ratios-and-Proportions-cr-35.png\" alt=\"Big Ideas Math Answers Grade 7 Chapter 5 Ratios and Proportions cr 35\" width=\"246\" height=\"64\" \/><\/p>\n<p>Answer:<br \/>\nThe scale is 7.62, scale factor is 39.3701 in<\/p>\n<p>Explanation:<br \/>\nThe length of drawing = 10 cm<br \/>\n10 cm = 30 in<br \/>\n1 cm = 0.393701<br \/>\n10 cm = 39.3701 in<br \/>\n10 cm : 30 in = 1 cm : 3 in<br \/>\n3 inch = 7.62<br \/>\nThe actual length is 39.3701 inch<br \/>\nSo, the scale is 7.62, scale factor is 39.3701 in<\/p>\n<p>Question 36<br \/>\n<img loading=\"lazy\" class=\"alignnone size-full wp-image-30491\" src=\"https:\/\/ccssmathanswers.com\/wp-content\/uploads\/2021\/01\/Big-Ideas-Math-Answers-Grade-7-Chapter-5-Ratios-and-Proportions-cr-36.png\" alt=\"Big Ideas Math Answers Grade 7 Chapter 5 Ratios and Proportions cr 36\" width=\"124\" height=\"58\" \/><\/p>\n<p>Answer:<br \/>\nThe scale is 19.05, scale factor is 19.05<\/p>\n<p>Explanation:<br \/>\nUisng the centimeter ruler, length is 4 cm<br \/>\n4 cm = 7.5 in<br \/>\n1 cm = 0.393701<br \/>\n4 cm = 1.5748 in<br \/>\n4 cm : 7.5 in<br \/>\n7.5 inch = 19.05<br \/>\n4 cm : 7.5 inch = 4 cm : 19.05 cm<br \/>\nthe scale is 19.05, scale factor is 19.05<\/p>\n<p>Question 37.<br \/>\nA scale model of a lighthouse has a scale of 1 in.: 8ft. The scale model is 20 inches tall. How tall is the lighthouse?<\/p>\n<p>Answer:<\/p>\n<p>Explanation:<br \/>\nA scale model of a lighthouse has a scale of 1 in.: 8ft<br \/>\nThe scale model is 20 inches tall<\/p>\n<h3><a id=\"Ratios_and_Proportions_Practice_Test\"><\/a>Ratios and Proportions Practice Test<\/h3>\n<p><strong>Find the unit rate.<\/strong><br \/>\nQuestion 1.<br \/>\n84 miles in 12 days<\/p>\n<p>Answer:<br \/>\n7 miles in 1 day<\/p>\n<p>Explanation:<br \/>\n84 miles in 12 days<br \/>\n= 84 : 12<br \/>\n= 84\/12 : 1<br \/>\n= 7 : 1<\/p>\n<p>Question 2.<br \/>\n2 \\(\\frac{2}{5}\\) kilometers in 3\\(\\frac{3}{4}\\) minutes<\/p>\n<p>Answer:<br \/>\n48 kilometers in 75 minutes.<\/p>\n<p>Explanation:<br \/>\n2 \\(\\frac{2}{5}\\) kilometers in 3\\(\\frac{3}{4}\\) minutes = 12\/5 : 15\/4<br \/>\n= 12\/5 \u2022 4\/15 : 1<br \/>\n= 48\/75 : 1<\/p>\n<p><strong>Tell whether the ratios form a proportion.<\/strong><br \/>\nQuestion 3.<br \/>\n1 to 0.4 and 9 to 3.6<\/p>\n<p>Answer:<br \/>\nThe ratios form a proportion.<\/p>\n<p>Explanation:<br \/>\n1 to 0.4 = 1 : 0.4<br \/>\n= 5\/2<br \/>\n9 to 3.6 = 9 : 3.6<br \/>\n= 5\/2<br \/>\nSo, the ratios form a proportion.<\/p>\n<p>Question 4.<br \/>\n2 : \\(\\frac{8}{3}\\) and \\(\\frac{2}{3}\\) : 6<\/p>\n<p>Answer:<br \/>\nThe ratios do not form a proportion.<\/p>\n<p>Explanation:<br \/>\n2 : \\(\\frac{8}{3}\\) = 6 : 8<br \/>\n= 3\/4<br \/>\n\\(\\frac{2}{3}\\) : 6 = 2 : 18<br \/>\n= 1\/9<br \/>\nSo, the ratios do not form a proportion.<\/p>\n<p><strong>Tell whether and are proportional. Explain your reasoning.<\/strong><br \/>\nQuestion 5.<br \/>\n<img loading=\"lazy\" class=\"alignnone size-full wp-image-30501\" src=\"https:\/\/ccssmathanswers.com\/wp-content\/uploads\/2021\/01\/Big-Ideas-Math-Solutions-Grade-7-Chapter-5-Ratios-and-Proportions-pt-5.png\" alt=\"Big Ideas Math Solutions Grade 7 Chapter 5 Ratios and Proportions pt 5\" width=\"219\" height=\"61\" \/><\/p>\n<p>Answer:<br \/>\nx and y are proportional<\/p>\n<p>Explanation:<br \/>\nx\/y = 2\/10 = 1\/5<br \/>\n4\/20 = 1\/5<br \/>\n6\/30 = 1\/5<br \/>\n8\/40 = 1\/5<br \/>\nSo, x and y are proportional<\/p>\n<p>Question 6.<br \/>\n<img loading=\"lazy\" class=\"alignnone size-full wp-image-30502\" src=\"https:\/\/ccssmathanswers.com\/wp-content\/uploads\/2021\/01\/Big-Ideas-Math-Solutions-Grade-7-Chapter-5-Ratios-and-Proportions-pt-6.png\" alt=\"Big Ideas Math Solutions Grade 7 Chapter 5 Ratios and Proportions pt 6\" width=\"219\" height=\"64\" \/><\/p>\n<p>Answer:<br \/>\nx and y are not proportional.<\/p>\n<p>Explanation:<br \/>\nx\/y = 1\/3, 3\/7, 5\/11, 7\/15<br \/>\nSo, x and y are not proportional.<\/p>\n<p>Question 7.<br \/>\nUse the table to write a proportion.<br \/>\n<img loading=\"lazy\" class=\"alignnone size-full wp-image-30503\" src=\"https:\/\/ccssmathanswers.com\/wp-content\/uploads\/2021\/01\/Big-Ideas-Math-Solutions-Grade-7-Chapter-5-Ratios-and-Proportions-pt-7.png\" alt=\"Big Ideas Math Solutions Grade 7 Chapter 5 Ratios and Proportions pt 7\" width=\"254\" height=\"96\" \/><\/p>\n<p>Answer:<br \/>\n1\/30 = 8\/m<\/p>\n<p>Explanation:<br \/>\nthe ratios are proportional<br \/>\nso, 6\/180 = 8\/m<br \/>\n1\/30 = 8\/m<\/p>\n<p><strong>Solve the proportion.<\/strong><br \/>\nQuestion 8.<br \/>\n\\(\\frac{x}{8}=\\frac{9}{4}\\)<\/p>\n<p>Answer:<br \/>\nx = 18<\/p>\n<p>Explanation:<br \/>\n\\(\\frac{x}{8}=\\frac{9}{4}\\)<br \/>\nCross multiply the fractions<br \/>\n4x = 9 * 8<br \/>\n4x = 72<br \/>\nx = 72\/4<br \/>\nx = 18<\/p>\n<p>Question 9.<br \/>\n\\(\\frac{17}{4}=\\frac{y}{6}\\)<\/p>\n<p>Answer:<br \/>\ny = 51\/2<\/p>\n<p>Explanation:<br \/>\n\\(\\frac{17}{4}=\\frac{y}{6}\\)<br \/>\nCross multiply the fractions<br \/>\n17 * 6 = 4y<br \/>\n102 = 4y<br \/>\ny = 102\/4<br \/>\ny = 51\/2<\/p>\n<p><strong>Tell whether and are proportional. If so, identify the constant of proportionality. Explain your reasoning.<\/strong><br \/>\nQuestion 10.<br \/>\nxy &#8211; 11 = 5<\/p>\n<p>Answer:<br \/>\nx, y are not proportional.<\/p>\n<p>Explanation:<br \/>\nxy &#8211; 11 = 5<br \/>\nxy = 5 + 11<br \/>\nxy = 16<br \/>\nx = 16\/y<\/p>\n<p>Question 11.<br \/>\n\\(\\frac{y}{x}\\) = 8<\/p>\n<p>Answer:<br \/>\nx and y are proportional<\/p>\n<p>Explanation:<br \/>\n\\(\\frac{y}{x}\\) = 8<br \/>\ny = 8x<br \/>\nSo, x and y are proportional<\/p>\n<p>Question 12.<br \/>\nA recipe calls for \\(\\frac{2}{3}\\) cup flour for every cup sugar. Write the ratio of sugar to flour. Then find and interpret the value of the ratio.<\/p>\n<p>Answer:<br \/>\nThe ratio of sugar to flour is 3 : 2.<\/p>\n<p>Explanation:<br \/>\nA recipe calls for \\(\\frac{2}{3}\\) cup flour for every cup sugar<br \/>\nFlour : sugar = 2\/3 : 1<br \/>\nSugar to flour = 1 : 2\/3<br \/>\n= 3 : 2<\/p>\n<p>Question 13.<br \/>\nThe graph shows the number of cycles of a crosswalk signal during the day and during the night.<br \/>\n<img loading=\"lazy\" class=\"alignnone size-full wp-image-30504\" src=\"https:\/\/ccssmathanswers.com\/wp-content\/uploads\/2021\/01\/Big-Ideas-Math-Solutions-Grade-7-Chapter-5-Ratios-and-Proportions-pt-13.png\" alt=\"Big Ideas Math Solutions Grade 7 Chapter 5 Ratios and Proportions pt 13\" width=\"200\" height=\"228\" \/><br \/>\na. Write equations that relate x and y for both the day and night periods.<br \/>\nb. Find how many more cycles occur during the day than during the night for a six-hour period.<\/p>\n<p>Answer:<br \/>\na. The equation for day is 40 x = y<br \/>\nthe equation for night is 30x = y<br \/>\nb. 60 more cycles occur during the day than during the night for a six-hour period.<\/p>\n<p>Explanation:<br \/>\na. For day, 2 hours is 80 cycles<br \/>\nx\/y = 2\/80 = 1\/40<br \/>\n40x = y<br \/>\nFor night, 3 hours is 90<br \/>\nx\/y = 3\/90 = 1\/30<br \/>\n30x = y<br \/>\na. For day, the number of cycles for 3 hours is 90<br \/>\n90 : 3 = 30 : 1<br \/>\nSo, 30 cycles per 1 hour<br \/>\nThe number of cycles per 6 hours is 30 * 6 = 180<br \/>\nFor night,<br \/>\nthe number of cycles is 80 for 2 hours<br \/>\n80 : 2 = 40 : 1<br \/>\nThe number of cycles for 6 hours is 40 * 6 = 240<br \/>\n240 &#8211; 180 = 60<\/p>\n<p>Question 14.<br \/>\nAn engineer is using computer-aided design (CAD) software to design a component for a space shuttle. The scale of the drawing is 1 cm : 60 in. The actual length of the component is 12.75 feet. What is the length of the component in the drawing?<\/p>\n<p>Answer:<br \/>\nThe length of the component in the drawing is 25 cm<\/p>\n<p>Explanation:<br \/>\nWrite the proportion relating the model length to the actual length. the scale has inches for the actual length units so you must use 12.5 feet = 15 inches in the proportion<br \/>\nmodel\/actual = 1 cm\/60 in = x cm\/150 in<br \/>\n60x = 150<br \/>\nx = 150\/6<br \/>\n= 25<\/p>\n<p>Question 15.<br \/>\nA specific shade of green glaze is made of 5 parts blue glaze to 3 parts yellow glaze. A glaze mixture contains 25 quarts of blue glaze and 9 quarts of yellow glaze. How can you fix the mixture to make the specific shade of green glaze?<\/p>\n<p>Answer:<br \/>\n25 parts blue to 15 parts yellow<\/p>\n<p>Explanation:<br \/>\n25 blue to 9 yellow<br \/>\nThe rate is not equal to the specific rate, 5 parts blue to 3 parts yellow<br \/>\n25 parts blue to 15 parts yellow<\/p>\n<h3><a id=\"Ratios_and_Proportions_Cumulative_Practice\"><\/a>Ratios and Proportions Cumulative Practice<\/h3>\n<p><img loading=\"lazy\" class=\"alignnone size-full wp-image-30492\" src=\"https:\/\/ccssmathanswers.com\/wp-content\/uploads\/2021\/01\/Big-Ideas-Math-Solutions-Grade-7-Chapter-5-Ratios-and-Proportions-cp-1.png\" alt=\"Big Ideas Math Solutions Grade 7 Chapter 5 Ratios and Proportions cp 1\" width=\"305\" height=\"352\" srcset=\"https:\/\/bigideasmathanswers.com\/wp-content\/uploads\/2021\/01\/Big-Ideas-Math-Solutions-Grade-7-Chapter-5-Ratios-and-Proportions-cp-1.png 305w, https:\/\/bigideasmathanswers.com\/wp-content\/uploads\/2021\/01\/Big-Ideas-Math-Solutions-Grade-7-Chapter-5-Ratios-and-Proportions-cp-1-260x300.png 260w\" sizes=\"(max-width: 305px) 100vw, 305px\" \/><br \/>\nQuestion 1.<br \/>\nThe school store sells 4 pencils for $0.80. What is the unit cost of a pencil?<br \/>\nA. $0.20<br \/>\nB. $0.80<br \/>\nC. $3.20<br \/>\nD. $5.00<\/p>\n<p>Answer:<br \/>\nA. $0.20<\/p>\n<p>Explanation:<br \/>\nThe school store sells 4 pencils for $0.80<br \/>\n= 0.80 : 4<br \/>\n= 0.80\/4 : 1<br \/>\n= 0.2 : 1<\/p>\n<p>Question 2.<br \/>\nWhat is the simplified form of the expression?<br \/>\n3x &#8211; (2x &#8211; 5)<br \/>\nF. x &#8211; 5<br \/>\nG. x + 5<br \/>\nH. 5x &#8211; 5<br \/>\nI. &#8211; x &#8211; 5<\/p>\n<p>Answer:<br \/>\nG. x + 5<\/p>\n<p>Explanation:<br \/>\nThe given expression is 3x &#8211; (2x &#8211; 5)<br \/>\n= 3x &#8211; 2x + 5<br \/>\n= x + 5<\/p>\n<p>Question 3.<br \/>\nWhich fraction is equivalent to &#8211; 1.25?\u201d<br \/>\n<img loading=\"lazy\" class=\"alignnone size-full wp-image-30493\" src=\"https:\/\/ccssmathanswers.com\/wp-content\/uploads\/2021\/01\/Big-Ideas-Math-Solutions-Grade-7-Chapter-5-Ratios-and-Proportions-cp-3.png\" alt=\"Big Ideas Math Solutions Grade 7 Chapter 5 Ratios and Proportions cp 3\" width=\"233\" height=\"95\" \/><\/p>\n<p>Answer:<br \/>\nB.<\/p>\n<p>Explanation:<br \/>\n-1.25 = -125\/100<br \/>\n= -5\/4<br \/>\n-1(1\/4) = -5\/4<\/p>\n<p>Question 4.<br \/>\nWhat is the value of for the proportion \\(\\frac{8}{12}=\\frac{x}{18}\\)?<br \/>\n<img loading=\"lazy\" class=\"alignnone size-full wp-image-30494\" src=\"https:\/\/ccssmathanswers.com\/wp-content\/uploads\/2021\/01\/Big-Ideas-Math-Solutions-Grade-7-Chapter-5-Ratios-and-Proportions-cp-4.png\" alt=\"Big Ideas Math Solutions Grade 7 Chapter 5 Ratios and Proportions cp 4\" width=\"90\" height=\"62\" \/><\/p>\n<p>Answer:<br \/>\nx = 12<\/p>\n<p>Explanation:<br \/>\n\\(\\frac{8}{12}=\\frac{x}{18}\\)<br \/>\nCross multiply the fractions<br \/>\n8 * 18 = 12x<br \/>\n144 = 12x<br \/>\nx = 144\/12<br \/>\nx = 12<\/p>\n<p>Question 5.<br \/>\nWhat inequality is represented by the graph?<br \/>\n<img loading=\"lazy\" class=\"alignnone size-full wp-image-30495\" src=\"https:\/\/ccssmathanswers.com\/wp-content\/uploads\/2021\/01\/Big-Ideas-Math-Solutions-Grade-7-Chapter-5-Ratios-and-Proportions-cp-5.png\" alt=\"Big Ideas Math Solutions Grade 7 Chapter 5 Ratios and Proportions cp 5\" width=\"379\" height=\"45\" srcset=\"https:\/\/bigideasmathanswers.com\/wp-content\/uploads\/2021\/01\/Big-Ideas-Math-Solutions-Grade-7-Chapter-5-Ratios-and-Proportions-cp-5.png 379w, https:\/\/bigideasmathanswers.com\/wp-content\/uploads\/2021\/01\/Big-Ideas-Math-Solutions-Grade-7-Chapter-5-Ratios-and-Proportions-cp-5-300x36.png 300w\" sizes=\"(max-width: 379px) 100vw, 379px\" \/><br \/>\nF. x &#8211; 3 &lt; 7<br \/>\nG. x + 6 \u2264 10<br \/>\nH. &#8211; 5 + x &lt; &#8211; 1 I. x &#8211; 8 &gt; &#8211; 4<\/p>\n<p>Answer:<br \/>\nG. x + 6 \u2264 10<\/p>\n<p>Explanation:<br \/>\nthe graph represents x \u2264 4.<br \/>\nSolve all the given options<br \/>\nx &#8211; 3 &lt; 7<br \/>\nx &lt; 7 + 3<br \/>\nx &lt; 10<br \/>\nG. x + 6 \u2264 10<br \/>\nx \u2264 10 &#8211; 6<br \/>\nx \u2264 4<br \/>\nH. &#8211; 5 + x &lt; &#8211; 1<br \/>\nx &lt; -1 + 5<br \/>\nx &lt; 4<br \/>\nI. x &#8211; 8 &gt; &#8211; 4<br \/>\nx &gt; -4 + 8<br \/>\nx &gt; 4<\/p>\n<p>Question 6.<br \/>\nWhat is the missing value in the ratio table?<br \/>\n<img loading=\"lazy\" class=\"alignnone size-full wp-image-30496\" src=\"https:\/\/ccssmathanswers.com\/wp-content\/uploads\/2021\/01\/Big-Ideas-Math-Solutions-Grade-7-Chapter-5-Ratios-and-Proportions-cp-6.png\" alt=\"Big Ideas Math Solutions Grade 7 Chapter 5 Ratios and Proportions cp 6\" width=\"384\" height=\"162\" srcset=\"https:\/\/bigideasmathanswers.com\/wp-content\/uploads\/2021\/01\/Big-Ideas-Math-Solutions-Grade-7-Chapter-5-Ratios-and-Proportions-cp-6.png 384w, https:\/\/bigideasmathanswers.com\/wp-content\/uploads\/2021\/01\/Big-Ideas-Math-Solutions-Grade-7-Chapter-5-Ratios-and-Proportions-cp-6-300x127.png 300w\" sizes=\"(max-width: 384px) 100vw, 384px\" \/><\/p>\n<p>Answer:<br \/>\nB. 30<\/p>\n<p>Explanation:<br \/>\n2\/3 \u2022 x = 10\/3<br \/>\nx = 10\/3 \u2022 3\/2<br \/>\nx = 5<br \/>\n6 \u2022 5 = 30<\/p>\n<p>Question 7.<br \/>\nWhich expression shows factoring 12x + 54 using the GCF?<br \/>\nF. 2(6x + 27)<br \/>\nG. 3(4x + 18)<br \/>\nH. 6(2x + 9)<br \/>\nI. 12(x + \\(\\frac{9}{2}\\))<\/p>\n<p>Answer:<br \/>\nH. 6(2x + 9)<\/p>\n<p>Explanation:<br \/>\n12x = 3 \u2022 2 \u2022 2 \u2022 x<br \/>\n54 = 2 \u2022 3 \u2022 9<br \/>\nThe common prime factors are 3 \u2022 2 = 6<br \/>\nSo, the GCF of 12x + 54 is 6<br \/>\n12x + 54 = 6(2x) + 6(9)<br \/>\n= 6(2x + 9)<\/p>\n<p>Question 8.<br \/>\nThe distance traveled by a high-speed train is proportional to the number of hours traveled. Which of the following is not a valid interpretation of the graph?<br \/>\n<img loading=\"lazy\" class=\"alignnone size-full wp-image-30497\" src=\"https:\/\/ccssmathanswers.com\/wp-content\/uploads\/2021\/01\/Big-Ideas-Math-Solutions-Grade-7-Chapter-5-Ratios-and-Proportions-cp-8.png\" alt=\"Big Ideas Math Solutions Grade 7 Chapter 5 Ratios and Proportions cp 8\" width=\"210\" height=\"231\" \/><br \/>\nA. The train travels 0 kilometers in 0 hours.<br \/>\nB. The unit rate is 200 kilometers per hour.<br \/>\nC. After 4 hours, the train is traveling 800 kilometers per hour.<br \/>\nD. The train travels 800 kilometers in 4 hours.<\/p>\n<p>Answer:<br \/>\nB. The unit rate is 200 kilometers per hour.<\/p>\n<p>Explanation:<br \/>\nThe distance traveled by a high-speed train is proportional to the number of hours traveled<br \/>\n200 proportional to 1 = 200 : 1<\/p>\n<p>Question 9.<br \/>\nWhich graph represents a number that is at most &#8211; 2?<br \/>\n<img loading=\"lazy\" class=\"alignnone size-full wp-image-30498\" src=\"https:\/\/ccssmathanswers.com\/wp-content\/uploads\/2021\/01\/Big-Ideas-Math-Solutions-Grade-7-Chapter-5-Ratios-and-Proportions-cp-9.png\" alt=\"Big Ideas Math Solutions Grade 7 Chapter 5 Ratios and Proportions cp 9\" width=\"404\" height=\"219\" srcset=\"https:\/\/bigideasmathanswers.com\/wp-content\/uploads\/2021\/01\/Big-Ideas-Math-Solutions-Grade-7-Chapter-5-Ratios-and-Proportions-cp-9.png 404w, https:\/\/bigideasmathanswers.com\/wp-content\/uploads\/2021\/01\/Big-Ideas-Math-Solutions-Grade-7-Chapter-5-Ratios-and-Proportions-cp-9-300x163.png 300w\" sizes=\"(max-width: 404px) 100vw, 404px\" \/><\/p>\n<p>Answer:<br \/>\nH.<\/p>\n<p>Explanation:<br \/>\nAt most means less than or equal to<br \/>\nx \u2264 -2<\/p>\n<p>Question 10.<br \/>\nA map of the state where your friend lives has the scale \\(\\frac{1}{2}\\) in. : 10 mi.<br \/>\n<img loading=\"lazy\" class=\"alignnone size-full wp-image-30499\" src=\"https:\/\/ccssmathanswers.com\/wp-content\/uploads\/2021\/01\/Big-Ideas-Math-Solutions-Grade-7-Chapter-5-Ratios-and-Proportions-cp-10.png\" alt=\"Big Ideas Math Solutions Grade 7 Chapter 5 Ratios and Proportions cp 10\" width=\"82\" height=\"68\" \/><br \/>\nPart A Your friend measured the distance between her town and the state capital on the map. Her measurement was 4\\(\\frac{1}{2}\\) inches. Based on your friend\u2019s measurement, what is the actual distance (in miles) between her town and the state capital? Show your work and explain your reasoning.<br \/>\nPart B Your friend wants to mark her favorite campsite on the map. She knows that the campsite is 65 miles north of her town. What distance on the map (in inches) represents an actual distance of 65 miles? Show your work and explain your reasoning.<\/p>\n<p>Answer:<br \/>\nA. 90 miles<br \/>\nB. 3(1\/4) inch<\/p>\n<p>Explanation:<br \/>\nA. Write the proportion relating the model distance on the map to the actual distance where x is the actual distance. Then solve the proportion by cross multiplying<br \/>\nmodel\/actual = 1\/2\/10 = 4(1\/2)\/x<br \/>\n0.5\/10 = 4.5\/x<br \/>\n0.5x = 45<br \/>\nx = 45\/0.5<br \/>\nx = 90 miles<br \/>\nB. Write the proportion relating the model distance to the actual distance where y is the model distance.<br \/>\n0.5\/10 = y\/65<br \/>\ncross multiply<br \/>\n10y = 0.5 * 65<br \/>\n10y = 32.5<br \/>\ny = 32.5\/10<br \/>\ny = 3.25<br \/>\n= 3(1\/4) inch<\/p>\n<p>Question 11.<br \/>\nWhat is the value of the expression &#8211; 56 \u00f7 (- 8)?<br \/>\n<img loading=\"lazy\" class=\"alignnone size-full wp-image-30494\" src=\"https:\/\/ccssmathanswers.com\/wp-content\/uploads\/2021\/01\/Big-Ideas-Math-Solutions-Grade-7-Chapter-5-Ratios-and-Proportions-cp-4.png\" alt=\"Big Ideas Math Solutions Grade 7 Chapter 5 Ratios and Proportions cp 4\" width=\"90\" height=\"62\" \/><\/p>\n<p>Answer:<br \/>\n&#8211; 56 \u00f7 (- 8) = 7<\/p>\n<p>Explanation:<br \/>\n&#8211; 56 \u00f7 (- 8)<br \/>\nThe quotient of two negative integers is positive<br \/>\n56 \u00f7 8 = 7<\/p>\n<p>Question 12.<br \/>\nThe quantities and are proportional. What is the missing value in the table?<br \/>\n<img loading=\"lazy\" class=\"alignnone size-full wp-image-30500\" src=\"https:\/\/ccssmathanswers.com\/wp-content\/uploads\/2021\/01\/Big-Ideas-Math-Solutions-Grade-7-Chapter-5-Ratios-and-Proportions-cp-12.png\" alt=\"Big Ideas Math Solutions Grade 7 Chapter 5 Ratios and Proportions cp 12\" width=\"120\" height=\"197\" \/><br \/>\nA. 38<br \/>\nB. 42<br \/>\nC. 46<br \/>\nD. 56<\/p>\n<p>Answer:<br \/>\nD. 56<\/p>\n<p>Explanation:<br \/>\nTwo quantities are proportional<br \/>\n5\/7x = 4<br \/>\nx = 4 (7\/5)<br \/>\nx = 28\/5<br \/>\nMissing value = 10(28\/5) = 2(28) = 56<\/p>\n<p>Question 13.<br \/>\nTo begin a board game, you place a playing piece at START. On your first three turns, you move ahead 8 spaces, move back 3 spaces, and then move ahead 2 spaces. How many spaces are you from START?<br \/>\nF. 2<br \/>\nG. 3<br \/>\nH. 7<br \/>\nI. 13<\/p>\n<p>Answer:<br \/>\nH. 7<\/p>\n<p>Explanation:<br \/>\nFor the first three turns, you move ahead 8 spaces and move back 3 spaces<br \/>\n= 8 &#8211; 3 = 5<br \/>\nmove ahead 2 spaces<br \/>\n5 + 2 = 7<\/p>\n<p><em>Final Words:<\/em><\/p>\n<p>Big Ideas Math Answers Grade 7 Chapter 5 Ratios and Proportions detailed pdf is here. Check Big Ideas Math Book Grade 7 Chapter 5 Ratios and proportions and make the learning easy. Therefore collect Big Ideas Math 7th Grade Chapter 5 Ratios and Proportions Answer Key and complete your preparation. Stay tuned to our website to know the trending information regarding Ratios and Proportions. Bookmark our page to know all the details of Grade 7. We wish all the best for all students.<\/p>\n","protected":false},"excerpt":{"rendered":"<p>For the best practice, the Big Ideas Math Grade 7 Chapter 5 Ratios and Proportions Answer Sheet is given here. A detailed explanation of solutions prepared by great math experts which are included in the below sections. 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