{"id":26616,"date":"2023-01-08T12:49:42","date_gmt":"2023-01-08T07:19:42","guid":{"rendered":"https:\/\/ccssanswers.com\/?p=26616"},"modified":"2023-01-09T09:43:56","modified_gmt":"2023-01-09T04:13:56","slug":"big-ideas-math-answers-grade-6-chapter-3","status":"publish","type":"post","link":"https:\/\/ccssanswers.com\/big-ideas-math-answers-grade-6-chapter-3\/","title":{"rendered":"Big Ideas Math Answers Grade 6 Chapter 3 Ratios and Rates"},"content":{"rendered":"<p>Free solutions to Big Ideas Math Grade 6 Chapter 3 Ratios and Rates are available here. So, the pupils those who are searching the Big Ideas Math Grade 6 Chapter 3 Ratios and Rates Solution Key can get them on this page. As per your convenience we have provided the solutions in the pdf format. So, Download <a href=\"https:\/\/ccssanswers.com\/big-ideas-math-answers-grade-6\/\">Big Ideas Math Answers Grade 6<\/a> Chapter 3 Ratios and Rates pdf for free of cost.<\/p>\n<h2>Big Ideas Math Book 6th Grade Answer Key Chapter 3 Ratios and Rates<\/h2>\n<p>The list of topics covered in this chapter are Ratios, Using Tape Diagrams, Ratio tables, Graphing Ratio Relationships and so on.\u00a0 Check out the topics and practice the problems number of times and score highest marks in the exams. 6th Grade Ratios and Rates Solution Key helps the students to complete the homework or assignment in time.<\/p>\n<p><strong>Performance Task<\/strong><\/p>\n<ul>\n<li><a href=\"#Ratios_and_Rates_STEAM_Video\/Performance_Task\">Ratios and Rates STEAM Video\/Performance Task<\/a><\/li>\n<li><a href=\"#Ratios_and_Rates_Getting_Ready_for_Chapter\">Ratios and Rates Getting Ready for Chapter<\/a><\/li>\n<\/ul>\n<p><strong>Lesson: 1 Ratios<\/strong><\/p>\n<ul>\n<li><a href=\"#Lesson_3.1_Ratios\">Lesson 3.1 Ratios<\/a><\/li>\n<li><a href=\"#Ratios_Homework_&amp;_Practice_3.1\">Ratios Homework &amp; Practice 3.1<\/a><\/li>\n<\/ul>\n<p><strong>Lesson: 2 Using Tape Diagrams<\/strong><\/p>\n<ul>\n<li><a href=\"#Lesson_3.2_Using_Tape_Diagrams\">Lesson 3.2 Using Tape Diagrams<\/a><\/li>\n<li><a href=\"#Using_Tape_Diagrams_Homework_&amp;_Practice_3.2\">Using Tape Diagrams Homework &amp; Practice 3.2<\/a><\/li>\n<\/ul>\n<p><strong>Lesson: 3 Using Ratio Tables<\/strong><\/p>\n<ul>\n<li><a href=\"#Lesson_3.3_Using_Ratio_Tables\">Lesson 3.3 Using Ratio Tables<\/a><\/li>\n<li><a href=\"#Using_Ratio_Tables_Homework_&amp;_Practice_3.3\">Using Ratio Tables Homework &amp; Practice 3.3<\/a><\/li>\n<\/ul>\n<p><strong>Lesson: 4 Graphing Ratio Relationships<\/strong><\/p>\n<ul>\n<li><a href=\"#Lesson_3.4_Graphing_Ratio_Relationships\">Lesson 3.4 Graphing Ratio Relationships<\/a><\/li>\n<li><a href=\"#Graphing_Ratio_Relationships_Homework_&amp;_Practice_3.4\">Graphing Ratio Relationships Homework &amp; Practice 3.4<\/a><\/li>\n<\/ul>\n<p><strong>Lesson: 5 Rates and Unit Rates<\/strong><\/p>\n<ul>\n<li><a href=\"#Lesson_3.5_Rates_and_Unit_Rates\">Lesson 3.5 Rates and Unit Rates<\/a><\/li>\n<li><a href=\"#Rates_and_Unit_Rates_Homework_&amp;_Practice_3.5\">Rates and Unit Rates Homework &amp; Practice 3.5<\/a><\/li>\n<\/ul>\n<p><strong>Lesson: 6 Converting Measures<\/strong><\/p>\n<ul>\n<li><a href=\"#Lesson_3.6_Converting_Measures\">Lesson 3.6 Converting Measures<\/a><\/li>\n<li><a href=\"#Converting_Measures_Homework_&amp;_Practice_3.6\">Converting Measures Homework &amp; Practice 3.6<\/a><\/li>\n<\/ul>\n<p><strong>Performance Task<\/strong><\/p>\n<ul>\n<li><a href=\"#Ratios_and_Rates_Connecting_Concepts\">Ratios and Rates Connecting Concepts<\/a><\/li>\n<li><a href=\"#Ratios_and_Rates_Chapter_Review\">Ratios and Rates Chapter Review<\/a><\/li>\n<li><a href=\"#Ratios_and_Rates_Practice_Test\">Ratios and Rates Practice Test<\/a><\/li>\n<li><a href=\"#Ratios_and_Rates_Cumulative_Practice\">Ratios and Rates Cumulative Practice<\/a><\/li>\n<\/ul>\n<h3><a id=\"Ratios_and_Rates_STEAM_Video\/Performance_Task\"><\/a>Ratios and Rates STEAM Video\/Performance Task<\/h3>\n<p><strong>STEAM Video<\/strong><\/p>\n<p>Human Circulatory System<br \/>\nWatch the STEAM Video \u201cHuman Circulatory System.\u201d Then answer the following questions.<br \/>\n<img decoding=\"async\" loading=\"lazy\" class=\"alignnone size-full wp-image-26617\" src=\"https:\/\/ccssanswers.com\/wp-content\/uploads\/2021\/01\/Big-Ideas-Math-Answer-Key-Grade-6-Chapter-3-Ratios-and-Rates-1.png\" alt=\"Big Ideas Math Answer Key Grade 6 Chapter 3 Ratios and Rates 1\" width=\"170\" height=\"338\" srcset=\"https:\/\/ccssanswers.com\/wp-content\/uploads\/2021\/01\/Big-Ideas-Math-Answer-Key-Grade-6-Chapter-3-Ratios-and-Rates-1.png 170w, https:\/\/ccssanswers.com\/wp-content\/uploads\/2021\/01\/Big-Ideas-Math-Answer-Key-Grade-6-Chapter-3-Ratios-and-Rates-1-151x300.png 151w\" sizes=\"(max-width: 170px) 100vw, 170px\" \/><br \/>\n1. Enid says the heart pumps about 5 liters of blood each minute. How can you find the amount of blood the heart pumps for any given number of minutes?<\/p>\n<p>Answer:<br \/>\nEnid says the heart pumps about 5 liters of blood each minute.<br \/>\n5 \u00d7 1 = 5 liters<br \/>\nWe have multiply number of minutes with 5<\/p>\n<p>2. Explain how you can estimate the amount of blood your heart pumps in one heart beat.<\/p>\n<p>Answer: Multiply your body surface area by the cardiac index to determine the liters of blood pumped by your heart in one minute.<\/p>\n<p>3. The table shows the amounts of blood contained in several different types of blood vessels. How can you make meaningful comparisons of the amounts?<br \/>\n<img decoding=\"async\" loading=\"lazy\" class=\"alignnone size-full wp-image-26618\" src=\"https:\/\/ccssanswers.com\/wp-content\/uploads\/2021\/01\/Big-Ideas-Math-Answer-Key-Grade-6-Chapter-3-Ratios-and-Rates-2.png\" alt=\"Big Ideas Math Answer Key Grade 6 Chapter 3 Ratios and Rates 2\" width=\"247\" height=\"167\" \/><\/p>\n<p>Answer:<br \/>\n1 liter = 1000 ml<br \/>\nThe volume of Aorta and large arteries is 300 ml<br \/>\n300\/1000 = 0.3 = 30%<br \/>\nSmall arteries = 0.4L<br \/>\n0.4 \u00d7 1000 = 400ml = 40%<br \/>\n40% of blood contained in small arteries<br \/>\nSmall veins = 2.43qt<br \/>\n2.43 qt = 2.299L<br \/>\nLarge Veins = 0.24 gal<br \/>\n0.24 gal = 0.908L<\/p>\n<p><strong>Performance Task<\/strong><\/p>\n<p>Oops! Unit Conversion Mistakes<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 shown unit conversion mistakes in the following real-life situations.<br \/>\n<img decoding=\"async\" loading=\"lazy\" class=\"alignnone size-full wp-image-26644\" src=\"https:\/\/ccssanswers.com\/wp-content\/uploads\/2021\/01\/Big-Ideas-Math-Answer-Key-Grade-6-Chapter-3-Ratios-and-Rates-3.png\" alt=\"Big Ideas Math Answer Key Grade 6 Chapter 3 Ratios and Rates 3\" width=\"391\" height=\"329\" srcset=\"https:\/\/ccssanswers.com\/wp-content\/uploads\/2021\/01\/Big-Ideas-Math-Answer-Key-Grade-6-Chapter-3-Ratios-and-Rates-3.png 391w, https:\/\/ccssanswers.com\/wp-content\/uploads\/2021\/01\/Big-Ideas-Math-Answer-Key-Grade-6-Chapter-3-Ratios-and-Rates-3-300x252.png 300w\" sizes=\"(max-width: 391px) 100vw, 391px\" \/><br \/>\nIn each situation, you will analyze and correct the mistake in the unit conversion. How accurate must conversions be in real-life situations?<\/p>\n<h3><a id=\"Ratios_and_Rates_Getting_Ready_for_Chapter\"><\/a>Ratios and Rates Getting Ready for Chapter<\/h3>\n<p><strong>Chapter Exploration<\/strong><\/p>\n<p>Work with a partner. What portion of the rectangle is red? How did you write your answer?<br \/>\nQuestion 1.<br \/>\n<img decoding=\"async\" loading=\"lazy\" class=\"alignnone size-full wp-image-26645\" src=\"https:\/\/ccssanswers.com\/wp-content\/uploads\/2021\/01\/Big-Ideas-Math-Answer-Key-Grade-6-Chapter-3-Ratios-and-Rates-4.png\" alt=\"Big Ideas Math Answer Key Grade 6 Chapter 3 Ratios and Rates 4\" width=\"83\" height=\"74\" \/><br \/>\nAnswer: 4 : 12<\/p>\n<p>Explanation:<br \/>\nCount the red portion shown in the image out of 12 potions<br \/>\nwhen we count we get Four-twelfths of the portion of the rectangle is red<\/p>\n<p>Question 2.<br \/>\n<img decoding=\"async\" loading=\"lazy\" class=\"alignnone size-full wp-image-26646\" src=\"https:\/\/ccssanswers.com\/wp-content\/uploads\/2021\/01\/Big-Ideas-Math-Answer-Key-Grade-6-Chapter-3-Ratios-and-Rates-5.png\" alt=\"Big Ideas Math Answer Key Grade 6 Chapter 3 Ratios and Rates 5\" width=\"129\" height=\"67\" \/><br \/>\nAnswer: 6 : 18<\/p>\n<p>Explanation:<br \/>\nCount the red portion shown in the image out of 18 potion<br \/>\nwhen we count we get Six out of eighteen of the portion of the rectangle is red<\/p>\n<p>Question 3.<br \/>\n<img decoding=\"async\" loading=\"lazy\" class=\"alignnone size-full wp-image-26647\" src=\"https:\/\/ccssanswers.com\/wp-content\/uploads\/2021\/01\/Big-Ideas-Math-Answer-Key-Grade-6-Chapter-3-Ratios-and-Rates-6.png\" alt=\"Big Ideas Math Answer Key Grade 6 Chapter 3 Ratios and Rates 6\" width=\"69\" height=\"70\" \/><br \/>\nAnswer: 5 : 9<\/p>\n<p>Explanation:<br \/>\nCount the red portion shown in the image out of 9 potion<br \/>\nwhen we count we get Five out of nine of the portion of the Square is red<\/p>\n<p>Question 4.<br \/>\n<img decoding=\"async\" loading=\"lazy\" class=\"alignnone size-full wp-image-26648\" src=\"https:\/\/ccssanswers.com\/wp-content\/uploads\/2021\/01\/Big-Ideas-Math-Answer-Key-Grade-6-Chapter-3-Ratios-and-Rates-7.png\" alt=\"Big Ideas Math Answer Key Grade 6 Chapter 3 Ratios and Rates 7\" width=\"68\" height=\"72\" \/><br \/>\nAnswer: 4\u00a0: 9<\/p>\n<p>Explanation:<br \/>\nCount the red portion shown in the image out of 9 potion<br \/>\nwhen we count we get four out of nine of the portion of the Square is red<\/p>\n<p>Question 5.<br \/>\n<img decoding=\"async\" loading=\"lazy\" class=\"alignnone size-full wp-image-26649\" src=\"https:\/\/ccssanswers.com\/wp-content\/uploads\/2021\/01\/Big-Ideas-Math-Answer-Key-Grade-6-Chapter-3-Ratios-and-Rates-8.png\" alt=\"Big Ideas Math Answer Key Grade 6 Chapter 3 Ratios and Rates 8\" width=\"70\" height=\"67\" \/><br \/>\nAnswer: 6\u00a0: 9<\/p>\n<p>Explanation:<br \/>\nCount the red portion shown in the image out of 9 potion<br \/>\nwhen we count we get six out of nine of the portion of the Square is red<\/p>\n<p>Question 6.<br \/>\n<img decoding=\"async\" loading=\"lazy\" class=\"alignnone size-full wp-image-26650\" src=\"https:\/\/ccssanswers.com\/wp-content\/uploads\/2021\/01\/Big-Ideas-Math-Answer-Key-Grade-6-Chapter-3-Ratios-and-Rates-9.png\" alt=\"Big Ideas Math Answer Key Grade 6 Chapter 3 Ratios and Rates 9\" width=\"125\" height=\"85\" \/><br \/>\nAnswer: 16 : 24<\/p>\n<p>Explanation:<br \/>\nCount the red portion shown in the image out of 24 potion<br \/>\nwhen we count we get sixteen out of twenty-four of the portion of the Rectangle is red<\/p>\n<p>Question 7.<br \/>\n<img decoding=\"async\" loading=\"lazy\" class=\"alignnone size-full wp-image-26651\" src=\"https:\/\/ccssanswers.com\/wp-content\/uploads\/2021\/01\/Big-Ideas-Math-Answer-Key-Grade-6-Chapter-3-Ratios-and-Rates-10.png\" alt=\"Big Ideas Math Answer Key Grade 6 Chapter 3 Ratios and Rates 10\" width=\"129\" height=\"54\" \/><br \/>\nAnswer: 4 : 12<\/p>\n<p>Explanation:<br \/>\nCount the red portion shown in the image out of 12 potion<br \/>\nwhen we count we get four out of twelve of the portion of the Rectangle is red<\/p>\n<p>Question 8.<br \/>\n<img decoding=\"async\" loading=\"lazy\" class=\"alignnone size-full wp-image-26652\" src=\"https:\/\/ccssanswers.com\/wp-content\/uploads\/2021\/01\/Big-Ideas-Math-Answer-Key-Grade-6-Chapter-3-Ratios-and-Rates-11.png\" alt=\"Big Ideas Math Answer Key Grade 6 Chapter 3 Ratios and Rates 11\" width=\"126\" height=\"49\" \/><br \/>\nAnswer: 5 : 12<\/p>\n<p>Explanation:<br \/>\nCount the red portion shown in the image out of 12 potion<br \/>\nwhen we count we get five out of twelve of the portion of the Rectangle is red<\/p>\n<p>Question 9.<br \/>\n<img decoding=\"async\" loading=\"lazy\" class=\"alignnone size-full wp-image-26653\" src=\"https:\/\/ccssanswers.com\/wp-content\/uploads\/2021\/01\/Big-Ideas-Math-Answer-Key-Grade-6-Chapter-3-Ratios-and-Rates-12.png\" alt=\"Big Ideas Math Answer Key Grade 6 Chapter 3 Ratios and Rates 12\" width=\"69\" height=\"50\" \/><br \/>\nAnswer: 6 : 6<\/p>\n<p>Explanation:<br \/>\nCount the red portion shown in the image out of 6 potion<br \/>\nwhen we count we get six out of six of the portion of the Rectangle is red<\/p>\n<p>Question 10.<br \/>\nWork with a partner. In Exercises 1\u20139, which of the rectangles have the same portion of red tiles? Explain your reasoning.<br \/>\nAnswer: 6 : 6 portion of the rectangles have the same portion of red tiles<br \/>\n<img decoding=\"async\" loading=\"lazy\" class=\"alignnone size-full wp-image-28578\" src=\"https:\/\/ccssanswers.com\/wp-content\/uploads\/2021\/01\/Big-Ideas-Math-Answer-Key-Grade-6-Chapter-3-Ratios-and-Rates-12-1.png\" alt=\"Big-Ideas-Math-Answer-Key-Grade-6-Chapter-3-Ratios-and-Rates-12\" width=\"69\" height=\"50\" \/><br \/>\nExplanation:<br \/>\nCount the red portion shown in the image out of 6 potions<br \/>\nwhen we count we get six out of six of the portion of the Rectangle is red<\/p>\n<p>Work with a partner. Use square color tiles to build two different-sized rectangles that represent the description.<br \/>\n<img decoding=\"async\" loading=\"lazy\" class=\"alignnone size-full wp-image-26654\" src=\"https:\/\/ccssanswers.com\/wp-content\/uploads\/2021\/01\/Big-Ideas-Math-Answer-Key-Grade-6-Chapter-3-Ratios-and-Rates-13.png\" alt=\"Big Ideas Math Answer Key Grade 6 Chapter 3 Ratios and Rates 13\" width=\"229\" height=\"169\" \/><br \/>\nQuestion 11.<br \/>\nFive-sixths of the tiles are blue.<br \/>\nAnswer: 5 : 6<br \/>\n<img decoding=\"async\" loading=\"lazy\" class=\"alignnone size-full wp-image-28579\" src=\"https:\/\/ccssanswers.com\/wp-content\/uploads\/2021\/01\/Big-Ideas-Math-Answer-Key-Grade-6-Chapter-3-Ratios-and-Rates-11-1.png\" alt=\"Big-Ideas-Math-Answer-Key-Grade-6-Chapter-3-Ratios-and-Rates-11\" width=\"134\" height=\"95\" \/><\/p>\n<p>Explanation: a ratio indicates how many times one number contains another.<br \/>\nso 5 : 6 of the tiles are blue.<\/p>\n<p>Question 12.<br \/>\nThree-fourths of the tiles are yellow.<br \/>\nAnswer: 3 : 4<br \/>\n<img decoding=\"async\" loading=\"lazy\" class=\"alignnone size-full wp-image-28580\" src=\"https:\/\/ccssanswers.com\/wp-content\/uploads\/2021\/01\/Big-Ideas-Math-Answer-Key-Grade-6-Chapter-3-Ratios-and-Rates-11-2.png\" alt=\"Big-Ideas-Math-Answer-Key-Grade-6-Chapter-3-Ratios-and-Rates-12\" width=\"134\" height=\"95\" \/><\/p>\n<p>Explanation: a ratio indicates how many times one number contains another.<br \/>\nso 3 : 4 of the tiles are yellow<\/p>\n<p>Question 13.<br \/>\nFour-fifths of the tiles are green.<br \/>\nAnswer: 4 : 5<br \/>\n<img decoding=\"async\" loading=\"lazy\" class=\"alignnone size-full wp-image-28581\" src=\"https:\/\/ccssanswers.com\/wp-content\/uploads\/2021\/01\/Big-Ideas-Math-Answer-Key-Grade-6-Chapter-3-Ratios-and-Rates-11-3.png\" alt=\"Big-Ideas-Math-Answer-Key-Grade-6-Chapter-3-Ratios-and-Rates-13\" width=\"134\" height=\"95\" \/><\/p>\n<p>Explanation: a ratio indicates how many times one number contains another.<br \/>\nso 4 : 5 of the tiles are green<\/p>\n<p>Question 14.<br \/>\nFive-sevenths of the tiles are red.<br \/>\nAnswer: 5 : 7<br \/>\n<img decoding=\"async\" loading=\"lazy\" class=\"alignnone size-full wp-image-28583\" src=\"https:\/\/ccssanswers.com\/wp-content\/uploads\/2021\/01\/Big-Ideas-Math-Answer-Key-Grade-6-Chapter-3-Ratios-and-Rates-14.png\" alt=\"Big-Ideas-Math-Answer-Key-Grade-6-Chapter-3-Ratios-and-Rates-14\" width=\"177\" height=\"95\" \/><\/p>\n<p>Explanation: a ratio indicates how many times one number contains another.<br \/>\nso 5 : 7 of the tiles are red<\/p>\n<p>Question 15.<br \/>\n<strong>MODELING REAL LIFE<\/strong><br \/>\nWork with a partner. The soccer committee has 8 girls and 6 boys. The tennis committee has 9 girls and 8 boys. A friend tells you that the tennis committee has a greater portion of girls than the soccer committee. Is your friend correct? Explain. If not, how many boys could you add to the soccer committee so that your friend is correct?<br \/>\nAnswer:<br \/>\nGiven,<br \/>\nThe soccer committee has 8 girls and 6 boys. The tennis committee has 9 girls and 8 boys.<br \/>\nThe ratio of soccer committee is 8:6<br \/>\nThe ratio of tennis committee is 9:8<br \/>\nCompare both the ratios<br \/>\n8 &lt; 9<br \/>\nThus number of girls in tennis committee are more than soccer committee.<br \/>\nThus we can say that your friend is correct.<\/p>\n<p><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 \/>\nratio<br \/>\nrate<br \/>\nequivalent rates<br \/>\nequivalent ratios<br \/>\nunit rate<\/p>\n<p>Answer:<br \/>\nRatio &#8211; a ratio indicates how many times one number contains another.<br \/>\nRate &#8211; a measure, quantity, or frequency, typically one measured against another quantity or measure.<br \/>\nEquivalent rates &#8211; Equivalent rates are rates that are equal.<br \/>\nEquivalent ratio &#8211; Two ratios that have the same value are called equivalent ratios.<br \/>\nUnit Rate &#8211; A unit rate is a rate with 1 in the denominator.<\/p>\n<h3><a id=\"Lesson_3.1_Ratios\"><\/a>Lesson 3.1 Ratios<\/h3>\n<p>A ratio is a comparison of two quantities. Consider two quantities a and b. The ratio a : b indicates that there are a units of the first quantity for every b units of the second quantity.<\/p>\n<p><strong>EXPLORATION 1<\/strong><\/p>\n<p>Writing Ratios<br \/>\nWork with a partner. A science class has two times as many girls as it has boys.<br \/>\n<img decoding=\"async\" loading=\"lazy\" class=\"alignnone size-full wp-image-26619\" src=\"https:\/\/ccssanswers.com\/wp-content\/uploads\/2021\/01\/Big-Ideas-Math-Answer-Key-Grade-6-Chapter-3-Ratios-and-Rates-3.1-1.png\" alt=\"Big Ideas Math Answer Key Grade 6 Chapter 3 Ratios and Rates 3.1 1\" width=\"362\" height=\"248\" srcset=\"https:\/\/ccssanswers.com\/wp-content\/uploads\/2021\/01\/Big-Ideas-Math-Answer-Key-Grade-6-Chapter-3-Ratios-and-Rates-3.1-1.png 362w, https:\/\/ccssanswers.com\/wp-content\/uploads\/2021\/01\/Big-Ideas-Math-Answer-Key-Grade-6-Chapter-3-Ratios-and-Rates-3.1-1-300x206.png 300w\" sizes=\"(max-width: 362px) 100vw, 362px\" \/><br \/>\na. Discuss possible numbers of boys and girls in the science class.<\/p>\n<p>Answer: 24 girls and 12 boys in the science class<br \/>\nb. What comparisons can you make between your class and the science class? Can you determine which class has more girls? more boys? Explain your reasoning.<\/p>\n<p>Answer:<br \/>\nNumber of girls and boys in your class are 42.<br \/>\nNumber of girls = 22<br \/>\nNumber of boys = 20<br \/>\nCompare the number of girls in your class and science class<br \/>\n22: 24<br \/>\nThus there are more girls in science class.<br \/>\n20:12<br \/>\nThus there are more boys in your class.<\/p>\n<p>c. Write three ratios that you observe in your classroom. Describe what each ratio represents.<br \/>\nAnswer:<br \/>\n36:42 &#8211; This represents number of students in science class and your class<br \/>\n22:24 &#8211; This represents number of girls in science class and your class<br \/>\n20:12 &#8211; This represents number of boys in science class and your class<\/p>\n<p><strong>EXPLORATION 2<\/strong><\/p>\n<p>Using Ratios in a Recipe<br \/>\nWork with a partner. The ratio of iced tea to lemonade in a recipe is 3 : 1. You begin by combining 3 cups of iced tea with 1 cup of lemonade.<br \/>\n<img decoding=\"async\" loading=\"lazy\" class=\"alignnone size-full wp-image-26620\" src=\"https:\/\/ccssanswers.com\/wp-content\/uploads\/2021\/01\/Big-Ideas-Math-Answer-Key-Grade-6-Chapter-3-Ratios-and-Rates-3.1-2.png\" alt=\"Big Ideas Math Answer Key Grade 6 Chapter 3 Ratios and Rates 3.1 2\" width=\"446\" height=\"202\" srcset=\"https:\/\/ccssanswers.com\/wp-content\/uploads\/2021\/01\/Big-Ideas-Math-Answer-Key-Grade-6-Chapter-3-Ratios-and-Rates-3.1-2.png 446w, https:\/\/ccssanswers.com\/wp-content\/uploads\/2021\/01\/Big-Ideas-Math-Answer-Key-Grade-6-Chapter-3-Ratios-and-Rates-3.1-2-300x136.png 300w\" sizes=\"(max-width: 446px) 100vw, 446px\" \/><br \/>\na. You add 1 cup of iced tea and 1 cup of lemonade to the mixture. Does this change the taste of the mixture?<\/p>\n<p>Answer:<br \/>\n3 + 1: 1 + 1<br \/>\n4:2<br \/>\nNo it will not change the taste of the mixture.<br \/>\nb. Describe how you can make larger amounts without changing the taste.<br \/>\nAnswer: If the number of portions and the size of each portion change, you will have to find a conversion factor using a similar approach.<\/p>\n<p><img decoding=\"async\" loading=\"lazy\" class=\"alignnone size-full wp-image-26621\" src=\"https:\/\/ccssanswers.com\/wp-content\/uploads\/2021\/01\/Big-Ideas-Math-Answer-Key-Grade-6-Chapter-3-Ratios-and-Rates-3.1-3.png\" alt=\"Big Ideas Math Answer Key Grade 6 Chapter 3 Ratios and Rates 3.1 3\" width=\"185\" height=\"97\" \/><\/p>\n<p><strong>Try It<\/strong><\/p>\n<p><strong>Write the indicated ratio using the coins in Example 1.<\/strong><br \/>\nQuestion 1.<br \/>\ndimes to pennies<br \/>\nAnswer:\u00a0 1 : 10<\/p>\n<p>Explanation:<br \/>\nwe have to convert the coins from dimes to pennies.<br \/>\nwe know that A dime is worth 10 pennies.<br \/>\nso the ratio is 1 : 10<\/p>\n<p>Question 2.<br \/>\nquarters to the total number of coins.<br \/>\nAnswer: 25 : 40<\/p>\n<p>The number \\(\\frac{a}{b}\\) associated with the ratio a : b is called the value of the ratio. It describes the multiplicative relationship between the quantities in a ratio.<\/p>\n<p>Question 3.<br \/>\nAn elephant sanctuary contains adult and baby elephants. The ratio of adult elephants to baby elephants is 5 : 1. Find and interpret the value of the ratio.<br \/>\n<img decoding=\"async\" loading=\"lazy\" class=\"alignnone size-full wp-image-26622\" src=\"https:\/\/ccssanswers.com\/wp-content\/uploads\/2021\/01\/Big-Ideas-Math-Answer-Key-Grade-6-Chapter-3-Ratios-and-Rates-3.1-4.png\" alt=\"Big Ideas Math Answer Key Grade 6 Chapter 3 Ratios and Rates 3.1 4\" width=\"195\" height=\"262\" \/><br \/>\nAnswer: five adult elephants and one baby elephant<\/p>\n<p><strong>Determine whether the ratios are equivalent.<\/strong><br \/>\nQuestion 4.<br \/>\n1 : 1 and 6 : 6<br \/>\nAnswer:\u00a0 The ratios are Equivalent.<\/p>\n<p>Explanation: Two ratios that have the same value are called equivalent ratios. To find an equivalent ratio, multiply or divide both quantities by the same number. It is the same process as finding equivalent fractions. Multiply both the numerator and denominator by 2.<br \/>\nHence the ratios 1 : 1 and 6 : 6 are Equivalent<\/p>\n<p>Question 5.<br \/>\n1 : 2 and 3 : 4<br \/>\nAnswer: The ratios are Not Equivalent.<\/p>\n<p>Explanation: Two ratios that have the same value are called equivalent ratios. To find an equivalent ratio, multiply or divide both quantities by the same number. It is the same process as finding equivalent fractions. Multiply both the numerator and denominator by 2.<br \/>\nhence the 1 : 2 and 3 : 4 The ratios are Not Equivalent.<\/p>\n<p>Question 6.<br \/>\n8 : 3 and 6 : 16<br \/>\nAnswer: The ratios are Not Equivalent.<\/p>\n<p>Explanation: Two ratios that have the same value are called equivalent ratios. To find an equivalent ratio, multiply or divide both quantities by the same number. It is the same process as finding equivalent fractions. Multiply both the numerator and denominator by 2.<br \/>\nhence the 8 : 3 and 6 : 16 ratios are Not Equivalent.<\/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>WRITING AND INTERPRETING RATIOS<\/strong> Write the ratio. Then find and interpret the value of the ratio.<br \/>\n<img decoding=\"async\" loading=\"lazy\" class=\"alignnone size-full wp-image-26623\" src=\"https:\/\/ccssanswers.com\/wp-content\/uploads\/2021\/01\/Big-Ideas-Math-Answer-Key-Grade-6-Chapter-3-Ratios-and-Rates-3.1-5.png\" alt=\"Big Ideas Math Answer Key Grade 6 Chapter 3 Ratios and Rates 3.1 5\" width=\"187\" height=\"212\" \/><br \/>\nQuestion 7.<br \/>\nsharks to dolphins<br \/>\nAnswer: 4 : 5<\/p>\n<p>Explanation: a ratio indicates how many times one number contains another.<br \/>\nso 4 : 5 of sharks to dolphins by observing the picture given<\/p>\n<p>Question 8.<br \/>\ndolphins : animals<br \/>\nAnswer: 5 : 0<\/p>\n<p>Explanation: a ratio indicates how many times one number contains another.<br \/>\nso 5 : 0 of dolphins: animals by observing the picture given<\/p>\n<p><strong>IDENTIFYING EQUIVALENT RATIOS<\/strong> Determine whether the ratios are equivalent. Explain your reasoning.<br \/>\nQuestion 9.<br \/>\n2 : 3 and 24 : 36<br \/>\nAnswer:\u00a0The ratios are Equivalent.<\/p>\n<p>Explanation: Two ratios that have the same value are called equivalent ratios. To find an equivalent ratio, multiply or divide both quantities by the same number. It is the same process as finding equivalent fractions. Multiply both the numerator and denominator by 2.<br \/>\nHence the ratios 2 : 3 and 24 : 36 are Equivalent<\/p>\n<p>Question 10.<br \/>\n5 : 7 and 20 : 28<br \/>\nAnswer: The ratios are Equivalent.<\/p>\n<p>Explanation: Two ratios that have the same value are called equivalent ratios. To find an equivalent ratio, multiply or divide both quantities by the same number. It is the same process as finding equivalent fractions. Multiply both the numerator and denominator by 2.<br \/>\nHence the ratios 5 : 7 and 20 : 28 are Equivalent<\/p>\n<p>Question 11.<br \/>\n3 : 10 and 9 : 25<br \/>\nAnswer: The ratios are Not Equivalent.<\/p>\n<p>Explanation: Two ratios that have the same value are called equivalent ratios. To find an equivalent ratio, multiply or divide both quantities by the same number. It is the same process as finding equivalent fractions. Multiply both the numerator and denominator by 2.<br \/>\nhence the 3 : 10 and 9 : 25 ratios are Not Equivalent.<\/p>\n<p>Question 12.<br \/>\n<strong>DIFFERENT WORDS, SAME QUESTION<\/strong> Which is different? Find \u201cboth\u201d answers.<br \/>\n<img decoding=\"async\" loading=\"lazy\" class=\"alignnone size-full wp-image-26624\" src=\"https:\/\/ccssanswers.com\/wp-content\/uploads\/2021\/01\/Big-Ideas-Math-Answer-Key-Grade-6-Chapter-3-Ratios-and-Rates-3.1-6.png\" alt=\"Big Ideas Math Answer Key Grade 6 Chapter 3 Ratios and Rates 3.1 6\" width=\"410\" height=\"119\" srcset=\"https:\/\/ccssanswers.com\/wp-content\/uploads\/2021\/01\/Big-Ideas-Math-Answer-Key-Grade-6-Chapter-3-Ratios-and-Rates-3.1-6.png 410w, https:\/\/ccssanswers.com\/wp-content\/uploads\/2021\/01\/Big-Ideas-Math-Answer-Key-Grade-6-Chapter-3-Ratios-and-Rates-3.1-6-300x87.png 300w\" sizes=\"(max-width: 410px) 100vw, 410px\" \/><br \/>\nAnswer:<br \/>\nOption B and C has same question but different words.<\/p>\n<p>Question 13.<br \/>\nThe ratio of wolves to cougars in a forest is 5 : 3. Find and interpret the value of the ratio.<br \/>\n<img decoding=\"async\" loading=\"lazy\" class=\"alignnone size-full wp-image-26625\" src=\"https:\/\/ccssanswers.com\/wp-content\/uploads\/2021\/01\/Big-Ideas-Math-Answer-Key-Grade-6-Chapter-3-Ratios-and-Rates-3.1-7.png\" alt=\"Big Ideas Math Answer Key Grade 6 Chapter 3 Ratios and Rates 3.1 7\" width=\"173\" height=\"205\" \/><br \/>\nAnswer: 5 to 3<\/p>\n<p>Explanation: A ratio takes one number and divides it into another number to determine a decimal that can later be converted to a percentage if desired The ratio of wolves to cougars in a forest is 5 : 3 so the interpret the value of the ratio is 5 to 3.<\/p>\n<p>Question 14.<br \/>\nYou are kayaking at a pace of 63 feet every 12 seconds. Your friend\u2019s pace is 21 feet every 3 seconds. Are you and your friend kayaking at the same pace? If not, who is faster?<br \/>\nAnswer: No, Me and my friend kayaking are not at the same pace. my friend is faster.<\/p>\n<p>Explanation:<br \/>\nGiven,<br \/>\nYou are kayaking at a pace of 63 feet every 12 seconds<br \/>\nYour friend\u2019s pace is 21 feet every 3 seconds<br \/>\nSo if I am kayaking at apace of 63 feet for every 12 seconds. then dividing 63 feet by 12 seconds we get 5.25 feet per second.<br \/>\nIn the same way friend\u2019s pace is 21 feet every 3 seconds. the dividing 21 feet by 3 second we get 7 feet per second.<br \/>\nHence me and my friend are not at the same pace.<br \/>\n7 feet per second my friend is faster than me<\/p>\n<p>Question 15.<br \/>\n<strong>DIG DEEPER!<\/strong><br \/>\nThe ratio of Jet Ski rentals to boat rentals at a store is 7 : 2. If the number of boat rentals doubles and the number of Jet Ski rentals stays the same, then the number of boat rentals is how many times the number of Jet Ski rentals?<br \/>\n<img decoding=\"async\" loading=\"lazy\" class=\"alignnone size-full wp-image-26626\" src=\"https:\/\/ccssanswers.com\/wp-content\/uploads\/2021\/01\/Big-Ideas-Math-Answer-Key-Grade-6-Chapter-3-Ratios-and-Rates-3.1-8.png\" alt=\"Big Ideas Math Answer Key Grade 6 Chapter 3 Ratios and Rates 3.1 8\" width=\"210\" height=\"188\" \/><br \/>\nAnswer: 0.571 times less than jet Ski rental<br \/>\nGiven,<br \/>\nhe ratio of Jet Ski rentals to boat rentals at a store is 7 : 2<br \/>\nIf the number of boat rentals doubles then we get 2 \u00d7 2 = 4 boats<br \/>\nthe number of Jet Ski rentals stays the same that is 7<br \/>\nthen the number of boat rentals is how many times the number of Jet Ski rental is divide 4 by 7 we get\u00a0 0.571 times less than jet Ski rental<\/p>\n<h3><a id=\"Ratios_Homework_&amp;_Practice_3.1\"><\/a>Ratios Homework &amp; Practice 3.1<\/h3>\n<p><strong>Review &amp; Refresh<\/strong><\/p>\n<p><strong>Divide. Check your answer.<\/strong><br \/>\nQuestion 1.<br \/>\n15.4 \u00f7 2.2<br \/>\nAnswer: 7<\/p>\n<p>Explanation:<br \/>\nGiven 15.4 \u00f7 2.2<br \/>\nso divide 15.4 by 2.2 we get 7<\/p>\n<p>Question 2.<br \/>\n56.07 \u00f7 8.9<br \/>\nAnswer: 6.9<\/p>\n<p>Explanation:<br \/>\nGiven 56.07 \u00f7 8.9<br \/>\nso divide 56.07 by 8.9 we get 6.9<\/p>\n<p>Question 3.<br \/>\n\\(\\sqrt [ 8.43 ]{ 12.645 } \\)<br \/>\nAnswer: 0.8164<\/p>\n<p>Explanation:<br \/>\nGiven \\(\\sqrt [ 8.43 ]{ 12.645 } \\)<br \/>\nso divide square root of 8.43 by 12.645 we get 0.8164<\/p>\n<p>Question 4.<br \/>\n\\(\\sqrt [ 11.6 ]{ 51.62 } \\)<br \/>\nAnswer: 0.474<\/p>\n<p>Explanation:<br \/>\nGiven \\(\\sqrt [ 11.6 ]{ 51.62 } \\)<br \/>\nso divide square root of 11.6 by 51.62 we get 0.474<\/p>\n<p>Find the value of the power.<br \/>\nQuestion 5.<br \/>\n8<sup>2<\/sup><br \/>\nAnswer: 8 \u00d7 8 = 64<\/p>\n<p>Explanation:<br \/>\ngiven 8<sup>2<\/sup><br \/>\nso by multiplying 8 \u00d7 8, we get 64<\/p>\n<p>Question 6.<br \/>\n1<sup>6<\/sup><br \/>\nAnswer: 1<\/p>\n<p>Explanation:<br \/>\ngiven 1 power of 6<br \/>\nso by multiplying 1 \u00d7 1 \u00d7 1 \u00d71 \u00d7 1 \u00d7 1 we get 1<\/p>\n<p>Question 7.<br \/>\n3<sup>4<\/sup><br \/>\nAnswer: 81<\/p>\n<p>Explanation:<br \/>\ngiven 3 power of 4<br \/>\nso by multiplying 3 \u00d7 3 \u00d7 3 \u00d7 3 we get 81<\/p>\n<p>Question 8.<br \/>\n2<sup>6<\/sup><br \/>\nAnswer: 64<\/p>\n<p>Explanation:<br \/>\ngiven 2 power of 6<br \/>\nso by multiplying 2 \u00d7 2 \u00d7 2 \u00d72 \u00d7 2 \u00d7 2 we get 64<\/p>\n<p>The Venn diagram shows the prime factors of two numbers. Identify the numbers. Then find the GCF and the LCM of the two numbers.<br \/>\nQuestion 9.<br \/>\n<img decoding=\"async\" loading=\"lazy\" class=\"alignnone size-full wp-image-26627\" src=\"https:\/\/ccssanswers.com\/wp-content\/uploads\/2021\/01\/Big-Ideas-Math-Answer-Key-Grade-6-Chapter-3-Ratios-and-Rates-3.1-9.png\" alt=\"Big Ideas Math Answer Key Grade 6 Chapter 3 Ratios and Rates 3.1 9\" width=\"192\" height=\"128\" \/><br \/>\nAnswer:<br \/>\nBy using the venn diagram we can find the prime factors of the two numbers.<br \/>\n2 \u00d7 2 \u00d7 3 \u00d7 3 \u00d7 3 \u00d7 5 = 540<br \/>\n2 \u00d7 3 \u00d7 3 \u00d7 5 \u00d7 5 = 450<br \/>\nLCM of 540 and 450 are<br \/>\nFind and list multiples of each number until the first common multiple is found. This is the lowest common multiple.<br \/>\nMultiples of 450:<br \/>\n450, 900, 1350, 1800, 2250, 2700, 3150, 3600<br \/>\nMultiples of 540:<br \/>\n540, 1080, 1620, 2160, 2700, 3240, 3780<br \/>\nTherefore,<br \/>\nLCM(450, 540) = 2700<br \/>\nGCF of 540 and 450 are<br \/>\nThe factors of 450 are: 1, 2, 3, 5, 6, 9, 10, 15, 18, 25, 30, 45, 50, 75, 90, 150, 225, 450<br \/>\nThe factors of 540 are: 1, 2, 3, 4, 5, 6, 9, 10, 12, 15, 18, 20, 27, 30, 36, 45, 54, 60, 90, 108, 135, 180, 270, 540<br \/>\nThen the greatest common factor is 90.<\/p>\n<p>Question 10.<br \/>\n<img decoding=\"async\" loading=\"lazy\" class=\"alignnone size-full wp-image-26628\" src=\"https:\/\/ccssanswers.com\/wp-content\/uploads\/2021\/01\/Big-Ideas-Math-Answer-Key-Grade-6-Chapter-3-Ratios-and-Rates-3.1-10.png\" alt=\"Big Ideas Math Answer Key Grade 6 Chapter 3 Ratios and Rates 3.1 10\" width=\"200\" height=\"118\" \/><br \/>\nAnswer:<br \/>\nBy using the venn diagram we can find the prime factors of the two numbers.<br \/>\n2 \u00d7 2 \u00d7 2 \u00d7 3 = 24<br \/>\n2 \u00d7 3 \u00d7 5 \u00d7 7 = 210<br \/>\nLCM of 24 and 210:<br \/>\nFind and list multiples of each number until the first common multiple is found. This is the lowest common multiple.<br \/>\nMultiples of 24:<br \/>\n24, 48, 72, 96, 120, 144, 168, 192, 216, 240, 264, 288, 312, 336, 360, 384, 408, 432, 456, 480, 504, 528, 552, 576, 600, 624, 648, 672, 696, 720, 744, 768, 792, 816, 840, 864, 888<br \/>\nMultiples of 210:<br \/>\n210, 420, 630, 840, 1050, 1260<br \/>\nTherefore,<br \/>\nLCM(24, 210) = 840<br \/>\nGCF of 24 and 210:<br \/>\nThe factors of 24 are: 1, 2, 3, 4, 6, 8, 12, 24<br \/>\nThe factors of 210 are: 1, 2, 3, 5, 6, 7, 10, 14, 15, 21, 30, 35, 42, 70, 105, 210<br \/>\nThen the greatest common factor is 6.<\/p>\n<p><strong>Concepts, Skills, &amp; Problem Solving<\/strong><\/p>\n<p><strong>USING RATIOS<\/strong> You mix the amounts of iced tea and lemonade shown. Describe how you can make larger amounts without changing the taste. (See Exploration 2, p. 107.)<br \/>\nQuestion 11.<br \/>\n<img decoding=\"async\" loading=\"lazy\" class=\"alignnone size-full wp-image-26629\" src=\"https:\/\/ccssanswers.com\/wp-content\/uploads\/2021\/01\/Big-Ideas-Math-Answer-Key-Grade-6-Chapter-3-Ratios-and-Rates-3.1-11.png\" alt=\"Big Ideas Math Answer Key Grade 6 Chapter 3 Ratios and Rates 3.1 11\" width=\"170\" height=\"85\" \/><br \/>\nAnswer:<br \/>\nThere are 2 iced tea and 1 lemonade.<br \/>\nSo, we can make 2:1 iced tea and lemonade without changing the taste.<\/p>\n<p>Question 12.<br \/>\n<img decoding=\"async\" loading=\"lazy\" class=\"alignnone size-full wp-image-26630\" src=\"https:\/\/ccssanswers.com\/wp-content\/uploads\/2021\/01\/Big-Ideas-Math-Answer-Key-Grade-6-Chapter-3-Ratios-and-Rates-3.1-12.png\" alt=\"Big Ideas Math Answer Key Grade 6 Chapter 3 Ratios and Rates 3.1 12\" width=\"240\" height=\"72\" \/><br \/>\nAnswer: 2:3<br \/>\nThere are 2 iced tea and 3 lemonade.<br \/>\nSo, we can make 2:3 iced tea and lemonade without changing the taste.<\/p>\n<p><strong>WRITING RATIOS<\/strong> Write the ratio.<br \/>\nQuestion 13.<br \/>\nfrogs to turtles<br \/>\n<img decoding=\"async\" loading=\"lazy\" class=\"alignnone size-full wp-image-26631\" src=\"https:\/\/ccssanswers.com\/wp-content\/uploads\/2021\/01\/Big-Ideas-Math-Answer-Key-Grade-6-Chapter-3-Ratios-and-Rates-3.1-13.png\" alt=\"Big Ideas Math Answer Key Grade 6 Chapter 3 Ratios and Rates 3.1 13\" width=\"210\" height=\"124\" \/><br \/>\nAnswer: 2 : 5<\/p>\n<p>Explanation: A ratio shows how much of one thing there is compared to another. Ratios are usually written in the form a:b.<br \/>\nThere are two frogs and five turtles in the shown image.<br \/>\nhence frogs to turtles is 2 : 5<\/p>\n<p>Question 14<br \/>\nbasketballs to soccer balls<br \/>\n<img decoding=\"async\" loading=\"lazy\" class=\"alignnone size-full wp-image-26632\" src=\"https:\/\/ccssanswers.com\/wp-content\/uploads\/2021\/01\/Big-Ideas-Math-Answer-Key-Grade-6-Chapter-3-Ratios-and-Rates-3.1-14.png\" alt=\"Big Ideas Math Answer Key Grade 6 Chapter 3 Ratios and Rates 3.1 14\" width=\"242\" height=\"107\" \/><br \/>\nAnswer: 6 : 4<\/p>\n<p>Explanation: A ratio shows how much of one thing there is compared to another. Ratios are usually written in the form a:b.<br \/>\nThere are six basketballs and four soccer balls in the shown image.<br \/>\nhence basketballs to soccer balls are 6 : 4<\/p>\n<p>Question 15.<br \/>\ncalculators : pencils<br \/>\n<img decoding=\"async\" loading=\"lazy\" class=\"alignnone size-full wp-image-26633\" src=\"https:\/\/ccssanswers.com\/wp-content\/uploads\/2021\/01\/Big-Ideas-Math-Answer-Key-Grade-6-Chapter-3-Ratios-and-Rates-3.1-15.png\" alt=\"Big Ideas Math Answer Key Grade 6 Chapter 3 Ratios and Rates 3.1 15\" width=\"218\" height=\"137\" \/><br \/>\nAnswer: 2 : 6<\/p>\n<p>Explanation: A ratio shows how much of one thing there is compared to another. Ratios are usually written in the form a:b.<br \/>\nThere are two calculators and six pencils in the shown image.<br \/>\nhence calculators : pencils are 2 : 6<\/p>\n<p>Question 16.<br \/>\nshirts : pants<br \/>\n<img decoding=\"async\" loading=\"lazy\" class=\"alignnone size-full wp-image-26634\" src=\"https:\/\/ccssanswers.com\/wp-content\/uploads\/2021\/01\/Big-Ideas-Math-Answer-Key-Grade-6-Chapter-3-Ratios-and-Rates-3.1-16.png\" alt=\"Big Ideas Math Answer Key Grade 6 Chapter 3 Ratios and Rates 3.1 16\" width=\"221\" height=\"133\" \/><br \/>\nAnswer: 3 : 6<\/p>\n<p>Explanation: A ratio shows how much of one thing there is compared to another. Ratios are usually written in the form a:b.<br \/>\nThere are three shirts and six pants in\u00a0the shown image.<br \/>\nhence shirts : pants are 3 : 6<\/p>\n<p>Question 17.<br \/>\n<strong>MODELING REAL LIFE<\/strong><br \/>\nTwelve of the 28 students in a class own a dog. What is the ratio of students who own a dog to students who do not?<br \/>\nAnswer: 12 : 28<\/p>\n<p>Explanation: A ratio shows how much of one thing there is compared to another. Ratios are usually written in the form a:b.<br \/>\nGiven Twelve of the 28 students in a class own a dog we get 12 students who have dogs out of 28 students<br \/>\nso in the students who do not have dogs are 28<br \/>\nhence the ratio of students who own a dog to students who do not is 12 : 28<\/p>\n<p>Question 18.<br \/>\n<strong>LOGIC<\/strong><br \/>\nName two things that you would like to have in a ratio of 5 : 1 but not in a ratio of 1 : 5. Explain your reasoning.<br \/>\nAnswer:<br \/>\n5 students in 1 class gives the ratio 5:1<br \/>\nIt is not possible to have 1 student in 5 classes.<\/p>\n<p><strong>OPEN-ENDED<\/strong> Describe a real-life relationship that can be represented by the ratio.<br \/>\nQuestion 19.<br \/>\n1 out of every 7<br \/>\nAnswer: 1 : 7<\/p>\n<p>Explanation: A ratio shows how much of one thing there is compared to another. Ratios are usually written in the form a:b.<br \/>\nhence 1 out of every 7 is 1 : 7<\/p>\n<p>Question 20.<br \/>\n5 to 26<br \/>\nAnswer: 5 : 26<\/p>\n<p>Explanation: A ratio shows how much of one thing there is compared to another. Ratios are usually written in the form a:b.<br \/>\nhence 5 to 26 7 is\u00a0 \u00a05 : 26<\/p>\n<p>Question 21.<br \/>\n2 per 5<br \/>\nAnswer: 2 : 5<\/p>\n<p>Explanation: A ratio shows how much of one thing there is compared to another. Ratios are usually written in the form a:b.<br \/>\nhence 2 per 5 is\u00a02 : 5<\/p>\n<p>Question 22.<br \/>\n7 : 1<br \/>\nAnswer:\u00a0 7\u00a0out of\u00a0 1<\/p>\n<p>Explanation: a ratio indicates how many times one number contains another.<br \/>\nHence 7 : 1 is 7\u00a0out of\u00a0 1<\/p>\n<p>Question 23.<br \/>\n<strong>MODELING REAL LIFE<\/strong><br \/>\nDuring a given month, the ratio of sunny days to rainy days is 4 : 1.<br \/>\n<img decoding=\"async\" loading=\"lazy\" class=\"alignnone size-full wp-image-26635\" src=\"https:\/\/ccssanswers.com\/wp-content\/uploads\/2021\/01\/Big-Ideas-Math-Answer-Key-Grade-6-Chapter-3-Ratios-and-Rates-3.1-17.png\" alt=\"Big Ideas Math Answer Key Grade 6 Chapter 3 Ratios and Rates 3.1 17\" width=\"289\" height=\"189\" \/><br \/>\na. Find and interpret the value of the ratio.<\/p>\n<p>Answer:<br \/>\nLet us consider the month be April<br \/>\nThe number of days in April are 30.<br \/>\n4:1<br \/>\n4 \u00d7 6 = 24 days<br \/>\n1 \u00d7 6 = 6 days<br \/>\n24 + 6 = 30 days<br \/>\nb. In another month, the number of sunny days is 5 times the number of rainy days. Write the ratio of sunny days to rainy days.<br \/>\nAnswer: 5:1<\/p>\n<p>Explanation:<br \/>\nGiven,<br \/>\nIn another month, the number of sunny days is 5 times the number of rainy days.<br \/>\nThe ratio of the sunny days to rainy days is 5 : 1<\/p>\n<p><strong>IDENTIFYING EQUIVALENT RATIOS<\/strong> Determine whether the ratios are equivalent.<br \/>\nQuestion 24.<br \/>\n2 : 3 and 4 : 9<\/p>\n<p>Answer: The ratios are Not Equivalent.<\/p>\n<p>Explanation: Two ratios that have the same value are called equivalent ratios. To find an equivalent ratio, multiply or divide both quantities by the same number. It is the same process as finding equivalent fractions. Multiply both the numerator and denominator by 2.<br \/>\nHence the ratios 2 : 3 and 4 : 9 are Not Equivalent<\/p>\n<p>Question 25.<br \/>\n3 : 8 and 9 : 24<\/p>\n<p>Answer: The ratios are Equivalent.<\/p>\n<p>Explanation: Two ratios that have the same value are called equivalent ratios. To find an equivalent ratio, multiply or divide both quantities by the same number. It is the same process as finding equivalent fractions. Multiply both the numerator and denominator by 2.<br \/>\nHence the ratios 3 : 8 and 9 : 24 are Equivalent<\/p>\n<p>Question 26.<br \/>\n1 : 4 and 2 : 6<\/p>\n<p>Answer: The ratios are Not Equivalent.<\/p>\n<p>Explanation: Two ratios that have the same value are called equivalent ratios. To find an equivalent ratio, multiply or divide both quantities by the same number. It is the same process as finding equivalent fractions. Multiply both the numerator and denominator by 2.<br \/>\nHence the ratios 1 : 4 and 2 : 6 are Not Equivalent<\/p>\n<p>Question 27.<br \/>\n5 : 3 and 15 : 12<br \/>\nAnswer: The ratios are Not Equivalent.<\/p>\n<p>Explanation: Two ratios that have the same value are called equivalent ratios. To find an equivalent ratio, multiply or divide both quantities by the same number. It is the same process as finding equivalent fractions. Multiply both the numerator and denominator by 2.<br \/>\nHence the ratios 5 : 3 and 15 : 12 are Not Equivalent<\/p>\n<p>Question 28.<br \/>\n6 : 10 and 12 : 20<br \/>\nAnswer: The ratios are Equivalent.<\/p>\n<p>Explanation: Two ratios that have the same value are called equivalent ratios. To find an equivalent ratio, multiply or divide both quantities by the same number. It is the same process as finding equivalent fractions. Multiply both the numerator and denominator by 2.<br \/>\nHence the ratios 6 : 10 and 12 : 20 are Equivalent.<\/p>\n<p>Question 29.<br \/>\n2 : 3 and 4 : 5<br \/>\nAnswer: The ratios are not Equivalent.<\/p>\n<p>Explanation: Two ratios that have the same value are called equivalent ratios. To find an equivalent ratio, multiply or divide both quantities by the same number. It is the same process as finding equivalent fractions. Multiply both the numerator and denominator by 2.<br \/>\nHence the ratios 2 : 3 and 4 : 5 are not Equivalent.<\/p>\n<p>Question 30.<br \/>\n28 : 32 and 7 : 8<br \/>\nAnswer: The ratios are Equivalent.<\/p>\n<p>Explanation: Two ratios that have the same value are called equivalent ratios. To find an equivalent ratio, multiply or divide both quantities by the same number. It is the same process as finding equivalent fractions. Multiply both the numerator and denominator by 2.<br \/>\nHence the ratios 28 : 32 and 7 : 8 are Equivalent.<\/p>\n<p>Question 31.<br \/>\n24 : 100 and 6 : 25<br \/>\nAnswer: The ratios are Not Equivalent.<\/p>\n<p>Explanation: Two ratios that have the same value are called equivalent ratios. To find an equivalent ratio, multiply or divide both quantities by the same number. It is the same process as finding equivalent fractions. Multiply both the numerator and denominator by 2.<br \/>\nHence the ratios 28 : 32 and 7 : 8 are Not Equivalent.<\/p>\n<p>Question 32.<br \/>\n85 : 210 and 340 : 735<br \/>\nAnswer: The ratios are Not Equivalent.<\/p>\n<p>Explanation: Two ratios that have the same value are called equivalent ratios. To find an equivalent ratio, multiply or divide both quantities by the same number. It is the same process as finding equivalent fractions. Multiply both the numerator and denominator by 2.<br \/>\nHence the ratios 85 : 210 and 340 : 735\u00a0 are Not Equivalent.<\/p>\n<p><strong>WRITING EQUIVALENT RATIOS<\/strong> Write a ratio that is equivalent to the given ratio. Justify your answer.<br \/>\nQuestion 33.<br \/>\n3 : 1<br \/>\nAnswer: 6: 2<\/p>\n<p>Explanation:<br \/>\nThe equivalent ratio of 3:1 is 6:2<br \/>\nTwo ratios that have the same value are called equivalent ratios.<br \/>\n6:2 = 3:1<\/p>\n<p>Question 34.<br \/>\n7 : 2<br \/>\nAnswer: 14: 4<\/p>\n<p>Explanation:<br \/>\nTwo ratios that have the same value are called equivalent ratios.<br \/>\nThe equivalent ratio of 7 : 2 is 14:4<br \/>\n7 \u00d7 2 : 2 \u00d7 2 = 14:4<\/p>\n<p>Question 35.<br \/>\n6 : 6<br \/>\nAnswer: 12:12<\/p>\n<p>Explanation:<br \/>\nTwo ratios that have the same value are called equivalent ratios.<br \/>\nThe equivalent ratio of 6:6 is 12:12<br \/>\n6 \u00d7 2 : 6 \u00d7 2 = 12:12<\/p>\n<p>Question 36.<br \/>\n0 : 8<br \/>\nAnswer: 0:16<\/p>\n<p>Explanation:<br \/>\nTwo ratios that have the same value are called equivalent ratios.<br \/>\nThe equivalent ratio of 0:8 is 0:16<br \/>\n0 \u00d7 2: 8 \u00d7 2 = 0 : 16<\/p>\n<p><strong>WRITING EQUIVALENT RATIOS<\/strong> Fill in the blank so that the ratios are equivalent.<br \/>\nQuestion 37.<br \/>\n<img decoding=\"async\" loading=\"lazy\" class=\"alignnone size-full wp-image-26636\" src=\"https:\/\/ccssanswers.com\/wp-content\/uploads\/2021\/01\/Big-Ideas-Math-Answer-Key-Grade-6-Chapter-3-Ratios-and-Rates-3.1-18.png\" alt=\"Big Ideas Math Answer Key Grade 6 Chapter 3 Ratios and Rates 3.1 18\" width=\"107\" height=\"36\" \/><br \/>\nAnswer:\u00a0 18<br \/>\n<img decoding=\"async\" loading=\"lazy\" class=\"alignnone size-full wp-image-30915\" src=\"https:\/\/ccssanswers.com\/wp-content\/uploads\/2021\/01\/Big-Ideas-Math-Answer-Key-Grade-6-Chapter-3-Ratios-and-Rates-3.1-18-1.png\" alt=\"Big-Ideas-Math-Answer-Key-Grade-6-Chapter-3-Ratios-and-Rates-3.1-18\" width=\"107\" height=\"36\" \/><\/p>\n<p>Explanation:<br \/>\nSince<br \/>\n3 : 9 = 6 : X<br \/>\nThen we know<br \/>\n9\/3 = X\/6<br \/>\nMultiplying both sides by 6 cancels on the right<br \/>\n6 \u00d7 (9\/3) = (X\/6) \u00d7 6<br \/>\n6 \u00d7 (9\/3) = X<br \/>\nThen solving for X<br \/>\nX = 6 \u00d7 (9\/3)<br \/>\nX = 18<br \/>\nTherefore<br \/>\n3 : 9 = 6 : 18<br \/>\nTwo ratios that have the same value are called equivalent ratios. To find an equivalent ratio, multiply or divide both quantities by the same number. It is the same process as finding equivalent fractions. Multiply both the numerator and denominator by 2.<\/p>\n<p>Question 38.<br \/>\n<img decoding=\"async\" loading=\"lazy\" class=\"alignnone size-full wp-image-26637\" src=\"https:\/\/ccssanswers.com\/wp-content\/uploads\/2021\/01\/Big-Ideas-Math-Answer-Key-Grade-6-Chapter-3-Ratios-and-Rates-3.1-19.png\" alt=\"Big Ideas Math Answer Key Grade 6 Chapter 3 Ratios and Rates 3.1 19\" width=\"115\" height=\"44\" \/><br \/>\nAnswer: 24<br \/>\n<img decoding=\"async\" loading=\"lazy\" class=\"alignnone size-full wp-image-30917\" src=\"https:\/\/ccssanswers.com\/wp-content\/uploads\/2021\/01\/Big-Ideas-Math-Answer-Key-Grade-6-Chapter-3-Ratios-and-Rates-3.1-19-1.png\" alt=\"Big-Ideas-Math-Answer-Key-Grade-6-Chapter-3-Ratios-and-Rates-3.1-19\" width=\"115\" height=\"44\" \/><br \/>\nExplanation:<br \/>\nSince<br \/>\n2 : 6 = 8 : X<br \/>\nThen we know<br \/>\n6\/2 = X\/8<br \/>\nMultiplying both sides by 8 cancels on the right<br \/>\n8 \u00d7 (6\/2) = (X\/8) \u00d7 8<br \/>\n8 \u00d7 (6\/2) = X<br \/>\nThen solving for X<br \/>\nX = 8 \u00d7 (6\/2)<br \/>\nX = 24<br \/>\nTherefore<br \/>\n2 : 6 = 8 : 24<br \/>\nTwo ratios that have the same value are called equivalent ratios. To find an equivalent ratio, multiply or divide both quantities by the same number. It is the same process as finding equivalent fractions. Multiply both the numerator and denominator by 2.<\/p>\n<p>Question 39.<br \/>\n<img decoding=\"async\" loading=\"lazy\" class=\"alignnone size-full wp-image-26638\" src=\"https:\/\/ccssanswers.com\/wp-content\/uploads\/2021\/01\/Big-Ideas-Math-Answer-Key-Grade-6-Chapter-3-Ratios-and-Rates-3.1-20.png\" alt=\"Big Ideas Math Answer Key Grade 6 Chapter 3 Ratios and Rates 3.1 20\" width=\"117\" height=\"41\" \/><br \/>\nAnswer: 21<br \/>\n<img decoding=\"async\" loading=\"lazy\" class=\"alignnone size-full wp-image-30918\" src=\"https:\/\/ccssanswers.com\/wp-content\/uploads\/2021\/01\/Big-Ideas-Math-Answer-Key-Grade-6-Chapter-3-Ratios-and-Rates-3.1-20-1.png\" alt=\"Big-Ideas-Math-Answer-Key-Grade-6-Chapter-3-Ratios-and-Rates-3.1-20\" width=\"117\" height=\"41\" \/><\/p>\n<p>Explanation:<br \/>\nSince<br \/>\nX : 6 = 7 : 2<br \/>\nThen we know<br \/>\nX\/6 = 7\/2<br \/>\nMultiplying both sides by 6 cancels on the left<br \/>\n6 \u00d7 (X\/6) = (7\/2) \u00d7 6<br \/>\nX = (7\/2) \u00d7 6<br \/>\nThen solving for X<br \/>\nX = 6 \u00d7 (7\/2)<br \/>\nX = 21<br \/>\nTherefore<br \/>\n21 : 6 = 7 : 2<br \/>\nTwo ratios that have the same value are called equivalent ratios. To find an equivalent ratio, multiply or divide both quantities by the same number. It is the same process as finding equivalent fractions. Multiply both the numerator and denominator by 2.<\/p>\n<p>Question 40.<br \/>\n<strong>YOU BE THE TEACHER<\/strong><br \/>\nYour friend says that the two ratios are equivalent. Is your friend correct? Explain your reasoning.<br \/>\n<img decoding=\"async\" loading=\"lazy\" class=\"alignnone size-full wp-image-26639\" src=\"https:\/\/ccssanswers.com\/wp-content\/uploads\/2021\/01\/Big-Ideas-Math-Answer-Key-Grade-6-Chapter-3-Ratios-and-Rates-3.1-21.png\" alt=\"Big Ideas Math Answer Key Grade 6 Chapter 3 Ratios and Rates 3.1 21\" width=\"217\" height=\"148\" \/><br \/>\nAnswer: incorrect, The ratios are Not Equivalent.<\/p>\n<p>Explanation: Two ratios that have the same value are called equivalent ratios. To find an equivalent ratio, multiply or divide both quantities by the same number. It is the same process as finding equivalent fractions. Multiply both the numerator and denominator by 2.<br \/>\nHence the ratios 4 : 8 and 8 : 12\u00a0 are Not Equivalent. after add 4 each to the ratios<\/p>\n<p>Question 41.<br \/>\n<strong>OPEN-ENDED<\/strong><br \/>\nA non-Newtonian liquid demonstrates properties of both a solid and a liquid. A recipe for a non-Newtonian liquid calls for 1 cup of water and 2 cups of cornstarch. Find two possible combinations of water and cornstarch that you can use to make a larger batch. Justify your answer.<br \/>\nAnswer:<br \/>\nGiven,<br \/>\nA non-Newtonian liquid demonstrates properties of both a solid and a liquid.<br \/>\nA recipe for a non-Newtonian liquid calls for 1 cup of water and 2 cups of cornstarch<br \/>\nThe ratio of water and cornstarch is 1 : 2<br \/>\nThe possible combinations of water and cornstarch are<br \/>\nYou can multiply 3 to each number in the first ratio to obtain the numbers in the second ratio, the ratios are equivalent.<br \/>\n1 \u00d7 3 : 2 \u00d7 3 = 3 : 6<br \/>\nYou can multiply 5 to each number in the first ratio to obtain the numbers in the second ratio, the ratios are equivalent.<br \/>\n1 \u00d7 5 : 2 \u00d7 5 = 5 : 10<\/p>\n<p>Question 42.<br \/>\n<strong>PROBLEM SOLVING<\/strong><br \/>\nYou are downloading songs to your tablet. The ratio of pop songs to rock songs is 5 : 4. You download 40 pop songs. How many rock songs do you download?<br \/>\nAnswer: 32<\/p>\n<p>Explanation:<br \/>\nGiven,<br \/>\n. The ratio of pop songs to rock songs is 5 : 4. You download 40 pop songs.<br \/>\nLet number of rock songs be x<br \/>\n5 : 4 :: 40 :: x<br \/>\n5 \u00d7 x = 4 \u00d7 40<br \/>\n5x = 160<br \/>\nx = 160\/5<br \/>\nx = 32<br \/>\nTherefore, number of rock songs = 32.<\/p>\n<p>Question 43.<br \/>\n<strong>PROBLEM SOLVING<\/strong><br \/>\nIn the contiguous United States, the ratio of states that border an ocean to states that do not border an ocean is 7 : 9. How many of the states border an ocean?<br \/>\n<img decoding=\"async\" loading=\"lazy\" class=\"alignnone size-full wp-image-26640\" src=\"https:\/\/ccssanswers.com\/wp-content\/uploads\/2021\/01\/Big-Ideas-Math-Answer-Key-Grade-6-Chapter-3-Ratios-and-Rates-3.1-22.png\" alt=\"Big Ideas Math Answer Key Grade 6 Chapter 3 Ratios and Rates 3.1 22\" width=\"271\" height=\"182\" \/><br \/>\nAnswer: 7<\/p>\n<p>Explanation:<br \/>\nGiven,<br \/>\nthe ratio of states that border an ocean to states that do not border an ocean is 7 : 9.<br \/>\nSo states that border an ocean is 7<br \/>\nand states that do not border an ocean is 9<br \/>\nhence the states border an ocean is 7<\/p>\n<p>Question 44.<br \/>\n<strong>REASONING<\/strong><br \/>\nThe value of a ratio is \\(\\frac{4}{3}\\). The second quantity in the ratio is how many times the first quantity in the ratio? Explain your reasoning.<br \/>\nAnswer: The second quantity is 1.3333 times the first quantity in the ratio.<\/p>\n<p>Explanation:<br \/>\nA ratio is given to us which is 4:3.<br \/>\nWhat we need to find out is, the second quantity in the ratio is how many times the first quantity in the ratio.<br \/>\nThe definition of ratio is, the quantitative relation between two amounts showing the number of times one value contains or is contained within the other.<br \/>\nSo according to the definition of ratio we get:<br \/>\n4\/3 = 1.33<br \/>\nSo we can say that 4 contains 3, 1.3333 times in it.<br \/>\nSo the second quantity is 1.3333 times the first quantity in the ratio.<\/p>\n<p>Question 45.<br \/>\n<strong>MODELING REAL LIFE<\/strong><br \/>\nA train moving at a constant speed travels 3 miles every 5 minutes. A car moving at a constant speed travels 12 miles every 20 minutes. Are the vehicles traveling at the same speed? If not, which is faster?<br \/>\n<img decoding=\"async\" loading=\"lazy\" class=\"alignnone size-full wp-image-26641\" src=\"https:\/\/ccssanswers.com\/wp-content\/uploads\/2021\/01\/Big-Ideas-Math-Answer-Key-Grade-6-Chapter-3-Ratios-and-Rates-3.1-23.png\" alt=\"Big Ideas Math Answer Key Grade 6 Chapter 3 Ratios and Rates 3.1 23\" width=\"288\" height=\"227\" \/><br \/>\nAnswer:<br \/>\nBoth vehicles traveling at the same speed 0.6 miles per minute<\/p>\n<p>Explanation:<br \/>\nGiven<br \/>\nA train moving at a constant speed travels 3 miles every 5 minutes.<br \/>\nby dividing 3 miles by 5 minutes we get 0.6 miles per minute<br \/>\nA car moving at a constant speed travels 12 miles every 20 minutes.<br \/>\nby dividing 12 miles by 20 minutes we get 0.6 miles per minute<br \/>\nHence both vehicle have the same speed<\/p>\n<p>Question 46.<br \/>\n<strong>CRITICAL THINKING<\/strong><br \/>\nTo win a relay race, you must swim 200 yards before your opponent swims 190 yards. You swim at a pace of 50 yards every 40 seconds. Your opponent swims at a pace of 10 yards every 8.5 seconds. Who wins the race? Justify your answer.<br \/>\nAnswer:<\/p>\n<p>Explanation:<br \/>\nGiven<br \/>\nYou swim at a pace of 50 yards every 40 seconds<br \/>\nBy dividing 50 yards by 40 seconds we get 1.25 yards per second<br \/>\nYour opponent swims at a pace of 10 yards every 8.5 seconds.<br \/>\nBy dividing 10 yards by 8.5 seconds we get 1.17 yards per second<br \/>\nYou swim at a pace of 50 yards every 40 seconds\u00a0 for completing 200 yards you take 160 seconds<br \/>\nyour opponent swims at a pace of 10 yards every 8.5 seconds\u00a0 for completing 190 yards you take 162.3\u00a0 seconds<br \/>\nhence you won the race by completing 200 yards in 160 seconds before your opponent completes 190 yards at 162.3 seconds<\/p>\n<p>Question 47.<br \/>\n<strong>DIG DEEPER!<\/strong><br \/>\nThere are 3 boys for every 2 girls in a dance competition. Does it make sense for there to be a total of 9 people in the competition? Explain.<br \/>\nAnswer: No<\/p>\n<p>Explanation:<br \/>\nGiven,<br \/>\nThere are 3 boys for every 2 girls in a dance competition.<br \/>\n3:2=5<br \/>\nso girls are 2:5<br \/>\nset up the proportion<br \/>\n2\/5=x\/9<br \/>\n5x=18<br \/>\nx=3.6 girls<br \/>\nanother way you can look at it is because there are 3 boys for every 2 girls, add 2 more girls, you\u2019ll get 3 more boys<br \/>\nthat makes the total of 10 people so 9 is impossible<\/p>\n<p>Question 48.<br \/>\n<strong>GEOMETRY<\/strong><br \/>\nUse the blue and green rectangles.<br \/>\n<img decoding=\"async\" loading=\"lazy\" class=\"alignnone size-full wp-image-26642\" src=\"https:\/\/ccssanswers.com\/wp-content\/uploads\/2021\/01\/Big-Ideas-Math-Answer-Key-Grade-6-Chapter-3-Ratios-and-Rates-3.1-24.png\" alt=\"Big Ideas Math Answer Key Grade 6 Chapter 3 Ratios and Rates 3.1 24\" width=\"267\" height=\"108\" \/><br \/>\na. Find the ratio of the length of the blue rectangle to the length of the green rectangle. Repeat this for width, perimeter, and area.<\/p>\n<p>Answer:<br \/>\nThe ratio of the length of the blue rectangle to the length of the green rectangle is 2 : 4<br \/>\nThe ratio of the width of the blue rectangle to the width of the green rectangle is 3 : 6<br \/>\nPerimeter of the rectangle = 2l + 2w<br \/>\nBlue rectangle:<br \/>\n2(3) + 2(2) = 6 + 4 = 10<br \/>\nGreen Rectangle:<br \/>\n2(6) + 2(4) = 12 + 8 = 20<br \/>\nRatio of perimeter of blue rectangle to the green rectangle is 10 : 20<br \/>\nArea of the rectangle = lb<br \/>\nBlue rectangle:<br \/>\nA = 2 \u00d7 3 = 6<br \/>\nGreen Rectangle:<br \/>\nA = 4 \u00d7 6 = 24<br \/>\nRatio of Area of blue rectangle to the green rectangle is 6 : 24<br \/>\nb. Compare your ratios in part(a).<br \/>\nAnswer:<br \/>\nThe ratio of the length of the blue rectangle to the length of the green rectangle is 2 : 4 equivalent to 1 : 2<br \/>\nThe ratio of the width of the blue rectangle to the width of the green rectangle is 3 : 6 equivalent to 1 : 2<br \/>\nRatio of perimeter of blue rectangle to the green rectangle is 10 : 20 equivalent to 1 : 2<br \/>\nRatio of Area of blue rectangle to the green rectangle is 6 : 24 equivalent to 1 : 4<\/p>\n<p>Question 49.<br \/>\n<strong>STRUCTURE<\/strong><br \/>\nThe ratio of the side lengths of a triangle is 2 : 3 : 4. The shortest side is 15 inches. What is the perimeter of the triangle? Explain.<br \/>\nAnswer: 67.5 inches<\/p>\n<p>Explanation:<br \/>\nGiven that,<br \/>\nThe ratio of the side lengths of a triangle is 2 : 3 : 4. The shortest side is 15 inches.<br \/>\nLet<br \/>\nx = the first side<br \/>\ny = the second side<br \/>\nz = the third side<br \/>\nWe know that<br \/>\nx\/y = 2\/3<br \/>\ny = 1.5x<br \/>\nx\/z = 2\/4<br \/>\nz = 2x<br \/>\nx = 15 inches<br \/>\nSubstitute the value of x in both the equations<br \/>\ny = 1.5(15) = 22.5 in<br \/>\nz = 2(15) = 30 in<br \/>\nNow find the perimeter of the triangle<br \/>\nP = x + y + z<br \/>\nP = 15 + 22.5 + 30 = 67.5 inches<\/p>\n<p>Question 50.<br \/>\n<strong>PROBLEM SOLVING<\/strong><br \/>\nA restaurant sells tokens that customers use to play games while waiting for their orders.<br \/>\n<img decoding=\"async\" loading=\"lazy\" class=\"alignnone size-full wp-image-26643\" src=\"https:\/\/ccssanswers.com\/wp-content\/uploads\/2021\/01\/Big-Ideas-Math-Answer-Key-Grade-6-Chapter-3-Ratios-and-Rates-3.1-25.png\" alt=\"Big Ideas Math Answer Key Grade 6 Chapter 3 Ratios and Rates 3.1 25\" width=\"233\" height=\"144\" \/><br \/>\na. Which option is the best deal? Justify your answer.<br \/>\nb. What suggestions, if any, would you give to the restaurant about how it could modify the prices of tokens?<br \/>\nAnswer:<br \/>\nIt would be 90 tokens<br \/>\n0.50 * 10 = $5<br \/>\n0.50 *25 = $12.5<br \/>\n0.50 * 50 = $25<br \/>\n0.50 * 90 = $45<br \/>\non 90 tokens you save $5 which is the most.<\/p>\n<p>Question 51.<br \/>\n<strong>DIG DEEPER!<\/strong><br \/>\nThere are 12 boys and 10 girls in your gym class. If 6 boys joined the class, how many girls would need to join for the ratio of boys to girls to remain the same? Justify your answer.<br \/>\nAnswer:<br \/>\nGiven,<br \/>\nThere are 12 boys and 10 girls in your gym class.<br \/>\n12\/10=6\/5<br \/>\n6 boys joined: 18\/(of girls)=6\/5, #of girls=18\u00d75\/6=15<br \/>\n5 more girls will keep the same ratio 6\/5<\/p>\n<h3><a id=\"Lesson_3.2_Using_Tape_Diagrams\"><\/a>Lesson 3.2 Using Tape Diagrams<\/h3>\n<p>You can use a visual model, called a tape diagram, to represent the relationship between two quantities in a ratio.<\/p>\n<p><strong>EXPLORATION 1<\/strong><\/p>\n<p>Using a Tape Diagram<br \/>\nWork with a partner. The tape diagram models the lengths of two snowboarding trails.<br \/>\n<img decoding=\"async\" loading=\"lazy\" class=\"alignnone size-full wp-image-26655\" src=\"https:\/\/ccssanswers.com\/wp-content\/uploads\/2021\/01\/Big-Ideas-Math-Answers-6th-Grade-Chapter-3-Ratios-and-Rates-3.2-1.png\" alt=\"Big Ideas Math Answers 6th Grade Chapter 3 Ratios and Rates 3.2 1\" width=\"458\" height=\"182\" srcset=\"https:\/\/ccssanswers.com\/wp-content\/uploads\/2021\/01\/Big-Ideas-Math-Answers-6th-Grade-Chapter-3-Ratios-and-Rates-3.2-1.png 458w, https:\/\/ccssanswers.com\/wp-content\/uploads\/2021\/01\/Big-Ideas-Math-Answers-6th-Grade-Chapter-3-Ratios-and-Rates-3.2-1-300x119.png 300w\" sizes=\"(max-width: 458px) 100vw, 458px\" \/><br \/>\na. What can you determine from the tape diagram?<\/p>\n<p>Answer:<br \/>\nWe determine from the tape diagram that the beginner trail has one rectangle and the expert trial has four rectangles.<\/p>\n<p>b. Choose a length for one of the trails. What conclusions can you make from the tape diagram? Explain your reasoning.<\/p>\n<p>Answer:<br \/>\nLet the length of one rectangle is 10.<br \/>\nThe length of the beginner trail is 10.<br \/>\nLength of the expert trail is 4 \u00d7 10 = 40<br \/>\n1 : 4<br \/>\nc. Suppose you know the combined length of the trails or the difference in the lengths of the trails. Explain how you can use that information to find the lengths of the two trails. Provide an example with your explanation.<br \/>\n<img decoding=\"async\" loading=\"lazy\" class=\"alignnone size-full wp-image-26656\" src=\"https:\/\/ccssanswers.com\/wp-content\/uploads\/2021\/01\/Big-Ideas-Math-Answers-6th-Grade-Chapter-3-Ratios-and-Rates-3.2-2.png\" alt=\"Big Ideas Math Answers 6th Grade Chapter 3 Ratios and Rates 3.2 2\" width=\"634\" height=\"419\" srcset=\"https:\/\/ccssanswers.com\/wp-content\/uploads\/2021\/01\/Big-Ideas-Math-Answers-6th-Grade-Chapter-3-Ratios-and-Rates-3.2-2.png 634w, https:\/\/ccssanswers.com\/wp-content\/uploads\/2021\/01\/Big-Ideas-Math-Answers-6th-Grade-Chapter-3-Ratios-and-Rates-3.2-2-300x198.png 300w\" sizes=\"(max-width: 634px) 100vw, 634px\" \/><br \/>\nAnswer:<br \/>\nLet the length of one rectangle is 10.<br \/>\nNow let us combine the length to find the length of the expert trail.<br \/>\nThe expert trail contains 4 rectangles.<br \/>\nSo, multiply 10 with 4.<br \/>\n4 \u00d7 10 = 40<br \/>\nExample:<br \/>\nThe tape diagram represents the ratio of gifts received to gifts given. You received 4 gifts.<br \/>\n<img decoding=\"async\" loading=\"lazy\" class=\"alignnone size-full wp-image-26657\" src=\"https:\/\/ccssanswers.com\/wp-content\/uploads\/2021\/01\/Big-Ideas-Math-Answers-6th-Grade-Chapter-3-Ratios-and-Rates-3.2-3.png\" alt=\"Big Ideas Math Answers 6th Grade Chapter 3 Ratios and Rates 3.2 3\" width=\"278\" height=\"65\" \/><\/p>\n<p>You can use tape diagrams to represent ratios and solve ratio problems.<\/p>\n<p><strong>Try It<\/strong><\/p>\n<p>Question 1.<br \/>\nThe tape diagram represents the ratio of gifts received to gifts given. You received 4 gifts. How many gifts did you give?<br \/>\n<img decoding=\"async\" loading=\"lazy\" class=\"alignnone size-full wp-image-26657\" src=\"https:\/\/ccssanswers.com\/wp-content\/uploads\/2021\/01\/Big-Ideas-Math-Answers-6th-Grade-Chapter-3-Ratios-and-Rates-3.2-3.png\" alt=\"Big Ideas Math Answers 6th Grade Chapter 3 Ratios and Rates 3.2 3\" width=\"278\" height=\"65\" \/><br \/>\nAnswer: 1 : 4<\/p>\n<p>Explanation:<br \/>\ngiven<br \/>\nThe tape diagram represents the ratio of gifts received to gifts given.<br \/>\nYou received 4 gifts<br \/>\nthe ratio by observing the given image is 1 : 4<br \/>\nhence you gave 1 gift<\/p>\n<p>Question 2.<br \/>\nThere are 8 bones in a large snake for every 3 bones in a small snake. The small snake has 150 bones. How many bones does the large snake have?<br \/>\nAnswer: 400<\/p>\n<p>Explanation:<br \/>\nGiven,<br \/>\nThere are 8 bones in a large snake for every 3 bones in a small snake.<br \/>\nThe small snake has 150 bones.<br \/>\n150\/3 = 50 bones<br \/>\n50 \u00d7 8 = 400 bones<br \/>\nThus the large snake has 400 bones.<\/p>\n<p>Question 3.<br \/>\n<strong>WHAT IF?<\/strong><br \/>\nRepeat Example 3 when the ratio of your monthly allowance to your friend\u2019s monthly allowance is 2 to 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>STRUCTURE<\/strong><br \/>\nWhat ratio is represented by the tape diagram? Can you use the tape diagram to model the ratio 6 : 9? Can you use the tape diagram to model the ratio 8 : 16? Explain your reasoning.<br \/>\n<img decoding=\"async\" loading=\"lazy\" class=\"alignnone size-full wp-image-26658\" src=\"https:\/\/ccssanswers.com\/wp-content\/uploads\/2021\/01\/Big-Ideas-Math-Answers-6th-Grade-Chapter-3-Ratios-and-Rates-3.2-4.png\" alt=\"Big Ideas Math Answers 6th Grade Chapter 3 Ratios and Rates 3.2 4\" width=\"170\" height=\"70\" \/><br \/>\nAnswer:<\/p>\n<p>Question 5.<br \/>\n<strong>REASONING<\/strong><br \/>\nYou are given a tape diagram and the total value of the parts. How can you find the value of 1 part?<br \/>\nAnswer:<\/p>\n<p>Question 6.<br \/>\n<strong>DRAWING A TAPE DIAGRAM<\/strong><br \/>\nDescribe two ways that you can represent the ratio 12 : 4 using a tape diagram.<br \/>\nAnswer:<\/p>\n<p><strong>USING A TAPE DIAGRAM<\/strong> You are given the number of tickets in a bag and the ratio of winning tickets to losing tickets. How many of each kind of ticket are in the bag?<br \/>\n<img decoding=\"async\" loading=\"lazy\" class=\"alignnone size-full wp-image-26659\" src=\"https:\/\/ccssanswers.com\/wp-content\/uploads\/2021\/01\/Big-Ideas-Math-Answers-6th-Grade-Chapter-3-Ratios-and-Rates-3.2-5.png\" alt=\"Big Ideas Math Answers 6th Grade Chapter 3 Ratios and Rates 3.2 5\" width=\"229\" height=\"117\" \/><br \/>\nQuestion 7.<br \/>\n35 tickets; 1 to 4<br \/>\nAnswer: 7 : 28<\/p>\n<p>Explanation:<br \/>\nNumber of winning tickets = 7<br \/>\nNumber of losing tickets = 28<br \/>\nThe ratio of winning tickets and losing tickets are 7 : 28<br \/>\nWe get 1 : 4<br \/>\nThus the answer is 7 : 28<\/p>\n<p>Question 8.<br \/>\n80 tickets; 2 : 8<br \/>\nAnswer: 16 : 64<\/p>\n<p>Explanation:<br \/>\nTotal number of tickets = 80<br \/>\nThe ratio of winning tickets to losing tickets is 2 : 8<br \/>\nLet 2x be the winning tickets and 8x be the losing tickets<br \/>\n2x + 8x = 80<br \/>\n10x = 80<br \/>\nx = 80\/10 = 8<br \/>\nNumber of winning tickets = 2x = 2(8) = 16<br \/>\nNumber of losing tickets = 8x = 8(8) = 64<br \/>\nThe ratio of winning tickets and losing tickets are 16 : 64<\/p>\n<p>Question 9.<br \/>\nThe tape diagram represents the ratio of the numbers of planets in two different solar systems. There are 8 planets in Solar System B. How many planets are in Solar System A?<br \/>\n<img decoding=\"async\" loading=\"lazy\" class=\"alignnone size-full wp-image-26660\" src=\"https:\/\/ccssanswers.com\/wp-content\/uploads\/2021\/01\/Big-Ideas-Math-Answers-6th-Grade-Chapter-3-Ratios-and-Rates-3.2-6.png\" alt=\"Big Ideas Math Answers 6th Grade Chapter 3 Ratios and Rates 3.2 6\" width=\"313\" height=\"72\" srcset=\"https:\/\/ccssanswers.com\/wp-content\/uploads\/2021\/01\/Big-Ideas-Math-Answers-6th-Grade-Chapter-3-Ratios-and-Rates-3.2-6.png 313w, https:\/\/ccssanswers.com\/wp-content\/uploads\/2021\/01\/Big-Ideas-Math-Answers-6th-Grade-Chapter-3-Ratios-and-Rates-3.2-6-300x69.png 300w\" sizes=\"(max-width: 313px) 100vw, 313px\" \/><br \/>\nAnswer:<br \/>\nThe ratio of the numbers of planets in two different solar systems is 3 : 4<br \/>\nGiven that<br \/>\nThere are 8 planets in Solar System B.<br \/>\nSolar System B contains 4 rectangles<br \/>\n4 \u00d7 2 = 8<br \/>\nSolar System A contains 3 rectangles<br \/>\n3 \u00d7 2 = 6<br \/>\nTherefore the solar system A contains 6 planets.<\/p>\n<p>Question 10.<br \/>\nYou and your friend play an arcade game. You score 5 points for every 9 points that your friend scores. You score 320 points less than your friend. How many points do you each score?<br \/>\n<img decoding=\"async\" loading=\"lazy\" class=\"alignnone size-full wp-image-26661\" src=\"https:\/\/ccssanswers.com\/wp-content\/uploads\/2021\/01\/Big-Ideas-Math-Answers-6th-Grade-Chapter-3-Ratios-and-Rates-3.2-7.png\" alt=\"Big Ideas Math Answers 6th Grade Chapter 3 Ratios and Rates 3.2 7\" width=\"199\" height=\"168\" \/><br \/>\nAnswer:<br \/>\nGiven<br \/>\nYou and your friend play an arcade game.<br \/>\nYou score 5 points for every 9 points that your friend scores.<br \/>\nYou score 320 points less than your friend.<br \/>\nEach time you score you gain 4 less points than your friend so, you can do this equation<br \/>\n9x &#8211; 320 = 5x<br \/>\n9x &#8211; 5x = 320<br \/>\n4x = 320<br \/>\nx = 320\/4<br \/>\nx = 80<br \/>\n9x = 9(80) = 720<br \/>\n5x = 5(80) = 400<br \/>\n720 &#8211; 400 = 320<\/p>\n<p>Question 11.<br \/>\n<strong>DIG DEEPER!<\/strong><br \/>\nYour team wins 18 medals at a track meet. The medals are gold, silver, and bronze in a ratio of 2 : 2 : 5. How many of each medal were won by your team?<br \/>\nAnswer: The team won 4 gold medals, 4 silver medals and 10 bronze medals.<\/p>\n<p>Explanation:<br \/>\nGiven,<br \/>\nTotal medals won = 18<br \/>\nRatio of gold, silver and bronze = 2:2:5<br \/>\nLet,<br \/>\nx be the original number.<br \/>\nTherefore,<br \/>\nGold medals = 2x<br \/>\nSilver medals = 2x<br \/>\nBronze medals = 5x<br \/>\nAccording to given statement<br \/>\n2x + 2x + 5x = 18<br \/>\n9x = 18<br \/>\nx = 2<br \/>\nGold medals = 2x = 2(2) = 4<br \/>\nSilver medals = 2x = 2(2) = 4<br \/>\nBronze medals = 5x = 5(2) = 10<\/p>\n<h3><a id=\"Using_Tape_Diagrams_Homework_&amp;_Practice_3.2\"><\/a>Using Tape Diagrams Homework &amp; Practice 3.2<\/h3>\n<p><strong>Review &amp; Refresh<\/strong><\/p>\n<p><strong>Determine whether the ratios are equivalent.<\/strong><br \/>\nQuestion 1.<br \/>\n11 : 4 and 22 : 8<br \/>\nAnswer: The ratios are Equivalent.<\/p>\n<p>Explanation: Two ratios that have the same value are called equivalent ratios. To find an equivalent ratio, multiply or divide both quantities by the same number. It is the same process as finding equivalent fractions. Multiply both the numerator and denominator by 2.<br \/>\nHence the ratios 11 : 4 and 22 : 8 are Equivalent.<\/p>\n<p>Question 2.<br \/>\n12 : 18 and 2 : 3<br \/>\nAnswer: The ratios are Equivalent.<\/p>\n<p>Explanation: Two ratios that have the same value are called equivalent ratios. To find an equivalent ratio, multiply or divide both quantities by the same number. It is the same process as finding equivalent fractions. Multiply both the numerator and denominator by 2.<br \/>\nHence the ratios 12 : 18 and 2 : 3 are Equivalent.<\/p>\n<p>Question 3.<br \/>\n56 : 81 and 7 : 9<br \/>\nAnswer: The ratios are not Equivalent.<\/p>\n<p>Explanation: Two ratios that have the same value are called equivalent ratios. To find an equivalent ratio, multiply or divide both quantities by the same number. It is the same process as finding equivalent fractions. Multiply both the numerator and denominator by 2.<br \/>\nHence the ratios 56 : 81 and 7 : 9 are not Equivalent.<\/p>\n<p>Question 4.<br \/>\n2 : 12 and 6 : 24<br \/>\nAnswer: The ratios are not Equivalent.<\/p>\n<p>Explanation: Two ratios that have the same value are called equivalent ratios. To find an equivalent ratio, multiply or divide both quantities by the same number. It is the same process as finding equivalent fractions. Multiply both the numerator and denominator by 2.<br \/>\nHence the ratios 2 : 12 and 6 : 24 are not Equivalent.<\/p>\n<p><strong>Multiply. Write the answer in the simplest form.<\/strong><br \/>\nQuestion 5.<br \/>\n\\(\\frac{7}{10}\\) . \\(\\frac{5}{7}\\)<br \/>\nAnswer: \\(\\frac{1}{2}\\)<br \/>\nFor fraction multiplication, multiply the numerators and then multiply the denominators to get<br \/>\n\\(\\frac{7}{10}\\) . \\(\\frac{5}{7}\\)<br \/>\nThis fraction can be reduced by dividing both the numerator and denominator by the Greatest Common Factor of 35 and 70 using<br \/>\nGCF(35,70) = 35<br \/>\n35\u00f735 divided by 70\u00f735= \\(\\frac{1}{2}\\)<br \/>\nTherefore:<br \/>\n\\(\\frac{7}{10}\\) . \\(\\frac{5}{7}\\) is 12<\/p>\n<p>Question 6.<br \/>\n2\\(\\frac{1}{3}\\) . \\(\\frac{3}{4}\\)<br \/>\nAnswer: \\(\\frac{1}{2}\\)<\/p>\n<p>Explanation:<br \/>\nFor fraction multiplication, multiply the numerators and then multiply the denominators to get<br \/>\n1\u00d733\u00d74=312<br \/>\nThis fraction can be reduced by dividing both the numerator and denominator by the Greatest Common Factor of 3 and 12 using<br \/>\nGCF(3,12) = 3<br \/>\n3\u00f73 divided by 12\u00f73= \\(\\frac{1}{4}\\)<br \/>\nTherefore:<br \/>\nas given in question 2\\(\\frac{1}{3}\\) . \\(\\frac{3}{4}\\) = 2 \u00d7 \\(\\frac{1}{4}\\)<br \/>\nwe get \\(\\frac{1}{2}\\)<\/p>\n<p>Question 7.<br \/>\n5\\(\\frac{3}{8}\\) . 2\\(\\frac{1}{2}\\)<br \/>\nAnswer: 13 \\(\\frac{7}{16}\\)<\/p>\n<p>Explanation:<br \/>\nConvert any mixed numbers to fractions.<br \/>\n5\\(\\frac{3}{8}\\) = \\(\\frac{43}{8}\\)<br \/>\n2\\(\\frac{1}{2}\\) = \\(\\frac{5}{2}\\)<br \/>\n\\(\\frac{43}{8}\\) \u00d7 \\(\\frac{5}{2}\\) = \\(\\frac{215}{16}\\)<br \/>\nNow convert it into the mixed fractions<br \/>\n\\(\\frac{215}{16}\\) = 13 \\(\\frac{7}{16}\\)<\/p>\n<p>Question 8.<br \/>\nMelissa earns $7.40 per hour working at a grocery store. She works 14.25 hours this week. How much does she earn?<br \/>\nA. $83.13<br \/>\nB. $105.45<br \/>\nC. $156.75<br \/>\nD. $1054.50<br \/>\nAnswer: $105.45<\/p>\n<p>Explanation:<br \/>\nGiven,<br \/>\nMelissa earns $7.40 per hour working at a grocery store.<br \/>\nShe works 14.25 hours this week.<br \/>\n14.25 \u00d7 7.40 = $105.45<br \/>\nThus Melissa earns $105.45 this week<\/p>\n<p><strong>Concepts, Skills, &amp; Problem Solving<\/strong><\/p>\n<p><strong>USING A TAPE DIAGRAM<\/strong> Use the tape diagram in Exploration 1 to answer the question. (See Exploration 1, p. 115.)<br \/>\n<img decoding=\"async\" loading=\"lazy\" class=\"alignnone size-full wp-image-26662\" src=\"https:\/\/ccssanswers.com\/wp-content\/uploads\/2021\/01\/Big-Ideas-Math-Answers-6th-Grade-Chapter-3-Ratios-and-Rates-3.2-8.png\" alt=\"Big Ideas Math Answers 6th Grade Chapter 3 Ratios and Rates 3.2 8\" width=\"161\" height=\"183\" \/><br \/>\nQuestion 9.<br \/>\nThe beginner trail is 200 meters long. How long is the expert trail?<br \/>\nAnswer:<br \/>\nFor the beginner&#8217;s trail, there is only one rectangle. For Expert Trail, there are 4 rectangles.<br \/>\nThen in total, we have 5 rectangles.<br \/>\nWe know that the combined length is 200 meters, then the 5 rectangles are equivalent to 200 meters.<br \/>\nThen each rectangle will be equivalent to:<br \/>\n200m\/5 = 40m.<br \/>\nNow, we know that the beginner&#8217;s trail has one rectangle, then the length of the beginner&#8217;s trail is 40 meters long.<br \/>\nThe expert&#8217;s trail has 4 rectangles, then it is:<br \/>\n4\u00d740m = 160m long.<\/p>\n<p>Question 10.<br \/>\nThe expert trail is 1200 meters long. How long is the beginner trail?<br \/>\nAnswer:<br \/>\nFor the beginner&#8217;s trail, there is only one rectangle. For Expert Trail, there are 4 rectangles.<br \/>\nThen in total, we have 5 rectangles.<br \/>\nWe know that the combined length is 1200 meters, then the 5 rectangles are equivalent to 1200 meters.<br \/>\nThen each rectangle will be equivalent to:<br \/>\n1200m\/5 = 240m<br \/>\nNow, we know that the beginner&#8217;s trail has one rectangle, then the length of the beginner&#8217;s trail is 240 meters long.<br \/>\nThe expert&#8217;s trail has 4 rectangles, then it is:<br \/>\n4\u00d7240m = 960m long.<\/p>\n<p>Question 11.<br \/>\nThe combined length of the trails is 2000 meters. How long is each trail?<br \/>\nAnswer:<br \/>\nFor the beginner&#8217;s trail, there is only one rectangle. For Expert Trail, there are 4 rectangles.<br \/>\nThen in total, we have 5 rectangles.<br \/>\nWe know that the combined length is 2000 meters, then the 5 rectangles are equivalent to 2000 meters.<br \/>\nThen each rectangle will be equivalent to:<br \/>\n2000m\/5 = 400m.<br \/>\nNow, we know that the beginner&#8217;s trail has one rectangle, then the length of the beginner&#8217;s trail is 400 meters long.<br \/>\nThe expert&#8217;s trail has 4 rectangles, then it is:<br \/>\n4\u00d7400m = 1600m long.<\/p>\n<p>Question 12.<br \/>\nThe expert trail is 750 meters longer than the beginner trail. How long is each trail?<br \/>\nAnswer:<br \/>\nFor the beginner&#8217;s trail, there is only one rectangle. For Expert Trail, there are 4 rectangles.<br \/>\nThen in total, we have 5 rectangles.<br \/>\nWe know that the combined length is 750 meters, then the 5 rectangles are equivalent to 750 meters.<br \/>\nThen each rectangle will be equivalent to:<br \/>\n750m\/5 = 150m<br \/>\nNow, we know that the beginner&#8217;s trail has one rectangle, then the length of the beginner&#8217;s trail is 150 meters long.<br \/>\nThe expert&#8217;s trail has 4 rectangles, then it is:<br \/>\n4\u00d7150m = 600m long.<\/p>\n<p><strong>INTERPRETING A TAPE DIAGRAM<\/strong> The tape diagram represents the ratio of the time you spend tutoring to the time your friend spends tutoring. You tutor for 3 hours. How many hours does your friend spend tutoring?<br \/>\nQuestion 13.<br \/>\n<img decoding=\"async\" loading=\"lazy\" class=\"alignnone size-full wp-image-26663\" src=\"https:\/\/ccssanswers.com\/wp-content\/uploads\/2021\/01\/Big-Ideas-Math-Answers-6th-Grade-Chapter-3-Ratios-and-Rates-3.2-9.png\" alt=\"Big Ideas Math Answers 6th Grade Chapter 3 Ratios and Rates 3.2 9\" width=\"166\" height=\"79\" \/><br \/>\nAnswer:<br \/>\nSo you have one block, and your friend has two.<br \/>\nWe know that you work for 3 hours, this means that your only block must represent 3 hours.<br \/>\nAnd all the blocks represent the same amount of time, then each one of the two blocks of your friend also represents 3 hours.<br \/>\nThen in total, he tutored for 3 hours + 3 hours = 6 hours.<\/p>\n<p>Question 14.<br \/>\n<img decoding=\"async\" loading=\"lazy\" class=\"alignnone size-full wp-image-26664\" src=\"https:\/\/ccssanswers.com\/wp-content\/uploads\/2021\/01\/Big-Ideas-Math-Answers-6th-Grade-Chapter-3-Ratios-and-Rates-3.2-10.png\" alt=\"Big Ideas Math Answers 6th Grade Chapter 3 Ratios and Rates 3.2 10\" width=\"299\" height=\"69\" \/><br \/>\nAnswer:<br \/>\nIn this case, you still have only one block, but now your friend has 5.<br \/>\nUsing the same reasoning as above, we can conclude that each block represents 3 hours, and your friend has 5 of them<br \/>\nthis means that he tutored for:<br \/>\n5\u00d73 hours = 15 hours<\/p>\n<p><strong>DRAWING A TAPE DIAGRAM<\/strong> A bag contains red marbles and blue marbles. You are given the number of red marbles in the bag and the ratio of red marbles to blue marbles. Find the number of blue marbles in the bag.<br \/>\nQuestion 15.<br \/>\n10 red marbles; 5 to 1<br \/>\nAnswer:<br \/>\nred : blue=5:1<br \/>\nred\/blue=5<br \/>\nred= 10<br \/>\nso blue= 2<\/p>\n<p>Question 16.<br \/>\n3 red marbles; 3 : 7<br \/>\nAnswer:<br \/>\nred : blue=3:7<br \/>\nred\/blue=3\/7<br \/>\nred= 3<br \/>\nso blue= 7<\/p>\n<p>Question 17.<br \/>\n12 red marbles; 4 : 3<br \/>\nAnswer:<br \/>\nred : blue=4:3<br \/>\nred\/blue= 12\/9<br \/>\nred= 12<br \/>\nso blue= 9<\/p>\n<p>Question 18.<br \/>\n6 red marbles; 2 for every 5<br \/>\nAnswer:<br \/>\nred : blue=2:5<br \/>\nred\/blue= 2\u00d73 : 5\u00d73<br \/>\nred= 6<br \/>\nso blue= 15<\/p>\n<p>Question 19.<br \/>\n18 red marbles; 6 to 9<br \/>\nAnswer:<br \/>\nred : blue=6:9<br \/>\nred\/blue=18\/27<br \/>\nred= 18<br \/>\nso blue= 27<\/p>\n<p>Question 20.<br \/>\n12 red marbles; 3 : 4<br \/>\nAnswer:<br \/>\nred : blue=3:4<br \/>\nred\/blue=12\/16<br \/>\nred= 12<br \/>\nso blue= 16<\/p>\n<p><strong>USING A TAPE DIAGRAM<\/strong> A bowl contains blueberries and strawberries. You are given the total number of berries in the bowl and the ratio of blueberries to strawberries. How many of each berry are in the bowl?<br \/>\nQuestion 21.<br \/>\n16 berries; 3 : 1<br \/>\nAnswer:<br \/>\nno of strawberries = 4<br \/>\nno of blueberries = 12<\/p>\n<p>Explanation:<br \/>\ntotal berries :- 16<br \/>\nration :- 3:1<br \/>\nno of strawberries :- 1x<br \/>\nno of blueberries :- 3x<br \/>\n3x + 1x = 16<br \/>\n4x = 16<br \/>\nx = 4<\/p>\n<p>Question 22.<br \/>\n10 berries; 2 for every 3<br \/>\nAnswer:<br \/>\nno of strawberries :- 3x<br \/>\nno of blueberries :- 2x<br \/>\n2x + 3x = 10<br \/>\n5x = 10<br \/>\nx = 2<br \/>\nno of strawberries :- 3x = 3(2) = 6<br \/>\nno of blueberries :- 2x = 2(2) = 4<\/p>\n<p>Question 23.<br \/>\n12 berries; 1 to 2<br \/>\nAnswer:<br \/>\nno of strawberries :- 2x<br \/>\nno of blueberries :- 1x<br \/>\n1x + 2x = 12<br \/>\n3x = 12<br \/>\nx = 4<br \/>\nno of strawberries :- 2x = 2(4) = 8<br \/>\nno of blueberries :- 1x = 1(4) = 4<\/p>\n<p>Question 24.<br \/>\n20 berries; 4 : 1<br \/>\nAnswer:<br \/>\nno of strawberries :- 1x<br \/>\nno of blueberries :- 4x<br \/>\n1x + 4x = 20<br \/>\n5x = 20<br \/>\nx = 4<br \/>\nno of strawberries :- 1x = 1(4) = 4<br \/>\nno of blueberries :- 4x = 4(4) = 16<\/p>\n<p>Question 25.<br \/>\n48 berries; 9 to 3<br \/>\nAnswer:<br \/>\nno of strawberries :- 3x<br \/>\nno of blueberries :- 9x<br \/>\n3x + 9x = 48<br \/>\n12x = 48<br \/>\nx = 4<br \/>\nno of strawberries :- 3x = 3(4) = 12<br \/>\nno of blueberries :- 9x = 9(4) = 36<\/p>\n<p>Question 26.<br \/>\n46 berries; 11 for every 12<br \/>\nAnswer:<br \/>\nno of strawberries :- 12x<br \/>\nno of blueberries :- 11x<br \/>\n12x + 11x = 46<br \/>\n23x = 46<br \/>\nx = 2<br \/>\nno of strawberries :- 12x = 12(2) = 24<br \/>\nno of blueberries :- 11x = 11(2) = 22<\/p>\n<p>Question 27.<br \/>\n<strong>PROBLEM SOLVING<\/strong><br \/>\nYou separate bulbs of garlic into two groups: one for planting and one for cooking. The tape diagram represents the ratio of bulbs for planting to bulbs for cooking. You use 6 bulbs for cooking. Each bulb has 8 cloves. How many cloves of garlic will you plant?<br \/>\n<img decoding=\"async\" loading=\"lazy\" class=\"alignnone size-full wp-image-26665\" src=\"https:\/\/ccssanswers.com\/wp-content\/uploads\/2021\/01\/Big-Ideas-Math-Answers-6th-Grade-Chapter-3-Ratios-and-Rates-3.2-11.png\" alt=\"Big Ideas Math Answers 6th Grade Chapter 3 Ratios and Rates 3.2 11\" width=\"594\" height=\"179\" srcset=\"https:\/\/ccssanswers.com\/wp-content\/uploads\/2021\/01\/Big-Ideas-Math-Answers-6th-Grade-Chapter-3-Ratios-and-Rates-3.2-11.png 594w, https:\/\/ccssanswers.com\/wp-content\/uploads\/2021\/01\/Big-Ideas-Math-Answers-6th-Grade-Chapter-3-Ratios-and-Rates-3.2-11-300x90.png 300w\" sizes=\"(max-width: 594px) 100vw, 594px\" \/><br \/>\nAnswer:<br \/>\nGiven,<br \/>\nYou separate bulbs of garlic into two groups: one for planting and one for cooking.<br \/>\nThe tape diagram represents the ratio of bulbs for planting to bulbs for cooking.<br \/>\nYou use 6 bulbs for cooking. Each bulb has 8 cloves.<br \/>\n6 : 8<br \/>\n6 \u00d7 6 = 36<br \/>\n36 \u00d7 8 = 288<br \/>\nThus you plant 288 cloves of garlic.<\/p>\n<p>Question 28.<br \/>\n<strong>MODELING REAL LIFE<\/strong><br \/>\nMethane gas contains carbon atoms and hydrogen atoms in the ratio of 1 : 4. A sample of methane gas contains 92 hydrogen atoms. How many carbon atoms are in the sample? How many total atoms are in the sample?<br \/>\n<img decoding=\"async\" loading=\"lazy\" class=\"alignnone size-full wp-image-26666\" src=\"https:\/\/ccssanswers.com\/wp-content\/uploads\/2021\/01\/Big-Ideas-Math-Answers-6th-Grade-Chapter-3-Ratios-and-Rates-3.2-12.png\" alt=\"Big Ideas Math Answers 6th Grade Chapter 3 Ratios and Rates 3.2 12\" width=\"230\" height=\"216\" \/><br \/>\nAnswer:<br \/>\nMethane: 1 carbon and 4 hydrogens<br \/>\nA sample of methane gas contains 92 hydrogen atoms.<br \/>\n1 : 4 :: x : 92<br \/>\nx = number of carbons<br \/>\nx = 92\/4<br \/>\nx = 23 carbons<br \/>\nTotal atoms = hydrogen atoms + carbon atoms<br \/>\n= 92 + 23<br \/>\n= 115 atoms<\/p>\n<p>Question 29.<br \/>\n<strong>MODELING REAL LIFE<\/strong><br \/>\nThere are 8 more girls than boys in a school play. The ratio of boys to girls is 5 : 7. How many boys and how many girls are in the play?<br \/>\nAnswer:<br \/>\nGiven,<br \/>\nThere are 8 more girls than boys in a school play. The ratio of boys to girls is 5 : 7<br \/>\n5x = 5(4) = 20 boys<br \/>\n7x = 7(4) = 28 girls<br \/>\nTo find how many more girls there are than boys in the play,<br \/>\nWe have to subtract the number of girls and number of boys<br \/>\n28 &#8211; 20 = 8<br \/>\nThus it means there are 8 more girls than boys in the school play.<\/p>\n<p>Question 30.<br \/>\n<strong>DIG DEEPER!<\/strong><br \/>\nA baseball team sells tickets for two games. The ratio of sold tickets to unsold tickets for the first game was 7 : 3. For the second game, the ratio was 13 : 2. There were 240 unsold tickets for the second game. How many tickets were sold for the first game?<br \/>\nAnswer: 1260 tickets were sold on the first game<\/p>\n<p>Explanation:<br \/>\nFor the second game, the ratio was 13 : 2.<br \/>\nTotal ratio = 13 + 2 = 15<br \/>\nThere were 240 unsold tickets for the second game.<br \/>\nLet the total number of tickets for the second game be x.<br \/>\n240 = 2\/15 \u00d7 x<br \/>\n2x = 15 \u00d7 240 = 3600<br \/>\nx = 3600\/2 = 1800<br \/>\n1800 tickets were sold for the second time.<br \/>\nAssuming total number of tickets for the first game is equal to total number of tickets for the second game.<br \/>\nTherefore total number of tickets sold for the first game is 1800<br \/>\nThe ratio of sold tickets to unsold tickets for the first game was 7: 3<br \/>\nTotal ratio 7 + 3 = 10<br \/>\nNumber of tickets sold for the first game would be 7\/10 \u00d7 1800 = 12600\/10 = 1260 tickets<\/p>\n<p>Question 31.<br \/>\n<strong>PROBLEM SOLVING<\/strong><br \/>\nYou have $150 in a savings account and you have some cash. The tape diagram represents the ratio of the amounts of money. You want to have twice the amount of money in your savings account as you have in cash. How much of your cash should you deposit into your savings account?<br \/>\n<img decoding=\"async\" loading=\"lazy\" class=\"alignnone size-full wp-image-26667\" src=\"https:\/\/ccssanswers.com\/wp-content\/uploads\/2021\/01\/Big-Ideas-Math-Answers-6th-Grade-Chapter-3-Ratios-and-Rates-3.2-13.png\" alt=\"Big Ideas Math Answers 6th Grade Chapter 3 Ratios and Rates 3.2 13\" width=\"366\" height=\"71\" srcset=\"https:\/\/ccssanswers.com\/wp-content\/uploads\/2021\/01\/Big-Ideas-Math-Answers-6th-Grade-Chapter-3-Ratios-and-Rates-3.2-13.png 366w, https:\/\/ccssanswers.com\/wp-content\/uploads\/2021\/01\/Big-Ideas-Math-Answers-6th-Grade-Chapter-3-Ratios-and-Rates-3.2-13-300x58.png 300w\" sizes=\"(max-width: 366px) 100vw, 366px\" \/><br \/>\nAnswer: $200<\/p>\n<p>Explanation:<br \/>\nWe know that:<br \/>\nYou have $150 in a savings account.<br \/>\nThis is represented with two tiles.<br \/>\nThen each tile represents:<br \/>\n$150\/2 = $75<br \/>\nAnd in cash you have 5 tiles, then in cash you have:<br \/>\n5\u00d7$75 = $375.<br \/>\nThen the problem is:<br \/>\nYou have $150 in the savings account<br \/>\nYou have $375 in cash.<br \/>\nYou want to deposit a quantity such that you have twice the amount of money in your savings account as you have in cash.<br \/>\nSuppose that you move a quantity X from cash to the savings account, then now we have the situation:<br \/>\nSav. Acc. = $150 + X<br \/>\nCash = $375 &#8211; X<br \/>\nAnd we want that:<br \/>\nSav. Acc. = 2\u00d7Cash<br \/>\n($150 + X) = 2\u00d7($375 &#8211; X)<br \/>\nLet&#8217;s solve this for X.<br \/>\n$150 + X = $750 &#8211; 2\u00d7X<br \/>\n3\u00d7X = $750 &#8211; $150 = $600<br \/>\nX = $600\/3 = $200<br \/>\nYou should deposit $200 in the Savings account.<\/p>\n<p>Question 32.<br \/>\n<strong>DIG DEEPER!<\/strong><br \/>\nA fish tank contains tetras, guppies, and minnows. The ratio of tetras to guppies is 4 : 2. The ratio of minnows to guppies is 1 : 3. There are 60 fish in the tank. How many more tetras are there than minnows? Justify your answer.<br \/>\n<img decoding=\"async\" loading=\"lazy\" class=\"alignnone size-full wp-image-26668\" src=\"https:\/\/ccssanswers.com\/wp-content\/uploads\/2021\/01\/Big-Ideas-Math-Answers-6th-Grade-Chapter-3-Ratios-and-Rates-3.2-14.png\" alt=\"Big Ideas Math Answers 6th Grade Chapter 3 Ratios and Rates 3.2 14\" width=\"329\" height=\"156\" srcset=\"https:\/\/ccssanswers.com\/wp-content\/uploads\/2021\/01\/Big-Ideas-Math-Answers-6th-Grade-Chapter-3-Ratios-and-Rates-3.2-14.png 329w, https:\/\/ccssanswers.com\/wp-content\/uploads\/2021\/01\/Big-Ideas-Math-Answers-6th-Grade-Chapter-3-Ratios-and-Rates-3.2-14-300x142.png 300w\" sizes=\"(max-width: 329px) 100vw, 329px\" \/><br \/>\nAnswer: 30<\/p>\n<p>Explanation:<br \/>\nA fish tank contains tetras, guppies, and minnows.<br \/>\nThe ratio of tetras to guppies is 4 : 2.<br \/>\nThe ratio of minnows to guppies is 1 : 3. There are 60 fish in the tank.<br \/>\nLet number of tetras be t<br \/>\nnumber of guppies be g<br \/>\nnumber of minnows be m<br \/>\nRatio of tetras to guppies is 4:2, or reducing, 2:1<br \/>\nm = g\/3<br \/>\nAlso, total there are 60 fish<br \/>\nt + g + m = 60<br \/>\n2g + g + g\/3 = 60<br \/>\nNow finding t and m:<br \/>\nm = g\/3 = 18\/3 = 6<br \/>\nm = 6<br \/>\nt = 2g<br \/>\nt = 2(18)<br \/>\nt = 36<br \/>\nThere are 36 tetras and 6 minnows. So, there are 36 &#8211; 6 = 30 more tetras than minnows<\/p>\n<p><strong>EXPLORATION 1<\/strong><\/p>\n<p>Making a Table of Equivalent Ratios<br \/>\nWork with a partner. You buy milk that contains 180 calories per 2 cups.<br \/>\na. You measure 2 cups of the milk for a recipe and pour it into a pitcher. You repeat this four more times. Make a table to show the numbers of calories and cups in the pitcher as you add the milk.<br \/>\nb. Describe any relationships you see in your table.<br \/>\nc. Describe ways that you can find equivalent ratios using different operations.<br \/>\n<img decoding=\"async\" loading=\"lazy\" class=\"alignnone size-full wp-image-26669\" src=\"https:\/\/ccssanswers.com\/wp-content\/uploads\/2021\/01\/Big-Ideas-Math-Answers-Grade-6-Chapter-3-Ratios-and-Rates-3.3-1.png\" alt=\"Big Ideas Math Answers Grade 6 Chapter 3 Ratios and Rates 3.3 1\" width=\"431\" height=\"223\" srcset=\"https:\/\/ccssanswers.com\/wp-content\/uploads\/2021\/01\/Big-Ideas-Math-Answers-Grade-6-Chapter-3-Ratios-and-Rates-3.3-1.png 431w, https:\/\/ccssanswers.com\/wp-content\/uploads\/2021\/01\/Big-Ideas-Math-Answers-Grade-6-Chapter-3-Ratios-and-Rates-3.3-1-300x155.png 300w\" sizes=\"(max-width: 431px) 100vw, 431px\" \/><br \/>\nAnswer:<\/p>\n<p><strong>EXPLORATION 2<\/strong><\/p>\n<p>Creating a Double Number Line<br \/>\nWork with a partner.<br \/>\na. Represent the ratio in Exploration 1 by labeling the increments on the double number line below. Can you label the increments in more than one way?<br \/>\n<img decoding=\"async\" loading=\"lazy\" class=\"alignnone size-full wp-image-26670\" src=\"https:\/\/ccssanswers.com\/wp-content\/uploads\/2021\/01\/Big-Ideas-Math-Answers-Grade-6-Chapter-3-Ratios-and-Rates-3.3-2.png\" alt=\"Big Ideas Math Answers Grade 6 Chapter 3 Ratios and Rates 3.3 2\" width=\"435\" height=\"93\" srcset=\"https:\/\/ccssanswers.com\/wp-content\/uploads\/2021\/01\/Big-Ideas-Math-Answers-Grade-6-Chapter-3-Ratios-and-Rates-3.3-2.png 435w, https:\/\/ccssanswers.com\/wp-content\/uploads\/2021\/01\/Big-Ideas-Math-Answers-Grade-6-Chapter-3-Ratios-and-Rates-3.3-2-300x64.png 300w\" sizes=\"(max-width: 435px) 100vw, 435px\" \/><br \/>\nb. How can you use the double number line to find the number of calories in 3 cups of milk? 3.5 cups of milk?<br \/>\nAnswer:<\/p>\n<h3><a id=\"Lesson_3.3_Using_Ratio_Tables\"><\/a>Lesson 3.3 Using Ratio Tables<\/h3>\n<p>You can find and organize equivalent ratios in a ratio table. You can generate a ratio table by using repeated addition or multiplication.<br \/>\n<img decoding=\"async\" loading=\"lazy\" class=\"alignnone size-full wp-image-26671\" src=\"https:\/\/ccssanswers.com\/wp-content\/uploads\/2021\/01\/Big-Ideas-Math-Answers-Grade-6-Chapter-3-Ratios-and-Rates-3.3-3.png\" alt=\"Big Ideas Math Answers Grade 6 Chapter 3 Ratios and Rates 3.3 3\" width=\"187\" height=\"68\" \/><\/p>\n<p><strong>Try It<\/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 decoding=\"async\" loading=\"lazy\" class=\"alignnone size-full wp-image-26672\" src=\"https:\/\/ccssanswers.com\/wp-content\/uploads\/2021\/01\/Big-Ideas-Math-Answers-Grade-6-Chapter-3-Ratios-and-Rates-3.3-4.png\" alt=\"Big Ideas Math Answers Grade 6 Chapter 3 Ratios and Rates 3.3 4\" width=\"198\" height=\"65\" \/><br \/>\nAnswer:<br \/>\n<img decoding=\"async\" loading=\"lazy\" class=\"alignnone size-full wp-image-34135\" src=\"https:\/\/ccssanswers.com\/wp-content\/uploads\/2021\/01\/Big-Ideas-Math-Answers-Grade-6-Chapter-3-Ratios-and-Rates-3.3-4.jpg\" alt=\"Big-Ideas-Math-Answers-Grade-6-Chapter-3-Ratios-and-Rates-3.3-4\" width=\"198\" height=\"65\" \/><\/p>\n<p>Question 2.<br \/>\n<img decoding=\"async\" loading=\"lazy\" class=\"alignnone size-full wp-image-26673\" src=\"https:\/\/ccssanswers.com\/wp-content\/uploads\/2021\/01\/Big-Ideas-Math-Answers-Grade-6-Chapter-3-Ratios-and-Rates-3.3-5.png\" alt=\"Big Ideas Math Answers Grade 6 Chapter 3 Ratios and Rates 3.3 5\" width=\"195\" height=\"68\" \/><br \/>\nAnswer:<br \/>\n<img decoding=\"async\" loading=\"lazy\" class=\"alignnone size-full wp-image-34194\" src=\"https:\/\/ccssanswers.com\/wp-content\/uploads\/2021\/01\/Big-Ideas-Math-Answers-Grade-6-Chapter-3-Ratios-and-Rates-3.3-5.jpg\" alt=\"Big-Ideas-Math-Answers-Grade-6-Chapter-3-Ratios-and-Rates-3.3-5\" width=\"195\" height=\"68\" \/><\/p>\n<p>You can also generate a ratio table by using subtraction or division. In summary, you can find equivalent ratios by:<br \/>\n\u2022 adding or subtracting quantities in equivalent ratios.<br \/>\n\u2022 multiplying or dividing each quantity in a ratio by the same number.<\/p>\n<p><strong>Try It<\/strong><\/p>\n<p><strong>Find the missing values in the ratio table. Then write the equivalent ratios.<\/strong><br \/>\nQuestion 3.<br \/>\n<img decoding=\"async\" loading=\"lazy\" class=\"alignnone size-full wp-image-26674\" src=\"https:\/\/ccssanswers.com\/wp-content\/uploads\/2021\/01\/Big-Ideas-Math-Answers-Grade-6-Chapter-3-Ratios-and-Rates-3.3-6.png\" alt=\"Big Ideas Math Answers Grade 6 Chapter 3 Ratios and Rates 3.3 6\" width=\"205\" height=\"62\" \/><br \/>\nAnswer:<br \/>\n<img decoding=\"async\" loading=\"lazy\" class=\"alignnone size-full wp-image-34197\" src=\"https:\/\/ccssanswers.com\/wp-content\/uploads\/2021\/01\/Big-Ideas-Math-Answers-Grade-6-Chapter-3-Ratios-and-Rates-3.3-6.jpg\" alt=\"Big-Ideas-Math-Answers-Grade-6-Chapter-3-Ratios-and-Rates-3.3-6\" width=\"205\" height=\"62\" \/><br \/>\n2:10 = 1:5<br \/>\n4:20 = 1:5<br \/>\n3:15 = 1:5<\/p>\n<p>Question 4.<br \/>\n<img decoding=\"async\" loading=\"lazy\" class=\"alignnone size-full wp-image-26675\" src=\"https:\/\/ccssanswers.com\/wp-content\/uploads\/2021\/01\/Big-Ideas-Math-Answers-Grade-6-Chapter-3-Ratios-and-Rates-3.3-7.png\" alt=\"Big Ideas Math Answers Grade 6 Chapter 3 Ratios and Rates 3.3 7\" width=\"208\" height=\"67\" \/><br \/>\nAnswer:<br \/>\n<img decoding=\"async\" loading=\"lazy\" class=\"alignnone size-full wp-image-34385\" src=\"https:\/\/ccssanswers.com\/wp-content\/uploads\/2021\/01\/Big-Ideas-Math-Answers-Grade-6-Chapter-3-Ratios-and-Rates-3.3-7.jpg\" alt=\"Big-Ideas-Math-Answers-Grade-6-Chapter-3-Ratios-and-Rates-3.3-7\" width=\"208\" height=\"67\" \/><br \/>\nThe ratio is 12:1<br \/>\nThe equivalent ratios are<br \/>\n24:2 = 12:1<br \/>\n48:4 = 12:1<br \/>\n36:3 = 12:1<\/p>\n<p>Question 5.<br \/>\n<strong>WHAT IF?<\/strong><br \/>\nYou eat 21 crackers. How much sodium do you consume?<br \/>\nAnswer:<br \/>\n<img decoding=\"async\" loading=\"lazy\" class=\"alignnone size-full wp-image-34201\" src=\"https:\/\/ccssanswers.com\/wp-content\/uploads\/2021\/01\/BIg-Ideas-Math-Answers-Grade-6-Chapter-3-Ratios-and-Rates.jpg\" alt=\"BIg Ideas Math Answers Grade 6 Chapter 3 Ratios and Rates\" width=\"571\" height=\"153\" srcset=\"https:\/\/ccssanswers.com\/wp-content\/uploads\/2021\/01\/BIg-Ideas-Math-Answers-Grade-6-Chapter-3-Ratios-and-Rates.jpg 571w, https:\/\/ccssanswers.com\/wp-content\/uploads\/2021\/01\/BIg-Ideas-Math-Answers-Grade-6-Chapter-3-Ratios-and-Rates-300x80.jpg 300w\" sizes=\"(max-width: 571px) 100vw, 571px\" \/><br \/>\nAdd the middle two columns<br \/>\n120 + 20 = 140<br \/>\n18 + 3 = 21 crackers<br \/>\nThus you consume 140 mg sodium.<\/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>COMPLETING A RATIO TABLE<\/strong> Find the missing values in the ratio table. Then write the equivalent ratios.<br \/>\nQuestion 6.<br \/>\n<img decoding=\"async\" loading=\"lazy\" class=\"alignnone size-full wp-image-26676\" src=\"https:\/\/ccssanswers.com\/wp-content\/uploads\/2021\/01\/Big-Ideas-Math-Answers-Grade-6-Chapter-3-Ratios-and-Rates-3.3-8.png\" alt=\"Big Ideas Math Answers Grade 6 Chapter 3 Ratios and Rates 3.3 8\" width=\"197\" height=\"65\" \/><br \/>\nAnswer:<br \/>\n<img decoding=\"async\" loading=\"lazy\" class=\"alignnone size-full wp-image-34386\" src=\"https:\/\/ccssanswers.com\/wp-content\/uploads\/2021\/01\/Big-Ideas-Math-Answers-Grade-6-Chapter-3-Ratios-and-Rates-3.3-8.jpg\" alt=\"Big-Ideas-Math-Answers-Grade-6-Chapter-3-Ratios-and-Rates-3.3-8\" width=\"197\" height=\"65\" \/><br \/>\nThe missing values in the ratio are 4, 12, 18<br \/>\nThe ratio is 2:6<br \/>\nThe equivalent ratio of 2:6 are 4:12, 6:18<\/p>\n<p>Question 7.<br \/>\n<img decoding=\"async\" loading=\"lazy\" class=\"alignnone size-full wp-image-26677\" src=\"https:\/\/ccssanswers.com\/wp-content\/uploads\/2021\/01\/Big-Ideas-Math-Answers-Grade-6-Chapter-3-Ratios-and-Rates-3.3-9.png\" alt=\"Big Ideas Math Answers Grade 6 Chapter 3 Ratios and Rates 3.3 9\" width=\"193\" height=\"68\" \/><br \/>\nAnswer:<br \/>\n<img decoding=\"async\" loading=\"lazy\" class=\"alignnone size-full wp-image-34387\" src=\"https:\/\/ccssanswers.com\/wp-content\/uploads\/2021\/01\/Big-Ideas-Math-Answers-Grade-6-Chapter-3-Ratios-and-Rates-3.3-9.jpg\" alt=\"Big-Ideas-Math-Answers-Grade-6-Chapter-3-Ratios-and-Rates-3.3-9\" width=\"193\" height=\"68\" \/><br \/>\nThe missing values in the ratio are 56, 7, 20<br \/>\nThe ratio is 2:8<br \/>\nThe equivalent ratio of 2:8 are 14:56, 7:28, 5:20<\/p>\n<p>Question 8.<br \/>\n<strong>WRITING<\/strong><br \/>\nExplain how creating a ratio table using repeated addition is similar to creating a ratio table using multiplication.<br \/>\nAnswer:<br \/>\nRatio tables are constructed in a special way. Each pair of values in the table will be equivalent to the same ratio. You can use repeated addition or multiplication to create a ratio table. There is a constant value that we can multiply the values in the first column by to get the values in the second column.<\/p>\n<p>Question 9.<br \/>\nYou mix 7 tablespoons of vinegar for every 4 tablespoons of baking soda to produce a chemical reaction. You use 15 tablespoons of baking soda. How much vinegar do you use?<br \/>\nAnswer:<br \/>\nGiven,<br \/>\nYou mix 7 tablespoons of vinegar for every 4 tablespoons of baking soda to produce a chemical reaction.<br \/>\nYou use 15 tablespoons of baking soda.<br \/>\nCase 1:<br \/>\nTablespoon of vinegar taken = 7<br \/>\nTablespoon of baking soda taken = 4<br \/>\nThe ratio between v and b = 7:4<br \/>\nCase 2:<br \/>\nTablespoon of vinegar taken = x<br \/>\nTablespoon of baking soda taken = 15<br \/>\nThe ratio between v and b = x:15<br \/>\n7:4 : : x:15<br \/>\n7 \u00d7 15 = 4 \u00d7 x<br \/>\n4x = 105<br \/>\nx = 105\/4<br \/>\nx = 26.25<br \/>\nThus you use 26.25 teaspoons.<\/p>\n<p>Question 10.<br \/>\nYou make a carbonated beverage by adding 7 ounces of soda water for every 3 ounces of regular water. Your friend uses 11 ounces of soda water for every 4 ounces of regular water. Whose beverage is more carbonated?<br \/>\n<img decoding=\"async\" loading=\"lazy\" class=\"alignnone size-full wp-image-26678\" src=\"https:\/\/ccssanswers.com\/wp-content\/uploads\/2021\/01\/Big-Ideas-Math-Answers-Grade-6-Chapter-3-Ratios-and-Rates-3.3-10.png\" alt=\"Big Ideas Math Answers Grade 6 Chapter 3 Ratios and Rates 3.3 10\" width=\"204\" height=\"139\" \/><br \/>\nAnswer:<br \/>\nThe proportion of soda in the drink will show us how carbonated a beverage is. The proportion of soda is the ounce of soda divided by the sum of the soda and water.<br \/>\nThe proportion of soda in the first beverage<br \/>\n7\/(7+3) = 7\/10 = 0.7<br \/>\nThe proportion of soda in the first beverage<br \/>\n11\/(11+4) = 11\/15 = 0.73<br \/>\nTherefore the second beverage is more carbonated.<\/p>\n<h3><a id=\"Using_Ratio_Tables_Homework_&amp;_Practice_3.3\"><\/a>Using Ratio Tables Homework &amp; Practice 3.3<\/h3>\n<p><strong>Review &amp; Refresh<\/strong><\/p>\n<p>A bag contains green tokens and black tokens. You are given the number of green tokens in the bag and the ratio of green tokens to black tokens. Find the number of black tokens in the bag.<br \/>\nQuestion 1.<br \/>\ngreen tokens; 4 for every 1<br \/>\nAnswer:<br \/>\nno of green tokens:- 4x<br \/>\nno of black tokens:- 1x<br \/>\nx = 1<br \/>\nno of green tokens:- 4x = 4(1) = 4<br \/>\nno of black tokens:- 1x = 1() = 1<\/p>\n<p>Question 2.<br \/>\n6 green tokens; 2 : 7<br \/>\nAnswer:<br \/>\nno of green tokens:- 2x<br \/>\nno of black tokens:- 7x<br \/>\n2x + 7x = 6<br \/>\n9x = 6<br \/>\nx = 6\/9<br \/>\nx = 2\/3<br \/>\nno of green tokens:- 2x = 2(2\/3) = 4\/3<br \/>\nno of black tokens:- 7x = 7(2\/3) = 14\/3<\/p>\n<p>Question 3.<br \/>\n24 green tokens; 8 to 5<br \/>\nAnswer:<br \/>\nno of green tokens:- 8x<br \/>\nno of black tokens:- 5x<br \/>\n8x + 5x = 24<br \/>\n13x = 24<br \/>\nx = 24\/13<br \/>\nno of green tokens:- 8x = 8(24\/13) = 14.7<br \/>\nno of black tokens:- 5x = 5(24\/13) = 9.23<\/p>\n<p>Question 4.<br \/>\n36 green tokens; 3 for every 4<br \/>\nAnswer:<br \/>\nno of green tokens:- 3x<br \/>\nno of black tokens:- 4x<br \/>\n3x + 4x = 36<br \/>\n7x = 36<br \/>\nx = 36\/7<br \/>\nno of green tokens:- 3x = 3(36\/7) = 15.42<br \/>\nno of black tokens:- 4x = 4(36\/7) = 20.57<\/p>\n<p><strong>Find the GCF of the numbers.<\/strong><br \/>\nQuestion 5.<br \/>\n8, 16<br \/>\nAnswer: 8<\/p>\n<p>Explanation:<br \/>\nThe factors of 8 are: 1, 2, 4, 8<br \/>\nThe factors of 16 are: 1, 2, 4, 8, 16<br \/>\nThen the greatest common factor is 8.<\/p>\n<p>Question 6.<br \/>\n48, 80<br \/>\nAnswer: 16<\/p>\n<p>Explanation:<br \/>\nThe factors of 48 are: 1, 2, 3, 4, 6, 8, 12, 16, 24, 48<br \/>\nThe factors of 80 are: 1, 2, 4, 5, 8, 10, 16, 20, 40, 80<br \/>\nThen the greatest common factor is 16.<\/p>\n<p>Question 7.<br \/>\n15, 45, 100<br \/>\nAnswer: 5<\/p>\n<p>Explanation:<br \/>\nThe factors of 15 are: 1, 3, 5, 15<br \/>\nThe factors of 45 are: 1, 3, 5, 9, 15, 45<br \/>\nThe factors of 100 are: 1, 2, 4, 5, 10, 20, 25, 50, 100<br \/>\nThen the greatest common factor is 5.<\/p>\n<p><strong>Evaluate the expression.<\/strong><br \/>\nQuestion 8.<br \/>\n35 &#8211; 2 \u00d7 4<sup>2<\/sup><br \/>\nAnswer:<br \/>\n35 &#8211; 2 \u00d7 4<sup>2<\/sup><br \/>\n35 &#8211; 2 \u00d7 16<br \/>\n35 &#8211; 32 = 3<\/p>\n<p>Question 9.<br \/>\n12 \u00f7 (1 + 3<sup>3<\/sup> &#8211; 2<sup>4<\/sup>)<br \/>\nAnswer:<br \/>\n12 \u00f7 (1 + 3<sup>3<\/sup> &#8211; 2<sup>4<\/sup>)<br \/>\n12 \u00f7 (1 + 27 &#8211; 16)<br \/>\n12 \u00f7 (28 &#8211; 16)<br \/>\n12 \u00f7 12 = 1<\/p>\n<p>Question 10.<br \/>\n8<sup>2<\/sup> \u00f7 [(11 &#8211; 3) . 2]<br \/>\nAnswer:<br \/>\n8<sup>2<\/sup> \u00f7 [(11 &#8211; 3) . 2]<br \/>\n8<sup>2<\/sup> \u00f7 [8 . 2]<br \/>\n8<sup>2<\/sup> \u00f7 16<br \/>\n64 \u00f7 16 = 4<\/p>\n<p><strong>Find the perimeter of the rectangle.<\/strong><br \/>\nQuestion 11.<br \/>\n<img decoding=\"async\" loading=\"lazy\" class=\"alignnone size-full wp-image-26679\" src=\"https:\/\/ccssanswers.com\/wp-content\/uploads\/2021\/01\/Big-Ideas-Math-Answers-Grade-6-Chapter-3-Ratios-and-Rates-3.3-11.png\" alt=\"Big Ideas Math Answers Grade 6 Chapter 3 Ratios and Rates 3.3 11\" width=\"139\" height=\"117\" \/><br \/>\nAnswer:<br \/>\nGiven Area = 48 sq. yd<br \/>\nLength = 8 yd<br \/>\nWidth = x<br \/>\nArea of the rectangle = l \u00d7 w<br \/>\n48 = 8 \u00d7 x<br \/>\nx = 48\/8 = 6<br \/>\nx = 6 yd<br \/>\nThus the width of the rectangle = 6 yd<br \/>\nPerimeter of the rectangle = 2l + 2w<br \/>\nP = 2(8) + 2(6)<br \/>\nP = 16 + 12<br \/>\nP = 28<br \/>\nThus the perimeter of the rectangle = 28 yards<\/p>\n<p>Question 12.<br \/>\n<img decoding=\"async\" loading=\"lazy\" class=\"alignnone size-full wp-image-26680\" src=\"https:\/\/ccssanswers.com\/wp-content\/uploads\/2021\/01\/Big-Ideas-Math-Answers-Grade-6-Chapter-3-Ratios-and-Rates-3.3-12.png\" alt=\"Big Ideas Math Answers Grade 6 Chapter 3 Ratios and Rates 3.3 12\" width=\"127\" height=\"129\" \/><br \/>\nAnswer:<br \/>\nGiven Area = 132 sq. mm<br \/>\nLength = 12 mm<br \/>\nWidth = x<br \/>\nArea of the rectangle = l \u00d7 w<br \/>\n132 = 12 \u00d7 x<br \/>\nx = 132\/12 = 11<br \/>\nx = 11 mm<br \/>\nThus the width of the rectangle = 11 mm<br \/>\nPerimeter of the rectangle = 2l + 2w<br \/>\nP = 2(12) + 2(11)<br \/>\nP = 24 + 22<br \/>\nP = 46<br \/>\nThus the perimeter of the rectangle = 46 mm<\/p>\n<p><strong>Concepts, Skills, &amp; Problem Solving<\/strong><\/p>\n<p><strong>USING A RATIO TABLE<\/strong> Use a ratio table to find the number of calories in the indicated number of cups of milk from Exploration 1. Explain your method. (See Exploration 1, p. 121.)<br \/>\nQuestion 13.<br \/>\n16 cups<br \/>\nAnswer:<br \/>\nYou buy milk that contains 180 calories per 2 cups.<br \/>\n1 cup = 180\/2 = 90 calories<br \/>\n16 cups = 16 \u00d7 90 = 1440 calories<\/p>\n<p>Question 14.<br \/>\n18 cups<br \/>\nAnswer:<br \/>\nYou buy milk that contains 180 calories per 2 cups.<br \/>\n1 cup = 180\/2 = 90 calories<br \/>\n18 cups = 18 \u00d7 90 = 1620 calories<\/p>\n<p>Question 15.<br \/>\n5.5 cups<br \/>\nAnswer:<br \/>\nYou buy milk that contains 180 calories per 2 cups.<br \/>\n1 cup = 180\/2 = 90 calories<br \/>\n5.5 cups = 5.5 \u00d7 90 = 495 calories<\/p>\n<p><strong>COMPLETING RATIO TABLES<\/strong> Find the missing value(s) in the ratio table. Then write the equivalent ratios.<br \/>\nQuestion 16.<br \/>\n<img decoding=\"async\" loading=\"lazy\" class=\"alignnone size-full wp-image-26681\" src=\"https:\/\/ccssanswers.com\/wp-content\/uploads\/2021\/01\/Big-Ideas-Math-Answers-Grade-6-Chapter-3-Ratios-and-Rates-3.3-15.png\" alt=\"Big Ideas Math Answers Grade 6 Chapter 3 Ratios and Rates 3.3 15\" width=\"120\" height=\"67\" \/><br \/>\nAnswer:<br \/>\n<img decoding=\"async\" loading=\"lazy\" class=\"alignnone size-full wp-image-35518\" src=\"https:\/\/ccssanswers.com\/wp-content\/uploads\/2021\/01\/Big-Ideas-Math-Answers-Grade-6-Chapter-3-Ratios-and-Rates-3.3-15-1.png\" alt=\"Big-Ideas-Math-Answers-Grade-6-Chapter-3-Ratios-and-Rates-3.3-15\" width=\"120\" height=\"67\" \/><br \/>\nThe ratio is 1 : 5<br \/>\nThe equivalent ratio with 10 is 2 : 10<\/p>\n<p>Question 17.<br \/>\n<img decoding=\"async\" loading=\"lazy\" class=\"alignnone size-full wp-image-26682\" src=\"https:\/\/ccssanswers.com\/wp-content\/uploads\/2021\/01\/Big-Ideas-Math-Answers-Grade-6-Chapter-3-Ratios-and-Rates-3.3-16.png\" alt=\"Big Ideas Math Answers Grade 6 Chapter 3 Ratios and Rates 3.3 16\" width=\"187\" height=\"66\" \/><br \/>\nAnswer:<br \/>\n<img decoding=\"async\" loading=\"lazy\" class=\"alignnone size-full wp-image-35519\" src=\"https:\/\/ccssanswers.com\/wp-content\/uploads\/2021\/01\/Big-Ideas-Math-Answers-Grade-6-Chapter-3-Ratios-and-Rates-3.3-16.jpg\" alt=\"Big-Ideas-Math-Answers-Grade-6-Chapter-3-Ratios-and-Rates-3.3-16\" width=\"187\" height=\"66\" \/><br \/>\nThe ratio is 3 : 5<br \/>\nThe equivalent ratio is 6 : 10, 9 : 15<\/p>\n<p>Question 18.<br \/>\n<img decoding=\"async\" loading=\"lazy\" class=\"alignnone size-full wp-image-26683\" src=\"https:\/\/ccssanswers.com\/wp-content\/uploads\/2021\/01\/Big-Ideas-Math-Answers-Grade-6-Chapter-3-Ratios-and-Rates-3.3-17.png\" alt=\"Big Ideas Math Answers Grade 6 Chapter 3 Ratios and Rates 3.3 17\" width=\"182\" height=\"64\" \/><br \/>\nAnswer:<br \/>\n<img decoding=\"async\" loading=\"lazy\" class=\"alignnone size-full wp-image-35521\" src=\"https:\/\/ccssanswers.com\/wp-content\/uploads\/2021\/01\/Big-Ideas-Math-Answers-Grade-6-Chapter-3-Ratios-and-Rates-3.3-17.jpg\" alt=\"Big-Ideas-Math-Answers-Grade-6-Chapter-3-Ratios-and-Rates-3.3-17\" width=\"182\" height=\"64\" \/><br \/>\nThe ratio is 6 : 3<br \/>\nThe equivalent ratio is 24 : 12, 18 : 9<\/p>\n<p>Question 19.<br \/>\n<img decoding=\"async\" loading=\"lazy\" class=\"alignnone size-full wp-image-26685\" src=\"https:\/\/ccssanswers.com\/wp-content\/uploads\/2021\/01\/Big-Ideas-Math-Answers-Grade-6-Chapter-3-Ratios-and-Rates-3.3-18.png\" alt=\"Big Ideas Math Answers Grade 6 Chapter 3 Ratios and Rates 3.3 18\" width=\"210\" height=\"65\" \/><br \/>\nAnswer:<br \/>\n<img decoding=\"async\" loading=\"lazy\" class=\"alignnone size-full wp-image-35522\" src=\"https:\/\/ccssanswers.com\/wp-content\/uploads\/2021\/01\/Big-Ideas-Math-Answers-Grade-6-Chapter-3-Ratios-and-Rates-3.3-18.jpg\" alt=\"Big-Ideas-Math-Answers-Grade-6-Chapter-3-Ratios-and-Rates-3.3-18\" width=\"210\" height=\"65\" \/><br \/>\nThe ratio is 2 : 14<br \/>\nThe equivalent ratio is 1 : 7, 3 : 21, 18 : 126<\/p>\n<p>Question 20.<br \/>\n<img decoding=\"async\" loading=\"lazy\" class=\"alignnone size-full wp-image-26686\" src=\"https:\/\/ccssanswers.com\/wp-content\/uploads\/2021\/01\/Big-Ideas-Math-Answers-Grade-6-Chapter-3-Ratios-and-Rates-3.3-19.png\" alt=\"Big Ideas Math Answers Grade 6 Chapter 3 Ratios and Rates 3.3 19\" width=\"205\" height=\"78\" \/><br \/>\nAnswer:<br \/>\n<img decoding=\"async\" loading=\"lazy\" class=\"alignnone size-full wp-image-35523\" src=\"https:\/\/ccssanswers.com\/wp-content\/uploads\/2021\/01\/Big-Ideas-Math-Answers-Grade-6-Chapter-3-Ratios-and-Rates-3.3-19.jpg\" alt=\"Big-Ideas-Math-Answers-Grade-6-Chapter-3-Ratios-and-Rates-3.3-19\" width=\"205\" height=\"78\" \/><\/p>\n<p>Question 21.<br \/>\n<img decoding=\"async\" loading=\"lazy\" class=\"alignnone size-full wp-image-26687\" src=\"https:\/\/ccssanswers.com\/wp-content\/uploads\/2021\/01\/Big-Ideas-Math-Answers-Grade-6-Chapter-3-Ratios-and-Rates-3.3-20.png\" alt=\"Big Ideas Math Answers Grade 6 Chapter 3 Ratios and Rates 3.3 20\" width=\"204\" height=\"69\" \/><br \/>\nAnswer:<br \/>\n<img decoding=\"async\" loading=\"lazy\" class=\"alignnone size-full wp-image-35524\" src=\"https:\/\/ccssanswers.com\/wp-content\/uploads\/2021\/01\/Big-Ideas-Math-Answers-Grade-6-Chapter-3-Ratios-and-Rates-3.3-20.jpg\" alt=\"Big-Ideas-Math-Answers-Grade-6-Chapter-3-Ratios-and-Rates-3.3-20\" width=\"204\" height=\"69\" \/><\/p>\n<p>Question 22.<br \/>\n<strong>YOU BE THE TEACHER<\/strong><br \/>\nYour friend creates a ratio table for the ratio 5 : 3. Is your friend correct? Explain your reasoning.<br \/>\n<img decoding=\"async\" loading=\"lazy\" class=\"alignnone size-full wp-image-26688\" src=\"https:\/\/ccssanswers.com\/wp-content\/uploads\/2021\/01\/Big-Ideas-Math-Answers-Grade-6-Chapter-3-Ratios-and-Rates-3.3-21.png\" alt=\"Big Ideas Math Answers Grade 6 Chapter 3 Ratios and Rates 3.3 21\" width=\"199\" height=\"93\" \/><br \/>\nAnswer: No your friend is incorrect. Because 125 : 27 is not the equivalent ratio of 5 : 3<\/p>\n<p><strong>COMPLETING RATIO TABLES<\/strong> Complete the ratio table to solve the problem.<br \/>\nQuestion 23.<br \/>\nFor every 3 tickets you sell, your friend sells 4 tickets. You sell a total of 12 tickets. How many tickets does your friend sell?<br \/>\n<img decoding=\"async\" loading=\"lazy\" class=\"alignnone size-full wp-image-26689\" src=\"https:\/\/ccssanswers.com\/wp-content\/uploads\/2021\/01\/Big-Ideas-Math-Answers-Grade-6-Chapter-3-Ratios-and-Rates-3.3-22.png\" alt=\"Big Ideas Math Answers Grade 6 Chapter 3 Ratios and Rates 3.3 22\" width=\"211\" height=\"69\" \/><br \/>\nAnswer:<br \/>\nThe ratio is 3 : 4<br \/>\nSo divide 12 by 3 = 4 and sells 16 tickets<br \/>\nThus the ratio is 12 : 16 = 3 : 4<\/p>\n<p>Question 24.<br \/>\nA store sells 2 printers for every 5 computers. The store sells 40 computers. How many printers does the store sell?<br \/>\n<img decoding=\"async\" loading=\"lazy\" class=\"alignnone size-full wp-image-26690\" src=\"https:\/\/ccssanswers.com\/wp-content\/uploads\/2021\/01\/Big-Ideas-Math-Answers-Grade-6-Chapter-3-Ratios-and-Rates-3.3-23.png\" alt=\"Big Ideas Math Answers Grade 6 Chapter 3 Ratios and Rates 3.3 23\" width=\"231\" height=\"68\" \/><br \/>\nAnswer:<br \/>\nLet us think of 2 printers for every 5 computers as a set.<br \/>\nFirst let us determine hoe many sets were sold to get to 40 computers<br \/>\n5x = 40<br \/>\nx = 8<br \/>\n2x = 2(8) = 16<br \/>\nThis means 16 printers were sold.<\/p>\n<p>Question 25.<br \/>\nFirst and second place in a contest use a ratio to share a cash prize. When first place pays $100, second place pays $60. How much does first place pay when second place pays $36?<br \/>\n<img decoding=\"async\" loading=\"lazy\" class=\"alignnone size-full wp-image-26691\" src=\"https:\/\/ccssanswers.com\/wp-content\/uploads\/2021\/01\/Big-Ideas-Math-Answers-Grade-6-Chapter-3-Ratios-and-Rates-3.3-24.png\" alt=\"Big Ideas Math Answers Grade 6 Chapter 3 Ratios and Rates 3.3 24\" width=\"172\" height=\"68\" \/><br \/>\nAnswer: $60<\/p>\n<p>Explanation:<br \/>\nGiven,<br \/>\nFirst and second place in a contest use a ratio to share a cash prize. When first place pays $100, second place pays $60.<br \/>\nLet x be the pay of the first place when the second place pays $36<br \/>\n100\/60 = x\/36<br \/>\nx = $60<\/p>\n<p>Question 26.<br \/>\nA grade has 81 girls and 72 boys. The grade is split into groups that have the same ratio of girls to boys as the whole grade. How many girls are in a group that has 16 boys?<br \/>\n<img decoding=\"async\" loading=\"lazy\" class=\"alignnone size-full wp-image-26692\" src=\"https:\/\/ccssanswers.com\/wp-content\/uploads\/2021\/01\/Big-Ideas-Math-Answers-Grade-6-Chapter-3-Ratios-and-Rates-3.3-25.png\" alt=\"Big Ideas Math Answers Grade 6 Chapter 3 Ratios and Rates 3.3 25\" width=\"153\" height=\"72\" srcset=\"https:\/\/ccssanswers.com\/wp-content\/uploads\/2021\/01\/Big-Ideas-Math-Answers-Grade-6-Chapter-3-Ratios-and-Rates-3.3-25.png 153w, https:\/\/ccssanswers.com\/wp-content\/uploads\/2021\/01\/Big-Ideas-Math-Answers-Grade-6-Chapter-3-Ratios-and-Rates-3.3-25-150x72.png 150w\" sizes=\"(max-width: 153px) 100vw, 153px\" \/><br \/>\nAnswer:<br \/>\nA grade has 81 girls and 72 boys. The grade is split into groups that have the same ratio of girls to boys as the whole grade.<br \/>\nWe have to find how many girls are in a group that has 16 boys<br \/>\n81 : 72 = x : 16<br \/>\n16 \u00d7 81 = 1296<br \/>\n1296\/72 = 18<br \/>\nTherefore the value of girls numbers is 18.<br \/>\nThe new ratio will be 18 : 16<\/p>\n<p><strong>USING A DOUBLE NUMBER LINE<\/strong> Find the missing quantity in the double number line.<br \/>\nQuestion 27.<br \/>\n<img decoding=\"async\" loading=\"lazy\" class=\"alignnone size-full wp-image-26693\" src=\"https:\/\/ccssanswers.com\/wp-content\/uploads\/2021\/01\/Big-Ideas-Math-Answers-Grade-6-Chapter-3-Ratios-and-Rates-3.3-26.png\" alt=\"Big Ideas Math Answers Grade 6 Chapter 3 Ratios and Rates 3.3 26\" width=\"240\" height=\"94\" \/><br \/>\nAnswer:<br \/>\nThe equivalent ratio of 460 : 4 is 1840 : 16<br \/>\n<img decoding=\"async\" loading=\"lazy\" class=\"alignnone size-full wp-image-35525\" src=\"https:\/\/ccssanswers.com\/wp-content\/uploads\/2021\/01\/Big-Ideas-Math-Answers-Grade-6-Chapter-3-Ratios-and-Rates-3.3-26.jpg\" alt=\"Big-Ideas-Math-Answers-Grade-6-Chapter-3-Ratios-and-Rates-3.3-26\" width=\"240\" height=\"94\" \/><\/p>\n<p>Question 28.<br \/>\n<img decoding=\"async\" loading=\"lazy\" class=\"alignnone size-full wp-image-26694\" src=\"https:\/\/ccssanswers.com\/wp-content\/uploads\/2021\/01\/Big-Ideas-Math-Answers-Grade-6-Chapter-3-Ratios-and-Rates-3.3-27.png\" alt=\"Big Ideas Math Answers Grade 6 Chapter 3 Ratios and Rates 3.3 27\" width=\"243\" height=\"90\" \/><br \/>\nAnswer:<br \/>\nThe equivalent ratio of 700 : 14 is 1050 : 21<br \/>\n<img decoding=\"async\" loading=\"lazy\" class=\"alignnone size-full wp-image-35526\" src=\"https:\/\/ccssanswers.com\/wp-content\/uploads\/2021\/01\/Big-Ideas-Math-Answers-Grade-6-Chapter-3-Ratios-and-Rates-3.3-27.jpg\" alt=\"Big-Ideas-Math-Answers-Grade-6-Chapter-3-Ratios-and-Rates-3.3-27\" width=\"243\" height=\"90\" \/><\/p>\n<p>Question 29.<br \/>\n<strong>PROBLEM SOLVING<\/strong><br \/>\nA company sets sales goals for employees each month.<br \/>\n<img decoding=\"async\" loading=\"lazy\" class=\"alignnone size-full wp-image-26695\" src=\"https:\/\/ccssanswers.com\/wp-content\/uploads\/2021\/01\/Big-Ideas-Math-Answers-Grade-6-Chapter-3-Ratios-and-Rates-3.3-28.png\" alt=\"Big Ideas Math Answers Grade 6 Chapter 3 Ratios and Rates 3.3 28\" width=\"322\" height=\"211\" srcset=\"https:\/\/ccssanswers.com\/wp-content\/uploads\/2021\/01\/Big-Ideas-Math-Answers-Grade-6-Chapter-3-Ratios-and-Rates-3.3-28.png 322w, https:\/\/ccssanswers.com\/wp-content\/uploads\/2021\/01\/Big-Ideas-Math-Answers-Grade-6-Chapter-3-Ratios-and-Rates-3.3-28-300x197.png 300w\" sizes=\"(max-width: 322px) 100vw, 322px\" \/><br \/>\na. At her current pace, how many items will Kristina sell in 28 days? Is she on track to meet the goal? Explain.<br \/>\nb. At his current pace, how many dollars worth of product will Jim sell in 28 days? Is he on track to meet the goal? Explain.<br \/>\nAnswer:<\/p>\n<p>Question 30.<br \/>\n<strong>MODELING REAL LIFE<\/strong><br \/>\nA gold alloy contains 15 milligrams of gold for every 4 milligrams of copper. A jeweler uses 48 milligrams of copper to make the alloy. How much gold does the jeweler use to make the alloy?<br \/>\n<img decoding=\"async\" loading=\"lazy\" class=\"alignnone size-full wp-image-26696\" src=\"https:\/\/ccssanswers.com\/wp-content\/uploads\/2021\/01\/Big-Ideas-Math-Answers-Grade-6-Chapter-3-Ratios-and-Rates-3.3-29.png\" alt=\"Big Ideas Math Answers Grade 6 Chapter 3 Ratios and Rates 3.3 29\" width=\"208\" height=\"146\" \/><br \/>\nAnswer:<br \/>\nThere are 180 milligrams of gold in the alloy.<\/p>\n<p>Explanation:<br \/>\nWe know that for every 4 milligrams of copper, there are 15 milligrams of gold.<br \/>\nif 48 milligrams of copper are used, we can separate them in &#8220;sets&#8221; of 4 milligrams.<br \/>\nWe have 48\/4 = 12 sets.<br \/>\nAnd for each one of these 12 sets, there are 15 milligrams of gold, then the total amount of gold in the alloy is:<br \/>\n12\u00d715mg = 180 mg<\/p>\n<p>Question 31.<br \/>\n<strong>MODELING REAL LIFE<\/strong><br \/>\nYou make candles by adding 2 fluid ounces of scented oil for every 22 fluid ounces of wax. Your friend makes candles by adding 3 \ufb02uid ounces of the same scented oil for every 37 fluid ounces of wax. Whose candles are more fragrant? Explain your reasoning.<br \/>\nAnswer: Your candles are more fragrant<\/p>\n<p>Explanation:<br \/>\nGiven,<br \/>\nYou make candles by adding 2 fluid ounces of scented oil for every 22 fluid ounces of wax.<br \/>\nYour friend makes candles by adding 3 \ufb02uid ounces of the same scented oil for every 37 fluid ounces of wax.<br \/>\nCompare 2\/22 and 3\/37<br \/>\n2\/22 &gt; 3\/37<br \/>\nBy this we can say that your candles are more fragrant.<\/p>\n<p>Question 32.<br \/>\n<strong>MODELING REAL LIFE<\/strong><br \/>\nA mint milk shake contains 1.25 fluid ounces of milk for every 4 ounces of ice cream. A strawberry milk shake contains 1.75 fluid ounces of milk for every 5 ounces of ice cream. Which milk shake is thicker? Explain.<br \/>\nAnswer:<\/p>\n<p><strong>CRITICAL THINKING<\/strong> Two whole numbers A and B satisfy the following conditions. Find A and B.<br \/>\nQuestion 33.<br \/>\nA + B = 30<br \/>\nA : B is equivalent to 2 : 3.<br \/>\nAnswer:<br \/>\nLet A = 2x<br \/>\nLet B = 3x<br \/>\n2x + 3x = 30<br \/>\n5x = 30<br \/>\nx = 30\/5 = 6<br \/>\nx = 6<br \/>\nA = 2x = 2(6) = 12<br \/>\nB = 3(6) = 18<br \/>\nA : B = 12 : 18<\/p>\n<p>Question 34.<br \/>\nA + B = 44<br \/>\nA : B is equivalent to 4 : 7.<br \/>\nAnswer:<br \/>\nLet A = 4x<br \/>\nLet B = 7x<br \/>\n4x + 7x = 44<br \/>\n11x = 44<br \/>\nx = 44\/11<br \/>\nx = 4<br \/>\nA = 4x = 4(4) = 16<br \/>\nB = 7x = 7(4) = 28<br \/>\nA : B = 16 : 28<\/p>\n<p>Question 35.<br \/>\nA &#8211; B = 18<br \/>\nA : B is equivalent to 11 : 5.<br \/>\nAnswer:<br \/>\nLet A = 11x<br \/>\nLet B = 5x<br \/>\n11x &#8211; 5x = 18<br \/>\n6x = 18<br \/>\nx = 18\/6<br \/>\nx = 3<br \/>\nA = 11x = 11(3) = 33<br \/>\nB = 5x = 5(3) = 15<br \/>\n33 &#8211; 15 = 18<br \/>\nA : B = 33 : 15<\/p>\n<p>Question 36.<br \/>\nA &#8211; B = 25<br \/>\nA : B is equivalent to 13 : 8.<br \/>\nAnswer:<br \/>\nLet A = 13x<br \/>\nLet B = 8x<br \/>\n13x &#8211; 8x = 25<br \/>\n5x = 25<br \/>\nx = 5<br \/>\nA = 13x = 13(5) = 65<br \/>\nB = 8(5) = 40<br \/>\nA : B = 65 : 40<\/p>\n<p>Question 37.<br \/>\n<strong>MODELING REAL LIFE<\/strong><br \/>\nA nutrition label shows that there are 161 calories in 28 grams of dry roasted cashews. You eat 9 cashews totaling 12 grams.<br \/>\n<img decoding=\"async\" loading=\"lazy\" class=\"alignnone size-full wp-image-26697\" src=\"https:\/\/ccssanswers.com\/wp-content\/uploads\/2021\/01\/Big-Ideas-Math-Answers-Grade-6-Chapter-3-Ratios-and-Rates-3.3-30.png\" alt=\"Big Ideas Math Answers Grade 6 Chapter 3 Ratios and Rates 3.3 30\" width=\"172\" height=\"315\" srcset=\"https:\/\/ccssanswers.com\/wp-content\/uploads\/2021\/01\/Big-Ideas-Math-Answers-Grade-6-Chapter-3-Ratios-and-Rates-3.3-30.png 172w, https:\/\/ccssanswers.com\/wp-content\/uploads\/2021\/01\/Big-Ideas-Math-Answers-Grade-6-Chapter-3-Ratios-and-Rates-3.3-30-164x300.png 164w\" sizes=\"(max-width: 172px) 100vw, 172px\" \/><br \/>\na. Do you think it is possible to find the number of calories you consume? Explain your reasoning.<\/p>\n<p>Answer:<br \/>\nThere are 161 calories in 28 grams. You eat 9 cashews totaling 12 grams.<br \/>\nWe need to find out how many calories in 12 grams<br \/>\nFor that we make a proportion<br \/>\nCalories\/grams = calories\/grams<br \/>\n161\/28 = x\/12<br \/>\n28x = 161 \u00d7 12<br \/>\nx = 1932\/28<br \/>\nx = 69<br \/>\nThere are 69 calories in 12 grams<\/p>\n<p>b. How many cashews are in one serving?<br \/>\nAnswer:<br \/>\nDivide 161 by 28 to get the calorie count for one gram<br \/>\nMultiply that by 12 to work out how many calories you have eaten in the 9 cashews 161\/28 = 5.75<br \/>\n5.75 x 12 = 69<\/p>\n<p>Question 38.<br \/>\n<strong>REASONING<\/strong><br \/>\nThe ratio of three numbers is 4 : 5 : 3. The sum of the numbers is 54. What are the three numbers?<br \/>\nAnswer:<br \/>\nLet it be x.<br \/>\n4x + 5x + 3x = 54<br \/>\n12x = 54<br \/>\nx = 54\/12<br \/>\nx = 4.5<br \/>\nNow 4x = 4\u00d7 4.5 = 18<br \/>\n3x = 3 \u00d7 4.5<br \/>\n=13.5<br \/>\n5x = 5\u00d7 4.5 = 22.5<\/p>\n<p>Question 39.<br \/>\n<strong>CRITICAL THINKING<\/strong><br \/>\nSeven out of every 8 students surveyed own a bike. The difference between the number of students who own a bike and those who do not is 72. How many students were surveyed?<br \/>\nAnswer:<br \/>\nSo if x people were surveyed, 7\/8 people owned a bike and 1\/8 did not.<br \/>\nThe difference between them is 72<br \/>\n7\/8 \u00d7 x &#8211; 1\/8 = 72<br \/>\nSo, this means that,<br \/>\n6\/8 x = 72<br \/>\nLet us simpify<br \/>\n3\/4 \u00d7 x = 72<br \/>\n1\/4 \u00d7 x = 24<br \/>\nand multiply by 4<br \/>\nx = 96<br \/>\nSo 96 people were surveyed<\/p>\n<p>Question 40.<br \/>\n<strong>LOGIC<\/strong><br \/>\nYou and a classmate have a bug collection for science class. You find 5 out of every 9 bugs in the collection. You find 4 more bugs than your classmate. How many bugs are in the collection?<br \/>\n<img decoding=\"async\" loading=\"lazy\" class=\"alignnone size-full wp-image-26698\" src=\"https:\/\/ccssanswers.com\/wp-content\/uploads\/2021\/01\/Big-Ideas-Math-Answers-Grade-6-Chapter-3-Ratios-and-Rates-3.3-31.png\" alt=\"Big Ideas Math Answers Grade 6 Chapter 3 Ratios and Rates 3.3 31\" width=\"265\" height=\"217\" \/><br \/>\nAnswer:<br \/>\nLet b represent the total amount bugs.<br \/>\n5\/9 \u00d7 b = 4\/9 \u00d7 b + 4<br \/>\n1\/9 \u00d7 b = 4<br \/>\nb = 4 \u00d7 9<br \/>\nb = 36<br \/>\nThere are 36 bugs in the collection.<\/p>\n<p>Question 41.<br \/>\n<strong>PROBLEM SOLVING<\/strong><br \/>\nYou earn $72 for every 8 hours you spend shoveling snow. You earn $60 for every 5 hours you spend babysitting. For every 3 hours you spend babysitting, you spend 2 hours shoveling snow. You babysit for 15 hours in January. How much money do you earn in January?<br \/>\nAnswer: $90<\/p>\n<p>Explanation:<br \/>\nEarning for 8 hours shoveling snow = $72<br \/>\nAmount per hour = $72\/8 = $9<br \/>\n3 hours of babysitting = 2 hours shoveling snow<br \/>\nBabysitting hours in January = 15 hours<br \/>\nHours of shoveling snow in January = (15\/3) x 2 = 10 hours<br \/>\nAmount earned in January = Hours shoveling snow x Hourly Rate<br \/>\n= 10 x $9 = $90<br \/>\nThat is, you earn $90 in January.<\/p>\n<p>Question 42.<br \/>\n<strong>DIG DEEPER!<\/strong><br \/>\nYou and a friend each have a collection of tokens. Initially, for every 8 tokens you had, your friend had 3. After you give half of your tokens to your friend, your friend now has 18 more tokens than you. Initially, how many more tokens did you have than your friend?<br \/>\nAnswer: 30 token<\/p>\n<p>Explanation:<br \/>\nInitially, for every 8 tokens I had, my friend had 3.<br \/>\nTherefore, ratio of tokens that me and my friend is 8 : 3<br \/>\nLet I have 8 x tokens and my friend has 3 x tokens, where x is any number.<br \/>\nThen again according to the question,<br \/>\nAfter I gave half of your friend, my friend now has 18 more tokens than you.<br \/>\nThat is, (3x + 4x) &#8211; 4x = 18<br \/>\n7x &#8211; 4x = 18<br \/>\n3x = 18<br \/>\nx = 6<br \/>\nTherefore , Initially the difference between me and my friend&#8217;s token = 8 x &#8211; 3 x = 5 x = 5 \u00d7 6 = 30<\/p>\n<h3><a id=\"Lesson_3.4_Graphing_Ratio_Relationships\"><\/a>Lesson 3.4 Graphing Ratio Relationships<\/h3>\n<p><strong>EXPLORATION 1<\/strong><\/p>\n<p>Using a Coordinate Plane<br \/>\nWork with a partner. An airplane travels 300 miles per hour.<br \/>\na. Represent the relationship between distance and time in a coordinate plane. Explain your choice for labeling and scaling the axes.<br \/>\nb. Write a question that can be answered using the graph. Exchange your question with another group. Answer their question and discuss the solution with the other group.<br \/>\n<img decoding=\"async\" loading=\"lazy\" class=\"alignnone size-full wp-image-26699\" src=\"https:\/\/ccssanswers.com\/wp-content\/uploads\/2021\/01\/Big-Ideas-Math-Solutions-Grade-6-Chapter-3-Ratios-and-Rates-3.4-1.png\" alt=\"Big Ideas Math Solutions Grade 6 Chapter 3 Ratios and Rates 3.4 1\" width=\"138\" height=\"156\" \/><br \/>\nAnswer:<\/p>\n<p><strong>EXPLORATION 2<\/strong><\/p>\n<p>Identifying Relationships in Graphs<br \/>\nWork with a partner. Use the graphs to make a ratio table. Explain how the blue, red, and green arrows correspond to the ratio table.<br \/>\n<img decoding=\"async\" loading=\"lazy\" class=\"alignnone size-full wp-image-26700\" src=\"https:\/\/ccssanswers.com\/wp-content\/uploads\/2021\/01\/Big-Ideas-Math-Solutions-Grade-6-Chapter-3-Ratios-and-Rates-3.4-2.png\" alt=\"Big Ideas Math Solutions Grade 6 Chapter 3 Ratios and Rates 3.4 2\" width=\"658\" height=\"355\" srcset=\"https:\/\/ccssanswers.com\/wp-content\/uploads\/2021\/01\/Big-Ideas-Math-Solutions-Grade-6-Chapter-3-Ratios-and-Rates-3.4-2.png 658w, https:\/\/ccssanswers.com\/wp-content\/uploads\/2021\/01\/Big-Ideas-Math-Solutions-Grade-6-Chapter-3-Ratios-and-Rates-3.4-2-300x162.png 300w\" sizes=\"(max-width: 658px) 100vw, 658px\" \/><br \/>\nAnswer:<\/p>\n<p>For a ratio of two quantities, you can use equivalent ratios to create ordered pairs of the form (first quantity, second quantity). You can plot these ordered pairs in a coordinate plane and draw a line, starting at(0, 0), through the points.<\/p>\n<p><strong>Try It<\/strong><\/p>\n<p><strong>Represent the ratio relationship using a graph.<\/strong><br \/>\nQuestion 1.<br \/>\n<img decoding=\"async\" loading=\"lazy\" class=\"alignnone size-full wp-image-26701\" src=\"https:\/\/ccssanswers.com\/wp-content\/uploads\/2021\/01\/Big-Ideas-Math-Solutions-Grade-6-Chapter-3-Ratios-and-Rates-3.4-3.png\" alt=\"Big Ideas Math Solutions Grade 6 Chapter 3 Ratios and Rates 3.4 3\" width=\"182\" height=\"137\" \/><br \/>\nAnswer:<\/p>\n<p>Question 2.<br \/>\n<img decoding=\"async\" loading=\"lazy\" class=\"alignnone size-full wp-image-26702\" src=\"https:\/\/ccssanswers.com\/wp-content\/uploads\/2021\/01\/Big-Ideas-Math-Solutions-Grade-6-Chapter-3-Ratios-and-Rates-3.4-4.png\" alt=\"Big Ideas Math Solutions Grade 6 Chapter 3 Ratios and Rates 3.4 4\" width=\"207\" height=\"138\" \/><br \/>\nAnswer:<\/p>\n<p>Question 3.<br \/>\n<strong>WHAT IF?<\/strong><br \/>\nRepeat Example 2 when the cost of the dark chocolate cashews is $15 per pound.<br \/>\nAnswer:<\/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>GRAPHING A RATIO RELATIONSHIP<\/strong><br \/>\nRepresent the ratio relationship using a graph.<br \/>\n<img decoding=\"async\" loading=\"lazy\" class=\"alignnone size-full wp-image-26703\" src=\"https:\/\/ccssanswers.com\/wp-content\/uploads\/2021\/01\/Big-Ideas-Math-Solutions-Grade-6-Chapter-3-Ratios-and-Rates-3.4-5.png\" alt=\"Big Ideas Math Solutions Grade 6 Chapter 3 Ratios and Rates 3.4 5\" width=\"150\" height=\"136\" \/><br \/>\nAnswer:<\/p>\n<p>Question 5.<br \/>\n<strong>CRITICAL THINKING<\/strong><br \/>\nUse what you know about equivalent ratios to explain why the graph of a ratio relationship passes through (0, 0).<br \/>\nAnswer:<\/p>\n<p>Question 6.<br \/>\n<strong>WHICH ONE DOESN\u2019T BELONG?<\/strong><br \/>\nWhich ordered pair does not belong with the other three? Explain your reasoning.<br \/>\n<img decoding=\"async\" loading=\"lazy\" class=\"alignnone size-full wp-image-26704\" src=\"https:\/\/ccssanswers.com\/wp-content\/uploads\/2021\/01\/Big-Ideas-Math-Solutions-Grade-6-Chapter-3-Ratios-and-Rates-3.4-6.png\" alt=\"Big Ideas Math Solutions Grade 6 Chapter 3 Ratios and Rates 3.4 6\" width=\"310\" height=\"50\" srcset=\"https:\/\/ccssanswers.com\/wp-content\/uploads\/2021\/01\/Big-Ideas-Math-Solutions-Grade-6-Chapter-3-Ratios-and-Rates-3.4-6.png 310w, https:\/\/ccssanswers.com\/wp-content\/uploads\/2021\/01\/Big-Ideas-Math-Solutions-Grade-6-Chapter-3-Ratios-and-Rates-3.4-6-300x48.png 300w\" sizes=\"(max-width: 310px) 100vw, 310px\" \/><br \/>\nAnswer: (24, 4) does not belong with the other three.<br \/>\n(4, 1) (8, 2) (12, 3) are the equivalent ordered pairs.<\/p>\n<p>Question 7.<br \/>\nYou are skateboarding at a pace of 30 meters every 5 seconds. Your friend is in-line skating at a pace of 9 meters every 2 seconds. Graph each ratio relationship in the same coordinate plane. Who is faster?<br \/>\n<img decoding=\"async\" loading=\"lazy\" class=\"alignnone size-full wp-image-26705\" src=\"https:\/\/ccssanswers.com\/wp-content\/uploads\/2021\/01\/Big-Ideas-Math-Solutions-Grade-6-Chapter-3-Ratios-and-Rates-3.4-7.png\" alt=\"Big Ideas Math Solutions Grade 6 Chapter 3 Ratios and Rates 3.4 7\" width=\"137\" height=\"235\" \/><br \/>\nAnswer:<\/p>\n<p>Question 8.<br \/>\nYou buy 2.5 pounds of pumpkin seeds and 2.5 pounds of sunflower seeds. Use a graph to find your total cost. Then use the graph to determine how much more you pay for pumpkin seeds than for sunflower seeds.<br \/>\n<img decoding=\"async\" loading=\"lazy\" class=\"alignnone size-full wp-image-26706\" src=\"https:\/\/ccssanswers.com\/wp-content\/uploads\/2021\/01\/Big-Ideas-Math-Solutions-Grade-6-Chapter-3-Ratios-and-Rates-3.4-8.png\" alt=\"Big Ideas Math Solutions Grade 6 Chapter 3 Ratios and Rates 3.4 8\" width=\"197\" height=\"205\" \/><br \/>\nAnswer:<\/p>\n<h3><a id=\"Graphing_Ratio_Relationships_Homework_&amp;_Practice_3.4\"><\/a>Graphing Ratio Relationships Homework &amp; Practice 3.4<\/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 decoding=\"async\" loading=\"lazy\" class=\"alignnone size-full wp-image-26707\" src=\"https:\/\/ccssanswers.com\/wp-content\/uploads\/2021\/01\/Big-Ideas-Math-Solutions-Grade-6-Chapter-3-Ratios-and-Rates-3.4-9.png\" alt=\"Big Ideas Math Solutions Grade 6 Chapter 3 Ratios and Rates 3.4 9\" width=\"179\" height=\"65\" \/><br \/>\nAnswer:<br \/>\n<img decoding=\"async\" loading=\"lazy\" class=\"alignnone size-full wp-image-35532\" src=\"https:\/\/ccssanswers.com\/wp-content\/uploads\/2021\/01\/Big-Ideas-Math-Solutions-Grade-6-Chapter-3-Ratios-and-Rates-3.4-9.jpg\" alt=\"Big-Ideas-Math-Solutions-Grade-6-Chapter-3-Ratios-and-Rates-3.4-9\" width=\"179\" height=\"65\" \/><br \/>\nThe pattern of chickens is multiple of 8.<br \/>\nSo, the missing values in the ratio table is 16.<br \/>\nThe pattern of Eggs is multiple of 6.<br \/>\nSo, the missing values in the ratio table is 18.<\/p>\n<p>Question 2.<br \/>\n<img decoding=\"async\" loading=\"lazy\" class=\"alignnone size-full wp-image-26708\" src=\"https:\/\/ccssanswers.com\/wp-content\/uploads\/2021\/01\/Big-Ideas-Math-Solutions-Grade-6-Chapter-3-Ratios-and-Rates-3.4-10.png\" alt=\"Big Ideas Math Solutions Grade 6 Chapter 3 Ratios and Rates 3.4 10\" width=\"194\" height=\"68\" \/><br \/>\nAnswer:<br \/>\n<img decoding=\"async\" loading=\"lazy\" class=\"alignnone size-full wp-image-35533\" src=\"https:\/\/ccssanswers.com\/wp-content\/uploads\/2021\/01\/Big-Ideas-Math-Solutions-Grade-6-Chapter-3-Ratios-and-Rates-3.4-10.jpg\" alt=\"Big-Ideas-Math-Solutions-Grade-6-Chapter-3-Ratios-and-Rates-3.4-10\" width=\"194\" height=\"68\" \/><br \/>\nThe missing values are 1, 12, 5<br \/>\nThe equivalent ratios are 3 : 1, 12:4, 15:5<\/p>\n<p><strong>Write the name of the decimal number.<\/strong><br \/>\nQuestion 3.<br \/>\n7.1<br \/>\nAnswer:<br \/>\nWe start by naming the number to the left of the decimal. We use the word \u201cand\u201d to indicate the decimal point. Then we name the number to the right of the decimal point as if it were a whole number.<br \/>\n7.1 can be written as seven and one.<\/p>\n<p>Question 4.<br \/>\n3.54<br \/>\nAnswer:<br \/>\nWe start by naming the number to the left of the decimal. We use the word \u201cand\u201d to indicate the decimal point. Then we name the number to the right of the decimal point as if it were a whole number.<br \/>\n3.54 can be written as three and five four<\/p>\n<p>Question 5.<br \/>\n13.6<br \/>\nAnswer:<br \/>\nWe start by naming the number to the left of the decimal. We use the word \u201cand\u201d to indicate the decimal point. Then we name the number to the right of the decimal point as if it were a whole number.<br \/>\n13.6 can be written as thirteen and six<\/p>\n<p>Question 6.<br \/>\n8.132<br \/>\nAnswer:<br \/>\nWe start by naming the number to the left of the decimal. We use the word \u201cand\u201d to indicate the decimal point. Then we name the number to the right of the decimal point as if it were a whole number.<br \/>\n8.132 can be written as eight and one thirty two<\/p>\n<p><strong>Write two equivalent ratios that describe the relationship.<\/strong><br \/>\nQuestion 7.<br \/>\nbaseballs to gloves<br \/>\n<img decoding=\"async\" loading=\"lazy\" class=\"alignnone size-full wp-image-26709\" src=\"https:\/\/ccssanswers.com\/wp-content\/uploads\/2021\/01\/Big-Ideas-Math-Solutions-Grade-6-Chapter-3-Ratios-and-Rates-3.4-11.png\" alt=\"Big Ideas Math Solutions Grade 6 Chapter 3 Ratios and Rates 3.4 11\" width=\"231\" height=\"124\" \/><br \/>\nAnswer: The ratio from baseballs to gloves is 8: 4<br \/>\nThe equivalent ratios are 2 : 1, 16 : 8<\/p>\n<p>Question 8.<br \/>\nladybugs to bees<br \/>\n<img decoding=\"async\" loading=\"lazy\" class=\"alignnone size-full wp-image-26710\" src=\"https:\/\/ccssanswers.com\/wp-content\/uploads\/2021\/01\/Big-Ideas-Math-Solutions-Grade-6-Chapter-3-Ratios-and-Rates-3.4-12.png\" alt=\"Big Ideas Math Solutions Grade 6 Chapter 3 Ratios and Rates 3.4 12\" width=\"273\" height=\"143\" \/><br \/>\nAnswer: The ratio from ladybugs to bees is 12 : 4<br \/>\nThe equivalent ratios are 3 : 1 and 24 : 8<\/p>\n<p><strong>Concepts, Skills, &amp; Problem Solving<\/strong><\/p>\n<p><strong>USING A COORDINATE PLANE<\/strong> Represent the relationship between distance and time in a coordinate plane. (See Exploration 1, p. 129.)<br \/>\nQuestion 9.<br \/>\nA train travels 45 miles per hour.<br \/>\nAnswer:<br \/>\n<img decoding=\"async\" loading=\"lazy\" class=\"alignnone size-full wp-image-31565\" src=\"https:\/\/ccssanswers.com\/wp-content\/uploads\/2021\/01\/Big-Ideas-Math-Grade-6-Chapter-3-Answer-Key-img_1.jpg\" alt=\"Big Ideas Math Grade 6 Chapter 3 Answer Key img_1\" width=\"612\" height=\"612\" srcset=\"https:\/\/ccssanswers.com\/wp-content\/uploads\/2021\/01\/Big-Ideas-Math-Grade-6-Chapter-3-Answer-Key-img_1.jpg 612w, https:\/\/ccssanswers.com\/wp-content\/uploads\/2021\/01\/Big-Ideas-Math-Grade-6-Chapter-3-Answer-Key-img_1-300x300.jpg 300w, https:\/\/ccssanswers.com\/wp-content\/uploads\/2021\/01\/Big-Ideas-Math-Grade-6-Chapter-3-Answer-Key-img_1-150x150.jpg 150w\" sizes=\"(max-width: 612px) 100vw, 612px\" \/><\/p>\n<p>Question 10.<br \/>\nA motorcycle travels 70 kilometers per hour.<br \/>\nAnswer:<br \/>\n<img decoding=\"async\" loading=\"lazy\" class=\"alignnone size-medium wp-image-36173\" src=\"https:\/\/ccssanswers.com\/wp-content\/uploads\/2021\/01\/Big-Ideas-Math-Grade-6-Chapter-3-Ratios-and-Rates-Img_1-300x217.jpg\" alt=\"Big Ideas Math Grade 6 Chapter 3 Ratios and Rates Img_1\" width=\"300\" height=\"217\" srcset=\"https:\/\/ccssanswers.com\/wp-content\/uploads\/2021\/01\/Big-Ideas-Math-Grade-6-Chapter-3-Ratios-and-Rates-Img_1-300x217.jpg 300w, https:\/\/ccssanswers.com\/wp-content\/uploads\/2021\/01\/Big-Ideas-Math-Grade-6-Chapter-3-Ratios-and-Rates-Img_1.jpg 541w\" sizes=\"(max-width: 300px) 100vw, 300px\" \/><\/p>\n<p>Question 11<br \/>\nA snail travels 80 centimeters per minute.<br \/>\nAnswer:<br \/>\n<img decoding=\"async\" loading=\"lazy\" class=\"alignnone size-medium wp-image-36178\" src=\"https:\/\/ccssanswers.com\/wp-content\/uploads\/2021\/01\/Big-Ideas-Math-Grade-6-Chapter-3-Ratios-and-Rates-Img_2-300x217.jpg\" alt=\"Big Ideas Math Grade 6 Chapter 3 Ratios and Rates Img_2\" width=\"300\" height=\"217\" srcset=\"https:\/\/ccssanswers.com\/wp-content\/uploads\/2021\/01\/Big-Ideas-Math-Grade-6-Chapter-3-Ratios-and-Rates-Img_2-300x217.jpg 300w, https:\/\/ccssanswers.com\/wp-content\/uploads\/2021\/01\/Big-Ideas-Math-Grade-6-Chapter-3-Ratios-and-Rates-Img_2.jpg 541w\" sizes=\"(max-width: 300px) 100vw, 300px\" \/><\/p>\n<p>Question 12.<br \/>\nA whale travels 800 yards per minute.<br \/>\nAnswer:<br \/>\n<img decoding=\"async\" loading=\"lazy\" class=\"alignnone size-medium wp-image-36180\" src=\"https:\/\/ccssanswers.com\/wp-content\/uploads\/2021\/01\/Big-Ideas-Math-Grade-6-Chapter-3-Ratios-and-Rates-Img_3-300x217.jpg\" alt=\"Big Ideas Math Grade 6 Chapter 3 Ratios and Rates Img_3\" width=\"300\" height=\"217\" srcset=\"https:\/\/ccssanswers.com\/wp-content\/uploads\/2021\/01\/Big-Ideas-Math-Grade-6-Chapter-3-Ratios-and-Rates-Img_3-300x217.jpg 300w, https:\/\/ccssanswers.com\/wp-content\/uploads\/2021\/01\/Big-Ideas-Math-Grade-6-Chapter-3-Ratios-and-Rates-Img_3.jpg 541w\" sizes=\"(max-width: 300px) 100vw, 300px\" \/><\/p>\n<p><strong>GRAPHING RATIO RELATIONSHIPS<\/strong> Represent the ratio relationship using a graph.<br \/>\nQuestion 13.<br \/>\n<img decoding=\"async\" loading=\"lazy\" class=\"alignnone size-full wp-image-26711\" src=\"https:\/\/ccssanswers.com\/wp-content\/uploads\/2021\/01\/Big-Ideas-Math-Solutions-Grade-6-Chapter-3-Ratios-and-Rates-3.4-13.png\" alt=\"Big Ideas Math Solutions Grade 6 Chapter 3 Ratios and Rates 3.4 13\" width=\"236\" height=\"67\" \/><br \/>\nAnswer:<br \/>\n<img decoding=\"async\" loading=\"lazy\" class=\"alignnone size-medium wp-image-36183\" src=\"https:\/\/ccssanswers.com\/wp-content\/uploads\/2021\/01\/Big-Ideas-Math-Grade-6-Chapter-3-Ratios-and-Rates-Img_4-300x217.jpg\" alt=\"Big Ideas Math Grade 6 Chapter 3 Ratios and Rates Img_4\" width=\"300\" height=\"217\" srcset=\"https:\/\/ccssanswers.com\/wp-content\/uploads\/2021\/01\/Big-Ideas-Math-Grade-6-Chapter-3-Ratios-and-Rates-Img_4-300x217.jpg 300w, https:\/\/ccssanswers.com\/wp-content\/uploads\/2021\/01\/Big-Ideas-Math-Grade-6-Chapter-3-Ratios-and-Rates-Img_4.jpg 541w\" sizes=\"(max-width: 300px) 100vw, 300px\" \/><\/p>\n<p>Question 14.<br \/>\n<img decoding=\"async\" loading=\"lazy\" class=\"alignnone size-full wp-image-26712\" src=\"https:\/\/ccssanswers.com\/wp-content\/uploads\/2021\/01\/Big-Ideas-Math-Solutions-Grade-6-Chapter-3-Ratios-and-Rates-3.4-14.png\" alt=\"Big Ideas Math Solutions Grade 6 Chapter 3 Ratios and Rates 3.4 14\" width=\"197\" height=\"68\" \/><br \/>\nAnswer:<br \/>\n<img decoding=\"async\" loading=\"lazy\" class=\"alignnone size-medium wp-image-36185\" src=\"https:\/\/ccssanswers.com\/wp-content\/uploads\/2021\/01\/Big-Ideas-Math-Grade-6-Chapter-3-Ratios-and-Rates-Img_5-300x217.jpg\" alt=\"Big Ideas Math Grade 6 Chapter 3 Ratios and Rates Img_5\" width=\"300\" height=\"217\" srcset=\"https:\/\/ccssanswers.com\/wp-content\/uploads\/2021\/01\/Big-Ideas-Math-Grade-6-Chapter-3-Ratios-and-Rates-Img_5-300x217.jpg 300w, https:\/\/ccssanswers.com\/wp-content\/uploads\/2021\/01\/Big-Ideas-Math-Grade-6-Chapter-3-Ratios-and-Rates-Img_5.jpg 541w\" sizes=\"(max-width: 300px) 100vw, 300px\" \/><\/p>\n<p>Question 15.<br \/>\n<img decoding=\"async\" loading=\"lazy\" class=\"alignnone size-full wp-image-26713\" src=\"https:\/\/ccssanswers.com\/wp-content\/uploads\/2021\/01\/Big-Ideas-Math-Solutions-Grade-6-Chapter-3-Ratios-and-Rates-3.4-15.png\" alt=\"Big Ideas Math Solutions Grade 6 Chapter 3 Ratios and Rates 3.4 15\" width=\"221\" height=\"66\" \/><br \/>\nAnswer:<br \/>\n<img decoding=\"async\" loading=\"lazy\" class=\"alignnone size-medium wp-image-36186\" src=\"https:\/\/ccssanswers.com\/wp-content\/uploads\/2021\/01\/Big-Ideas-Math-Grade-6-Chapter-3-Ratios-and-Rates-Img_6-300x217.jpg\" alt=\"Big Ideas Math Grade 6 Chapter 3 Ratios and Rates Img_6\" width=\"300\" height=\"217\" srcset=\"https:\/\/ccssanswers.com\/wp-content\/uploads\/2021\/01\/Big-Ideas-Math-Grade-6-Chapter-3-Ratios-and-Rates-Img_6-300x217.jpg 300w, https:\/\/ccssanswers.com\/wp-content\/uploads\/2021\/01\/Big-Ideas-Math-Grade-6-Chapter-3-Ratios-and-Rates-Img_6.jpg 541w\" sizes=\"(max-width: 300px) 100vw, 300px\" \/><\/p>\n<p>Question 16.<br \/>\n<img decoding=\"async\" loading=\"lazy\" class=\"alignnone size-full wp-image-26714\" src=\"https:\/\/ccssanswers.com\/wp-content\/uploads\/2021\/01\/Big-Ideas-Math-Solutions-Grade-6-Chapter-3-Ratios-and-Rates-3.4-16.png\" alt=\"Big Ideas Math Solutions Grade 6 Chapter 3 Ratios and Rates 3.4 16\" width=\"223\" height=\"70\" \/><br \/>\nAnswer:<br \/>\n<img decoding=\"async\" loading=\"lazy\" class=\"alignnone size-full wp-image-36191\" src=\"https:\/\/ccssanswers.com\/wp-content\/uploads\/2021\/01\/Big-Ideas-Math-Grade-6-Chapter-3-Ratios-and-Rates-Img_7.jpg\" alt=\"Big Ideas Math Grade 6 Chapter 3 Ratios and Rates Img_7\" width=\"541\" height=\"391\" srcset=\"https:\/\/ccssanswers.com\/wp-content\/uploads\/2021\/01\/Big-Ideas-Math-Grade-6-Chapter-3-Ratios-and-Rates-Img_7.jpg 541w, https:\/\/ccssanswers.com\/wp-content\/uploads\/2021\/01\/Big-Ideas-Math-Grade-6-Chapter-3-Ratios-and-Rates-Img_7-300x217.jpg 300w\" sizes=\"(max-width: 541px) 100vw, 541px\" \/><\/p>\n<p>Question 17.<br \/>\n<img decoding=\"async\" loading=\"lazy\" class=\"alignnone size-full wp-image-26715\" src=\"https:\/\/ccssanswers.com\/wp-content\/uploads\/2021\/01\/Big-Ideas-Math-Solutions-Grade-6-Chapter-3-Ratios-and-Rates-3.4-17.png\" alt=\"Big Ideas Math Solutions Grade 6 Chapter 3 Ratios and Rates 3.4 17\" width=\"174\" height=\"71\" \/><br \/>\nAnswer:<br \/>\n<img decoding=\"async\" loading=\"lazy\" class=\"alignnone size-full wp-image-36192\" src=\"https:\/\/ccssanswers.com\/wp-content\/uploads\/2021\/01\/Big-Ideas-Math-Grade-6-Chapter-3-Ratios-and-Rates-Img_8.jpg\" alt=\"Big Ideas Math Grade 6 Chapter 3 Ratios and Rates Img_8\" width=\"541\" height=\"391\" srcset=\"https:\/\/ccssanswers.com\/wp-content\/uploads\/2021\/01\/Big-Ideas-Math-Grade-6-Chapter-3-Ratios-and-Rates-Img_8.jpg 541w, https:\/\/ccssanswers.com\/wp-content\/uploads\/2021\/01\/Big-Ideas-Math-Grade-6-Chapter-3-Ratios-and-Rates-Img_8-300x217.jpg 300w\" sizes=\"(max-width: 541px) 100vw, 541px\" \/><\/p>\n<p>Question 18.<br \/>\n<img decoding=\"async\" loading=\"lazy\" class=\"alignnone size-full wp-image-26716\" src=\"https:\/\/ccssanswers.com\/wp-content\/uploads\/2021\/01\/Big-Ideas-Math-Solutions-Grade-6-Chapter-3-Ratios-and-Rates-3.4-18.png\" alt=\"Big Ideas Math Solutions Grade 6 Chapter 3 Ratios and Rates 3.4 18\" width=\"240\" height=\"68\" \/><br \/>\nAnswer:<br \/>\n<img decoding=\"async\" loading=\"lazy\" class=\"alignnone size-full wp-image-36193\" src=\"https:\/\/ccssanswers.com\/wp-content\/uploads\/2021\/01\/Big-Ideas-Math-Grade-6-Chapter-3-Ratios-and-Rates-Img_9.jpg\" alt=\"Big Ideas Math Grade 6 Chapter 3 Ratios and Rates Img_9\" width=\"541\" height=\"391\" srcset=\"https:\/\/ccssanswers.com\/wp-content\/uploads\/2021\/01\/Big-Ideas-Math-Grade-6-Chapter-3-Ratios-and-Rates-Img_9.jpg 541w, https:\/\/ccssanswers.com\/wp-content\/uploads\/2021\/01\/Big-Ideas-Math-Grade-6-Chapter-3-Ratios-and-Rates-Img_9-300x217.jpg 300w\" sizes=\"(max-width: 541px) 100vw, 541px\" \/><\/p>\n<p>Question 19.<br \/>\n<strong>MODELING REAL LIFE<\/strong><br \/>\nA radio station collects donations for a new broadcast tower. The cost to construct the tower is $25.50 per inch.<br \/>\na. Represent the ratio relationship using a graph.<br \/>\nb. How much does it cost to fund 4.5 inches of the construction?<br \/>\nAnswer:<\/p>\n<p>Question 20.<br \/>\n<strong>MODELING REAL LIFE<\/strong><br \/>\nYour school organizes a clothing drive as a fundraiser for a class trip. The school earns $100 for every 400 pounds of donated clothing.<br \/>\na. Represent the ratio relationship using a graph.<br \/>\nb. How much money does your school earn for donating 2200 pounds of clothing?<br \/>\nAnswer:<\/p>\n<p>Question 21.<br \/>\n<strong>NUMBER SENSE<\/strong><br \/>\nJust by looking at the graph, determine who earns a greater hourly wage. Explain.<br \/>\n<img decoding=\"async\" loading=\"lazy\" class=\"alignnone size-full wp-image-26717\" src=\"https:\/\/ccssanswers.com\/wp-content\/uploads\/2021\/01\/Big-Ideas-Math-Solutions-Grade-6-Chapter-3-Ratios-and-Rates-3.4-19.png\" alt=\"Big Ideas Math Solutions Grade 6 Chapter 3 Ratios and Rates 3.4 19\" width=\"232\" height=\"180\" \/><br \/>\nAnswer: By seeing the above graph we can say that you earns greater hourly wage.<\/p>\n<p>Question 22.<br \/>\n<strong>MODELING REAL LIFE<\/strong><br \/>\nAn airplane traveling from Chicago to Los Angeles travels 15 miles every 2 minutes. On the return trip, the plane travels 25 miles every 3 minutes. Graph each ratio relationship in the same coordinate plane. Does the plane \ufb02y faster when traveling to Los Angeles or to Chicago?<br \/>\nAnswer:<\/p>\n<p>Question 23.<br \/>\n<strong>MODELING REAL LIFE<\/strong><br \/>\nYour freezer produces 8 ice cubes every 2 hours. Your friend\u2019s freezer produces 24 ice cubes every 5 hours. Graph each ratio relationship in the same coordinate plane. Whose freezer produces ice faster?<br \/>\nAnswer:<\/p>\n<p>Question 24.<br \/>\n<strong>CHOOSE TOOLS<\/strong><br \/>\nA chemist prepares two acid solutions.<br \/>\n<img decoding=\"async\" loading=\"lazy\" class=\"alignnone size-full wp-image-26718\" src=\"https:\/\/ccssanswers.com\/wp-content\/uploads\/2021\/01\/Big-Ideas-Math-Solutions-Grade-6-Chapter-3-Ratios-and-Rates-3.4-20.png\" alt=\"Big Ideas Math Solutions Grade 6 Chapter 3 Ratios and Rates 3.4 20\" width=\"218\" height=\"267\" \/><br \/>\na. Use a ratio table to determine which solution is more acidic.<br \/>\nb. Use a graph to determine which solution is more acidic.<br \/>\nc. Which method do you prefer? Explain.<br \/>\nAnswer:<\/p>\n<p>Question 25.<br \/>\n<strong>DIG DEEPER!<\/strong><br \/>\nA company offers a nut mixture with 7 peanuts for every 3 almonds. The company changes the mixture to have 9 peanuts for every 5 almonds, but the number of nuts per container does not change.<br \/>\n<img decoding=\"async\" loading=\"lazy\" class=\"alignnone size-full wp-image-26719\" src=\"https:\/\/ccssanswers.com\/wp-content\/uploads\/2021\/01\/Big-Ideas-Math-Solutions-Grade-6-Chapter-3-Ratios-and-Rates-3.4-21.png\" alt=\"Big Ideas Math Solutions Grade 6 Chapter 3 Ratios and Rates 3.4 21\" width=\"242\" height=\"299\" \/><br \/>\na. How many nuts are in the smallest possible container?<br \/>\nb. Graph each ratio relationship. What can you conclude?<br \/>\nc. Almonds cost more than peanuts. Should the company change the price of the mixture? Explain your reasoning.<br \/>\nAnswer:<\/p>\n<p>Question 26.<br \/>\n<strong>STRUCTURE<\/strong><br \/>\nThe point (p, q) is on the graph of values from a ratio table. What are two additional points on the graph?<br \/>\nAnswer:<\/p>\n<h3><a id=\"Lesson_3.5_Rates_and_Unit_Rates\"><\/a>Lesson 3.5 Rates and Unit Rates<\/h3>\n<p><strong>EXPLORATION 1<\/strong><\/p>\n<p>Using a Diagram<br \/>\nWork with a partner. The diagram shows a story problem.<br \/>\n<img decoding=\"async\" loading=\"lazy\" class=\"alignnone size-full wp-image-26724\" src=\"https:\/\/ccssanswers.com\/wp-content\/uploads\/2021\/01\/Big-Ideas-Math-Answer-Key-Grade-6-Chapter-3-Ratios-and-Rates-3.5-1.png\" alt=\"Big Ideas Math Answer Key Grade 6 Chapter 3 Ratios and Rates 3.5 1\" width=\"620\" height=\"164\" srcset=\"https:\/\/ccssanswers.com\/wp-content\/uploads\/2021\/01\/Big-Ideas-Math-Answer-Key-Grade-6-Chapter-3-Ratios-and-Rates-3.5-1.png 620w, https:\/\/ccssanswers.com\/wp-content\/uploads\/2021\/01\/Big-Ideas-Math-Answer-Key-Grade-6-Chapter-3-Ratios-and-Rates-3.5-1-300x79.png 300w\" sizes=\"(max-width: 620px) 100vw, 620px\" \/><br \/>\na. What information can you obtain from the diagram?<br \/>\nb. Assuming that the car travels at a constant speed, how far does the car travel in 3.25 hours? Explain your method.<br \/>\nc. Draw a speedometer that shows the speed of the car. How can you use the speedometer to answer part(b)?<br \/>\nAnswer:<\/p>\n<p><strong>EXPLORATION 2<\/strong><\/p>\n<p>Using Equivalent Ratios<br \/>\nWork with a partner. Count the number of times you can clap your hands in 12 seconds. Have your partner record your results. Then switch roles with your partner and repeat the process.<br \/>\na. Using your results and your partner\u2019s results, write ratios that represent the numbers of claps for every 12 seconds.<br \/>\nb. Explain how you can use the ratios in part(a) to find the numbers of times you and your partner can clap your hands in 2 minutes, in 2.5 minutes, and in 3 minutes.<br \/>\n<img decoding=\"async\" loading=\"lazy\" class=\"alignnone size-full wp-image-26725\" src=\"https:\/\/ccssanswers.com\/wp-content\/uploads\/2021\/01\/Big-Ideas-Math-Answer-Key-Grade-6-Chapter-3-Ratios-and-Rates-3.5-2.png\" alt=\"Big Ideas Math Answer Key Grade 6 Chapter 3 Ratios and Rates 3.5 2\" width=\"235\" height=\"208\" \/><br \/>\nAnswer:<\/p>\n<p>A rate is a ratio of two quantities using different units. You solved various ratio problems in the previous sections that involved rates. Now you will use unit rates to solve rate problems.<br \/>\n<img decoding=\"async\" loading=\"lazy\" class=\"alignnone size-full wp-image-26726\" src=\"https:\/\/ccssanswers.com\/wp-content\/uploads\/2021\/01\/Big-Ideas-Math-Answer-Key-Grade-6-Chapter-3-Ratios-and-Rates-3.5-3.png\" alt=\"Big Ideas Math Answer Key Grade 6 Chapter 3 Ratios and Rates 3.5 3\" width=\"182\" height=\"103\" \/><\/p>\n<p><strong>Try It<\/strong><\/p>\n<p>Question 1.<br \/>\n<strong>WHAT IF?<\/strong><br \/>\nRepeat Example 1 when you add 4 pints of water for every 3 cups of concentrate.<br \/>\nAnswer:<\/p>\n<p>Question 2.<br \/>\n<strong>WHAT IF?<\/strong><br \/>\nRepeat Example 2 when the space junk travels 3 miles every 5 seconds.<br \/>\nAnswer:<\/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>FINDING UNIT RATES<\/strong> Write a unit rate for the situation.<br \/>\nQuestion 3.<br \/>\nrevolutions in 50 seconds<br \/>\nAnswer:<\/p>\n<p>Question 4.<br \/>\n1400 words for every 4 pages<br \/>\nAnswer:<br \/>\n1400 &#8211; 4 pages<br \/>\nx &#8211; 1 page<br \/>\n4 \u00d7 x = 1400<br \/>\nx = 1400\/4<br \/>\nx = 350<br \/>\nThus 350 words for every 1 page.<\/p>\n<p>Question 5.<br \/>\n<strong>WHICH ONE DOESN\u2019T BELONG?<\/strong><br \/>\nWhich rate does not belong with the other three? Explain your reasoning.<br \/>\n<img decoding=\"async\" loading=\"lazy\" class=\"alignnone size-full wp-image-26727\" src=\"https:\/\/ccssanswers.com\/wp-content\/uploads\/2021\/01\/Big-Ideas-Math-Answer-Key-Grade-6-Chapter-3-Ratios-and-Rates-3.5-4.png\" alt=\"Big Ideas Math Answer Key Grade 6 Chapter 3 Ratios and Rates 3.5 4\" width=\"400\" height=\"98\" srcset=\"https:\/\/ccssanswers.com\/wp-content\/uploads\/2021\/01\/Big-Ideas-Math-Answer-Key-Grade-6-Chapter-3-Ratios-and-Rates-3.5-4.png 400w, https:\/\/ccssanswers.com\/wp-content\/uploads\/2021\/01\/Big-Ideas-Math-Answer-Key-Grade-6-Chapter-3-Ratios-and-Rates-3.5-4-300x74.png 300w\" sizes=\"(max-width: 400px) 100vw, 400px\" \/><br \/>\nAnswer: 20 pounds per 4 feet does not belong with the other three.<\/p>\n<p>Explanation:<br \/>\n8 pounds for every 2 feet<br \/>\n8\/2 = 4 feet<br \/>\n12 pounds per 3 feet<br \/>\n12\/3 = 4 feet<br \/>\n20 pounds per 4 feet<br \/>\n20\/4 = 5 feet<br \/>\n24 pounds for every 6 feet<br \/>\n24\/6 = 4 feet<\/p>\n<p>Question 6.<br \/>\nYou buy 10 pounds of birdseed at Store A for $11.50. Your friend buys 15 pounds of birdseed at Store B for $19.50. How much less would you spend by buying 20 pounds of birdseed at the store with the better deal?<br \/>\nAnswer: Store A<\/p>\n<p>Explanation:<br \/>\nGiven,<br \/>\nYou buy 10 pounds of birdseed at Store A for $11.50.<br \/>\n10 pounds &#8211; $11.50<br \/>\n1 pound &#8211; $1.15<br \/>\n20 pounds = 20 \u00d7 1.15 = $23<br \/>\nYour friend buys 15 pounds of birdseed at Store B for $19.50.<br \/>\n15 pounds &#8211; $19.50<br \/>\n1 pound &#8211; $1.3<br \/>\n1.3 \u00d7 20 = $26<br \/>\n$23 &lt; $26<\/p>\n<p>Question 7.<br \/>\nA person hikes 4 miles in 2.5 hours. Find the unit rate in miles per hour. Then find the unit rate in hours per mile. How is each unit rate useful in a real-life situation?<br \/>\nAnswer: 1.6 kilometer per hour<\/p>\n<p>Explanation:<br \/>\nThe unit rate is the number of miles in 1 hour.<br \/>\nGiven,<br \/>\nDistance = 4 miles<br \/>\nTime = 2.5 hours<br \/>\nSo if he hike 4 miles in 2.5 hours<br \/>\nthen he will hike x mile in 1 hour<br \/>\nx = 4\/2.5<br \/>\nx = 1.6 miles per hour<\/p>\n<p>Question 8.<br \/>\n<strong>DIG DEEPER!<\/strong><br \/>\nYou buy 11 bagels with a $20 bill. How much change do you receive? How many more bagels could you buy?<br \/>\n<img decoding=\"async\" loading=\"lazy\" class=\"alignnone size-full wp-image-26728\" src=\"https:\/\/ccssanswers.com\/wp-content\/uploads\/2021\/01\/Big-Ideas-Math-Answer-Key-Grade-6-Chapter-3-Ratios-and-Rates-3.5-5.png\" alt=\"Big Ideas Math Answer Key Grade 6 Chapter 3 Ratios and Rates 3.5 5\" width=\"137\" height=\"157\" \/><br \/>\nAnswer:<\/p>\n<h3><a id=\"Rates_and_Unit_Rates_Homework_&amp;_Practice_3.5\"><\/a>Rates and Unit Rates Homework &amp; Practice 3.5<\/h3>\n<p><strong>Review &amp; Refresh<\/strong><\/p>\n<p><strong>Represent the ratio relationship using a graph.<\/strong><br \/>\nQuestion 1.<br \/>\n<img decoding=\"async\" loading=\"lazy\" class=\"alignnone size-full wp-image-26729\" src=\"https:\/\/ccssanswers.com\/wp-content\/uploads\/2021\/01\/Big-Ideas-Math-Answer-Key-Grade-6-Chapter-3-Ratios-and-Rates-3.5-6.png\" alt=\"Big Ideas Math Answer Key Grade 6 Chapter 3 Ratios and Rates 3.5 6\" width=\"183\" height=\"62\" \/><br \/>\nAnswer:<br \/>\n<img decoding=\"async\" loading=\"lazy\" class=\"alignnone size-full wp-image-36196\" src=\"https:\/\/ccssanswers.com\/wp-content\/uploads\/2021\/01\/Big-Ideas-Math-Grade-6-Chapter-3-Ratios-and-Rates-Img_10.jpg\" alt=\"Big Ideas Math Grade 6 Chapter 3 Ratios and Rates Img_10\" width=\"484\" height=\"352\" srcset=\"https:\/\/ccssanswers.com\/wp-content\/uploads\/2021\/01\/Big-Ideas-Math-Grade-6-Chapter-3-Ratios-and-Rates-Img_10.jpg 484w, https:\/\/ccssanswers.com\/wp-content\/uploads\/2021\/01\/Big-Ideas-Math-Grade-6-Chapter-3-Ratios-and-Rates-Img_10-300x218.jpg 300w\" sizes=\"(max-width: 484px) 100vw, 484px\" \/><\/p>\n<p>Question 2.<br \/>\n<img decoding=\"async\" loading=\"lazy\" class=\"alignnone size-full wp-image-26730\" src=\"https:\/\/ccssanswers.com\/wp-content\/uploads\/2021\/01\/Big-Ideas-Math-Answer-Key-Grade-6-Chapter-3-Ratios-and-Rates-3.5-7.png\" alt=\"Big Ideas Math Answer Key Grade 6 Chapter 3 Ratios and Rates 3.5 7\" width=\"211\" height=\"62\" \/><br \/>\nAnswer:<br \/>\n<img decoding=\"async\" loading=\"lazy\" class=\"alignnone size-full wp-image-36198\" src=\"https:\/\/ccssanswers.com\/wp-content\/uploads\/2021\/01\/Big-Ideas-Math-Grade-6-Chapter-3-Ratios-and-Rates-Img_11.jpg\" alt=\"Big Ideas Math Grade 6 Chapter 3 Ratios and Rates Img_11\" width=\"541\" height=\"391\" srcset=\"https:\/\/ccssanswers.com\/wp-content\/uploads\/2021\/01\/Big-Ideas-Math-Grade-6-Chapter-3-Ratios-and-Rates-Img_11.jpg 541w, https:\/\/ccssanswers.com\/wp-content\/uploads\/2021\/01\/Big-Ideas-Math-Grade-6-Chapter-3-Ratios-and-Rates-Img_11-300x217.jpg 300w\" sizes=\"(max-width: 541px) 100vw, 541px\" \/><\/p>\n<p>Question 3.<br \/>\n<img decoding=\"async\" loading=\"lazy\" class=\"alignnone size-full wp-image-26731\" src=\"https:\/\/ccssanswers.com\/wp-content\/uploads\/2021\/01\/Big-Ideas-Math-Answer-Key-Grade-6-Chapter-3-Ratios-and-Rates-3.5-8.png\" alt=\"Big Ideas Math Answer Key Grade 6 Chapter 3 Ratios and Rates 3.5 8\" width=\"168\" height=\"61\" \/><br \/>\nAnswer:<br \/>\n<img decoding=\"async\" loading=\"lazy\" class=\"alignnone size-full wp-image-36204\" src=\"https:\/\/ccssanswers.com\/wp-content\/uploads\/2021\/01\/Big-Ideas-Math-Grade-6-Chapter-3-Ratios-and-Rates-Img_12.jpg\" alt=\"Big Ideas Math Grade 6 Chapter 3 Ratios and Rates Img_12\" width=\"541\" height=\"391\" srcset=\"https:\/\/ccssanswers.com\/wp-content\/uploads\/2021\/01\/Big-Ideas-Math-Grade-6-Chapter-3-Ratios-and-Rates-Img_12.jpg 541w, https:\/\/ccssanswers.com\/wp-content\/uploads\/2021\/01\/Big-Ideas-Math-Grade-6-Chapter-3-Ratios-and-Rates-Img_12-300x217.jpg 300w\" sizes=\"(max-width: 541px) 100vw, 541px\" \/><\/p>\n<p>Question 4.<br \/>\n<img decoding=\"async\" loading=\"lazy\" class=\"alignnone size-full wp-image-26732\" src=\"https:\/\/ccssanswers.com\/wp-content\/uploads\/2021\/01\/Big-Ideas-Math-Answer-Key-Grade-6-Chapter-3-Ratios-and-Rates-3.5-9.png\" alt=\"Big Ideas Math Answer Key Grade 6 Chapter 3 Ratios and Rates 3.5 9\" width=\"230\" height=\"65\" \/><br \/>\nAnswer:<br \/>\n<img decoding=\"async\" loading=\"lazy\" class=\"alignnone size-full wp-image-36206\" src=\"https:\/\/ccssanswers.com\/wp-content\/uploads\/2021\/01\/Big-Ideas-Math-Grade-6-Chapter-3-Ratios-and-Rates-Img_13.jpg\" alt=\"Big Ideas Math Grade 6 Chapter 3 Ratios and Rates Img_13\" width=\"541\" height=\"391\" srcset=\"https:\/\/ccssanswers.com\/wp-content\/uploads\/2021\/01\/Big-Ideas-Math-Grade-6-Chapter-3-Ratios-and-Rates-Img_13.jpg 541w, https:\/\/ccssanswers.com\/wp-content\/uploads\/2021\/01\/Big-Ideas-Math-Grade-6-Chapter-3-Ratios-and-Rates-Img_13-300x217.jpg 300w\" sizes=\"(max-width: 541px) 100vw, 541px\" \/><\/p>\n<p><strong>Divide. Write the answer in simplest form.<\/strong><br \/>\nQuestion 5.<br \/>\n\\(\\frac{1}{5}\\) \u00f7 \\(\\frac{3}{10}\\)<br \/>\nAnswer: \\(\\frac{2}{3}\\)<\/p>\n<p>Explanation:<br \/>\nDividing two fractions is the same as multiplying the first fraction by the reciprocal of the second fraction.<br \/>\nTake the reciprocal of the second fraction by flipping the numerator and denominator and changing the operation to multiplication. Then the equation becomes<br \/>\n\\(\\frac{1}{5}\\) \u00d7 \\(\\frac{10}{3}\\) = \\(\\frac{10}{15}\\) = \\(\\frac{2}{3}\\)<\/p>\n<p>Question 6.<br \/>\n\\(\\frac{3}{8}\\) \u00f7 6<br \/>\nAnswer: \\(\\frac{1}{16}\\)<\/p>\n<p>Explanation:<br \/>\nDividing two fractions is the same as multiplying the first fraction by the reciprocal of the second fraction.<br \/>\nTake the reciprocal of the second fraction by flipping the numerator and denominator and changing the operation to multiplication. Then the equation becomes<br \/>\n\\(\\frac{3}{8}\\) \u00d7 \\(\\frac{1}{6}\\) = \\(\\frac{1}{16}\\)<\/p>\n<p>Question 7.<br \/>\n3\\(\\frac{1}{6}\\) \u00f7 2<br \/>\nAnswer: 1 \\(\\frac{7}{12}\\)<\/p>\n<p>Explanation:<br \/>\nDividing two fractions is the same as multiplying the first fraction by the reciprocal of the second fraction.<br \/>\nTake the reciprocal of the second fraction by flipping the numerator and denominator and changing the operation to multiplication. Then the equation becomes<br \/>\n3\\(\\frac{1}{6}\\) = \\(\\frac{19}{6}\\)<br \/>\n\\(\\frac{19}{6}\\) \u00d7 \\(\\frac{1}{2}\\) = 1 \\(\\frac{7}{12}\\)<\/p>\n<p>Question 8.<br \/>\n5\\(\\frac{1}{3}\\) \u00f7 2\\(\\frac{2}{3}\\)<br \/>\nAnswer: 2<\/p>\n<p>Explanation:<br \/>\nConvert any mixed numbers to fractions.<br \/>\n5\\(\\frac{1}{3}\\) = \\(\\frac{16}{3}\\)<br \/>\n2\\(\\frac{2}{3}\\) = \\(\\frac{8}{3}\\)<br \/>\n\\(\\frac{16}{3}\\) \u00d7 \\(\\frac{3}{8}\\) = \\(\\frac{48}{24}\\) = 2<\/p>\n<p><strong>Add or subtract.<\/strong><br \/>\nQuestion 9.<br \/>\n6.94 + 12.301<br \/>\nAnswer: 19.241<\/p>\n<p>Question 10.<br \/>\n8.753 &#8211; 7.71<br \/>\nAnswer: 1.043<\/p>\n<p>Question 11.<br \/>\n14.532 &#8211; 6.613<br \/>\nAnswer: 7.919<\/p>\n<p>Question 12.<br \/>\nThe winner in an election for class president received \\(\\frac{3}{4}\\) of the 240 votes. How many votes did the winner receive?<br \/>\nA. 60<br \/>\nB. 150<br \/>\nC. 180<br \/>\nD. 320<br \/>\nAnswer: 180<\/p>\n<p>Explanation:<br \/>\nGiven,<br \/>\nThe winner in an election for class president received \\(\\frac{3}{4}\\) of the 240 votes.<br \/>\n\\(\\frac{3}{4}\\) \u00d7 240 = 180<br \/>\nThe winner receive 180 votes.<br \/>\nThus the correct answer is option C<\/p>\n<p><strong>Concepts, Skills, &amp; Problem Solving<\/strong><\/p>\n<p><strong>USING EQUIVALENT RATIOS<\/strong> Use the ratio in Exploration 2 to estimate the number of times you can clap your hands in the given amount of time. (See Exploration 2, p. 135.)<br \/>\nQuestion 13.<br \/>\n0.5 minute<br \/>\nAnswer:<\/p>\n<p>Question 14.<br \/>\n1.75 minutes<br \/>\nAnswer:<\/p>\n<p>Question 15.<br \/>\n2.25 minutes<br \/>\nAnswer:<\/p>\n<p><strong>FINDING UNIT RATES<\/strong> Write a unit rate for the situation.<br \/>\nQuestion 16.<br \/>\n24 animals in 2 square miles<br \/>\nAnswer: 12 animals<\/p>\n<p>Explanation:<br \/>\nGiven,<br \/>\n24 animals in 2 square miles<br \/>\n24\/2 = 12<br \/>\n12 animals in 1 square mile<\/p>\n<p>Question 17.<br \/>\n$100 for every 5 guests<br \/>\nAnswer: $20<\/p>\n<p>Explanation:<br \/>\nGiven,<br \/>\n$100 for every 5 guests<br \/>\n100\/5 = $20<br \/>\n$20 per guest.<\/p>\n<p>Question 18.<br \/>\n$28 saved in 4 weeks<br \/>\nAnswer: $7<\/p>\n<p>Explanation:<br \/>\nGiven,<br \/>\n$28 saved in 4 weeks<br \/>\n28\/4 = $7<br \/>\n$7 per week<\/p>\n<p>Question 19.<br \/>\n18 necklaces made in 3 hours<br \/>\nAnswer: 6 necklaces<\/p>\n<p>Explanation:<br \/>\nGiven,<br \/>\n18 necklaces made in 3 hours<br \/>\n18\/3 = 6<br \/>\n6 necklaces made in 1 hour<\/p>\n<p>Question 20.<br \/>\n270 miles in 6 hours<br \/>\nAnswer: 45 miles per hour<\/p>\n<p>Explanation:<br \/>\nGiven,<br \/>\n270 miles in 6 hours<br \/>\n270\/6 = 45<br \/>\n45 miles in 1 hour<\/p>\n<p>Question 21.<br \/>\n228 students in 12 classes<br \/>\nAnswer: 24 students per class<\/p>\n<p>Explanation:<br \/>\nGiven,<br \/>\n228 students in 12 classes<br \/>\n228\/12 = 24<br \/>\n24 students in 1 class<\/p>\n<p>Question 22.<br \/>\n2520 kilobytes in 18 seconds<br \/>\nAnswer: 140 kilobytes per second<\/p>\n<p>Explanation:<br \/>\nGiven,<br \/>\n2520 kilobytes in 18 seconds<br \/>\n2520\/18 = 140 kilobytes<br \/>\n140 kilobytes per second<\/p>\n<p>Question 23.<br \/>\n880 calories in 8 servings<br \/>\nAnswer: 110 calories in 1 serving<\/p>\n<p>Explanation:<br \/>\nGiven,<br \/>\n880 calories in 8 servings<br \/>\n880\/8 = 110<br \/>\n110 calories in 1 serving<\/p>\n<p>Question 24.<br \/>\n1080 miles on 15 gallons<br \/>\nAnswer: 72 miles in 1 gallon<\/p>\n<p>Explanation:<br \/>\nGiven,<br \/>\n1080 miles on 15 gallons<br \/>\n1080\/15 = 72 miles<br \/>\n72 miles in 1 gallon<\/p>\n<p>Question 25.<br \/>\n$12.50 for 5 ounces<br \/>\nAnswer: 2.5<\/p>\n<p>Explanation:<br \/>\nGiven,<br \/>\n$12.50 for 5 ounces<br \/>\n12.50\/5 = 2.5<br \/>\n$2.5 per ounce<\/p>\n<p><strong>USING UNIT RATES<\/strong> Find the missing values in the ratio table.<br \/>\nQuestion 26.<br \/>\n<img decoding=\"async\" loading=\"lazy\" class=\"alignnone size-full wp-image-26733\" src=\"https:\/\/ccssanswers.com\/wp-content\/uploads\/2021\/01\/Big-Ideas-Math-Answer-Key-Grade-6-Chapter-3-Ratios-and-Rates-3.5-10.png\" alt=\"Big Ideas Math Answer Key Grade 6 Chapter 3 Ratios and Rates 3.5 10\" width=\"169\" height=\"62\" \/><br \/>\nAnswer:<\/p>\n<p>Question 27.<br \/>\n<img decoding=\"async\" loading=\"lazy\" class=\"alignnone size-full wp-image-26734\" src=\"https:\/\/ccssanswers.com\/wp-content\/uploads\/2021\/01\/Big-Ideas-Math-Answer-Key-Grade-6-Chapter-3-Ratios-and-Rates-3.5-11.png\" alt=\"Big Ideas Math Answer Key Grade 6 Chapter 3 Ratios and Rates 3.5 11\" width=\"175\" height=\"61\" \/><br \/>\nAnswer:<\/p>\n<p>Question 28.<br \/>\n<strong>MODELING REAL LIFE<\/strong><br \/>\nLightning strikes Earth 1000 times in 10 seconds.<br \/>\n<img decoding=\"async\" loading=\"lazy\" class=\"alignnone size-full wp-image-26735\" src=\"https:\/\/ccssanswers.com\/wp-content\/uploads\/2021\/01\/Big-Ideas-Math-Answer-Key-Grade-6-Chapter-3-Ratios-and-Rates-3.5-12.png\" alt=\"Big Ideas Math Answer Key Grade 6 Chapter 3 Ratios and Rates 3.5 12\" width=\"251\" height=\"173\" \/><br \/>\na. How many times does lightning strike in 12 seconds?<br \/>\nb. How many seconds does it take for lightning to strike 7250 times?<br \/>\nAnswer:<\/p>\n<p>Question 29.<br \/>\n<strong>MODELING REAL LIFE<\/strong><br \/>\nYou earn $35 for washing 7 cars.<br \/>\na. How much do you earn for washing 4 cars?<\/p>\n<p>Answer:<br \/>\nGiven,<br \/>\nYou earn $35 for washing 7 cars.<br \/>\n7 cars = $35<br \/>\n1 car = x<br \/>\nx \u00d7 7 = $35<br \/>\nx = 35\/7 = 5<br \/>\nThus you earn $5 per car<br \/>\n4 cars = 4 \u00d7 5 = $20<br \/>\nYou earn $20 for washing 4 cars..<\/p>\n<p>b. You earn $45. How many cars did you wash?<br \/>\nAnswer:<br \/>\nyou earn $5 per car<br \/>\n45\/5 = 9<br \/>\nYou wash 9 cars for $45<\/p>\n<p><strong>COMPARING RATES<\/strong> Decide whether the rates are equivalent.<br \/>\nQuestion 30.<br \/>\n24 laps in 6 minutes<br \/>\n72 laps in 18 minutes<br \/>\nAnswer: Yes<\/p>\n<p>Explanation:<br \/>\n24:6 = 4 : 1<br \/>\n72 : 18 = 4 : 1<br \/>\nThus the rates are equivalent.<\/p>\n<p>Question 31.<br \/>\n126 points for every 3 games<br \/>\n210 points for every 5 games<br \/>\nAnswer: Yes<\/p>\n<p>Explanation:<br \/>\nGiven<br \/>\n126 points for every 3 games<br \/>\n210 points for every 5 games<br \/>\n126 : 3 = 42 : 1<br \/>\n210 : 5 = 42 : 1<br \/>\nThus the rates are equivalent.<\/p>\n<p>Question 32.<br \/>\n15 breaths for every 36 seconds<br \/>\n90 breaths for every 3 minutes<br \/>\nAnswer: No<\/p>\n<p>Explanation:<br \/>\nGiven<br \/>\n15 breaths for every 36 seconds<br \/>\n90 breaths for every 3 minutes<br \/>\n15 : 36 = 0.41<br \/>\n90 : 180 = 0.5<br \/>\nThus the rates are not equivalent.<\/p>\n<p>Question 33.<br \/>\n$16 for 4 pounds<br \/>\n$1 for 4 ounces<br \/>\nAnswer: Yes<\/p>\n<p>Explanation:<br \/>\nGiven<br \/>\n$16 for 4 pounds<br \/>\n$1 for 4 ounces<br \/>\n1 pound = 16 ounces<br \/>\n4 pounds = 64 ounces<br \/>\n16 : 64 = 1 : 4<br \/>\nThus the rates are equivalent.<\/p>\n<p>Question 34.<br \/>\n<strong>MODELING REAL LIFE<\/strong><br \/>\nAn office printer prints 25 photos in 12.5 minutes. A home printer prints 15 photos in 6 minutes. Which printer is faster? How many more photos can you print in 12 minutes using the faster printer?<br \/>\nAnswer: The home printer is faster<\/p>\n<p>Explanation:<br \/>\nGiven,<br \/>\nAn office printer prints 25 photos in 12.5 minutes. A home printer prints 15 photos in 6 minutes.<br \/>\n23 photos in 12.5 minutes<br \/>\n12.5 is half of 25 and therefore this is a two to one ratio<br \/>\nSo 2 photos print in 1 minute with the office printer.<br \/>\nAnd 4 photos in 2 minutes.<br \/>\nThe home printer prints 15 photos in 6 minutes.<br \/>\nSince 15 is not divisible by 6 without a remainder divide both by 3.<br \/>\nSo 5 photos in 2 minutes. This is faster than the office printer.<br \/>\nThis leaves you with an answer of 30 photos in 12 minutes.<\/p>\n<p>Question 35.<br \/>\n<strong>MODELING REAL LIFE<\/strong><br \/>\nYou jog 2 kilometers in 12 minutes. Your friend jogs 3 kilometers in 16.5 minutes. Who jogs faster? How much sooner will the faster jogger finish a five-kilometer race?<br \/>\nAnswer:<br \/>\nFirst, we have to calculate the speed of person 1 and 2.<br \/>\nSpeed = Distance\/time<br \/>\nSpeed of person 1 = 2\/12 = 0.167 km\/min<br \/>\nSpeed of person 2 = 3\/16.5 = 0.182 km\/min<br \/>\nFrom this we conclude that, person 2 jogs faster as compared to person 1.<br \/>\nNow we have to calculate the time taken by the faster jogger to finish a 5 kilometer race.<br \/>\nFaster jogger speed = 0.182 km\/min<br \/>\nDistance = 5 km<br \/>\nS = d\/t<br \/>\nTime = 27.5 min<br \/>\nThus, the time taken by the faster jogger finish a 5 kilometer race will be, 27.5 minutes.<\/p>\n<p>Question 36.<br \/>\n<strong>PROBLEM SOLVING<\/strong><br \/>\nA softball team has a budget of $200 for visors. The athletic director pays $90 for 12 sun visors. Is there enough money in the budget to purchase 15 more sun visors? Explain your reasoning.<br \/>\nAnswer: $112.5<\/p>\n<p>Explanation:<br \/>\nAn athletic director pays $90 for 12 sun visors for the softball team.<br \/>\nThe rate per sun visor is equal to $90\/12 = $7.5<br \/>\nSo the athletic director should pay<br \/>\n$7.5 \u00d7 15 = $112.5<\/p>\n<p>Question 37.<br \/>\n<strong>DIG DEEPER!<\/strong><br \/>\nThe table shows the amounts of food collected by two homerooms. Homeroom A collects 21 additional items of food. How many more items does Homeroom B need to collect to have more items per student?<br \/>\n<img decoding=\"async\" loading=\"lazy\" class=\"alignnone size-full wp-image-26736\" src=\"https:\/\/ccssanswers.com\/wp-content\/uploads\/2021\/01\/Big-Ideas-Math-Answer-Key-Grade-6-Chapter-3-Ratios-and-Rates-3.5-13.png\" alt=\"Big Ideas Math Answer Key Grade 6 Chapter 3 Ratios and Rates 3.5 13\" width=\"313\" height=\"123\" srcset=\"https:\/\/ccssanswers.com\/wp-content\/uploads\/2021\/01\/Big-Ideas-Math-Answer-Key-Grade-6-Chapter-3-Ratios-and-Rates-3.5-13.png 313w, https:\/\/ccssanswers.com\/wp-content\/uploads\/2021\/01\/Big-Ideas-Math-Answer-Key-Grade-6-Chapter-3-Ratios-and-Rates-3.5-13-300x118.png 300w\" sizes=\"(max-width: 313px) 100vw, 313px\" \/><br \/>\nAnswer:<\/p>\n<p>Question 38.<br \/>\n<strong>REASONING<\/strong><br \/>\nA runner completed a 26.2-mile marathon in 210 minutes.<br \/>\na. Estimate the unit rate, in miles per minute.<br \/>\nb. Estimate the unit rate, in minutes per mile.<br \/>\nc. Another runner says, \u201cI averaged 10-minute miles in the marathon.\u201d Is this runner talking about the unit rate described in part(a) or in part(b)? Explain your reasoning.<br \/>\n<img decoding=\"async\" loading=\"lazy\" class=\"alignnone size-full wp-image-26737\" src=\"https:\/\/ccssanswers.com\/wp-content\/uploads\/2021\/01\/Big-Ideas-Math-Answer-Key-Grade-6-Chapter-3-Ratios-and-Rates-3.5-14.png\" alt=\"Big Ideas Math Answer Key Grade 6 Chapter 3 Ratios and Rates 3.5 14\" width=\"259\" height=\"322\" srcset=\"https:\/\/ccssanswers.com\/wp-content\/uploads\/2021\/01\/Big-Ideas-Math-Answer-Key-Grade-6-Chapter-3-Ratios-and-Rates-3.5-14.png 259w, https:\/\/ccssanswers.com\/wp-content\/uploads\/2021\/01\/Big-Ideas-Math-Answer-Key-Grade-6-Chapter-3-Ratios-and-Rates-3.5-14-241x300.png 241w\" sizes=\"(max-width: 259px) 100vw, 259px\" \/><br \/>\nAnswer:<\/p>\n<p>Question 39.<br \/>\n<strong>DIG DEEPER!<\/strong><br \/>\nYou can complete one-half of a job in an hour. Your friend can complete one-third of the same job in an hour. How long will it take to complete the job if you work together?<br \/>\nAnswer:<br \/>\nGiven,<br \/>\nYou can complete one-half of a job in an hour. Your friend can complete one-third of the same job in an hour<br \/>\n1 1\/2 + 1 1\/3 = 1\/x<br \/>\nhas to be between 1\/4 min to 1\/6 hours. first guess is about (1\/2)(1\/4+1\/6) = 5\/24= 0.21 hours<br \/>\n2 + 3 = 1\/x<br \/>\n5 = 1\/x<br \/>\nx = 1\/5 = 0.20 hours<\/p>\n<h3><a id=\"Lesson_3.6_Converting_Measures\"><\/a>Lesson 3.6 Converting Measures<\/h3>\n<p><strong>EXPLORATION 1<\/strong><\/p>\n<p>Estimating Unit Conversions<br \/>\nWork with a partner. You are given 4 one-liter containers and a one-gallon container.<br \/>\na. A full one-gallon container can be used to fill the one-liter containers, as shown below. Write a unit rate that estimates the number of liters per gallon.<br \/>\n<img decoding=\"async\" loading=\"lazy\" class=\"alignnone size-full wp-image-26738\" src=\"https:\/\/ccssanswers.com\/wp-content\/uploads\/2021\/01\/Big-Ideas-Math-Answers-6th-Grade-Chapter-3-Ratios-and-Rates-3.6-1.png\" alt=\"Big Ideas Math Answers 6th Grade Chapter 3 Ratios and Rates 3.6 1\" width=\"257\" height=\"109\" \/><br \/>\nb. A full one-liter container can be used to partially foll the one-gallon container, as shown below. Write a unit rate that estimates the number of gallons per liter.<br \/>\n<img decoding=\"async\" loading=\"lazy\" class=\"alignnone size-full wp-image-26739\" src=\"https:\/\/ccssanswers.com\/wp-content\/uploads\/2021\/01\/Big-Ideas-Math-Answers-6th-Grade-Chapter-3-Ratios-and-Rates-3.6-2.png\" alt=\"Big Ideas Math Answers 6th Grade Chapter 3 Ratios and Rates 3.6 2\" width=\"163\" height=\"108\" \/><br \/>\nc. Estimate the number of liters in 5.5 gallons and the number of gallons in 12 liters. What method(s) did you use? What other methods could you have used?<br \/>\nAnswer:<\/p>\n<p><strong>EXPLORATION 2<\/strong><\/p>\n<p>Converting Units in a Rate<br \/>\nWork with a partner. The rate that a caterpillar moves is given in inches per minute. Using the rulers below, how can you convert the rate to centimeters per second? Justify your answer.<br \/>\n<img decoding=\"async\" loading=\"lazy\" class=\"alignnone size-full wp-image-26740\" src=\"https:\/\/ccssanswers.com\/wp-content\/uploads\/2021\/01\/Big-Ideas-Math-Answers-6th-Grade-Chapter-3-Ratios-and-Rates-3.6-3.png\" alt=\"Big Ideas Math Answers 6th Grade Chapter 3 Ratios and Rates 3.6 3\" width=\"601\" height=\"180\" srcset=\"https:\/\/ccssanswers.com\/wp-content\/uploads\/2021\/01\/Big-Ideas-Math-Answers-6th-Grade-Chapter-3-Ratios-and-Rates-3.6-3.png 601w, https:\/\/ccssanswers.com\/wp-content\/uploads\/2021\/01\/Big-Ideas-Math-Answers-6th-Grade-Chapter-3-Ratios-and-Rates-3.6-3-300x90.png 300w\" sizes=\"(max-width: 601px) 100vw, 601px\" \/><br \/>\nAnswer:<\/p>\n<p>The U.S. customary system is a system of measurement that contains units for length, capacity, and weight. The metric system is a decimal system of measurement, based on powers of 10, that contains units for length, capacity, and mass. Key Vocabulary U.S. customary system, p. 142 metric system,p. 142 You can use unit rates and ratio tables to convert measures within the same system and between systems.<\/p>\n<p><img decoding=\"async\" loading=\"lazy\" class=\"alignnone size-full wp-image-26741\" src=\"https:\/\/ccssanswers.com\/wp-content\/uploads\/2021\/01\/Big-Ideas-Math-Answers-6th-Grade-Chapter-3-Ratios-and-Rates-3.6-4.png\" alt=\"Big Ideas Math Answers 6th Grade Chapter 3 Ratios and Rates 3.6 4\" width=\"185\" height=\"140\" \/><\/p>\n<p><strong>Try It<\/strong><\/p>\n<p>Question 1.<br \/>\nConvert 48 feet to yards.<br \/>\nAnswer: 16 yards<\/p>\n<p>Explanation:<br \/>\nConvert from feets to yards<br \/>\nWe know that<br \/>\n1 yard = 3 feet<br \/>\nSo, 48 feet = 48\/3 = 16 yards<\/p>\n<p>Question 2.<br \/>\nConvert 7 miles to kilometers. Round to the nearest hundredth if necessary.<br \/>\nAnswer:<br \/>\nConvert from miles to kilometers.<br \/>\n1 mile = 1.6 km<br \/>\n7 miles = 7 \u00d7 1.6 = 11.2 kilometers<\/p>\n<p>Question 3.<br \/>\nConvert 20 quarts to liters. Round to the nearest hundredth if necessary.<br \/>\nAnswer:<br \/>\nConvert from quarts to liters.<br \/>\n1 quart = 0.94 liters<br \/>\n20 quarts = 20 \u00d7 0.94 = 18.92 liters<\/p>\n<p>Question 4.<br \/>\nConvert 60 kilometers per hour to miles per hour. Round to the nearest hundredth if necessary.<br \/>\nAnswer:<br \/>\nConvert from kilometers per hour to miles per hour.<br \/>\n1 kilometer per hour = 0.621 miles per hour<br \/>\n60 kilometer per hour = 37.28 miles per hour<\/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 5.<br \/>\n<strong>DIFFERENT WORDS, SAME QUESTION<\/strong><br \/>\nWhich is different? Find \u201cboth\u201d answers.<br \/>\n<img decoding=\"async\" loading=\"lazy\" class=\"alignnone size-full wp-image-26742\" src=\"https:\/\/ccssanswers.com\/wp-content\/uploads\/2021\/01\/Big-Ideas-Math-Answers-6th-Grade-Chapter-3-Ratios-and-Rates-3.6-5.png\" alt=\"Big Ideas Math Answers 6th Grade Chapter 3 Ratios and Rates 3.6 5\" width=\"395\" height=\"131\" srcset=\"https:\/\/ccssanswers.com\/wp-content\/uploads\/2021\/01\/Big-Ideas-Math-Answers-6th-Grade-Chapter-3-Ratios-and-Rates-3.6-5.png 395w, https:\/\/ccssanswers.com\/wp-content\/uploads\/2021\/01\/Big-Ideas-Math-Answers-6th-Grade-Chapter-3-Ratios-and-Rates-3.6-5-300x99.png 300w\" sizes=\"(max-width: 395px) 100vw, 395px\" \/><br \/>\nAnswer:<br \/>\n&#8220;Find the number of inches in 5 centimeters&#8221; has different words.<\/p>\n<p><strong>CONVERTING MEASURES<\/strong> Copy and complete the statement. Round to the nearest hundredth if necessary.<br \/>\nQuestion 6.<br \/>\n<img decoding=\"async\" loading=\"lazy\" class=\"alignnone size-full wp-image-26743\" src=\"https:\/\/ccssanswers.com\/wp-content\/uploads\/2021\/01\/Big-Ideas-Math-Answers-6th-Grade-Chapter-3-Ratios-and-Rates-3.6-6.png\" alt=\"Big Ideas Math Answers 6th Grade Chapter 3 Ratios and Rates 3.6 6\" width=\"132\" height=\"62\" \/><br \/>\nAnswer:<br \/>\nConvert from meters per minute to feet per minute.<br \/>\n1 meter per minute = 3.2 feet per minute<br \/>\n12 meter per minute = 39.37 feet per minute<\/p>\n<p>Question 7.<br \/>\n<img decoding=\"async\" loading=\"lazy\" class=\"alignnone size-full wp-image-26744\" src=\"https:\/\/ccssanswers.com\/wp-content\/uploads\/2021\/01\/Big-Ideas-Math-Answers-6th-Grade-Chapter-3-Ratios-and-Rates-3.6-7.png\" alt=\"Big Ideas Math Answers 6th Grade Chapter 3 Ratios and Rates 3.6 7\" width=\"130\" height=\"67\" \/><br \/>\nAnswer:<br \/>\nConvert from feet per second to yard per minute<br \/>\n12 feet per second = 240 yard per minute<\/p>\n<p>Question 8.<br \/>\nWill all of the water from a full two-liter bottle \ufb01t into a two-quart pitcher? Explain.<br \/>\nAnswer:<br \/>\n1 liter = 1.05669 quarts<br \/>\nq\/L = 1.05669\/1<br \/>\nq\/2 = 1.05669\/1<br \/>\nq = 2 \u00d7 1.05669<br \/>\nq = 2.11338<\/p>\n<p>Question 9.<br \/>\n<strong>DIG DEEPER!<\/strong><br \/>\nThe speed of light is about 300,000 kilometers per second. The Sun is about 93 million miles from Earth. How many minutes does it take for sunlight to reach Earth?<br \/>\nAnswer:<\/p>\n<p>Question 10.<br \/>\nA race car driver\u2019s goal is to complete a 1000-kilometer auto race in 4 hours or less. The driver\u2019s average speed is 4200 meters per minute. Does the driver meet the goal? If not, how much faster (in meters per minute) must the driver be to meet the goal?<br \/>\n<img decoding=\"async\" loading=\"lazy\" class=\"alignnone size-full wp-image-26745\" src=\"https:\/\/ccssanswers.com\/wp-content\/uploads\/2021\/01\/Big-Ideas-Math-Answers-6th-Grade-Chapter-3-Ratios-and-Rates-3.6-8.png\" alt=\"Big Ideas Math Answers 6th Grade Chapter 3 Ratios and Rates 3.6 8\" width=\"247\" height=\"285\" \/><br \/>\nAnswer:<\/p>\n<h3><a id=\"Converting_Measures_Homework_&amp;_Practice_3.6\"><\/a>Converting Measures Homework &amp; Practice 3.6<\/h3>\n<p><strong>Review &amp; Refresh<\/strong><\/p>\n<p><strong>Write a unit rate for the situation.<\/strong><br \/>\nQuestion 1.<br \/>\n102 beats per 2 minutes<br \/>\nAnswer: 51 per minute<\/p>\n<p>Explanation:<br \/>\n102 beats per 2 minutes<br \/>\n102\/2 = 51 beats per minute<\/p>\n<p>Question 2.<br \/>\n60 shirts for every 5 clothing racks<br \/>\nAnswer: 12 for 1 clothing racks<\/p>\n<p>Explanation:<br \/>\n60 shirts for every 5 clothing racks<br \/>\n60\/5 = 12<br \/>\n12 for 1 clothing racks<\/p>\n<p>Question 3.<br \/>\n$100 donated for every 5 volunteers<br \/>\nAnswer: 20 for 1 volunteer<\/p>\n<p>Explanation:<br \/>\n$100 donated for every 5 volunteers<br \/>\n100\/5 = 20<br \/>\n$20 donated for 1 volunteer<\/p>\n<p>Question 4.<br \/>\n30 milliliters every 4 hours<br \/>\nAnswer: 7.5 ml per hour<\/p>\n<p>Explanation:<br \/>\n30 milliliters every 4 hours<br \/>\n30\/4 = 7.5<br \/>\nSo, 7.5 ml per hour<\/p>\n<p>Question 5.<br \/>\nWhat is the LCM of 6, 12, and 18?<br \/>\nA. 6<br \/>\nB. 18<br \/>\nC. 36<br \/>\nD. 72<br \/>\nAnswer: C<\/p>\n<p>Explanation:<br \/>\nFind and list multiples of each number until the first common multiple is found. This is the lowest common multiple.<br \/>\nMultiples of 6:<br \/>\n6, 12, 18, 24, 30, 36, 42, 48<br \/>\nMultiples of 12:<br \/>\n12, 24, 36, 48, 60<br \/>\nMultiples of 18:<br \/>\n18, 36, 54, 72<br \/>\nTherefore,<br \/>\nLCM(6, 12, 18) = 36<br \/>\nThus the correct answer is option C.<\/p>\n<p><strong>Write the prime factorization of the number.<\/strong><br \/>\nQuestion 6.<br \/>\n56<br \/>\nAnswer: 2 x 2 x 2 x 7<\/p>\n<p>Explanation:<br \/>\n56 = 2 \u00d7 28<br \/>\n= 2 \u00d7 2 \u00d7 14<br \/>\n= 2 \u00d7 2 \u00d7 2 \u00d7 7<br \/>\nThus the prime factorization of the number 56 is 2 x 2 x 2 x 7<\/p>\n<p>Question 7.<br \/>\n74<br \/>\nAnswer: 2 \u00d7 37<\/p>\n<p>Explanation:<br \/>\n74 = 2 \u00d7 37<br \/>\nThus the prime factorization of the number 74 is 2 x 37<\/p>\n<p>Question 8.<br \/>\n63<br \/>\nAnswer: 3 \u00d7 3 \u00d7 7<\/p>\n<p>Explanation:<br \/>\n63 = 3 \u00d7 21<br \/>\n= 3 \u00d7 3 \u00d7 7<br \/>\nThus the prime factorization of the number 63 is 3 \u00d7 3 \u00d7 7<\/p>\n<p>Question 9.<br \/>\n132<br \/>\nAnswer: 2 x 2 x 3 x 11<\/p>\n<p>Explanation:<br \/>\n132 = 2 \u00d7 66<br \/>\n= 2 \u00d7 2 \u00d7 33<br \/>\n= 2 \u00d7 2 \u00d7 3 \u00d7 11<br \/>\nThus the prime factorization of the number 132 is 2 x 2 x 3 x 11<\/p>\n<p><strong>Write the product as a power.<\/strong><br \/>\nQuestion 10.<br \/>\n6 \u00d7 6<br \/>\nAnswer: The product of 6\u00d76 is 6\u00b2<\/p>\n<p>Question 11.<br \/>\n18 \u00d7 18 \u00d7 18 \u00d7 18<br \/>\nAnswer: The product of 18\u00d718\u00d718\u00d718 is 18\u2074<\/p>\n<p>Question 12.<br \/>\n12 \u00d7 12 \u00d7 12 \u00d7 12 \u00d7 12<br \/>\nAnswer: The product of 12\u00d712\u00d712\u00d712\u00d712 is 12\u2075<\/p>\n<p><strong>Concepts, Skills, &amp; Problem Solving<\/strong><\/p>\n<p><strong>COMPARING MEASURES<\/strong> Answer the question. Explain your answer. (See Explorations 1 &amp; 2, p. 141.)<br \/>\nQuestion 13.<br \/>\nWhich juice container is larger: 2 L or 1 gal?<br \/>\nAnswer:<br \/>\nConvert from liters to gal<br \/>\n1 liter = 0.26 gal<br \/>\n2 liter = 0.52 gal<br \/>\n1 gal = 3.78 liter<br \/>\nThus the juice container with 1 gal is larger<\/p>\n<p>Question 14.<br \/>\nWhich is longer:1 in. or 2 cm?<br \/>\nAnswer: 1 inch is longer than 2 cm<\/p>\n<p>Explanation:<br \/>\nConvert from inches to cm<br \/>\n1 inch = 2.54 cm<br \/>\n2.54 cm &gt; 2 cm<\/p>\n<p><strong>CONVERTING MEASURES<\/strong> Copy and complete the statement.<br \/>\nQuestion 15.<br \/>\n<img decoding=\"async\" loading=\"lazy\" class=\"alignnone size-full wp-image-26746\" src=\"https:\/\/ccssanswers.com\/wp-content\/uploads\/2021\/01\/Big-Ideas-Math-Answers-6th-Grade-Chapter-3-Ratios-and-Rates-3.6-9.png\" alt=\"Big Ideas Math Answers 6th Grade Chapter 3 Ratios and Rates 3.6 9\" width=\"116\" height=\"36\" \/><br \/>\nAnswer: 6 cups<\/p>\n<p>Explanation:<br \/>\nConvert from pints to cups.<br \/>\n1 pint = 2 cups<br \/>\n3 pints = 3 \u00d7 2 cups = 6 cups<\/p>\n<p>Question 16.<br \/>\n<img decoding=\"async\" loading=\"lazy\" class=\"alignnone size-full wp-image-26747\" src=\"https:\/\/ccssanswers.com\/wp-content\/uploads\/2021\/01\/Big-Ideas-Math-Answers-6th-Grade-Chapter-3-Ratios-and-Rates-3.6-10.png\" alt=\"Big Ideas Math Answers 6th Grade Chapter 3 Ratios and Rates 3.6 10\" width=\"156\" height=\"44\" \/><br \/>\nAnswer: 1.5 L<\/p>\n<p>Explanation:<br \/>\nConvert from mL to L<br \/>\n1000 mL = 1 L<br \/>\n1500 mL = 1.5 L<\/p>\n<p>Question 17.<br \/>\n<img decoding=\"async\" loading=\"lazy\" class=\"alignnone size-full wp-image-26748\" src=\"https:\/\/ccssanswers.com\/wp-content\/uploads\/2021\/01\/Big-Ideas-Math-Answers-6th-Grade-Chapter-3-Ratios-and-Rates-3.6-11.png\" alt=\"Big Ideas Math Answers 6th Grade Chapter 3 Ratios and Rates 3.6 11\" width=\"131\" height=\"48\" \/><br \/>\nAnswer: 2.5 lb<\/p>\n<p>Explanation:<br \/>\nConvert from ounces to lb<br \/>\n1 ounce = 0.0625<br \/>\n40 oz = 2.5 lb<\/p>\n<p>Question 18.<br \/>\n<img decoding=\"async\" loading=\"lazy\" class=\"alignnone size-full wp-image-26749\" src=\"https:\/\/ccssanswers.com\/wp-content\/uploads\/2021\/01\/Big-Ideas-Math-Answers-6th-Grade-Chapter-3-Ratios-and-Rates-3.6-12.png\" alt=\"Big Ideas Math Answers 6th Grade Chapter 3 Ratios and Rates 3.6 12\" width=\"129\" height=\"36\" \/><br \/>\nAnswer: 60 in.<\/p>\n<p>Explanation:<br \/>\nConvert from feet to inches.<br \/>\n1 feet = 12 inches<br \/>\n5 feet = 5 \u00d7 12 = 60 inches<br \/>\nSo, 5 ft = 60 in.<\/p>\n<p>Question 19.<br \/>\n<img decoding=\"async\" loading=\"lazy\" class=\"alignnone size-full wp-image-26750\" src=\"https:\/\/ccssanswers.com\/wp-content\/uploads\/2021\/01\/Big-Ideas-Math-Answers-6th-Grade-Chapter-3-Ratios-and-Rates-3.6-13.png\" alt=\"Big Ideas Math Answers 6th Grade Chapter 3 Ratios and Rates 3.6 13\" width=\"128\" height=\"37\" \/><br \/>\nAnswer: 24 qt<\/p>\n<p>Explanation:<br \/>\nConvert from gallons to quarts<br \/>\n1 gal = 4 qt<br \/>\n6 gal = 6 \u00d7 4 qt = 24 qt<br \/>\nSo, 6 gal = 24 qt<\/p>\n<p>Question 20.<br \/>\n<img decoding=\"async\" loading=\"lazy\" class=\"alignnone size-full wp-image-26751\" src=\"https:\/\/ccssanswers.com\/wp-content\/uploads\/2021\/01\/Big-Ideas-Math-Answers-6th-Grade-Chapter-3-Ratios-and-Rates-3.6-14.png\" alt=\"Big Ideas Math Answers 6th Grade Chapter 3 Ratios and Rates 3.6 14\" width=\"149\" height=\"43\" \/><br \/>\nAnswer: 480 mm<\/p>\n<p>Explanation:<br \/>\nConvert from cm to mm<br \/>\n1 cm = 10 mm<br \/>\n48 cm = 48 \u00d7 10 mm = 480 mm<br \/>\nSo, 48 cm = 480 mm<\/p>\n<p>Question 21.<br \/>\n<img decoding=\"async\" loading=\"lazy\" class=\"alignnone size-full wp-image-26752\" src=\"https:\/\/ccssanswers.com\/wp-content\/uploads\/2021\/01\/Big-Ideas-Math-Answers-6th-Grade-Chapter-3-Ratios-and-Rates-3.6-15.png\" alt=\"Big Ideas Math Answers 6th Grade Chapter 3 Ratios and Rates 3.6 15\" width=\"154\" height=\"41\" srcset=\"https:\/\/ccssanswers.com\/wp-content\/uploads\/2021\/01\/Big-Ideas-Math-Answers-6th-Grade-Chapter-3-Ratios-and-Rates-3.6-15.png 154w, https:\/\/ccssanswers.com\/wp-content\/uploads\/2021\/01\/Big-Ideas-Math-Answers-6th-Grade-Chapter-3-Ratios-and-Rates-3.6-15-150x41.png 150w\" sizes=\"(max-width: 154px) 100vw, 154px\" \/><br \/>\nAnswer: 5 m<\/p>\n<p>Explanation:<br \/>\nConvert from cm to m<br \/>\n1 cm = 0.01 m<br \/>\n500 cm = 500 \u00d7 0.01 m = 5 meters<br \/>\nSo, 500 cm = 5 meters<\/p>\n<p>Question 22.<br \/>\n<img decoding=\"async\" loading=\"lazy\" class=\"alignnone size-full wp-image-26753\" src=\"https:\/\/ccssanswers.com\/wp-content\/uploads\/2021\/01\/Big-Ideas-Math-Answers-6th-Grade-Chapter-3-Ratios-and-Rates-3.6-16.png\" alt=\"Big Ideas Math Answers 6th Grade Chapter 3 Ratios and Rates 3.6 16\" width=\"141\" height=\"44\" \/><br \/>\nAnswer: 6<\/p>\n<p>Explanation:<br \/>\nConvert from grams to kilograms<br \/>\n1 kg = 1000 g<br \/>\n6000g = 6 kg<\/p>\n<p>Question 23.<br \/>\n<img decoding=\"async\" loading=\"lazy\" class=\"alignnone size-full wp-image-26754\" src=\"https:\/\/ccssanswers.com\/wp-content\/uploads\/2021\/01\/Big-Ideas-Math-Answers-6th-Grade-Chapter-3-Ratios-and-Rates-3.6-17.png\" alt=\"Big Ideas Math Answers 6th Grade Chapter 3 Ratios and Rates 3.6 17\" width=\"141\" height=\"38\" \/><br \/>\nAnswer:<\/p>\n<p>Explanation:<br \/>\nConvert from fl ounce to cups<br \/>\n1 fl oz = 0.125 cups<br \/>\n32 fl ouz = 4 cups<\/p>\n<p><strong>CONVERTING MEASURES<\/strong> Copy and complete the statement. Round to the nearest hundredth if necessary.<br \/>\nQuestion 24.<br \/>\n<img decoding=\"async\" loading=\"lazy\" class=\"alignnone size-full wp-image-26755\" src=\"https:\/\/ccssanswers.com\/wp-content\/uploads\/2021\/01\/Big-Ideas-Math-Answers-6th-Grade-Chapter-3-Ratios-and-Rates-3.6-18.png\" alt=\"Big Ideas Math Answers 6th Grade Chapter 3 Ratios and Rates 3.6 18\" width=\"135\" height=\"43\" \/><br \/>\nAnswer: 13 qt<\/p>\n<p>Explanation:<br \/>\nConvert from liters to quarts.<br \/>\n1 L = 1.05 qt<br \/>\n12 L = 12.608 qt<br \/>\n12 L \u2248 13 qt<\/p>\n<p>Question 25.<br \/>\n<img decoding=\"async\" loading=\"lazy\" class=\"alignnone size-full wp-image-26756\" src=\"https:\/\/ccssanswers.com\/wp-content\/uploads\/2021\/01\/Big-Ideas-Math-Answers-6th-Grade-Chapter-3-Ratios-and-Rates-3.6-19.png\" alt=\"Big Ideas Math Answers 6th Grade Chapter 3 Ratios and Rates 3.6 19\" width=\"125\" height=\"44\" \/><br \/>\nAnswer: 46 ft<\/p>\n<p>Explanation:<br \/>\nConvert from meters to feet<br \/>\n1 meter = 3.28 feet<br \/>\n14 meter = 45.93 feet<br \/>\n14 m \u2248 46 feet<\/p>\n<p>Question 26.<br \/>\n<img decoding=\"async\" loading=\"lazy\" class=\"alignnone size-full wp-image-26757\" src=\"https:\/\/ccssanswers.com\/wp-content\/uploads\/2021\/01\/Big-Ideas-Math-Answers-6th-Grade-Chapter-3-Ratios-and-Rates-3.6-20.png\" alt=\"Big Ideas Math Answers 6th Grade Chapter 3 Ratios and Rates 3.6 20\" width=\"126\" height=\"39\" \/><br \/>\nAnswer: 1 m<\/p>\n<p>Explanation:<br \/>\nConvert from feet to meter<br \/>\n1 feet = 0.3 m<br \/>\n4 feet = 1.21 m<br \/>\n4 ft \u2248 1 m<\/p>\n<p>Question 27.<br \/>\n<img decoding=\"async\" loading=\"lazy\" class=\"alignnone size-full wp-image-26758\" src=\"https:\/\/ccssanswers.com\/wp-content\/uploads\/2021\/01\/Big-Ideas-Math-Answers-6th-Grade-Chapter-3-Ratios-and-Rates-3.6-21.png\" alt=\"Big Ideas Math Answers 6th Grade Chapter 3 Ratios and Rates 3.6 21\" width=\"135\" height=\"38\" \/><br \/>\nAnswer: 29 kg<\/p>\n<p>Explanation:<br \/>\nConvert from lb to kgs.<br \/>\n1 lb = 0.45 kg<br \/>\n64 lb = 29.02 kg<br \/>\n64 lb \u2248 29 kg<\/p>\n<p>Question 28.<br \/>\n<img decoding=\"async\" loading=\"lazy\" class=\"alignnone size-full wp-image-26759\" src=\"https:\/\/ccssanswers.com\/wp-content\/uploads\/2021\/01\/Big-Ideas-Math-Answers-6th-Grade-Chapter-3-Ratios-and-Rates-3.6-22.png\" alt=\"Big Ideas Math Answers 6th Grade Chapter 3 Ratios and Rates 3.6 22\" width=\"156\" height=\"34\" srcset=\"https:\/\/ccssanswers.com\/wp-content\/uploads\/2021\/01\/Big-Ideas-Math-Answers-6th-Grade-Chapter-3-Ratios-and-Rates-3.6-22.png 156w, https:\/\/ccssanswers.com\/wp-content\/uploads\/2021\/01\/Big-Ideas-Math-Answers-6th-Grade-Chapter-3-Ratios-and-Rates-3.6-22-150x34.png 150w\" sizes=\"(max-width: 156px) 100vw, 156px\" \/><br \/>\nAnswer: 0.186 mi<\/p>\n<p>Explanation:<br \/>\nConvert from kg to miles<br \/>\n1 km = 0.621 miles<br \/>\n0.3 km = 0.186 miles<\/p>\n<p>Question 29.<br \/>\n<img decoding=\"async\" loading=\"lazy\" class=\"alignnone size-full wp-image-26760\" src=\"https:\/\/ccssanswers.com\/wp-content\/uploads\/2021\/01\/Big-Ideas-Math-Answers-6th-Grade-Chapter-3-Ratios-and-Rates-3.6-23.png\" alt=\"Big Ideas Math Answers 6th Grade Chapter 3 Ratios and Rates 3.6 23\" width=\"159\" height=\"35\" \/><br \/>\nAnswer: 191 cm<\/p>\n<p>Explanation:<br \/>\nConvert from inches to centimeters.<br \/>\n1 inch = 2.54 centimeter<br \/>\n75.2 inch = 191.008 centimeter<br \/>\n75.2 in \u2248 191 cm<\/p>\n<p>Question 30.<br \/>\n<img decoding=\"async\" loading=\"lazy\" class=\"alignnone size-full wp-image-26761\" src=\"https:\/\/ccssanswers.com\/wp-content\/uploads\/2021\/01\/Big-Ideas-Math-Answers-6th-Grade-Chapter-3-Ratios-and-Rates-3.6-24.png\" alt=\"Big Ideas Math Answers 6th Grade Chapter 3 Ratios and Rates 3.6 24\" width=\"131\" height=\"42\" \/><br \/>\nAnswer: 34 lb<\/p>\n<p>Explanation:<br \/>\nConvert from kg to lb<br \/>\n1 kg = 2.20 lb<br \/>\n17 kg = 37.47 lb<br \/>\n17 kg \u2248 34 lb<\/p>\n<p>Question 31.<br \/>\n<img decoding=\"async\" loading=\"lazy\" class=\"alignnone size-full wp-image-26762\" src=\"https:\/\/ccssanswers.com\/wp-content\/uploads\/2021\/01\/Big-Ideas-Math-Answers-6th-Grade-Chapter-3-Ratios-and-Rates-3.6-25.png\" alt=\"Big Ideas Math Answers 6th Grade Chapter 3 Ratios and Rates 3.6 25\" width=\"144\" height=\"41\" \/><br \/>\nAnswer: 6 inches<\/p>\n<p>Explanation:<br \/>\nConvert from cm to inches.<br \/>\n1 cm = 0.39 in<br \/>\n15 cm = 5.90 in<br \/>\n15 cm \u2248 6 in<\/p>\n<p>Question 32.<br \/>\n<img decoding=\"async\" loading=\"lazy\" class=\"alignnone size-full wp-image-26763\" src=\"https:\/\/ccssanswers.com\/wp-content\/uploads\/2021\/01\/Big-Ideas-Math-Answers-6th-Grade-Chapter-3-Ratios-and-Rates-3.6-26.png\" alt=\"Big Ideas Math Answers 6th Grade Chapter 3 Ratios and Rates 3.6 26\" width=\"141\" height=\"38\" \/><br \/>\nAnswer: 14 km<\/p>\n<p>Explanation:<br \/>\nConvert from miles to kilometers<br \/>\n1 mile = 1.609 km<br \/>\n9 miles = 14.48 km<br \/>\n9 miles \u2248 14 km<\/p>\n<p>Question 33.<br \/>\n<strong>GRAPHING RELATIONSHIPS<\/strong><br \/>\nRepresent the relationship between each pair of units in a coordinate plane.<br \/>\na. feet and yards<br \/>\nb. pounds and kilograms<br \/>\nAnswer:<\/p>\n<p>Question 34.<br \/>\n<strong>MODELING REAL LIFE<\/strong><br \/>\nEarth travels 30 kilometers each second as it revolves around the Sun. How many miles does Earth travel in 1 second?<br \/>\nAnswer:<\/p>\n<p>Question 35.<br \/>\n<strong>MODELING REAL LIFE<\/strong><br \/>\nThe Mackinac Bridge in Michigan is the third-longest suspension bridge in the United States.<br \/>\na. How high above the water is the roadway in meters?<br \/>\nb. The bridge has a length of 26,372 feet. What is the length in kilometers?<br \/>\n<img decoding=\"async\" loading=\"lazy\" class=\"alignnone size-full wp-image-26764\" src=\"https:\/\/ccssanswers.com\/wp-content\/uploads\/2021\/01\/Big-Ideas-Math-Answers-6th-Grade-Chapter-3-Ratios-and-Rates-3.6-27.png\" alt=\"Big Ideas Math Answers 6th Grade Chapter 3 Ratios and Rates 3.6 27\" width=\"574\" height=\"189\" srcset=\"https:\/\/ccssanswers.com\/wp-content\/uploads\/2021\/01\/Big-Ideas-Math-Answers-6th-Grade-Chapter-3-Ratios-and-Rates-3.6-27.png 574w, https:\/\/ccssanswers.com\/wp-content\/uploads\/2021\/01\/Big-Ideas-Math-Answers-6th-Grade-Chapter-3-Ratios-and-Rates-3.6-27-300x99.png 300w\" sizes=\"(max-width: 574px) 100vw, 574px\" \/><br \/>\nAnswer:<\/p>\n<p><strong>USING CONVERSION FACTORS<\/strong> Copy and complete the statement. Round to the nearest hundredth if necessary.<br \/>\nQuestion 36.<br \/>\n<img decoding=\"async\" loading=\"lazy\" class=\"alignnone size-full wp-image-26765\" src=\"https:\/\/ccssanswers.com\/wp-content\/uploads\/2021\/01\/Big-Ideas-Math-Answers-6th-Grade-Chapter-3-Ratios-and-Rates-3.6-28.png\" alt=\"Big Ideas Math Answers 6th Grade Chapter 3 Ratios and Rates 3.6 28\" width=\"154\" height=\"39\" srcset=\"https:\/\/ccssanswers.com\/wp-content\/uploads\/2021\/01\/Big-Ideas-Math-Answers-6th-Grade-Chapter-3-Ratios-and-Rates-3.6-28.png 154w, https:\/\/ccssanswers.com\/wp-content\/uploads\/2021\/01\/Big-Ideas-Math-Answers-6th-Grade-Chapter-3-Ratios-and-Rates-3.6-28-150x39.png 150w\" sizes=\"(max-width: 154px) 100vw, 154px\" \/><br \/>\nAnswer: 90 gal<\/p>\n<p>Explanation:<br \/>\nConvert from cubic feet to the gallon<br \/>\n1 cu ft = 7.48 gal<br \/>\n12 cu ft = 12 \u00d7 7.48 gal = 89.76 gal<br \/>\n12 cu ft \u2248 90 gal<\/p>\n<p>Question 37.<br \/>\n<img decoding=\"async\" loading=\"lazy\" class=\"alignnone size-full wp-image-26766\" src=\"https:\/\/ccssanswers.com\/wp-content\/uploads\/2021\/01\/Big-Ideas-Math-Answers-6th-Grade-Chapter-3-Ratios-and-Rates-3.6-29.png\" alt=\"Big Ideas Math Answers 6th Grade Chapter 3 Ratios and Rates 3.6 29\" width=\"115\" height=\"44\" \/><br \/>\nAnswer: 6 L<\/p>\n<p>Explanation:<br \/>\nConvert from quart to liter<br \/>\n1 qt = 0.94 L<br \/>\n6 qt = 5.67 L<br \/>\n6 qt \u2248 6 L<\/p>\n<p>Question 38.<br \/>\n<img decoding=\"async\" loading=\"lazy\" class=\"alignnone size-full wp-image-26767\" src=\"https:\/\/ccssanswers.com\/wp-content\/uploads\/2021\/01\/Big-Ideas-Math-Answers-6th-Grade-Chapter-3-Ratios-and-Rates-3.6-30.png\" alt=\"Big Ideas Math Answers 6th Grade Chapter 3 Ratios and Rates 3.6 30\" width=\"131\" height=\"40\" \/><br \/>\nAnswer: 1 gal<\/p>\n<p>Explanation:<br \/>\nConvert from liters to gal<br \/>\n1 L = 0.264 gal<br \/>\n5 L = 5 \u00d7 0.264 gal = 1.32 gal<br \/>\n5 L \u2248 1 gal<\/p>\n<p>Question 39.<br \/>\n<img decoding=\"async\" loading=\"lazy\" class=\"alignnone size-full wp-image-26768\" src=\"https:\/\/ccssanswers.com\/wp-content\/uploads\/2021\/01\/Big-Ideas-Math-Answers-6th-Grade-Chapter-3-Ratios-and-Rates-3.6-31.png\" alt=\"Big Ideas Math Answers 6th Grade Chapter 3 Ratios and Rates 3.6 31\" width=\"148\" height=\"62\" \/><br \/>\nAnswer: 8 miles per hour<\/p>\n<p>Explanation:<br \/>\nConvert from km per hour to miles per hour<br \/>\n1 km per hour = 0.621 miles per hour<br \/>\n13 km per hour = 8.07 miles per hour<\/p>\n<p>Question 40.<br \/>\n<img decoding=\"async\" loading=\"lazy\" class=\"alignnone size-full wp-image-26769\" src=\"https:\/\/ccssanswers.com\/wp-content\/uploads\/2021\/01\/Big-Ideas-Math-Answers-6th-Grade-Chapter-3-Ratios-and-Rates-3.6-32.png\" alt=\"Big Ideas Math Answers 6th Grade Chapter 3 Ratios and Rates 3.6 32\" width=\"122\" height=\"58\" \/><br \/>\nAnswer: 1320 liter per hour<\/p>\n<p>Explanation:<br \/>\nConvert from liter per minute to liter per hour<br \/>\n1 liter per minute = 60 liter per hour<br \/>\n22 liter per minute = 1320 liter per hour<\/p>\n<p>Question 41.<br \/>\n<img decoding=\"async\" loading=\"lazy\" class=\"alignnone size-full wp-image-26770\" src=\"https:\/\/ccssanswers.com\/wp-content\/uploads\/2021\/01\/Big-Ideas-Math-Answers-6th-Grade-Chapter-3-Ratios-and-Rates-3.6-33.png\" alt=\"Big Ideas Math Answers 6th Grade Chapter 3 Ratios and Rates 3.6 33\" width=\"138\" height=\"61\" \/><br \/>\nAnswer: 0.175 miles per second<\/p>\n<p>Explanation:<br \/>\nConvert from miles per hour to miles per second.<br \/>\n1 miles per hour = 0.0002 miles per second<br \/>\n63 miles per hour = 0.175 miles per second<\/p>\n<p>Question 42.<br \/>\n<strong>YOU BE THE TEACHER<\/strong><br \/>\nYour friend converts 8 liters to quarts. Is your friend correct? Explain your reasoning.<br \/>\n<img decoding=\"async\" loading=\"lazy\" class=\"alignnone size-full wp-image-26771\" src=\"https:\/\/ccssanswers.com\/wp-content\/uploads\/2021\/01\/Big-Ideas-Math-Answers-6th-Grade-Chapter-3-Ratios-and-Rates-3.6-34.png\" alt=\"Big Ideas Math Answers 6th Grade Chapter 3 Ratios and Rates 3.6 34\" width=\"206\" height=\"121\" \/><br \/>\nAnswer:<br \/>\nConvert from liters to quarts<br \/>\n1 liter = 1.05 qt<br \/>\n8 liter = 8.45 qt (approx)<br \/>\nYes, your friend is correct.<\/p>\n<p>Question 43.<br \/>\n<strong>MODELING REAL LIFE<\/strong><br \/>\nThe diagram shows the number of quarts of blood the human heart pumps per minute.<br \/>\n<img decoding=\"async\" loading=\"lazy\" class=\"alignnone size-full wp-image-26772\" src=\"https:\/\/ccssanswers.com\/wp-content\/uploads\/2021\/01\/Big-Ideas-Math-Answers-6th-Grade-Chapter-3-Ratios-and-Rates-3.6-35.png\" alt=\"Big Ideas Math Answers 6th Grade Chapter 3 Ratios and Rates 3.6 35\" width=\"269\" height=\"183\" \/><br \/>\na. How many quarts of blood does the human heart pump per hour?<\/p>\n<p>Answer:<br \/>\n1 hour = 60 minutes<br \/>\nThe heart pumps 5 quarts of blood per minute<br \/>\n1 min = 5 quarts<br \/>\n60 min = 60 \u00d7 5 quarts = 300 quarts<br \/>\nThus the heart pumps 300 quarts of blood per hour.<\/p>\n<p>b. How many liters of blood does the human heart pump per minute?<br \/>\nAnswer:<br \/>\nGiven,<br \/>\nThe heart pumps 5 quarts of blood per minute<br \/>\nConvert from quarts to liters<br \/>\n1 quart = 0.94 L<br \/>\n5 quarts = 4.73 L<br \/>\nThus it pumps 4.73 L of blood per minute.<\/p>\n<p>Question 44.<br \/>\n<strong>PROBLEM SOLVING<\/strong><br \/>\nAfter washing dishes, water drips from the faucet. The graph shows the number of cups of water that drip from the faucet over time. How many gallons of water drip from the faucet in 24 hours?<br \/>\n<img decoding=\"async\" loading=\"lazy\" class=\"alignnone size-full wp-image-26773\" src=\"https:\/\/ccssanswers.com\/wp-content\/uploads\/2021\/01\/Big-Ideas-Math-Answers-6th-Grade-Chapter-3-Ratios-and-Rates-3.6-36.png\" alt=\"Big Ideas Math Answers 6th Grade Chapter 3 Ratios and Rates 3.6 36\" width=\"208\" height=\"237\" \/><br \/>\nAnswer:<\/p>\n<p><strong>COMPARING MEASURES<\/strong> Copy and complete the statement using &lt; or &gt;.<br \/>\nQuestion 45.<br \/>\n<img decoding=\"async\" loading=\"lazy\" class=\"alignnone size-full wp-image-26774\" src=\"https:\/\/ccssanswers.com\/wp-content\/uploads\/2021\/01\/Big-Ideas-Math-Answers-6th-Grade-Chapter-3-Ratios-and-Rates-3.6-37.png\" alt=\"Big Ideas Math Answers 6th Grade Chapter 3 Ratios and Rates 3.6 37\" width=\"124\" height=\"40\" \/><br \/>\nAnswer: &lt;<\/p>\n<p>Explanation:<br \/>\nConvert from ounce to kg<br \/>\n1 oz = 0.02kg<br \/>\n30 oz = 0.85kg<br \/>\nThus 30 oz &lt; 8 kg<\/p>\n<p>Question 46.<br \/>\n<img decoding=\"async\" loading=\"lazy\" class=\"alignnone size-full wp-image-26775\" src=\"https:\/\/ccssanswers.com\/wp-content\/uploads\/2021\/01\/Big-Ideas-Math-Answers-6th-Grade-Chapter-3-Ratios-and-Rates-3.6-38.png\" alt=\"Big Ideas Math Answers 6th Grade Chapter 3 Ratios and Rates 3.6 38\" width=\"139\" height=\"36\" \/><br \/>\nAnswer: &lt;<\/p>\n<p>Explanation:<br \/>\nConvert from feet to centimeter<br \/>\n1 feet = 30.48 cm<br \/>\n6 feet = 182.88<br \/>\nThus 6 feet &lt; 300 cm<\/p>\n<p>Question 47.<br \/>\n<img decoding=\"async\" loading=\"lazy\" class=\"alignnone size-full wp-image-26776\" src=\"https:\/\/ccssanswers.com\/wp-content\/uploads\/2021\/01\/Big-Ideas-Math-Answers-6th-Grade-Chapter-3-Ratios-and-Rates-3.6-39.png\" alt=\"Big Ideas Math Answers 6th Grade Chapter 3 Ratios and Rates 3.6 39\" width=\"123\" height=\"38\" \/><br \/>\nAnswer: &gt;<\/p>\n<p>Explanation:<br \/>\nConvert from gal to liter<br \/>\n1 gal = 3.78L<br \/>\n3 gal = 11.35L<br \/>\nThus 3 gal &gt; 6L<\/p>\n<p>Question 48.<br \/>\n<img decoding=\"async\" loading=\"lazy\" class=\"alignnone size-full wp-image-26777\" src=\"https:\/\/ccssanswers.com\/wp-content\/uploads\/2021\/01\/Big-Ideas-Math-Answers-6th-Grade-Chapter-3-Ratios-and-Rates-3.6-40.png\" alt=\"Big Ideas Math Answers 6th Grade Chapter 3 Ratios and Rates 3.6 40\" width=\"169\" height=\"41\" \/><br \/>\nAnswer: &gt;<\/p>\n<p>Explanation:<br \/>\nConvert from inches to mm.<br \/>\n1 in = 25.4mm<br \/>\n10 in = 254 mm<br \/>\nThus 254mm &gt; 200 mm<\/p>\n<p>Question 49.<br \/>\n<img decoding=\"async\" loading=\"lazy\" class=\"alignnone size-full wp-image-26778\" src=\"https:\/\/ccssanswers.com\/wp-content\/uploads\/2021\/01\/Big-Ideas-Math-Answers-6th-Grade-Chapter-3-Ratios-and-Rates-3.6-41.png\" alt=\"Big Ideas Math Answers 6th Grade Chapter 3 Ratios and Rates 3.6 41\" width=\"134\" height=\"41\" \/><br \/>\nAnswer: &gt;<\/p>\n<p>Explanation:<br \/>\nConvert from lb to grams<br \/>\n1 lb = 453.5g<br \/>\n5 lb = 2268g<br \/>\n2268g &gt; 1200g<br \/>\nThus 5 lb &gt; 1200g<\/p>\n<p>Question 50.<br \/>\n<img decoding=\"async\" loading=\"lazy\" class=\"alignnone size-full wp-image-26779\" src=\"https:\/\/ccssanswers.com\/wp-content\/uploads\/2021\/01\/Big-Ideas-Math-Answers-6th-Grade-Chapter-3-Ratios-and-Rates-3.6-42.png\" alt=\"Big Ideas Math Answers 6th Grade Chapter 3 Ratios and Rates 3.6 42\" width=\"165\" height=\"42\" \/><br \/>\nAnswer: &gt;<\/p>\n<p>Explanation:<br \/>\nConvert from meters to feet<br \/>\n1 meter = 3.28 ft<br \/>\n1500 meter = 4921.26 ft<br \/>\n4921.26 ft &gt; 3000 ft<br \/>\nThus 1500 m &gt; 3000 ft<\/p>\n<p><strong>USING DERIVED UNITS<\/strong> Copy and complete the statement. Round to the nearest hundredth if necessary.<br \/>\nQuestion 51.<br \/>\n<img decoding=\"async\" loading=\"lazy\" class=\"alignnone size-full wp-image-26780\" src=\"https:\/\/ccssanswers.com\/wp-content\/uploads\/2021\/01\/Big-Ideas-Math-Answers-6th-Grade-Chapter-3-Ratios-and-Rates-3.6-43.png\" alt=\"Big Ideas Math Answers 6th Grade Chapter 3 Ratios and Rates 3.6 43\" width=\"140\" height=\"64\" \/><br \/>\nAnswer: 112 miles per hour<\/p>\n<p>Explanation:<br \/>\nConvert from km per min to miles per hour<br \/>\n1 km per min = 37.28 miles per hour<br \/>\n3 km per min = 111.84 miles per hour<br \/>\n3 km per min \u2248 112 miles per hour<\/p>\n<p>Question 52.<br \/>\n<img decoding=\"async\" loading=\"lazy\" class=\"alignnone size-full wp-image-26781\" src=\"https:\/\/ccssanswers.com\/wp-content\/uploads\/2021\/01\/Big-Ideas-Math-Answers-6th-Grade-Chapter-3-Ratios-and-Rates-3.6-44.png\" alt=\"Big Ideas Math Answers 6th Grade Chapter 3 Ratios and Rates 3.6 44\" width=\"149\" height=\"60\" \/><br \/>\nAnswer: 1.13 qt per minute<\/p>\n<p>Explanation:<br \/>\nConvert from gal per hour to qt per minute<br \/>\n1 gal per hour = 0.06 qt per minute<br \/>\n17 gal per hour = 1.13 qt per minute<\/p>\n<p>Question 53.<br \/>\n<img decoding=\"async\" loading=\"lazy\" class=\"alignnone size-full wp-image-26782\" src=\"https:\/\/ccssanswers.com\/wp-content\/uploads\/2021\/01\/Big-Ideas-Math-Answers-6th-Grade-Chapter-3-Ratios-and-Rates-3.6-45.png\" alt=\"Big Ideas Math Answers 6th Grade Chapter 3 Ratios and Rates 3.6 45\" width=\"158\" height=\"65\" \/><br \/>\nAnswer: 4 inches per second<\/p>\n<p>Explanation:<br \/>\nConvert from cm per minute to inches per second<br \/>\n1 cm per minute = 0.006 inches per second<br \/>\n600 cm per minute = 3.93 inches per second<br \/>\n600 cm per minute \u2248 4 inches per second<\/p>\n<p>Question 54.<br \/>\n<strong>MODELING REAL LIFE<\/strong><br \/>\nYou are riding on a zip line. Your speed is 15 miles per hour. What is your speed in feet per second?<br \/>\nAnswer: 22 feet per second<\/p>\n<p>Explanation:<br \/>\nGiven,<br \/>\nYou are riding on a zip line. Your speed is 15 miles per hour.<br \/>\nConvert from mile per hour to feet per second<br \/>\n1 mile per hour = 1.46 feet per second<br \/>\n15 miles per hour = 22 feet per second<\/p>\n<p>Question 55.<br \/>\n<strong>PROBLEM SOLVING<\/strong><br \/>\nThunder is the sound caused by lightning. You hear thunder 5 seconds after a lightning strike. The speed of sound is about 1225 kilometers per hour. About how many miles away was the lightning?<br \/>\nAnswer:<\/p>\n<p>Question 56.<br \/>\n<strong>PROBLEM SOLVING<\/strong><br \/>\nBoston, Massachusetts, and Buffalo, New York, are hit by snowstorms that last 3 days. Boston accumulates snow at a rate of 1.5 feet every 36 hours. Buffalo accumulates snow at a rate of 0.01 inch every minute. Which city accumulates more snow in 3 days? How much more snow?<br \/>\n<img decoding=\"async\" loading=\"lazy\" class=\"alignnone size-full wp-image-26783\" src=\"https:\/\/ccssanswers.com\/wp-content\/uploads\/2021\/01\/Big-Ideas-Math-Answers-6th-Grade-Chapter-3-Ratios-and-Rates-3.6-46.png\" alt=\"Big Ideas Math Answers 6th Grade Chapter 3 Ratios and Rates 3.6 46\" width=\"206\" height=\"149\" \/><br \/>\nAnswer:<\/p>\n<p>Question 57.<br \/>\n<strong>DIG DEEPER!<\/strong><br \/>\nYou travel 4000 feet every minute on a snowmobile.<br \/>\na. The evening speed limit for snowmobiles in your state is 55 miles per hour. Is your speed less than or equal to the speed limit? Justify your answer.<br \/>\nb. What is your pace in minutes per mile?<br \/>\nc. You are 22 miles from your house at 6:00 P.M. If you continue to travel at this speed, do you reach your house in time for dinner at 6:30 P.M.?<br \/>\nAnswer:<\/p>\n<p>Question 58.<br \/>\n<strong>REASONING<\/strong><br \/>\nThe table shows the flying speeds of several birds.<br \/>\n<img decoding=\"async\" loading=\"lazy\" class=\"alignnone size-full wp-image-26784\" src=\"https:\/\/ccssanswers.com\/wp-content\/uploads\/2021\/01\/Big-Ideas-Math-Answers-6th-Grade-Chapter-3-Ratios-and-Rates-3.6-47.png\" alt=\"Big Ideas Math Answers 6th Grade Chapter 3 Ratios and Rates 3.6 47\" width=\"251\" height=\"287\" \/><br \/>\na. Which bird is the fastest? Which is the slowest?<br \/>\nb. The peregrine falcon has a dive speed of 322 kilometers per hour. Is the dive speed of the peregrine falcon faster than the flying speed of any of the birds? Explain.<br \/>\nAnswer:<\/p>\n<p>Question 59.<br \/>\n<strong>STRUCTURE<\/strong><br \/>\nConsider the conversion facts 1 inch = 2.54 centimeters and 1 centimeter \u2248 0.39 inch.<br \/>\na. Write an expression for the exact number of inches in 1 centimeter.<br \/>\nb. Use a calculator to evaluate your expression in part(a). Explain why measurement conversions may be slightly different when converting between metric units and U.S. customary units using the conversion facts in the back of the book.<br \/>\nAnswer:<\/p>\n<p>Question 60.<br \/>\n<strong>DIG DEEPER!<\/strong><br \/>\nOne liter of paint covers 100 square feet. How many gallons of paint does it take to cover a room whose walls have an area of 800 square meters?<br \/>\nAnswer:<br \/>\nGiven,<br \/>\nOne liter of paint covers 100 square feet.<br \/>\nFirst, convert 800 square meters to square feet. I calculated it to be 8611.13 sq ft<br \/>\n100 sq.ft\/1 L x L = 8611.13.<br \/>\nNow convert L to gallons.<br \/>\n1gallon = 3.785 L<\/p>\n<h3><a id=\"Ratios_and_Rates_Connecting_Concepts\"><\/a>Ratios and Rates Connecting Concepts<\/h3>\n<p><strong>Using the Problem-Solving Plan<\/strong><\/p>\n<p>Question 1.<br \/>\nYou mix water, glue, and borax in the ratio of 3 : 1 : 2 to make slime. How many gallons of each ingredient should you use to make 0.75 gallon of slime?<br \/>\n<img decoding=\"async\" loading=\"lazy\" class=\"alignnone size-full wp-image-26785\" src=\"https:\/\/ccssanswers.com\/wp-content\/uploads\/2021\/01\/Big-Ideas-Math-Answers-Grade-6-Chapter-3-Ratios-and-Rates-cc-1.png\" alt=\"Big Ideas Math Answers Grade 6 Chapter 3 Ratios and Rates cc 1\" width=\"189\" height=\"259\" \/><br \/>\nUnderstand the problem.<br \/>\nYou know the ratio of the ingredients in the slime and that you are making 0.75 gallon of slime. You are asked to find the number of gallons of each ingredient needed to make 0.75 gallon of slime.<\/p>\n<p>Make a plan.<br \/>\nRepresent the ratio 3 : 1 : 2 using a tape diagram. Because there are 6 parts that represent 0.75 gallon, divide 0.75 by6 to find the value of one part of the tape diagram. Then use the value of one part to find the number of gallons of each ingredient you should use.<\/p>\n<p>Solve and check.<br \/>\nUse the plan to solve the problem. Then check your solution.<br \/>\nAnswer:<\/p>\n<p>Question 2.<br \/>\nYou buy yogurt cups and frozen fruit bars for a party. Yogurt cups are sold in packages of six. The ratio of the number of yogurt cups in a package to the number of frozen fruit bars in a package is 3 : 2. What are the least numbers of packages you should buy in order to have the same numbers of yogurt cups and frozen fruit bars?<br \/>\n<img decoding=\"async\" loading=\"lazy\" class=\"alignnone size-full wp-image-26786\" src=\"https:\/\/ccssanswers.com\/wp-content\/uploads\/2021\/01\/Big-Ideas-Math-Answers-Grade-6-Chapter-3-Ratios-and-Rates-cc-2.png\" alt=\"Big Ideas Math Answers Grade 6 Chapter 3 Ratios and Rates cc 2\" width=\"227\" height=\"111\" \/><br \/>\nAnswer:<\/p>\n<p>Question 3.<br \/>\nThe greatest common factor of two whole numbers is 9. The ratio of the greater number to the lesser number is 6 : 5. What are the two numbers? Justify your answer.<br \/>\nAnswer:<\/p>\n<p><strong>Performance Task<\/strong><\/p>\n<p>Oops! Unit Conversion Mistakes<br \/>\nAt the beginning of this chapter, you watched a STEAM Video called \u201cHuman Circulatory System.\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 decoding=\"async\" loading=\"lazy\" class=\"alignnone size-full wp-image-26787\" src=\"https:\/\/ccssanswers.com\/wp-content\/uploads\/2021\/01\/Big-Ideas-Math-Answers-Grade-6-Chapter-3-Ratios-and-Rates-cc-3.png\" alt=\"Big Ideas Math Answers Grade 6 Chapter 3 Ratios and Rates cc 3\" width=\"317\" height=\"173\" srcset=\"https:\/\/ccssanswers.com\/wp-content\/uploads\/2021\/01\/Big-Ideas-Math-Answers-Grade-6-Chapter-3-Ratios-and-Rates-cc-3.png 317w, https:\/\/ccssanswers.com\/wp-content\/uploads\/2021\/01\/Big-Ideas-Math-Answers-Grade-6-Chapter-3-Ratios-and-Rates-cc-3-300x164.png 300w\" sizes=\"(max-width: 317px) 100vw, 317px\" \/><\/p>\n<h3><a id=\"Ratios_and_Rates_Chapter_Review\"><\/a>Ratios and Rates 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 decoding=\"async\" loading=\"lazy\" class=\"alignnone size-full wp-image-26788\" src=\"https:\/\/ccssanswers.com\/wp-content\/uploads\/2021\/01\/Big-Ideas-Math-Answers-Grade-6-Chapter-3-Ratios-and-Rates-cr-1.png\" alt=\"Big Ideas Math Answers Grade 6 Chapter 3 Ratios and Rates cr 1\" width=\"558\" height=\"103\" srcset=\"https:\/\/ccssanswers.com\/wp-content\/uploads\/2021\/01\/Big-Ideas-Math-Answers-Grade-6-Chapter-3-Ratios-and-Rates-cr-1.png 558w, https:\/\/ccssanswers.com\/wp-content\/uploads\/2021\/01\/Big-Ideas-Math-Answers-Grade-6-Chapter-3-Ratios-and-Rates-cr-1-300x55.png 300w\" sizes=\"(max-width: 558px) 100vw, 558px\" \/><\/p>\n<p><strong>Graphic Organizers<\/strong><br \/>\nYou can use a Definition and Example Chart to organize information about a concept. Here is an example of a Definition and Example Chart for the vocabulary term ratio.<br \/>\n<img decoding=\"async\" loading=\"lazy\" class=\"alignnone size-full wp-image-26789\" src=\"https:\/\/ccssanswers.com\/wp-content\/uploads\/2021\/01\/Big-Ideas-Math-Answers-Grade-6-Chapter-3-Ratios-and-Rates-cr-2.png\" alt=\"Big Ideas Math Answers Grade 6 Chapter 3 Ratios and Rates cr 2\" width=\"472\" height=\"281\" srcset=\"https:\/\/ccssanswers.com\/wp-content\/uploads\/2021\/01\/Big-Ideas-Math-Answers-Grade-6-Chapter-3-Ratios-and-Rates-cr-2.png 472w, https:\/\/ccssanswers.com\/wp-content\/uploads\/2021\/01\/Big-Ideas-Math-Answers-Grade-6-Chapter-3-Ratios-and-Rates-cr-2-300x179.png 300w\" sizes=\"(max-width: 472px) 100vw, 472px\" \/><\/p>\n<p>Choose and complete a graphic organizer to help you study the concept.<br \/>\n<img decoding=\"async\" loading=\"lazy\" class=\"alignnone size-full wp-image-26790\" src=\"https:\/\/ccssanswers.com\/wp-content\/uploads\/2021\/01\/Big-Ideas-Math-Answers-Grade-6-Chapter-3-Ratios-and-Rates-cr-3.png\" alt=\"Big Ideas Math Answers Grade 6 Chapter 3 Ratios and Rates cr 3\" width=\"285\" height=\"275\" \/><br \/>\n1. value of a ratio<br \/>\n2. equivalent ratios<br \/>\n3. tape diagram<br \/>\n4. ratio table<br \/>\n5. rate<br \/>\n6. unit rate<br \/>\n7. conversion factor<\/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 decoding=\"async\" loading=\"lazy\" class=\"alignnone size-full wp-image-26791\" src=\"https:\/\/ccssanswers.com\/wp-content\/uploads\/2021\/01\/Big-Ideas-Math-Answers-Grade-6-Chapter-3-Ratios-and-Rates-cr-4.png\" alt=\"Big Ideas Math Answers Grade 6 Chapter 3 Ratios and Rates cr 4\" width=\"579\" height=\"72\" srcset=\"https:\/\/ccssanswers.com\/wp-content\/uploads\/2021\/01\/Big-Ideas-Math-Answers-Grade-6-Chapter-3-Ratios-and-Rates-cr-4.png 579w, https:\/\/ccssanswers.com\/wp-content\/uploads\/2021\/01\/Big-Ideas-Math-Answers-Grade-6-Chapter-3-Ratios-and-Rates-cr-4-300x37.png 300w\" sizes=\"(max-width: 579px) 100vw, 579px\" \/><\/p>\n<p><strong>3.1 Ratios (pp. 107\u2013114)<\/strong><br \/>\nLearning Target: Understand the concepts of ratios and equivalent ratios.<\/p>\n<p>Write the ratio.<br \/>\nQuestion 1.<br \/>\nbutter\ufb02ies : caterpillars<br \/>\n<img decoding=\"async\" loading=\"lazy\" class=\"alignnone size-full wp-image-26792\" src=\"https:\/\/ccssanswers.com\/wp-content\/uploads\/2021\/01\/Big-Ideas-Math-Answers-Grade-6-Chapter-3-Ratios-and-Rates-cr-5.png\" alt=\"Big Ideas Math Answers Grade 6 Chapter 3 Ratios and Rates cr 5\" width=\"235\" height=\"106\" \/><br \/>\nAnswer: 3 : 2<\/p>\n<p>Explanation:<br \/>\nThere are 3 butterflies and 2 caterpillars<br \/>\nThus the ratio is 3 : 2<\/p>\n<p>Question 2.<br \/>\nsaxophones : trumpets<br \/>\n<img decoding=\"async\" loading=\"lazy\" class=\"alignnone size-full wp-image-26793\" src=\"https:\/\/ccssanswers.com\/wp-content\/uploads\/2021\/01\/Big-Ideas-Math-Answers-Grade-6-Chapter-3-Ratios-and-Rates-cr-6.png\" alt=\"Big Ideas Math Answers Grade 6 Chapter 3 Ratios and Rates cr 6\" width=\"238\" height=\"111\" \/><br \/>\nAnswer: 6 : 3<\/p>\n<p>Explanation:<br \/>\nThere are 6 saxophones and 3 trumpets<br \/>\nThus the ratio is 6: 3 and the equivalent ratio is 1 : 2<\/p>\n<p>Question 3.<br \/>\nThe ratio of hydrogen atoms to nitrogen atoms in a container is 2 : 3.<br \/>\n<img decoding=\"async\" loading=\"lazy\" class=\"alignnone size-full wp-image-26794\" src=\"https:\/\/ccssanswers.com\/wp-content\/uploads\/2021\/01\/Big-Ideas-Math-Answers-Grade-6-Chapter-3-Ratios-and-Rates-cr-7.png\" alt=\"Big Ideas Math Answers Grade 6 Chapter 3 Ratios and Rates cr 7\" width=\"126\" height=\"274\" \/><br \/>\na. Find and interpret the value of the ratio.<br \/>\nb. In another container, the number of hydrogen atoms is 3 times the number of nitrogen atoms. Write the ratio of hydrogen atoms to nitrogen atoms.<br \/>\nAnswer:<\/p>\n<p><strong>Determine whether the ratios are equivalent.<\/strong><br \/>\nQuestion 4.<br \/>\n5 : 2 and 30 : 12<br \/>\nAnswer: Yes<\/p>\n<p>Explanation:<br \/>\n30\/12 = 5\/2<br \/>\n5 : 2 = 5 : 2<br \/>\nThus the ratios are equivalent<\/p>\n<p>Question 5.<br \/>\n4 : 3 and 8 : 7<br \/>\nAnswer: No<\/p>\n<p>Explanation:<br \/>\n4\/3 \u2260 8\/7<br \/>\nThus the ratios are not equivalent<\/p>\n<p>Question 6.<br \/>\n6 : 4 and 18 : 6<br \/>\nAnswer: No<\/p>\n<p>Explanation:<br \/>\n6 : 4 and 18 : 6<br \/>\n6\/4 = 3\/2<br \/>\n18\/6 = 3<br \/>\n3\/2 \u2260 3<br \/>\nThus the ratios are not equivalent<\/p>\n<p>Question 7.<br \/>\n18 : 12 and 3 : 2<br \/>\nAnswer: Yes<\/p>\n<p>Explanation:<br \/>\n18 : 12 and 3 : 2<br \/>\n18\/12 = 3\/2<br \/>\n3 : 2 = 3 : 2<br \/>\nThus the ratios are equivalent<\/p>\n<p>Question 8.<br \/>\nWrite two equivalent ratios that have values of \\(\\frac{5}{7}\\)<br \/>\nAnswer: \\(\\frac{10}{14}\\) and \\(\\frac{15}{21}\\)<\/p>\n<p>Question 9.<br \/>\nDuring a chess match, there are 12 pieces left on the board. The ratio of white pieces to black pieces is 2 : 1. How many white pieces are on the board?<br \/>\nAnswer:<\/p>\n<p>Question 10.<br \/>\nYou run at a pace of 2 miles every 17 minutes. Your friend runs at a pace of 3 miles every 24 minutes. Are you and your friend running at the same pace? If not, who is running faster?<br \/>\nAnswer:<\/p>\n<p><strong>3.2 Using Tape Diagram (pp. 115-120)<\/strong><br \/>\nLearning Target: Use tape diagrams to model and solve ratio problems.<\/p>\n<p>The tape diagram represents the ratio of the time you spend reading to the time your friend spends reading. You read for 8 hours. How many hours does your friend spend reading?<br \/>\nQuestion 11.<br \/>\n<img decoding=\"async\" loading=\"lazy\" class=\"alignnone size-full wp-image-26795\" src=\"https:\/\/ccssanswers.com\/wp-content\/uploads\/2021\/01\/Big-Ideas-Math-Answers-Grade-6-Chapter-3-Ratios-and-Rates-cr-11.png\" alt=\"Big Ideas Math Answers Grade 6 Chapter 3 Ratios and Rates cr 11\" width=\"175\" height=\"63\" \/><br \/>\nAnswer:<\/p>\n<p>Question 12.<br \/>\n<img decoding=\"async\" loading=\"lazy\" class=\"alignnone size-full wp-image-26796\" src=\"https:\/\/ccssanswers.com\/wp-content\/uploads\/2021\/01\/Big-Ideas-Math-Answers-Grade-6-Chapter-3-Ratios-and-Rates-cr-12.png\" alt=\"Big Ideas Math Answers Grade 6 Chapter 3 Ratios and Rates cr 12\" width=\"254\" height=\"70\" \/><br \/>\nAnswer:<\/p>\n<p>Question 13.<br \/>\nThe tape diagram represents the ratio of customers to guides on a mountain climbing trip. There are 6 guides on the trip. How many customers are on the trip?<br \/>\n<img decoding=\"async\" loading=\"lazy\" class=\"alignnone size-full wp-image-26797\" src=\"https:\/\/ccssanswers.com\/wp-content\/uploads\/2021\/01\/Big-Ideas-Math-Answers-Grade-6-Chapter-3-Ratios-and-Rates-cr-13.png\" alt=\"Big Ideas Math Answers Grade 6 Chapter 3 Ratios and Rates cr 13\" width=\"378\" height=\"77\" srcset=\"https:\/\/ccssanswers.com\/wp-content\/uploads\/2021\/01\/Big-Ideas-Math-Answers-Grade-6-Chapter-3-Ratios-and-Rates-cr-13.png 378w, https:\/\/ccssanswers.com\/wp-content\/uploads\/2021\/01\/Big-Ideas-Math-Answers-Grade-6-Chapter-3-Ratios-and-Rates-cr-13-300x61.png 300w\" sizes=\"(max-width: 378px) 100vw, 378px\" \/><br \/>\nAnswer:<\/p>\n<p>A container has peppermint gum and spearmint gum. You are given the number of pieces of peppermint gum in the container and the ratio of peppermint gum to spearmint gum. Find the number of pieces of spearmint gum in the container.<br \/>\nQuestion 14.<br \/>\n24 peppermint; 8 to 5<br \/>\nAnswer:<br \/>\nLet the total number of peppermint gum and spearmint gum in the container = x<br \/>\nThe ratio is 8 : 5<br \/>\n8 + 5 = 13<br \/>\n8\/13 \u00d7 x = 24<br \/>\nx = 24 \u00d7 13\/8<br \/>\nx = 39<br \/>\n5\/13 \u00d7 39 = 15<\/p>\n<p>Question 15.<br \/>\n18 peppermint; 2 : 3<br \/>\nAnswer:<br \/>\nLet the total number of peppermint gum and spearmint gum in the container = x<br \/>\nThe ratio is 2 : 3<br \/>\n2 + 3 = 5<br \/>\n2\/5 \u00d7 x = 18<br \/>\nx = 18 \u00d7 5\/2<br \/>\nx = 45<br \/>\nNumber of spearmint gum will be now<br \/>\nRatio of spearmint\/total ratio \u00d7 total number of gums = number of spearmint<br \/>\n3\/5 \u00d7 45 = 27<br \/>\nThus the number of spearmint gum = 27<\/p>\n<p>Question 16.<br \/>\n32 peppermint; 8 to 7<br \/>\nAnswer:<br \/>\nLet the total number of peppermint gum and spearmint gum in the container = x<br \/>\nThe ratio is 8 : 7<br \/>\n8 + 7 = 15<br \/>\n8\/15 \u00d7 x = 32<br \/>\nx = 32 \u00d7 15\/8<br \/>\nx = 4 \u00d7 15<br \/>\nx = 60<br \/>\nNumber of spearmint gum will be now<br \/>\nRatio of spearmint\/total ratio \u00d7 total number of gums = number of spearmint<br \/>\n7\/15 \u00d7 60 = 28<\/p>\n<p>Question 17.<br \/>\n40 peppermint; 5 : 2<br \/>\nAnswer:<br \/>\nLet the total number of peppermint gum and spearmint gum in the container = x<br \/>\nThe ratio is 5 : 2<br \/>\n5 + 2 = 7<br \/>\n5\/7 \u00d7 x = 40<br \/>\nx = 40 \u00d7 7\/5<br \/>\nx = 8 \u00d7 7<br \/>\nx = 56<br \/>\nNumber of spearmint gum will be now<br \/>\nRatio of spearmint\/total ratio \u00d7 total number of gums = number of spearmint<br \/>\n2\/7 \u00d7 56 = 16<\/p>\n<p>A theater sells adult tickets and student tickets. You are given the total number of tickets sold and the ratio of adult tickets sold to student tickets sold. How many of each type of ticket are sold?<br \/>\n<img decoding=\"async\" loading=\"lazy\" class=\"alignnone size-full wp-image-26798\" src=\"https:\/\/ccssanswers.com\/wp-content\/uploads\/2021\/01\/Big-Ideas-Math-Answers-Grade-6-Chapter-3-Ratios-and-Rates-cr-18.png\" alt=\"Big Ideas Math Answers Grade 6 Chapter 3 Ratios and Rates cr 18\" width=\"167\" height=\"245\" \/><br \/>\nQuestion 18.<br \/>\n120 tickets; 6 to 4<br \/>\nAnswer:<br \/>\nThe ratio of adult tickets sold to student tickets sold is 6 : 4<br \/>\n6 + 4 = 10<br \/>\n6\/10 = x\/120<br \/>\n6 \u00d7 120 = x \u00d7 10<br \/>\n10x = 720<br \/>\nx = 720\/10 = 72<br \/>\nx = 72<br \/>\nThe number of student tickets would be 120 &#8211; 72 = 48 student tickets<\/p>\n<p>Question 19.<br \/>\n165 tickets; 8 to 7<br \/>\nAnswer:<br \/>\nThe ratio of adult tickets sold to student tickets sold is 8 : 7<br \/>\n8 + 7 = 15<br \/>\n8\/15 = x\/165<br \/>\n8 \u00d7 165 = x \u00d7 15<br \/>\n1320 = 15x<br \/>\nx = 1320\/15<br \/>\nx = 88<br \/>\nThe number of student tickets would be 165 &#8211; 88 = 77 student tickets<\/p>\n<p>Question 20.<br \/>\n210 tickets; 16 : 5<br \/>\nAnswer:<br \/>\nThe ratio of adult tickets sold to student tickets sold is 16 : 5<br \/>\n16 + 5 = 21<br \/>\n16\/21 = x\/210<br \/>\n16 \u00d7 210 = x \u00d7 21<br \/>\n3360 = 21x<br \/>\nx = 3360\/21<br \/>\nx = 160<br \/>\nThe number of student tickets would be 210 &#8211; 160 = 50 student tickets<\/p>\n<p>Question 21.<br \/>\n248 tickets; 5 : 3<br \/>\nAnswer:<br \/>\nThe ratio of adult tickets sold to student tickets sold is 5 : 3<br \/>\n5 + 3 = 8<br \/>\n5\/8 = x\/248<br \/>\n5 \u00d7 248 = 8 \u00d7 x<br \/>\n1240 = 8x<br \/>\nx = 1240\/8<br \/>\nx = 155<br \/>\nThe number of student tickets would be 248 &#8211; 155 = 93 student tickets<\/p>\n<p>Question 22.<br \/>\nYou perform 7 sit-ups for every 2 pull-ups as part of an exercise routine. You perform 25 more sit-ups than pull-ups. How many sit-ups and how many pull-ups do you perform?<br \/>\nAnswer: 35 sit ups and 10 pullups<\/p>\n<p>Explanation:<br \/>\nGiven,<br \/>\nYou perform 7 sit-ups for every 2 pull-ups as part of an exercise routine.<br \/>\nYou perform 25 more sit-ups than pull-ups.<br \/>\nso we know that for 7 situps you do 2 pullups<br \/>\nso the possible values would be<br \/>\n7,2<br \/>\n14,4<br \/>\n21, 6<br \/>\n28, 8<br \/>\n35, 10, and so on<br \/>\nso now you just look at which two numbers have a difference of 25<br \/>\nwhen subtracting them, you&#8217;ll notice that 35 and 10 have a difference of 25.<\/p>\n<p><strong>3.3 Using Ratio Tables (pp. 121-128)<\/strong><br \/>\nLearning Target: Use ratio tables to represent equivalent ratios and solve ratio problems.<\/p>\n<p>Find the missing values in the ratio table. Then write the equivalent ratios.<br \/>\nQuestion 23.<br \/>\n<img decoding=\"async\" loading=\"lazy\" class=\"alignnone size-full wp-image-26799\" src=\"https:\/\/ccssanswers.com\/wp-content\/uploads\/2021\/01\/Big-Ideas-Math-Answers-Grade-6-Chapter-3-Ratios-and-Rates-cr-23.png\" alt=\"Big Ideas Math Answers Grade 6 Chapter 3 Ratios and Rates cr 23\" width=\"167\" height=\"66\" \/><br \/>\nAnswer:<br \/>\n<img decoding=\"async\" loading=\"lazy\" class=\"alignnone size-full wp-image-36221\" src=\"https:\/\/ccssanswers.com\/wp-content\/uploads\/2021\/01\/Big-Ideas-Math-Answers-Grade-6-Chapter-3-Ratios-and-Rates-cr-23.jpg\" alt=\"Big-Ideas-Math-Answers-Grade-6-Chapter-3-Ratios-and-Rates-cr-23\" width=\"167\" height=\"66\" \/><\/p>\n<p>Question 24.<br \/>\n<img decoding=\"async\" loading=\"lazy\" class=\"alignnone size-full wp-image-26800\" src=\"https:\/\/ccssanswers.com\/wp-content\/uploads\/2021\/01\/Big-Ideas-Math-Answers-Grade-6-Chapter-3-Ratios-and-Rates-cr-24.png\" alt=\"Big Ideas Math Answers Grade 6 Chapter 3 Ratios and Rates cr 24\" width=\"169\" height=\"67\" \/><br \/>\nAnswer:<br \/>\n<img decoding=\"async\" loading=\"lazy\" class=\"alignnone size-full wp-image-36222\" src=\"https:\/\/ccssanswers.com\/wp-content\/uploads\/2021\/01\/Big-Ideas-Math-Answers-Grade-6-Chapter-3-Ratios-and-Rates-cr-24.jpg\" alt=\"Big-Ideas-Math-Answers-Grade-6-Chapter-3-Ratios-and-Rates-cr-24\" width=\"169\" height=\"67\" \/><\/p>\n<p>Question 25.<br \/>\n<img decoding=\"async\" loading=\"lazy\" class=\"alignnone size-full wp-image-26801\" src=\"https:\/\/ccssanswers.com\/wp-content\/uploads\/2021\/01\/Big-Ideas-Math-Answers-Grade-6-Chapter-3-Ratios-and-Rates-cr-25.png\" alt=\"Big Ideas Math Answers Grade 6 Chapter 3 Ratios and Rates cr 25\" width=\"169\" height=\"67\" \/><br \/>\nAnswer:<br \/>\n<img decoding=\"async\" loading=\"lazy\" class=\"alignnone size-full wp-image-36224\" src=\"https:\/\/ccssanswers.com\/wp-content\/uploads\/2021\/01\/Big-Ideas-Math-Answers-Grade-6-Chapter-3-Ratios-and-Rates-cr-25.jpg\" alt=\"Big-Ideas-Math-Answers-Grade-6-Chapter-3-Ratios-and-Rates-cr-25\" width=\"169\" height=\"67\" \/><\/p>\n<p>Question 26.<br \/>\n<img decoding=\"async\" loading=\"lazy\" class=\"alignnone size-full wp-image-26802\" src=\"https:\/\/ccssanswers.com\/wp-content\/uploads\/2021\/01\/Big-Ideas-Math-Answers-Grade-6-Chapter-3-Ratios-and-Rates-cr-26.png\" alt=\"Big Ideas Math Answers Grade 6 Chapter 3 Ratios and Rates cr 26\" width=\"194\" height=\"64\" \/><br \/>\nAnswer:<br \/>\n<img decoding=\"async\" loading=\"lazy\" class=\"alignnone size-full wp-image-36225\" src=\"https:\/\/ccssanswers.com\/wp-content\/uploads\/2021\/01\/Big-Ideas-Math-Answers-Grade-6-Chapter-3-Ratios-and-Rates-cr-26.jpg\" alt=\"Big-Ideas-Math-Answers-Grade-6-Chapter-3-Ratios-and-Rates-cr-26\" width=\"194\" height=\"64\" \/><\/p>\n<p><strong>Find the missing quantity in the double number line.<\/strong><br \/>\nQuestion 27.<br \/>\n<img decoding=\"async\" loading=\"lazy\" class=\"alignnone size-full wp-image-26803\" src=\"https:\/\/ccssanswers.com\/wp-content\/uploads\/2021\/01\/Big-Ideas-Math-Answers-Grade-6-Chapter-3-Ratios-and-Rates-cr-27.png\" alt=\"Big Ideas Math Answers Grade 6 Chapter 3 Ratios and Rates cr 27\" width=\"226\" height=\"90\" \/><br \/>\nAnswer:<br \/>\n<img decoding=\"async\" loading=\"lazy\" class=\"alignnone size-full wp-image-36231\" src=\"https:\/\/ccssanswers.com\/wp-content\/uploads\/2021\/01\/Big-Ideas-Math-Answers-Grade-6-Chapter-3-Ratios-and-Rates-cr-27.jpg\" alt=\"Big-Ideas-Math-Answers-Grade-6-Chapter-3-Ratios-and-Rates-cr-27\" width=\"226\" height=\"90\" \/><\/p>\n<p>Question 28.<br \/>\n<img decoding=\"async\" loading=\"lazy\" class=\"alignnone size-full wp-image-26804\" src=\"https:\/\/ccssanswers.com\/wp-content\/uploads\/2021\/01\/Big-Ideas-Math-Answers-Grade-6-Chapter-3-Ratios-and-Rates-cr-28.png\" alt=\"Big Ideas Math Answers Grade 6 Chapter 3 Ratios and Rates cr 28\" width=\"241\" height=\"97\" \/><br \/>\nAnswer:<br \/>\n<img decoding=\"async\" loading=\"lazy\" class=\"alignnone size-full wp-image-36232\" src=\"https:\/\/ccssanswers.com\/wp-content\/uploads\/2021\/01\/Big-Ideas-Math-Answers-Grade-6-Chapter-3-Ratios-and-Rates-cr-28.jpg\" alt=\"Big-Ideas-Math-Answers-Grade-6-Chapter-3-Ratios-and-Rates-cr-28\" width=\"241\" height=\"97\" \/><\/p>\n<p>Question 29.<br \/>\nUse all four operations to complete the ratio table. Justify your answer.<br \/>\n<img decoding=\"async\" loading=\"lazy\" class=\"alignnone size-full wp-image-26805\" src=\"https:\/\/ccssanswers.com\/wp-content\/uploads\/2021\/01\/Big-Ideas-Math-Answers-Grade-6-Chapter-3-Ratios-and-Rates-cr-29.png\" alt=\"Big Ideas Math Answers Grade 6 Chapter 3 Ratios and Rates cr 29\" width=\"297\" height=\"70\" \/><br \/>\nAnswer:<br \/>\n<img decoding=\"async\" loading=\"lazy\" class=\"alignnone size-full wp-image-36233\" src=\"https:\/\/ccssanswers.com\/wp-content\/uploads\/2021\/01\/Big-Ideas-Math-Answers-Grade-6-Chapter-3-Ratios-and-Rates-cr-29.jpg\" alt=\"Big-Ideas-Math-Answers-Grade-6-Chapter-3-Ratios-and-Rates-cr-29\" width=\"297\" height=\"70\" \/><\/p>\n<p>Question 30.<br \/>\nA song has 12 beats every 5 seconds. How many beats are there in 30 seconds?<br \/>\nAnswer: 72 beats in 30 seconds<\/p>\n<p>Explanation:<br \/>\nGiven,<br \/>\nA song has 12 beats every 5 seconds.<br \/>\n5 seconds = 12 beats<br \/>\n1 second = 12\/5 = 2.4 beats<br \/>\n30 seconds = 30 \u00d7 2.4 beats = 72 beats<br \/>\nThus 72 beats are there in 30 seconds.<\/p>\n<p>Question 31.<br \/>\nOn New Year\u2019sEve, the Times Square ball is lowered 47 feet every 20 seconds. How long does it take for the ball to be lowered 141 feet?<br \/>\nAnswer: 60 seconds<\/p>\n<p>Explanation:<br \/>\nOn New Year\u2019sEve, the Times Square ball is lowered 47 feet every 20 seconds.<br \/>\nAll you have to do is cross multiply and isolate x.<br \/>\n47\/20 \u00d7 141\/x<br \/>\n47x = 2820<br \/>\nx = 60 seconds<\/p>\n<p>Question 32.<br \/>\nWelder A charges $300 for every 4 hours of labor. Welder B charges $240 for every 3 hours of labor. Which welder offers a better deal?<br \/>\n<img decoding=\"async\" loading=\"lazy\" class=\"alignnone size-full wp-image-26806\" src=\"https:\/\/ccssanswers.com\/wp-content\/uploads\/2021\/01\/Big-Ideas-Math-Answers-Grade-6-Chapter-3-Ratios-and-Rates-cr-32.png\" alt=\"Big Ideas Math Answers Grade 6 Chapter 3 Ratios and Rates cr 32\" width=\"179\" height=\"188\" \/><br \/>\nAnswer:<br \/>\nWelder A has a better deal because for each hour welder A would charge $75 while welder B would charge $80<br \/>\nWelder A:<br \/>\n300\/4 = $75<br \/>\nWelder B:<br \/>\n240\/3 = $80<\/p>\n<p>Question 33.<br \/>\nYou make lemonade by adding 11 cups of water for every 3 cups of lemon juice. Your friend makes lemonade by adding 9 cups of water for every 2 cups of lemon juice. Whose lemonade is more watered down?<br \/>\nAnswer:<br \/>\nWell first I did was I found out that both 3 and 2 go into 12.<br \/>\n2 goes into 12 6 times. 9 \u00d7 6 is 54.<br \/>\n3 goes into 12 four times.<br \/>\n11 \u00d7 4 is 44.<br \/>\n54 is greater than 44 therefore the answer would be your friend.<\/p>\n<p><strong>3.4 Graphing Ratio Relationships (pp. 129-134)<\/strong><br \/>\nLearning Target: Represent ratio relationships in a coordinate plane.<\/p>\n<p><strong>Represent the ratio relationship using a graph.<\/strong><br \/>\nQuestion 34.<br \/>\n<img decoding=\"async\" loading=\"lazy\" class=\"alignnone size-full wp-image-26807\" src=\"https:\/\/ccssanswers.com\/wp-content\/uploads\/2021\/01\/Big-Ideas-Math-Answers-Grade-6-Chapter-3-Ratios-and-Rates-cr-34.png\" alt=\"Big Ideas Math Answers Grade 6 Chapter 3 Ratios and Rates cr 34\" width=\"197\" height=\"67\" \/><br \/>\nAnswer:<\/p>\n<p>Question 35.<br \/>\n<img decoding=\"async\" loading=\"lazy\" class=\"alignnone size-full wp-image-26808\" src=\"https:\/\/ccssanswers.com\/wp-content\/uploads\/2021\/01\/Big-Ideas-Math-Answers-Grade-6-Chapter-3-Ratios-and-Rates-cr-35.png\" alt=\"Big Ideas Math Answers Grade 6 Chapter 3 Ratios and Rates cr 35\" width=\"202\" height=\"70\" \/><br \/>\nAnswer:<\/p>\n<p>Question 36.<br \/>\nYou buy magnesium sulfate for $1.50 per pound.<br \/>\na. Represent the ratio relationship using a graph.<br \/>\nb. How much does 3.5 pounds of magnesium sulfate cost?<br \/>\nAnswer:<\/p>\n<p>Question 37.<br \/>\nA 5-ounce can of tuna costs $0.90. A 12-ounce can of tuna costs $2.40. Graph each ratio relationship in the same coordinate plane. Which is the better buy?<br \/>\n<img decoding=\"async\" loading=\"lazy\" class=\"alignnone size-full wp-image-26809\" src=\"https:\/\/ccssanswers.com\/wp-content\/uploads\/2021\/01\/Big-Ideas-Math-Answers-Grade-6-Chapter-3-Ratios-and-Rates-cr-37.png\" alt=\"Big Ideas Math Answers Grade 6 Chapter 3 Ratios and Rates cr 37\" width=\"306\" height=\"194\" srcset=\"https:\/\/ccssanswers.com\/wp-content\/uploads\/2021\/01\/Big-Ideas-Math-Answers-Grade-6-Chapter-3-Ratios-and-Rates-cr-37.png 306w, https:\/\/ccssanswers.com\/wp-content\/uploads\/2021\/01\/Big-Ideas-Math-Answers-Grade-6-Chapter-3-Ratios-and-Rates-cr-37-300x190.png 300w\" sizes=\"(max-width: 306px) 100vw, 306px\" \/><br \/>\nAnswer:<\/p>\n<p><strong>3.5 Rates and Unit Rates (pp. 135\u2013140)<\/strong><br \/>\nLearning Target: Understand the concept of a unit rate and solve rate problems.<\/p>\n<p>Write a unit rate for the situation.<br \/>\nQuestion 38.<br \/>\n12 stunts in 4 movies<br \/>\nAnswer: 3<\/p>\n<p>Explanation:<br \/>\n12 stunts in 4 movies<br \/>\n12\/4 = 3<br \/>\n3 stunts in 1 movie<\/p>\n<p>Question 39.<br \/>\n3600 stitches in 3 minutes<br \/>\nAnswer: 1200<\/p>\n<p>Explanation:<br \/>\n3600 stitches in 3 minutes<br \/>\n3600\/3 = 1200<br \/>\n1200 stiches in 1 minute<\/p>\n<p>Question 40.<br \/>\n$18 for 6 pounds<br \/>\nAnswer: 3<\/p>\n<p>Explanation:<br \/>\n$18 for 6 pounds<br \/>\n18\/6 = 3<br \/>\n$3 for 1 pound<\/p>\n<p>Question 41.<br \/>\n240 people in 5 buses<br \/>\nAnswer: 48<\/p>\n<p>Explanation:<br \/>\n240 people in 5 buses<br \/>\n240\/5 = 48<br \/>\n48 people in 1 bus<\/p>\n<p>Question 42.<br \/>\nA train travels 120 miles in 3 hours. Write two unit rates that describe the relationship between the number of miles and the number of hours the train travels.<br \/>\nAnswer:<\/p>\n<p>Question 43.<br \/>\nMercury orbits the Sun 3 times in 264 days.<br \/>\na. How many times does Mercury orbit the Sun in 440 days?<br \/>\nb. How many days does it take Mercury to orbit the Sun 8 times?<br \/>\nAnswer:<\/p>\n<p>Question 44.<br \/>\nA cyclist travels 4 miles in 20 minutes. At this rate, how many miles does the cyclist travel in 30 minutes?<br \/>\nAnswer:<br \/>\nGiven,<br \/>\nA cyclist travels 4 miles in 20 minutes.<br \/>\n20\/4 = 5 minutes<br \/>\n1 mile in 5 minutes<br \/>\n30 minutes divided by 5<br \/>\n30\/5 = 6 minutes<br \/>\nSo, 6 miles in 6 minutes<\/p>\n<p><strong>Decide whether the rates are equivalent.<\/strong><br \/>\nQuestion 45.<br \/>\n18 keystrokes in 3 seconds<br \/>\n48 keystrokes in 16 seconds<br \/>\nAnswer: No<\/p>\n<p>Explanation:<br \/>\n18 keystrokes in 3 seconds<br \/>\n48 keystrokes in 16 seconds<br \/>\n18 : 3 :: 48 : 16<br \/>\n6 : 1 :: 3 : 1<br \/>\nThe rates are not equivalent<\/p>\n<p>Question 46.<br \/>\n210 miles in 3 hours<br \/>\n780 miles in 12 hours<br \/>\nAnswer: No<\/p>\n<p>Explanation:<br \/>\n210 miles in 3 hours<br \/>\n780 miles in 12 hours<br \/>\n210 : 3 = 70<br \/>\n780 : 12 = 65<br \/>\nThe rates are not equivalent<\/p>\n<p>Question 47.<br \/>\nYou and a friend are picking up trash on a beach. You fill 2 bags with trash in 28 minutes. Your friend fills 3 bags with trash in 48 minutes. Who fills bags with trash faster? How much sooner will the faster person fill 7 bags with trash?<\/p>\n<p><img decoding=\"async\" loading=\"lazy\" class=\"alignnone size-full wp-image-26810\" src=\"https:\/\/ccssanswers.com\/wp-content\/uploads\/2021\/01\/Big-Ideas-Math-Answers-Grade-6-Chapter-3-Ratios-and-Rates-cr-47.png\" alt=\"Big Ideas Math Answers Grade 6 Chapter 3 Ratios and Rates cr 47\" width=\"296\" height=\"200\" \/><br \/>\nAnswer:<br \/>\nDivide 28 minutes by the 2 bags of trash.<br \/>\nYou fill 1 bag of trash every 14 minutes.<br \/>\n28 \u00f7 2 = 14<br \/>\nYour friend fills 1 bag of trash every 16 minutes.<br \/>\n48 \u00f7 3 = 16<br \/>\n7 bags \u00d7 16 min = 105 min<br \/>\n7 bags \u00d7 14 min = 98 min<br \/>\n105 &#8211; 98 = 7 minutes<\/p>\n<p><strong>3.6 Converting Measures (pp. 141\u2013148)<\/strong><br \/>\nLearning Target: Use ratio reasoning to convert units of measure.<\/p>\n<p>Copy and complete the statement. Round to the nearest hundredth if necessary.<br \/>\nQuestion 48.<br \/>\n<img decoding=\"async\" loading=\"lazy\" class=\"alignnone size-full wp-image-26811\" src=\"https:\/\/ccssanswers.com\/wp-content\/uploads\/2021\/01\/Big-Ideas-Math-Answers-Grade-6-Chapter-3-Ratios-and-Rates-cr-48.png\" alt=\"Big Ideas Math Answers Grade 6 Chapter 3 Ratios and Rates cr 48\" width=\"145\" height=\"35\" \/><br \/>\nAnswer: 20 fl. oz<\/p>\n<p>Explanation:<br \/>\nConvert from cups to fluid ounces<br \/>\n1 cup = 8 fluid ounce<br \/>\n2.5 cups = 20 fluid ounces<\/p>\n<p>Question 49.<br \/>\n<img decoding=\"async\" loading=\"lazy\" class=\"alignnone size-full wp-image-26812\" src=\"https:\/\/ccssanswers.com\/wp-content\/uploads\/2021\/01\/Big-Ideas-Math-Answers-Grade-6-Chapter-3-Ratios-and-Rates-cr-49.png\" alt=\"Big Ideas Math Answers Grade 6 Chapter 3 Ratios and Rates cr 49\" width=\"129\" height=\"42\" \/><br \/>\nAnswer: 4 yd<\/p>\n<p>Explanation:<br \/>\nConvert from feet to yards<br \/>\n1 feet = 0.33 yard<br \/>\n12 feet = 4 yards<\/p>\n<p>Question 50.<br \/>\n<img decoding=\"async\" loading=\"lazy\" class=\"alignnone size-full wp-image-26813\" src=\"https:\/\/ccssanswers.com\/wp-content\/uploads\/2021\/01\/Big-Ideas-Math-Answers-Grade-6-Chapter-3-Ratios-and-Rates-cr-50.png\" alt=\"Big Ideas Math Answers Grade 6 Chapter 3 Ratios and Rates cr 50\" width=\"154\" height=\"42\" srcset=\"https:\/\/ccssanswers.com\/wp-content\/uploads\/2021\/01\/Big-Ideas-Math-Answers-Grade-6-Chapter-3-Ratios-and-Rates-cr-50.png 154w, https:\/\/ccssanswers.com\/wp-content\/uploads\/2021\/01\/Big-Ideas-Math-Answers-Grade-6-Chapter-3-Ratios-and-Rates-cr-50-150x42.png 150w\" sizes=\"(max-width: 154px) 100vw, 154px\" \/><br \/>\nAnswer: 3.5<\/p>\n<p>Explanation:<br \/>\nConvert from milligrams to grams<br \/>\n1 mg = 0.001 g<br \/>\n3500 mg = 3.5 grams<\/p>\n<p>Question 51.<br \/>\n<img decoding=\"async\" loading=\"lazy\" class=\"alignnone size-full wp-image-26814\" src=\"https:\/\/ccssanswers.com\/wp-content\/uploads\/2021\/01\/Big-Ideas-Math-Answers-Grade-6-Chapter-3-Ratios-and-Rates-cr-51.png\" alt=\"Big Ideas Math Answers Grade 6 Chapter 3 Ratios and Rates cr 51\" width=\"119\" height=\"41\" \/><br \/>\nAnswer:<br \/>\nConvert from liters to quarts<br \/>\n1 L = 1.05 qt<br \/>\n3 L = 3.17 qt<br \/>\nThus 3 L \u2248 3 qt<\/p>\n<p>Question 52.<br \/>\n<img decoding=\"async\" loading=\"lazy\" class=\"alignnone size-full wp-image-26815\" src=\"https:\/\/ccssanswers.com\/wp-content\/uploads\/2021\/01\/Big-Ideas-Math-Answers-Grade-6-Chapter-3-Ratios-and-Rates-cr-52.png\" alt=\"Big Ideas Math Answers Grade 6 Chapter 3 Ratios and Rates cr 52\" width=\"146\" height=\"41\" \/><br \/>\nAnswer: 23 cm<\/p>\n<p>Explanation:<br \/>\nConvert from inches to centimeters<br \/>\n1 in = 2.54 cm<br \/>\n9.2 in = 23.36 cm<br \/>\n9.2 in \u2248 23 cm<\/p>\n<p>Question 53.<br \/>\n<img decoding=\"async\" loading=\"lazy\" class=\"alignnone size-full wp-image-26816\" src=\"https:\/\/ccssanswers.com\/wp-content\/uploads\/2021\/01\/Big-Ideas-Math-Answers-Grade-6-Chapter-3-Ratios-and-Rates-cr-53.png\" alt=\"Big Ideas Math Answers Grade 6 Chapter 3 Ratios and Rates cr 53\" width=\"138\" height=\"41\" \/><br \/>\nAnswer: 7 kg<\/p>\n<p>Explanation:<br \/>\nConvert from lb to kg<br \/>\n1 lb = 0.45 kg<br \/>\n15 lb = 6.80 kg<br \/>\n15 lb \u2248 7 kg<\/p>\n<p>Question 54.<br \/>\n<img decoding=\"async\" loading=\"lazy\" class=\"alignnone size-full wp-image-26817\" src=\"https:\/\/ccssanswers.com\/wp-content\/uploads\/2021\/01\/Big-Ideas-Math-Answers-Grade-6-Chapter-3-Ratios-and-Rates-cr-54.png\" alt=\"Big Ideas Math Answers Grade 6 Chapter 3 Ratios and Rates cr 54\" width=\"121\" height=\"65\" \/><br \/>\nAnswer: $120<\/p>\n<p>Explanation:<br \/>\nConvert from hours to minutes<br \/>\n1 hour = 60 minutes<br \/>\n1 min = $2<br \/>\n60 min = x<br \/>\nx = 60 \u00d7 2<br \/>\nx = $120<\/p>\n<p>Question 55.<br \/>\n<img decoding=\"async\" loading=\"lazy\" class=\"alignnone size-full wp-image-26818\" src=\"https:\/\/ccssanswers.com\/wp-content\/uploads\/2021\/01\/Big-Ideas-Math-Answers-Grade-6-Chapter-3-Ratios-and-Rates-cr-55.png\" alt=\"Big Ideas Math Answers Grade 6 Chapter 3 Ratios and Rates cr 55\" width=\"139\" height=\"65\" \/><br \/>\nAnswer: 52<\/p>\n<p>Explanation:<br \/>\nConvert from gal to qt<br \/>\n1 gal = 4 qt<br \/>\n13 gal = 52 qt<\/p>\n<p>Question 56.<br \/>\n<img decoding=\"async\" loading=\"lazy\" class=\"alignnone size-full wp-image-26819\" src=\"https:\/\/ccssanswers.com\/wp-content\/uploads\/2021\/01\/Big-Ideas-Math-Answers-Grade-6-Chapter-3-Ratios-and-Rates-cr-56.png\" alt=\"Big Ideas Math Answers Grade 6 Chapter 3 Ratios and Rates cr 56\" width=\"121\" height=\"67\" \/><br \/>\nAnswer: 0.040<\/p>\n<p>Question 57.<br \/>\nExplain how to use conversion factors to find the number of fluid ounces in any given number of quarts of a liquid.<br \/>\nAnswer:<\/p>\n<p>Question 58.<br \/>\nWater flows through a pipe at a rate of 10 gallons per minute. How many gallons of water flow through the pipe in an hour?<br \/>\nAnswer:<br \/>\nGiven,<br \/>\nWater flows through a pipe at a rate of 10 gallons per minute.<br \/>\n1 hour = 60 minute<br \/>\n1 minute = 10 gallon<br \/>\n60 minutes = 60 \u00d7 10 gallon = 600 gallon<br \/>\nThus 600 gallons of water flow through the pipe in an hour.<\/p>\n<p>Question 59.<br \/>\nGermany suggests a speed limit of 130 kilometers per hour on highways. Is the speed shown greater than the suggested limit?<br \/>\n<img decoding=\"async\" loading=\"lazy\" class=\"alignnone size-full wp-image-26820\" src=\"https:\/\/ccssanswers.com\/wp-content\/uploads\/2021\/01\/Big-Ideas-Math-Answers-Grade-6-Chapter-3-Ratios-and-Rates-cr-59.png\" alt=\"Big Ideas Math Answers Grade 6 Chapter 3 Ratios and Rates cr 59\" width=\"147\" height=\"144\" \/><br \/>\nAnswer:<\/p>\n<p>Question 60.<br \/>\nThe distance between two stars increases at a rate of 3 centimeters per month. What is the rate in inches per year?<br \/>\nAnswer: 14.17 inches<\/p>\n<p>Explanation:<br \/>\nGiven,<br \/>\nThe distance between two stars increases at a rate of 3 centimeters per month.<br \/>\n3 cm &#8211; 1 month<br \/>\n1 year = 12 months<br \/>\n3 \u00d7 12 = 36 centimeters<br \/>\nConvert from centimeters to inches<br \/>\n36 centimeters = 14.17 inches<\/p>\n<h3><a id=\"Ratios_and_Rates_Practice_Test\"><\/a>Ratios and Rates Practice Test<\/h3>\n<p>Question 1.<br \/>\nWrite the ratio of scooters to bikes.<br \/>\n<img decoding=\"async\" loading=\"lazy\" class=\"alignnone size-full wp-image-26829\" src=\"https:\/\/ccssanswers.com\/wp-content\/uploads\/2021\/01\/Big-Ideas-Math-Solutions-Grade-6-Chapter-3-Ratios-and-Rates-pt-1.png\" alt=\"Big Ideas Math Solutions Grade 6 Chapter 3 Ratios and Rates pt 1\" width=\"200\" height=\"102\" \/><br \/>\nAnswer:<br \/>\nThere are 3 scooter and 3 bikes<br \/>\nThus the ratio of scooters to bikes is 3 : 3<\/p>\n<p>Question 2.<br \/>\nDetermine whether the ratios 8 : 7 and 15 : 14 are equivalent.<br \/>\nAnswer: The ratios 8 : 7 and 15 : 14 are not equivalent.<br \/>\nThe equivalent ratio of 8:7 is 16 : 14.<\/p>\n<p><strong>Find the missing values in the ratio table. Then write the equivalent ratios.<\/strong><br \/>\nQuestion 3.<br \/>\n<img decoding=\"async\" loading=\"lazy\" class=\"alignnone size-full wp-image-26830\" src=\"https:\/\/ccssanswers.com\/wp-content\/uploads\/2021\/01\/Big-Ideas-Math-Solutions-Grade-6-Chapter-3-Ratios-and-Rates-pt-3.png\" alt=\"Big Ideas Math Solutions Grade 6 Chapter 3 Ratios and Rates pt 3\" width=\"170\" height=\"74\" \/><br \/>\nAnswer:<br \/>\n<img decoding=\"async\" loading=\"lazy\" class=\"alignnone size-full wp-image-34660\" src=\"https:\/\/ccssanswers.com\/wp-content\/uploads\/2021\/01\/Big-Ideas-Math-Solutions-Grade-6-Chapter-3-Ratios-and-Rates-pt-3.jpg\" alt=\"Big-Ideas-Math-Solutions-Grade-6-Chapter-3-Ratios-and-Rates-pt-3\" width=\"170\" height=\"74\" \/><br \/>\nThe missing values are 12, 18<br \/>\nThe ratio is 2:1<br \/>\nThe equivalent ratio of 2 : 1 is 12 : 6 and 36 : 18<\/p>\n<p>Question 4.<br \/>\n<img decoding=\"async\" loading=\"lazy\" class=\"alignnone size-full wp-image-26831\" src=\"https:\/\/ccssanswers.com\/wp-content\/uploads\/2021\/01\/Big-Ideas-Math-Solutions-Grade-6-Chapter-3-Ratios-and-Rates-pt-4.png\" alt=\"Big Ideas Math Solutions Grade 6 Chapter 3 Ratios and Rates pt 4\" width=\"194\" height=\"74\" \/><br \/>\nAnswer:<br \/>\n<img decoding=\"async\" loading=\"lazy\" class=\"alignnone size-full wp-image-34663\" src=\"https:\/\/ccssanswers.com\/wp-content\/uploads\/2021\/01\/Big-Ideas-Math-Solutions-Grade-6-Chapter-3-Ratios-and-Rates-pt-4.jpg\" alt=\"Big-Ideas-Math-Solutions-Grade-6-Chapter-3-Ratios-and-Rates-pt-4\" width=\"194\" height=\"74\" \/><br \/>\nThe missing values are 54, 10<br \/>\nThe ratio is 2 : 9<br \/>\nThe equivalent ratio of 2 : 9 is 12 : 54 and 10 : 45<\/p>\n<p>Question 5.<br \/>\nRepresent the ratio relationship using a graph.<br \/>\n<img decoding=\"async\" loading=\"lazy\" class=\"alignnone size-full wp-image-26832\" src=\"https:\/\/ccssanswers.com\/wp-content\/uploads\/2021\/01\/Big-Ideas-Math-Solutions-Grade-6-Chapter-3-Ratios-and-Rates-pt-5.png\" alt=\"Big Ideas Math Solutions Grade 6 Chapter 3 Ratios and Rates pt 5\" width=\"269\" height=\"71\" \/><br \/>\nAnswer:<br \/>\n<img decoding=\"async\" loading=\"lazy\" class=\"alignnone size-full wp-image-34672\" src=\"https:\/\/ccssanswers.com\/wp-content\/uploads\/2021\/01\/Big-Ideas-Math-Grade-6-Chapter-3-Answers-img_2.jpg\" alt=\"Big Ideas Math Grade 6 Chapter 3 Answers img_2\" width=\"555\" height=\"325\" srcset=\"https:\/\/ccssanswers.com\/wp-content\/uploads\/2021\/01\/Big-Ideas-Math-Grade-6-Chapter-3-Answers-img_2.jpg 555w, https:\/\/ccssanswers.com\/wp-content\/uploads\/2021\/01\/Big-Ideas-Math-Grade-6-Chapter-3-Answers-img_2-300x176.jpg 300w\" sizes=\"(max-width: 555px) 100vw, 555px\" \/><\/p>\n<p>Question 6.<br \/>\nYou travel 224 miles in 4 hours. Find the unit rate.<br \/>\nAnswer: 56<\/p>\n<p>Explanation:<br \/>\nGiven,<br \/>\nYou travel 224 miles in 4 hours.<br \/>\n1 hour = x<br \/>\n4 \u00d7 x = 224<br \/>\nx = 224\/4<br \/>\nx = 56 miles<br \/>\nThe unit rate is 56 miles.<\/p>\n<p><strong>Copy and complete the statement. Round to the nearest hundredth if necessary.<\/strong><br \/>\nQuestion 7.<br \/>\n<img decoding=\"async\" loading=\"lazy\" class=\"alignnone size-full wp-image-26833\" src=\"https:\/\/ccssanswers.com\/wp-content\/uploads\/2021\/01\/Big-Ideas-Math-Solutions-Grade-6-Chapter-3-Ratios-and-Rates-pt-7.png\" alt=\"Big Ideas Math Solutions Grade 6 Chapter 3 Ratios and Rates pt 7\" width=\"135\" height=\"39\" \/><br \/>\nAnswer:<br \/>\n<img decoding=\"async\" loading=\"lazy\" class=\"alignnone size-full wp-image-34665\" src=\"https:\/\/ccssanswers.com\/wp-content\/uploads\/2021\/01\/Big-Ideas-Math-Solutions-Grade-6-Chapter-3-Ratios-and-Rates-pt-7.jpg\" alt=\"Big-Ideas-Math-Solutions-Grade-6-Chapter-3-Ratios-and-Rates-pt-7\" width=\"135\" height=\"39\" \/><\/p>\n<p>Explanation:<br \/>\nConvert from centimeters to inches.<br \/>\n1 cm = 0.39<br \/>\n6 cm = 6 \u00d7 0.39<br \/>\n6 cm = 2.34 inches<\/p>\n<p>Question 8.<br \/>\n<img decoding=\"async\" loading=\"lazy\" class=\"alignnone size-full wp-image-26834\" src=\"https:\/\/ccssanswers.com\/wp-content\/uploads\/2021\/01\/Big-Ideas-Math-Solutions-Grade-6-Chapter-3-Ratios-and-Rates-pt-8.png\" alt=\"Big Ideas Math Solutions Grade 6 Chapter 3 Ratios and Rates pt 8\" width=\"128\" height=\"45\" \/><br \/>\nAnswer:<br \/>\n<img decoding=\"async\" loading=\"lazy\" class=\"alignnone size-full wp-image-34668\" src=\"https:\/\/ccssanswers.com\/wp-content\/uploads\/2021\/01\/Big-Ideas-Math-Solutions-Grade-6-Chapter-3-Ratios-and-Rates-pt-8.jpg\" alt=\"Big-Ideas-Math-Solutions-Grade-6-Chapter-3-Ratios-and-Rates-pt-8\" width=\"128\" height=\"45\" \/><\/p>\n<p>Explanation:<br \/>\nConvert from liters to gal<br \/>\n1 liter = 0.26 gal<br \/>\n30 liter = 7.92 gal<\/p>\n<p>Question 9.<br \/>\n<img decoding=\"async\" loading=\"lazy\" class=\"alignnone size-full wp-image-26835\" src=\"https:\/\/ccssanswers.com\/wp-content\/uploads\/2021\/01\/Big-Ideas-Math-Solutions-Grade-6-Chapter-3-Ratios-and-Rates-pt-9.png\" alt=\"Big Ideas Math Solutions Grade 6 Chapter 3 Ratios and Rates pt 9\" width=\"151\" height=\"65\" \/><br \/>\nAnswer:<br \/>\n<img decoding=\"async\" loading=\"lazy\" class=\"alignnone size-full wp-image-34669\" src=\"https:\/\/ccssanswers.com\/wp-content\/uploads\/2021\/01\/Big-Ideas-Math-Solutions-Grade-6-Chapter-3-Ratios-and-Rates-pt-9.jpg\" alt=\"Big-Ideas-Math-Solutions-Grade-6-Chapter-3-Ratios-and-Rates-pt-9\" width=\"151\" height=\"65\" \/><\/p>\n<p>Explanation:<br \/>\nConvert from hours to week<br \/>\n1 hour = 0.005 = 5\/1000<br \/>\n10 gal\/h = 2000\/wk<\/p>\n<p>Question 10.<br \/>\n<img decoding=\"async\" loading=\"lazy\" class=\"alignnone size-full wp-image-26836\" src=\"https:\/\/ccssanswers.com\/wp-content\/uploads\/2021\/01\/Big-Ideas-Math-Solutions-Grade-6-Chapter-3-Ratios-and-Rates-pt-10.png\" alt=\"Big Ideas Math Solutions Grade 6 Chapter 3 Ratios and Rates pt 10\" width=\"121\" height=\"66\" \/><br \/>\nAnswer:<br \/>\n<img decoding=\"async\" loading=\"lazy\" class=\"alignnone size-full wp-image-34671\" src=\"https:\/\/ccssanswers.com\/wp-content\/uploads\/2021\/01\/Big-Ideas-Math-Solutions-Grade-6-Chapter-3-Ratios-and-Rates-pt-10.jpg\" alt=\"Big-Ideas-Math-Solutions-Grade-6-Chapter-3-Ratios-and-Rates-pt-10\" width=\"121\" height=\"66\" \/><\/p>\n<p>Explanation:<br \/>\nConvert from feet to meters<br \/>\n1 feet = 0.30m<br \/>\n4 feet = 1.21 m<br \/>\n4 ft \u2248 1m<\/p>\n<p>Question 11.<br \/>\nDuring a baseball season, Team A scores 9 runs for every 7 runs that Team B scores. The total number of runs scored by both teams is 1440. How many runs does each team score?<br \/>\nAnswer:<br \/>\nTeam A scores 810<br \/>\nTeam B scores 630<\/p>\n<p>Explanation:<br \/>\nDuring a baseball season, Team A scores 9 runs for every 7 runs that Team B scores.<br \/>\nThe total number of runs scored by both teams is 1440.<br \/>\nLet b scores x runs<br \/>\nThen a scores x + (2 \u00d7 x\/7)<br \/>\nBecause every 7 runs of b, a is scores more 2 runs.<br \/>\nTotal number of runs scored by both teams is 1440<br \/>\na + b = 1440<br \/>\nx + (2 \u00d7 x\/7) + x = 1440<br \/>\n(16 \u00d7 x)\/7 = 1440<br \/>\n16 \u00d7 x = 1440 \u00d7 7<br \/>\n16x = 10080<br \/>\nx = 10080\/16<br \/>\nx = 630<br \/>\nThus team b scores 630 runs<br \/>\nTeam a scores is x + (2 \u00d7 x\/7) = 810 runs<\/p>\n<p>Question 12.<br \/>\nAt a movie theater, the ratio of filled seats to empty seats is 6 : 5. There are 120 empty seats. How many seats are filled?<br \/>\nAnswer: 144<\/p>\n<p>Explanation:<br \/>\nGiven,<br \/>\nAt a movie theater, the ratio of filled seats to empty seats is 6 : 5. There are 120 empty seats.<br \/>\nNumber of filled = 6<br \/>\nNumber of empty = 5<br \/>\n120\/5 = 24 then multiply it by 6 to get 144.<br \/>\nThus the number of filled seats = 144<\/p>\n<p>Question 13.<br \/>\nYou and your friend mix water and citric acid. You add 3 cups of citric acid for every 16 cups of water. Your friend adds 2 cups of citric acid for every 12 cups of water. Whose mixture is more acidic?<br \/>\nAnswer: A&#8217;s mixture is more acidic<\/p>\n<p>Explanation:<br \/>\nGiven,<br \/>\nYou and your friend mix water and citric acid.<br \/>\nYou add 3 cups of citric acid for every 16 cups of water.<br \/>\nYour friend adds 2 cups of citric acid for every 12 cups of water.<br \/>\nA add 3 cups of citric acid for every 16 cups of water, the ratio = 3\/16<br \/>\nB adds 2 cups of citric acid for every 12 cups of water = 2\/12<br \/>\nLCM of 16 and 12 are 48<br \/>\n16 &#8211; 16, 32, 48, 64, 80, 96<br \/>\n12 &#8211; 12, 24, 36, 48, 60, 72<br \/>\nA &#8211; 3\/16 \u00d7 3\/3 = 9\/48<br \/>\nB &#8211; 2\/12 \u00d7 4\/4 = 8\/48<br \/>\nWe found that in terms of 48 cups of water, friend A mixes 9 cups of acid while friend B mixes 8 cups of acid, means A is adding more acid than B and hence friend A&#8217;s mixture is more acidic.<\/p>\n<p>Question 14.<br \/>\nDetermine which windsurfer is faster. Explain your reasoning.<br \/>\n<img decoding=\"async\" loading=\"lazy\" class=\"alignnone size-full wp-image-26837\" src=\"https:\/\/ccssanswers.com\/wp-content\/uploads\/2021\/01\/Big-Ideas-Math-Solutions-Grade-6-Chapter-3-Ratios-and-Rates-pt-14.png\" alt=\"Big Ideas Math Solutions Grade 6 Chapter 3 Ratios and Rates pt 14\" width=\"440\" height=\"129\" srcset=\"https:\/\/ccssanswers.com\/wp-content\/uploads\/2021\/01\/Big-Ideas-Math-Solutions-Grade-6-Chapter-3-Ratios-and-Rates-pt-14.png 440w, https:\/\/ccssanswers.com\/wp-content\/uploads\/2021\/01\/Big-Ideas-Math-Solutions-Grade-6-Chapter-3-Ratios-and-Rates-pt-14-300x88.png 300w\" sizes=\"(max-width: 440px) 100vw, 440px\" \/><br \/>\nAnswer: The second windsurfer is faster than the first windsurfer.<br \/>\nFirst convert from meter to feet<br \/>\n1 meter = 3.28<br \/>\n5 meter = 16.40<br \/>\nConvert from minute to second<br \/>\n1 min = 60 sec<br \/>\n16.40 \u00d7 60 = 984 feet<br \/>\n984 feet is greater than 720 feet<\/p>\n<p>Question 15.<br \/>\nIn a rectangle, the ratio of the length to the width is 5 : 2. The length of the rectangle is 13.875 feet greater than the width. What are the perimeter and the area of the rectangle?<br \/>\nAnswer:<br \/>\nP = 64.75 feet<br \/>\nA = 213.91 feet<\/p>\n<p>Explanation:<br \/>\nGiven,<br \/>\nIn a rectangle, the ratio of the length to the width is 5 : 2.<br \/>\nThe length of the rectangle is 13.875 feet greater than the width.<br \/>\n13.875 \u00f7 3 = 4.625 feet<br \/>\n4.625 \u00d7 5 = 23.125 feet<br \/>\nSo, the length of the rectangle is 23.125 feet<br \/>\n4.625 \u00d7 2 = 9.25 feet<br \/>\nSo, the width of the rectangle is 9.25 feet<br \/>\nWe know that, Perimeter of the rectangle = 2l + 2w<br \/>\nP = 2(23.125) + 2(9.25)<br \/>\nP = 64.75 feet<br \/>\nArea of the rectangle = l \u00d7 w<br \/>\nA = 23.125 \u00d7 9.25<br \/>\nArea = 213.91 sq. feet<\/p>\n<h3><a id=\"Ratios_and_Rates_Cumulative_Practice\"><\/a>Ratios and Rates Cumulative Practice<\/h3>\n<p><img decoding=\"async\" loading=\"lazy\" class=\"alignnone size-full wp-image-26821\" src=\"https:\/\/ccssanswers.com\/wp-content\/uploads\/2021\/01\/Big-Ideas-Math-Solutions-Grade-6-Chapter-3-Ratios-and-Rates-cp-1.png\" alt=\"Big Ideas Math Solutions Grade 6 Chapter 3 Ratios and Rates cp 1\" width=\"316\" height=\"379\" srcset=\"https:\/\/ccssanswers.com\/wp-content\/uploads\/2021\/01\/Big-Ideas-Math-Solutions-Grade-6-Chapter-3-Ratios-and-Rates-cp-1.png 316w, https:\/\/ccssanswers.com\/wp-content\/uploads\/2021\/01\/Big-Ideas-Math-Solutions-Grade-6-Chapter-3-Ratios-and-Rates-cp-1-250x300.png 250w\" sizes=\"(max-width: 316px) 100vw, 316px\" \/><br \/>\nQuestion 1.<br \/>\nWhich number is equivalent to \\(\\frac{2}{9}\\) \u00f7 \\(\\frac{4}{5}\\)?<br \/>\nA. \\(\\frac{8}{14}\\)<br \/>\nB. \\(\\frac{5}{18}\\)<br \/>\nC. \\(\\frac{7}{13}\\)<br \/>\nD. 3\\(\\frac{3}{5}\\)<br \/>\nAnswer: \\(\\frac{5}{18}\\)<\/p>\n<p>Explanation:<br \/>\nDividing two fractions is the same as multiplying the first fraction by the reciprocal (inverse) of the second fraction.<br \/>\nTake the reciprocal of the second fraction by flipping the numerator and denominator and changing the operation to multiplication. Then the equation becomes<br \/>\n\\(\\frac{2}{9}\\) \u00d7 \\(\\frac{5}{4}\\) = \\(\\frac{10}{36}\\)<br \/>\nThis fraction can be reduced by dividing both the numerator and denominator by the Greatest Common Factor of 10 and 36 using<br \/>\nGCF is 2<br \/>\n\\(\\frac{10}{36}\\) \u00f7 \\(\\frac{2}{2}\\) = \\(\\frac{5}{18}\\)<br \/>\nThus the correct answer is option B.<\/p>\n<p>Question 2.<br \/>\nYour speed while waterskiing is 22 miles per hour. How fast are you traveling in kilometers per hour? Round your answer to the nearest hundredth.<br \/>\n<img decoding=\"async\" loading=\"lazy\" class=\"alignnone size-full wp-image-26822\" src=\"https:\/\/ccssanswers.com\/wp-content\/uploads\/2021\/01\/Big-Ideas-Math-Solutions-Grade-6-Chapter-3-Ratios-and-Rates-cp-2.png\" alt=\"Big Ideas Math Solutions Grade 6 Chapter 3 Ratios and Rates cp 2\" width=\"71\" height=\"64\" \/><br \/>\nAnswer: 35 kilometers<\/p>\n<p>Explanation:<br \/>\nGiven,<br \/>\nYour speed while waterskiing is 22 miles per hour.<br \/>\nConvert from miles to kilometers<br \/>\n1 mile = 1.609 kilometer<br \/>\n22 miles = 22 \u00d7 1.609 = 35.40 kilometers<\/p>\n<p>Question 3.<br \/>\nWhich number is equivalent to the expression below?<br \/>\n2 . 4<sup>2<\/sup> + 3(6 \u00f7 2)<br \/>\nF. 25<br \/>\nG. 41<br \/>\nH. 73<br \/>\nI. 105<br \/>\nAnswer:<br \/>\n2 . 4<sup>2<\/sup> + 3(6 \u00f7 2)<br \/>\n2 . 4<sup>2<\/sup> + 3(3)<br \/>\n2 . 4<sup>2<\/sup> + 9<br \/>\n2 \u00d7 16 + 9<br \/>\n32+9 = 41<br \/>\nThus the correct answer is option G.<\/p>\n<p>Question 4.<br \/>\nThe tape diagram models the ratio of red beads to green beads in a bracelet. The bracelet uses 12 red beads. How many green beads are in the bracelet?<br \/>\n<img decoding=\"async\" loading=\"lazy\" class=\"alignnone size-full wp-image-26823\" src=\"https:\/\/ccssanswers.com\/wp-content\/uploads\/2021\/01\/Big-Ideas-Math-Solutions-Grade-6-Chapter-3-Ratios-and-Rates-cp-4.png\" alt=\"Big Ideas Math Solutions Grade 6 Chapter 3 Ratios and Rates cp 4\" width=\"262\" height=\"71\" \/><br \/>\nA. 4 green beads<br \/>\nB. 8 green beads<br \/>\nC. 12 green beads<br \/>\nD. 20 green beads<br \/>\nAnswer: 8 green beads<\/p>\n<p>Explanation:<br \/>\nGiven,<br \/>\nThe tape diagram models the ratio of red beads to green beads in a bracelet. The bracelet uses 12 red beads.<br \/>\nFrom the above figure we observe that there are 3<br \/>\n3 \u00d7 4 = 12<br \/>\n1 box = 4 beads<br \/>\nThere are 2 green boxes<br \/>\n2 \u00d7 4 = 8<br \/>\nThus there 8 green beads in the bracelet.<\/p>\n<p>Question 5.<br \/>\nWhat is the least common multiple of 8, 12, and 20?<br \/>\nF. 24<br \/>\nG. 40<br \/>\nH. 60<br \/>\nI. 120<br \/>\nAnswer: 120<\/p>\n<p>Explanation:<br \/>\nFind and list multiples of each number until the first common multiple is found. This is the lowest common multiple.<br \/>\nMultiples of 8:<br \/>\n8, 16, 24, 32, 40, 48, 56, 64, 72, 80, 88, 96, 104, 112, 120, 128, 136<br \/>\nMultiples of 12:<br \/>\n12, 24, 36, 48, 60, 72, 84, 96, 108, 120, 132, 144<br \/>\nMultiples of 20:<br \/>\n20, 40, 60, 80, 100, 120, 140, 160<br \/>\nTherefore,<br \/>\nLCM(8, 12, 20) = 120<br \/>\nThus the correct answer is option I.<\/p>\n<p>Question 6.<br \/>\nWhich number is equivalent to 2.34 \u00d7 1.08 \u00d7 5.6?<br \/>\nA. 12.787632<br \/>\nB. 14.15232<br \/>\nC. 23.5872<br \/>\nD. 14,152.32<br \/>\nAnswer: 14.15232<\/p>\n<p>Explanation:<br \/>\nMultiply the three numbers<br \/>\n2.34 \u00d7 1.08 \u00d7 5.6 we get 14.15232<br \/>\nThus the correct answer is option B.<\/p>\n<p>Question 7.<br \/>\nThe school store sells 4 pencils for $0.50. At this rate, what is the cost (in dollars) of 10 pencils?<br \/>\n<img decoding=\"async\" loading=\"lazy\" class=\"alignnone size-full wp-image-26824\" src=\"https:\/\/ccssanswers.com\/wp-content\/uploads\/2021\/01\/Big-Ideas-Math-Solutions-Grade-6-Chapter-3-Ratios-and-Rates-cp-6.png\" alt=\"Big Ideas Math Solutions Grade 6 Chapter 3 Ratios and Rates cp 6\" width=\"73\" height=\"61\" \/><br \/>\nAnswer: $1.25<\/p>\n<p>Explanation:<br \/>\nGiven,<br \/>\nThe school store sells 4 pencils for $0.50.<br \/>\nCost of 1 pencil is 0.50\/4 = 0.125<br \/>\n0.125 \u00d7 10 = 1.25<br \/>\nThus the cost of 10 pencils is $1.25<\/p>\n<p>Question 8.<br \/>\nA factor tree for 14,700 is shown. Which factor of 14,700 is not a perfect square?<br \/>\n<img decoding=\"async\" loading=\"lazy\" class=\"alignnone size-full wp-image-26825\" src=\"https:\/\/ccssanswers.com\/wp-content\/uploads\/2021\/01\/Big-Ideas-Math-Solutions-Grade-6-Chapter-3-Ratios-and-Rates-cp-7.png\" alt=\"Big Ideas Math Solutions Grade 6 Chapter 3 Ratios and Rates cp 7\" width=\"142\" height=\"135\" \/><br \/>\nF. 25<br \/>\nG. 49<br \/>\nH. 196<br \/>\nI. 588<br \/>\nAnswer:<br \/>\nThe given number is 14700<br \/>\nNow we prime factorize the number.<br \/>\n14700 = 147 \u00d7 100<br \/>\n= 7 \u00d7 21 \u00d7 10 \u00d7 10<br \/>\n= 7 \u00d7 7 \u00d7 3 \u00d7 5 \u00d7 2 \u00d7 5 \u00d7 2<br \/>\n= 2 \u00d7 2 \u00d7 3 \u00d7 5 \u00d7 5 \u00d7 7 \u00d7 7<br \/>\nWe see that each of 2, 5 and 7 appears twice in the factorization. But 3 appears only once, for which the number 14700 is not a perfect square.<br \/>\n\u2234 we divide 14700 by 3 to get a perfect square.<br \/>\n\u2234 the perfect square number is<br \/>\n= 14700 \u00f7 3<br \/>\n= 4900<br \/>\n= 70<em>\u00b2<\/em><br \/>\n588 is not a perfect square<br \/>\nThus the correct answer is option I.<\/p>\n<p>Question 9.<br \/>\nWhich of the following is a ratio of frogs to snakes?<br \/>\n<img decoding=\"async\" loading=\"lazy\" class=\"alignnone size-full wp-image-26826\" src=\"https:\/\/ccssanswers.com\/wp-content\/uploads\/2021\/01\/Big-Ideas-Math-Solutions-Grade-6-Chapter-3-Ratios-and-Rates-cp-8.png\" alt=\"Big Ideas Math Solutions Grade 6 Chapter 3 Ratios and Rates cp 8\" width=\"362\" height=\"167\" srcset=\"https:\/\/ccssanswers.com\/wp-content\/uploads\/2021\/01\/Big-Ideas-Math-Solutions-Grade-6-Chapter-3-Ratios-and-Rates-cp-8.png 362w, https:\/\/ccssanswers.com\/wp-content\/uploads\/2021\/01\/Big-Ideas-Math-Solutions-Grade-6-Chapter-3-Ratios-and-Rates-cp-8-300x138.png 300w\" sizes=\"(max-width: 362px) 100vw, 362px\" \/><br \/>\nA. 4 : 8<br \/>\nB. 8 : 12<br \/>\nC. 8 : 4<br \/>\nD. 4 : 12<br \/>\nAnswer: 8:4<\/p>\n<p>Explanation:<br \/>\nBy seeing the above figure we can write the ratio from frogs to snakes.<br \/>\nThere are 8 frogs<br \/>\nThere are 4 snakes<br \/>\n8:4<br \/>\nThus the correct answer is option C.<\/p>\n<p>Question 10.<br \/>\nWhich expression is equivalent to 3<sup>6<\/sup>?<br \/>\nF. 3 \u00d7 3 \u00d7 3 \u00d7 3 \u00d7 3<br \/>\nG. 3 \u00d7 5<br \/>\nH. 5 \u00d7 5 \u00d7 5<br \/>\nI. 3 + 3 + 3 + 3 + 3<br \/>\nAnswer: 3 \u00d7 3 \u00d7 3 \u00d7 3 \u00d7 3<br \/>\nThe expression equivalent to 3<sup>6 <\/sup>is 3 \u00d7 3 \u00d7 3 \u00d7 3 \u00d7 3<br \/>\nThus the correct answer is option F.<\/p>\n<p>Question 11.<br \/>\nWhich is the correct order of operations when evaluating 5 + 4 \u00d7 2<sup>3<\/sup>?<br \/>\n<img decoding=\"async\" loading=\"lazy\" class=\"alignnone size-full wp-image-26827\" src=\"https:\/\/ccssanswers.com\/wp-content\/uploads\/2021\/01\/Big-Ideas-Math-Solutions-Grade-6-Chapter-3-Ratios-and-Rates-cp-11.png\" alt=\"Big Ideas Math Solutions Grade 6 Chapter 3 Ratios and Rates cp 11\" width=\"349\" height=\"118\" srcset=\"https:\/\/ccssanswers.com\/wp-content\/uploads\/2021\/01\/Big-Ideas-Math-Solutions-Grade-6-Chapter-3-Ratios-and-Rates-cp-11.png 349w, https:\/\/ccssanswers.com\/wp-content\/uploads\/2021\/01\/Big-Ideas-Math-Solutions-Grade-6-Chapter-3-Ratios-and-Rates-cp-11-300x101.png 300w\" sizes=\"(max-width: 349px) 100vw, 349px\" \/><br \/>\nA. k, t, u<br \/>\nB. n, s, q<br \/>\nC. m, k, r<br \/>\nD. m, p, l<br \/>\nAnswer: k, t, u<\/p>\n<p>Explanation:<br \/>\nThe correct order of operations when evaluating 5 + 4 \u00d7 2<sup>3 <\/sup>is Add 5 and 4, Multiply 9 and 2 and Evaluate 18\u00b3<br \/>\nThus the correct answer is option A.<\/p>\n<p>Question 12.<br \/>\nThe ratio of scrambled eggs to hard-boiled eggs served at a restaurant is 6 : 2.<br \/>\nPart A Make a ratio table showing three possible combinations of<br \/>\nPart B Represent the ratio relationship using a graph.<br \/>\n<img decoding=\"async\" loading=\"lazy\" class=\"alignnone size-full wp-image-26828\" src=\"https:\/\/ccssanswers.com\/wp-content\/uploads\/2021\/01\/Big-Ideas-Math-Solutions-Grade-6-Chapter-3-Ratios-and-Rates-cp-12.png\" alt=\"Big Ideas Math Solutions Grade 6 Chapter 3 Ratios and Rates cp 12\" width=\"337\" height=\"146\" srcset=\"https:\/\/ccssanswers.com\/wp-content\/uploads\/2021\/01\/Big-Ideas-Math-Solutions-Grade-6-Chapter-3-Ratios-and-Rates-cp-12.png 337w, https:\/\/ccssanswers.com\/wp-content\/uploads\/2021\/01\/Big-Ideas-Math-Solutions-Grade-6-Chapter-3-Ratios-and-Rates-cp-12-300x130.png 300w\" sizes=\"(max-width: 337px) 100vw, 337px\" \/><br \/>\nPart C Use the graph to find the number of hard-boiled eggs served when the restaurant serves 15 scrambled eggs.<br \/>\nAnswer:<br \/>\nPart A &#8211; The three possible combinations are<br \/>\n3 : 1<br \/>\n12 : 4<br \/>\n18 : 6<br \/>\nPart B &#8211;<br \/>\n<img decoding=\"async\" loading=\"lazy\" class=\"alignnone size-full wp-image-34226\" src=\"https:\/\/ccssanswers.com\/wp-content\/uploads\/2021\/01\/Big-Ideas-Math-Solutions-Grade-6-Chapter-3-Ratios-and-Rates-cp-12.jpg\" alt=\"Big-Ideas-Math-Solutions-Grade-6-Chapter-3-Ratios-and-Rates-cp-12\" width=\"337\" height=\"180\" srcset=\"https:\/\/ccssanswers.com\/wp-content\/uploads\/2021\/01\/Big-Ideas-Math-Solutions-Grade-6-Chapter-3-Ratios-and-Rates-cp-12.jpg 337w, https:\/\/ccssanswers.com\/wp-content\/uploads\/2021\/01\/Big-Ideas-Math-Solutions-Grade-6-Chapter-3-Ratios-and-Rates-cp-12-300x160.jpg 300w\" sizes=\"(max-width: 337px) 100vw, 337px\" \/><br \/>\nPart C-<br \/>\nThe ratio is 3:1<br \/>\nThe ratio for 15 scrambled eggs<br \/>\n15 :5<\/p>\n<p><em>Conclusion:<\/em><\/p>\n<p>You can Download Middle School Big Ideas Math Answers Grade 6 Chapter 3 Ratios and Rates through the direct links provided here. Make use of the links and practice well for the exams. Keep in touch with our site to get the latest updates regarding the BIM 6th Grade Answer Key Chapter wise.<\/p>\n","protected":false},"excerpt":{"rendered":"<p>Free solutions to Big Ideas Math Grade 6 Chapter 3 Ratios and Rates are available here. So, the pupils those who are searching the Big Ideas Math Grade 6 Chapter 3 Ratios and Rates Solution Key can get them on this page. As per your convenience we have provided the solutions in the pdf format. &#8230; <a title=\"Big Ideas Math Answers Grade 6 Chapter 3 Ratios and Rates\" class=\"read-more\" href=\"https:\/\/ccssanswers.com\/big-ideas-math-answers-grade-6-chapter-3\/\" aria-label=\"More on Big Ideas Math Answers Grade 6 Chapter 3 Ratios and Rates\">Read more<\/a><\/p>\n","protected":false},"author":3,"featured_media":0,"comment_status":"open","ping_status":"open","sticky":false,"template":"","format":"standard","meta":{"footnotes":""},"categories":[4],"tags":[],"jetpack_sharing_enabled":true,"jetpack_featured_media_url":"","_links":{"self":[{"href":"https:\/\/ccssanswers.com\/wp-json\/wp\/v2\/posts\/26616"}],"collection":[{"href":"https:\/\/ccssanswers.com\/wp-json\/wp\/v2\/posts"}],"about":[{"href":"https:\/\/ccssanswers.com\/wp-json\/wp\/v2\/types\/post"}],"author":[{"embeddable":true,"href":"https:\/\/ccssanswers.com\/wp-json\/wp\/v2\/users\/3"}],"replies":[{"embeddable":true,"href":"https:\/\/ccssanswers.com\/wp-json\/wp\/v2\/comments?post=26616"}],"version-history":[{"count":1,"href":"https:\/\/ccssanswers.com\/wp-json\/wp\/v2\/posts\/26616\/revisions"}],"predecessor-version":[{"id":138572,"href":"https:\/\/ccssanswers.com\/wp-json\/wp\/v2\/posts\/26616\/revisions\/138572"}],"wp:attachment":[{"href":"https:\/\/ccssanswers.com\/wp-json\/wp\/v2\/media?parent=26616"}],"wp:term":[{"taxonomy":"category","embeddable":true,"href":"https:\/\/ccssanswers.com\/wp-json\/wp\/v2\/categories?post=26616"},{"taxonomy":"post_tag","embeddable":true,"href":"https:\/\/ccssanswers.com\/wp-json\/wp\/v2\/tags?post=26616"}],"curies":[{"name":"wp","href":"https:\/\/api.w.org\/{rel}","templated":true}]}}