{"id":29847,"date":"2023-01-09T14:50:11","date_gmt":"2023-01-09T09:20:11","guid":{"rendered":"https:\/\/ccssanswers.com\/?p=29847"},"modified":"2023-01-10T09:17:46","modified_gmt":"2023-01-10T03:47:46","slug":"big-ideas-math-answers-grade-7-chapter-2","status":"publish","type":"post","link":"https:\/\/ccssanswers.com\/big-ideas-math-answers-grade-7-chapter-2\/","title":{"rendered":"Big Ideas Math Answers Grade 7 Chapter 2 Multiplying and Dividing Rational Numbers"},"content":{"rendered":"<p>The best Big Ideas Math Grade 7 Chapter 2 Multiplying and Dividing Rational Numbers Answer Key PDF is available here. The students who are seeking help in math learning in an easy way can refer to this page. You can find the professionals suggested ways of solving Multiplying and Dividing Rational Numbers questions and learn the best methods to solve the problems. The students can practice all the questions from <a href=\"https:\/\/ccssanswers.com\/big-ideas-math-answers-grade-7\/\">Big Ideas Math Answers Grade 2<\/a> Chapter 2 Multiplying and Dividing Rational Numbers to score good marks in the examination.<\/p>\n<h2>Big Ideas Math Book 7th Grade Answer Key Chapter 2 Multiplying and Dividing Rational Numbers<\/h2>\n<p>The topics covered in Big Ideas Math Answers Grade 7 Chapter 2 are multiplying integers, dividing integers, conversion between fractions and decimals, multiplying rational numbers, and dividing rational numbers. Students who are willing to practice exercise questions can go through the Chapter Review, Practice Test, Cumulative Practice which is provided at the end of the chapter.<\/p>\n<p><strong>Performance<\/strong><\/p>\n<ul>\n<li><a href=\"#Multiplying_and_Dividing_Rational_Numbers_STEAM_Video\/Performance\">Multiplying and Dividing Rational Numbers STEAM Video\/Performance<\/a><\/li>\n<li><a href=\"#Multiplying_and_Dividing_Rational_Numbers_Getting_Ready_for_Chapter_2\">Multiplying and Dividing Rational Numbers Getting Ready for Chapter 2<\/a><\/li>\n<\/ul>\n<p><strong>Lesson: 1 Multiplying Integers<\/strong><\/p>\n<ul>\n<li><a href=\"#Lesson_2.1_Multiplying_Integers\">Lesson 2.1 Multiplying Integers<\/a><\/li>\n<li><a href=\"#Multiplying_Integers_Homework_&amp;_Practice_2.1\">Multiplying Integers Homework &amp; Practice 2.1<\/a><\/li>\n<\/ul>\n<p><strong>Lesson: 2 Dividing Integers<\/strong><\/p>\n<ul>\n<li><a href=\"#Lesson_2.2_Dividing_Integers\">Lesson 2.2 Dividing Integers<\/a><\/li>\n<li><a href=\"#Dividing_Integers_Homework_&amp;_Practice_2.2\">Dividing Integers Homework &amp; Practice 2.2<\/a><\/li>\n<\/ul>\n<p><strong>Lesson: 3 Converting Between Fractions and Decimals<\/strong><\/p>\n<ul>\n<li><a href=\"#Lesson_2.3_Converting_Between_Fractions_and_Decimals\">Lesson 2.3 Converting Between Fractions and Decimals<\/a><\/li>\n<li><a href=\"#Converting_Between_Fractions_and_Decimals_Homework_&amp;_Practice_2.3\">Converting Between Fractions and Decimals Homework &amp; Practice 2.3<\/a><\/li>\n<\/ul>\n<p><strong>Lesson: 4 Multiplying Rational Numbers<\/strong><\/p>\n<ul>\n<li><a href=\"#Lesson_2.4_Multiplying_Rational_Numbers\">Lesson 2.4 Multiplying Rational Numbers<\/a><\/li>\n<li><a href=\"#Multiplying_Rational_Numbers_Homework_&amp;_Practice_2.4\">Multiplying Rational Numbers Homework &amp; Practice 2.4<\/a><\/li>\n<\/ul>\n<p><strong>Lesson: 5 Dividing Rational Numbers<\/strong><\/p>\n<ul>\n<li><a href=\"#Lesson_2.5_Dividing_Rational_Numbers\">Lesson 2.5 Dividing Rational Numbers<\/a><\/li>\n<li><a href=\"#Dividing_Rational_Numbers_Homework_&amp;_Practice_2.5\">Dividing Rational Numbers Homework &amp; Practice 2.5<\/a><\/li>\n<\/ul>\n<p><strong>Chapter: 2 &#8211; Multiplying and Dividing Rational Numbers<\/strong><\/p>\n<ul>\n<li><a href=\"#Multiplying_and_Dividing_Rational_Numbers_Connecting_Concepts\">Multiplying and Dividing Rational Numbers Connecting Concepts<\/a><\/li>\n<li><a href=\"#Multiplying_and_Dividing_Rational_Numbers_Chapter_Review\">Multiplying and Dividing Rational Numbers Chapter Review<\/a><\/li>\n<li><a href=\"#Multiplying_and_Dividing_Rational_Numbers_Practice_Test\">Multiplying and Dividing Rational Numbers Practice Test<\/a><\/li>\n<li><a href=\"#Multiplying_and_Dividing_Rational_Numbers_Cumulative_Practice\">Multiplying and Dividing Rational Numbers Cumulative Practice<\/a><\/li>\n<\/ul>\n<h3><a id=\"Multiplying_and_Dividing_Rational_Numbers_STEAM_Video\/Performance\"><\/a>Multiplying and Dividing Rational Numbers STEAM Video\/Performance<\/h3>\n<p><strong>STEAM Video<\/strong><\/p>\n<p><strong>Carpenter or Joiner<\/strong><\/p>\n<p>Carpenters and joiners must be precise with their measurements when building structures. In what other real-life situations must measurements be precise?<br \/>\n<img decoding=\"async\" loading=\"lazy\" class=\"alignnone size-full wp-image-30193\" src=\"https:\/\/ccssanswers.com\/wp-content\/uploads\/2021\/01\/Big-Ideas-Math-Answers-Grade-7-Chapter-2-Multiplying-and-Dividing-Rational-Numbers-1.png\" alt=\"Big Ideas Math Answers Grade 7 Chapter 2 Multiplying and Dividing Rational Numbers 1\" width=\"219\" height=\"319\" srcset=\"https:\/\/ccssanswers.com\/wp-content\/uploads\/2021\/01\/Big-Ideas-Math-Answers-Grade-7-Chapter-2-Multiplying-and-Dividing-Rational-Numbers-1.png 219w, https:\/\/ccssanswers.com\/wp-content\/uploads\/2021\/01\/Big-Ideas-Math-Answers-Grade-7-Chapter-2-Multiplying-and-Dividing-Rational-Numbers-1-206x300.png 206w\" sizes=\"(max-width: 219px) 100vw, 219px\" \/><\/p>\n<p><strong>Watch the STEAM Video \u201cCarpenter or Joiner.\u201d Then answer the following questions.<\/strong><\/p>\n<p>Question 1.<br \/>\nRobert says that changes in water content cause wood to shrink or expand across the grain more than along the grain. What does this mean?<\/p>\n<p>Answer:<br \/>\nRobert says that changes in water content cause wood to expand across the grain. So, the carpenter has to make the measurements 1\/16 inches.<\/p>\n<p>Question 2.<br \/>\nDescribe how you can cut a log so that the pieces shrink in different ways as they dry out.<br \/>\n<img decoding=\"async\" loading=\"lazy\" class=\"alignnone size-full wp-image-30092\" src=\"https:\/\/ccssanswers.com\/wp-content\/uploads\/2021\/01\/Big-Ideas-Math-Answer-Key-Grade-7-Chapter-2-Multiplying-and-Dividing-Rational-Numbers-1.1.png\" alt=\"Big Ideas Math Answer Key Grade 7 Chapter 2 Multiplying and Dividing Rational Numbers 1.1\" width=\"228\" height=\"198\" \/><\/p>\n<p>Answer:<br \/>\nWhile cutting the log, you need to take the correct measurement to avoid the pieces shrink in different ways as they dry out.<\/p>\n<p><strong>Performance Task<\/strong><\/p>\n<p><strong>Precisely Perfect<\/strong><\/p>\n<p>After completing this chapter, you will be able to use the concepts you learned to answer the questions in the Video Performance Task. You will be given the accuracies of seven telescopes. For example:<br \/>\n<img decoding=\"async\" loading=\"lazy\" class=\"alignnone size-full wp-image-30093\" src=\"https:\/\/ccssanswers.com\/wp-content\/uploads\/2021\/01\/Big-Ideas-Math-Answer-Key-Grade-7-Chapter-2-Multiplying-and-Dividing-Rational-Numbers-2.png\" alt=\"Big Ideas Math Answer Key Grade 7 Chapter 2 Multiplying and Dividing Rational Numbers 2\" width=\"294\" height=\"145\" \/><br \/>\n<img decoding=\"async\" loading=\"lazy\" class=\"alignnone size-full wp-image-30094\" src=\"https:\/\/ccssanswers.com\/wp-content\/uploads\/2021\/01\/Big-Ideas-Math-Answer-Key-Grade-7-Chapter-2-Multiplying-and-Dividing-Rational-Numbers-3.png\" alt=\"Big Ideas Math Answer Key Grade 7 Chapter 2 Multiplying and Dividing Rational Numbers 3\" width=\"294\" height=\"369\" srcset=\"https:\/\/ccssanswers.com\/wp-content\/uploads\/2021\/01\/Big-Ideas-Math-Answer-Key-Grade-7-Chapter-2-Multiplying-and-Dividing-Rational-Numbers-3.png 294w, https:\/\/ccssanswers.com\/wp-content\/uploads\/2021\/01\/Big-Ideas-Math-Answer-Key-Grade-7-Chapter-2-Multiplying-and-Dividing-Rational-Numbers-3-239x300.png 239w\" sizes=\"(max-width: 294px) 100vw, 294px\" \/><br \/>\nYou will be asked to compare the accuracies of the telescopes. Why do different telescopes have different accuracies?<\/p>\n<h3><a id=\"Multiplying_and_Dividing_Rational_Numbers_Getting_Ready_for_Chapter_2\"><\/a>Multiplying and Dividing Rational Numbers Getting Ready for Chapter 2<\/h3>\n<p><strong>Chapter Exploration<\/strong><\/p>\n<p>Question 1.<br \/>\nWork with a partner. Use integer counters to \ufb01nd each product. <img decoding=\"async\" loading=\"lazy\" class=\"alignnone size-full wp-image-30103\" src=\"https:\/\/ccssanswers.com\/wp-content\/uploads\/2021\/01\/Big-Ideas-Math-Answer-Key-Grade-7-Chapter-2-Multiplying-and-Dividing-Rational-Numbers-4.png\" alt=\"Big Ideas Math Answer Key Grade 7 Chapter 2 Multiplying and Dividing Rational Numbers 4\" width=\"84\" height=\"72\" \/><br \/>\n<img decoding=\"async\" loading=\"lazy\" class=\"alignnone size-full wp-image-30095\" src=\"https:\/\/ccssanswers.com\/wp-content\/uploads\/2021\/01\/Big-Ideas-Math-Answer-Key-Grade-7-Chapter-2-Multiplying-and-Dividing-Rational-Numbers-4.1.png\" alt=\"Big Ideas Math Answer Key Grade 7 Chapter 2 Multiplying and Dividing Rational Numbers 4.1\" width=\"614\" height=\"385\" srcset=\"https:\/\/ccssanswers.com\/wp-content\/uploads\/2021\/01\/Big-Ideas-Math-Answer-Key-Grade-7-Chapter-2-Multiplying-and-Dividing-Rational-Numbers-4.1.png 614w, https:\/\/ccssanswers.com\/wp-content\/uploads\/2021\/01\/Big-Ideas-Math-Answer-Key-Grade-7-Chapter-2-Multiplying-and-Dividing-Rational-Numbers-4.1-300x188.png 300w\" sizes=\"(max-width: 614px) 100vw, 614px\" \/><\/p>\n<p>Work with a partner. Use integer counters to \ufb01nd the product.<\/p>\n<p>Answer:<br \/>\n<img decoding=\"async\" loading=\"lazy\" class=\"alignnone size-full wp-image-40486\" src=\"https:\/\/ccssanswers.com\/wp-content\/uploads\/2021\/01\/big-ideas-math-answers-grade-7-chapter-2-multiplying-and-dividing-rational-numbers-1.jpg\" alt=\"Big Ideas Math Answers Grade 7 Chapter 2 Multiplying and Dividing Rational Numbers 1\" width=\"758\" height=\"515\" srcset=\"https:\/\/ccssanswers.com\/wp-content\/uploads\/2021\/01\/big-ideas-math-answers-grade-7-chapter-2-multiplying-and-dividing-rational-numbers-1.jpg 758w, https:\/\/ccssanswers.com\/wp-content\/uploads\/2021\/01\/big-ideas-math-answers-grade-7-chapter-2-multiplying-and-dividing-rational-numbers-1-300x204.jpg 300w\" sizes=\"(max-width: 758px) 100vw, 758px\" \/><\/p>\n<p>Explanation:<br \/>\na. (+3) x (-2) = -6<br \/>\nThe integers have different signs, so the product is a negative value.<br \/>\nb. (-2) x (-2) = 4<br \/>\nThe integers have the same sign, so the product is a positive value.<br \/>\nc. (-2) x (+3) = -6<\/p>\n<p>Question 2.<br \/>\n(+3) \u00d7 (+2)<\/p>\n<p>Answer:<br \/>\n(+3) x (+2) = +6<\/p>\n<p>Explanation:<br \/>\nThe given expression is (+3) x (+2)<br \/>\nThe integers have the same sign. So the product is a positive value.<br \/>\n(+3) x (+2) = +6<\/p>\n<p>Question 3.<br \/>\n(+3) \u00d7 (-1)<\/p>\n<p>Answer:<br \/>\n(+3) \u00d7 (-1) = -3<\/p>\n<p>Explanation:<br \/>\nThe given expression is (+3) \u00d7 (-1)<br \/>\nThe integers have different signs. So the product is a negative value.<br \/>\n(+3) \u00d7 (-1) = -3<\/p>\n<p>Question 4.<br \/>\n(+2) \u00d7 (-4)<\/p>\n<p>Answer:<br \/>\n(+2) \u00d7 (-4) = -8<\/p>\n<p>Explanation:<br \/>\nThe given expression is (+2) \u00d7 (-4)<br \/>\nThe integers have different signs. So the product is a negative value.<br \/>\n(+2) \u00d7 (-4) =-8<\/p>\n<p>Question 5.<br \/>\n(-3) \u00d7 (+2)<\/p>\n<p>Answer:<br \/>\n(-3) \u00d7 (+2) = -6<\/p>\n<p>Explanation:<br \/>\nThe given expression is<br \/>\nThe integers have different signs. So the product is a negative value.<br \/>\n(-3) \u00d7 (+2) = -6<\/p>\n<p>Question 6.<br \/>\n(-2) \u00d7 (-3)<\/p>\n<p>Answer:<br \/>\n(-2) \u00d7 (-3) = +6<\/p>\n<p>Explanation:<br \/>\nThe given expression is (-2) \u00d7 (-3)<br \/>\nThe integers have the same sign. So the product is a positive value.<br \/>\n(-2) \u00d7 (-3) = +6<\/p>\n<p>Question 7.<br \/>\n(-1) \u00d7 (-4)<\/p>\n<p>Answer:<br \/>\n(-1) \u00d7 (-4) = +4<\/p>\n<p>Explanation:<br \/>\nThe given expression is (-1) \u00d7 (-4)<br \/>\nThe integers have the same sign. So the product is a positive value.<br \/>\n(-1) \u00d7 (-4) = +4<\/p>\n<p>Question 8.<br \/>\n(-1) \u00d7 (-2)<\/p>\n<p>Answer:<br \/>\n(-1) \u00d7 (-2) = +2<\/p>\n<p>Explanation:<br \/>\nThe given expression is (-1) \u00d7 (-2)<br \/>\nThe integers have the same sign. So the product is a positive value.<br \/>\n(-1) \u00d7 (-2) = +2<\/p>\n<p>Question 9.<br \/>\n(+3) \u00d7 (+1)<\/p>\n<p>Answer:<br \/>\n(+3) \u00d7 (+1) = 3<\/p>\n<p>Explanation:<br \/>\nThe given expression is (+3) \u00d7 (+1) = 3<br \/>\nThe integers have the same sign. So the product is a positive value.<br \/>\n(+3) \u00d7 (+1) = 3<\/p>\n<p>Question 10.<br \/>\n(-3) \u00d7 (-2)<\/p>\n<p>Answer:<br \/>\n(-3) \u00d7 (-2) = +6<\/p>\n<p>Explanation:<br \/>\nThe given expression is (-3) \u00d7 (-2)<br \/>\nThe integers have the same sign. So the product is a positive value.<br \/>\n(-3) \u00d7 (-2) = +6<\/p>\n<p>Question 11.<br \/>\n(-2) \u00d7 (+2)<\/p>\n<p>Answer:<br \/>\n(-2) \u00d7 (+2) = -4<\/p>\n<p>Explanation:<br \/>\nThe given expression is (-2) \u00d7 (+2)<br \/>\nThe integers have different signs. So the product is a negative value.<br \/>\n(-2) \u00d7 (+2) = -4<\/p>\n<p>Question 12.<br \/>\n(-2) \u00d7 (+4)<\/p>\n<p>Answer:<br \/>\n(-2) \u00d7 (+4) = -8<\/p>\n<p>Explanation:<br \/>\nThe given expression is (-2) \u00d7 (+4)<br \/>\nThe integers have different signs. So the product is a negative value.<br \/>\n(-2) \u00d7 (+4) = -8<\/p>\n<p>Question 13.<br \/>\n(-4) \u00d7 (-2)<\/p>\n<p>Answer:<br \/>\n(-4) \u00d7 (-2) = +8<\/p>\n<p>Explanation:<br \/>\nThe given expression is (-4) \u00d7 (-2)<br \/>\nThe integers have the same sign. So the product is a positive value.<br \/>\n(-4) \u00d7 (-2) = +8<\/p>\n<p>Question 14.<br \/>\n<strong>MAKE A CONJECTURE<\/strong><br \/>\nUse your results in Exercises 1\u201313 to determine the sign of each product.<br \/>\na. negative integer and a positive integer<br \/>\nb. two negative integers<br \/>\nc. two positive integers<\/p>\n<p>Answer:<br \/>\na. When you multiply a negative integer and a positive integer, the product is a negative integer.<br \/>\nb. When you multiply two negative integers, then the product is a positive integer.<br \/>\nc. If you multiply two positive integers, then the product is a positive integer.<\/p>\n<p>Explanation:<br \/>\na. negative integer and a positive integer<br \/>\nWhen you multiply a negative integer and a positive integer, the product is a negative integer.<br \/>\nb. two negative integers<br \/>\nWhen you multiply two negative integers, then the product is a positive integer.<br \/>\nc. two positive integers<br \/>\nIf you multiply two positive integers, then the product is a positive integer.<\/p>\n<p><strong>Vocabulary<\/strong><\/p>\n<p>The following vocabulary terms are de\ufb01ned in this chapter. Think about what each term might mean and record your thoughts.<br \/>\n<img decoding=\"async\" loading=\"lazy\" class=\"alignnone size-full wp-image-30096\" src=\"https:\/\/ccssanswers.com\/wp-content\/uploads\/2021\/01\/Big-Ideas-Math-Answer-Key-Grade-7-Chapter-2-Multiplying-and-Dividing-Rational-Numbers-4.2.png\" alt=\"Big Ideas Math Answer Key Grade 7 Chapter 2 Multiplying and Dividing Rational Numbers 4.2\" width=\"523\" height=\"35\" srcset=\"https:\/\/ccssanswers.com\/wp-content\/uploads\/2021\/01\/Big-Ideas-Math-Answer-Key-Grade-7-Chapter-2-Multiplying-and-Dividing-Rational-Numbers-4.2.png 523w, https:\/\/ccssanswers.com\/wp-content\/uploads\/2021\/01\/Big-Ideas-Math-Answer-Key-Grade-7-Chapter-2-Multiplying-and-Dividing-Rational-Numbers-4.2-300x20.png 300w\" sizes=\"(max-width: 523px) 100vw, 523px\" \/><\/p>\n<h3><a id=\"Lesson_2.1_Multiplying_Integers\"><\/a>Lesson 2.1 Multiplying Integers<\/h3>\n<p><strong>EXPLORATION 1<\/strong><br \/>\n<strong>Understanding Products Involving Negative Integers<\/strong><br \/>\n<strong>Work with a partner.<\/strong><br \/>\na. The number line and integer counters model the product 3 \u2022 2. How can you \ufb01nd 3 \u2022 (-2)? Explain.<br \/>\n<img decoding=\"async\" loading=\"lazy\" class=\"alignnone size-full wp-image-30097\" src=\"https:\/\/ccssanswers.com\/wp-content\/uploads\/2021\/01\/Big-Ideas-Math-Answer-Key-Grade-7-Chapter-2-Multiplying-and-Dividing-Rational-Numbers-4.3.png\" alt=\"Big Ideas Math Answer Key Grade 7 Chapter 2 Multiplying and Dividing Rational Numbers 4.3\" width=\"131\" height=\"89\" \/><br \/>\n<img decoding=\"async\" loading=\"lazy\" class=\"alignnone size-full wp-image-30098\" src=\"https:\/\/ccssanswers.com\/wp-content\/uploads\/2021\/01\/Big-Ideas-Math-Answer-Key-Grade-7-Chapter-2-Multiplying-and-Dividing-Rational-Numbers-4.4.png\" alt=\"Big Ideas Math Answer Key Grade 7 Chapter 2 Multiplying and Dividing Rational Numbers 4.4\" width=\"334\" height=\"76\" srcset=\"https:\/\/ccssanswers.com\/wp-content\/uploads\/2021\/01\/Big-Ideas-Math-Answer-Key-Grade-7-Chapter-2-Multiplying-and-Dividing-Rational-Numbers-4.4.png 334w, https:\/\/ccssanswers.com\/wp-content\/uploads\/2021\/01\/Big-Ideas-Math-Answer-Key-Grade-7-Chapter-2-Multiplying-and-Dividing-Rational-Numbers-4.4-300x68.png 300w\" sizes=\"(max-width: 334px) 100vw, 334px\" \/><br \/>\nb. Use the tables to \ufb01nd -3 \u2022 2 and -3 \u2022 (-2). Explain your reasoning.<br \/>\n<img decoding=\"async\" loading=\"lazy\" class=\"alignnone size-full wp-image-30099\" src=\"https:\/\/ccssanswers.com\/wp-content\/uploads\/2021\/01\/Big-Ideas-Math-Answer-Key-Grade-7-Chapter-2-Multiplying-and-Dividing-Rational-Numbers-4.5.png\" alt=\"Big Ideas Math Answer Key Grade 7 Chapter 2 Multiplying and Dividing Rational Numbers 4.5\" width=\"470\" height=\"187\" srcset=\"https:\/\/ccssanswers.com\/wp-content\/uploads\/2021\/01\/Big-Ideas-Math-Answer-Key-Grade-7-Chapter-2-Multiplying-and-Dividing-Rational-Numbers-4.5.png 470w, https:\/\/ccssanswers.com\/wp-content\/uploads\/2021\/01\/Big-Ideas-Math-Answer-Key-Grade-7-Chapter-2-Multiplying-and-Dividing-Rational-Numbers-4.5-300x119.png 300w\" sizes=\"(max-width: 470px) 100vw, 470px\" \/><br \/>\nc.<br \/>\n<strong>INDUCTIVE REASONING<\/strong><br \/>\nComplete the table. Then write general rules for multiplying<\/p>\n<ol>\n<li>two integers with the same sign and<\/li>\n<li>two integers with different signs.<\/li>\n<\/ol>\n<p><img decoding=\"async\" loading=\"lazy\" class=\"alignnone size-full wp-image-30100\" src=\"https:\/\/ccssanswers.com\/wp-content\/uploads\/2021\/01\/Big-Ideas-Math-Answer-Key-Grade-7-Chapter-2-Multiplying-and-Dividing-Rational-Numbers-4.6.png\" alt=\"Big Ideas Math Answer Key Grade 7 Chapter 2 Multiplying and Dividing Rational Numbers 4.6\" width=\"719\" height=\"320\" srcset=\"https:\/\/ccssanswers.com\/wp-content\/uploads\/2021\/01\/Big-Ideas-Math-Answer-Key-Grade-7-Chapter-2-Multiplying-and-Dividing-Rational-Numbers-4.6.png 719w, https:\/\/ccssanswers.com\/wp-content\/uploads\/2021\/01\/Big-Ideas-Math-Answer-Key-Grade-7-Chapter-2-Multiplying-and-Dividing-Rational-Numbers-4.6-300x134.png 300w\" sizes=\"(max-width: 719px) 100vw, 719px\" \/><\/p>\n<p>Answer:<br \/>\na. 3 . 2 = 6<br \/>\n3 . (-2) = -6<br \/>\nb. <img decoding=\"async\" loading=\"lazy\" class=\"alignnone size-full wp-image-40799\" src=\"https:\/\/ccssanswers.com\/wp-content\/uploads\/2021\/01\/big-ideas-math-answers-grade-7-chapter-2-multiplying-and-dividing-rational-numbers-2.jpg\" alt=\"Big Ideas Math Answers Grade 7 Chapter 2 Multiplying and Dividing Rational Numbers 2\" width=\"462\" height=\"178\" srcset=\"https:\/\/ccssanswers.com\/wp-content\/uploads\/2021\/01\/big-ideas-math-answers-grade-7-chapter-2-multiplying-and-dividing-rational-numbers-2.jpg 462w, https:\/\/ccssanswers.com\/wp-content\/uploads\/2021\/01\/big-ideas-math-answers-grade-7-chapter-2-multiplying-and-dividing-rational-numbers-2-300x116.jpg 300w\" sizes=\"(max-width: 462px) 100vw, 462px\" \/><br \/>\nc. <img decoding=\"async\" loading=\"lazy\" class=\"alignnone size-full wp-image-40923\" src=\"https:\/\/ccssanswers.com\/wp-content\/uploads\/2021\/01\/big-ideas-math-answers-grade-7-chapter-2-multiplying-and-dividing-rational-numbers-3.jpg\" alt=\"Big Ideas Math Answers Grade 7 Chapter 2 Multiplying and Dividing Rational Numbers 3\" width=\"641\" height=\"389\" srcset=\"https:\/\/ccssanswers.com\/wp-content\/uploads\/2021\/01\/big-ideas-math-answers-grade-7-chapter-2-multiplying-and-dividing-rational-numbers-3.jpg 641w, https:\/\/ccssanswers.com\/wp-content\/uploads\/2021\/01\/big-ideas-math-answers-grade-7-chapter-2-multiplying-and-dividing-rational-numbers-3-300x182.jpg 300w\" sizes=\"(max-width: 641px) 100vw, 641px\" \/><\/p>\n<p>Explanation:<br \/>\na. The product of 3 and 2 is 6<br \/>\nBoth the integers are positive. So, the product is also positive.<br \/>\n3 . (-2) = -6<br \/>\nThe reason is one integer is positive and another integer is negative. So, the result is negative.<br \/>\nb. The product of two positive or negative integers is a positive integer. The product of one positive and second negative integers is a negative integer.<br \/>\nc. In any expression, integers are having the same sign, which means the product is positive. If the integers are having a different sign, then the product is negative.<\/p>\n<p><strong>2.1 Lesson<\/strong><\/p>\n<p><strong>Try It<\/strong><\/p>\n<p><strong>Find the product.<\/strong><\/p>\n<p>Question 1.<br \/>\n5 \u2022 5<\/p>\n<p>Answer:<br \/>\n5 . 5 = 25<\/p>\n<p>Explanation:<br \/>\nThe given expression is 5 . 5<br \/>\nThe given integers have the same sign. So the product is a positive integer.<br \/>\n5 . 5 = 25<\/p>\n<p>Question 2.<br \/>\n-1(-9)<\/p>\n<p>Answer:<br \/>\n-1(-9) = +9<\/p>\n<p>Explanation:<br \/>\nThe given expression is -1(-9)<br \/>\nThe given integers have the same sign. So the product is a positive integer.<br \/>\n-1(-9) = +9<\/p>\n<p>Question 3.<br \/>\n-7 \u2022 (-8)<\/p>\n<p>Answer:<br \/>\n-7 \u2022 (-8) = 56<\/p>\n<p>Explanation:<br \/>\nThe given expression is -7 \u2022 (-8)<br \/>\nThe given integers have the same sign. So the product is a positive integer.<br \/>\n-7 \u2022 (-8) = 56<\/p>\n<p>Question 4.<br \/>\n12 \u2022 (-2)<\/p>\n<p>Answer:<br \/>\n12 \u2022 (-2) = -24<\/p>\n<p>Explanation:<br \/>\nThe given integers are 12, -2<br \/>\nIntegers have different signs. So, the product is a negative integer.<br \/>\n12 \u2022 (-2) = -24<\/p>\n<p>Question 5.<br \/>\n4(-6)<\/p>\n<p>Answer:<br \/>\n4(-6) = -24<\/p>\n<p>Explanation:<br \/>\nThe given integers are 4, -6<br \/>\nIntegers have different signs. So, the product is a negative integer.<br \/>\n4(-6) = -24<\/p>\n<p>Question 6.<br \/>\n-25(0)<\/p>\n<p>Answer:<br \/>\n-25(0) = 0<\/p>\n<p>Explanation:<br \/>\nThe given integers are -25, 0<br \/>\nIntegers have different signs. So, the product is a negative integer.<br \/>\n-25(0) = 0<br \/>\nWhen you multiply any number with zero, the product is also zero.<\/p>\n<p><strong>Try It<\/strong><\/p>\n<p><strong>Evaluate the expression.<\/strong><\/p>\n<p>Question 7.<br \/>\n8 \u2022 (-15) \u2022 0<\/p>\n<p>Answer:<br \/>\n8 \u2022 (-15) \u2022 0 = 0<\/p>\n<p>Explanation:<br \/>\nThe given expression is 8 \u2022 (-15) \u2022 0<br \/>\nUse the commutative property of the multiplication<br \/>\n= -120 . 0<br \/>\n= 0<\/p>\n<p>Question 8.<br \/>\n24 &#8211; 3<sup>3<\/sup><\/p>\n<p>Answer:<br \/>\n24 &#8211; 3\u00b3 = -3<\/p>\n<p>Explanation:<br \/>\nThe given expression is 24 &#8211; 3\u00b3<br \/>\nWrite 3\u00b3 as a repeated multiplication<br \/>\n= 24 &#8211; (3 . 3 . 3)<br \/>\n= 24 &#8211; 27<br \/>\n= -3<\/p>\n<p>Question 9.<br \/>\n10 &#8211; 7(3 &#8211; 5)<\/p>\n<p>Answer:<br \/>\n10 &#8211; 7(3 &#8211; 5) = 24<\/p>\n<p>Explanation:<br \/>\nThe given expression is 10 &#8211; 7(3 &#8211; 5)<br \/>\nPerform the operations in the parenthesis<br \/>\n= 10 &#8211; 7(-2)<br \/>\n= 10 + 14<br \/>\n= 24<\/p>\n<p><strong>Self-Assessment for Concepts &amp; Skills<\/strong><\/p>\n<p>Solve each exercise. Then rate your understanding of the success criteria in your journal.<\/p>\n<p>Question 10.<br \/>\n<strong>WRITING<\/strong><br \/>\nWhat can you conclude about two integers whose product is (a) positive and (b) negative?<\/p>\n<p>Answer:<br \/>\nIf the product of two integers is positive, then those integers are with the same sign. If the product of two integers is negative, then those integers are having different signs.<\/p>\n<p>Explanation:<br \/>\nThe two integers product is a positive integer means those integers are with two positive signs or two negative signs.<br \/>\nFor example 4 . 2 = 8, (-4) . (-2) = 8<br \/>\nThe two integers is a negative integer means those are having one positive integer and negative integer irrespective of the order.<br \/>\nExamples are -4 . 2 = -8, 4 . -2 = -8<\/p>\n<p><strong>EVALUATING AN EXPRESSION<\/strong><br \/>\n<strong>Evaluate the expression.<\/strong><\/p>\n<p>Question 11.<br \/>\n4(-8)<\/p>\n<p>Answer:<br \/>\n4(-8) = -32<\/p>\n<p>Explanation:<br \/>\nThe given expression is 4(-8)<br \/>\nHere integers are having different signs. So the product is a negative integer.<br \/>\n4(-8) = -32<\/p>\n<p>Question 12.<br \/>\n-5(-7)<\/p>\n<p>Answer:<br \/>\n-5(-7) = 35<\/p>\n<p>Explanation:<br \/>\nThe given expression is -5(-7)<br \/>\nThe product of two integers with the same sign is positive.<br \/>\n-5(-7) = 35<\/p>\n<p>Question 13.<br \/>\n12 &#8211; 3<sup>2<\/sup> \u2022 (-2)<\/p>\n<p>Answer:<br \/>\n12 &#8211; 3\u00b2 \u2022 (-2) = 30<\/p>\n<p>Explanation:<br \/>\nThe given expression is 12 &#8211; 3\u00b2 \u2022 (-2)<br \/>\nWrite 3\u00b2 as a repeated multiplication<br \/>\n= 12 &#8211; (3 . 3) . (-2)<br \/>\n= 12 &#8211; 9 . (-2)<br \/>\nThe product of two integers with the same sign is positive.<br \/>\n= 12 + 18<br \/>\n= 30<\/p>\n<p><strong>REASONING<\/strong><br \/>\n<strong>Tell whether the statement is true or false. Explain your reasoning.<\/strong><\/p>\n<p>Question 14.<br \/>\nThe product of three positive integers is positive.<\/p>\n<p>Answer:<br \/>\nTrue<\/p>\n<p>Explanation:<br \/>\nThe product of three positive integers is positive The reason is the product of two positive integers is positive. Again perform the product of an obtained positive integer with the third positive integer to get a positive integer.<\/p>\n<p>Question 15.<br \/>\nThe product of three negative integers is positive.<\/p>\n<p>Answer:<br \/>\nFalse<\/p>\n<p>Explanation:<br \/>\nThe product of three negative integers is always a negative integer. Because the product of two negative integers is a positive integer. The product of obtained positive integer and remaining negative integer is a negative integer. So, the product of three integers is not positive.<\/p>\n<p><strong>Self-Assessment for Problem Solving<\/strong><\/p>\n<p>Solve each exercise. Then rate your understanding of the success criteria in your journal.<\/p>\n<p>Question 16.<br \/>\nOn a mountain, the temperature decreases by 18\u00b0F for each 5000-foot increase in elevation. At 7000 feet, the temperature is 41\u00b0F. What is the temperature at 22,000 feet? Justify your answer.<\/p>\n<p>Answer:<br \/>\nThe temperature at 22,000 feet is 95\u00b0F<\/p>\n<p>Explanation:<br \/>\nChange in temperature over 5000 feet = 18\u00b0F<br \/>\nThe temperature at 7000 feet = 41\u00b0F<br \/>\nThe temperature at 22000 feet = 7000 + 5000x<br \/>\n22000 &#8211; 7000 = 5000x<br \/>\n15000 = 5000x<br \/>\nx = 15000\/5000<br \/>\nx = 3<br \/>\nSo, the temperature at 22000 feet is 41 + 3(18)<br \/>\n= 41 + 54 = 95\u00b0F<\/p>\n<p>Question 17.<br \/>\nPlayers in a racing game earn 3 points for each coin they collect. Each player loses 5 points for each second that he or she \ufb01nishes after the \ufb01rst-place \ufb01nisher. The table shows the results of a race. List the players in order from greatest to least number of points.<br \/>\n<img decoding=\"async\" loading=\"lazy\" class=\"alignnone size-full wp-image-30101\" src=\"https:\/\/ccssanswers.com\/wp-content\/uploads\/2021\/01\/Big-Ideas-Math-Answer-Key-Grade-7-Chapter-2-Multiplying-and-Dividing-Rational-Numbers-4.7.png\" alt=\"Big Ideas Math Answer Key Grade 7 Chapter 2 Multiplying and Dividing Rational Numbers 4.7\" width=\"229\" height=\"119\" \/><br \/>\n<img decoding=\"async\" loading=\"lazy\" class=\"alignnone size-full wp-image-30102\" src=\"https:\/\/ccssanswers.com\/wp-content\/uploads\/2021\/01\/Big-Ideas-Math-Answer-Key-Grade-7-Chapter-2-Multiplying-and-Dividing-Rational-Numbers-4.8.png\" alt=\"Big Ideas Math Answer Key Grade 7 Chapter 2 Multiplying and Dividing Rational Numbers 4.8\" width=\"201\" height=\"170\" \/><\/p>\n<p>Answer:<br \/>\nPlayer 3, Player 2, Player 1, Player 4.<\/p>\n<p>Explanation:<br \/>\nPlayers in a racing game earn 3 points for each coin they collect.<br \/>\nThe number of coins earned by the players are listed here.<br \/>\nPlayer 2 = 18 x 3 = 54 points<br \/>\nPlayer 3 takes 3 seconds more than player 2 to finish the game.<br \/>\nSo, player 3 number of points = (24 . 3) &#8211; (5 . 3) = 72 &#8211; 15 = 57<br \/>\nPlayer 4 takes 6 seconds more than player 2 to finish the game.<br \/>\nSo, the number of points earned by player 4 = (27 . 3) &#8211; (5 . 6)<br \/>\n= 81 &#8211; 30 = 51<br \/>\nPlayer 1 takes 8 seconds more than player 2 to finish the game.<br \/>\nSo, the number of points earned by player 1 = (31 . 3) &#8211; (5 . 8)<br \/>\n= 93 &#8211; 40 = 53<br \/>\nHence, the number of coins earned by the players are Player 3 = 57, Player 2 = 53, Player 1 = 53, Player 4 = 51<\/p>\n<h3><a id=\"Multiplying_Integers_Homework_&amp;_Practice_2.1\"><\/a>Multiplying Integers Homework &amp; Practice 2.1<\/h3>\n<p><strong>Review &amp; Refresh<\/strong><\/p>\n<p><strong>Find the distance between the two numbers on a number line.<\/strong><\/p>\n<p>Question 1.<br \/>\n-4.3 and 0.8<\/p>\n<p>Answer:<br \/>\n5.1<\/p>\n<p>Explanation:<br \/>\nThe distance between -4.3 and 0.8 = | 0.8 &#8211; (-4.3) |<br \/>\n= | 0.8 + 4.3 | = | 5.1 |<br \/>\n<img decoding=\"async\" loading=\"lazy\" class=\"alignnone size-full wp-image-40940\" src=\"https:\/\/ccssanswers.com\/wp-content\/uploads\/2021\/01\/big-ideas-math-answers-grade-7-chapter-2-multiplying-and-dividing-rational-numbers-4.jpg\" alt=\"Big Ideas Math Answers Grade 7 Chapter 2 Multiplying and Dividing Rational Numbers4\" width=\"542\" height=\"72\" srcset=\"https:\/\/ccssanswers.com\/wp-content\/uploads\/2021\/01\/big-ideas-math-answers-grade-7-chapter-2-multiplying-and-dividing-rational-numbers-4.jpg 542w, https:\/\/ccssanswers.com\/wp-content\/uploads\/2021\/01\/big-ideas-math-answers-grade-7-chapter-2-multiplying-and-dividing-rational-numbers-4-300x40.jpg 300w\" sizes=\"(max-width: 542px) 100vw, 542px\" \/><\/p>\n<p>Question 2.<br \/>\n-7.7 and -6.4<\/p>\n<p>Answer:<br \/>\n1.3<\/p>\n<p>Explanation:<br \/>\nThe distance between -7.7 and -6.4 = | -6.4 &#8211; (-7.7) |<br \/>\n= | -6.4 + 7.7 | = | 1.3 |<br \/>\n<img decoding=\"async\" loading=\"lazy\" class=\"alignnone size-full wp-image-40941\" src=\"https:\/\/ccssanswers.com\/wp-content\/uploads\/2021\/01\/big-ideas-math-answers-grade-7-chapter-2-multiplying-and-dividing-rational-numbers-5.jpg\" alt=\"Big Ideas Math Answers Grade 7 Chapter 2 Multiplying and Dividing Rational Numbers 5\" width=\"549\" height=\"77\" srcset=\"https:\/\/ccssanswers.com\/wp-content\/uploads\/2021\/01\/big-ideas-math-answers-grade-7-chapter-2-multiplying-and-dividing-rational-numbers-5.jpg 549w, https:\/\/ccssanswers.com\/wp-content\/uploads\/2021\/01\/big-ideas-math-answers-grade-7-chapter-2-multiplying-and-dividing-rational-numbers-5-300x42.jpg 300w\" sizes=\"(max-width: 549px) 100vw, 549px\" \/><\/p>\n<p>Question 3.<br \/>\n-2\\(\\frac{3}{5}\\) and -1<\/p>\n<p>Answer:<br \/>\n3.6<\/p>\n<p>Explanation:<br \/>\nThe distance between -2(3\/5) or -13\/5 and 1 = | 1 &#8211; (-13\/5) |<br \/>\n= | 1 + 13\/5 | = | (5 + 13)\/5 |<br \/>\n= | 18\/5 | = | 3.6 |<br \/>\n<img decoding=\"async\" loading=\"lazy\" class=\"alignnone size-full wp-image-40943\" src=\"https:\/\/ccssanswers.com\/wp-content\/uploads\/2021\/01\/big-ideas-math-answers-grade-7-chapter-2-multiplying-and-dividing-rational-numbers-6.jpg\" alt=\"Big Ideas Math Answers Grade 7 Chapter 2 Multiplying and Dividing Rational Numbers 6\" width=\"551\" height=\"86\" srcset=\"https:\/\/ccssanswers.com\/wp-content\/uploads\/2021\/01\/big-ideas-math-answers-grade-7-chapter-2-multiplying-and-dividing-rational-numbers-6.jpg 551w, https:\/\/ccssanswers.com\/wp-content\/uploads\/2021\/01\/big-ideas-math-answers-grade-7-chapter-2-multiplying-and-dividing-rational-numbers-6-300x47.jpg 300w\" sizes=\"(max-width: 551px) 100vw, 551px\" \/><\/p>\n<p><strong>Divide.<\/strong><\/p>\n<p>Question 4.<br \/>\n27 \u00f7 9<\/p>\n<p>Answer:<br \/>\n27 \u00f7 9 = 3<\/p>\n<p>Explanation:<br \/>\n<img decoding=\"async\" loading=\"lazy\" class=\"alignnone size-full wp-image-40946\" src=\"https:\/\/ccssanswers.com\/wp-content\/uploads\/2021\/01\/big-ideas-math-answers-grade-7-chapter-2-multiplying-and-dividing-rational-numbers-7.jpg\" alt=\"Big Ideas Math Answers Grade 7 Chapter 2 Multiplying and Dividing Rational Numbers 7\" width=\"105\" height=\"268\" \/><\/p>\n<p>Question 5.<br \/>\n48 \u00f7 6<\/p>\n<p>Answer:<br \/>\n48 \u00f7 6 = 8<\/p>\n<p>Explanation:<br \/>\n<img decoding=\"async\" loading=\"lazy\" class=\"alignnone size-full wp-image-40947\" src=\"https:\/\/ccssanswers.com\/wp-content\/uploads\/2021\/01\/big-ideas-math-answers-grade-7-chapter-2-multiplying-and-dividing-rational-numbers-8.jpg\" alt=\"Big Ideas Math Answers Grade 7 Chapter 2 Multiplying and Dividing Rational Numbers 8\" width=\"100\" height=\"255\" \/><\/p>\n<p>Question 6.<br \/>\n56 \u00f7 4<\/p>\n<p>Answer:<br \/>\n56 \u00f7 4 = 14<\/p>\n<p>Explanation:<br \/>\n<img decoding=\"async\" loading=\"lazy\" class=\"alignnone size-full wp-image-40949\" src=\"https:\/\/ccssanswers.com\/wp-content\/uploads\/2021\/01\/big-ideas-math-answers-grade-7-chapter-2-multiplying-and-dividing-rational-numbers-9.jpg\" alt=\"Big Ideas Math Answers Grade 7 Chapter 2 Multiplying and Dividing Rational Numbers 9\" width=\"100\" height=\"258\" \/><\/p>\n<p>Question 7.<br \/>\n153 \u00f7 8<\/p>\n<p>Answer:<br \/>\n153 \u00f7 8 = 19 R 1<\/p>\n<p>Explanation:<br \/>\n<img decoding=\"async\" loading=\"lazy\" class=\"alignnone size-full wp-image-40950\" src=\"https:\/\/ccssanswers.com\/wp-content\/uploads\/2021\/01\/big-ideas-math-answers-grade-7-chapter-2-multiplying-and-dividing-rational-numbers10.jpg\" alt=\"Big Ideas Math Answers Grade 7 Chapter 2 Multiplying and Dividing Rational Numbers 10\" width=\"131\" height=\"344\" srcset=\"https:\/\/ccssanswers.com\/wp-content\/uploads\/2021\/01\/big-ideas-math-answers-grade-7-chapter-2-multiplying-and-dividing-rational-numbers10.jpg 131w, https:\/\/ccssanswers.com\/wp-content\/uploads\/2021\/01\/big-ideas-math-answers-grade-7-chapter-2-multiplying-and-dividing-rational-numbers10-114x300.jpg 114w\" sizes=\"(max-width: 131px) 100vw, 131px\" \/><\/p>\n<p>Question 8.<br \/>\nWhat is the prime factorization of 84?<br \/>\nA. 2<sup>2<\/sup> \u00d7 3<sup>2<\/sup><br \/>\nB. 2<sup>3<\/sup> \u00d7 7<br \/>\nC. 3<sup>3<\/sup> \u00d7 7<br \/>\nD. 2<sup>2<\/sup> \u00d7 3 \u00d7 7<\/p>\n<p>Answer:<br \/>\nD. 2\u00b2 x 3 x 7<\/p>\n<p>Explanation:<br \/>\nDivide 84 by 2<br \/>\n84\/2 = 42<br \/>\nDivide 42 by 2<br \/>\n42\/2 = 21<br \/>\ndivide 21 by 3<br \/>\n21\/3 = 7<br \/>\nDivide 7 by 7<br \/>\n7\/7 = 1<br \/>\nSo, the prime factorization of 84 is 2 x 2 x 3 x 7 = 2\u00b2 x 3 x 7<\/p>\n<p><strong>Concepts, Skills, &amp; Problem Solving<br \/>\n<\/strong><strong>CHOOSE TOOLS<\/strong><br \/>\n<strong>Use a number line or integer counters to \ufb01nd the product.<\/strong> (See Exploration 1, p. 49.)<\/p>\n<p>Question 9.<br \/>\n2(-4)<\/p>\n<p>Answer:<br \/>\n2(-4) = -8<\/p>\n<p>Explanation:<br \/>\n2 . -4<br \/>\n<img decoding=\"async\" loading=\"lazy\" class=\"alignnone size-full wp-image-40978\" src=\"https:\/\/ccssanswers.com\/wp-content\/uploads\/2021\/01\/big-ideas-math-answers-grade-7-chapter-2-multiplying-and-dividing-rational-numbers-11.jpg\" alt=\"Big Ideas Math Answers Grade 7 Chapter 2 Multiplying and Dividing Rational Numbers 11\" width=\"524\" height=\"96\" srcset=\"https:\/\/ccssanswers.com\/wp-content\/uploads\/2021\/01\/big-ideas-math-answers-grade-7-chapter-2-multiplying-and-dividing-rational-numbers-11.jpg 524w, https:\/\/ccssanswers.com\/wp-content\/uploads\/2021\/01\/big-ideas-math-answers-grade-7-chapter-2-multiplying-and-dividing-rational-numbers-11-300x55.jpg 300w\" sizes=\"(max-width: 524px) 100vw, 524px\" \/><\/p>\n<p>Question 10.<br \/>\n-6(3) = -18<\/p>\n<p>Answer:<br \/>\n-6(3)<\/p>\n<p>Explanation:<br \/>\n-6. 3<br \/>\n<img decoding=\"async\" loading=\"lazy\" class=\"alignnone size-full wp-image-40980\" src=\"https:\/\/ccssanswers.com\/wp-content\/uploads\/2021\/01\/big-ideas-math-answers-grade-7-chapter-2-multiplying-and-dividing-rational-numbers-12.jpg\" alt=\"Big Ideas Math Answers Grade 7 Chapter 2 Multiplying and Dividing Rational Numbers 12\" width=\"540\" height=\"102\" srcset=\"https:\/\/ccssanswers.com\/wp-content\/uploads\/2021\/01\/big-ideas-math-answers-grade-7-chapter-2-multiplying-and-dividing-rational-numbers-12.jpg 540w, https:\/\/ccssanswers.com\/wp-content\/uploads\/2021\/01\/big-ideas-math-answers-grade-7-chapter-2-multiplying-and-dividing-rational-numbers-12-300x57.jpg 300w\" sizes=\"(max-width: 540px) 100vw, 540px\" \/><\/p>\n<p>Question 11.<br \/>\n4(-5)<\/p>\n<p>Answer:<br \/>\n4(-5) = -20<\/p>\n<p>Explanation:<br \/>\n4(-5)<br \/>\n<img decoding=\"async\" loading=\"lazy\" class=\"alignnone size-full wp-image-40981\" src=\"https:\/\/ccssanswers.com\/wp-content\/uploads\/2021\/01\/big-ideas-math-answers-grade-7-chapter-2-multiplying-and-dividing-rational-numbers-13.jpg\" alt=\"Big Ideas Math Answers Grade 7 Chapter 2 Multiplying and Dividing Rational Numbers 13\" width=\"551\" height=\"86\" srcset=\"https:\/\/ccssanswers.com\/wp-content\/uploads\/2021\/01\/big-ideas-math-answers-grade-7-chapter-2-multiplying-and-dividing-rational-numbers-13.jpg 551w, https:\/\/ccssanswers.com\/wp-content\/uploads\/2021\/01\/big-ideas-math-answers-grade-7-chapter-2-multiplying-and-dividing-rational-numbers-13-300x47.jpg 300w\" sizes=\"(max-width: 551px) 100vw, 551px\" \/><br \/>\nSo, 4(-5) = -20<\/p>\n<p><strong>MULTIPLYING INTEGERS<\/strong><br \/>\n<strong>Find the product.<\/strong><\/p>\n<p>Question 12.<br \/>\n6 \u2022 4<\/p>\n<p>Answer:<br \/>\n6 \u2022 4 = 24<\/p>\n<p>Explanation:<br \/>\nThe product of two integers with the same sign is positive.<br \/>\n6 \u2022 4 = 24<\/p>\n<p>Question 13.<br \/>\n7(-3)<\/p>\n<p>Answer:<br \/>\n7(-3) = -21<\/p>\n<p>Explanation:<br \/>\nThe product of two integers with the different sign is negative.<br \/>\n7(-3) = -21<\/p>\n<p>Question 14.<br \/>\n-2(8)<\/p>\n<p>Answer:<br \/>\n-2(8) = -16<\/p>\n<p>Explanation:<br \/>\nThe product of two integers with different sign is negative.<br \/>\n-2(8) = -16<\/p>\n<p>Question 15.<br \/>\n-3(-4)<\/p>\n<p>Answer:<br \/>\n-3(-4) = 12<\/p>\n<p>Explanation:<br \/>\nThe product of two integers with the same sign is positive.<br \/>\n-3(-4)= 12<\/p>\n<p>Question 16.<br \/>\n-6 \u2022 7<\/p>\n<p>Answer:<br \/>\n-6 \u2022 7= -42<\/p>\n<p>Explanation:<br \/>\nThe product of two integers with different sign is negative.<br \/>\n-6 \u2022 7 = -42<\/p>\n<p>Question 17.<br \/>\n3 \u2022 9<\/p>\n<p>Answer:<br \/>\n3 \u2022 9 = 27<\/p>\n<p>Explanation:<br \/>\nThe product of two integers with the same sign is positive.<br \/>\n3 \u2022 9 = 27<\/p>\n<p>Question 18.<br \/>\n8 \u2022 (-5)<\/p>\n<p>Answer:<br \/>\n8 \u2022 (-5) = -40<\/p>\n<p>Explanation:<br \/>\nThe product of two integers with different sign is negative.<br \/>\n8 \u2022 (-5) = -40<\/p>\n<p>Question 19.<br \/>\n-1 \u2022 (-12)<\/p>\n<p>Answer:<br \/>\n-1 \u2022 (-12) = 12<\/p>\n<p>Explanation:<br \/>\nThe product of two integers with the same sign is positive.<br \/>\n-1 \u2022 (-12) = 12<\/p>\n<p>Question 20.<br \/>\n-5(10)<\/p>\n<p>Answer:<br \/>\n-5(10) = -50<\/p>\n<p>Explanation:<br \/>\nThe product of two integers with different sign is negative.<br \/>\n-5(10) = -50<\/p>\n<p>Question 21.<br \/>\n-13(0)<\/p>\n<p>Answer:<br \/>\n-13(0) = 0<\/p>\n<p>Explanation:<br \/>\nThe product of two integers with different sign is negative.<br \/>\n-13(0) = -0 = 0<\/p>\n<p>Question 22.<br \/>\n-9 \u2022 9<\/p>\n<p>Answer:<br \/>\n-9 \u2022 9 = -81<\/p>\n<p>Explanation:<br \/>\nThe product of two integers with different sign is negative.<br \/>\n-9 \u2022 9 = -81<\/p>\n<p>Question 23.<br \/>\n15(-2)<\/p>\n<p>Answer:<br \/>\n15(-2) = -30<\/p>\n<p>Explanation:<br \/>\nThe product of two integers with different sign is negative.<br \/>\n15(-2) = -30<\/p>\n<p>Question 24.<br \/>\n-10 \u2022 11<\/p>\n<p>Answer:<br \/>\n-10 \u2022 11 = -110<\/p>\n<p>Explanation:<br \/>\nThe product of two integers with different sign is negative.<br \/>\n-10 \u2022 11 = -110<\/p>\n<p>Question 25.<br \/>\n-6 \u2022 (-13)<\/p>\n<p>Answer:<br \/>\n-6 \u2022 (-13) = 78<\/p>\n<p>Explanation:<br \/>\nThe product of two integers with the same sign is positive.<br \/>\n-6 \u2022 (-13) = 78<\/p>\n<p>Question 26.<br \/>\n7(-14)<\/p>\n<p>Answer:<br \/>\n7(-14) = -98<\/p>\n<p>Explanation:<br \/>\nThe product of two integers with different sign is negative.<br \/>\n7(-14) = -98<\/p>\n<p>Question 27.<br \/>\n-11 \u2022 (-11)<\/p>\n<p>Answer:<br \/>\n-11 \u2022 (-11) = 121<\/p>\n<p>Explanation:<br \/>\nThe product of two integers with the same sign is positive.<br \/>\n-11 \u2022 (-11) = 121<\/p>\n<p>Question 28.<br \/>\n<strong>MODELING REAL LIFE<\/strong><br \/>\nYou burn 10 calories each minute you jog. What integer represents the change in your calories after you jog for 20 minutes?<\/p>\n<p>Answer:<br \/>\nThe change in your calories after you jog for 20 minutes is 200.<\/p>\n<p>Explanation:<br \/>\nThe number of calories you burn per minute = 10<br \/>\nThe change in your calories after you jog for 20 minutes = 20 x 10 = 200<\/p>\n<p>Question 29.<br \/>\n<strong>MODELING REAL LIFE<\/strong><br \/>\nIn a four-year period, about 80,000 acres of coastal wetlands in the United States are lost each year. What integer represents the total change in coastal wetlands?<br \/>\n<img decoding=\"async\" loading=\"lazy\" class=\"alignnone size-full wp-image-30104\" src=\"https:\/\/ccssanswers.com\/wp-content\/uploads\/2021\/01\/Big-Ideas-Math-Answer-Key-Grade-7-Chapter-2-Multiplying-and-Dividing-Rational-Numbers-6.png\" alt=\"Big Ideas Math Answer Key Grade 7 Chapter 2 Multiplying and Dividing Rational Numbers 6\" width=\"206\" height=\"205\" srcset=\"https:\/\/ccssanswers.com\/wp-content\/uploads\/2021\/01\/Big-Ideas-Math-Answer-Key-Grade-7-Chapter-2-Multiplying-and-Dividing-Rational-Numbers-6.png 206w, https:\/\/ccssanswers.com\/wp-content\/uploads\/2021\/01\/Big-Ideas-Math-Answer-Key-Grade-7-Chapter-2-Multiplying-and-Dividing-Rational-Numbers-6-150x150.png 150w\" sizes=\"(max-width: 206px) 100vw, 206px\" \/><\/p>\n<p>Answer:<br \/>\nThe total change in coastal wetlands is 20000 acres.<\/p>\n<p>Explanation:<br \/>\nIn A 4 year period, About 80,000 acres of coastal wetlands in United States are lost each year.<br \/>\nso, total area =80000 acres<br \/>\ntotal time = 4 years<br \/>\nnow, we can use formula<br \/>\ntotal change in wetlands = ( total area)\/(total time)<br \/>\nnow, we can put values<br \/>\ntotal change in wetlands = 80000\/4 = 20000<\/p>\n<p><strong>EVALUATING EXPRESSIONS<\/strong><br \/>\n<strong>Evaluate the expression.<\/strong><\/p>\n<p>Question 30.<br \/>\n(-4)<sup>2<\/sup><\/p>\n<p>Answer:<br \/>\n(-4)\u00b2 = 16<\/p>\n<p>Explanation:<br \/>\n(-4)\u00b2 = -4 . -4 = 16<\/p>\n<p>Question 31.<br \/>\n-6<sup>2<\/sup><\/p>\n<p>Answer:<br \/>\n-6\u00b2 = -36<\/p>\n<p>Explanation:<br \/>\n-6\u00b2 = -6. 6 = -36<\/p>\n<p>Question 32.<br \/>\n-5 \u2022 3 \u2022 (-2)<\/p>\n<p>Answer:<br \/>\n-5 \u2022 3 \u2022 (-2) = 30<\/p>\n<p>Explanation:<br \/>\n-5 \u2022 3 \u2022 (-2) = -15 . (-2)<br \/>\n= 30<\/p>\n<p>Question 33.<br \/>\n3 \u2022 (-12) \u2022 0<\/p>\n<p>Answer:<br \/>\n3 \u2022 (-12) \u2022 0 = 0<\/p>\n<p>Explanation:<br \/>\n3 \u2022 (-12) \u2022 0 = -36 . 0 = 0<\/p>\n<p>Question 34.<br \/>\n-5(-7)(-20)<\/p>\n<p>Answer:<br \/>\n-5(-7)(-20) = -700<\/p>\n<p>Explanation:<br \/>\n-5(-7)(-20) = -5 . -7 (-20) = 35 . -20 = -700<\/p>\n<p>Question 35.<br \/>\n5 &#8211; 8<sup>2<\/sup><\/p>\n<p>Answer:<br \/>\n5 &#8211; 8\u00b2 = -59<\/p>\n<p>Explanation:<br \/>\n5 &#8211; 8\u00b2 = 5 &#8211; (8 . 8)<br \/>\n= 5 &#8211; 64 = -59<\/p>\n<p>Question 36.<br \/>\n-5<sup>2<\/sup> \u2022 4<\/p>\n<p>Answer:<br \/>\n-5\u00b2 . 4 = -100<\/p>\n<p>Explanation:<br \/>\n-5\u00b2 . 4 = -5 . 5 . 4<br \/>\n= -25 . 4 = -100<\/p>\n<p>Question 37.<br \/>\n-2 \u2022 (-3)<sup>3<\/sup><\/p>\n<p>Answer:<br \/>\n-2 \u2022 (-3)\u00b3 = 54<\/p>\n<p>Explanation:<br \/>\n-2 \u2022 (-3)\u00b3 = -2 . (-3 . -3 . -3)<br \/>\n= -2 . (-3 . 9)<br \/>\n= -2 . -27 = 54<\/p>\n<p>Question 38.<br \/>\n2 + 1 \u2022 (-7 + 5)<\/p>\n<p>Answer:<br \/>\n2 + 1 \u2022 (-7 + 5) = 0<\/p>\n<p>Explanation:<br \/>\n2 + 1 \u2022 (-7 + 5) = 2 + 1 . (-2)<br \/>\n= 2 &#8211; 2 = 0<\/p>\n<p>Question 39.<br \/>\n4 &#8211; (-2)<sup>3<\/sup><\/p>\n<p>Answer:<br \/>\n4 &#8211; (-2)\u00b3 = 12<\/p>\n<p>Explanation:<br \/>\n4 &#8211; (-2)\u00b3 = 4 &#8211; (-2 . -2 . -2)<br \/>\n= 4 &#8211; (-2 . 4) = 4 &#8211; (-8)<br \/>\n= 4 + 8 = 12<\/p>\n<p>Question 40.<br \/>\n4 \u2022 (25 \u2022 3<sup>2<\/sup>)<\/p>\n<p>Answer:<br \/>\n4 \u2022 (25 \u2022 3\u00b2) = 900<\/p>\n<p>Explanation:<br \/>\n4 \u2022 (25 \u2022 3\u00b2) = 4 . (25 . 3 . 3)<br \/>\n= 4 . (25 . 9) = 4 . 225<br \/>\n= 900<\/p>\n<p>Question 41.<br \/>\n-4(3<sup>2<\/sup> &#8211; 8) + 1<\/p>\n<p>Answer:<br \/>\n-4(3\u00b2 &#8211; 8) + 1 = -3<\/p>\n<p>Explanation:<br \/>\n-4(3\u00b2 &#8211; 8) + 1 = -4(3 . 3 &#8211; 8) + 1<br \/>\n= -4(9 &#8211; 8) + 1<br \/>\n= -4(1) + 1 = -4 + 1 = -3<\/p>\n<p><strong>YOU BE THE TEACHER<\/strong><br \/>\n<strong>Your friend evaluates the expression. Is your friend correct? Explain your reasoning.<\/strong><\/p>\n<p>Question 42.<br \/>\n<img decoding=\"async\" loading=\"lazy\" class=\"alignnone size-full wp-image-30105\" src=\"https:\/\/ccssanswers.com\/wp-content\/uploads\/2021\/01\/Big-Ideas-Math-Answer-Key-Grade-7-Chapter-2-Multiplying-and-Dividing-Rational-Numbers-7.png\" alt=\"Big Ideas Math Answer Key Grade 7 Chapter 2 Multiplying and Dividing Rational Numbers 7\" width=\"160\" height=\"76\" \/><\/p>\n<p>Answer:<br \/>\nWrong<\/p>\n<p>Explanation:<br \/>\nThe product of two integers with the same sign is positive.<br \/>\nSo, -2(-7) = 14<\/p>\n<p>Question 43.<br \/>\n<img decoding=\"async\" loading=\"lazy\" class=\"alignnone size-full wp-image-30106\" src=\"https:\/\/ccssanswers.com\/wp-content\/uploads\/2021\/01\/Big-Ideas-Math-Answer-Key-Grade-7-Chapter-2-Multiplying-and-Dividing-Rational-Numbers-8.png\" alt=\"Big Ideas Math Answer Key Grade 7 Chapter 2 Multiplying and Dividing Rational Numbers 8\" width=\"150\" height=\"76\" \/><\/p>\n<p>Answer:<br \/>\nCorrect<\/p>\n<p>Explanation:<br \/>\nThe product of two integers with different sign is negative.<br \/>\n-10\u00b2 = -10 . 10 = -100<\/p>\n<p><strong>PATTERNS<br \/>\n<\/strong><strong>Find the next two numbers in the pattern.<\/strong><\/p>\n<p>Question 44.<br \/>\n-12, 60, -300, 1500, &#8230;.<\/p>\n<p>Answer:<br \/>\nThe next two numbers in the pattern are -7500, 37500<\/p>\n<p>Explanation:<br \/>\nMultiply each integer by -5<br \/>\n-12 x -5 = 60<br \/>\n60 x -5 = -300<br \/>\n-300 x -5 = 1500<br \/>\n1500 x -5 = -7500<br \/>\n-7500 x -5 = 37500<\/p>\n<p>Question 45.<br \/>\n7, -28, 112, -448,&#8230;..<\/p>\n<p>Answer:<br \/>\nThe next two numbers in the pattern are 1792, -7168<\/p>\n<p>Explanation:<br \/>\nMultiply each integer by -4<br \/>\n7 x -4 = -28<br \/>\n-28 x -4 = 112<br \/>\n112 x -4 = -448<br \/>\n-448 x -4 = 1792<br \/>\n1792 x -4 = -7168<\/p>\n<p>Question 46.<br \/>\n<strong>PROBLEM SOLVING<\/strong><br \/>\nIn a scavenger hunt, each team earns 25 points for each item that they \ufb01nd. Each team loses 15 points for every minute after 4:00 P.M. that they report to the city park. The table shows the number of items found by each team and the time that each team reported to the park. Which team wins the scavenger hunt? Justify your answer.<br \/>\n<img decoding=\"async\" loading=\"lazy\" class=\"alignnone size-full wp-image-30107\" src=\"https:\/\/ccssanswers.com\/wp-content\/uploads\/2021\/01\/Big-Ideas-Math-Answer-Key-Grade-7-Chapter-2-Multiplying-and-Dividing-Rational-Numbers-9.png\" alt=\"Big Ideas Math Answer Key Grade 7 Chapter 2 Multiplying and Dividing Rational Numbers 9\" width=\"241\" height=\"167\" \/><\/p>\n<p>Answer:<br \/>\nTeam D wins the scavenger hunt.<\/p>\n<p>Explanation:<br \/>\nEach team earns 25 points for each item that they \ufb01nd. Each team loses 15 points for every minute after 4:00 P.M<br \/>\nThe points earned by Team A = (13 x 25) &#8211; (15 x 3) = 325 &#8211; 45 = 280<br \/>\nThe points earned by Team B = (15 x 25) &#8211; (15 x 7) = 375 &#8211; 105 = 270<br \/>\nThe points earned by Team C = (11 x 25) = 275<br \/>\nThe points earned by Team D = (12 x 25) &#8211; (1 x 15) = 300 &#8211; 15 = 285<br \/>\nFinally, Team D scores the highest points.<br \/>\nHence, Team D wins the scavenger hunt.<\/p>\n<p>Question 47.<br \/>\n<strong>REASONING<\/strong><br \/>\nThe height of an airplane during a landing is given by 22,000 + (-480t), where t is the time in minutes. Estimate how many minutes it takes the plane to land. Explain your reasoning.<\/p>\n<p>Answer:<br \/>\nIt takes 45 minutes for the plane to land.<\/p>\n<p>Explanation:<br \/>\nThe height of an airplane during a landing = 22,000 + (-480t)<br \/>\n= 22,000 &#8211; 480t<br \/>\nAfter landing, the height of the airplane = 0<br \/>\nSo, 22,000 &#8211; 480t = 0<br \/>\n22000 = 0 + 480t<br \/>\n480t = 22000<br \/>\nt = 22000\/480<br \/>\nt = 2200\/48<br \/>\n<img decoding=\"async\" loading=\"lazy\" class=\"alignnone size-full wp-image-41027\" src=\"https:\/\/ccssanswers.com\/wp-content\/uploads\/2021\/01\/big-ideas-math-answers-grade-7-chapter-2-multiplying-and-dividing-rational-numbers-14.jpg\" alt=\"Big Ideas Math Answers Grade 7 Chapter 2 Multiplying and Dividing Rational Numbers 14\" width=\"181\" height=\"418\" srcset=\"https:\/\/ccssanswers.com\/wp-content\/uploads\/2021\/01\/big-ideas-math-answers-grade-7-chapter-2-multiplying-and-dividing-rational-numbers-14.jpg 181w, https:\/\/ccssanswers.com\/wp-content\/uploads\/2021\/01\/big-ideas-math-answers-grade-7-chapter-2-multiplying-and-dividing-rational-numbers-14-130x300.jpg 130w\" sizes=\"(max-width: 181px) 100vw, 181px\" \/><br \/>\nSo, it takes 45 minutes for the plane to land.<\/p>\n<p>Question 48.<br \/>\n<strong>PROBLEM SOLVING<\/strong><br \/>\nThe table shows the price of a bluetooth speaker each month for 4 months.<br \/>\n<img decoding=\"async\" loading=\"lazy\" class=\"alignnone size-full wp-image-30108\" src=\"https:\/\/ccssanswers.com\/wp-content\/uploads\/2021\/01\/Big-Ideas-Math-Answer-Key-Grade-7-Chapter-2-Multiplying-and-Dividing-Rational-Numbers-10.png\" alt=\"Big Ideas Math Answer Key Grade 7 Chapter 2 Multiplying and Dividing Rational Numbers 10\" width=\"545\" height=\"244\" srcset=\"https:\/\/ccssanswers.com\/wp-content\/uploads\/2021\/01\/Big-Ideas-Math-Answer-Key-Grade-7-Chapter-2-Multiplying-and-Dividing-Rational-Numbers-10.png 545w, https:\/\/ccssanswers.com\/wp-content\/uploads\/2021\/01\/Big-Ideas-Math-Answer-Key-Grade-7-Chapter-2-Multiplying-and-Dividing-Rational-Numbers-10-300x134.png 300w\" sizes=\"(max-width: 545px) 100vw, 545px\" \/><br \/>\na. Describe the change in the price of the speaker.<br \/>\nb. The table at the right shows the amount of money you save each month. When do you have enough money saved to buy the speaker? Explain your reasoning.<br \/>\n<img decoding=\"async\" loading=\"lazy\" class=\"alignnone size-full wp-image-30109\" src=\"https:\/\/ccssanswers.com\/wp-content\/uploads\/2021\/01\/Big-Ideas-Math-Answer-Key-Grade-7-Chapter-2-Multiplying-and-Dividing-Rational-Numbers-11.png\" alt=\"Big Ideas Math Answer Key Grade 7 Chapter 2 Multiplying and Dividing Rational Numbers 11\" width=\"185\" height=\"168\" \/><\/p>\n<p>Answer:<br \/>\na. The Bluetooth speaker price decreased by 12 dollars every month.<br \/>\nb. You can buy the speaker in the month of September.<\/p>\n<p>Explanation:<br \/>\na. The table shows that the change in the price of the Bluetooth speaker per every month is -12. So, the Bluetooth speaker price decreased by 12 dollars per every month.<br \/>\nb.<br \/>\nThe amount of money you saved in June is $35, the price of the speaker is $165.<br \/>\nThe amount of money you saved in July is 35 + 55 = $90, the price of the speaker is 165 &#8211; 12 = $153<br \/>\nThe amount of money you saved in august is 90 + 45 = $135, the price of the speaker is 165 &#8211; 24 = $141<br \/>\nThe amount of money you saved in September is 135 + 18 = $153, the price of the speaker is 165 &#8211; 36 = 129<br \/>\nSo, you can buy the speaker in the month of September.<\/p>\n<p>Question 49.<br \/>\n<strong>DIG DEEPER!<\/strong><br \/>\nTwo integers, a and b, have a product of 24. What is the least possible sum of a and b?<\/p>\n<p>Answer:<br \/>\nThe least possible sum of a and b is -25.<\/p>\n<p>Explanation:<br \/>\nThe product of a and b = 24<br \/>\n<img decoding=\"async\" loading=\"lazy\" class=\"alignnone size-full wp-image-41039\" src=\"https:\/\/ccssanswers.com\/wp-content\/uploads\/2021\/01\/big-ideas-math-answers-grade-7-chapter-2-multiplying-and-dividing-rational-numbers-15.jpg\" alt=\"Big Ideas Math Answers Grade 7 Chapter 2 Multiplying and Dividing Rational Numbers 15\" width=\"329\" height=\"231\" srcset=\"https:\/\/ccssanswers.com\/wp-content\/uploads\/2021\/01\/big-ideas-math-answers-grade-7-chapter-2-multiplying-and-dividing-rational-numbers-15.jpg 329w, https:\/\/ccssanswers.com\/wp-content\/uploads\/2021\/01\/big-ideas-math-answers-grade-7-chapter-2-multiplying-and-dividing-rational-numbers-15-300x211.jpg 300w\" sizes=\"(max-width: 329px) 100vw, 329px\" \/><br \/>\nThe least possible sum of a and b is -25.<\/p>\n<p>Question 50.<br \/>\n<strong>NUMBER SENSE<\/strong><br \/>\nConsider two integers p and q. Explain why p \u00d7 (-q) = (-p) \u00d7 q = -pq<\/p>\n<p>Answer:<br \/>\nWe know that,<br \/>\nthe product of two integers with the different sign is negative.<br \/>\np \u00d7 (-q)<br \/>\nHere p is a positive integer, q is a negative integer<br \/>\n(-p) \u00d7 q<br \/>\nHere p is a negative integer and q is a positive integer.<br \/>\nSo, the product is negative<\/p>\n<h3><a id=\"Lesson_2.2_Dividing_Integers\"><\/a>Lesson 2.2 Dividing Integers<\/h3>\n<p><strong>EXPLORATION 1<\/strong><\/p>\n<p><strong>Understanding Quotients Involving Negative Integers<\/strong><br \/>\n<strong>Work with a partner.<\/strong><br \/>\na. Discuss the relationship between multiplication and division with your partner.<br \/>\n<strong>b. INDUCTIVE REASONING<\/strong><br \/>\nComplete the table. Then write general rules for dividing<\/p>\n<ol>\n<li>two integers with the same sign and<\/li>\n<li>two integers with different signs.<\/li>\n<\/ol>\n<p><img decoding=\"async\" loading=\"lazy\" class=\"alignnone size-full wp-image-30110\" src=\"https:\/\/ccssanswers.com\/wp-content\/uploads\/2021\/01\/Big-Ideas-Math-Answer-Key-Grade-7-Chapter-2-Multiplying-and-Dividing-Rational-Numbers-12.png\" alt=\"Big Ideas Math Answer Key Grade 7 Chapter 2 Multiplying and Dividing Rational Numbers 12\" width=\"738\" height=\"419\" srcset=\"https:\/\/ccssanswers.com\/wp-content\/uploads\/2021\/01\/Big-Ideas-Math-Answer-Key-Grade-7-Chapter-2-Multiplying-and-Dividing-Rational-Numbers-12.png 738w, https:\/\/ccssanswers.com\/wp-content\/uploads\/2021\/01\/Big-Ideas-Math-Answer-Key-Grade-7-Chapter-2-Multiplying-and-Dividing-Rational-Numbers-12-300x170.png 300w\" sizes=\"(max-width: 738px) 100vw, 738px\" \/><br \/>\nc. Find the values of <img decoding=\"async\" loading=\"lazy\" class=\"alignnone size-full wp-image-30112\" src=\"https:\/\/ccssanswers.com\/wp-content\/uploads\/2021\/01\/Big-Ideas-Math-Answer-Key-Grade-7-Chapter-2-Multiplying-and-Dividing-Rational-Numbers-13.png\" alt=\"Big Ideas Math Answer Key Grade 7 Chapter 2 Multiplying and Dividing Rational Numbers 13\" width=\"110\" height=\"51\" \/> What do you notice? Is this true for <img decoding=\"async\" loading=\"lazy\" class=\"alignnone size-full wp-image-30114\" src=\"https:\/\/ccssanswers.com\/wp-content\/uploads\/2021\/01\/Big-Ideas-Math-Answer-Key-Grade-7-Chapter-2-Multiplying-and-Dividing-Rational-Numbers-14.png\" alt=\"Big Ideas Math Answer Key Grade 7 Chapter 2 Multiplying and Dividing Rational Numbers 14\" width=\"110\" height=\"47\" \/> when a and b are integers? Explain.<br \/>\nd. Is every quotient of integers a rational number? Explain your reasoning.<\/p>\n<p>Answer:<br \/>\na. Multiplication and division are two opposite operations.<br \/>\nb. <img decoding=\"async\" loading=\"lazy\" class=\"alignnone size-full wp-image-41048\" src=\"https:\/\/ccssanswers.com\/wp-content\/uploads\/2021\/01\/big-ideas-math-answers-grade-7-chapter-2-multiplying-and-dividing-rational-numbers-16.jpg\" alt=\"Big Ideas Math Answers Grade 7 Chapter 2 Multiplying and Dividing Rational Numbers 16\" width=\"672\" height=\"491\" srcset=\"https:\/\/ccssanswers.com\/wp-content\/uploads\/2021\/01\/big-ideas-math-answers-grade-7-chapter-2-multiplying-and-dividing-rational-numbers-16.jpg 672w, https:\/\/ccssanswers.com\/wp-content\/uploads\/2021\/01\/big-ideas-math-answers-grade-7-chapter-2-multiplying-and-dividing-rational-numbers-16-300x219.jpg 300w\" sizes=\"(max-width: 672px) 100vw, 672px\" \/><br \/>\nc. True<br \/>\nd. Yes<\/p>\n<p>Explanation:<br \/>\na. Multiplication and division are the reverse operations. When you multiply two numbers, you will get the product. Divide the product by any one of the multiplicand to get another multiplicand.<br \/>\nb. When two integers have the same sign then the quotient is positive. If two integers have different signs then the quotient is negative. When any one of the integers is zero, then the quotient is zero.<br \/>\nc. -(8\/4) = -(2) = -2<br \/>\n-8\/4 = -2<br \/>\n8\/-4 = -2<br \/>\nYes, -(8\/4), 8\/-4, -8\/4 are true.<br \/>\nd. Every quotient of integers a rational number.<\/p>\n<p><strong>2.2 Lesson<br \/>\n<\/strong><\/p>\n<p><strong>Try It<\/strong><\/p>\n<p><strong>Find the quotient.<\/strong><\/p>\n<p>Question 1.<br \/>\n14 \u00f7 2<\/p>\n<p>Answer:<br \/>\n14 \u00f7 2 = 7<\/p>\n<p>Explanation:<br \/>\nThe quotient of two integers with the same sign is positive.<br \/>\n14 \u00f7 2 = 7<\/p>\n<p>Question 2.<br \/>\n-32 \u00f7 (-4)<\/p>\n<p>Answer:<br \/>\n-32 \u00f7 (-4) = 8<\/p>\n<p>Explanation:<br \/>\nThe quotient of two integers with the same sign is positive.<br \/>\n-32 \u00f7 (-4) = 8<\/p>\n<p>Question 3.<br \/>\n-40 \u00f7 (-8)<\/p>\n<p>Answer:<br \/>\n-40 \u00f7 (-8) = 5<\/p>\n<p>Explanation:<br \/>\nThe quotient of two integers with the same sign is positive.<br \/>\n-40 \u00f7 (-8) = 5<\/p>\n<p><strong>Try It<\/strong><\/p>\n<p><strong>Find the quotient.<\/strong><\/p>\n<p>Question 4.<br \/>\n0 \u00f7 (-6)<\/p>\n<p>Answer:<br \/>\n0 \u00f7 (-6) = 0<\/p>\n<p>Explanation:<br \/>\nThe quotient of two integers with the different signs is negative.<br \/>\n0 \u00f7 (-6) = 0<\/p>\n<p>Question 5.<br \/>\n\\(\\frac{-49}{7}\\)<\/p>\n<p>Answer:<br \/>\n-49 \u00f7 7 = -7<\/p>\n<p>Explanation:<br \/>\nThe quotient of two integers with the different signs is negative.<br \/>\n-49 \u00f7 7 = -7<\/p>\n<p>Question 6.<br \/>\n\\(\\frac{21}{-3}\\)<\/p>\n<p>Answer:<br \/>\n21 \u00f7 -3 = -7<\/p>\n<p>Explanation:<br \/>\nThe quotient of two integers with the different signs is negative.<br \/>\n21 \u00f7 -3 = -7<\/p>\n<p><strong>Try It<\/strong><\/p>\n<p><strong>Evaluate the expression when a = 18 and b = -6.<\/strong><\/p>\n<p>Question 7.<br \/>\na \u00f7 b<\/p>\n<p>Answer:<br \/>\n18 \u00f7 -6 = -3<\/p>\n<p>Explanation:<br \/>\na \u00f7 b<br \/>\nPut a = 18, b = -6<br \/>\n18 \u00f7 -6 = -3<br \/>\nThe quotient of two integers with the different signs is negative.<\/p>\n<p>Question 8.<br \/>\n<img decoding=\"async\" loading=\"lazy\" class=\"alignnone size-full wp-image-30111\" src=\"https:\/\/ccssanswers.com\/wp-content\/uploads\/2021\/01\/Big-Ideas-Math-Answer-Key-Grade-7-Chapter-2-Multiplying-and-Dividing-Rational-Numbers-13.1.png\" alt=\"Big Ideas Math Answer Key Grade 7 Chapter 2 Multiplying and Dividing Rational Numbers 13.1\" width=\"49\" height=\"43\" \/><\/p>\n<p>Answer:<br \/>\n8<\/p>\n<p>Explanation:<br \/>\nThe given expression is (a + 6)\/3<br \/>\nPut a = 18<br \/>\n= (18 + 6)\/3 = 24\/3<br \/>\nThe quotient of two integers with the same sign is positive.<br \/>\n24\/3 = 8<\/p>\n<p>Question 9.<br \/>\n<img decoding=\"async\" loading=\"lazy\" class=\"alignnone size-full wp-image-30113\" src=\"https:\/\/ccssanswers.com\/wp-content\/uploads\/2021\/01\/Big-Ideas-Math-Answer-Key-Grade-7-Chapter-2-Multiplying-and-Dividing-Rational-Numbers-14.1.png\" alt=\"Big Ideas Math Answer Key Grade 7 Chapter 2 Multiplying and Dividing Rational Numbers 14.1\" width=\"60\" height=\"52\" \/><\/p>\n<p>Answer:<br \/>\n-50<\/p>\n<p>Explanation:<br \/>\nThe given expression is b\u00b2\/a + 4<br \/>\nPut a = 18, b = -6<br \/>\n= 18\u00b2\/-6 + 4<br \/>\n= 324\/-6 + 4<br \/>\nThe quotient of two integers with the different signs is negative.<br \/>\n= -54 + 4 = -50<\/p>\n<p><strong>Self-Assessment for Concepts &amp; Skills<\/strong><\/p>\n<p>Solve each exercise. Then rate your understanding of the success criteria in your journal.<\/p>\n<p>Question 10.<br \/>\n<strong>WRITING<\/strong><br \/>\nWhat can you conclude about two integers whose quotient is (a) positive, (b) negative, or (c) zero?<\/p>\n<p>Answer:<br \/>\nIf the quotient of two integers is positive then the integers are having the same sign.<br \/>\nThe quotient of two integers is negative when the integers are having different signs.<br \/>\nThe quotient of two integers is zero when any one of the integers is zero.<\/p>\n<p><strong>DIVIDING INTEGERS<\/strong><br \/>\n<strong>Find the quotient.<\/strong><\/p>\n<p>Question 11.<br \/>\n-12 \u00f7 4<\/p>\n<p>Answer:<br \/>\n-12 \u00f7 4 = -3<\/p>\n<p>Explanation:<br \/>\nThe quotient of two integers with the different signs is negative.<br \/>\n-12 \u00f7 4 = -3<\/p>\n<p>Question 12.<br \/>\n\\(\\frac{-6}{-2}\\)<\/p>\n<p>Answer:<br \/>\n-6 \u00f7 -2 = 3<\/p>\n<p>Explanation:<br \/>\nThe quotient of two integers with the same sign is positive.<br \/>\n-6 \u00f7 -2 = 3<\/p>\n<p>Question 13.<br \/>\n15 \u00f7 (-3)<\/p>\n<p>Answer:<br \/>\n15 \u00f7 (-3) = -5<\/p>\n<p>Explanation:<br \/>\nThe quotient of two integers with the different signs is negative.<br \/>\n15 \u00f7 (-3) = -5<\/p>\n<p>Question 14.<br \/>\n<strong>WHICH ONE DOESN\u2019T BELONG?<\/strong><br \/>\nWhich expression does not belong with the other three? Explain your reasoning.<br \/>\n<img decoding=\"async\" loading=\"lazy\" class=\"alignnone size-full wp-image-30116\" src=\"https:\/\/ccssanswers.com\/wp-content\/uploads\/2021\/01\/Big-Ideas-Math-Answer-Key-Grade-7-Chapter-2-Multiplying-and-Dividing-Rational-Numbers-15.png\" alt=\"Big Ideas Math Answer Key Grade 7 Chapter 2 Multiplying and Dividing Rational Numbers 15\" width=\"297\" height=\"63\" \/><\/p>\n<p>Answer:<br \/>\n-10\/-5<\/p>\n<p>Explanation:<br \/>\nOut of all expressions, -10\/-5 is different. Because in all remaining expressions, the negative sign is applicable to either numerator or denominator. But in -10\/-5 the negative sign is applicable to both numerator and denominator.<\/p>\n<p><strong>Self-Assessment for Problem Solving<\/strong><\/p>\n<p>Solve each exercise. Then rate your understanding of the success criteria in your journal.<\/p>\n<p>Question 15.<br \/>\nA female grizzly bear weighs 500 pounds. After hibernating for 6 months, she weighs only 350 pounds. What is the mean monthly change in weight?<br \/>\n<img decoding=\"async\" loading=\"lazy\" class=\"alignnone size-full wp-image-30115\" src=\"https:\/\/ccssanswers.com\/wp-content\/uploads\/2021\/01\/Big-Ideas-Math-Answer-Key-Grade-7-Chapter-2-Multiplying-and-Dividing-Rational-Numbers-15.2.png\" alt=\"Big Ideas Math Answer Key Grade 7 Chapter 2 Multiplying and Dividing Rational Numbers 15.2\" width=\"188\" height=\"243\" \/><\/p>\n<p>Answer:<br \/>\nThe mean change in weight per month is 50 pounds.<\/p>\n<p>Explanation:<br \/>\nA female grizzly bear weighs 500 pounds<br \/>\nAfter hibernating for 6 months, she weighs only 200 pounds<br \/>\nMean change in weight = 500 &#8211; 200 = 300<br \/>\n6 months = 300 pounds<br \/>\nDivide both sides by 6<br \/>\n6 months\/6 = 300\/6<br \/>\n1 month = 50 pounds<br \/>\nThe mean change in weight per month is 50 pounds.<\/p>\n<p>Question 16.<br \/>\nThe table shows the change in the number of crimes committed in a city each year for 4 years. What is the mean yearly change in the number of crimes?<br \/>\n<img decoding=\"async\" loading=\"lazy\" class=\"alignnone size-full wp-image-30117\" src=\"https:\/\/ccssanswers.com\/wp-content\/uploads\/2021\/01\/Big-Ideas-Math-Answer-Key-Grade-7-Chapter-2-Multiplying-and-Dividing-Rational-Numbers-16.png\" alt=\"Big Ideas Math Answer Key Grade 7 Chapter 2 Multiplying and Dividing Rational Numbers 16\" width=\"392\" height=\"73\" srcset=\"https:\/\/ccssanswers.com\/wp-content\/uploads\/2021\/01\/Big-Ideas-Math-Answer-Key-Grade-7-Chapter-2-Multiplying-and-Dividing-Rational-Numbers-16.png 392w, https:\/\/ccssanswers.com\/wp-content\/uploads\/2021\/01\/Big-Ideas-Math-Answer-Key-Grade-7-Chapter-2-Multiplying-and-Dividing-Rational-Numbers-16-300x56.png 300w\" sizes=\"(max-width: 392px) 100vw, 392px\" \/><\/p>\n<p>Answer:<br \/>\nThe mean yearly change in the number of crimes are -49.<\/p>\n<p>Explanation:<br \/>\nMean = (sum of observations)\/ number of observations<br \/>\n= (215 &#8211; 321 &#8211; 185 + 95)\/4<br \/>\n= -196\/4 = -49<br \/>\nThe mean yearly change in the number of crimes are -49.<\/p>\n<p>Question 17.<br \/>\n<strong>DIG DEEPER!<\/strong><br \/>\nAt a restaurant, when a customer buys 4 pretzels, the \ufb01fth pretzel is free. Soft pretzels cost $3.90 each. You order 12 soft pretzels. What is your mean cost per pretzel?<\/p>\n<p>Answer:<br \/>\nThe mean cost per pretzel is $2.925.<\/p>\n<p>Explanation:<br \/>\nAt a restaurant, when a customer buys 4 pretzels, the \ufb01fth pretzel is free.<br \/>\nThe cost of soft pretzels is $3.90<br \/>\nYou order 12 soft pretzels<br \/>\nSo, you need to pay for (4 + 4 + 4) &#8211; 3 = 12 &#8211; 3 = 9<br \/>\nThe cost for 9 soft pretzels = 9 x 3.90 =35.1<br \/>\nThe mean cost per pretzel = (35.1)\/12 = $2.925<\/p>\n<h3><a id=\"Dividing_Integers_Homework_&amp;_Practice_2.2\"><\/a>Dividing Integers Homework &amp; Practice 2.2<\/h3>\n<p><strong>Review &amp; Refresh<\/strong><\/p>\n<p>Find the product.<\/p>\n<p>Question 1.<br \/>\n8 \u2022 10<\/p>\n<p>Answer:<br \/>\n8 \u2022 10 = 80<\/p>\n<p>Explanation:<br \/>\nThe product of two integers with the same sign is positive.<br \/>\n8 \u2022 10 = 80<\/p>\n<p>Question 2.<br \/>\n-6(9)<\/p>\n<p>Answer:<br \/>\n-6(9) = -54<\/p>\n<p>Explanation:<br \/>\nThe product of two integers with different signs is negative.<br \/>\n-6(9) = -54<\/p>\n<p>Question 3.<br \/>\n4(7)<\/p>\n<p>Answer:<br \/>\n4(7) = 28<\/p>\n<p>Explanation:<br \/>\nThe product of two integers with the same sign is positive.<br \/>\n4(7) = 28<\/p>\n<p>Question 4.<br \/>\n-9(-8)<\/p>\n<p>Answer:<br \/>\n-9(-8) = 72<\/p>\n<p>Explanation:<br \/>\nThe product of two integers with the same sign is positive.<br \/>\n-9(-8) = 72<\/p>\n<p><strong>Order the numbers from least to greatest.<\/strong><\/p>\n<p>Question 5.<br \/>\n<img decoding=\"async\" loading=\"lazy\" class=\"alignnone size-full wp-image-30118\" src=\"https:\/\/ccssanswers.com\/wp-content\/uploads\/2021\/01\/Big-Ideas-Math-Answer-Key-Grade-7-Chapter-2-Multiplying-and-Dividing-Rational-Numbers-17.png\" alt=\"Big Ideas Math Answer Key Grade 7 Chapter 2 Multiplying and Dividing Rational Numbers 17\" width=\"93\" height=\"51\" \/><\/p>\n<p>Answer:<br \/>\n0.24, 1\/4, 28%<\/p>\n<p>Explanation:<br \/>\n28% = 28\/100 = 0.28<br \/>\n1\/4 = 0.25<br \/>\n0.24<br \/>\nThe order of numbers from the least to greatest is 0.24, 0.25, 0.28<\/p>\n<p>Question 6.<br \/>\n<img decoding=\"async\" loading=\"lazy\" class=\"alignnone size-full wp-image-30119\" src=\"https:\/\/ccssanswers.com\/wp-content\/uploads\/2021\/01\/Big-Ideas-Math-Answer-Key-Grade-7-Chapter-2-Multiplying-and-Dividing-Rational-Numbers-18.png\" alt=\"Big Ideas Math Answer Key Grade 7 Chapter 2 Multiplying and Dividing Rational Numbers 18\" width=\"100\" height=\"43\" \/><\/p>\n<p>Answer:<br \/>\n2\/5, 42%, 0.45<\/p>\n<p>Explanation:<br \/>\n42% = 42\/100 = 0.42<br \/>\n0.45<br \/>\n2\/5 = 0.4<br \/>\nThe order of numbers from the least to greatest is 0.4, 0.42, 0.45<\/p>\n<p>Question 7.<br \/>\n<img decoding=\"async\" loading=\"lazy\" class=\"alignnone size-full wp-image-30120\" src=\"https:\/\/ccssanswers.com\/wp-content\/uploads\/2021\/01\/Big-Ideas-Math-Answer-Key-Grade-7-Chapter-2-Multiplying-and-Dividing-Rational-Numbers-19.png\" alt=\"Big Ideas Math Answer Key Grade 7 Chapter 2 Multiplying and Dividing Rational Numbers 19\" width=\"156\" height=\"56\" \/><\/p>\n<p>Answer:<br \/>\n0.69, 7\/10, 71%, 0.84, 9\/10<\/p>\n<p>Explanation:<br \/>\n7\/10 = 0.7<br \/>\n0.69<br \/>\n71% = 71\/100 = 0.71<br \/>\n9\/10 = 0.9<br \/>\n0.84<br \/>\nThe order of numbers from the least to greatest is 0.69, 0.7, 0.71, 0.84, 0.9<\/p>\n<p><strong>Write an addition expression and write a subtraction expression represented by the number line. Then evaluate the expressions.<\/strong><\/p>\n<p>Question 8.<br \/>\n<img decoding=\"async\" loading=\"lazy\" class=\"alignnone size-full wp-image-30121\" src=\"https:\/\/ccssanswers.com\/wp-content\/uploads\/2021\/01\/Big-Ideas-Math-Answer-Key-Grade-7-Chapter-2-Multiplying-and-Dividing-Rational-Numbers-20.png\" alt=\"Big Ideas Math Answer Key Grade 7 Chapter 2 Multiplying and Dividing Rational Numbers 20\" width=\"260\" height=\"97\" \/><\/p>\n<p>Answer:<br \/>\nAddition expression is 0 + 5 = 5<br \/>\nSubtraction expression is 5 &#8211; 1 = 4<\/p>\n<p>Explanation:<br \/>\nThe red line on the number line represents<br \/>\n5 &#8211; 1 = 4<br \/>\nThe blue line on the number line represents<br \/>\n0 + 5 = 5<\/p>\n<p>Question 9.<br \/>\n<img decoding=\"async\" loading=\"lazy\" class=\"alignnone size-full wp-image-30122\" src=\"https:\/\/ccssanswers.com\/wp-content\/uploads\/2021\/01\/Big-Ideas-Math-Answer-Key-Grade-7-Chapter-2-Multiplying-and-Dividing-Rational-Numbers-21.png\" alt=\"Big Ideas Math Answer Key Grade 7 Chapter 2 Multiplying and Dividing Rational Numbers 21\" width=\"256\" height=\"99\" \/><\/p>\n<p>Answer:<br \/>\nThe addition expression is -3 + 3 = 0<br \/>\nThe subtraction expression is 0 &#8211; 3 = -3<\/p>\n<p>Explanation:<br \/>\nThe red line on the number line represents<br \/>\n0 &#8211; 3 = -3<br \/>\nThe blue line on the number line represents<br \/>\n-3 + 3 = 0<\/p>\n<p><strong>Concepts, Skills, &amp; Problem Solving<\/strong><br \/>\n<strong>CHOOSE TOOLS<\/strong><br \/>\n<strong>Complete the table.<\/strong> (See Exploration 1, p. 55.)<br \/>\n<img decoding=\"async\" loading=\"lazy\" class=\"alignnone size-full wp-image-30123\" src=\"https:\/\/ccssanswers.com\/wp-content\/uploads\/2021\/01\/Big-Ideas-Math-Answer-Key-Grade-7-Chapter-2-Multiplying-and-Dividing-Rational-Numbers-22.png\" alt=\"Big Ideas Math Answer Key Grade 7 Chapter 2 Multiplying and Dividing Rational Numbers 22\" width=\"587\" height=\"172\" srcset=\"https:\/\/ccssanswers.com\/wp-content\/uploads\/2021\/01\/Big-Ideas-Math-Answer-Key-Grade-7-Chapter-2-Multiplying-and-Dividing-Rational-Numbers-22.png 587w, https:\/\/ccssanswers.com\/wp-content\/uploads\/2021\/01\/Big-Ideas-Math-Answer-Key-Grade-7-Chapter-2-Multiplying-and-Dividing-Rational-Numbers-22-300x88.png 300w\" sizes=\"(max-width: 587px) 100vw, 587px\" \/><\/p>\n<p>Answer:<br \/>\n<img decoding=\"async\" loading=\"lazy\" class=\"alignnone size-full wp-image-41263\" src=\"https:\/\/ccssanswers.com\/wp-content\/uploads\/2021\/01\/big-ideas-math-answers-grade-7-chapter-2-multiplying-and-dividing-rational-numbers-17.jpg\" alt=\"Big Ideas Math Answers Grade 7 Chapter 2 Multiplying and Dividing Rational Numbers 17\" width=\"996\" height=\"285\" srcset=\"https:\/\/ccssanswers.com\/wp-content\/uploads\/2021\/01\/big-ideas-math-answers-grade-7-chapter-2-multiplying-and-dividing-rational-numbers-17.jpg 996w, https:\/\/ccssanswers.com\/wp-content\/uploads\/2021\/01\/big-ideas-math-answers-grade-7-chapter-2-multiplying-and-dividing-rational-numbers-17-300x86.jpg 300w, https:\/\/ccssanswers.com\/wp-content\/uploads\/2021\/01\/big-ideas-math-answers-grade-7-chapter-2-multiplying-and-dividing-rational-numbers-17-768x220.jpg 768w\" sizes=\"(max-width: 996px) 100vw, 996px\" \/><\/p>\n<p>Explanation:<br \/>\n10. 14 \u00f7 (-2) = -7<br \/>\n11. -24 \u00f7 12 = -2<br \/>\n12. -55 \u00f7 (-5) = 11<\/p>\n<p><strong>DIVIDING INTEGERS<\/strong><br \/>\n<strong>Find the quotient, if possible.<\/strong><\/p>\n<p>Question 13.<br \/>\n4 \u00f7 (-2)<\/p>\n<p>Answer:<br \/>\n4 \u00f7 (-2) = -2<\/p>\n<p>Explanation:<br \/>\nThe quotient of two integers with the different signs is negative.<br \/>\n4 \u00f7 (-2) = -2<\/p>\n<p>Question 14.<br \/>\n21 \u00f7 (-7)<\/p>\n<p>Answer:<br \/>\n21 \u00f7 (-7) = -3<\/p>\n<p>Explanation:<br \/>\nThe quotient of two integers with the different signs is negative.<br \/>\n21 \u00f7 (-7) = -3<\/p>\n<p>Question 15.<br \/>\n-20 \u00f7 4<\/p>\n<p>Answer:<br \/>\n-20 \u00f7 4 = -5<\/p>\n<p>Explanation:<br \/>\nThe quotient of two integers with the different signs is negative.<br \/>\n-20 \u00f7 4 = -5<\/p>\n<p>Question 16.<br \/>\n-18 \u00f7 (-3)<\/p>\n<p>Answer:<br \/>\n-18 \u00f7 (-3) = 6<\/p>\n<p>Explanation:<br \/>\nThe quotient of two integers with the same sign is positive.<br \/>\n-18 \u00f7 (-3) = 6<\/p>\n<p>Question 17.<br \/>\n\\(\\frac{-14}{2}\\)<\/p>\n<p>Answer:<br \/>\n-14 \u00f7 2 = -7<\/p>\n<p>Explanation:<br \/>\nThe quotient of two integers with the different signs is negative.<br \/>\n-14 \u00f7 2 = -7<\/p>\n<p>Question 18.<br \/>\n\\(\\frac{0}{6}\\)<\/p>\n<p>Answer:<br \/>\n0 \u00f7 6 = 0<\/p>\n<p>Explanation:<br \/>\nIf any of the integers is zero in the division expression, then the quotient is zero.<br \/>\n0 \u00f7 6 = 0<\/p>\n<p>Question 19.<br \/>\n\\(\\frac{-15}{-5}\\)<\/p>\n<p>Answer:<br \/>\n-15 \u00f7 -5 = 3<\/p>\n<p>Explanation:<br \/>\nThe quotient of two integers with the same sign is positive.<br \/>\n-15 \u00f7 -5 = 3<\/p>\n<p>Question 20.<br \/>\n\\(\\frac{54}{-9}\\)<\/p>\n<p>Answer:<br \/>\n54 \u00f7 -9 = -6<\/p>\n<p>Explanation:<br \/>\nThe quotient of two integers with the different signs is negative.<br \/>\n54 \u00f7 -9 = -6<\/p>\n<p>Question 21.<br \/>\n\\(-\\frac{33}{11}\\)<\/p>\n<p>Answer:<br \/>\n-33 \u00f7 11 = -3<\/p>\n<p>Explanation:<br \/>\nThe quotient of two integers with the different signs is negative.<br \/>\n-33 \u00f7 11 = -3<\/p>\n<p>Question 22.<br \/>\n-49 \u00f7 (-7)<\/p>\n<p>Answer:<br \/>\n-49 \u00f7 (-7) = 7<\/p>\n<p>Explanation:<br \/>\nThe quotient of two integers with the same sign is positive.<br \/>\n-49 \u00f7 (-7) = 7<\/p>\n<p>Question 23.<br \/>\n0 \u00f7 (-2)<\/p>\n<p>Answer:<br \/>\n0 \u00f7 (-2) = 0<\/p>\n<p>Explanation:<br \/>\nIf any of the integers is zero in the division expression, then the quotient is zero.<br \/>\n0 \u00f7 (-2) = 0<\/p>\n<p>Question 24.<br \/>\n\\(\\frac{60}{-6}\\)<\/p>\n<p>Answer:<br \/>\n60 \u00f7 -6 = -10<\/p>\n<p>Explanation:<br \/>\nThe quotient of two integers with the different signs is negative.<br \/>\n60 \u00f7 -6 = -10<\/p>\n<p>Question 25.<br \/>\n\\(\\frac{-56}{14}\\)<\/p>\n<p>Answer:<br \/>\n-56 \u00f7 14 = -4<\/p>\n<p>Explanation:<br \/>\nThe quotient of two integers with the different signs is negative.<br \/>\n-56 \u00f7 14 = -4<\/p>\n<p>Question 26.<br \/>\n\\(\\frac{18}{0}\\)<\/p>\n<p>Answer:<br \/>\n18 \u00f7 0 = 0<\/p>\n<p>Explanation:<br \/>\nIf any of the integers is zero in the division expression, then the quotient is zero.<br \/>\n18 \u00f7 0 = 0<\/p>\n<p>Question 27.<br \/>\n\\(-\\frac{65}{5}\\)<\/p>\n<p>Answer:<br \/>\n-65 \u00f7 5 = -13<\/p>\n<p>Explanation:<br \/>\nThe quotient of two integers with the different signs is negative.<br \/>\n-65 \u00f7 5 = -13<\/p>\n<p>Question 28.<br \/>\n\\(\\frac{-84}{-7}\\)<\/p>\n<p>Answer:<br \/>\n-84 \u00f7 -7 = 12<\/p>\n<p>Explanation:<br \/>\nThe quotient of two integers with the same sign is positive.<br \/>\n-84 \u00f7 -7 = 12<\/p>\n<p><strong>YOU BE THE TEACHER<\/strong><br \/>\n<strong>Your friend \ufb01nds the quotient. Is your friend correct? Explain your reasoning.<\/strong><\/p>\n<p>Question 29.<br \/>\n<img decoding=\"async\" loading=\"lazy\" class=\"alignnone size-full wp-image-30124\" src=\"https:\/\/ccssanswers.com\/wp-content\/uploads\/2021\/01\/Big-Ideas-Math-Answer-Key-Grade-7-Chapter-2-Multiplying-and-Dividing-Rational-Numbers-23.png\" alt=\"Big Ideas Math Answer Key Grade 7 Chapter 2 Multiplying and Dividing Rational Numbers 23\" width=\"157\" height=\"79\" \/><\/p>\n<p>Answer:<br \/>\nWrong<\/p>\n<p>Explanation:<br \/>\nThe quotient of two integers with the same sign is positive.<br \/>\n-63 \u00f7 -9 = 7<\/p>\n<p>Question 30.<br \/>\n<img decoding=\"async\" loading=\"lazy\" class=\"alignnone size-full wp-image-30126\" src=\"https:\/\/ccssanswers.com\/wp-content\/uploads\/2021\/01\/Big-Ideas-Math-Answer-Key-Grade-7-Chapter-2-Multiplying-and-Dividing-Rational-Numbers-24.png\" alt=\"Big Ideas Math Answer Key Grade 7 Chapter 2 Multiplying and Dividing Rational Numbers 24\" width=\"153\" height=\"85\" \/><\/p>\n<p>Answer:<br \/>\n0 \u00f7 (-5) = 0<\/p>\n<p>Explanation:<br \/>\nIf any of the integers is zero in the division expression, then the quotient is zero.<br \/>\n0 \u00f7 (-5) = 0<\/p>\n<p>Question 31.<br \/>\n<strong>MODELING REAL LIFE<\/strong><br \/>\nYou read 105 pages of a novel over 7 days. What is the mean number of pages you read each day?<br \/>\n<img decoding=\"async\" loading=\"lazy\" class=\"alignnone size-full wp-image-30125\" src=\"https:\/\/ccssanswers.com\/wp-content\/uploads\/2021\/01\/Big-Ideas-Math-Answer-Key-Grade-7-Chapter-2-Multiplying-and-Dividing-Rational-Numbers-24.1.png\" alt=\"Big Ideas Math Answer Key Grade 7 Chapter 2 Multiplying and Dividing Rational Numbers 24.1\" width=\"214\" height=\"176\" \/><\/p>\n<p>Answer:<br \/>\nThe mean is 15 pages a day.<\/p>\n<p>Explanation:<br \/>\nTo find the mean of the pages we read each day we will evaluate the quotient of the division of the number of pages we read over these days (105 days) by the number of days (7 days).<br \/>\n105 \/ 7 = 15<br \/>\nThe mean is 15 pages a day.<\/p>\n<p><strong>USING ORDER OF OPERATIONS<\/strong><br \/>\n<strong>Evaluate the expression.<\/strong><\/p>\n<p>Question 32.<br \/>\n-8 &#8211; 14 \u00f7 2 + 5<\/p>\n<p>Answer:<br \/>\n-8 &#8211; 14 \u00f7 2 + 5 = -10<\/p>\n<p>Explanation:<br \/>\nThe given expression is -8 &#8211; 14 \u00f7 2 + 5<br \/>\n-8 &#8211; (14 \/ 2) + 5<br \/>\n= -8 &#8211; 7 + 5<br \/>\n= -15 + 5 = -10<\/p>\n<p>Question 33.<br \/>\n24 \u00f7 (-4) + (-2) \u2022 (-5)<\/p>\n<p>Answer:<br \/>\n24 \u00f7 (-4) + (-2) \u2022 (-5) = 4<\/p>\n<p>Explanation:<br \/>\nThe given expression is 24 \u00f7 (-4) + (-2) \u2022 (-5)<br \/>\n= -6 + (-2) . (-5)<br \/>\n= -6 + 10<br \/>\n= 4<\/p>\n<p><strong>EVALUATING EXPRESSIONS<\/strong><br \/>\n<strong>Evaluate the expression when x = 10, y = -2, and z = -5.<\/strong><\/p>\n<p>Question 34.<br \/>\nx \u00f7 y<\/p>\n<p>Answer:<br \/>\n-5<\/p>\n<p>Explanation:<br \/>\nThe given expression is x \u00f7 y<br \/>\nPut x = 10, y = -2<br \/>\n= 10 \u00f7 -2<br \/>\nThe quotient of two integers with the different signs is negative.<br \/>\n= -5<\/p>\n<p>Question 35.<br \/>\n12 \u00f7 3y<\/p>\n<p>Answer:<br \/>\n-2<\/p>\n<p>Explanation:<br \/>\nThe given expression is 12 \u00f7 3y<br \/>\nPut y = -2<br \/>\n= 12 \u00f7 3(-2)<br \/>\n= 12 \u00f7 -6<br \/>\nThe quotient of two integers with the different signs is negative.<br \/>\n= -2<\/p>\n<p>Question 36.<br \/>\n\\(\\frac{2 z}{y}\\)<\/p>\n<p>Answer:<br \/>\n5<\/p>\n<p>Explanation:<br \/>\nThe given expression is 2z\/y<br \/>\nPut y = -2, and z = -5.<br \/>\n= 2(-5)\/(-2)<br \/>\n= -10\/-2<br \/>\nThe quotient of two integers with the same sign is positive.<br \/>\n= 5<\/p>\n<p>Question 37.<br \/>\n<img decoding=\"async\" loading=\"lazy\" class=\"alignnone size-full wp-image-30131\" src=\"https:\/\/ccssanswers.com\/wp-content\/uploads\/2021\/01\/Big-Ideas-Math-Answer-Key-Grade-7-Chapter-2-Multiplying-and-Dividing-Rational-Numbers-25.png\" alt=\"Big Ideas Math Answer Key Grade 7 Chapter 2 Multiplying and Dividing Rational Numbers 25\" width=\"65\" height=\"47\" \/><\/p>\n<p>Answer:<br \/>\n-2<\/p>\n<p>Explanation:<br \/>\nThe given expression is (-x + y)\/6<br \/>\nPut x = 10, y = -2<br \/>\n= (-10 + (-2))\/6<br \/>\n= (-10 &#8211; 2)\/6<br \/>\n= -12\/6<br \/>\nThe quotient of two integers with the different signs is negative.<br \/>\n= -2<\/p>\n<p>Question 38.<br \/>\n100 \u00f7 (-z<sup>2<\/sup>)<\/p>\n<p>Answer:<br \/>\n4<\/p>\n<p>Explanation:<br \/>\nThe given expression is 100 \u00f7 (-z<sup>2<\/sup>)<br \/>\nPut z = -5<br \/>\n= 100 \u00f7(-(-5)\u00b2)<br \/>\n= 100 \u00f7 (25)<br \/>\nThe quotient of two integers with the same sign is positive.<br \/>\n= 4<\/p>\n<p>Question 39.<br \/>\n<img decoding=\"async\" loading=\"lazy\" class=\"alignnone size-full wp-image-30127\" src=\"https:\/\/ccssanswers.com\/wp-content\/uploads\/2021\/01\/Big-Ideas-Math-Answer-Key-Grade-7-Chapter-2-Multiplying-and-Dividing-Rational-Numbers-25.1.png\" alt=\"Big Ideas Math Answer Key Grade 7 Chapter 2 Multiplying and Dividing Rational Numbers 25.1\" width=\"50\" height=\"57\" \/><\/p>\n<p>Answer:<br \/>\n-8<\/p>\n<p>Explanation:<br \/>\nThe given expression is (10y\u00b2)\/z<br \/>\nPut y = -2, and z = -5<br \/>\n= (10(-2)\u00b2)\/-5<br \/>\n= 10(4)\/-5<br \/>\n= 40\/-5<br \/>\nThe quotient of two integers with the different signs is negative.<br \/>\n= -8<\/p>\n<p>Question 40.<br \/>\n<img decoding=\"async\" loading=\"lazy\" class=\"alignnone size-full wp-image-30128\" src=\"https:\/\/ccssanswers.com\/wp-content\/uploads\/2021\/01\/Big-Ideas-Math-Answer-Key-Grade-7-Chapter-2-Multiplying-and-Dividing-Rational-Numbers-25.2.png\" alt=\"Big Ideas Math Answer Key Grade 7 Chapter 2 Multiplying and Dividing Rational Numbers 25.2\" width=\"63\" height=\"56\" \/><\/p>\n<p>Answer:<br \/>\n25<\/p>\n<p>Explanation:<br \/>\nThe given expression is | (xz)\/-y |<br \/>\nPut x = 10, y = -2, and z = -5<br \/>\n= | (10 . -5)\/-(-2) |<br \/>\n= | -50\/2 |<br \/>\n= 50\/2<br \/>\n= 25<\/p>\n<p>Question 41.<br \/>\n<img decoding=\"async\" loading=\"lazy\" class=\"alignnone size-full wp-image-30129\" src=\"https:\/\/ccssanswers.com\/wp-content\/uploads\/2021\/01\/Big-Ideas-Math-Answer-Key-Grade-7-Chapter-2-Multiplying-and-Dividing-Rational-Numbers-25.3.png\" alt=\"Big Ideas Math Answer Key Grade 7 Chapter 2 Multiplying and Dividing Rational Numbers 25.3\" width=\"80\" height=\"55\" \/><\/p>\n<p>Answer:<br \/>\n65<\/p>\n<p>Explanation:<br \/>\nThe given expression is (-x\u00b2 + 6z)\/y<br \/>\nPut x = 10, y = -2, and z = -5<br \/>\n= (-(10)\u00b2 + 6(-5))\/-2<br \/>\n= (-100 &#8211; 30)\/-2<br \/>\n= -130\/-2<br \/>\n= 65<\/p>\n<p>Question 42.<br \/>\n<strong>PATTERNS<\/strong><br \/>\nFind the next two numbers in the pattern -128, 64, -32, 16, . . .. Explain your reasoning.<\/p>\n<p>Answer:<br \/>\nThe next two numbers in the pattern are -8, 4.<\/p>\n<p>Explanation:<br \/>\nDivide each integer by -2<br \/>\n-128\/-2 = 64<br \/>\n64\/-2 = -32<br \/>\n-32\/-2 = 16<br \/>\n16\/-2 = -8<br \/>\n-8\/-2 = 4<br \/>\nSo, the next two numbers in the pattern are -8, 4.<\/p>\n<p>Question 43.<br \/>\n<strong>MODELING REAL LIFE<\/strong><br \/>\nThe Detroit-Windsor Tunnel is an underwater highway that connects the cities of Detroit, Michigan, and Windsor, Ontario. How many times deeper is the roadway than the bottom of the ship?<br \/>\n<img decoding=\"async\" loading=\"lazy\" class=\"alignnone size-full wp-image-30132\" src=\"https:\/\/ccssanswers.com\/wp-content\/uploads\/2021\/01\/Big-Ideas-Math-Answer-Key-Grade-7-Chapter-2-Multiplying-and-Dividing-Rational-Numbers-26.png\" alt=\"Big Ideas Math Answer Key Grade 7 Chapter 2 Multiplying and Dividing Rational Numbers 26\" width=\"538\" height=\"148\" srcset=\"https:\/\/ccssanswers.com\/wp-content\/uploads\/2021\/01\/Big-Ideas-Math-Answer-Key-Grade-7-Chapter-2-Multiplying-and-Dividing-Rational-Numbers-26.png 538w, https:\/\/ccssanswers.com\/wp-content\/uploads\/2021\/01\/Big-Ideas-Math-Answer-Key-Grade-7-Chapter-2-Multiplying-and-Dividing-Rational-Numbers-26-300x83.png 300w\" sizes=\"(max-width: 538px) 100vw, 538px\" \/><\/p>\n<p>Answer:<br \/>\n5 times deeper is the roadway than the bottom of the ship.<\/p>\n<p>Explanation:<br \/>\nThe deep of the bottom of the ship = -15 ft<br \/>\nThe deep of the roadway = -75 ft<br \/>\nTo find out how many times deeper is the roadway than the bottom of the ship, divide the deep of the roadway by the deep of the bottom of the ship<br \/>\n-75 \/ -15 = 5 times<br \/>\nSo, 5 times deeper is the roadway than the bottom of the ship<\/p>\n<p>Question 44.<br \/>\n<strong>MODELING REAL LIFE<\/strong><br \/>\nA snowboarder descends from an elevation of 2253 feet to an elevation of 1011 feet in 3 minutes. What is the mean change in elevation per minute?<\/p>\n<p>Answer:<br \/>\nThe mean change in elevation per minute is 414 ft.<\/p>\n<p>Explanation:<br \/>\nA snowboarder descends from an elevation of 2253 feet to an elevation of 1011 feet in 3 minutes<br \/>\nSo, the mean change in elevation per minute = (2253 &#8211; 1011)\/3<br \/>\n= 1242\/3 = 414 ft<\/p>\n<p>Question 45.<br \/>\n<strong>REASONING<\/strong><br \/>\nThe table shows a golfer\u2019s scores relative to par for three out of four rounds of a tournament.<br \/>\na. What was the golfer\u2019s mean score per round for the \ufb01rst 3 rounds?<br \/>\nb. The golfer&#8217;s goal for the tournament is to have a mean score no greater than -3. Describe how the golfer can achieve this goal.<br \/>\n<img decoding=\"async\" loading=\"lazy\" class=\"alignnone size-full wp-image-30130\" src=\"https:\/\/ccssanswers.com\/wp-content\/uploads\/2021\/01\/Big-Ideas-Math-Answer-Key-Grade-7-Chapter-2-Multiplying-and-Dividing-Rational-Numbers-25.5.png\" alt=\"Big Ideas Math Answer Key Grade 7 Chapter 2 Multiplying and Dividing Rational Numbers 25.5\" width=\"156\" height=\"141\" \/><br \/>\n<img decoding=\"async\" loading=\"lazy\" class=\"alignnone size-full wp-image-30133\" src=\"https:\/\/ccssanswers.com\/wp-content\/uploads\/2021\/01\/Big-Ideas-Math-Answer-Key-Grade-7-Chapter-2-Multiplying-and-Dividing-Rational-Numbers-28.png\" alt=\"Big Ideas Math Answer Key Grade 7 Chapter 2 Multiplying and Dividing Rational Numbers 28\" width=\"844\" height=\"132\" srcset=\"https:\/\/ccssanswers.com\/wp-content\/uploads\/2021\/01\/Big-Ideas-Math-Answer-Key-Grade-7-Chapter-2-Multiplying-and-Dividing-Rational-Numbers-28.png 844w, https:\/\/ccssanswers.com\/wp-content\/uploads\/2021\/01\/Big-Ideas-Math-Answer-Key-Grade-7-Chapter-2-Multiplying-and-Dividing-Rational-Numbers-28-300x47.png 300w, https:\/\/ccssanswers.com\/wp-content\/uploads\/2021\/01\/Big-Ideas-Math-Answer-Key-Grade-7-Chapter-2-Multiplying-and-Dividing-Rational-Numbers-28-768x120.png 768w\" sizes=\"(max-width: 844px) 100vw, 844px\" \/><\/p>\n<p>Answer:<br \/>\na. The golfer\u2019s mean score per round for the \ufb01rst 3 rounds is -2<br \/>\nb. The score in round 4 should be less than -6.<\/p>\n<p>Explanation:<br \/>\na. The golfer\u2019s mean score per round for the \ufb01rst 3 rounds = (1 + (-4) + (-3))\/3<br \/>\n= (1 &#8211; 4 &#8211; 3)\/3 = (1 &#8211; 7)\/3<br \/>\n= -6\/3 = -2<br \/>\nb. The golfer&#8217;s goal for the tournament is to have a mean score no greater than -3.<br \/>\n(1 + (-4) + (-3) + x)\/4 &lt; -3<br \/>\n(1 &#8211; 4 &#8211; 3 + x)\/4 &lt;-3<br \/>\n(1 &#8211; 7 + x)\/4 &lt;-3<br \/>\n(-6 + x)\/4 &lt; -3<br \/>\n(-6 + x) &lt; -3 . 4<br \/>\n(-6 + x) &lt; -12<br \/>\nx &lt; -12 + 6<br \/>\nx &lt; -6<br \/>\nThe score at the round 4 should be less than -6.<\/p>\n<p>Question 46.<br \/>\n<strong>PROBLEM SOLVING<\/strong><br \/>\nThe regular admission price for an amusement park is $72. For a group of 15 or more, the admission price is reduced by $25 per person. How many people need to be in a group to save $500?<\/p>\n<p>Answer:<br \/>\n20 people needed in the group to save $500.<\/p>\n<p>Explanation:<br \/>\nLet the number of people is x<br \/>\nThe price of the person reduced by $25<br \/>\nThe total price we want to save is $500<br \/>\nx = 500\/25 = 20<br \/>\nSo, the number of people x needs to be in the group to save $500 is 20 people.<\/p>\n<p>Question 47.<br \/>\n<strong>DIG DEEPER!<\/strong><br \/>\nWrite a set of \ufb01ve different integers that has a mean of -10. Explain how you found your answer.<\/p>\n<p>Answer:<br \/>\nThe set of five different integers whose mean is -10 are (-12, -11, -10, -9 -8).<\/p>\n<p>Explanation:<br \/>\nLet us take the 5 integers as x, x + 1, x + 2, x + 3, x + 4<br \/>\nThe mean of these integers is -10<br \/>\n(x + x + 1 + x + 2 + x + 3 + x + 4)\/5 = -10<br \/>\n(5x + 10)\/5 = -10<br \/>\n5x + 10 = -10 . 5<br \/>\n5x + 10 = -50<br \/>\n5x = -50 &#8211; 10<br \/>\n5x = -60<br \/>\nx = -60\/5<br \/>\nx = -12<br \/>\nSo, the set of 5 integers are -12, -12 + 1 = -11, -12 + 2 = -10, -12 +3 = -9, -12 + 4 = -8<\/p>\n<h3><a id=\"Lesson_2.3_Converting_Between_Fractions_and_Decimals\"><\/a>Lesson 2.3 Converting Between Fractions and Decimals<\/h3>\n<p><strong>EXPLORATION 1<\/strong><\/p>\n<p><strong>Analyzing Denominators of Decimal Fractions<\/strong><br \/>\n<strong>Work with a partner.<\/strong><br \/>\na. Write each decimal as a fraction or mixed number.<br \/>\n<img decoding=\"async\" loading=\"lazy\" class=\"alignnone size-full wp-image-30134\" src=\"https:\/\/ccssanswers.com\/wp-content\/uploads\/2021\/01\/Big-Ideas-Math-Answer-Key-Grade-7-Chapter-2-Multiplying-and-Dividing-Rational-Numbers-29.png\" alt=\"Big Ideas Math Answer Key Grade 7 Chapter 2 Multiplying and Dividing Rational Numbers 29\" width=\"377\" height=\"165\" srcset=\"https:\/\/ccssanswers.com\/wp-content\/uploads\/2021\/01\/Big-Ideas-Math-Answer-Key-Grade-7-Chapter-2-Multiplying-and-Dividing-Rational-Numbers-29.png 377w, https:\/\/ccssanswers.com\/wp-content\/uploads\/2021\/01\/Big-Ideas-Math-Answer-Key-Grade-7-Chapter-2-Multiplying-and-Dividing-Rational-Numbers-29-300x131.png 300w\" sizes=\"(max-width: 377px) 100vw, 377px\" \/><br \/>\nb. What do the factors of the denominators of the fractions you wrote have in common? Is this always true for decimal fractions?<br \/>\n<img decoding=\"async\" loading=\"lazy\" class=\"alignnone size-full wp-image-30135\" src=\"https:\/\/ccssanswers.com\/wp-content\/uploads\/2021\/01\/Big-Ideas-Math-Answer-Key-Grade-7-Chapter-2-Multiplying-and-Dividing-Rational-Numbers-30.png\" alt=\"Big Ideas Math Answer Key Grade 7 Chapter 2 Multiplying and Dividing Rational Numbers 30\" width=\"164\" height=\"231\" \/><\/p>\n<p><strong>EXPLORATION 2<\/strong><br \/>\n<strong>Exploring Decimal Representations<\/strong><br \/>\n<strong>Work with a partner.<\/strong><br \/>\na. A fraction \\(\\frac{a}{b}\\) can be interpreted as a \u00f7 b. Use a calculator to convert each unit fraction to a decimal. Do some of the decimals look different than the others? Explain.<br \/>\n<img decoding=\"async\" loading=\"lazy\" class=\"alignnone size-full wp-image-30136\" src=\"https:\/\/ccssanswers.com\/wp-content\/uploads\/2021\/01\/Big-Ideas-Math-Answer-Key-Grade-7-Chapter-2-Multiplying-and-Dividing-Rational-Numbers-31.png\" alt=\"Big Ideas Math Answer Key Grade 7 Chapter 2 Multiplying and Dividing Rational Numbers 31\" width=\"362\" height=\"162\" srcset=\"https:\/\/ccssanswers.com\/wp-content\/uploads\/2021\/01\/Big-Ideas-Math-Answer-Key-Grade-7-Chapter-2-Multiplying-and-Dividing-Rational-Numbers-31.png 362w, https:\/\/ccssanswers.com\/wp-content\/uploads\/2021\/01\/Big-Ideas-Math-Answer-Key-Grade-7-Chapter-2-Multiplying-and-Dividing-Rational-Numbers-31-300x134.png 300w\" sizes=\"(max-width: 362px) 100vw, 362px\" \/><br \/>\nb. Compare and contrast the fractions in part(a) with the fractions you wrote in Exploration 1. What conclusions can you make?<br \/>\n<img decoding=\"async\" loading=\"lazy\" class=\"alignnone size-full wp-image-30137\" src=\"https:\/\/ccssanswers.com\/wp-content\/uploads\/2021\/01\/Big-Ideas-Math-Answer-Key-Grade-7-Chapter-2-Multiplying-and-Dividing-Rational-Numbers-32.png\" alt=\"Big Ideas Math Answer Key Grade 7 Chapter 2 Multiplying and Dividing Rational Numbers 32\" width=\"156\" height=\"227\" \/><br \/>\nc. Does every fraction have a decimal form that either terminates or repeats? Explain your reasoning.<\/p>\n<p><strong>2.3 Lesson<\/strong><\/p>\n<p><strong>Try It<\/strong><\/p>\n<p><strong>Write the fraction or mixed number as a decimal.<\/strong><\/p>\n<p>Question 1.<br \/>\n\\(-\\frac{6}{5}\\)<\/p>\n<p>Answer:<br \/>\n-6\/5 = -1.2<\/p>\n<p>Explanation:<br \/>\n<img decoding=\"async\" loading=\"lazy\" class=\"alignnone size-full wp-image-41659\" src=\"https:\/\/ccssanswers.com\/wp-content\/uploads\/2021\/01\/big-ideas-math-answers-grade-7-chapter-2-multiplying-and-dividing-rational-numbers-19.jpg\" alt=\"Big Ideas Math Answers Grade 7 Chapter 2 Multiplying and Dividing Rational Numbers 19\" width=\"107\" height=\"263\" \/><\/p>\n<p>Question 2.<br \/>\n-7\\(\\frac{3}{8}\\)<\/p>\n<p>Answer:<br \/>\n-7(3\/8) = -7.375<\/p>\n<p>Explanation:<br \/>\n-7(3\/8) = -59\/8<br \/>\nUse long division to divide 59 by 8<br \/>\n<img decoding=\"async\" loading=\"lazy\" class=\"alignnone size-full wp-image-41661\" src=\"https:\/\/ccssanswers.com\/wp-content\/uploads\/2021\/01\/big-ideas-math-answers-grade-7-chapter-2-multiplying-and-dividing-rational-numbers-20.jpg\" alt=\"g Ideas Math Answers Grade 7 Chapter 2 Multiplying and Dividing Rational Numbers 20\" width=\"194\" height=\"507\" srcset=\"https:\/\/ccssanswers.com\/wp-content\/uploads\/2021\/01\/big-ideas-math-answers-grade-7-chapter-2-multiplying-and-dividing-rational-numbers-20.jpg 194w, https:\/\/ccssanswers.com\/wp-content\/uploads\/2021\/01\/big-ideas-math-answers-grade-7-chapter-2-multiplying-and-dividing-rational-numbers-20-115x300.jpg 115w\" sizes=\"(max-width: 194px) 100vw, 194px\" \/><\/p>\n<p>Question 3.<br \/>\n\\(-\\frac{3}{11}\\)<\/p>\n<p>Answer:<br \/>\n-3\/11 = 0.2727<\/p>\n<p>Explanation:<br \/>\n<img decoding=\"async\" loading=\"lazy\" class=\"alignnone size-full wp-image-41662\" src=\"https:\/\/ccssanswers.com\/wp-content\/uploads\/2021\/01\/big-ideas-math-answers-grade-7-chapter-2-multiplying-and-dividing-rational-numbers-21.jpg\" alt=\"Big Ideas Math Answers Grade 7 Chapter 2 Multiplying and Dividing Rational Numbers 21\" width=\"225\" height=\"504\" srcset=\"https:\/\/ccssanswers.com\/wp-content\/uploads\/2021\/01\/big-ideas-math-answers-grade-7-chapter-2-multiplying-and-dividing-rational-numbers-21.jpg 225w, https:\/\/ccssanswers.com\/wp-content\/uploads\/2021\/01\/big-ideas-math-answers-grade-7-chapter-2-multiplying-and-dividing-rational-numbers-21-134x300.jpg 134w\" sizes=\"(max-width: 225px) 100vw, 225px\" \/><br \/>\nThe remainder repeats. So, it is a repeating decimal.<\/p>\n<p>Question 4.<br \/>\n1\\(\\frac{5}{27}\\)<\/p>\n<p>Answer:<br \/>\n1(5\/27) =1.185<\/p>\n<p>Explanation:<br \/>\n1(5\/27) =32\/27<br \/>\n<img decoding=\"async\" loading=\"lazy\" class=\"alignnone size-full wp-image-41666\" src=\"https:\/\/ccssanswers.com\/wp-content\/uploads\/2021\/01\/big-ideas-math-answers-grade-7-chapter-2-multiplying-and-dividing-rational-numbers-22.jpg\" alt=\"Big Ideas Math Answers Grade 7 Chapter 2 Multiplying and Dividing Rational Numbers 22\" width=\"281\" height=\"670\" srcset=\"https:\/\/ccssanswers.com\/wp-content\/uploads\/2021\/01\/big-ideas-math-answers-grade-7-chapter-2-multiplying-and-dividing-rational-numbers-22.jpg 281w, https:\/\/ccssanswers.com\/wp-content\/uploads\/2021\/01\/big-ideas-math-answers-grade-7-chapter-2-multiplying-and-dividing-rational-numbers-22-126x300.jpg 126w\" sizes=\"(max-width: 281px) 100vw, 281px\" \/><\/p>\n<p><strong>Try It<\/strong><\/p>\n<p><strong>Write the decimal as a fraction or mixed number in simplest form.<\/strong><\/p>\n<p>Question 5.<br \/>\n-0.3<\/p>\n<p>Answer:<br \/>\n-0.3 = -3\/10<\/p>\n<p>Explanation:<br \/>\n-0.3 = -3\/10<\/p>\n<p>Question 6.<br \/>\n0.125<\/p>\n<p>Answer:<br \/>\n0.125 = 1\/8<\/p>\n<p>Explanation:<br \/>\n0.125 = 125\/1000<br \/>\n= (5 . 25)\/(5 . 200)<br \/>\n= (5 . 5)\/(5 . 40)<br \/>\n= 5\/(8 . 5)<br \/>\n= 1\/8<\/p>\n<p>Question 7.<br \/>\n-3.1<\/p>\n<p>Answer:<br \/>\n-3.1 = -31\/10<\/p>\n<p>Explanation:<br \/>\n-3.1 = -31\/10<\/p>\n<p>Question 8.<br \/>\n-10.25<\/p>\n<p>Answer:<br \/>\n-10.25 = -41\/4<\/p>\n<p>Explanation:<br \/>\n-10.25 = -1025\/100<br \/>\n= -(5 . 205)\/(20 . 5)<br \/>\n= -(5 . 41)\/(5 . 4)<br \/>\n= -41\/4<\/p>\n<p><strong>Self-Assessment for Concepts &amp; Skills<\/strong><br \/>\nSolve each exercise. Then rate your understanding of the success criteria in your journal.<\/p>\n<p>Question 9.<br \/>\n<strong>WRITING<\/strong><br \/>\nCompare and contrast terminating decimals and repeating decimals.<\/p>\n<p>Answer:<br \/>\nA rational number can be expressed as either a terminating decimal or a repeating decimal. Divide numerator by the denominator you will get a remainder of 0, then you have a terminating decimal. The remainders will begin to repeat after some point, and you have a repeating decimal.<br \/>\nThe example for terminating decimal is 5\/8 = 0.625<br \/>\nThe example for repeating decimal is 7\/12 = 0.58333.<\/p>\n<p><strong>WRITING A FRACTION OR MIXED NUMBER AS A DECIMAL<\/strong><br \/>\n<strong>Write the fraction or mixed number as a decimal.<\/strong><\/p>\n<p>Question 10.<br \/>\n\\(\\frac{3}{16}\\)<\/p>\n<p>Answer:<br \/>\n3\/16 = 0.1875<\/p>\n<p>Explanation:<br \/>\n<img decoding=\"async\" loading=\"lazy\" class=\"alignnone size-full wp-image-41672\" src=\"https:\/\/ccssanswers.com\/wp-content\/uploads\/2021\/01\/big-ideas-math-answers-grade-7-chapter-2-multiplying-and-dividing-rational-numbers-23.jpg\" alt=\"Big Ideas Math Answers Grade 7 Chapter 2 Multiplying and Dividing Rational Numbers 23\" width=\"222\" height=\"506\" srcset=\"https:\/\/ccssanswers.com\/wp-content\/uploads\/2021\/01\/big-ideas-math-answers-grade-7-chapter-2-multiplying-and-dividing-rational-numbers-23.jpg 222w, https:\/\/ccssanswers.com\/wp-content\/uploads\/2021\/01\/big-ideas-math-answers-grade-7-chapter-2-multiplying-and-dividing-rational-numbers-23-132x300.jpg 132w\" sizes=\"(max-width: 222px) 100vw, 222px\" \/><\/p>\n<p>Question 11.<br \/>\n&#8211;\\(\\frac{7}{15}\\)<\/p>\n<p>Answer:<br \/>\n-7\/15 = -0.4666<\/p>\n<p>Explanation:<br \/>\n<img decoding=\"async\" loading=\"lazy\" class=\"alignnone size-full wp-image-41673\" src=\"https:\/\/ccssanswers.com\/wp-content\/uploads\/2021\/01\/big-ideas-math-answers-grade-7-chapter-2-multiplying-and-dividing-rational-numbers-24.jpg\" alt=\"Big Ideas Math Answers Grade 7 Chapter 2 Multiplying and Dividing Rational Numbers 24\" width=\"226\" height=\"505\" srcset=\"https:\/\/ccssanswers.com\/wp-content\/uploads\/2021\/01\/big-ideas-math-answers-grade-7-chapter-2-multiplying-and-dividing-rational-numbers-24.jpg 226w, https:\/\/ccssanswers.com\/wp-content\/uploads\/2021\/01\/big-ideas-math-answers-grade-7-chapter-2-multiplying-and-dividing-rational-numbers-24-134x300.jpg 134w\" sizes=\"(max-width: 226px) 100vw, 226px\" \/><\/p>\n<p>Question 12.<br \/>\n6\\(\\frac{17}{20}\\)<\/p>\n<p>Answer:<br \/>\n6(17\/20) = 6.85<\/p>\n<p>Explanation:<br \/>\n6(17\/20) = 137\/20<br \/>\n<img decoding=\"async\" loading=\"lazy\" class=\"alignnone size-full wp-image-41675\" src=\"https:\/\/ccssanswers.com\/wp-content\/uploads\/2021\/01\/big-ideas-math-answers-grade-7-chapter-2-multiplying-and-dividing-rational-numbers-25.jpg\" alt=\"Big Ideas Math Answers Grade 7 Chapter 2 Multiplying and Dividing Rational Numbers 25\" width=\"223\" height=\"506\" srcset=\"https:\/\/ccssanswers.com\/wp-content\/uploads\/2021\/01\/big-ideas-math-answers-grade-7-chapter-2-multiplying-and-dividing-rational-numbers-25.jpg 223w, https:\/\/ccssanswers.com\/wp-content\/uploads\/2021\/01\/big-ideas-math-answers-grade-7-chapter-2-multiplying-and-dividing-rational-numbers-25-132x300.jpg 132w\" sizes=\"(max-width: 223px) 100vw, 223px\" \/><\/p>\n<p><strong>WRITING A DECIMAL AS A FRACTION OR MIXED NUMBER<\/strong><br \/>\n<strong>Write the decimal as a fraction or mixed number in simplest form.<\/strong><\/p>\n<p>Question 13.<br \/>\n0.6<\/p>\n<p>Answer:<br \/>\n0.6 = 3\/5<\/p>\n<p>Explanation:<br \/>\n0.6 = 6\/10<br \/>\n= 3\/5<\/p>\n<p>Question 14.<br \/>\n-12.48<\/p>\n<p>Answer:<br \/>\n-12.48 = -312\/25<\/p>\n<p>Explanation:<br \/>\n-12.48 = -1248\/100<br \/>\n= -(4 . 312)\/(4 . 25)<br \/>\n= -312\/25<\/p>\n<p>Question 15.<br \/>\n0.408<\/p>\n<p>Answer:<br \/>\n0.408 = 51\/125<\/p>\n<p>Explanation:<br \/>\n0.408 = 408\/1000<br \/>\n= (51 . 8)\/(125 . 8)<br \/>\n= 51\/125<\/p>\n<p><strong>Self-Assessment for Problem Solving<\/strong><\/p>\n<p>Solve each exercise. Then rate your understanding of the success criteria in your journal.<\/p>\n<p>Question 16.<br \/>\nA box turtle hibernates in sand at an elevation of 1.625 feet. A spotted turtle hibernates at an elevation of -1\\(\\frac{7}{12}\\) feet. Which turtle hibernates deeper in the sand? How much deeper?<br \/>\n<img decoding=\"async\" loading=\"lazy\" class=\"alignnone size-full wp-image-30138\" src=\"https:\/\/ccssanswers.com\/wp-content\/uploads\/2021\/01\/Big-Ideas-Math-Answer-Key-Grade-7-Chapter-2-Multiplying-and-Dividing-Rational-Numbers-33.png\" alt=\"Big Ideas Math Answer Key Grade 7 Chapter 2 Multiplying and Dividing Rational Numbers 33\" width=\"216\" height=\"109\" \/><\/p>\n<p>Answer:<br \/>\nBox turtle hibernates deeper in the sand.<\/p>\n<p>Explanation:<br \/>\nA box turtle hibernates in sand at an elevation of 1.625 feet.<br \/>\nA spotted turtle hibernates at an elevation of -1(7\/12) feet<br \/>\n= -19\/12 = -1.58333<br \/>\n<img decoding=\"async\" loading=\"lazy\" class=\"alignnone size-full wp-image-41680\" src=\"https:\/\/ccssanswers.com\/wp-content\/uploads\/2021\/01\/big-ideas-math-answers-grade-7-chapter-2-multiplying-and-dividing-rational-numbers-26.jpg\" alt=\"Big Ideas Math Answers Grade 7 Chapter 2 Multiplying and Dividing Rational Numbers 26\" width=\"255\" height=\"588\" srcset=\"https:\/\/ccssanswers.com\/wp-content\/uploads\/2021\/01\/big-ideas-math-answers-grade-7-chapter-2-multiplying-and-dividing-rational-numbers-26.jpg 255w, https:\/\/ccssanswers.com\/wp-content\/uploads\/2021\/01\/big-ideas-math-answers-grade-7-chapter-2-multiplying-and-dividing-rational-numbers-26-130x300.jpg 130w\" sizes=\"(max-width: 255px) 100vw, 255px\" \/><br \/>\n1.625 is greater than -1.5833.<br \/>\nSo, box turtle hibernates deeper in the sand.<\/p>\n<p>Question 17.<br \/>\nA red sprite is an electrical \ufb02ash that occurs in Earth\u2019s upper atmosphere. The table shows the elevations of four red sprites. What is the range of the elevations?<br \/>\n<img decoding=\"async\" loading=\"lazy\" class=\"alignnone size-full wp-image-30139\" src=\"https:\/\/ccssanswers.com\/wp-content\/uploads\/2021\/01\/Big-Ideas-Math-Answer-Key-Grade-7-Chapter-2-Multiplying-and-Dividing-Rational-Numbers-34.png\" alt=\"Big Ideas Math Answer Key Grade 7 Chapter 2 Multiplying and Dividing Rational Numbers 34\" width=\"174\" height=\"136\" \/><\/p>\n<p>Answer:<br \/>\nThe range of elevations are 51.66 miles, 50.6 miles, 50.53 miles, 50.52 miles.<\/p>\n<p>Explanation:<br \/>\nFirst, write each fraction or mixed fraction as a decimal.<br \/>\n50.6<br \/>\n50(8\/15) = 758\/15 = 50.533<br \/>\n<img decoding=\"async\" loading=\"lazy\" class=\"alignnone size-full wp-image-41681\" src=\"https:\/\/ccssanswers.com\/wp-content\/uploads\/2021\/01\/big-ideas-math-answers-grade-7-chapter-2-multiplying-and-dividing-rational-numbers-27.jpg\" alt=\"Big Ideas Math Answers Grade 7 Chapter 2 Multiplying and Dividing Rational Numbers 27\" width=\"285\" height=\"668\" srcset=\"https:\/\/ccssanswers.com\/wp-content\/uploads\/2021\/01\/big-ideas-math-answers-grade-7-chapter-2-multiplying-and-dividing-rational-numbers-27.jpg 285w, https:\/\/ccssanswers.com\/wp-content\/uploads\/2021\/01\/big-ideas-math-answers-grade-7-chapter-2-multiplying-and-dividing-rational-numbers-27-128x300.jpg 128w\" sizes=\"(max-width: 285px) 100vw, 285px\" \/><br \/>\n50(13\/25) = 1263\/25 = 50.52<br \/>\n<img decoding=\"async\" loading=\"lazy\" class=\"alignnone size-full wp-image-41683\" src=\"https:\/\/ccssanswers.com\/wp-content\/uploads\/2021\/01\/big-ideas-math-answers-grade-7-chapter-2-multiplying-and-dividing-rational-numbers-28.jpg\" alt=\"Big Ideas Math Answers Grade 7 Chapter 2 Multiplying and Dividing Rational Numbers 28\" width=\"250\" height=\"594\" srcset=\"https:\/\/ccssanswers.com\/wp-content\/uploads\/2021\/01\/big-ideas-math-answers-grade-7-chapter-2-multiplying-and-dividing-rational-numbers-28.jpg 250w, https:\/\/ccssanswers.com\/wp-content\/uploads\/2021\/01\/big-ideas-math-answers-grade-7-chapter-2-multiplying-and-dividing-rational-numbers-28-126x300.jpg 126w\" sizes=\"(max-width: 250px) 100vw, 250px\" \/><br \/>\n155\/3 = 51.66<br \/>\n<img decoding=\"async\" loading=\"lazy\" class=\"alignnone size-full wp-image-41684\" src=\"https:\/\/ccssanswers.com\/wp-content\/uploads\/2021\/01\/big-ideas-math-answers-grade-7-chapter-2-multiplying-and-dividing-rational-numbers-29.jpg\" alt=\"Big Ideas Math Answers Grade 7 Chapter 2 Multiplying and Dividing Rational Numbers 29\" width=\"190\" height=\"499\" srcset=\"https:\/\/ccssanswers.com\/wp-content\/uploads\/2021\/01\/big-ideas-math-answers-grade-7-chapter-2-multiplying-and-dividing-rational-numbers-29.jpg 190w, https:\/\/ccssanswers.com\/wp-content\/uploads\/2021\/01\/big-ideas-math-answers-grade-7-chapter-2-multiplying-and-dividing-rational-numbers-29-114x300.jpg 114w\" sizes=\"(max-width: 190px) 100vw, 190px\" \/><br \/>\nSo, the range of elevations are 51.66, 50.6, 50.53, 50.52<\/p>\n<h3><a id=\"Converting_Between_Fractions_and_Decimals_Homework_&amp;_Practice_2.3\"><\/a>Converting Between Fractions and Decimals Homework &amp; Practice 2.3<\/h3>\n<p><strong>Review &amp; Refresh<\/strong><\/p>\n<p><strong>Find the quotient.<\/strong><\/p>\n<p>Question 1.<br \/>\n12 \u00f7 (-6)<\/p>\n<p>Answer:<br \/>\n12 \u00f7 (-6) = -2<\/p>\n<p>Explanation:<br \/>\nThe quotient of two integers with the different signs is negative.<br \/>\n12 \u00f7 (-6) = -2<\/p>\n<p>Question 2.<br \/>\n-48 \u00f7 8<\/p>\n<p>Answer:<br \/>\n-48 \u00f7 8 = -6<\/p>\n<p>Explanation:<br \/>\nThe quotient of two integers with the different signs is negative.<br \/>\n-48 \u00f7 8 = -6<\/p>\n<p>Question 3.<br \/>\n-42 \u00f7 (-7)<\/p>\n<p>Answer:<br \/>\n-42 \u00f7 (-7) = 6<\/p>\n<p>Explanation:<br \/>\nThe quotient of two integers with the same sign is positive.<br \/>\n-42 \u00f7 (-7) = 6<\/p>\n<p>Question 4.<br \/>\n-33 \u00f7 (-3)<\/p>\n<p>Answer:<br \/>\n-33 \u00f7 (-3) = 11<\/p>\n<p>Explanation:<br \/>\nThe quotient of two integers with the same sign is positive.<br \/>\n-33 \u00f7 (-3) = 11<\/p>\n<p><strong>Find the product.<\/strong><\/p>\n<p>Question 5.<br \/>\n<img decoding=\"async\" loading=\"lazy\" class=\"alignnone size-full wp-image-30140\" src=\"https:\/\/ccssanswers.com\/wp-content\/uploads\/2021\/01\/Big-Ideas-Math-Answer-Key-Grade-7-Chapter-2-Multiplying-and-Dividing-Rational-Numbers-35.png\" alt=\"Big Ideas Math Answer Key Grade 7 Chapter 2 Multiplying and Dividing Rational Numbers 35\" width=\"69\" height=\"53\" \/><\/p>\n<p>Answer:<br \/>\n35.28<\/p>\n<p>Explanation:<br \/>\n<img decoding=\"async\" loading=\"lazy\" class=\"alignnone size-full wp-image-41686\" src=\"https:\/\/ccssanswers.com\/wp-content\/uploads\/2021\/01\/big-ideas-math-answers-grade-7-chapter-2-multiplying-and-dividing-rational-numbers-30.jpg\" alt=\"Big Ideas Math Answers Grade 7 Chapter 2 Multiplying and Dividing Rational Numbers 30\" width=\"200\" height=\"198\" srcset=\"https:\/\/ccssanswers.com\/wp-content\/uploads\/2021\/01\/big-ideas-math-answers-grade-7-chapter-2-multiplying-and-dividing-rational-numbers-30.jpg 200w, https:\/\/ccssanswers.com\/wp-content\/uploads\/2021\/01\/big-ideas-math-answers-grade-7-chapter-2-multiplying-and-dividing-rational-numbers-30-150x150.jpg 150w\" sizes=\"(max-width: 200px) 100vw, 200px\" \/><\/p>\n<p>Question 6.<br \/>\n2.0035 \u2022 4<\/p>\n<p>Answer:<br \/>\n2.0035 \u2022 4 = 8.0140<\/p>\n<p>Explanation:<br \/>\n<img decoding=\"async\" loading=\"lazy\" class=\"alignnone size-full wp-image-41688\" src=\"https:\/\/ccssanswers.com\/wp-content\/uploads\/2021\/01\/big-ideas-math-answers-grade-7-chapter-2-multiplying-and-dividing-rational-numbers-31.jpg\" alt=\"Big Ideas Math Answers Grade 7 Chapter 2 Multiplying and Dividing Rational Numbers 31\" width=\"236\" height=\"195\" \/><\/p>\n<p>Question 7.<br \/>\n5.49 \u00d7 13.509<\/p>\n<p>Answer:<br \/>\n5.49 \u00d7 13.509 = 74.16441<\/p>\n<p>Explanation:<br \/>\n<img decoding=\"async\" loading=\"lazy\" class=\"alignnone size-full wp-image-41689\" src=\"https:\/\/ccssanswers.com\/wp-content\/uploads\/2021\/01\/big-ideas-math-answers-grade-7-chapter-2-multiplying-and-dividing-rational-numbers-32.jpg\" alt=\"Big Ideas Math Answers Grade 7 Chapter 2 Multiplying and Dividing Rational Numbers 32\" width=\"297\" height=\"377\" srcset=\"https:\/\/ccssanswers.com\/wp-content\/uploads\/2021\/01\/big-ideas-math-answers-grade-7-chapter-2-multiplying-and-dividing-rational-numbers-32.jpg 297w, https:\/\/ccssanswers.com\/wp-content\/uploads\/2021\/01\/big-ideas-math-answers-grade-7-chapter-2-multiplying-and-dividing-rational-numbers-32-236x300.jpg 236w\" sizes=\"(max-width: 297px) 100vw, 297px\" \/><\/p>\n<p>Question 8.<br \/>\n<img decoding=\"async\" loading=\"lazy\" class=\"alignnone size-full wp-image-30141\" src=\"https:\/\/ccssanswers.com\/wp-content\/uploads\/2021\/01\/Big-Ideas-Math-Answer-Key-Grade-7-Chapter-2-Multiplying-and-Dividing-Rational-Numbers-36.png\" alt=\"Big Ideas Math Answer Key Grade 7 Chapter 2 Multiplying and Dividing Rational Numbers 36\" width=\"81\" height=\"58\" \/><\/p>\n<p>Answer:<br \/>\n0.0030018<\/p>\n<p>Explanation:<br \/>\n<img decoding=\"async\" loading=\"lazy\" class=\"alignnone size-full wp-image-41690\" src=\"https:\/\/ccssanswers.com\/wp-content\/uploads\/2021\/01\/big-ideas-math-answers-grade-7-chapter-2-multiplying-and-dividing-rational-numbers-33.jpg\" alt=\"Big Ideas Math Answers Grade 7 Chapter 2 Multiplying and Dividing Rational Numbers 33\" width=\"226\" height=\"196\" \/><\/p>\n<p>Question 9.<br \/>\nFind the missing values in the ratio table. Then write the equivalent ratios.<br \/>\n<img decoding=\"async\" loading=\"lazy\" class=\"alignnone size-full wp-image-30142\" src=\"https:\/\/ccssanswers.com\/wp-content\/uploads\/2021\/01\/Big-Ideas-Math-Answer-Key-Grade-7-Chapter-2-Multiplying-and-Dividing-Rational-Numbers-37.png\" alt=\"Big Ideas Math Answer Key Grade 7 Chapter 2 Multiplying and Dividing Rational Numbers 37\" width=\"293\" height=\"88\" \/><\/p>\n<p>Answer:<br \/>\n<img decoding=\"async\" loading=\"lazy\" class=\"alignnone size-full wp-image-41691\" src=\"https:\/\/ccssanswers.com\/wp-content\/uploads\/2021\/01\/big-ideas-math-answers-grade-7-chapter-2-multiplying-and-dividing-rational-numbers-34.jpg\" alt=\"Big Ideas Math Answers Grade 7 Chapter 2 Multiplying and Dividing Rational Numbers 34\" width=\"531\" height=\"138\" srcset=\"https:\/\/ccssanswers.com\/wp-content\/uploads\/2021\/01\/big-ideas-math-answers-grade-7-chapter-2-multiplying-and-dividing-rational-numbers-34.jpg 531w, https:\/\/ccssanswers.com\/wp-content\/uploads\/2021\/01\/big-ideas-math-answers-grade-7-chapter-2-multiplying-and-dividing-rational-numbers-34-300x78.jpg 300w\" sizes=\"(max-width: 531px) 100vw, 531px\" \/><\/p>\n<p>Explanation:<br \/>\n72\/18 = 4. So, x\/2 = 4<br \/>\nx = 4 . 2<br \/>\nx = 8<br \/>\n2 . 2\/3 = 4\/3<br \/>\nSo, 18 . 2\/3 = 36\/3 = 12<\/p>\n<p><strong>Concepts, Skills, &amp; Problem Solving<\/strong><\/p>\n<p><strong>STRUCTURE<\/strong><br \/>\n<strong>Without dividing, determine whether the decimal form of the terminates or repeats. Explain.<\/strong> (See Explorations 1 &amp; 2, p. 61.)<\/p>\n<p>Question 10.<br \/>\n\\(\\frac{3}{8}\\)<\/p>\n<p>Answer:<br \/>\n3\/8 is a terminating decimal.<\/p>\n<p>Explanation:<br \/>\n3, 8 have no common factors.<br \/>\nThe denominator 8 is in the form of 2<sup>m<\/sup> x 5<sup>n<\/sup><br \/>\nHence, 3\/8 is a terminating decimal.<br \/>\n3\/8 = 0.375<\/p>\n<p>Question 11.<br \/>\n\\(\\frac{5}{7}\\)<\/p>\n<p>Answer:<br \/>\n5\/7 is a repeating decimal.<\/p>\n<p>Explanation:<br \/>\n5, 7 have no common factors<br \/>\nThe denominator 7 is not in the form of 2<sup>m<\/sup> x 5<sup>n<\/sup><br \/>\nHence, 5\/7 is a repeating decimal.<\/p>\n<p>Question 12.<br \/>\n\\(\\frac{11}{40}\\)<\/p>\n<p>Answer:<br \/>\n11\/40 is a terminating decimal.<\/p>\n<p>Explanation:<br \/>\n11, 40 have no common factors<br \/>\nThe denominator 40 is in the form of 2\u00b3 x 5\u00b9<br \/>\nHence, 11\/40 is a terminating decimal.<\/p>\n<p>Question 13.<br \/>\n\\(\\frac{5}{24}\\)<\/p>\n<p>Answer:<br \/>\n5\/24 is a repeating decimal.<\/p>\n<p>Explanation:<br \/>\n5, 24 have no common factors<br \/>\nThe denominator 24 is not in the form of 2<sup>m<\/sup> x 5<sup>n<\/sup><br \/>\nHence, 5\/24 is a repeating decimal.<\/p>\n<p><strong>WRITING A FRACTION OR MIXED NUMBER AS A DECIMAL<\/strong><br \/>\n<strong>Write the fraction or mixed number as a decimal.<\/strong><\/p>\n<p>Question 14.<br \/>\n\\(\\frac{7}{8}\\)<\/p>\n<p>Answer:<br \/>\n7\/8 = 0.875<\/p>\n<p>Explanation:<br \/>\n<img decoding=\"async\" loading=\"lazy\" class=\"alignnone size-full wp-image-41732\" src=\"https:\/\/ccssanswers.com\/wp-content\/uploads\/2021\/01\/big-ideas-math-answers-grade-7-chapter-2-multiplying-and-dividing-rational-numbers-35.jpg\" alt=\"Big Ideas Math Answers Grade 7 Chapter 2 Multiplying and Dividing Rational Numbers 35\" width=\"165\" height=\"423\" srcset=\"https:\/\/ccssanswers.com\/wp-content\/uploads\/2021\/01\/big-ideas-math-answers-grade-7-chapter-2-multiplying-and-dividing-rational-numbers-35.jpg 165w, https:\/\/ccssanswers.com\/wp-content\/uploads\/2021\/01\/big-ideas-math-answers-grade-7-chapter-2-multiplying-and-dividing-rational-numbers-35-117x300.jpg 117w\" sizes=\"(max-width: 165px) 100vw, 165px\" \/><\/p>\n<p>Question 15.<br \/>\n\\(\\frac{1}{11}\\)<\/p>\n<p>Answer:<br \/>\n1\/11 = 0.9090<\/p>\n<p>Explanation:<br \/>\n<img decoding=\"async\" loading=\"lazy\" class=\"alignnone size-full wp-image-41733\" src=\"https:\/\/ccssanswers.com\/wp-content\/uploads\/2021\/01\/big-ideas-math-answers-grade-7-chapter-2-multiplying-and-dividing-rational-numbers-36.jpg\" alt=\"Big Ideas Math Answers Grade 7 Chapter 2 Multiplying and Dividing Rational Numbers 36\" width=\"228\" height=\"504\" srcset=\"https:\/\/ccssanswers.com\/wp-content\/uploads\/2021\/01\/big-ideas-math-answers-grade-7-chapter-2-multiplying-and-dividing-rational-numbers-36.jpg 228w, https:\/\/ccssanswers.com\/wp-content\/uploads\/2021\/01\/big-ideas-math-answers-grade-7-chapter-2-multiplying-and-dividing-rational-numbers-36-136x300.jpg 136w\" sizes=\"(max-width: 228px) 100vw, 228px\" \/><\/p>\n<p>Question 16.<br \/>\n-3\\(\\frac{1}{2}\\)<\/p>\n<p>Answer:<br \/>\n-3(1\/2) = -3.5<\/p>\n<p>Explanation:<br \/>\n-3(1\/2) = -7\/2<br \/>\n<img decoding=\"async\" loading=\"lazy\" class=\"alignnone size-full wp-image-41734\" src=\"https:\/\/ccssanswers.com\/wp-content\/uploads\/2021\/01\/big-ideas-math-answers-grade-7-chapter-2-multiplying-and-dividing-rational-numbers-37.jpg\" alt=\"Big Ideas Math Answers Grade 7 Chapter 2 Multiplying and Dividing Rational Numbers 37\" width=\"108\" height=\"263\" \/><\/p>\n<p>Question 17.<br \/>\n&#8211;\\(\\frac{7}{9}\\)<\/p>\n<p>Answer:<br \/>\n-7\/9 = -0.77<\/p>\n<p>Explanation:<br \/>\n<img decoding=\"async\" loading=\"lazy\" class=\"alignnone size-full wp-image-41735\" src=\"https:\/\/ccssanswers.com\/wp-content\/uploads\/2021\/01\/big-ideas-math-answers-grade-7-chapter-2-multiplying-and-dividing-rational-numbers-38.jpg\" alt=\"Big Ideas Math Answers Grade 7 Chapter 2 Multiplying and Dividing Rational Numbers 38\" width=\"136\" height=\"345\" srcset=\"https:\/\/ccssanswers.com\/wp-content\/uploads\/2021\/01\/big-ideas-math-answers-grade-7-chapter-2-multiplying-and-dividing-rational-numbers-38.jpg 136w, https:\/\/ccssanswers.com\/wp-content\/uploads\/2021\/01\/big-ideas-math-answers-grade-7-chapter-2-multiplying-and-dividing-rational-numbers-38-118x300.jpg 118w\" sizes=\"(max-width: 136px) 100vw, 136px\" \/><\/p>\n<p>Question 18.<br \/>\n&#8211;\\(\\frac{17}{40}\\)<\/p>\n<p>Answer:<br \/>\n-17\/40 = -0.425<\/p>\n<p>Explanation:<br \/>\n<img decoding=\"async\" loading=\"lazy\" class=\"alignnone size-full wp-image-41737\" src=\"https:\/\/ccssanswers.com\/wp-content\/uploads\/2021\/01\/big-ideas-math-answers-grade-7-chapter-2-multiplying-and-dividing-rational-numbers-39.jpg\" alt=\"Big Ideas Math Answers Grade 7 Chapter 2 Multiplying and Dividing Rational Numbers 39\" width=\"220\" height=\"502\" srcset=\"https:\/\/ccssanswers.com\/wp-content\/uploads\/2021\/01\/big-ideas-math-answers-grade-7-chapter-2-multiplying-and-dividing-rational-numbers-39.jpg 220w, https:\/\/ccssanswers.com\/wp-content\/uploads\/2021\/01\/big-ideas-math-answers-grade-7-chapter-2-multiplying-and-dividing-rational-numbers-39-131x300.jpg 131w\" sizes=\"(max-width: 220px) 100vw, 220px\" \/><\/p>\n<p>Question 19.<br \/>\n1\\(\\frac{5}{6}\\)<\/p>\n<p>Answer:<br \/>\n1(5\/6) = 1.83333<\/p>\n<p>Explanation:<br \/>\n1(5\/6) = 11\/6<br \/>\n<img decoding=\"async\" loading=\"lazy\" class=\"alignnone size-full wp-image-41741\" src=\"https:\/\/ccssanswers.com\/wp-content\/uploads\/2021\/01\/big-ideas-math-answers-grade-7-chapter-2-multiplying-and-dividing-rational-numbers-40.jpg\" alt=\"Big Ideas Math Answers Grade 7 Chapter 2 Multiplying and Dividing Rational Numbers 40\" width=\"198\" height=\"510\" srcset=\"https:\/\/ccssanswers.com\/wp-content\/uploads\/2021\/01\/big-ideas-math-answers-grade-7-chapter-2-multiplying-and-dividing-rational-numbers-40.jpg 198w, https:\/\/ccssanswers.com\/wp-content\/uploads\/2021\/01\/big-ideas-math-answers-grade-7-chapter-2-multiplying-and-dividing-rational-numbers-40-116x300.jpg 116w\" sizes=\"(max-width: 198px) 100vw, 198px\" \/><\/p>\n<p>Question 20.<br \/>\n4\\(\\frac{2}{15}\\)<\/p>\n<p>Answer:<br \/>\n4(2\/15) = 4.133<\/p>\n<p>Explanation:<br \/>\n4(2\/15) = 62\/15<br \/>\n<img decoding=\"async\" loading=\"lazy\" class=\"alignnone size-full wp-image-41773\" src=\"https:\/\/ccssanswers.com\/wp-content\/uploads\/2021\/01\/big-ideas-math-answers-grade-7-chapter-2-multiplying-and-dividing-rational-numbers-41.jpg\" alt=\"Big Ideas Math Answers Grade 7 Chapter 2 Multiplying and Dividing Rational Numbers 41\" width=\"232\" height=\"508\" srcset=\"https:\/\/ccssanswers.com\/wp-content\/uploads\/2021\/01\/big-ideas-math-answers-grade-7-chapter-2-multiplying-and-dividing-rational-numbers-41.jpg 232w, https:\/\/ccssanswers.com\/wp-content\/uploads\/2021\/01\/big-ideas-math-answers-grade-7-chapter-2-multiplying-and-dividing-rational-numbers-41-137x300.jpg 137w\" sizes=\"(max-width: 232px) 100vw, 232px\" \/><\/p>\n<p>Question 21.<br \/>\n\\(\\frac{25}{24}\\)<\/p>\n<p>Answer:<br \/>\n25\/24 = 1.04166<\/p>\n<p>Explanation:<br \/>\n<img decoding=\"async\" loading=\"lazy\" class=\"alignnone size-full wp-image-41802\" src=\"https:\/\/ccssanswers.com\/wp-content\/uploads\/2021\/01\/big-ideas-math-answers-grade-7-chapter-2-multiplying-and-dividing-rational-numbers-42.jpg\" alt=\"Big Ideas Math Answers Grade 7 Chapter 2 Multiplying and Dividing Rational Numbers 42\" width=\"291\" height=\"671\" srcset=\"https:\/\/ccssanswers.com\/wp-content\/uploads\/2021\/01\/big-ideas-math-answers-grade-7-chapter-2-multiplying-and-dividing-rational-numbers-42.jpg 291w, https:\/\/ccssanswers.com\/wp-content\/uploads\/2021\/01\/big-ideas-math-answers-grade-7-chapter-2-multiplying-and-dividing-rational-numbers-42-130x300.jpg 130w\" sizes=\"(max-width: 291px) 100vw, 291px\" \/><\/p>\n<p>Question 22.<br \/>\n&#8211;\\(\\frac{13}{11}\\)<\/p>\n<p>Answer:<br \/>\n-13 \/ 11 = -1.1818<\/p>\n<p>Explanation:<br \/>\n<img decoding=\"async\" loading=\"lazy\" class=\"alignnone size-full wp-image-41832\" src=\"https:\/\/ccssanswers.com\/wp-content\/uploads\/2021\/01\/big-ideas-math-answers-grade-7-chapter-2-multiplying-and-dividing-rational-numbers-43.jpg\" alt=\"Big Ideas Math Answers Grade 7 Chapter 2 Multiplying and Dividing Rational Numbers 43\" width=\"282\" height=\"677\" srcset=\"https:\/\/ccssanswers.com\/wp-content\/uploads\/2021\/01\/big-ideas-math-answers-grade-7-chapter-2-multiplying-and-dividing-rational-numbers-43.jpg 282w, https:\/\/ccssanswers.com\/wp-content\/uploads\/2021\/01\/big-ideas-math-answers-grade-7-chapter-2-multiplying-and-dividing-rational-numbers-43-125x300.jpg 125w\" sizes=\"(max-width: 282px) 100vw, 282px\" \/><\/p>\n<p>Question 23.<br \/>\n-2\\(\\frac{17}{18}\\)<\/p>\n<p>Answer:<br \/>\n-2(17\/18) = -2.944<\/p>\n<p>Explanation:<br \/>\n-2(17\/18) = -53\/18<br \/>\n<img decoding=\"async\" loading=\"lazy\" class=\"alignnone size-full wp-image-41873\" src=\"https:\/\/ccssanswers.com\/wp-content\/uploads\/2021\/01\/big-ideas-math-answers-grade-7-chapter-2-multiplying-and-dividing-rational-numbers-44.jpg\" alt=\"Big Ideas Math Answers Grade 7 Chapter 2 Multiplying and Dividing Rational Numbers 44\" width=\"227\" height=\"506\" srcset=\"https:\/\/ccssanswers.com\/wp-content\/uploads\/2021\/01\/big-ideas-math-answers-grade-7-chapter-2-multiplying-and-dividing-rational-numbers-44.jpg 227w, https:\/\/ccssanswers.com\/wp-content\/uploads\/2021\/01\/big-ideas-math-answers-grade-7-chapter-2-multiplying-and-dividing-rational-numbers-44-135x300.jpg 135w\" sizes=\"(max-width: 227px) 100vw, 227px\" \/><\/p>\n<p>Question 24.<br \/>\n-5\\(\\frac{7}{12}\\)<\/p>\n<p>Answer:<br \/>\n-5(7\/12) = -5.5833<\/p>\n<p>Explanation:<br \/>\n-5(7\/12) = -67\/12<br \/>\n<img decoding=\"async\" loading=\"lazy\" class=\"alignnone size-full wp-image-41900\" src=\"https:\/\/ccssanswers.com\/wp-content\/uploads\/2021\/01\/big-ideas-math-answers-grade-7-chapter-2-multiplying-and-dividing-rational-numbers-45.jpg\" alt=\"Big Ideas Math Answers Grade 7 Chapter 2 Multiplying and Dividing Rational Numbers 45\" width=\"260\" height=\"589\" srcset=\"https:\/\/ccssanswers.com\/wp-content\/uploads\/2021\/01\/big-ideas-math-answers-grade-7-chapter-2-multiplying-and-dividing-rational-numbers-45.jpg 260w, https:\/\/ccssanswers.com\/wp-content\/uploads\/2021\/01\/big-ideas-math-answers-grade-7-chapter-2-multiplying-and-dividing-rational-numbers-45-132x300.jpg 132w\" sizes=\"(max-width: 260px) 100vw, 260px\" \/><\/p>\n<p>Question 25.<br \/>\n8\\(\\frac{15}{22}\\)<\/p>\n<p>Answer:<br \/>\n8(15\/22) = 8.681818<\/p>\n<p>Explanation:<br \/>\n8(15\/22) = 191\/22<br \/>\n<img decoding=\"async\" loading=\"lazy\" class=\"alignnone size-full wp-image-41928\" src=\"https:\/\/ccssanswers.com\/wp-content\/uploads\/2021\/01\/big-ideas-math-answers-grade-7-chapter-2-multiplying-and-dividing-rational-numbers-46.jpg\" alt=\"Big Ideas Math Answers Grade 7 Chapter 2 Multiplying and Dividing Rational Numbers 46\" width=\"339\" height=\"828\" srcset=\"https:\/\/ccssanswers.com\/wp-content\/uploads\/2021\/01\/big-ideas-math-answers-grade-7-chapter-2-multiplying-and-dividing-rational-numbers-46.jpg 339w, https:\/\/ccssanswers.com\/wp-content\/uploads\/2021\/01\/big-ideas-math-answers-grade-7-chapter-2-multiplying-and-dividing-rational-numbers-46-123x300.jpg 123w\" sizes=\"(max-width: 339px) 100vw, 339px\" \/><\/p>\n<p>Question 26.<br \/>\n<strong>YOU BE THE TEACHER<\/strong><br \/>\nYour friend writes &#8211;\\(\\frac{7}{11}\\) as a decimal. Is your friend correct? Explain your reasoning.<br \/>\n<img decoding=\"async\" loading=\"lazy\" class=\"alignnone size-full wp-image-30143\" src=\"https:\/\/ccssanswers.com\/wp-content\/uploads\/2021\/01\/Big-Ideas-Math-Answer-Key-Grade-7-Chapter-2-Multiplying-and-Dividing-Rational-Numbers-38.png\" alt=\"Big Ideas Math Answer Key Grade 7 Chapter 2 Multiplying and Dividing Rational Numbers 38\" width=\"151\" height=\"73\" \/><\/p>\n<p>Answer:<br \/>\nCorrect<\/p>\n<p>Explanation:<br \/>\n-7\/11 = -0.636363<br \/>\n<img decoding=\"async\" loading=\"lazy\" class=\"alignnone size-full wp-image-41929\" src=\"https:\/\/ccssanswers.com\/wp-content\/uploads\/2021\/01\/big-ideas-math-answers-grade-7-chapter-2-multiplying-and-dividing-rational-numbers-47.jpg\" alt=\"Big Ideas Math Answers Grade 7 Chapter 2 Multiplying and Dividing Rational Numbers 47\" width=\"224\" height=\"506\" srcset=\"https:\/\/ccssanswers.com\/wp-content\/uploads\/2021\/01\/big-ideas-math-answers-grade-7-chapter-2-multiplying-and-dividing-rational-numbers-47.jpg 224w, https:\/\/ccssanswers.com\/wp-content\/uploads\/2021\/01\/big-ideas-math-answers-grade-7-chapter-2-multiplying-and-dividing-rational-numbers-47-133x300.jpg 133w\" sizes=\"(max-width: 224px) 100vw, 224px\" \/><\/p>\n<p><strong>WRITING A DECIMAL AS A FRACTION OR MIXED NUMBER<\/strong><br \/>\n<strong>Write the decimal as a fraction or mixed number in simplest form.<\/strong><\/p>\n<p>Question 27.<br \/>\n-0.9<\/p>\n<p>Answer:<br \/>\n-0.9 = -9\/10<\/p>\n<p>Explanation:<br \/>\n-0.9 = -9\/10<\/p>\n<p>Question 28.<br \/>\n0.45<\/p>\n<p>Answer:<br \/>\n0.45 = 9\/20<\/p>\n<p>Explanation:<br \/>\n0.45 = 45\/100<br \/>\n= (9 . 5)\/(20 . 5)<br \/>\n= 9\/20<\/p>\n<p>Question 29.<br \/>\n-0.258<\/p>\n<p>Answer:<br \/>\n-0.258 = -129\/500<\/p>\n<p>Explanation:<br \/>\n-0.258 = -258\/1000<br \/>\n= -(129 . 2)\/(500 . 2)<br \/>\n= -129\/500<\/p>\n<p>Question 30.<br \/>\n-0.312<\/p>\n<p>Answer:<br \/>\n-0.312 = 39\/125<\/p>\n<p>Explanation:<br \/>\n-0.312 = -312\/1000<br \/>\n= (39 . 8) \/ (125 . 8)<br \/>\n= 39\/125<\/p>\n<p>Question 31.<br \/>\n-2.32<\/p>\n<p>Answer:<br \/>\n-2.32 = -58\/25<\/p>\n<p>Explanation:<br \/>\n-2.32 = -232\/100<br \/>\n= -(58 . 4)\/(25 . 4)<br \/>\n= -58\/25<\/p>\n<p>Question 32.<br \/>\n-1.64<\/p>\n<p>Answer:<br \/>\n-1.64 = -41\/25<\/p>\n<p>Explanation:<br \/>\n-1.64 = -164\/100<br \/>\n= -(41 . 4)\/(25 . 4)<br \/>\n= -41\/25<\/p>\n<p>Question 33.<br \/>\n6.012<\/p>\n<p>Answer:<br \/>\n6.012 = 1503\/250<\/p>\n<p>Explanation:<br \/>\n6.012 = 6012\/1000<br \/>\n= (1503 . 4)\/(250 . 4)<br \/>\n= 1503\/250<\/p>\n<p>Question 34.<br \/>\n-12.405<\/p>\n<p>Answer:<br \/>\n-12.405 = -2481\/200<\/p>\n<p>Explanation:<br \/>\n-12.405 = -12405\/1000<br \/>\n= -(2481 . 5)\/(200 . 5)<br \/>\n= -2481\/200<\/p>\n<p>Question 35.<br \/>\n<strong>MODELING REAL LIFE<\/strong><br \/>\nYou \ufb01nd one quarter, two dimes, and two nickels.<br \/>\na. Write the dollar amount as a decimal.<br \/>\nb. Write the dollar amount as a fraction or mixed number in simplest form.<br \/>\n<img decoding=\"async\" loading=\"lazy\" class=\"alignnone size-full wp-image-30144\" src=\"https:\/\/ccssanswers.com\/wp-content\/uploads\/2021\/01\/Big-Ideas-Math-Answer-Key-Grade-7-Chapter-2-Multiplying-and-Dividing-Rational-Numbers-39.png\" alt=\"Big Ideas Math Answer Key Grade 7 Chapter 2 Multiplying and Dividing Rational Numbers 39\" width=\"146\" height=\"118\" \/><\/p>\n<p>Answer:<br \/>\na. $0.55<br \/>\nb. 11\/20<\/p>\n<p>Explanation:<br \/>\nYou \ufb01nd one quarter, two dimes, and two nickels.<br \/>\na. Convert each one into dollars<br \/>\n1 quarter is equal to 0.25 dollars<br \/>\n1 dime is equal to 0.1 dollars.<br \/>\n1 nickels is equal to 0.05 dollars.<br \/>\n$0.25 + 2(0.1) + 2(0.05)<br \/>\n= 0.25 + 0.2 + 0.1<br \/>\n= $0.55<br \/>\nb. $0.55 = 55\/100<br \/>\n= (5 . 11)\/(5. 20)<br \/>\n= 11\/20<\/p>\n<p><strong>COMPARING RATIONAL NUMBERS<\/strong><br \/>\n<strong>Copy and complete the statement using &lt; or &gt;.<\/strong><\/p>\n<p>Question 36.<br \/>\n<img decoding=\"async\" loading=\"lazy\" class=\"alignnone size-full wp-image-30145\" src=\"https:\/\/ccssanswers.com\/wp-content\/uploads\/2021\/01\/Big-Ideas-Math-Answer-Key-Grade-7-Chapter-2-Multiplying-and-Dividing-Rational-Numbers-40.png\" alt=\"Big Ideas Math Answer Key Grade 7 Chapter 2 Multiplying and Dividing Rational Numbers 40\" width=\"126\" height=\"53\" \/><\/p>\n<p>Answer:<br \/>\n-4(6\/10) &gt; -4.65<\/p>\n<p>Explanation:<br \/>\n-4(6\/10) = -46\/10 = -4.6<br \/>\n-4.65 &lt; -4.6<br \/>\nSo, -4(6\/10) &gt; -4.65<\/p>\n<p>Question 37.<br \/>\n<img decoding=\"async\" loading=\"lazy\" class=\"alignnone size-full wp-image-30146\" src=\"https:\/\/ccssanswers.com\/wp-content\/uploads\/2021\/01\/Big-Ideas-Math-Answer-Key-Grade-7-Chapter-2-Multiplying-and-Dividing-Rational-Numbers-41.png\" alt=\"Big Ideas Math Answer Key Grade 7 Chapter 2 Multiplying and Dividing Rational Numbers 41\" width=\"128\" height=\"58\" \/><\/p>\n<p>Answer:<br \/>\n<img decoding=\"async\" loading=\"lazy\" class=\"alignnone size-full wp-image-42230\" src=\"https:\/\/ccssanswers.com\/wp-content\/uploads\/2021\/01\/big-ideas-math-answers-grade-7-chapter-2-multiplying-and-dividing-rational-numbers-49.jpg\" alt=\"Big Ideas Math Answers Grade 7 Chapter 2 Multiplying and Dividing Rational Numbers 49\" width=\"120\" height=\"48\" \/><\/p>\n<p>Explanation:<br \/>\n-5(3\/11) = -58\/11 = -5.2727<br \/>\n<img decoding=\"async\" loading=\"lazy\" class=\"alignnone size-full wp-image-42226\" src=\"https:\/\/ccssanswers.com\/wp-content\/uploads\/2021\/01\/big-ideas-math-answers-grade-7-chapter-2-multiplying-and-dividing-rational-numbers-48.jpg\" alt=\"Big Ideas Math Answers Grade 7 Chapter 2 Multiplying and Dividing Rational Numbers 48\" width=\"255\" height=\"589\" srcset=\"https:\/\/ccssanswers.com\/wp-content\/uploads\/2021\/01\/big-ideas-math-answers-grade-7-chapter-2-multiplying-and-dividing-rational-numbers-48.jpg 255w, https:\/\/ccssanswers.com\/wp-content\/uploads\/2021\/01\/big-ideas-math-answers-grade-7-chapter-2-multiplying-and-dividing-rational-numbers-48-130x300.jpg 130w\" sizes=\"(max-width: 255px) 100vw, 255px\" \/><br \/>\n-5.2727 &lt; -5.222<\/p>\n<p>Question 38.<br \/>\n<img decoding=\"async\" loading=\"lazy\" class=\"alignnone size-full wp-image-30147\" src=\"https:\/\/ccssanswers.com\/wp-content\/uploads\/2021\/01\/Big-Ideas-Math-Answer-Key-Grade-7-Chapter-2-Multiplying-and-Dividing-Rational-Numbers-42.png\" alt=\"Big Ideas Math Answer Key Grade 7 Chapter 2 Multiplying and Dividing Rational Numbers 42\" width=\"126\" height=\"54\" \/><\/p>\n<p>Answer:<br \/>\n-2(13\/16) &lt; -2(11\/14)<\/p>\n<p>Explanation:<br \/>\n-2(13\/16) = -45\/16 = -2.8125<br \/>\n<img decoding=\"async\" loading=\"lazy\" class=\"alignnone size-full wp-image-42251\" src=\"https:\/\/ccssanswers.com\/wp-content\/uploads\/2021\/01\/big-ideas-math-answers-grade-7-chapter-2-multiplying-and-dividing-rational-numbers-50.jpg\" alt=\"Big Ideas Math Answers Grade 7 Chapter 2 Multiplying and Dividing Rational Numbers 50\" width=\"246\" height=\"585\" srcset=\"https:\/\/ccssanswers.com\/wp-content\/uploads\/2021\/01\/big-ideas-math-answers-grade-7-chapter-2-multiplying-and-dividing-rational-numbers-50.jpg 246w, https:\/\/ccssanswers.com\/wp-content\/uploads\/2021\/01\/big-ideas-math-answers-grade-7-chapter-2-multiplying-and-dividing-rational-numbers-50-126x300.jpg 126w\" sizes=\"(max-width: 246px) 100vw, 246px\" \/><br \/>\n-2(11\/14) = -39\/14 = -2.7857<br \/>\n<img decoding=\"async\" loading=\"lazy\" class=\"alignnone size-full wp-image-42252\" src=\"https:\/\/ccssanswers.com\/wp-content\/uploads\/2021\/01\/big-ideas-math-answers-grade-7-chapter-2-multiplying-and-dividing-rational-numbers-51.jpg\" alt=\"Big Ideas Math Answers Grade 7 Chapter 2 Multiplying and Dividing Rational Numbers 51\" width=\"252\" height=\"589\" srcset=\"https:\/\/ccssanswers.com\/wp-content\/uploads\/2021\/01\/big-ideas-math-answers-grade-7-chapter-2-multiplying-and-dividing-rational-numbers-51.jpg 252w, https:\/\/ccssanswers.com\/wp-content\/uploads\/2021\/01\/big-ideas-math-answers-grade-7-chapter-2-multiplying-and-dividing-rational-numbers-51-128x300.jpg 128w\" sizes=\"(max-width: 252px) 100vw, 252px\" \/><br \/>\n-2(13\/16) &lt; -2(11\/14)<\/p>\n<p>Question 39.<br \/>\n<strong>MODELING REAL LIFE<\/strong><br \/>\nIs the half pipe deeper than the skating bowl? Explain.<br \/>\n<img decoding=\"async\" loading=\"lazy\" class=\"alignnone size-full wp-image-30148\" src=\"https:\/\/ccssanswers.com\/wp-content\/uploads\/2021\/01\/Big-Ideas-Math-Answer-Key-Grade-7-Chapter-2-Multiplying-and-Dividing-Rational-Numbers-43.png\" alt=\"Big Ideas Math Answer Key Grade 7 Chapter 2 Multiplying and Dividing Rational Numbers 43\" width=\"551\" height=\"129\" srcset=\"https:\/\/ccssanswers.com\/wp-content\/uploads\/2021\/01\/Big-Ideas-Math-Answer-Key-Grade-7-Chapter-2-Multiplying-and-Dividing-Rational-Numbers-43.png 551w, https:\/\/ccssanswers.com\/wp-content\/uploads\/2021\/01\/Big-Ideas-Math-Answer-Key-Grade-7-Chapter-2-Multiplying-and-Dividing-Rational-Numbers-43-300x70.png 300w\" sizes=\"(max-width: 551px) 100vw, 551px\" \/><\/p>\n<p>Answer:<br \/>\nNo. They have the same depth.<\/p>\n<p>Explanation:<br \/>\nAs a decimal, 5\/6 = 0.833333<br \/>\n9(5\/6) = 59\/6 = 9.838383<br \/>\nThis means that half-pipe and the skating bowl have the same depth.<br \/>\nNo. They have the same depth.<\/p>\n<p>Question 40.<br \/>\n<strong>MODELING REAL LIFE<\/strong><br \/>\nIn softball, a batting average is the number of hits divided by the number of times at bat. Does Player 1 or Player 2 have the greater batting average?<br \/>\n<img decoding=\"async\" loading=\"lazy\" class=\"alignnone size-full wp-image-30149\" src=\"https:\/\/ccssanswers.com\/wp-content\/uploads\/2021\/01\/Big-Ideas-Math-Answer-Key-Grade-7-Chapter-2-Multiplying-and-Dividing-Rational-Numbers-44.png\" alt=\"Big Ideas Math Answer Key Grade 7 Chapter 2 Multiplying and Dividing Rational Numbers 44\" width=\"198\" height=\"117\" \/><\/p>\n<p>Answer:<br \/>\nPlayer 2 has the greater batting average.<\/p>\n<p>Explanation:<br \/>\nBatting average = Number of hits \/ number of times at bat<br \/>\nPlayer 1 average = 42 \/ 90 = 0.466<br \/>\n<img decoding=\"async\" loading=\"lazy\" class=\"alignnone size-full wp-image-42256\" src=\"https:\/\/ccssanswers.com\/wp-content\/uploads\/2021\/01\/big-ideas-math-answers-grade-7-chapter-2-multiplying-and-dividing-rational-numbers-52.jpg\" alt=\"Big Ideas Math Answers Grade 7 Chapter 2 Multiplying and Dividing Rational Numbers 52\" width=\"229\" height=\"510\" srcset=\"https:\/\/ccssanswers.com\/wp-content\/uploads\/2021\/01\/big-ideas-math-answers-grade-7-chapter-2-multiplying-and-dividing-rational-numbers-52.jpg 229w, https:\/\/ccssanswers.com\/wp-content\/uploads\/2021\/01\/big-ideas-math-answers-grade-7-chapter-2-multiplying-and-dividing-rational-numbers-52-135x300.jpg 135w\" sizes=\"(max-width: 229px) 100vw, 229px\" \/><br \/>\nPlayer 2 average = 38\/80 = 0.475<br \/>\n<img decoding=\"async\" loading=\"lazy\" class=\"alignnone size-full wp-image-42257\" src=\"https:\/\/ccssanswers.com\/wp-content\/uploads\/2021\/01\/big-ideas-math-answers-grade-7-chapter-2-multiplying-and-dividing-rational-numbers-53.jpg\" alt=\"Big Ideas Math Answers Grade 7 Chapter 2 Multiplying and Dividing Rational Numbers 53\" width=\"232\" height=\"509\" srcset=\"https:\/\/ccssanswers.com\/wp-content\/uploads\/2021\/01\/big-ideas-math-answers-grade-7-chapter-2-multiplying-and-dividing-rational-numbers-53.jpg 232w, https:\/\/ccssanswers.com\/wp-content\/uploads\/2021\/01\/big-ideas-math-answers-grade-7-chapter-2-multiplying-and-dividing-rational-numbers-53-137x300.jpg 137w\" sizes=\"(max-width: 232px) 100vw, 232px\" \/><br \/>\nPlayer 2 has the greater batting average<\/p>\n<p><strong>ORDERING RATIONAL NUMBERS<\/strong><br \/>\n<strong>Order the numbers from least to greatest.<\/strong><\/p>\n<p>Question 41.<br \/>\n<img decoding=\"async\" loading=\"lazy\" class=\"alignnone size-full wp-image-30150\" src=\"https:\/\/ccssanswers.com\/wp-content\/uploads\/2021\/01\/Big-Ideas-Math-Answer-Key-Grade-7-Chapter-2-Multiplying-and-Dividing-Rational-Numbers-45.png\" alt=\"Big Ideas Math Answer Key Grade 7 Chapter 2 Multiplying and Dividing Rational Numbers 45\" width=\"129\" height=\"52\" \/><\/p>\n<p>Answer:<br \/>\nThe order from least to greatest -7\/3, -3\/4, 0.5, 2\/3, 1.2<\/p>\n<p>Explanation:<br \/>\nExpress each term as a decimal<br \/>\n-3\/4 = -0.75<br \/>\n2\/3 = 0.666<br \/>\n-7\/3 = -2.333<br \/>\nThe order from least to greatest -7\/3, -3\/4, 0.5, 2\/3, 1.2<\/p>\n<p>Question 42.<br \/>\n<img decoding=\"async\" loading=\"lazy\" class=\"alignnone size-full wp-image-30151\" src=\"https:\/\/ccssanswers.com\/wp-content\/uploads\/2021\/01\/Big-Ideas-Math-Answer-Key-Grade-7-Chapter-2-Multiplying-and-Dividing-Rational-Numbers-46.png\" alt=\"Big Ideas Math Answer Key Grade 7 Chapter 2 Multiplying and Dividing Rational Numbers 46\" width=\"156\" height=\"47\" \/><\/p>\n<p>Answer:<br \/>\nThe order from least to greatest is -2.5, -1.1, -4\/5, 0.8, 9\/5<\/p>\n<p>Explanation:<br \/>\nExpress each term as a decimal<br \/>\n9\/5 = 1.8<br \/>\n-4\/5 = -0.8<br \/>\nThe order from least to greatest is -2.5, -1.1, -4\/5, 0.8, 9\/5<\/p>\n<p>Question 43.<br \/>\n<img decoding=\"async\" loading=\"lazy\" class=\"alignnone size-full wp-image-30152\" src=\"https:\/\/ccssanswers.com\/wp-content\/uploads\/2021\/01\/Big-Ideas-Math-Answer-Key-Grade-7-Chapter-2-Multiplying-and-Dividing-Rational-Numbers-47.png\" alt=\"Big Ideas Math Answer Key Grade 7 Chapter 2 Multiplying and Dividing Rational Numbers 47\" width=\"155\" height=\"49\" \/><\/p>\n<p>Answer:<br \/>\nThe order from least to greatest is -8\/5, -1.4, -0.9, 1\/4, 0.6<\/p>\n<p>Explanation:<br \/>\nExpress each term as a decimal<br \/>\n-8\/5 = -1.6<br \/>\n1\/4 = 0.25<br \/>\nThe order from least to greatest is -1.6 &lt; -1.4 &lt; -0.9 &lt; 0.25 &lt; 0.6<\/p>\n<p>Question 44.<br \/>\n<img decoding=\"async\" loading=\"lazy\" class=\"alignnone size-full wp-image-30153\" src=\"https:\/\/ccssanswers.com\/wp-content\/uploads\/2021\/01\/Big-Ideas-Math-Answers-7th-Grade-Chapter-2-Multiplying-and-Dividing-Rational-Numbers-48.png\" alt=\"Big Ideas Math Answers 7th Grade Chapter 2 Multiplying and Dividing Rational Numbers 48\" width=\"151\" height=\"53\" \/><\/p>\n<p>Answer:<br \/>\nThe order from least to greatest is -9\/4, -0.75, -6\/10, 5\/3, 2.1<\/p>\n<p>Explanation:<br \/>\nExpress each term as a decimal<br \/>\n-6\/10 = -0.6<br \/>\n-9\/4 = -2.25<br \/>\n5\/3 = 1.666<br \/>\nThe order from least to greatest is -2.25 &lt; -0.75 &lt; -0.6 &lt; 1.666 &lt; 2.1<\/p>\n<p>Question 45.<br \/>\n<img decoding=\"async\" loading=\"lazy\" class=\"alignnone size-full wp-image-30154\" src=\"https:\/\/ccssanswers.com\/wp-content\/uploads\/2021\/01\/Big-Ideas-Math-Answers-7th-Grade-Chapter-2-Multiplying-and-Dividing-Rational-Numbers-49.png\" alt=\"Big Ideas Math Answers 7th Grade Chapter 2 Multiplying and Dividing Rational Numbers 49\" width=\"147\" height=\"57\" \/><\/p>\n<p>Answer:<br \/>\nThe order from least to greatest is -7\/2, -2.8, -5\/4, 1.3, 4\/3<\/p>\n<p>Explanation:<br \/>\nExpress each term as a decimal<br \/>\n-7\/2 = -3.5<br \/>\n-5\/4 = -1.25<br \/>\n4\/3 = 1.333<br \/>\nThe order from least to greatest is -3.5 &lt; -2.8 &lt; -1.25 &lt; 1.3 &lt; 1.333<\/p>\n<p>Question 46.<br \/>\n<img decoding=\"async\" loading=\"lazy\" class=\"alignnone size-full wp-image-30155\" src=\"https:\/\/ccssanswers.com\/wp-content\/uploads\/2021\/01\/Big-Ideas-Math-Answers-7th-Grade-Chapter-2-Multiplying-and-Dividing-Rational-Numbers-50.png\" alt=\"Big Ideas Math Answers 7th Grade Chapter 2 Multiplying and Dividing Rational Numbers 50\" width=\"185\" height=\"51\" \/><\/p>\n<p>Answer:<br \/>\nThe order from least to greatest is -2.4 -2.25, -11\/5, 15\/10, 1.6<\/p>\n<p>Explanation:<br \/>\nExpress each term as a decimal<br \/>\n-11\/5 = -2.2<br \/>\n15\/10 = 1.5<br \/>\nThe order from least to greatest is -2.4 &lt; -2.25 &lt; -2.2 &lt; 1.5 &lt; 1.6<\/p>\n<p>Question 47.<br \/>\n<strong>MODELING REAL LIFE<\/strong><br \/>\nThe table shows the changes in the water level of a pond over several weeks. Order the numbers from least to greatest.<br \/>\n<img decoding=\"async\" loading=\"lazy\" class=\"alignnone size-full wp-image-30156\" src=\"https:\/\/ccssanswers.com\/wp-content\/uploads\/2021\/01\/Big-Ideas-Math-Answers-7th-Grade-Chapter-2-Multiplying-and-Dividing-Rational-Numbers-51.png\" alt=\"Big Ideas Math Answers 7th Grade Chapter 2 Multiplying and Dividing Rational Numbers 51\" width=\"321\" height=\"135\" srcset=\"https:\/\/ccssanswers.com\/wp-content\/uploads\/2021\/01\/Big-Ideas-Math-Answers-7th-Grade-Chapter-2-Multiplying-and-Dividing-Rational-Numbers-51.png 321w, https:\/\/ccssanswers.com\/wp-content\/uploads\/2021\/01\/Big-Ideas-Math-Answers-7th-Grade-Chapter-2-Multiplying-and-Dividing-Rational-Numbers-51-300x126.png 300w\" sizes=\"(max-width: 321px) 100vw, 321px\" \/><\/p>\n<p>Answer:<br \/>\nThe order from the least to greatest is Week 4, Week 2, Week 3, Week 1.<\/p>\n<p>Explanation:<br \/>\nWeek 1 = -7\/5 = -1.4<br \/>\nWeek 2 = -1(5\/11) = -1.4545<br \/>\nWeek 3 = -1.45<br \/>\nWeek 4 = -1(91\/200) = -1.455<br \/>\nThe order from the least to greatest is Week 4 &lt; Week 2 &lt; Week 3 &lt; Week 1<\/p>\n<p>Question 48.<br \/>\n<strong>OPEN-ENDED<\/strong><br \/>\nFind one terminating decimal and one repeating decimal between \\(-\\frac{1}{2}\\) and \\(-\\frac{1}{3}\\).<\/p>\n<p>Answer:<br \/>\n-23\/60 = -0.383333 is a repeating decimal<br \/>\n-24\/60 = -0.4 is a terminating decimal.<\/p>\n<p>Explanation:<br \/>\nTo find one terminating decimal and one repeating decimal between -1\/2 and -1\/3 multiply each fraction by the denominator of the other fraction<br \/>\n-1\/2 . 3\/3 = -3\/6 and -1\/3 . 2\/2 = -2\/6<br \/>\nMultiply the resulting fractions by 10<br \/>\n-3\/6 . 10\/10 = -30\/60 and -2\/6 . 10\/10 = -20\/60<br \/>\nFind two numbers between -20 and -30<br \/>\n-23\/60 = -0.383333 is a repeating decimal<br \/>\n-24\/60 = -0.4 is a terminating decimal.<\/p>\n<p>Question 49.<br \/>\n<strong>PROBLEM SOLVING<\/strong><br \/>\nYou miss 3 out of 10 questions on a science quiz and 4 out of 15 questions on a math quiz. On which quiz did you have a greater percentage of correct answers?<\/p>\n<p>Answer:<br \/>\nYou have a higher percent of correct answers on a math quiz.<\/p>\n<p>Explanation:<br \/>\nYou miss 3 out of 10 questions on a science quiz<br \/>\nSo, the coorect answers = 10 &#8211; 3 = 7<br \/>\nThe percent of correct answers on a science quiz = 7\/10 . 100 = 70%<br \/>\nYou miss 4 out of 15 questions on a math quiz<br \/>\nSo, the correct answers = 15 &#8211; 4 = 11<br \/>\nThe percent of correct answers on a math quiz = 11\/15 . 100 = 73.3%<br \/>\nThus, you have a higher percent of correct answers on a math quiz.<\/p>\n<p>Question 50.<br \/>\n<strong>CRITICAL THINKING<\/strong><br \/>\nA hackberry tree has roots that reach a depth of 6\\(\\frac{5}{12}\\) meters. The top of the tree is \\(18.2 \\overline{8}\\) meters above the ground. Find the total height from the bottom of the roots to the top of the tree.<br \/>\n<img decoding=\"async\" loading=\"lazy\" class=\"alignnone size-full wp-image-30157\" src=\"https:\/\/ccssanswers.com\/wp-content\/uploads\/2021\/01\/Big-Ideas-Math-Answers-7th-Grade-Chapter-2-Multiplying-and-Dividing-Rational-Numbers-52.png\" alt=\"Big Ideas Math Answers 7th Grade Chapter 2 Multiplying and Dividing Rational Numbers 52\" width=\"274\" height=\"188\" \/><\/p>\n<p>Answer:<br \/>\nThe total height from the bottom of the roots to the top of the tree is 23.70544 meters.<\/p>\n<p>Explanation:<br \/>\nThe depth of the tree = 6(5\/12) = 65\/12 meters<br \/>\nThe top of the tree = 18.288 meters<br \/>\nThe total height from the bottom of the roots to the top of the tree = 65\/12 + 18.288<br \/>\n= 5.41666 + 18.2888<br \/>\n= 23.70544 meters<br \/>\nSo, the total height from the bottom of the roots to the top of the tree is 23.70544 meters.<\/p>\n<p>Question 51.<br \/>\n<strong>DIG DEEPER!<\/strong><br \/>\nLet a and b be integers.<br \/>\na. When can &#8211;\\(\\frac{1}{a}\\) be written as a positive, repeating decimal?<br \/>\nb. When can \\(\\frac{1}{ab}\\) be written as a positive, terminating decimal?<\/p>\n<p>Answer:<br \/>\na. a = -7<br \/>\nb. b = -2<\/p>\n<p>Explanation:<br \/>\na. Let us take a = -7<br \/>\nThen -1\/a = -1\/-7 = 0.142857142<br \/>\nb. 1\/ab = 1\/(-7)(-2) = 1\/14 = 0.7142<\/p>\n<h3><a id=\"Lesson_2.4_Multiplying_Rational_Numbers\"><\/a>Lesson 2.4 Multiplying Rational Numbers<\/h3>\n<p><strong>EXPLORATION 1<\/strong><br \/>\n<strong>Finding Products of Rational Numbers<\/strong><br \/>\n<strong>Work with a partner.<\/strong><br \/>\na. Write a multiplication expression represented by each area model. Then \ufb01nd the product.<br \/>\n<img decoding=\"async\" loading=\"lazy\" class=\"alignnone size-full wp-image-30158\" src=\"https:\/\/ccssanswers.com\/wp-content\/uploads\/2021\/01\/Big-Ideas-Math-Answers-7th-Grade-Chapter-2-Multiplying-and-Dividing-Rational-Numbers-53.png\" alt=\"Big Ideas Math Answers 7th Grade Chapter 2 Multiplying and Dividing Rational Numbers 53\" width=\"428\" height=\"195\" srcset=\"https:\/\/ccssanswers.com\/wp-content\/uploads\/2021\/01\/Big-Ideas-Math-Answers-7th-Grade-Chapter-2-Multiplying-and-Dividing-Rational-Numbers-53.png 428w, https:\/\/ccssanswers.com\/wp-content\/uploads\/2021\/01\/Big-Ideas-Math-Answers-7th-Grade-Chapter-2-Multiplying-and-Dividing-Rational-Numbers-53-300x137.png 300w\" sizes=\"(max-width: 428px) 100vw, 428px\" \/><br \/>\nb. Complete the table.<br \/>\n<img decoding=\"async\" loading=\"lazy\" class=\"alignnone size-full wp-image-30160\" src=\"https:\/\/ccssanswers.com\/wp-content\/uploads\/2021\/01\/Big-Ideas-Math-Answers-7th-Grade-Chapter-2-Multiplying-and-Dividing-Rational-Numbers-54.png\" alt=\"Big Ideas Math Answers 7th Grade Chapter 2 Multiplying and Dividing Rational Numbers 54\" width=\"512\" height=\"357\" srcset=\"https:\/\/ccssanswers.com\/wp-content\/uploads\/2021\/01\/Big-Ideas-Math-Answers-7th-Grade-Chapter-2-Multiplying-and-Dividing-Rational-Numbers-54.png 512w, https:\/\/ccssanswers.com\/wp-content\/uploads\/2021\/01\/Big-Ideas-Math-Answers-7th-Grade-Chapter-2-Multiplying-and-Dividing-Rational-Numbers-54-300x209.png 300w\" sizes=\"(max-width: 512px) 100vw, 512px\" \/><br \/>\n<img decoding=\"async\" loading=\"lazy\" class=\"alignnone size-full wp-image-30159\" src=\"https:\/\/ccssanswers.com\/wp-content\/uploads\/2021\/01\/Big-Ideas-Math-Answers-7th-Grade-Chapter-2-Multiplying-and-Dividing-Rational-Numbers-54.1.png\" alt=\"Big Ideas Math Answers 7th Grade Chapter 2 Multiplying and Dividing Rational Numbers 54.1\" width=\"164\" height=\"195\" \/><br \/>\nc. Do the rules for multiplying integers apply to all rational numbers? Explain your reasoning.<\/p>\n<p>Answer:<br \/>\na. 9 x 10 = 90<br \/>\n5 x 10 = 50<br \/>\nb. <img decoding=\"async\" loading=\"lazy\" class=\"alignnone size-full wp-image-42283\" src=\"https:\/\/ccssanswers.com\/wp-content\/uploads\/2021\/01\/big-ideas-math-answers-grade-7-chapter-2-multiplying-and-dividing-rational-numbers-54.jpg\" alt=\"Big Ideas Math Answers Grade 7 Chapter 2 Multiplying and Dividing Rational Numbers 54\" width=\"517\" height=\"378\" srcset=\"https:\/\/ccssanswers.com\/wp-content\/uploads\/2021\/01\/big-ideas-math-answers-grade-7-chapter-2-multiplying-and-dividing-rational-numbers-54.jpg 517w, https:\/\/ccssanswers.com\/wp-content\/uploads\/2021\/01\/big-ideas-math-answers-grade-7-chapter-2-multiplying-and-dividing-rational-numbers-54-300x219.jpg 300w\" sizes=\"(max-width: 517px) 100vw, 517px\" \/><br \/>\nc. The rules for multiplying integers apply to all rational numbers.<\/p>\n<p><strong>2.4 Lesson<\/strong><\/p>\n<p><strong>Try It<\/strong><\/p>\n<p><strong>Find the product. Write fractions in simplest form.<\/strong><\/p>\n<p>Question 1.<br \/>\n-5.1 \u00d7 1.8<\/p>\n<p>Answer:<br \/>\n-5.1 \u00d7 1.8 = -9.18<\/p>\n<p>Explanation:<br \/>\n<img decoding=\"async\" loading=\"lazy\" class=\"alignnone size-full wp-image-42285\" src=\"https:\/\/ccssanswers.com\/wp-content\/uploads\/2021\/01\/big-ideas-math-answers-grade-7-chapter-2-multiplying-and-dividing-rational-numbers-55.jpg\" alt=\"Big Ideas Math Answers Grade 7 Chapter 2 Multiplying and Dividing Rational Numbers 55\" width=\"168\" height=\"249\" \/><\/p>\n<p>Question 2.<br \/>\n-6.3(-0.6) = 3.78<\/p>\n<p>Answer:<br \/>\n-6.3(-0.6)<\/p>\n<p>Explanation:<br \/>\n<img decoding=\"async\" loading=\"lazy\" class=\"alignnone size-full wp-image-42288\" src=\"https:\/\/ccssanswers.com\/wp-content\/uploads\/2021\/01\/big-ideas-math-answers-grade-7-chapter-2-multiplying-and-dividing-rational-numbers-56.jpg\" alt=\"Big Ideas Math Answers Grade 7 Chapter 2 Multiplying and Dividing Rational Numbers 56\" width=\"168\" height=\"197\" \/><\/p>\n<p>Question 3.<br \/>\n<img decoding=\"async\" loading=\"lazy\" class=\"alignnone size-full wp-image-30161\" src=\"https:\/\/ccssanswers.com\/wp-content\/uploads\/2021\/01\/Big-Ideas-Math-Answers-7th-Grade-Chapter-2-Multiplying-and-Dividing-Rational-Numbers-55.png\" alt=\"Big Ideas Math Answers 7th Grade Chapter 2 Multiplying and Dividing Rational Numbers 55\" width=\"73\" height=\"54\" \/><\/p>\n<p>Answer:<br \/>\n-4\/5(-2\/3) = 8\/15<\/p>\n<p>Explanation:<br \/>\n-4\/5(-2\/3) = (-4 . -2)\/(5 . 3)<br \/>\n= 8\/15<\/p>\n<p>Question 4.<br \/>\n<img decoding=\"async\" loading=\"lazy\" class=\"alignnone size-full wp-image-30162\" src=\"https:\/\/ccssanswers.com\/wp-content\/uploads\/2021\/01\/Big-Ideas-Math-Answers-7th-Grade-Chapter-2-Multiplying-and-Dividing-Rational-Numbers-56.png\" alt=\"Big Ideas Math Answers 7th Grade Chapter 2 Multiplying and Dividing Rational Numbers 56\" width=\"94\" height=\"54\" \/><\/p>\n<p>Answer:<br \/>\n4(1\/2) . (-2(1\/3)) = -21\/2<\/p>\n<p>Explanation:<br \/>\n4(1\/2) . (-2(1\/3)) = 9\/2 . (-7\/3)<br \/>\n= (9 . -7)\/(2 . 3)<br \/>\n= (-7 . 3)\/2 = -21\/2<\/p>\n<p><strong>Try It<\/strong><\/p>\n<p><strong>Find the product. Write fractions in simplest form.<\/strong><\/p>\n<p>Question 5.<br \/>\n<img decoding=\"async\" loading=\"lazy\" class=\"alignnone size-full wp-image-30163\" src=\"https:\/\/ccssanswers.com\/wp-content\/uploads\/2021\/01\/Big-Ideas-Math-Answers-7th-Grade-Chapter-2-Multiplying-and-Dividing-Rational-Numbers-57.png\" alt=\"Big Ideas Math Answers 7th Grade Chapter 2 Multiplying and Dividing Rational Numbers 57\" width=\"93\" height=\"48\" \/><\/p>\n<p>Answer:<br \/>\n-2\/3 . 7(7\/8) . 3\/2 = -63\/8<\/p>\n<p>Explanation:<br \/>\n-2\/3 . 7(7\/8) . 3\/2 = -2\/3 . 63\/8 . 3\/2<br \/>\n= (-2 . 63 . 3)\/(3 . 8 . 2)<br \/>\n= -63\/8<\/p>\n<p>Question 6.<br \/>\n-7.02(0.1)(100)(-10)<\/p>\n<p>Answer:<br \/>\n-7.02(0.1)(100)(-10) = 702<\/p>\n<p>Explanation:<br \/>\n-7.02(0.1)(100)(-10) = (-7.02 . 0.1)(100 . -10)<br \/>\n= (-0.702)(-1000)<br \/>\n= 702<\/p>\n<p><strong>Self-Assessmentfor Concepts &amp; Skills<\/strong><\/p>\n<p>Solve each exercise. Then rate your understanding of the success criteria in your journal.<\/p>\n<p>Question 7.<br \/>\n<strong>WRITING<\/strong><br \/>\nExplain how to determine whether a product of two rational numbers is positive or negative.<\/p>\n<p>Answer:<br \/>\nThe product of two rational numbers is positive when they have the same sign.<br \/>\nThe product of two rational numbers is negative when they have different signs.<\/p>\n<p><strong>MULTIPLYING RATIONAL NUMBERS<\/strong><br \/>\n<strong>Find the product. Write fractions in simplest form.<\/strong><\/p>\n<p>Question 8.<br \/>\n<img decoding=\"async\" loading=\"lazy\" class=\"alignnone size-full wp-image-30164\" src=\"https:\/\/ccssanswers.com\/wp-content\/uploads\/2021\/01\/Big-Ideas-Math-Answers-7th-Grade-Chapter-2-Multiplying-and-Dividing-Rational-Numbers-58.png\" alt=\"Big Ideas Math Answers 7th Grade Chapter 2 Multiplying and Dividing Rational Numbers 58\" width=\"100\" height=\"54\" \/><\/p>\n<p>Answer:<br \/>\n-3\/10 x (-8\/15) = 4\/25<\/p>\n<p>Explanation:<br \/>\n-3\/10 x (-8\/15) = (-3 x -8)\/(10 x 15)<br \/>\n= 24\/150 = 4\/25<\/p>\n<p>Question 9.<br \/>\n<img decoding=\"async\" loading=\"lazy\" class=\"alignnone size-full wp-image-30165\" src=\"https:\/\/ccssanswers.com\/wp-content\/uploads\/2021\/01\/Big-Ideas-Math-Answers-7th-Grade-Chapter-2-Multiplying-and-Dividing-Rational-Numbers-59.png\" alt=\"Big Ideas Math Answers 7th Grade Chapter 2 Multiplying and Dividing Rational Numbers 59\" width=\"65\" height=\"53\" \/><\/p>\n<p>Answer:<br \/>\n-2\/3 . 1(1\/3) = -8\/9<\/p>\n<p>Explanation:<br \/>\n-2\/3 . 1(1\/3) = -2\/3 . 4\/3<br \/>\n= (-2 . 4)\/(3 . 3) = -8\/9<\/p>\n<p>Question 10.<br \/>\n-2.8(-1.7)<\/p>\n<p>Answer:<br \/>\n-2.8(-1.7) = 4.76<\/p>\n<p>Explanation:<br \/>\n<img decoding=\"async\" loading=\"lazy\" class=\"alignnone size-full wp-image-42296\" src=\"https:\/\/ccssanswers.com\/wp-content\/uploads\/2021\/01\/big-ideas-math-answers-grade-7-chapter-2-multiplying-and-dividing-rational-numbers-57.jpg\" alt=\"Big Ideas Math Answers Grade 7 Chapter 2 Multiplying and Dividing Rational Numbers 57\" width=\"167\" height=\"242\" \/><\/p>\n<p>Question 11.<br \/>\n<img decoding=\"async\" loading=\"lazy\" class=\"alignnone size-full wp-image-30166\" src=\"https:\/\/ccssanswers.com\/wp-content\/uploads\/2021\/01\/Big-Ideas-Math-Answers-7th-Grade-Chapter-2-Multiplying-and-Dividing-Rational-Numbers-60.png\" alt=\"Big Ideas Math Answers 7th Grade Chapter 2 Multiplying and Dividing Rational Numbers 60\" width=\"85\" height=\"49\" \/><\/p>\n<p>Answer:<br \/>\n1(3\/5) . (-3(3\/4)) = -10<\/p>\n<p>Explanation:<br \/>\n1(3\/5) . (-3(3\/4)) = 8\/3 . -15\/4<br \/>\n= (8 . -15)\/(3 . 4)<br \/>\n= (2 . -5) = -10<\/p>\n<p><strong>Self-Assessment for Problem Solving<\/strong><\/p>\n<p>Solve each exercise. Then rate your understanding of the success criteria in your journal.<\/p>\n<p>Question 12.<br \/>\nA swimmer&#8217;s best time in an event is 53.87 seconds. On average, his best time decreases by 0.28 second each of the next \ufb01ve times he swims the event. Does he accomplish his goal of swimming the event in less than 52.5 seconds?<br \/>\n<img decoding=\"async\" loading=\"lazy\" class=\"alignnone size-full wp-image-30167\" src=\"https:\/\/ccssanswers.com\/wp-content\/uploads\/2021\/01\/Big-Ideas-Math-Answers-7th-Grade-Chapter-2-Multiplying-and-Dividing-Rational-Numbers-61.png\" alt=\"Big Ideas Math Answers 7th Grade Chapter 2 Multiplying and Dividing Rational Numbers 61\" width=\"295\" height=\"172\" \/><\/p>\n<p>Answer:<br \/>\nYes. This is because his fifth attempt was 52.47 seconds<\/p>\n<p>Explanation:<br \/>\nFrom the question, we are informed that Swimmers best time in an event is 53.87 seconds and that on average, his best time decreases by 0.28 seconds each of the next five times he swims the event.<br \/>\nThe time for the fifth time he swims will be = 53.87 &#8211; 5(0.28)<br \/>\n= 53.87 &#8211; 1.4<br \/>\n= 52.47 seconds<br \/>\nThis means that he accomplishes his goal of swimming the event in less than 52.5 seconds.<\/p>\n<p>Question 13.<br \/>\n<strong>DIG DEEPER!<\/strong><br \/>\nTerminal velocity is the fastest speed that an object can fall through the air. A skydiver reaches a terminal velocity of 120 miles per hour. What is the change in elevation of the skydiver after falling at terminal velocity for 15 seconds? Justify your answer.<\/p>\n<p>Answer:<br \/>\nThe change in elevation of the skydiver after falling at terminal velocity for 15 seconds is 30 miles.<\/p>\n<p>Explanation:<br \/>\nA skydiver reaches a terminal velocity of 120 miles per hour = 120\/60 = 2 miles per seconds<br \/>\nThe change in elevation of the skydiver after falling at terminal velocity for 15 seconds is 2 x 15 = 30 miles<\/p>\n<h3><a id=\"Multiplying_Rational_Numbers_Homework_&amp;_Practice_2.4\"><\/a>Multiplying Rational Numbers Homework &amp; Practice 2.4<\/h3>\n<p><strong>Review &amp; Refresh<\/strong><\/p>\n<p>Write the fraction or mixed number as a decimal.<\/p>\n<p>Question 1.<br \/>\n\\(\\frac{5}{16}\\)<\/p>\n<p>Answer:<br \/>\n5\/16 = 0.3125<\/p>\n<p>Explanation:<br \/>\n<img decoding=\"async\" loading=\"lazy\" class=\"alignnone size-full wp-image-42299\" src=\"https:\/\/ccssanswers.com\/wp-content\/uploads\/2021\/01\/big-ideas-math-answers-grade-7-chapter-2-multiplying-and-dividing-rational-numbers-58.jpg\" alt=\"Big Ideas Math Answers Grade 7 Chapter 2 Multiplying and Dividing Rational Numbers 58\" width=\"227\" height=\"504\" srcset=\"https:\/\/ccssanswers.com\/wp-content\/uploads\/2021\/01\/big-ideas-math-answers-grade-7-chapter-2-multiplying-and-dividing-rational-numbers-58.jpg 227w, https:\/\/ccssanswers.com\/wp-content\/uploads\/2021\/01\/big-ideas-math-answers-grade-7-chapter-2-multiplying-and-dividing-rational-numbers-58-135x300.jpg 135w\" sizes=\"(max-width: 227px) 100vw, 227px\" \/><\/p>\n<p>Question 2.<br \/>\n&#8211;\\(\\frac{9}{22}\\)<\/p>\n<p>Answer:<br \/>\n-9\/22 = -0.4090909<\/p>\n<p>Explanation:<br \/>\n<img decoding=\"async\" loading=\"lazy\" class=\"alignnone size-full wp-image-42300\" src=\"https:\/\/ccssanswers.com\/wp-content\/uploads\/2021\/01\/big-ideas-math-answers-grade-7-chapter-2-multiplying-and-dividing-rational-numbers-59.jpg\" alt=\"Big Ideas Math Answers Grade 7 Chapter 2 Multiplying and Dividing Rational Numbers 59\" width=\"250\" height=\"586\" srcset=\"https:\/\/ccssanswers.com\/wp-content\/uploads\/2021\/01\/big-ideas-math-answers-grade-7-chapter-2-multiplying-and-dividing-rational-numbers-59.jpg 250w, https:\/\/ccssanswers.com\/wp-content\/uploads\/2021\/01\/big-ideas-math-answers-grade-7-chapter-2-multiplying-and-dividing-rational-numbers-59-128x300.jpg 128w\" sizes=\"(max-width: 250px) 100vw, 250px\" \/><\/p>\n<p>Question 3.<br \/>\n6\\(\\frac{8}{11}\\)<\/p>\n<p>Answer:<br \/>\n6(8\/11) = 6.727272<\/p>\n<p>Explanation:<br \/>\n6(8\/11) = 74\/11<br \/>\n<img decoding=\"async\" loading=\"lazy\" class=\"alignnone size-full wp-image-42301\" src=\"https:\/\/ccssanswers.com\/wp-content\/uploads\/2021\/01\/big-ideas-math-answers-grade-7-chapter-2-multiplying-and-dividing-rational-numbers-60.jpg\" alt=\"Big Ideas Math Answers Grade 7 Chapter 2 Multiplying and Dividing Rational Numbers 60\" width=\"251\" height=\"583\" srcset=\"https:\/\/ccssanswers.com\/wp-content\/uploads\/2021\/01\/big-ideas-math-answers-grade-7-chapter-2-multiplying-and-dividing-rational-numbers-60.jpg 251w, https:\/\/ccssanswers.com\/wp-content\/uploads\/2021\/01\/big-ideas-math-answers-grade-7-chapter-2-multiplying-and-dividing-rational-numbers-60-129x300.jpg 129w\" sizes=\"(max-width: 251px) 100vw, 251px\" \/><\/p>\n<p>Question 4.<br \/>\n&#8211;\\(\\frac{26}{24}\\)<\/p>\n<p>Answer:<br \/>\n-26\/24 = -1.08333<\/p>\n<p>Explanation:<br \/>\n<img decoding=\"async\" loading=\"lazy\" class=\"alignnone size-full wp-image-42303\" src=\"https:\/\/ccssanswers.com\/wp-content\/uploads\/2021\/01\/big-ideas-math-answers-grade-7-chapter-2-multiplying-and-dividing-rational-numbers-61.jpg\" alt=\"Big Ideas Math Answers Grade 7 Chapter 2 Multiplying and Dividing Rational Numbers 61\" width=\"255\" height=\"586\" srcset=\"https:\/\/ccssanswers.com\/wp-content\/uploads\/2021\/01\/big-ideas-math-answers-grade-7-chapter-2-multiplying-and-dividing-rational-numbers-61.jpg 255w, https:\/\/ccssanswers.com\/wp-content\/uploads\/2021\/01\/big-ideas-math-answers-grade-7-chapter-2-multiplying-and-dividing-rational-numbers-61-131x300.jpg 131w\" sizes=\"(max-width: 255px) 100vw, 255px\" \/><\/p>\n<p><strong>Find the area of the \ufb01gure.<\/strong><\/p>\n<p>Question 5.<br \/>\n<img decoding=\"async\" loading=\"lazy\" class=\"alignnone size-full wp-image-30168\" src=\"https:\/\/ccssanswers.com\/wp-content\/uploads\/2021\/01\/Big-Ideas-Math-Answers-7th-Grade-Chapter-2-Multiplying-and-Dividing-Rational-Numbers-62.png\" alt=\"Big Ideas Math Answers 7th Grade Chapter 2 Multiplying and Dividing Rational Numbers 62\" width=\"170\" height=\"132\" \/><\/p>\n<p>Answer:<br \/>\nArea is 36 sq inches<\/p>\n<p>Explanation:<br \/>\nGiven that,<br \/>\na = 2 in, b = 10 in, h = 6 in<br \/>\nArea of the trapezoid = 1\/2 (a + b) . h<br \/>\n= 1\/2 (2 + 10) . 6<br \/>\n= (12) . 3<br \/>\n= 36 sq inches<\/p>\n<p>Question 6.<br \/>\n<img decoding=\"async\" loading=\"lazy\" class=\"alignnone size-full wp-image-30169\" src=\"https:\/\/ccssanswers.com\/wp-content\/uploads\/2021\/01\/Big-Ideas-Math-Answers-7th-Grade-Chapter-2-Multiplying-and-Dividing-Rational-Numbers-63.png\" alt=\"Big Ideas Math Answers 7th Grade Chapter 2 Multiplying and Dividing Rational Numbers 63\" width=\"149\" height=\"130\" \/><\/p>\n<p>Answer:<br \/>\nArea is 9 m\u00b2.<\/p>\n<p>Explanation:<br \/>\np = 1.5 + 3 = 4.5 m<br \/>\nq = 2 + 2 = 4 m<br \/>\nArea of rhombus = (pq)\/2<br \/>\n= (4.5 . 4)\/2<br \/>\n= 18\/2 = 9 m\u00b2<\/p>\n<p>Question 7.<br \/>\n<img decoding=\"async\" loading=\"lazy\" class=\"alignnone size-full wp-image-30170\" src=\"https:\/\/ccssanswers.com\/wp-content\/uploads\/2021\/01\/Big-Ideas-Math-Answers-7th-Grade-Chapter-2-Multiplying-and-Dividing-Rational-Numbers-64.png\" alt=\"Big Ideas Math Answers 7th Grade Chapter 2 Multiplying and Dividing Rational Numbers 64\" width=\"171\" height=\"152\" \/><\/p>\n<p>Answer:<br \/>\nThe area is 121 ft\u00b2.<\/p>\n<p>Explanation:<br \/>\nThe area of the rectangle formed by extending the base line and the top line is l x b<br \/>\n= 13 x 11 = 143 ft\u00b2<br \/>\nThe area of the formed triangle is 1\/2 x b x h<br \/>\nbase = 13 &#8211; 9 = 4 ft<br \/>\nheight = 11 ft<br \/>\nTriangle area = 1\/2 x 4 x 11<br \/>\n= 2 x 11 = 22 ft\u00b2<br \/>\nArea of the given shape = Area of the rectangle &#8211; area of the triangle<br \/>\n= 143 &#8211; 22 = 121 ft\u00b2<\/p>\n<p><strong>Concepts, Skills, &amp;Problem Solving<\/strong><br \/>\n<strong>FINDING PRODUCTS OF RATIONAL NUMBERS<\/strong><br \/>\n<strong>Write a multiplication expression represented by the area model. Then \ufb01nd the product.<\/strong> (See Exploration 1, p. 67.)<\/p>\n<p>Question 8.<br \/>\n<img decoding=\"async\" loading=\"lazy\" class=\"alignnone size-full wp-image-30171\" src=\"https:\/\/ccssanswers.com\/wp-content\/uploads\/2021\/01\/Big-Ideas-Math-Answers-7th-Grade-Chapter-2-Multiplying-and-Dividing-Rational-Numbers-65.png\" alt=\"Big Ideas Math Answers 7th Grade Chapter 2 Multiplying and Dividing Rational Numbers 65\" width=\"203\" height=\"193\" \/><\/p>\n<p>Answer:<br \/>\nThe area is 90 sq units.<\/p>\n<p>Explanation:<br \/>\nThe number of shaded rows = 9<br \/>\nThe number of shaded columns = 10<br \/>\nArea model = rows x columns<br \/>\n= 9 . 10 = 90<\/p>\n<p>Question 9.<br \/>\n<img decoding=\"async\" loading=\"lazy\" class=\"alignnone size-full wp-image-30172\" src=\"https:\/\/ccssanswers.com\/wp-content\/uploads\/2021\/01\/Big-Ideas-Math-Answers-7th-Grade-Chapter-2-Multiplying-and-Dividing-Rational-Numbers-66.png\" alt=\"Big Ideas Math Answers 7th Grade Chapter 2 Multiplying and Dividing Rational Numbers 66\" width=\"198\" height=\"192\" \/><\/p>\n<p>Answer:<br \/>\nThe area is 50 sq units.<\/p>\n<p>Explanation:<br \/>\nThe number of shaded rows = 5<br \/>\nThe number of shaded columns = 10<br \/>\nArea model = rows x columns<br \/>\n= 5 . 10 = 50<\/p>\n<p><strong>REASONING<\/strong><br \/>\n<strong>Without multiplying, tell whether the value of the expression is positive or negative. Explain your reasoning.<\/strong><\/p>\n<p>Question 10.<br \/>\n<img decoding=\"async\" loading=\"lazy\" class=\"alignnone size-full wp-image-30173\" src=\"https:\/\/ccssanswers.com\/wp-content\/uploads\/2021\/01\/Big-Ideas-Math-Answers-7th-Grade-Chapter-2-Multiplying-and-Dividing-Rational-Numbers-67.png\" alt=\"Big Ideas Math Answers 7th Grade Chapter 2 Multiplying and Dividing Rational Numbers 67\" width=\"57\" height=\"58\" \/><\/p>\n<p>Answer:<br \/>\nThe expression is negative.<\/p>\n<p>Explanation:<br \/>\nWhen you multiply a positive fraction by a negative integer, you will get a negative fraction.<\/p>\n<p>Question 11.<br \/>\n<img decoding=\"async\" loading=\"lazy\" class=\"alignnone size-full wp-image-30174\" src=\"https:\/\/ccssanswers.com\/wp-content\/uploads\/2021\/01\/Big-Ideas-Math-Answers-7th-Grade-Chapter-2-Multiplying-and-Dividing-Rational-Numbers-68.png\" alt=\"Big Ideas Math Answers 7th Grade Chapter 2 Multiplying and Dividing Rational Numbers 68\" width=\"85\" height=\"50\" \/><\/p>\n<p>Answer:<br \/>\nThe expression is negative.<\/p>\n<p>Explanation:<br \/>\nThe product of two fractions with different signs is negative.<\/p>\n<p>Question 12.<br \/>\n-0.25(-3.659)<\/p>\n<p>Answer:<br \/>\nThe expression is positive.<\/p>\n<p>Explanation:<br \/>\nThe product of two fractions with different signs is positive.<\/p>\n<p><strong>MULTIPLYING RATIONAL NUMBERS<\/strong><br \/>\n<strong>Find the product. Write fractions in simplest form.<\/strong><\/p>\n<p>Question 13.<br \/>\n<img decoding=\"async\" loading=\"lazy\" class=\"alignnone size-full wp-image-30175\" src=\"https:\/\/ccssanswers.com\/wp-content\/uploads\/2021\/01\/Big-Ideas-Math-Answers-7th-Grade-Chapter-2-Multiplying-and-Dividing-Rational-Numbers-69.png\" alt=\"Big Ideas Math Answers 7th Grade Chapter 2 Multiplying and Dividing Rational Numbers 69\" width=\"89\" height=\"60\" \/><\/p>\n<p>Answer:<br \/>\n-1\/4 x (-4\/3) = 1\/3<\/p>\n<p>Explanation:<br \/>\n-1\/4 x (-4\/3) = (-1 . -4)\/(4 . 3)<br \/>\n= 1\/3<\/p>\n<p>Question 14.<br \/>\n<img decoding=\"async\" loading=\"lazy\" class=\"alignnone size-full wp-image-30176\" src=\"https:\/\/ccssanswers.com\/wp-content\/uploads\/2021\/01\/Big-Ideas-Math-Answers-7th-Grade-Chapter-2-Multiplying-and-Dividing-Rational-Numbers-70.png\" alt=\"Big Ideas Math Answers 7th Grade Chapter 2 Multiplying and Dividing Rational Numbers 70\" width=\"71\" height=\"60\" \/><\/p>\n<p>Answer:<br \/>\n5\/6(-8\/15) = -4\/9<\/p>\n<p>Explanation:<br \/>\n5\/6(-8\/15) = (5 . -8) \/ (6 . 15)<br \/>\n= (5 . -2 . 4) \/ (3 . 2 . 5 . 3)<br \/>\n= -4\/9<\/p>\n<p>Question 15.<br \/>\n<img decoding=\"async\" loading=\"lazy\" class=\"alignnone size-full wp-image-30177\" src=\"https:\/\/ccssanswers.com\/wp-content\/uploads\/2021\/01\/Big-Ideas-Math-Answers-7th-Grade-Chapter-2-Multiplying-and-Dividing-Rational-Numbers-71.png\" alt=\"Big Ideas Math Answers 7th Grade Chapter 2 Multiplying and Dividing Rational Numbers 71\" width=\"81\" height=\"63\" \/><\/p>\n<p>Answer:<br \/>\n-2(-1(1\/4)) = 5\/2<\/p>\n<p>Explanation:<br \/>\n-2(-1(1\/4)) = -2(-5\/4)<br \/>\n= -2(-5\/2 . 2) = 5\/2<\/p>\n<p>Question 16.<br \/>\n<img decoding=\"async\" loading=\"lazy\" class=\"alignnone size-full wp-image-30178\" src=\"https:\/\/ccssanswers.com\/wp-content\/uploads\/2021\/01\/Big-Ideas-Math-Answers-7th-Grade-Chapter-2-Multiplying-and-Dividing-Rational-Numbers-72.png\" alt=\"Big Ideas Math Answers 7th Grade Chapter 2 Multiplying and Dividing Rational Numbers 72\" width=\"111\" height=\"60\" \/><\/p>\n<p>Answer:<br \/>\n-3(1\/3) . (-2(7\/10)) = 9<\/p>\n<p>Explanation:<br \/>\n-3(1\/3) . (-2(7\/10)) = -10\/3 . -27\/10<br \/>\n= (-10 . -27)\/(3 . 10)<br \/>\n= (9 . 3)\/3 = 9<\/p>\n<p>Question 17.<br \/>\n0.4 \u00d7 (-0.03)<\/p>\n<p>Answer:<br \/>\n0.4 \u00d7 (-0.03) = -3\/250<\/p>\n<p>Explanation:<br \/>\n0.4 \u00d7 (-0.03) = 4\/10 . (-3\/100)<br \/>\n= (4 . -3)\/(10 . 100)<br \/>\n= (2 . 2 . -3)\/(5 . 2 . 50 . 2)<br \/>\n= -3\/250<\/p>\n<p>Question 18.<br \/>\n-0.05 \u00d7 (-0.5)<\/p>\n<p>Answer:<br \/>\n-0.05 \u00d7 (-0.5) = 1\/40<\/p>\n<p>Explanation:<br \/>\n-0.05 \u00d7 (-0.5) = -5\/100 x -5\/10<br \/>\n= (-5 x -5)\/(100 x 10)<br \/>\n= (-5 x -5)\/(5 x 20 x 5 x 2)<br \/>\n= 1\/40<\/p>\n<p>Question 19.<br \/>\n-8(0.09)(-0.5)<\/p>\n<p>Answer:<br \/>\n-8(0.09)(-0.5) = 9\/25<\/p>\n<p>Explanation:<br \/>\n-8(0.09)(-0.5) = -8(9\/100)(-5\/10)<br \/>\n= (-8 . 9 . -5)\/(100 . 10)<br \/>\n= 9\/25<\/p>\n<p>Question 20.<br \/>\n<img decoding=\"async\" loading=\"lazy\" class=\"alignnone size-full wp-image-30179\" src=\"https:\/\/ccssanswers.com\/wp-content\/uploads\/2021\/01\/Big-Ideas-Math-Answers-7th-Grade-Chapter-2-Multiplying-and-Dividing-Rational-Numbers-74.png\" alt=\"Big Ideas Math Answers 7th Grade Chapter 2 Multiplying and Dividing Rational Numbers 74\" width=\"138\" height=\"63\" \/><\/p>\n<p>Answer:<br \/>\n5\/6 . (-4(1\/2)) . (-2(1\/5)) = 33\/4<\/p>\n<p>Explanation:<br \/>\n5\/6 . (-4(1\/2)) . (-2(1\/5)) = 5\/6 . -9\/2 . -11\/5<br \/>\n= (5 . -9 . -11)\/(6 . 2 . 5) = 33\/4<\/p>\n<p>Question 21.<br \/>\n<img decoding=\"async\" loading=\"lazy\" class=\"alignnone size-full wp-image-30180\" src=\"https:\/\/ccssanswers.com\/wp-content\/uploads\/2021\/01\/Big-Ideas-Math-Answers-7th-Grade-Chapter-2-Multiplying-and-Dividing-Rational-Numbers-75.png\" alt=\"Big Ideas Math Answers 7th Grade Chapter 2 Multiplying and Dividing Rational Numbers 75\" width=\"67\" height=\"56\" \/><\/p>\n<p>Answer:<br \/>\n(-1(2\/3))\u00b3 = -125\/27<\/p>\n<p>Explanation:<br \/>\n(-1(2\/3))\u00b3 = (-5\/3)\u00b3<br \/>\n= (-5 . -5 . -5)\/(3 . 3 . 3)<br \/>\n= -125\/27<\/p>\n<p><strong>YOU BE THE TEACHER<\/strong><br \/>\n<strong>Your friend evaluates the expression. Is your friend correct? Explain your reasoning.<\/strong><\/p>\n<p>Question 22.<br \/>\n<img decoding=\"async\" loading=\"lazy\" class=\"alignnone size-full wp-image-30181\" src=\"https:\/\/ccssanswers.com\/wp-content\/uploads\/2021\/01\/Big-Ideas-Math-Answers-7th-Grade-Chapter-2-Multiplying-and-Dividing-Rational-Numbers-76.png\" alt=\"Big Ideas Math Answers 7th Grade Chapter 2 Multiplying and Dividing Rational Numbers 76\" width=\"188\" height=\"125\" \/><\/p>\n<p>Answer:<br \/>\nCorrect<\/p>\n<p>Explanation:<br \/>\n-14 x 3\/2 = (-1 . 3)\/(4 . 2)<br \/>\n= -3\/8<\/p>\n<p>Question 23.<br \/>\n<img decoding=\"async\" loading=\"lazy\" class=\"alignnone size-full wp-image-30182\" src=\"https:\/\/ccssanswers.com\/wp-content\/uploads\/2021\/01\/Big-Ideas-Math-Answers-7th-Grade-Chapter-2-Multiplying-and-Dividing-Rational-Numbers-77.png\" alt=\"Big Ideas Math Answers 7th Grade Chapter 2 Multiplying and Dividing Rational Numbers 77\" width=\"258\" height=\"79\" \/><\/p>\n<p>Answer:<br \/>\nWrong<\/p>\n<p>Explanation:<br \/>\n-2.2 x (-3.7) = 8.14<\/p>\n<p>Question 24.<br \/>\n<strong>MODELING REAL LIFE<\/strong><br \/>\nThe hour hand of a clock moves 30\u00b0 every hour. How many degrees does it move in 2\\(\\frac{1}{5}\\) hours?<br \/>\n<img decoding=\"async\" loading=\"lazy\" class=\"alignnone size-full wp-image-30183\" src=\"https:\/\/ccssanswers.com\/wp-content\/uploads\/2021\/01\/Big-Ideas-Math-Answers-7th-Grade-Chapter-2-Multiplying-and-Dividing-Rational-Numbers-78.png\" alt=\"Big Ideas Math Answers 7th Grade Chapter 2 Multiplying and Dividing Rational Numbers 78\" width=\"166\" height=\"158\" \/><\/p>\n<p>Answer:<br \/>\nIn 2(1\/5) hours, the hour hand of a clock moves -66 degrees.<\/p>\n<p>Explanation:<br \/>\n2(1\/5) = 11\/5 = 2.2You can here use the rule of three as an easier way, and let x be the degrees it moves in 2(1\/5) hours.<br \/>\n1 hour &#8211;&gt; -30<br \/>\n2.2 hour &#8211;&gt;x<br \/>\nx = 2.2 * -30<br \/>\nx = -66<br \/>\nSo, in 2(1\/5) hours, the hour hand of a clock moves -66 degrees.<\/p>\n<p>Question 25.<br \/>\n<strong>MODELING REAL LIFE<\/strong><br \/>\nA 14.5-gallon gasoline tank is \\(\\frac{3}{4}\\) full. How many gallons will it take to \ufb01ll the tank?<\/p>\n<p>Answer:<br \/>\nWe need 3.625 gallons to fill the tank.<\/p>\n<p>Explanation:<br \/>\n3\/4 of the tank is full so, 1\/4 of the tank is empty<br \/>\nThe number of gallons will it take to fill the tank = 1\/4 * 14.5<br \/>\n= 0.25 * 14.5 = 3.625<br \/>\n<img decoding=\"async\" loading=\"lazy\" class=\"alignnone size-full wp-image-42338\" src=\"https:\/\/ccssanswers.com\/wp-content\/uploads\/2021\/01\/big-ideas-math-answers-grade-7-chapter-2-multiplying-and-dividing-rational-numbers-62.jpg\" alt=\"Big Ideas Math Answers Grade 7 Chapter 2 Multiplying and Dividing Rational Numbers 62\" width=\"196\" height=\"288\" \/><br \/>\nWe need 3.625 gallons to fill the tank.<\/p>\n<p>Question 26.<br \/>\n<strong>OPEN-ENDED<\/strong><br \/>\nWrite two fractions whose product is &#8211;\\(\\frac{3}{5}\\).<\/p>\n<p>Answer:<br \/>\nThe two fractions are -2\/3 and 9\/10<\/p>\n<p>Explanation:<br \/>\n= -2\/3 . 9\/10<br \/>\n= (-2 . 9)\/(3 . 10)<br \/>\n= -3\/5<\/p>\n<p><strong>USING PROPERTIES<\/strong><br \/>\n<strong>Find the product. Write fractions in simplest form.<\/strong><\/p>\n<p>Question 27.<br \/>\n<img decoding=\"async\" loading=\"lazy\" class=\"alignnone size-full wp-image-30184\" src=\"https:\/\/ccssanswers.com\/wp-content\/uploads\/2021\/01\/Big-Ideas-Math-Answers-7th-Grade-Chapter-2-Multiplying-and-Dividing-Rational-Numbers-79.png\" alt=\"Big Ideas Math Answers 7th Grade Chapter 2 Multiplying and Dividing Rational Numbers 79\" width=\"95\" height=\"51\" \/><\/p>\n<p>Answer:<br \/>\n1\/5 . 3\/8 . (-5) = -3\/8<\/p>\n<p>Explanation:<br \/>\n1\/5 . 3\/8 . (-5) = (1 . 3 . -5)\/(5 . 8)<br \/>\n= -3\/8<\/p>\n<p>Question 28.<br \/>\n0.01(4.6)(-200)<\/p>\n<p>Answer:<br \/>\n0.01(4.6)(-200) = -46\/5<\/p>\n<p>Explanation:<br \/>\n0.01(4.6)(-200) = 1\/100 . 46\/10 . -200<br \/>\n= (1 . 46 . -200)\/(100 . 10)<br \/>\n= -46\/5<\/p>\n<p>Question 29.<br \/>\n(-17.2 \u00d7 2.5) \u00d7 4<\/p>\n<p>Answer:<br \/>\n(-17.2 \u00d7 2.5) \u00d7 4 = -172<\/p>\n<p>Explanation:<br \/>\n(-17.2 \u00d7 2.5) \u00d7 4 = (-172\/10 x 25\/10) x 4<br \/>\n= (-172 x 25)\/(10 x 10) x 4<br \/>\n= (-172 \/ 2 x 2) x 4<br \/>\n= -172<\/p>\n<p>Question 30.<br \/>\n<img decoding=\"async\" loading=\"lazy\" class=\"alignnone size-full wp-image-30185\" src=\"https:\/\/ccssanswers.com\/wp-content\/uploads\/2021\/01\/Big-Ideas-Math-Answers-7th-Grade-Chapter-2-Multiplying-and-Dividing-Rational-Numbers-80.png\" alt=\"Big Ideas Math Answers 7th Grade Chapter 2 Multiplying and Dividing Rational Numbers 80\" width=\"138\" height=\"51\" \/><\/p>\n<p>Answer:<br \/>\n(-5\/9 x 2\/7) x (-7\/2) = 5\/9<\/p>\n<p>Explanation:<br \/>\n(-5\/9 x 2\/7) x (-7\/2) = (-5 x 2)\/(9 x 7) x (-7\/2)<br \/>\n= (-10\/63)\u00a0 (-7\/2)<br \/>\n= (-10 x -7)\/(63 x 2)<br \/>\n= 5\/9<\/p>\n<p>Question 31.<br \/>\n<img decoding=\"async\" loading=\"lazy\" class=\"alignnone size-full wp-image-30186\" src=\"https:\/\/ccssanswers.com\/wp-content\/uploads\/2021\/01\/Big-Ideas-Math-Answers-7th-Grade-Chapter-2-Multiplying-and-Dividing-Rational-Numbers-81.png\" alt=\"Big Ideas Math Answers 7th Grade Chapter 2 Multiplying and Dividing Rational Numbers 81\" width=\"150\" height=\"57\" \/><\/p>\n<p>Answer:<br \/>\n[-2\/3 . (-5\/7)] . (-9\/4) = -15\/14<\/p>\n<p>Explanation:<br \/>\n[-2\/3 . (-5\/7)] . (-9\/4) = (-2 . -5)\/(3 . 7) . (-9\/4)<br \/>\n= 10\/21 . (-9\/4)<br \/>\n= (10 . -9)\/(21 . 4)<br \/>\n= (5 . -3)\/(7 . 2)<br \/>\n= -15\/14<\/p>\n<p>Question 32.<br \/>\n<img decoding=\"async\" loading=\"lazy\" class=\"alignnone size-full wp-image-30187\" src=\"https:\/\/ccssanswers.com\/wp-content\/uploads\/2021\/01\/Big-Ideas-Math-Answers-7th-Grade-Chapter-2-Multiplying-and-Dividing-Rational-Numbers-82.png\" alt=\"Big Ideas Math Answers 7th Grade Chapter 2 Multiplying and Dividing Rational Numbers 82\" width=\"146\" height=\"58\" \/><\/p>\n<p>Answer:<br \/>\n(-4.5 . 8.61) . (-2\/9) = 861\/100<\/p>\n<p>Explanation:<br \/>\n(-4.5 . 8.61) . (-2\/9) = (-45\/10 . 861\/100) . (-2\/9)<br \/>\n= (-45 . 861)\/(10 . 100) . (-2\/9)<br \/>\n= 861\/100<\/p>\n<p>Question 33.<br \/>\n<strong>PROBLEM SOLVING<\/strong><br \/>\nFencing costs $25.80 per yard. How much does it cost to enclose two adjacent rectangular pastures as shown? Justify your answer.<br \/>\n<img decoding=\"async\" loading=\"lazy\" class=\"alignnone size-full wp-image-30188\" src=\"https:\/\/ccssanswers.com\/wp-content\/uploads\/2021\/01\/Big-Ideas-Math-Answers-7th-Grade-Chapter-2-Multiplying-and-Dividing-Rational-Numbers-83.png\" alt=\"Big Ideas Math Answers 7th Grade Chapter 2 Multiplying and Dividing Rational Numbers 83\" width=\"324\" height=\"145\" srcset=\"https:\/\/ccssanswers.com\/wp-content\/uploads\/2021\/01\/Big-Ideas-Math-Answers-7th-Grade-Chapter-2-Multiplying-and-Dividing-Rational-Numbers-83.png 324w, https:\/\/ccssanswers.com\/wp-content\/uploads\/2021\/01\/Big-Ideas-Math-Answers-7th-Grade-Chapter-2-Multiplying-and-Dividing-Rational-Numbers-83-300x134.png 300w\" sizes=\"(max-width: 324px) 100vw, 324px\" \/><\/p>\n<p>Answer:<br \/>\nThe cost of fencing is $3558.249312.<\/p>\n<p>Explanation:<br \/>\nFencing costs $25.80 per yard.<br \/>\nLength = 30(2\/9) = 272\/9 yd<br \/>\nWidth = 50(5\/8) = 405\/8 yd<br \/>\nThe rectangular pastures perimeter = 2(length + width) + length<br \/>\n= 2(272\/9 + 405\/8) + 272\/9<br \/>\n= 2(30.222 + 50.625) + 30.2222<br \/>\n= 2(53.8472) + 30.2222<br \/>\n= 107.6944 + 30.2222<br \/>\n= 137.91664 yards<br \/>\nMultiply the perimeter by $25.80 to get the cost<br \/>\n= 137.91664 x 25.80 = $3558.249312<br \/>\n<img decoding=\"async\" loading=\"lazy\" class=\"alignnone size-full wp-image-42345\" src=\"https:\/\/ccssanswers.com\/wp-content\/uploads\/2021\/01\/big-ideas-math-answers-grade-7-chapter-2-multiplying-and-dividing-rational-numbers-63.jpg\" alt=\"Big Ideas Math Answers Grade 7 Chapter 2 Multiplying and Dividing Rational Numbers 63\" width=\"420\" height=\"327\" srcset=\"https:\/\/ccssanswers.com\/wp-content\/uploads\/2021\/01\/big-ideas-math-answers-grade-7-chapter-2-multiplying-and-dividing-rational-numbers-63.jpg 420w, https:\/\/ccssanswers.com\/wp-content\/uploads\/2021\/01\/big-ideas-math-answers-grade-7-chapter-2-multiplying-and-dividing-rational-numbers-63-300x234.jpg 300w\" sizes=\"(max-width: 420px) 100vw, 420px\" \/><br \/>\nSo, the cost of fencing is $3558.249312.<\/p>\n<p><strong>ALGEBRA<\/strong><br \/>\n<strong>Evaluate the expression when x = -2, y = 3, and z = &#8211;\\(\\frac{1}{5}\\).<\/strong><\/p>\n<p>Question 34.<br \/>\nx \u2022 z<\/p>\n<p>Answer:<br \/>\n2\/5<\/p>\n<p>Explanation:<br \/>\nThe given expression is x \u2022 z<br \/>\nPut x = -2, z = -1\/5<br \/>\n= -2 . (-1\/5)<br \/>\n= 2\/5<\/p>\n<p>Question 35.<br \/>\nxyz<\/p>\n<p>Answer:<br \/>\n6\/5<\/p>\n<p>Explanation:<br \/>\nThe given expression is xyz<br \/>\nx = -2, y = 3, and z = &#8211;\\(\\frac{1}{5}\\)<br \/>\n= -2 . 3 . (-1\/5)<br \/>\n= -6 . (-1\/5)<br \/>\n= 6\/5<\/p>\n<p>Question 36.<br \/>\n\\(\\frac{1}{3}\\) + x \u2022 z<\/p>\n<p>Answer:<br \/>\n11\/15<\/p>\n<p>Explanation:<br \/>\nThe given expression is 1\/3 + x . z<br \/>\nPut x = -2, z = -1\/5<br \/>\n= 1\/3 + (-2) . (-1\/5)<br \/>\n= 1\/3 + 2\/5<br \/>\n= (5 + 6)\/15<br \/>\n= 11\/15<\/p>\n<p>Question 37.<br \/>\n\\(\\frac{1}{2}\\)z &#8211; \\(\\frac{2}{3}\\)y<\/p>\n<p>Answer:<br \/>\n-21\/10<\/p>\n<p>Explanation:<br \/>\nThe given expression is 1\/2 z &#8211; 2\/3 y<br \/>\nPut y = 3 , z = -1\/5<br \/>\n= 1\/2 . (-1\/5) &#8211; 2\/3 . 3<br \/>\n= -1\/10 &#8211; 2<br \/>\n= (-1 &#8211; 20)\/10<br \/>\n= -21\/10<\/p>\n<p><strong>EVALUATING AN EXPRESSION<\/strong><br \/>\n<strong>Evaluate the expression. Write fractions in simplest form.<\/strong><\/p>\n<p>Question 38.<br \/>\n-4.2 + 8.1 \u00d7 (-1.9)<\/p>\n<p>Answer:<br \/>\n-4.2 + 8.1 \u00d7 (-1.9) = -19.59<\/p>\n<p>Explanation:<br \/>\n-4.2 + 8.1 \u00d7 (-1.9) = -4.2 + (8.1 x -1.9)<br \/>\n= -4.2 &#8211; 15.39<br \/>\n= -19.59<\/p>\n<p>Question 39.<br \/>\n<img decoding=\"async\" loading=\"lazy\" class=\"alignnone size-full wp-image-30189\" src=\"https:\/\/ccssanswers.com\/wp-content\/uploads\/2021\/01\/Big-Ideas-Math-Answers-7th-Grade-Chapter-2-Multiplying-and-Dividing-Rational-Numbers-84.png\" alt=\"Big Ideas Math Answers 7th Grade Chapter 2 Multiplying and Dividing Rational Numbers 84\" width=\"118\" height=\"60\" \/><\/p>\n<p>Answer:<br \/>\n-3(3\/4) x 5\/6 &#8211; 2(1\/3) = -131\/24<\/p>\n<p>Explanation:<br \/>\n-3(3\/4) x 5\/6 &#8211; 2(1\/3) = (-15\/4) x 5\/6 &#8211; 7\/3<br \/>\n= (-15 . 5)\/(4 . 6) &#8211; 7\/3<br \/>\n= -25\/8 &#8211; 7\/3<br \/>\n= (-75 &#8211; 56)\/24<br \/>\n= -131\/24<\/p>\n<p>Question 40.<br \/>\n<img decoding=\"async\" loading=\"lazy\" class=\"alignnone size-full wp-image-30190\" src=\"https:\/\/ccssanswers.com\/wp-content\/uploads\/2021\/01\/Big-Ideas-Math-Answers-7th-Grade-Chapter-2-Multiplying-and-Dividing-Rational-Numbers-85.png\" alt=\"Big Ideas Math Answers 7th Grade Chapter 2 Multiplying and Dividing Rational Numbers 85\" width=\"115\" height=\"62\" \/><\/p>\n<p>Answer:<br \/>\n(-2\/3)\u00b2 &#8211; 3\/4 (2(1\/3)) = -47\/36<\/p>\n<p>Explanation:<br \/>\n(-2\/3)\u00b2 &#8211; 3\/4 (2(1\/3)) = (-2\/3).(-2\/3) &#8211; 3\/4 (7\/3)<br \/>\n= 4\/9 &#8211; 7\/4<br \/>\n= (16 &#8211; 63)\/36<br \/>\n= -47\/36<\/p>\n<p>Question 41.<br \/>\n<strong>DIG DEEPER!<\/strong><br \/>\nUse positive or negative integers to \ufb01ll in the blanks so that the product is \\(\\frac{1}{4}\\). Justify your answer.<br \/>\n<img decoding=\"async\" loading=\"lazy\" class=\"alignnone size-full wp-image-30191\" src=\"https:\/\/ccssanswers.com\/wp-content\/uploads\/2021\/01\/Big-Ideas-Math-Answers-7th-Grade-Chapter-2-Multiplying-and-Dividing-Rational-Numbers-86.png\" alt=\"Big Ideas Math Answers 7th Grade Chapter 2 Multiplying and Dividing Rational Numbers 86\" width=\"193\" height=\"86\" \/><\/p>\n<p>Answer:<br \/>\n<img decoding=\"async\" loading=\"lazy\" class=\"alignnone size-full wp-image-42354\" src=\"https:\/\/ccssanswers.com\/wp-content\/uploads\/2021\/01\/big-ideas-math-answers-grade-7-chapter-2-multiplying-and-dividing-rational-numbers-64.jpg\" alt=\"Big Ideas Math Answers Grade 7 Chapter 2 Multiplying and Dividing Rational Numbers 64\" width=\"196\" height=\"76\" \/>= 1\/4<\/p>\n<p>Explanation:<br \/>\nOne of the possibilities of arranging numbers in the fill in the blanks are as follows:<br \/>\n9\/2 x (-5\/144) x (8\/-5) = (9 x -5 x 8)\/(2 x\u00a0 x -5)<br \/>\n= 1\/4<\/p>\n<h3><a id=\"Lesson_2.5_Dividing_Rational_Numbers\"><\/a>Lesson 2.5 Dividing Rational Numbers<\/h3>\n<p><strong>EXPLORATION 1<\/strong><br \/>\n<strong>Work with a partner<\/strong><br \/>\na. Write two division expressions represented by the area model. Then \ufb01nd the quotients.<br \/>\n<img decoding=\"async\" loading=\"lazy\" class=\"alignnone size-full wp-image-30192\" src=\"https:\/\/ccssanswers.com\/wp-content\/uploads\/2021\/01\/Big-Ideas-Math-Answers-7th-Grade-Chapter-2-Multiplying-and-Dividing-Rational-Numbers-87.png\" alt=\"Big Ideas Math Answers 7th Grade Chapter 2 Multiplying and Dividing Rational Numbers 87\" width=\"370\" height=\"194\" srcset=\"https:\/\/ccssanswers.com\/wp-content\/uploads\/2021\/01\/Big-Ideas-Math-Answers-7th-Grade-Chapter-2-Multiplying-and-Dividing-Rational-Numbers-87.png 370w, https:\/\/ccssanswers.com\/wp-content\/uploads\/2021\/01\/Big-Ideas-Math-Answers-7th-Grade-Chapter-2-Multiplying-and-Dividing-Rational-Numbers-87-300x157.png 300w\" sizes=\"(max-width: 370px) 100vw, 370px\" \/><br \/>\nb. Complete the table.<br \/>\n<img decoding=\"async\" loading=\"lazy\" class=\"alignnone size-full wp-image-30194\" src=\"https:\/\/ccssanswers.com\/wp-content\/uploads\/2021\/01\/Big-Ideas-Math-Answers-Grade-7-Chapter-2-Multiplying-and-Dividing-Rational-Numbers-88.png\" alt=\"Big Ideas Math Answers Grade 7 Chapter 2 Multiplying and Dividing Rational Numbers 88\" width=\"508\" height=\"318\" srcset=\"https:\/\/ccssanswers.com\/wp-content\/uploads\/2021\/01\/Big-Ideas-Math-Answers-Grade-7-Chapter-2-Multiplying-and-Dividing-Rational-Numbers-88.png 508w, https:\/\/ccssanswers.com\/wp-content\/uploads\/2021\/01\/Big-Ideas-Math-Answers-Grade-7-Chapter-2-Multiplying-and-Dividing-Rational-Numbers-88-300x188.png 300w\" sizes=\"(max-width: 508px) 100vw, 508px\" \/><br \/>\n<img decoding=\"async\" loading=\"lazy\" class=\"alignnone size-full wp-image-30195\" src=\"https:\/\/ccssanswers.com\/wp-content\/uploads\/2021\/01\/Big-Ideas-Math-Answers-Grade-7-Chapter-2-Multiplying-and-Dividing-Rational-Numbers-89.png\" alt=\"Big Ideas Math Answers Grade 7 Chapter 2 Multiplying and Dividing Rational Numbers 89\" width=\"153\" height=\"194\" \/><br \/>\nc. Do the rules for dividing integers apply to all rational numbers? Explain your reasoning.<br \/>\nd. Write a real-life story involving the quotient 0.75 \u00f7 3. Interpret the quotient in the context of the story.<\/p>\n<p>Answer:<br \/>\na. 100 \u00f7 60 = 1.666, 200 \u00f7 120 = 1.666<br \/>\nb. <img decoding=\"async\" loading=\"lazy\" class=\"alignnone size-full wp-image-42872\" src=\"https:\/\/ccssanswers.com\/wp-content\/uploads\/2021\/01\/big-ideas-math-answers-grade-7-chapter-2-multiplying-and-dividing-rational-numbers-66.jpg\" alt=\"Big Ideas Math Answers Grade 7 Chapter 2 Multiplying and Dividing Rational Numbers 66\" width=\"499\" height=\"324\" srcset=\"https:\/\/ccssanswers.com\/wp-content\/uploads\/2021\/01\/big-ideas-math-answers-grade-7-chapter-2-multiplying-and-dividing-rational-numbers-66.jpg 499w, https:\/\/ccssanswers.com\/wp-content\/uploads\/2021\/01\/big-ideas-math-answers-grade-7-chapter-2-multiplying-and-dividing-rational-numbers-66-300x195.jpg 300w\" sizes=\"(max-width: 499px) 100vw, 499px\" \/><br \/>\nc. Yes<br \/>\nd. 0.75 \u00f7 3 = 0.25<\/p>\n<p><strong>2.5 Lesson<\/strong><\/p>\n<p><strong>Try It<\/strong><\/p>\n<p><strong>Find the quotient. Write fractions in simplest form.<\/strong><\/p>\n<p>Question 1.<br \/>\n-2.4 \u00f7 3.2<\/p>\n<p>Answer:<br \/>\n-2.4 \u00f7 3.2 = -0.75<\/p>\n<p>Explanation:<br \/>\n-2.4 \u00f7 3.2<br \/>\nWrite the division expression as a fraction.<br \/>\n= -24\/32 = -0.75<br \/>\n<img decoding=\"async\" loading=\"lazy\" class=\"alignnone size-full wp-image-43059\" src=\"https:\/\/ccssanswers.com\/wp-content\/uploads\/2021\/01\/big-ideas-math-answers-grade-7-chapter-2-multiplying-and-dividing-rational-numbers-67.jpg\" alt=\"Big Ideas Math Answers Grade 7 Chapter 2 Multiplying and Dividing Rational Numbers 67\" width=\"196\" height=\"424\" srcset=\"https:\/\/ccssanswers.com\/wp-content\/uploads\/2021\/01\/big-ideas-math-answers-grade-7-chapter-2-multiplying-and-dividing-rational-numbers-67.jpg 196w, https:\/\/ccssanswers.com\/wp-content\/uploads\/2021\/01\/big-ideas-math-answers-grade-7-chapter-2-multiplying-and-dividing-rational-numbers-67-139x300.jpg 139w\" sizes=\"(max-width: 196px) 100vw, 196px\" \/><\/p>\n<p>Question 2.<br \/>\n-6 \u00f7 (-1.1)<\/p>\n<p>Answer:<br \/>\n-6 \u00f7 (-1.1) = 5.454545<\/p>\n<p>Explanation:<br \/>\n-6 \u00f7 (-1.1)<br \/>\n= 60\/11<br \/>\n<img decoding=\"async\" loading=\"lazy\" class=\"alignnone size-full wp-image-43097\" src=\"https:\/\/ccssanswers.com\/wp-content\/uploads\/2021\/01\/big-ideas-math-answers-grade-7-chapter-2-multiplying-and-dividing-rational-numbers-68.jpg\" alt=\"Big Ideas Math Answers Grade 7 Chapter 2 Multiplying and Dividing Rational Numbers 68\" width=\"258\" height=\"589\" srcset=\"https:\/\/ccssanswers.com\/wp-content\/uploads\/2021\/01\/big-ideas-math-answers-grade-7-chapter-2-multiplying-and-dividing-rational-numbers-68.jpg 258w, https:\/\/ccssanswers.com\/wp-content\/uploads\/2021\/01\/big-ideas-math-answers-grade-7-chapter-2-multiplying-and-dividing-rational-numbers-68-131x300.jpg 131w\" sizes=\"(max-width: 258px) 100vw, 258px\" \/><\/p>\n<p>Question 3.<br \/>\n<img decoding=\"async\" loading=\"lazy\" class=\"alignnone size-full wp-image-30196\" src=\"https:\/\/ccssanswers.com\/wp-content\/uploads\/2021\/01\/Big-Ideas-Math-Answers-Grade-7-Chapter-2-Multiplying-and-Dividing-Rational-Numbers-90.png\" alt=\"Big Ideas Math Answers Grade 7 Chapter 2 Multiplying and Dividing Rational Numbers 90\" width=\"87\" height=\"51\" \/><\/p>\n<p>Answer:<br \/>\n-6\/5 \u00f7 (-1\/2) = 12\/5<\/p>\n<p>Explanation:<br \/>\n-6\/5 \u00f7 (-1\/2)<br \/>\n= 6\/5 \u00f7 1\/2<br \/>\n= 6\/5 . (2\/1)<br \/>\n= (6 . 2)\/(5 . 1)<br \/>\n= 12\/5<\/p>\n<p>Question 4.<br \/>\n<img decoding=\"async\" loading=\"lazy\" class=\"alignnone size-full wp-image-30197\" src=\"https:\/\/ccssanswers.com\/wp-content\/uploads\/2021\/01\/Big-Ideas-Math-Answers-Grade-7-Chapter-2-Multiplying-and-Dividing-Rational-Numbers-91.png\" alt=\"Big Ideas Math Answers Grade 7 Chapter 2 Multiplying and Dividing Rational Numbers 91\" width=\"77\" height=\"55\" \/><\/p>\n<p>Answer:<br \/>\n-1\/3 \u00f7 2(2\/3) = -1\/8<\/p>\n<p>Explanation:<br \/>\n-1\/3 \u00f7 2(2\/3)<br \/>\n= -1\/3 \u00f7 8\/3<br \/>\n= -1\/3 . (3\/8)<br \/>\n= (-1 . 3)\/(3 . 8)<br \/>\n= -1\/8<\/p>\n<p><strong>Try It<\/strong><\/p>\n<p><strong>Evaluate the expression. Write fractions in simplest form.<\/strong><\/p>\n<p>Question 5.<br \/>\n<img decoding=\"async\" loading=\"lazy\" class=\"alignnone size-full wp-image-30198\" src=\"https:\/\/ccssanswers.com\/wp-content\/uploads\/2021\/01\/Big-Ideas-Math-Answers-Grade-7-Chapter-2-Multiplying-and-Dividing-Rational-Numbers-92.png\" alt=\"Big Ideas Math Answers Grade 7 Chapter 2 Multiplying and Dividing Rational Numbers 92\" width=\"43\" height=\"67\" \/><\/p>\n<p>Answer:<br \/>\n-1\/2 \/ 6 = -1\/12<\/p>\n<p>Explanation:<br \/>\n-1\/2 \/ 6 = (-1\/2) . (1\/6)<br \/>\n= (-1 . 1)\/(2 . 6)<br \/>\n= -1\/12<\/p>\n<p>Question 6.<br \/>\n<img decoding=\"async\" loading=\"lazy\" class=\"alignnone size-full wp-image-30199\" src=\"https:\/\/ccssanswers.com\/wp-content\/uploads\/2021\/01\/Big-Ideas-Math-Answers-Grade-7-Chapter-2-Multiplying-and-Dividing-Rational-Numbers-93.png\" alt=\"Big Ideas Math Answers Grade 7 Chapter 2 Multiplying and Dividing Rational Numbers 93\" width=\"54\" height=\"92\" \/><\/p>\n<p>Answer:<br \/>\n-2(1\/2) \/ -3\/4 = 10\/3<\/p>\n<p>Explanation:<br \/>\n-2(1\/2) \/ -3\/4 = -5\/2 \/ -3\/4<br \/>\n= (-5\/2) . (4\/-3)<br \/>\n= (-5 . 4)\/(2 . -3)<br \/>\n= 10\/3<\/p>\n<p>Question 7.<br \/>\n<img decoding=\"async\" loading=\"lazy\" class=\"alignnone size-full wp-image-30200\" src=\"https:\/\/ccssanswers.com\/wp-content\/uploads\/2021\/01\/Big-Ideas-Math-Answers-Grade-7-Chapter-2-Multiplying-and-Dividing-Rational-Numbers-94.png\" alt=\"Big Ideas Math Answers Grade 7 Chapter 2 Multiplying and Dividing Rational Numbers 94\" width=\"102\" height=\"88\" \/><\/p>\n<p>Answer:<br \/>\n[-1(2\/3) . (-3\/5)] \/ (1\/3)\u00b2 = 9<\/p>\n<p>Explanation:<br \/>\n[-1(2\/3) . (-3\/5)] \/ (1\/3)\u00b2 = [(-5\/3) . (-3\/5)] \/ (1\/9)<br \/>\n= [(-5 . -3)\/(3 . 5)]\/(1\/9)<br \/>\n= (1\/1) \/ (1\/9)<br \/>\n= (1\/1) . (9\/1)<br \/>\n= 9<\/p>\n<p><strong>Self-Assessmentfor Concepts &amp; Skills<\/strong><\/p>\n<p>Solve each exercise. Then rate your understanding of the success criteria in your journal.<\/p>\n<p>Question 8.<br \/>\n<strong>WRITING<\/strong><br \/>\nExplain how to determine whether a quotient of two rational numbers is positive or negative.<\/p>\n<p>Answer:<br \/>\nThe simple and easy strategy to find whether the quotient of two rational numbers is positive or negative is mentioned here.<br \/>\nThe quotient of two rational numbers is positive when those numbers have the same sign.<br \/>\nThe quotient of two rational numbers is negative when they have different signs.<\/p>\n<p><strong>EVALUATING AN EXPRESSION<\/strong><br \/>\n<strong>Evaluate the expression. Write fractions in simplest form.<\/strong><\/p>\n<p>Question 9.<br \/>\n<img decoding=\"async\" loading=\"lazy\" class=\"alignnone size-full wp-image-30201\" src=\"https:\/\/ccssanswers.com\/wp-content\/uploads\/2021\/01\/Big-Ideas-Math-Answers-Grade-7-Chapter-2-Multiplying-and-Dividing-Rational-Numbers-95.png\" alt=\"Big Ideas Math Answers Grade 7 Chapter 2 Multiplying and Dividing Rational Numbers 95\" width=\"74\" height=\"59\" \/><\/p>\n<p>Answer:<br \/>\n3\/8 \u00f7 (-9\/5) = -5\/24<\/p>\n<p>Explanation:<br \/>\n3\/8 \u00f7 (-9\/5) = 3\/8 . (-5\/9)<br \/>\n= (3 . -5)\/(8 . 9)<br \/>\n= -5\/(8 . 3)<br \/>\n= -5\/24<\/p>\n<p>Question 10.<br \/>\n-6.8 \u00f7 (-3.6)<\/p>\n<p>Answer:<br \/>\n-6.8 \u00f7 (-3.6) = 17\/9<\/p>\n<p>Explanation:<br \/>\n-6.8 \u00f7 (-3.6) = -68\/10 \u00f7 (-36\/10)<br \/>\n= -68\/10 . (-10\/36)<br \/>\n= (-68 . -10)\/(10 . 36)<br \/>\n= 68\/36<br \/>\n= 17\/9<\/p>\n<p>Question 11.<br \/>\n<img decoding=\"async\" loading=\"lazy\" class=\"alignnone size-full wp-image-30202\" src=\"https:\/\/ccssanswers.com\/wp-content\/uploads\/2021\/01\/Big-Ideas-Math-Answers-Grade-7-Chapter-2-Multiplying-and-Dividing-Rational-Numbers-97.png\" alt=\"Big Ideas Math Answers Grade 7 Chapter 2 Multiplying and Dividing Rational Numbers 97\" width=\"41\" height=\"73\" \/><\/p>\n<p>Answer:<br \/>\n(-2\/9)\/(2(2\/5)) = -5\/54<\/p>\n<p>Explanation:<br \/>\n(-2\/9)\/(2(2\/5)) = (-2\/9)\/(12\/5)<br \/>\n= -2\/9 . 5\/12<br \/>\n= (-2 . 5)\/(9 . 12)<br \/>\n= (-5)\/(9 . 6)<br \/>\n= -5\/54<\/p>\n<p><strong>Self-Assessment for Problem Solving<\/strong><\/p>\n<p>Solve each exercise. Then rate your understanding of the success criteria in your journal.<\/p>\n<p>Question 12.<br \/>\n<strong>DIG DEEPER!<\/strong><br \/>\nSoil is composed of several layers. A geologist measures the depths of the subsoil and the bedrock, as shown. Find and interpret two quotients involving the depths of the subsoil and the bedrock.<br \/>\n<img decoding=\"async\" loading=\"lazy\" class=\"alignnone size-full wp-image-30203\" src=\"https:\/\/ccssanswers.com\/wp-content\/uploads\/2021\/01\/Big-Ideas-Math-Answers-Grade-7-Chapter-2-Multiplying-and-Dividing-Rational-Numbers-98.png\" alt=\"Big Ideas Math Answers Grade 7 Chapter 2 Multiplying and Dividing Rational Numbers 98\" width=\"194\" height=\"285\" \/><\/p>\n<p>Answer:<br \/>\nThe depths of the subsoil and the bedrock is 2.244 ft<\/p>\n<p>Explanation:<br \/>\nThe depth of the subsoil = -22.5 ft<br \/>\nThe depth of the bedrock = -50.5 ft<br \/>\nThe distance between subsoil and bedrock =50.5 &#8211; 22.5<br \/>\n= 28 ft<br \/>\nThe depths of the subsoil and the bedrock = -50.5\/-22.5<br \/>\n= 2.244<br \/>\n<img decoding=\"async\" loading=\"lazy\" class=\"alignnone size-full wp-image-43115\" src=\"https:\/\/ccssanswers.com\/wp-content\/uploads\/2021\/01\/big-ideas-math-answers-grade-7-chapter-2-multiplying-and-dividing-rational-numbers-69.jpg\" alt=\"Big Ideas Math Answers Grade 7 Chapter 2 Multiplying and Dividing Rational Numbers 69\" width=\"283\" height=\"591\" srcset=\"https:\/\/ccssanswers.com\/wp-content\/uploads\/2021\/01\/big-ideas-math-answers-grade-7-chapter-2-multiplying-and-dividing-rational-numbers-69.jpg 283w, https:\/\/ccssanswers.com\/wp-content\/uploads\/2021\/01\/big-ideas-math-answers-grade-7-chapter-2-multiplying-and-dividing-rational-numbers-69-144x300.jpg 144w\" sizes=\"(max-width: 283px) 100vw, 283px\" \/><\/p>\n<p>Question 13.<br \/>\nThe restaurant in Example 3 receives additional scores of 0.75, 1.5, 1.25, 4.75, 0.25, 0.5, 5, and 0.5 for the lasagna. Given the additional data, should the restaurant consider changing the recipe? Explain.<\/p>\n<p>Answer:<br \/>\nThe restaurant should not change the recipe.<\/p>\n<p>Explanation:<br \/>\nThe restaurant received scores are 2.25, -3.5, 0, -4.5, 1.75, -1, 3.5, -2.5, -0.75, -1.5, -1.25, 4.75, -0.25, -0.5, 5 and -0.5<br \/>\nThe mean of scores = sum of scores \/ number of scores<br \/>\n= (2.25 + (-3.5) + 0 + (-4.5) + 1.75 + (-1) + 3.5 + (-2.5) + (-0.75) + (-1.5) + (-1.25) + 4.75 + (-0.25) + (-0.5) + 5 + (-0.5))\/16<br \/>\n= (2.25 &#8211; 3.5 &#8211; 4.5 + 1.75 &#8211; 1 + 3.5 &#8211; 2.5 &#8211; 0.75 &#8211; 1.5 &#8211; 1.25 + 4.75 &#8211; 0.25 &#8211; 0.5 + 5 &#8211; 0.5)\/16<br \/>\n= 1\/16 = 0.0625<br \/>\nThe mean score is above 0.<br \/>\nSo, the restaurant should not change the recipe.<\/p>\n<h3><a id=\"Dividing_Rational_Numbers_Homework_&amp;_Practice_2.5\"><\/a>Dividing Rational Numbers Homework &amp; Practice 2.5<\/h3>\n<p><strong>Review &amp; Refresh<\/strong><\/p>\n<p><strong>Find the product. Write fractions in simplest form.<\/strong><\/p>\n<p>Question 1.<br \/>\n-0.5(1.31)<\/p>\n<p>Answer:<br \/>\n-0.5(1.31) = -131\/200<\/p>\n<p>Explanation:<br \/>\n-0.5(1.31) = -5\/10 (131\/100)<br \/>\n= (-5 . 131) \/ (10 . 100)<br \/>\n= -131\/(2 . 100)<br \/>\n= -131\/200<\/p>\n<p>Question 2.<br \/>\n<img decoding=\"async\" loading=\"lazy\" class=\"alignnone size-full wp-image-30204\" src=\"https:\/\/ccssanswers.com\/wp-content\/uploads\/2021\/01\/Big-Ideas-Math-Answers-Grade-7-Chapter-2-Multiplying-and-Dividing-Rational-Numbers-99.png\" alt=\"Big Ideas Math Answers Grade 7 Chapter 2 Multiplying and Dividing Rational Numbers 99\" width=\"76\" height=\"56\" \/><\/p>\n<p>Answer:<br \/>\n9\/10 (-1(1\/4)) = -9\/8<\/p>\n<p>Explanation:<br \/>\n9\/10 (-1(1\/4)) = 9\/10 (-5\/4)<br \/>\n= (9 . -5)\/(10 . 4)<br \/>\n= -9\/(2 . 4)<br \/>\n= -9\/8<\/p>\n<p>Question 3.<br \/>\n<img decoding=\"async\" loading=\"lazy\" class=\"alignnone size-full wp-image-30205\" src=\"https:\/\/ccssanswers.com\/wp-content\/uploads\/2021\/01\/Big-Ideas-Math-Answers-Grade-7-Chapter-2-Multiplying-and-Dividing-Rational-Numbers-100.png\" alt=\"Big Ideas Math Answers Grade 7 Chapter 2 Multiplying and Dividing Rational Numbers 100\" width=\"89\" height=\"58\" \/><\/p>\n<p>Answer:<br \/>\n-7\/12 (-3\/14) = 1\/8<\/p>\n<p>Explanation:<br \/>\n-7\/12 (-3\/14) = (-7 . -3) \/ (12 . 14)<br \/>\n= (-1 . -1)\/(4 . 2)<br \/>\n= 1\/8<\/p>\n<p><strong>Identify the terms, coefficients, and constants in the expression.<\/strong><\/p>\n<p>Question 4.<br \/>\n3b + 12<\/p>\n<p>Answer:<br \/>\nThe coefficients are 3, the constant is 12, terms are 3b, 12<\/p>\n<p>Explanation:<br \/>\nThe coefficients are 3, the constant is 12, terms are 3b, 12<\/p>\n<p>Question 5.<br \/>\n14 + z + 6f<\/p>\n<p>Answer:<br \/>\nThe terms are 14, z, 6f, coefficients are 6, 1 and constant is 14 in 14 + z + 6f<\/p>\n<p>Explanation:<br \/>\nThe terms are 14, z, 6f, coefficients are 6, 1 and constant is 14 in 14 + z + 6f<\/p>\n<p>Question 6.<br \/>\n8g + 14 + 5c + 7<\/p>\n<p>Answer:<br \/>\nThe terms are 8g, 14, 5c, 7 and coefficients are 8, 5, and constants are 14, 7<\/p>\n<p>Explanation:<br \/>\nThe terms are 8g, 14, 5c, 7 and coefficients are 8, 5, and constants are 14, 7<\/p>\n<p>Question 7.<br \/>\n42m + 18 + 12c<sup>2<\/sup><\/p>\n<p>Answer:<br \/>\nThe terms are 42m, 18, 12c\u00b2, coefficients are 42, 12 and constants are 18.<\/p>\n<p>Explanation:<br \/>\nThe terms are 42m, 18, 12c\u00b2, coefficients are 42, 12 and constants are 18.<\/p>\n<p><strong>Concepts, Skills, &amp;Problem Solving<\/strong><br \/>\n<strong>USING TOOLS<\/strong><br \/>\n<strong>Write two division expressions represented by the area model. Then \ufb01nd the quotients.<\/strong> (See Exploration 1, p. 73.)<\/p>\n<p>Question 8.<br \/>\n<img decoding=\"async\" loading=\"lazy\" class=\"alignnone size-full wp-image-30206\" src=\"https:\/\/ccssanswers.com\/wp-content\/uploads\/2021\/01\/Big-Ideas-Math-Answers-Grade-7-Chapter-2-Multiplying-and-Dividing-Rational-Numbers-101.png\" alt=\"Big Ideas Math Answers Grade 7 Chapter 2 Multiplying and Dividing Rational Numbers 101\" width=\"193\" height=\"186\" \/><\/p>\n<p>Answer:<br \/>\n20\/50, 40\/100<\/p>\n<p>Explanation:<br \/>\nThe first division expression is 20\/50 = 0.4<br \/>\nThe second division expression is 40\/100 = 0.4<\/p>\n<p>Question 9.<br \/>\n<img decoding=\"async\" loading=\"lazy\" class=\"alignnone size-full wp-image-30207\" src=\"https:\/\/ccssanswers.com\/wp-content\/uploads\/2021\/01\/Big-Ideas-Math-Answers-Grade-7-Chapter-2-Multiplying-and-Dividing-Rational-Numbers-102.png\" alt=\"Big Ideas Math Answers Grade 7 Chapter 2 Multiplying and Dividing Rational Numbers 102\" width=\"197\" height=\"194\" \/><\/p>\n<p>Answer:<br \/>\n6\/10, 54\/100<\/p>\n<p>Explanation:<br \/>\nThe first division expression is 6\/10 = 0.6<br \/>\nThe second division expression is 54\/100 = 0.54<\/p>\n<p><strong>DIVIDING RATIONAL NUMBERS<\/strong><br \/>\n<strong>Find the quotient. Write fractions in simplest form.<\/strong><\/p>\n<p>Question 10.<br \/>\n<img decoding=\"async\" loading=\"lazy\" class=\"alignnone size-full wp-image-30208\" src=\"https:\/\/ccssanswers.com\/wp-content\/uploads\/2021\/01\/Big-Ideas-Math-Answers-Grade-7-Chapter-2-Multiplying-and-Dividing-Rational-Numbers-103.png\" alt=\"Big Ideas Math Answers Grade 7 Chapter 2 Multiplying and Dividing Rational Numbers 103\" width=\"81\" height=\"57\" \/><\/p>\n<p>Answer:<br \/>\n-7\/5 \u00f7 2\/5 = -3.5<\/p>\n<p>Explanation:<br \/>\n-7\/5 \u00f7 2\/5 = -7\/5 . 5\/2<br \/>\n= (-7 . 5)\/(5 . 2)<br \/>\n= -7\/2<br \/>\n= -3.5<\/p>\n<p>Question 11.<br \/>\n-0.18 \u00f7 0.03<\/p>\n<p>Answer:<br \/>\n-0.18 \u00f7 0.03 = -6<\/p>\n<p>Explanation:<br \/>\n-0.18 \u00f7 0.03 = -18\/100 \u00f7 3\/100<br \/>\n= -18\/100 . 100\/3<br \/>\n= (-18 . 100) \/ (100 . 3)<br \/>\n= -6<\/p>\n<p>Question 12.<br \/>\n-3.45 \u00f7 (-15)<\/p>\n<p>Answer:<br \/>\n-3.45 \u00f7 (-15) = 0.03<\/p>\n<p>Explanation:<br \/>\n-3.45 \u00f7 (-15) = -45\/100 \u00f7 -15\/1<br \/>\n= -45\/100 . -1\/15<br \/>\n= (-45 . -1)\/(100 . 15)<br \/>\n= 3\/100<br \/>\n= 0.03<\/p>\n<p>Question 13.<br \/>\n-8 \u00f7 (-2.2)<\/p>\n<p>Answer:<br \/>\n-8 \u00f7 (-2.2) = 3.636363<\/p>\n<p>Explanation:<br \/>\n-8 \u00f7 (-2.2) = -8 \u00f7 -22\/10<br \/>\n= -8\/1 . -10\/22<br \/>\n= (-8 . -10) \/ (1 . 22)<br \/>\n= (-4 . -10) \/ 11<br \/>\n= 40\/11 = 3.636363<br \/>\n<img decoding=\"async\" loading=\"lazy\" class=\"alignnone size-full wp-image-43163\" src=\"https:\/\/ccssanswers.com\/wp-content\/uploads\/2021\/01\/big-ideas-math-answers-grade-7-chapter-2-multiplying-and-dividing-rational-numbers-70.jpg\" alt=\"Big Ideas Math Answers Grade 7 Chapter 2 Multiplying and Dividing Rational Numbers 70\" width=\"221\" height=\"504\" srcset=\"https:\/\/ccssanswers.com\/wp-content\/uploads\/2021\/01\/big-ideas-math-answers-grade-7-chapter-2-multiplying-and-dividing-rational-numbers-70.jpg 221w, https:\/\/ccssanswers.com\/wp-content\/uploads\/2021\/01\/big-ideas-math-answers-grade-7-chapter-2-multiplying-and-dividing-rational-numbers-70-132x300.jpg 132w\" sizes=\"(max-width: 221px) 100vw, 221px\" \/><\/p>\n<p>Question 14.<br \/>\n<img decoding=\"async\" loading=\"lazy\" class=\"alignnone size-full wp-image-30209\" src=\"https:\/\/ccssanswers.com\/wp-content\/uploads\/2021\/01\/Big-Ideas-Math-Answers-Grade-7-Chapter-2-Multiplying-and-Dividing-Rational-Numbers-104.png\" alt=\"Big Ideas Math Answers Grade 7 Chapter 2 Multiplying and Dividing Rational Numbers 104\" width=\"80\" height=\"57\" \/><\/p>\n<p>Answer:<br \/>\n1\/4 \u00f7 (-3\/8) = -0.6666<\/p>\n<p>Explanation:<br \/>\n1\/4 \u00f7 (-3\/8) = 1\/4 . (-8\/3)<br \/>\n= (1 . -8) \/ (4 . 3)<br \/>\n= -2\/3<br \/>\n= -0.66666<\/p>\n<p>Question 15.<br \/>\n8.722 \u00f7 (-3.56)<\/p>\n<p>Answer:<br \/>\n8.722 \u00f7 (-3.56) = -2.45<\/p>\n<p>Explanation:<br \/>\n8.722 \u00f7 (-3.56) = 8722\/1000 \u00f7 (-356\/100)<br \/>\n= 8722\/1000 . (100\/-356)<br \/>\n= (8722 . 100)\/(1000 . -356)<br \/>\n= (8722) \/ (10 . -356)<br \/>\n= -8722\/3560 = -2.45<br \/>\n<img decoding=\"async\" loading=\"lazy\" class=\"alignnone size-full wp-image-43167\" src=\"https:\/\/ccssanswers.com\/wp-content\/uploads\/2021\/01\/big-ideas-math-answers-grade-7-chapter-2-multiplying-and-dividing-rational-numbers-71.jpg\" alt=\"Big Ideas Math Answers Grade 7 Chapter 2 Multiplying and Dividing Rational Numbers 71\" width=\"310\" height=\"587\" srcset=\"https:\/\/ccssanswers.com\/wp-content\/uploads\/2021\/01\/big-ideas-math-answers-grade-7-chapter-2-multiplying-and-dividing-rational-numbers-71.jpg 310w, https:\/\/ccssanswers.com\/wp-content\/uploads\/2021\/01\/big-ideas-math-answers-grade-7-chapter-2-multiplying-and-dividing-rational-numbers-71-158x300.jpg 158w\" sizes=\"(max-width: 310px) 100vw, 310px\" \/><\/p>\n<p>Question 16.<br \/>\n12.42 \u00f7 (-4.8)<\/p>\n<p>Answer:<br \/>\n12.42 \u00f7 (-4.8) = -2.5875<\/p>\n<p>Explanation:<br \/>\n12.42 \u00f7 (-4.8) = 1242\/100 \u00f7 (-48\/10)<br \/>\n= 1242\/100 . (-10\/48)<br \/>\n= (1242 . -10)\/(100 . 48)<br \/>\n= (-1242) \/ (480)<br \/>\n= -2.5875<br \/>\n<img decoding=\"async\" loading=\"lazy\" class=\"alignnone size-full wp-image-43169\" src=\"https:\/\/ccssanswers.com\/wp-content\/uploads\/2021\/01\/big-ideas-math-answers-grade-7-chapter-2-multiplying-and-dividing-rational-numbers-72.jpg\" alt=\"Big Ideas Math Answers Grade 7 Chapter 2 Multiplying and Dividing Rational Numbers 72\" width=\"347\" height=\"758\" srcset=\"https:\/\/ccssanswers.com\/wp-content\/uploads\/2021\/01\/big-ideas-math-answers-grade-7-chapter-2-multiplying-and-dividing-rational-numbers-72.jpg 347w, https:\/\/ccssanswers.com\/wp-content\/uploads\/2021\/01\/big-ideas-math-answers-grade-7-chapter-2-multiplying-and-dividing-rational-numbers-72-137x300.jpg 137w\" sizes=\"(max-width: 347px) 100vw, 347px\" \/><\/p>\n<p>Question 17.<br \/>\n<img decoding=\"async\" loading=\"lazy\" class=\"alignnone size-full wp-image-30210\" src=\"https:\/\/ccssanswers.com\/wp-content\/uploads\/2021\/01\/Big-Ideas-Math-Answers-Grade-7-Chapter-2-Multiplying-and-Dividing-Rational-Numbers-105.png\" alt=\"Big Ideas Math Answers Grade 7 Chapter 2 Multiplying and Dividing Rational Numbers 105\" width=\"103\" height=\"42\" \/><\/p>\n<p>Answer:<br \/>\n-2(4\/5) \u00f7 (-7) = 0.4<\/p>\n<p>Explanation:<br \/>\n-2(4\/5) \u00f7 (-7) = -14\/5 \u00f7 (-7)<br \/>\n= -14\/5 . -1\/7<br \/>\n= (-14 . -1) \/ (7 . 5)<br \/>\n= 2\/5<br \/>\n= 0.4<\/p>\n<p>Question 18.<br \/>\n<img decoding=\"async\" loading=\"lazy\" class=\"alignnone size-full wp-image-30211\" src=\"https:\/\/ccssanswers.com\/wp-content\/uploads\/2021\/01\/Big-Ideas-Math-Answers-Grade-7-Chapter-2-Multiplying-and-Dividing-Rational-Numbers-106.png\" alt=\"Big Ideas Math Answers Grade 7 Chapter 2 Multiplying and Dividing Rational Numbers 106\" width=\"130\" height=\"59\" \/><\/p>\n<p>Answer:<br \/>\n-10(2\/7) \u00f7 (-4(4\/11)) = 2.3571<\/p>\n<p>Explanation:<br \/>\n-10(2\/7) \u00f7 (-4(4\/11)) = -72\/7 \u00f7 -48\/11<br \/>\n= -72\/7 . (-11\/48)<br \/>\n= (-72 . -11) \/ (7 . 48)<br \/>\n= 99\/42 = 2.3571<br \/>\n<img decoding=\"async\" loading=\"lazy\" class=\"alignnone size-full wp-image-43172\" src=\"https:\/\/ccssanswers.com\/wp-content\/uploads\/2021\/01\/big-ideas-math-answers-grade-7-chapter-2-multiplying-and-dividing-rational-numbers-73.jpg\" alt=\"Big Ideas Math Answers Grade 7 Chapter 2 Multiplying and Dividing Rational Numbers 73\" width=\"244\" height=\"580\" srcset=\"https:\/\/ccssanswers.com\/wp-content\/uploads\/2021\/01\/big-ideas-math-answers-grade-7-chapter-2-multiplying-and-dividing-rational-numbers-73.jpg 244w, https:\/\/ccssanswers.com\/wp-content\/uploads\/2021\/01\/big-ideas-math-answers-grade-7-chapter-2-multiplying-and-dividing-rational-numbers-73-126x300.jpg 126w\" sizes=\"(max-width: 244px) 100vw, 244px\" \/><\/p>\n<p><strong>YOU BE THE TEACHER<\/strong><br \/>\n<strong>Your friend evaluates the expression. Is your friend correct? Explain your reasoning.<\/strong><\/p>\n<p>Question 19.<br \/>\n<img decoding=\"async\" loading=\"lazy\" class=\"alignnone size-full wp-image-30212\" src=\"https:\/\/ccssanswers.com\/wp-content\/uploads\/2021\/01\/Big-Ideas-Math-Answers-Grade-7-Chapter-2-Multiplying-and-Dividing-Rational-Numbers-107.png\" alt=\"Big Ideas Math Answers Grade 7 Chapter 2 Multiplying and Dividing Rational Numbers 107\" width=\"176\" height=\"178\" \/><\/p>\n<p>Answer:<br \/>\nwrong<\/p>\n<p>Explanation:<br \/>\n-2\/3 \u00f7 4\/5 = -2\/3 . 5\/4<br \/>\n= (-2 . 5)\/(3 . 4)<br \/>\n= -5\/6<\/p>\n<p>Question 20.<br \/>\n<img decoding=\"async\" loading=\"lazy\" class=\"alignnone size-full wp-image-30213\" src=\"https:\/\/ccssanswers.com\/wp-content\/uploads\/2021\/01\/Big-Ideas-Math-Answers-Grade-7-Chapter-2-Multiplying-and-Dividing-Rational-Numbers-108.png\" alt=\"Big Ideas Math Answers Grade 7 Chapter 2 Multiplying and Dividing Rational Numbers 108\" width=\"188\" height=\"82\" \/><\/p>\n<p>Answer:<br \/>\nWrong<\/p>\n<p>Explanation:<br \/>\n-4.25 \u00f7 1.7 = -2.5<br \/>\n<img decoding=\"async\" loading=\"lazy\" class=\"alignnone size-full wp-image-43177\" src=\"https:\/\/ccssanswers.com\/wp-content\/uploads\/2021\/01\/big-ideas-math-answers-grade-7-chapter-2-multiplying-and-dividing-rational-numbers-74.jpg\" alt=\"Big Ideas Math Answers Grade 7 Chapter 2 Multiplying and Dividing Rational Numbers 74\" width=\"167\" height=\"348\" srcset=\"https:\/\/ccssanswers.com\/wp-content\/uploads\/2021\/01\/big-ideas-math-answers-grade-7-chapter-2-multiplying-and-dividing-rational-numbers-74.jpg 167w, https:\/\/ccssanswers.com\/wp-content\/uploads\/2021\/01\/big-ideas-math-answers-grade-7-chapter-2-multiplying-and-dividing-rational-numbers-74-144x300.jpg 144w\" sizes=\"(max-width: 167px) 100vw, 167px\" \/><\/p>\n<p>Question 21.<br \/>\n<strong>MODELING REAL LIFE<\/strong><br \/>\nHow many 0.75-pound packages can you make with 4.5 pounds of sun\ufb02ower seeds?<\/p>\n<p>Answer:<br \/>\n6 0.75-pound packages are required to make 4.5 pounds of sun\ufb02ower seeds.<\/p>\n<p>Explanation:<br \/>\nDivide 4.5 by 0.75 to get the solution.<br \/>\n= 4.5 \u00f7 0.75 = 45\/10 \u00f7 75\/100<br \/>\n= 45\/10 . 100\/75<br \/>\n= (45 . 100)\/ (10 . 75)<br \/>\n= 6<br \/>\nSo, 6 0.75-pound packages are required to make 4.5 pounds of sun\ufb02ower seeds.<\/p>\n<p><strong>EVALUATING AN EXPRESSION<\/strong><br \/>\n<strong>Evaluate the expression. Write fractions in simplest form.<\/strong><\/p>\n<p>Question 22.<br \/>\n<img decoding=\"async\" loading=\"lazy\" class=\"alignnone size-full wp-image-30214\" src=\"https:\/\/ccssanswers.com\/wp-content\/uploads\/2021\/01\/Big-Ideas-Math-Answers-Grade-7-Chapter-2-Multiplying-and-Dividing-Rational-Numbers-109.png\" alt=\"Big Ideas Math Answers Grade 7 Chapter 2 Multiplying and Dividing Rational Numbers 109\" width=\"62\" height=\"84\" \/><\/p>\n<p>Answer:<br \/>\n(14\/9) \/ (-1\/3-1\/6) = -28\/9<\/p>\n<p>Explanation:<br \/>\n(14\/9) \/ (-1\/3-1\/6) = (14\/9) \/ ((-2 &#8211; 1)\/6)<br \/>\n= 14\/9 \/ -3\/6<br \/>\n= 14\/9 . (-6\/3)<br \/>\n= (14 . -6) \/ (3 . 9)<br \/>\n= -28\/9<\/p>\n<p>Question 23.<br \/>\n<img decoding=\"async\" loading=\"lazy\" class=\"alignnone size-full wp-image-30215\" src=\"https:\/\/ccssanswers.com\/wp-content\/uploads\/2021\/01\/Big-Ideas-Math-Answers-Grade-7-Chapter-2-Multiplying-and-Dividing-Rational-Numbers-110.png\" alt=\"Big Ideas Math Answers Grade 7 Chapter 2 Multiplying and Dividing Rational Numbers 110\" width=\"94\" height=\"97\" \/><\/p>\n<p>Answer:<br \/>\n(-125 + 3\/10) \/ (11\/4 &#8211; (-9\/14)) = -77\/100<\/p>\n<p>Explanation:<br \/>\n(-125 + 3\/10) \/ (11\/4 &#8211; (-9\/14)) = (-24 + 13)\/10 \/ (11\/14 + 9\/14)<br \/>\n= -11\/10 \/ (20\/14)<br \/>\n= -11\/10 . 14\/20<br \/>\n= (-11 . 14) \/ (10 . 20)<br \/>\n= (-11 . 7) \/ (5 . 20)<br \/>\n= -77\/100<\/p>\n<p>Question 24.<br \/>\n-0.42 \u00f7 0.8 + 0.2<\/p>\n<p>Answer:<br \/>\n-0.42 \u00f7 0.8 + 0.2 = -13\/40<\/p>\n<p>Explanation:<br \/>\n-0.42 \u00f7 0.8 + 0.2 = -4.2 \u00f7 8 + 0.2<br \/>\n= -0.525 + 0.2<br \/>\n= -0.325 = -325\/1000<br \/>\n= -13\/40<\/p>\n<p>Question 25.<br \/>\n2.85 \u00f7 6.2 \u00f7 2<sup>2<\/sup><\/p>\n<p>Answer:<br \/>\n2.85 \u00f7 6.2 \u00f7 2\u00b2 = 28.25\/248<\/p>\n<p>Explanation:<br \/>\n2.85 \u00f7 6.2 \u00f7 2\u00b2 = 2.85 \u00f7 6.2 \u00f7 4<br \/>\n= (2.825 \u00f7 6.2) \u00f7 4<br \/>\n= 2.825\/6.2 . 1\/4<br \/>\n= (2.825 . 1) \/ (6.2 . 4)<br \/>\n= 2.825\/24.8<br \/>\n= 28.25\/248<\/p>\n<p>Question 26.<br \/>\n<img decoding=\"async\" loading=\"lazy\" class=\"alignnone size-full wp-image-30216\" src=\"https:\/\/ccssanswers.com\/wp-content\/uploads\/2021\/01\/Big-Ideas-Math-Answers-Grade-7-Chapter-2-Multiplying-and-Dividing-Rational-Numbers-111.png\" alt=\"Big Ideas Math Answers Grade 7 Chapter 2 Multiplying and Dividing Rational Numbers 111\" width=\"140\" height=\"57\" \/><\/p>\n<p>Answer:<br \/>\n3\/4 + 7\/10 &#8211; 1\/8 \u00f7 (-1\/2) = 17\/10<\/p>\n<p>Explanation:<br \/>\n3\/4 + 7\/10 &#8211; 1\/8 \u00f7 (-1\/2) = 3\/4 + 7\/10 + (1\/8 \u00f7 1\/2)<br \/>\n= 3\/4 + 7\/10 + (1\/8 . 2)<br \/>\n= 3\/4 + 7\/10 + 1\/4<br \/>\n= 1 + 7\/10<br \/>\n= 17\/10<\/p>\n<p>Question 27.<br \/>\n<img decoding=\"async\" loading=\"lazy\" class=\"alignnone size-full wp-image-30217\" src=\"https:\/\/ccssanswers.com\/wp-content\/uploads\/2021\/01\/Big-Ideas-Math-Answers-Grade-7-Chapter-2-Multiplying-and-Dividing-Rational-Numbers-112.png\" alt=\"Big Ideas Math Answers Grade 7 Chapter 2 Multiplying and Dividing Rational Numbers 112\" width=\"128\" height=\"85\" \/><\/p>\n<p>Answer:<br \/>\n7\/6 \/ [(-11\/5)(10(1\/2))(-5\/11)] = 1\/9<\/p>\n<p>Explanation:<br \/>\n7\/6 \/ [(-11\/5)(10(1\/2))(-5\/11)] = 7\/6 \/ [(-11\/5)(21\/2)(-5\/11)]<br \/>\n= 7\/6 \/ [(-11 . 21 . -5) \/ (5 . 2 . 11)]<br \/>\n= 7\/6 \/ [21\/2]<br \/>\n= 7\/6 . 2\/21<br \/>\n= (7 . 2) \/ (6 . 21)<br \/>\n= 1\/9<\/p>\n<p>Question 28.<br \/>\n<strong>PROBLEM SOLVING<\/strong><br \/>\nThe section of the boardwalk shown is made using boards that are each 9\\(\\frac{1}{4}\\)inches wide. The spacing between each board is equal. What is the width of the spacing between each board?<br \/>\n<img decoding=\"async\" loading=\"lazy\" class=\"alignnone size-full wp-image-30218\" src=\"https:\/\/ccssanswers.com\/wp-content\/uploads\/2021\/01\/Big-Ideas-Math-Answers-Grade-7-Chapter-2-Multiplying-and-Dividing-Rational-Numbers-113.png\" alt=\"Big Ideas Math Answers Grade 7 Chapter 2 Multiplying and Dividing Rational Numbers 113\" width=\"347\" height=\"114\" srcset=\"https:\/\/ccssanswers.com\/wp-content\/uploads\/2021\/01\/Big-Ideas-Math-Answers-Grade-7-Chapter-2-Multiplying-and-Dividing-Rational-Numbers-113.png 347w, https:\/\/ccssanswers.com\/wp-content\/uploads\/2021\/01\/Big-Ideas-Math-Answers-Grade-7-Chapter-2-Multiplying-and-Dividing-Rational-Numbers-113-300x99.png 300w\" sizes=\"(max-width: 347px) 100vw, 347px\" \/><\/p>\n<p>Answer:<br \/>\nThe width of the spacing between each section is 5.25 inches<\/p>\n<p>Explanation:<br \/>\n15 boards each board is 9(1\/4) inches wide<br \/>\nThe total width of 15 boards = 9(1\/4) . 15<br \/>\n= 37\/4 . 15<br \/>\n= 555\/4 = 138.75<br \/>\n<img decoding=\"async\" loading=\"lazy\" class=\"alignnone size-full wp-image-43201\" src=\"https:\/\/ccssanswers.com\/wp-content\/uploads\/2021\/01\/big-ideas-math-answers-grade-7-chapter-2-multiplying-and-dividing-rational-numbers-77.jpg\" alt=\"Big Ideas Math Answers Grade 7 Chapter 2 Multiplying and Dividing Rational Numbers 77\" width=\"197\" height=\"511\" srcset=\"https:\/\/ccssanswers.com\/wp-content\/uploads\/2021\/01\/big-ideas-math-answers-grade-7-chapter-2-multiplying-and-dividing-rational-numbers-77.jpg 197w, https:\/\/ccssanswers.com\/wp-content\/uploads\/2021\/01\/big-ideas-math-answers-grade-7-chapter-2-multiplying-and-dividing-rational-numbers-77-116x300.jpg 116w\" sizes=\"(max-width: 197px) 100vw, 197px\" \/><br \/>\nThe total width of 15 boards = 138.75 inches<br \/>\nThe total width of the section = 144 inches<br \/>\nThe width of the spacing between each section = 144 &#8211; 138.75 = 5.25 inches<\/p>\n<p>Question 29.<br \/>\n<strong>REASONING<\/strong><br \/>\nThe table shows the daily changes in the barometric pressure(in inches of mercury) for four days.<br \/>\na. What is the mean change?<br \/>\nb. The mean change for Monday through Friday is -0.01 inch. What is the change in the barometric pressure on Friday? Explain.<br \/>\n<img decoding=\"async\" loading=\"lazy\" class=\"alignnone size-full wp-image-30219\" src=\"https:\/\/ccssanswers.com\/wp-content\/uploads\/2021\/01\/Big-Ideas-Math-Answers-Grade-7-Chapter-2-Multiplying-and-Dividing-Rational-Numbers-114.png\" alt=\"Big Ideas Math Answers Grade 7 Chapter 2 Multiplying and Dividing Rational Numbers 114\" width=\"213\" height=\"194\" \/><\/p>\n<p>Answer:<br \/>\na. Mean change is -0.02<br \/>\nb. The change in the barometric pressure on Friday is 0.03<\/p>\n<p>Explanation:<br \/>\na. Mean change = sum of observations \/ total number of observations<br \/>\n= (-0.05 + 0.09 &#8211; 0.04 &#8211; 0.08)\/4<br \/>\n= -0.08\/4<br \/>\n= -0.02<br \/>\nb. The mean change for Monday through Friday is -0.01 inch<br \/>\nMean change = sum of observations \/ total number of observations<br \/>\n-0.01 = (-0.05 + 0.09 &#8211; 0.04 &#8211; 0.08 + x)\/5<br \/>\n-0.01 =\u00a0 (-0.08 + x)\/5<br \/>\n5 * -0.01 = -0.08 + x<br \/>\n-0.05 = -0.08 + x<br \/>\n-0.05 + 0.08 = x<br \/>\n0.03 = x<br \/>\nSo, the change in the barometric pressure on Friday is 0.03<\/p>\n<p>Question 30.<br \/>\n<strong>LOGIC<\/strong><br \/>\nIn an online survey, gym members react to the statement shown by adjusting the position of the needle. The responses have values of -4.2, 1.6, 0.4, 0, 2.1, -5.0, -4.7, 0.6, 1.1, 0.8, 0.4, and 2.1. Explain how two people can use the results of the survey to reach different conclusions about whether the gym should adjust its membership prices.<br \/>\n<img decoding=\"async\" loading=\"lazy\" class=\"alignnone size-full wp-image-30220\" src=\"https:\/\/ccssanswers.com\/wp-content\/uploads\/2021\/01\/Big-Ideas-Math-Answers-Grade-7-Chapter-2-Multiplying-and-Dividing-Rational-Numbers-115.png\" alt=\"Big Ideas Math Answers Grade 7 Chapter 2 Multiplying and Dividing Rational Numbers 115\" width=\"270\" height=\"177\" \/><\/p>\n<p>Answer:<br \/>\nThe gym should adjust its membership prices.<\/p>\n<p>Explanation:<br \/>\nUse mean to determine whether adjust the gym membership prices or not.<br \/>\nMean = sum of observations \/ total number of observations<br \/>\n= (-4.2 + 1.6 + 0.4 + 0 + 2.1 &#8211; 5.0 &#8211; 4.7 + 0.6 + 1.1 + 0.8 + 0.4 + 2.1)\/12<br \/>\n= -4.8\/12<br \/>\n= -0.4<br \/>\nThe mean score is below 0.<br \/>\nSo, the gym should adjust its membership prices.<\/p>\n<p>Question 31.<br \/>\n<strong>CRITICAL THINKING<\/strong><br \/>\nDetermine whether the statement is sometimes, always, or never true. Explain your reasoning.<br \/>\na. The product of two terminating decimals is a terminating decimal.<br \/>\nb. The quotient of two terminating decimals is a terminating decimal.<\/p>\n<p>Answer:<br \/>\na. The product of two terminating decimals is always a terminating decimal<br \/>\nb. The quotient of two terminating decimals is always a terminating decimal.<\/p>\n<p>Explanation:<br \/>\na. The product of two terminating decimals is always a terminating decimal<br \/>\nThe example to check the product of terminating decimals is a terminating decimal<br \/>\n4.5 x 6.27 = 28.215<br \/>\nb. The quotient of two terminating decimals is a terminating decimal.<br \/>\nThe example is 36.257 \/ 24.85<br \/>\n= 1.459034205<\/p>\n<h3><a id=\"Multiplying_and_Dividing_Rational_Numbers_Connecting_Concepts\"><\/a>Multiplying and Dividing Rational Numbers Connecting Concepts<\/h3>\n<p><strong>Using the Problem-Solving Plan<\/strong><\/p>\n<p>Question 1.<br \/>\nYou feed several adult hamsters equal amounts of a new food recipe over a period of 1 month. You record the changes in the weights of the hamsters in the table. Use the data to answer the question &#8220;What is the typical weight change of a hamster that is fed the new recipe?<br \/>\n<img decoding=\"async\" loading=\"lazy\" class=\"alignnone size-full wp-image-30221\" src=\"https:\/\/ccssanswers.com\/wp-content\/uploads\/2021\/01\/Big-Ideas-Math-Answers-Grade-7-Chapter-2-Multiplying-and-Dividing-Rational-Numbers-116.png\" alt=\"Big Ideas Math Answers Grade 7 Chapter 2 Multiplying and Dividing Rational Numbers 116\" width=\"272\" height=\"191\" \/><br \/>\n<img decoding=\"async\" loading=\"lazy\" class=\"alignnone size-full wp-image-30222\" src=\"https:\/\/ccssanswers.com\/wp-content\/uploads\/2021\/01\/Big-Ideas-Math-Answers-Grade-7-Chapter-2-Multiplying-and-Dividing-Rational-Numbers-117.png\" alt=\"Big Ideas Math Answers Grade 7 Chapter 2 Multiplying and Dividing Rational Numbers 117\" width=\"315\" height=\"133\" srcset=\"https:\/\/ccssanswers.com\/wp-content\/uploads\/2021\/01\/Big-Ideas-Math-Answers-Grade-7-Chapter-2-Multiplying-and-Dividing-Rational-Numbers-117.png 315w, https:\/\/ccssanswers.com\/wp-content\/uploads\/2021\/01\/Big-Ideas-Math-Answers-Grade-7-Chapter-2-Multiplying-and-Dividing-Rational-Numbers-117-300x127.png 300w\" sizes=\"(max-width: 315px) 100vw, 315px\" \/><\/p>\n<p><strong>Understand the problem.<br \/>\n<\/strong>You know the weight changes of 15 hamsters. You want to use this information to \ufb01nd the typical weight change.<br \/>\n<strong>Make a plan.<\/strong><br \/>\nDisplay the data in a dot plot to see the distribution of the data. Then use the distribution to determine the most appropriate measure of center.<br \/>\n<strong>Solve and check.<\/strong><br \/>\nUse the plan to solve the problem. Then check your solution.<\/p>\n<p>Answer:<br \/>\nThe typical weight change of a hamster that is fed the new recipe is -0.06266 ounces.<\/p>\n<p>Explanation:<br \/>\nThe typical weight change is measured by calculating the mean change.<br \/>\nMean = (-0.07 &#8211; 0.03 &#8211; 0.11 &#8211; 0.04 &#8211; 0.08 + 0.02 &#8211; 0.08 &#8211; 0.08 &#8211; 0.06 &#8211; 0.05 &#8211; 0.11 &#8211; 0.1 + 0 &#8211; 0.07 &#8211; 0.08)\/15<br \/>\n= -0.94\/15<br \/>\n= -0.06266<br \/>\nSo, typical weight change of a hamster that is fed the new recipe is -0.06266 ounces<\/p>\n<p>Question 2.<br \/>\nEvaluate the expression shown at the right. Write your answer in simplest form.<br \/>\n<img decoding=\"async\" loading=\"lazy\" class=\"alignnone size-full wp-image-30223\" src=\"https:\/\/ccssanswers.com\/wp-content\/uploads\/2021\/01\/Big-Ideas-Math-Answers-Grade-7-Chapter-2-Multiplying-and-Dividing-Rational-Numbers-118.png\" alt=\"Big Ideas Math Answers Grade 7 Chapter 2 Multiplying and Dividing Rational Numbers 118\" width=\"120\" height=\"128\" \/><\/p>\n<p>Answer:<br \/>\n-4\/9<\/p>\n<p>Explanation:<br \/>\n(-1\/2 + 2\/3) \/ [3\/5(3\/4 &#8211; 11\/8)] = [(-3 + 4)\/6] \/ [3\/5((6 &#8211; 11)\/8)]<br \/>\n= 1\/6 \/ [3\/5(-5\/8)<br \/>\n= 1\/6 \/ -3\/8<br \/>\n= 1\/6 . -8\/3<br \/>\n= (1 . -8) \/ (3 . 6)<br \/>\n= -4\/9<\/p>\n<p>Question 3.<br \/>\nYou drop a racquetball from a height of 60 inches. On each bounce, the racquetball bounces to a height that is 70% of its previous height. What is the change in the height of the racquetball after 3 bounces?<\/p>\n<p>Answer:<br \/>\nThe change in height of the racquetball after 3 bounces is 20.58 inches<\/p>\n<p>Explanation:<br \/>\nYou drop a racquetball from a height of 60 inches. On each bounce, the racquetball bounces to a height that is 70% of its previous height.<br \/>\nThe change in height of the racquetball after 1 bounce = (60 x 70)\/100<br \/>\n= 4200 \/ 100 = 42 inches<br \/>\nThe change in height of the racquetball after 2 bounces = (42 x 70)\/100<br \/>\n= 29.4<br \/>\nThe change in height of the racquetball after 3 bounces = (29.4 x 70)\/100<br \/>\n= 2058\/100 = 20.58 inches<\/p>\n<p><strong>Performance Task<\/strong><\/p>\n<p><strong>Precisely Perfect<\/strong><\/p>\n<p>At the beginning of this chapter, you watched a STEAM Video called \u201cCarpenter or Joiner.\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-30224\" src=\"https:\/\/ccssanswers.com\/wp-content\/uploads\/2021\/01\/Big-Ideas-Math-Answers-Grade-7-Chapter-2-Multiplying-and-Dividing-Rational-Numbers-119.png\" alt=\"Big Ideas Math Answers Grade 7 Chapter 2 Multiplying and Dividing Rational Numbers 119\" width=\"280\" height=\"200\" \/><\/p>\n<h3><a id=\"Multiplying_and_Dividing_Rational_Numbers_Chapter_Review\"><\/a>Multiplying and Dividing Rational Numbers Chapter Review<\/h3>\n<p><strong>Review Vocabulary<\/strong><\/p>\n<p>Write the de\ufb01nition and give an example of each vocabulary term.<br \/>\n<img decoding=\"async\" loading=\"lazy\" class=\"alignnone size-full wp-image-30226\" src=\"https:\/\/ccssanswers.com\/wp-content\/uploads\/2021\/01\/Big-Ideas-Math-Solutions-Grade-7-Chapter-2-Multiplying-and-Dividing-Rational-Numbers-120.png\" alt=\"Big Ideas Math Solutions Grade 7 Chapter 2 Multiplying and Dividing Rational Numbers 120\" width=\"590\" height=\"41\" srcset=\"https:\/\/ccssanswers.com\/wp-content\/uploads\/2021\/01\/Big-Ideas-Math-Solutions-Grade-7-Chapter-2-Multiplying-and-Dividing-Rational-Numbers-120.png 590w, https:\/\/ccssanswers.com\/wp-content\/uploads\/2021\/01\/Big-Ideas-Math-Solutions-Grade-7-Chapter-2-Multiplying-and-Dividing-Rational-Numbers-120-300x21.png 300w\" sizes=\"(max-width: 590px) 100vw, 590px\" \/><\/p>\n<p><strong>Graphic Organizers<\/strong><\/p>\n<p>You can use an Information Frame to help organize and remember a concept. Here is an example of an Information Frame for multiplying integers.<br \/>\n<img decoding=\"async\" loading=\"lazy\" class=\"alignnone size-full wp-image-30227\" src=\"https:\/\/ccssanswers.com\/wp-content\/uploads\/2021\/01\/Big-Ideas-Math-Solutions-Grade-7-Chapter-2-Multiplying-and-Dividing-Rational-Numbers-121.png\" alt=\"Big Ideas Math Solutions Grade 7 Chapter 2 Multiplying and Dividing Rational Numbers 121\" width=\"544\" height=\"364\" srcset=\"https:\/\/ccssanswers.com\/wp-content\/uploads\/2021\/01\/Big-Ideas-Math-Solutions-Grade-7-Chapter-2-Multiplying-and-Dividing-Rational-Numbers-121.png 544w, https:\/\/ccssanswers.com\/wp-content\/uploads\/2021\/01\/Big-Ideas-Math-Solutions-Grade-7-Chapter-2-Multiplying-and-Dividing-Rational-Numbers-121-300x201.png 300w\" sizes=\"(max-width: 544px) 100vw, 544px\" \/><br \/>\nChoose and complete a graphic organizer to help you study the concept.<\/p>\n<ol>\n<li>dividing integers<\/li>\n<li>writing fractions or mixed numbers as decimals<\/li>\n<li>writing decimals as fractions or mixed numbers<\/li>\n<li>multiplying rational numbers<\/li>\n<li>dividing rational numbers<\/li>\n<\/ol>\n<p><img decoding=\"async\" loading=\"lazy\" class=\"alignnone size-full wp-image-30228\" src=\"https:\/\/ccssanswers.com\/wp-content\/uploads\/2021\/01\/Big-Ideas-Math-Solutions-Grade-7-Chapter-2-Multiplying-and-Dividing-Rational-Numbers-122.png\" alt=\"Big Ideas Math Solutions Grade 7 Chapter 2 Multiplying and Dividing Rational Numbers 122\" width=\"280\" height=\"352\" srcset=\"https:\/\/ccssanswers.com\/wp-content\/uploads\/2021\/01\/Big-Ideas-Math-Solutions-Grade-7-Chapter-2-Multiplying-and-Dividing-Rational-Numbers-122.png 280w, https:\/\/ccssanswers.com\/wp-content\/uploads\/2021\/01\/Big-Ideas-Math-Solutions-Grade-7-Chapter-2-Multiplying-and-Dividing-Rational-Numbers-122-239x300.png 239w\" sizes=\"(max-width: 280px) 100vw, 280px\" \/><\/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-30229\" src=\"https:\/\/ccssanswers.com\/wp-content\/uploads\/2021\/01\/Big-Ideas-Math-Solutions-Grade-7-Chapter-2-Multiplying-and-Dividing-Rational-Numbers-123.png\" alt=\"Big Ideas Math Solutions Grade 7 Chapter 2 Multiplying and Dividing Rational Numbers 123\" width=\"642\" height=\"82\" srcset=\"https:\/\/ccssanswers.com\/wp-content\/uploads\/2021\/01\/Big-Ideas-Math-Solutions-Grade-7-Chapter-2-Multiplying-and-Dividing-Rational-Numbers-123.png 642w, https:\/\/ccssanswers.com\/wp-content\/uploads\/2021\/01\/Big-Ideas-Math-Solutions-Grade-7-Chapter-2-Multiplying-and-Dividing-Rational-Numbers-123-300x38.png 300w\" sizes=\"(max-width: 642px) 100vw, 642px\" \/><\/p>\n<p><strong>2.1 Multiplying Integers<\/strong> (pp. 49\u201354)<\/p>\n<p>Find the product.<\/p>\n<p><strong>Question 1.<\/strong><br \/>\n-8 \u2022 6<\/p>\n<p>Answer:<br \/>\n-8 \u2022 6 = -48<\/p>\n<p>Explanation:<br \/>\nThe product of two integers with different signs is negative.<br \/>\n-8 \u2022 6 = -48<\/p>\n<p>Question 2.<br \/>\n10(-7)<\/p>\n<p>Answer:<br \/>\n10(-7) = -70<\/p>\n<p>Explanation:<br \/>\nThe product of two integers with different signs is negative.<br \/>\n10(-7) = -70<\/p>\n<p>Question 3.<br \/>\n-3 \u2022 (-6)<\/p>\n<p>Answer:<br \/>\n-3 \u2022 (-6) = 18<\/p>\n<p>Explanation:<br \/>\n-3 \u2022 (-6) = 18<br \/>\nThe product of two integers with the same sign is positive.<\/p>\n<p>Question 4.<br \/>\nYou and a group of friends participate in a game where you must use clues to escape from a room. You have a limited amount of time to escape and are allowed 3 free clues. Additional clues may be requested, but each removes 5 minutes from your remaining time. What integer represents the total change in the time when you use 5 clues?<\/p>\n<p>Answer:<br \/>\nThe total change in time when you use 5 clues is -10 minutes<\/p>\n<p>Explanation:<br \/>\nYou are allowed 3 clues for free<br \/>\nThe amount of time removes for each clue is 5 minutes<br \/>\nIf you want to take 2 clues, then 5 x 2 = 10 minutes are removed<br \/>\nSo, the total change in time when you use 5 clues is -10 minutes<\/p>\n<p><strong>Evaluate the expression.<\/strong><\/p>\n<p>Question 5.<br \/>\n(-3)<sup>3<\/sup><\/p>\n<p>Answer:<br \/>\n(-3)\u00b3 = -27<\/p>\n<p>Explanation:<br \/>\n(-3)\u00b3 = -3 \u2022 -3 \u2022 -3<br \/>\n= 9 \u2022 -3<br \/>\n= -27<\/p>\n<p>Question 6.<br \/>\n(-3)(-4)(10)<\/p>\n<p>Answer:<br \/>\n(-3)(-4)(10) = 120<\/p>\n<p>Explanation:<br \/>\n(-3)(-4)(10) = 12(10)<br \/>\n= 120<\/p>\n<p>Question 7.<br \/>\n24 &#8211; 3(2 &#8211; 4<sup>2<\/sup>)<\/p>\n<p>Answer:<br \/>\n24 &#8211; 3(2 &#8211; 4\u00b2) = 66<\/p>\n<p>Explanation:<br \/>\n24 &#8211; 3(2 &#8211; 4\u00b2) = 24 &#8211; 3(2 &#8211; 16)<br \/>\n= 24 &#8211; 3(-14)<br \/>\n= 24 + 42<br \/>\n= 66<\/p>\n<p>Question 8.<br \/>\nWrite three integers whose product is negative.<\/p>\n<p>Answer:<br \/>\n-5, -2, 6<\/p>\n<p>Explanation:<br \/>\nIf three integers product is negative, then all integers would have negative signs or only one integer should have a negative sign.<br \/>\n(-5)(-2)6 = 10(6)<br \/>\n= 60<\/p>\n<p>Question 9.<br \/>\nYou are playing laser tag. The table shows how many points you gain or lose when you tag or are tagged by another player in different locations. You are tagged three times on the back, twice on the shoulder, and twice on the laser. You tag two players on the front, four players on the back, and one player on the laser. What is your score?<br \/>\n<img decoding=\"async\" loading=\"lazy\" class=\"alignnone size-full wp-image-30230\" src=\"https:\/\/ccssanswers.com\/wp-content\/uploads\/2021\/01\/Big-Ideas-Math-Solutions-Grade-7-Chapter-2-Multiplying-and-Dividing-Rational-Numbers-124.png\" alt=\"Big Ideas Math Solutions Grade 7 Chapter 2 Multiplying and Dividing Rational Numbers 124\" width=\"250\" height=\"184\" \/><\/p>\n<p>Answer:<br \/>\nScore = 727 points<\/p>\n<p>Explanation:<br \/>\nYou are tagged three times on the back, twice on the shoulder, and twice on the laser.<br \/>\nYou have tagged means points lost.<br \/>\n= 3(25) + 2(12) + 2(12)<br \/>\n= 123<br \/>\nYou tag two players on the front, four players on the back, and one player on the laser.<br \/>\nyou tagged others means points gained<br \/>\n= 2(200) + 4(100) + 1(50)<br \/>\n= 850<br \/>\nScore = points gained &#8211; points lost<br \/>\n= 850 &#8211; 123 = 727<\/p>\n<p>Question 10.<br \/>\nThe product of three integers is positive. How many of the integers can be negative? Explain.<\/p>\n<p>Answer:<br \/>\nIf the product of three integers is positive, then only 2 integers can be negative.<\/p>\n<p>Explanation:<br \/>\nIf the product of three integers is positive, then only 2 integers can be negative.<br \/>\nWe know the product of two negative integers is positive.<br \/>\nFind the product of an obtained positive integer with the third integer.<\/p>\n<p>Question 11.<br \/>\nTwo integers, c and d, have a product of -6. What is the greatest possible sum of c and d?<\/p>\n<p>Answer:<br \/>\nThe greatest possible sum of c and d are {-1, 6}<\/p>\n<p>Explanation:<br \/>\nTwo integers, c and d, have a product of -6<br \/>\ncd = -6<br \/>\nThe possibilities of c, d are {-1, 6}, {1, -6}, {6, -1}, {-6, 1}, {-2, 3}, {3, -2}, {2, -3}, {-3, 2}<br \/>\nFind sum of c and d = 5, -5, 5, -5, 1, 1, -1, -1<br \/>\nThe greatest possible sum of c and d are {-1, 6}<\/p>\n<p><strong>Dividing Integers<\/strong> (pp. 55\u201360)<\/p>\n<p><strong>Find the quotient.<\/strong><\/p>\n<p>Question 12.<br \/>\n-18 \u00f7 9<\/p>\n<p>Answer:<br \/>\n-18 \u00f7 9 = -2<\/p>\n<p>Explanation:<br \/>\n-18 \u00f7 9 = -2<br \/>\nThe quotient of two integers with the different signs is negative.<\/p>\n<p>Question 13.<br \/>\n\\(\\frac{-42}{-6}\\)<\/p>\n<p>Answer:<br \/>\n-42\/-6 = 7<\/p>\n<p>Explanation:<br \/>\nThe quotient of two integers with the same sign is positive.<br \/>\n-42\/-6 = 7<\/p>\n<p>Question 14.<br \/>\n\\(\\frac{-30}{6}\\)<\/p>\n<p>Answer:<br \/>\n-30\/6 = -5<\/p>\n<p>Explanation:<br \/>\nThe quotient of two integers with the different signs is negative.<br \/>\n-30\/6 = -5<\/p>\n<p>Question 15.<br \/>\n84 \u00f7 (-7)<\/p>\n<p>Answer:<br \/>\n84 \u00f7 (-7) = -12<\/p>\n<p>Explanation:<br \/>\nThe quotient of two integers with the different signs is negative.<br \/>\n84 \u00f7 (-7) = -12<\/p>\n<p>Evaluate the expression when x = 3, y = -4, and z = -6.<\/p>\n<p>Question 16.<br \/>\nz \u00f7 x<\/p>\n<p>Answer:<br \/>\nz \u00f7 x = -2<\/p>\n<p>Explanation:<br \/>\nThe given expression is z \u00f7 x<br \/>\nPut x = 3, z = -6<br \/>\n-6 \u00f7 3 = -2<\/p>\n<p>Question 17.<br \/>\n\\(\\frac{xy}{z}\\)<\/p>\n<p>Answer:<br \/>\nxy\/z = 2<\/p>\n<p>Explanation:<br \/>\nThe given expression is xy\/z<br \/>\nPut x = 3, y = -4, and z = -6<br \/>\n= (3 . -4)\/-6<br \/>\n= -4\/-2<br \/>\n= 2<\/p>\n<p>Question 18.<br \/>\n\\(\\frac{z &#8211; 2x}{y}\\)<\/p>\n<p>Answer:<br \/>\n(z &#8211; 2x)\/y = 3<\/p>\n<p>Explanation:<br \/>\nThe given expression is (z &#8211; 2x)\/y<br \/>\nPut x = 3, y = -4, and z = -6<br \/>\n= (-6 &#8211; 2(3))\/-4<br \/>\n= (-6 &#8211; 6)\/-4<br \/>\n= -12\/-4<br \/>\n= 3<\/p>\n<p><strong>Find the mean of the integers.<\/strong><\/p>\n<p>Question 19.<br \/>\n-3, -8, 12, -15, 9<\/p>\n<p>Answer:<br \/>\nMean = -1<\/p>\n<p>Explanation:<br \/>\nMean = sum of integers \/ total number of integers<br \/>\n= (-3 &#8211; 8 + 12 &#8211; 15 + 9)\/5<br \/>\n= -5\/5<br \/>\n= -1<\/p>\n<p>Question 20.<br \/>\n-54, -32, -70, -25, -65, -42<\/p>\n<p>Answer:<br \/>\nMean = -48<\/p>\n<p>Explanation:<br \/>\nMean = (-54 &#8211; 32 &#8211; 70 &#8211; 25 &#8211; 65 &#8211; 42)\/6<br \/>\n= -288\/6<br \/>\n= -48<\/p>\n<p>Question 21.<br \/>\nThe table shows the weekly pro\ufb01ts of a fruit vendor. What is the mean pro\ufb01t for these weeks?<br \/>\n<img decoding=\"async\" loading=\"lazy\" class=\"alignnone size-full wp-image-30231\" src=\"https:\/\/ccssanswers.com\/wp-content\/uploads\/2021\/01\/Big-Ideas-Math-Solutions-Grade-7-Chapter-2-Multiplying-and-Dividing-Rational-Numbers-125.png\" alt=\"Big Ideas Math Solutions Grade 7 Chapter 2 Multiplying and Dividing Rational Numbers 125\" width=\"297\" height=\"87\" \/><br \/>\n<img decoding=\"async\" loading=\"lazy\" class=\"alignnone size-full wp-image-30232\" src=\"https:\/\/ccssanswers.com\/wp-content\/uploads\/2021\/01\/Big-Ideas-Math-Solutions-Grade-7-Chapter-2-Multiplying-and-Dividing-Rational-Numbers-126.png\" alt=\"Big Ideas Math Solutions Grade 7 Chapter 2 Multiplying and Dividing Rational Numbers 126\" width=\"241\" height=\"222\" \/><\/p>\n<p>Answer:<br \/>\nThe mean profit for 4 weeks is -$48<\/p>\n<p>Explanation:<br \/>\nThe mean profit = (sum of the profits) \/ number of weeks<br \/>\n= (-125 &#8211; 86 + 54 &#8211; 35)\/4<br \/>\n= -192\/4<br \/>\n= -48<br \/>\nThe mean profit for 4 weeks is -$48.<\/p>\n<p><strong>2.3 Converting Between Fractions and Decimals<\/strong> (pp. 61\u201366)<\/p>\n<p><strong>Write the fraction or mixed number as a decimal.<\/strong><\/p>\n<p>Question 22.<br \/>\n&#8211; \\(\\frac{8}{15}\\)<\/p>\n<p>Answer:<br \/>\n-8\/15 = -0.533333<\/p>\n<p>Explanation:<br \/>\n-8\/15 = -0.533333<br \/>\n<img decoding=\"async\" loading=\"lazy\" class=\"alignnone size-full wp-image-43238\" src=\"https:\/\/ccssanswers.com\/wp-content\/uploads\/2021\/01\/big-ideas-math-answers-grade-7-chapter-2-multiplying-and-dividing-rational-numbers-78.jpg\" alt=\"Big Ideas Math Answers Grade 7 Chapter 2 Multiplying and Dividing Rational Numbers 78\" width=\"197\" height=\"429\" srcset=\"https:\/\/ccssanswers.com\/wp-content\/uploads\/2021\/01\/big-ideas-math-answers-grade-7-chapter-2-multiplying-and-dividing-rational-numbers-78.jpg 197w, https:\/\/ccssanswers.com\/wp-content\/uploads\/2021\/01\/big-ideas-math-answers-grade-7-chapter-2-multiplying-and-dividing-rational-numbers-78-138x300.jpg 138w\" sizes=\"(max-width: 197px) 100vw, 197px\" \/><\/p>\n<p>Question 23.<br \/>\n\\(\\frac{5}{8}\\)<\/p>\n<p>Answer:<br \/>\n5\/8 = 0.625<\/p>\n<p>Explanation:<br \/>\n5\/8 = 0.625<br \/>\n<img decoding=\"async\" loading=\"lazy\" class=\"alignnone size-full wp-image-43239\" src=\"https:\/\/ccssanswers.com\/wp-content\/uploads\/2021\/01\/big-ideas-math-answers-grade-7-chapter-2-multiplying-and-dividing-rational-numbers-79.jpg\" alt=\"Big Ideas Math Answers Grade 7 Chapter 2 Multiplying and Dividing Rational Numbers 79\" width=\"171\" height=\"422\" srcset=\"https:\/\/ccssanswers.com\/wp-content\/uploads\/2021\/01\/big-ideas-math-answers-grade-7-chapter-2-multiplying-and-dividing-rational-numbers-79.jpg 171w, https:\/\/ccssanswers.com\/wp-content\/uploads\/2021\/01\/big-ideas-math-answers-grade-7-chapter-2-multiplying-and-dividing-rational-numbers-79-122x300.jpg 122w\" sizes=\"(max-width: 171px) 100vw, 171px\" \/><\/p>\n<p>Question 24.<br \/>\n&#8211;\\(\\frac{13}{6}\\)<\/p>\n<p>Answer:<br \/>\n-13\/6 = -2.16666<\/p>\n<p>Explanation:<br \/>\n-13\/6 = -2.16666<br \/>\n<img decoding=\"async\" loading=\"lazy\" class=\"alignnone size-full wp-image-43243\" src=\"https:\/\/ccssanswers.com\/wp-content\/uploads\/2021\/01\/big-ideas-math-answers-grade-7-chapter-2-multiplying-and-dividing-rational-numbers-80.jpg\" alt=\"Big Ideas Math Answers Grade 7 Chapter 2 Multiplying and Dividing Rational Numbers 80\" width=\"197\" height=\"506\" srcset=\"https:\/\/ccssanswers.com\/wp-content\/uploads\/2021\/01\/big-ideas-math-answers-grade-7-chapter-2-multiplying-and-dividing-rational-numbers-80.jpg 197w, https:\/\/ccssanswers.com\/wp-content\/uploads\/2021\/01\/big-ideas-math-answers-grade-7-chapter-2-multiplying-and-dividing-rational-numbers-80-117x300.jpg 117w\" sizes=\"(max-width: 197px) 100vw, 197px\" \/><\/p>\n<p>Question 25.<br \/>\n1\\(\\frac{7}{16}\\)<\/p>\n<p>Answer:<br \/>\n1\\(\\frac{7}{16}\\) = 1.4375<\/p>\n<p>Explanation:<br \/>\n1(7\/16) = 23\/16<br \/>\n<img decoding=\"async\" loading=\"lazy\" class=\"alignnone size-full wp-image-43245\" src=\"https:\/\/ccssanswers.com\/wp-content\/uploads\/2021\/01\/big-ideas-math-answers-grade-7-chapter-2-multiplying-and-dividing-rational-numbers-81.jpg\" alt=\"Big Ideas Math Answers Grade 7 Chapter 2 Multiplying and Dividing Rational Numbers 81\" width=\"253\" height=\"586\" srcset=\"https:\/\/ccssanswers.com\/wp-content\/uploads\/2021\/01\/big-ideas-math-answers-grade-7-chapter-2-multiplying-and-dividing-rational-numbers-81.jpg 253w, https:\/\/ccssanswers.com\/wp-content\/uploads\/2021\/01\/big-ideas-math-answers-grade-7-chapter-2-multiplying-and-dividing-rational-numbers-81-130x300.jpg 130w\" sizes=\"(max-width: 253px) 100vw, 253px\" \/><\/p>\n<p><strong>Write the decimal as a fraction or mixed number in simplest form.<\/strong><\/p>\n<p>Question 26.<br \/>\n-0.6<\/p>\n<p>Answer:<br \/>\n-0.6 = -3\/5<\/p>\n<p>Explanation:<br \/>\n-0.6 = -6\/10<br \/>\n= -3\/5<\/p>\n<p>Question 27.<br \/>\n-0.35<\/p>\n<p>Answer:<br \/>\n-0.35 = -7\/20<\/p>\n<p>Explanation:<br \/>\n-0.35 = -35\/100<br \/>\n= -7\/20<\/p>\n<p>Question 28.<br \/>\n-5.8<\/p>\n<p>Answer:<br \/>\n-5.8 = -29\/5<\/p>\n<p>Explanation:<br \/>\n-5.8 = -58\/10<br \/>\n= -29\/5<\/p>\n<p>Question 29.<br \/>\n24.23<\/p>\n<p>Answer:<br \/>\n24.23 = 2423\/100<\/p>\n<p>Explanation:<br \/>\n24.23 = 2423\/100<\/p>\n<p>Question 30.<br \/>\nThe table shows the changes in the average yearly precipitation (in inches) in a city for several months. Order the numbers from least to greatest.<br \/>\n<img decoding=\"async\" loading=\"lazy\" class=\"alignnone size-full wp-image-30233\" src=\"https:\/\/ccssanswers.com\/wp-content\/uploads\/2021\/01\/Big-Ideas-Math-Solutions-Grade-7-Chapter-2-Multiplying-and-Dividing-Rational-Numbers-127.png\" alt=\"Big Ideas Math Solutions Grade 7 Chapter 2 Multiplying and Dividing Rational Numbers 127\" width=\"316\" height=\"111\" srcset=\"https:\/\/ccssanswers.com\/wp-content\/uploads\/2021\/01\/Big-Ideas-Math-Solutions-Grade-7-Chapter-2-Multiplying-and-Dividing-Rational-Numbers-127.png 316w, https:\/\/ccssanswers.com\/wp-content\/uploads\/2021\/01\/Big-Ideas-Math-Solutions-Grade-7-Chapter-2-Multiplying-and-Dividing-Rational-Numbers-127-300x105.png 300w\" sizes=\"(max-width: 316px) 100vw, 316px\" \/><\/p>\n<p>Answer:<br \/>\nThe order of numbers from least to greatest is -1(7\/9), -1.75, 3\/11, 0.3<\/p>\n<p>Explanation:<br \/>\nOrder the numbers -1.75, 3\/11, 0.3, -1(7\/9) from least to greatest<br \/>\nExpress each number as a decimal<br \/>\n3\/11 = 0.272727<br \/>\n-1(7\/9) = -16\/9 = -1.77777<br \/>\n-1.7777 &lt; -1.75 &lt; 0.272727 &lt; 0.3<br \/>\nThe order of numbers from least to greatest is -1(7\/9), -1.75, 3\/11, 0.3<\/p>\n<p><strong>2.4 Multiplying Rational Numbers<\/strong> (pp. 67\u201372)<\/p>\n<p><strong>Find the product. Write fractions in simplest form.<\/strong><\/p>\n<p>Question 31.<br \/>\n<img decoding=\"async\" loading=\"lazy\" class=\"alignnone size-full wp-image-30234\" src=\"https:\/\/ccssanswers.com\/wp-content\/uploads\/2021\/01\/Big-Ideas-Math-Solutions-Grade-7-Chapter-2-Multiplying-and-Dividing-Rational-Numbers-128.png\" alt=\"Big Ideas Math Solutions Grade 7 Chapter 2 Multiplying and Dividing Rational Numbers 128\" width=\"69\" height=\"59\" \/><\/p>\n<p>Answer:<br \/>\n-4\/9(-7\/9) = 28\/81<\/p>\n<p>Explanation:<br \/>\n-4\/9(-7\/9) = (-4 . -7)\/(9 . 9)<br \/>\n= 28\/81<\/p>\n<p>Question 32.<br \/>\n<img decoding=\"async\" loading=\"lazy\" class=\"alignnone size-full wp-image-30235\" src=\"https:\/\/ccssanswers.com\/wp-content\/uploads\/2021\/01\/Big-Ideas-Math-Solutions-Grade-7-Chapter-2-Multiplying-and-Dividing-Rational-Numbers-129.png\" alt=\"Big Ideas Math Solutions Grade 7 Chapter 2 Multiplying and Dividing Rational Numbers 129\" width=\"64\" height=\"61\" \/><\/p>\n<p>Answer:<br \/>\n8\/15(-2\/3) = -16\/45<\/p>\n<p>Explanation:<br \/>\n8\/15(-2\/3) = (8 . -2)\/(15 . 3)<br \/>\n= -16\/45<\/p>\n<p>Question 33.<br \/>\n-5.9(-9.7)<\/p>\n<p>Answer:<br \/>\n-5.9(-9.7) = 5723\/100<\/p>\n<p>Explanation:<br \/>\n-5.9(-9.7) = -59\/10 (-97\/10)<br \/>\n= (-59 . -97)\/100<br \/>\n= 5723\/100<br \/>\n<img decoding=\"async\" loading=\"lazy\" class=\"alignnone size-full wp-image-43504\" src=\"https:\/\/ccssanswers.com\/wp-content\/uploads\/2021\/01\/big-ideas-math-answers-grade-7-chapter-2-multiplying-and-dividing-rational-numbers-82.jpg\" alt=\"Big Ideas Math Answers Grade 7 Chapter 2 Multiplying and Dividing Rational Numbers 82\" width=\"200\" height=\"245\" \/><\/p>\n<p>Question 34.<br \/>\n4.5(-5.26)<\/p>\n<p>Answer:<br \/>\n4.5(-5.26) = 2367\/100<\/p>\n<p>Explanation:<br \/>\n4.5(-5.26) = 45\/10 (-526\/100)<br \/>\n= (45 . -526) \/ (10 . 100)<br \/>\n= (9 . 263) \/ 100<br \/>\n= 2367\/100<br \/>\n<img decoding=\"async\" loading=\"lazy\" class=\"alignnone size-full wp-image-43513\" src=\"https:\/\/ccssanswers.com\/wp-content\/uploads\/2021\/01\/big-ideas-math-answers-grade-7-chapter-2-multiplying-and-dividing-rational-numbers-83.jpg\" alt=\"Big Ideas Math Answers Grade 7 Chapter 2 Multiplying and Dividing Rational Numbers 83\" width=\"198\" height=\"198\" srcset=\"https:\/\/ccssanswers.com\/wp-content\/uploads\/2021\/01\/big-ideas-math-answers-grade-7-chapter-2-multiplying-and-dividing-rational-numbers-83.jpg 198w, https:\/\/ccssanswers.com\/wp-content\/uploads\/2021\/01\/big-ideas-math-answers-grade-7-chapter-2-multiplying-and-dividing-rational-numbers-83-150x150.jpg 150w\" sizes=\"(max-width: 198px) 100vw, 198px\" \/><\/p>\n<p>Question 35.<br \/>\n<img decoding=\"async\" loading=\"lazy\" class=\"alignnone size-full wp-image-30236\" src=\"https:\/\/ccssanswers.com\/wp-content\/uploads\/2021\/01\/Big-Ideas-Math-Solutions-Grade-7-Chapter-2-Multiplying-and-Dividing-Rational-Numbers-130.png\" alt=\"Big Ideas Math Solutions Grade 7 Chapter 2 Multiplying and Dividing Rational Numbers 130\" width=\"97\" height=\"58\" \/><\/p>\n<p>Answer:<br \/>\n-2\/3 (2(1\/2))(-3) = -5<\/p>\n<p>Explanation:<br \/>\n-2\/3 (2(1\/2))(-3) = -2\/3 (5\/2) (-3)<br \/>\n= (-2 . 5 . -3) \/ (2 . 3)<br \/>\n= -5<\/p>\n<p>Question 36.<br \/>\n-1.6(0.5)(-20)<\/p>\n<p>Answer:<br \/>\n-1.6(0.5)(-20) = 16<\/p>\n<p>Explanation:<br \/>\n-1.6(0.5)(-20) = -16\/10(5\/10)(-20)<br \/>\n= (-16 . 5 . -20)\/(10 . 10)<br \/>\n= 16<\/p>\n<p>Question 37.<br \/>\nThe elevation of a sunken ship is -120 feet. You are in a submarine at an elevation that is \\(\\frac{5}{8}\\) of the ship\u2019s elevation. What is your elevation?<br \/>\n<img decoding=\"async\" loading=\"lazy\" class=\"alignnone size-full wp-image-30237\" src=\"https:\/\/ccssanswers.com\/wp-content\/uploads\/2021\/01\/Big-Ideas-Math-Solutions-Grade-7-Chapter-2-Multiplying-and-Dividing-Rational-Numbers-131.png\" alt=\"Big Ideas Math Solutions Grade 7 Chapter 2 Multiplying and Dividing Rational Numbers 131\" width=\"279\" height=\"199\" \/><\/p>\n<p>Answer:<br \/>\nYour elevation is -300 feet.<\/p>\n<p>Explanation:<br \/>\nYou are in a submarine at an elevation that is 5\/8 of the ship\u2019s elevation<br \/>\nShip elevation = -120 feet<br \/>\nYour elevation = 5\/8 (-120)<br \/>\n= 15(-20) = -300<\/p>\n<p>Question 38.<br \/>\nWrite two fractions whose product \\(\\frac{1}{5}\\) and \\(\\frac{1}{2}\\), and whose sum is negative.<\/p>\n<p>Answer:<br \/>\nTwo fractions are-1\/2 and -1\/2<\/p>\n<p>Explanation:<br \/>\nThe product of two fractions is between 1\/5 and 1\/2 and sum is negative.<br \/>\nLet us say the product of fractions is 1\/4.<br \/>\nThen two fractions are -1\/2 and -1\/2<br \/>\nthe sum is -1\/2 &#8211; 1\/2 = -2\/2 = -1<\/p>\n<p><strong>2.5 Dividing Rational Numbers<\/strong> (pp. 73\u201378)<\/p>\n<p><strong>Find the quotient. Write fractions in simplest form.<\/strong><\/p>\n<p>Question 39.<br \/>\n<img decoding=\"async\" loading=\"lazy\" class=\"alignnone size-full wp-image-30238\" src=\"https:\/\/ccssanswers.com\/wp-content\/uploads\/2021\/01\/Big-Ideas-Math-Solutions-Grade-7-Chapter-2-Multiplying-and-Dividing-Rational-Numbers-132.png\" alt=\"Big Ideas Math Solutions Grade 7 Chapter 2 Multiplying and Dividing Rational Numbers 132\" width=\"83\" height=\"50\" \/><\/p>\n<p>Answer:<br \/>\n-3\/4<\/p>\n<p>Explanation:<br \/>\n9\/10 \u00f7 (-6\/5) = 9\/10 \u2022 (-5\/6)<br \/>\n= (9 \u2022 -5)\/ (10 . 6)<br \/>\n= -3\/4<\/p>\n<p>Question 40.<br \/>\n<img decoding=\"async\" loading=\"lazy\" class=\"alignnone size-full wp-image-30239\" src=\"https:\/\/ccssanswers.com\/wp-content\/uploads\/2021\/01\/Big-Ideas-Math-Solutions-Grade-7-Chapter-2-Multiplying-and-Dividing-Rational-Numbers-133.png\" alt=\"Big Ideas Math Solutions Grade 7 Chapter 2 Multiplying and Dividing Rational Numbers 133\" width=\"76\" height=\"57\" \/><\/p>\n<p>Answer:<br \/>\n-14\/11<\/p>\n<p>Explanation:<br \/>\n-4\/11 \u00f7 2\/7 = -4\/11 \u2022 7\/2<br \/>\n= (-4 \u2022 7) \/ (2 \u2022 11)<br \/>\n= -14\/11<\/p>\n<p>Question 41.<br \/>\n<img decoding=\"async\" loading=\"lazy\" class=\"alignnone size-full wp-image-30240\" src=\"https:\/\/ccssanswers.com\/wp-content\/uploads\/2021\/01\/Big-Ideas-Math-Solutions-Grade-7-Chapter-2-Multiplying-and-Dividing-Rational-Numbers-134.png\" alt=\"Big Ideas Math Solutions Grade 7 Chapter 2 Multiplying and Dividing Rational Numbers 134\" width=\"96\" height=\"56\" \/><\/p>\n<p>Answer:<br \/>\n21\/10<\/p>\n<p>Explanation:<br \/>\n-7\/8 \u00f7 (-5\/12) = -7\/8 \u2022 (-12\/5)<br \/>\n= (-7 \u2022 -12) \/ (8 \u2022 5)<br \/>\n= 21\/10<\/p>\n<p>Question 42.<br \/>\n6.4 \u00f7 (-3.2)<\/p>\n<p>Answer:<br \/>\n-512\/25<\/p>\n<p>Explanation:<br \/>\n6.4 \u00f7 (-3.2) = 64\/10 \u00f7 (-32\/10)<br \/>\n= (64 \u2022 -32) \/ (10 \u2022 10)<br \/>\n= -512\/25<\/p>\n<p>Question 43.<br \/>\n-15.4 \u00f7 (-2.5)<\/p>\n<p>Answer:<br \/>\n77\/2<\/p>\n<p>Explanation:<br \/>\n-15.4 \u00f7 (-2.5) = -154\/10 \u00f7(-25\/10)<br \/>\n= (-154 \u2022 -25)\/(10 \u2022 10)<br \/>\n= 77\/2<\/p>\n<p>Question 44.<br \/>\n-23.8 \u00f7 5.6<\/p>\n<p>Answer:<br \/>\n-3332\/25<\/p>\n<p>Explanation:<br \/>\n-23.8 \u00f7 5.6 = -238\/10 \u00f7 56\/10<br \/>\n= (-238 \u2022 56) \/ (10 \u2022 10)<br \/>\n= -3332\/25<\/p>\n<p>Question 45.<br \/>\nYou use a debit card to purchase several shirts. Your account balance after buying the shirts changes by -$30.60. For each shirt you purchased, the change in your account balance was -$6.12. How many shirts did you buy?<\/p>\n<p>Answer:<br \/>\nThe number of T-shirts bought was 5<\/p>\n<p>Explanation:<br \/>\nAfter using a debit card, to purchase several t-shirts. Your account balance after buying the t-shirts changes by -$30.60. The negative sign means there was a total debit of $30.6 after your transactions.<br \/>\nFor each t-shirt you purchased, the changes in your account balance were -6.12. If you purchased n T-shirts, the changes would be n \u00d7 -6.12 = -6.12n. This means a total debit of 6.12n for all the T-shirts you bought.<br \/>\nTherefore, 6.12n = 30.6<br \/>\nn = 30.6\/6.12 = 5<br \/>\nSo the number of T-shirts bought was 5<\/p>\n<p>Question 46.<br \/>\nEvaluate <img decoding=\"async\" loading=\"lazy\" class=\"alignnone size-full wp-image-30242\" src=\"https:\/\/ccssanswers.com\/wp-content\/uploads\/2021\/01\/Big-Ideas-Math-Solutions-Grade-7-Chapter-2-Multiplying-and-Dividing-Rational-Numbers-136.png\" alt=\"Big Ideas Math Solutions Grade 7 Chapter 2 Multiplying and Dividing Rational Numbers 136\" width=\"64\" height=\"61\" \/> when x = 4, y = -3, and \\(-\\frac{1}{8}\\).<\/p>\n<p>Answer:<br \/>\n-1\/2<\/p>\n<p>Explanation:<br \/>\nThe given expression is z \/ (y &#8211; 3\/4 + x)<br \/>\nPut x = 4, y = -3 and z = -1\/8<br \/>\n= -1\/8 \/ (-3 &#8211; 3\/4 + 4)<br \/>\n= -1\/8 \/ ((-12 &#8211; 3 + 16)\/4)<br \/>\n= -1\/8 \/ (1\/4)<br \/>\n= -1\/8 \u2022 4\/1<br \/>\n= -1\/2<\/p>\n<h3><a id=\"Multiplying_and_Dividing_Rational_Numbers_Practice_Test\"><\/a>Multiplying and Dividing Rational Numbers Practice Test<\/h3>\n<p><strong>Evaluate the expression. Write fractions in simplest form.<\/strong><\/p>\n<p>Question 1.<br \/>\n-9 \u2022 2<\/p>\n<p>Answer:<br \/>\n-9 \u2022 2 = -18<\/p>\n<p>Explanation:<br \/>\n-9 \u2022 2 = -18<br \/>\nThe product of two integers with different signs is negative.<\/p>\n<p>Question 2.<br \/>\n-72 \u00f7 (-3)<\/p>\n<p>Answer:<br \/>\n-72 \u00f7 (-3) = 24<\/p>\n<p>Explanation:<br \/>\n-72 \u00f7 (-3) = 24<br \/>\nThe quotient of two integers with the same sign is positive.<\/p>\n<p>Question 3.<br \/>\n<img decoding=\"async\" loading=\"lazy\" class=\"alignnone size-full wp-image-30241\" src=\"https:\/\/ccssanswers.com\/wp-content\/uploads\/2021\/01\/Big-Ideas-Math-Solutions-Grade-7-Chapter-2-Multiplying-and-Dividing-Rational-Numbers-136.1.png\" alt=\"Big Ideas Math Solutions Grade 7 Chapter 2 Multiplying and Dividing Rational Numbers 136.1\" width=\"94\" height=\"58\" \/><\/p>\n<p>Answer:<br \/>\n-52\/5<\/p>\n<p>Explanation:<br \/>\n3(9\/10) x (-8\/3) = 39\/10 x (-8\/3)<br \/>\n= (39 . -8) \/ (10 . 3)<br \/>\n= (13 . -4)\/5<br \/>\n= -52\/5<\/p>\n<p>Question 4.<br \/>\n<img decoding=\"async\" loading=\"lazy\" class=\"alignnone size-full wp-image-30243\" src=\"https:\/\/ccssanswers.com\/wp-content\/uploads\/2021\/01\/Big-Ideas-Math-Solutions-Grade-7-Chapter-2-Multiplying-and-Dividing-Rational-Numbers-137.png\" alt=\"Big Ideas Math Solutions Grade 7 Chapter 2 Multiplying and Dividing Rational Numbers 137\" width=\"88\" height=\"56\" \/><\/p>\n<p>Answer:<br \/>\n-11\/25<\/p>\n<p>Explanation:<br \/>\n-1(5\/6) \u00f7 4(1\/6) = -11\/6 \u00f7 25\/6<br \/>\n= -11\/6 \u2022 6\/25<br \/>\n= (-11 \u2022 6) \/ (6 \u2022 25)<br \/>\n= -11\/25<\/p>\n<p>Question 5.<br \/>\n-4.4 \u00d7 (-6.02)<\/p>\n<p>Answer:<br \/>\n-4.4 \u00d7 (-6.02) = 6622\/25<\/p>\n<p>Explanation:<br \/>\n-4.4 \u00d7 (-6.02) = -44\/10 x -602\/10<br \/>\n= (-44 x -602) \/ (10 x 10)<br \/>\n= (-11 x -602)\/25<br \/>\n= 6622\/25<\/p>\n<p>Question 6.<br \/>\n-5 \u00f7 1.5<\/p>\n<p>Answer:<br \/>\n-5 \u00f7 1.5 = -10\/3<\/p>\n<p>Explanation:<br \/>\n-5 \u00f7 1.5 = -5 \u00f7 15\/10<br \/>\n= -5 \u2022 10\/15<br \/>\n=(-5 \u2022 10) \/ 15<br \/>\n= -10\/3<\/p>\n<p><strong>Write the fraction or mixed number as a decimal.<\/strong><\/p>\n<p>Question 7.<br \/>\n\\(\\frac{7}{40}\\)<\/p>\n<p>Answer:<br \/>\n\\(\\frac{7}{40}\\) = 0.175<\/p>\n<p>Explanation:<br \/>\n<img decoding=\"async\" loading=\"lazy\" class=\"alignnone size-full wp-image-43520\" src=\"https:\/\/ccssanswers.com\/wp-content\/uploads\/2021\/01\/big-ideas-math-answers-grade-7-chapter-2-multiplying-and-dividing-rational-numbers-84.jpg\" alt=\"Big Ideas Math Answers Grade 7 Chapter 2 Multiplying and Dividing Rational Numbers 84\" width=\"194\" height=\"420\" srcset=\"https:\/\/ccssanswers.com\/wp-content\/uploads\/2021\/01\/big-ideas-math-answers-grade-7-chapter-2-multiplying-and-dividing-rational-numbers-84.jpg 194w, https:\/\/ccssanswers.com\/wp-content\/uploads\/2021\/01\/big-ideas-math-answers-grade-7-chapter-2-multiplying-and-dividing-rational-numbers-84-139x300.jpg 139w\" sizes=\"(max-width: 194px) 100vw, 194px\" \/><\/p>\n<p>Question 8.<br \/>\n\\(-\\frac{1}{9}\\)<\/p>\n<p>Answer:<br \/>\n\\(-\\frac{1}{9}\\) = -0.11111<\/p>\n<p>Explanation:<br \/>\n<img decoding=\"async\" loading=\"lazy\" class=\"alignnone size-full wp-image-43521\" src=\"https:\/\/ccssanswers.com\/wp-content\/uploads\/2021\/01\/big-ideas-math-answers-grade-7-chapter-2-multiplying-and-dividing-rational-numbers-85.jpg\" alt=\"Big Ideas Math Answers Grade 7 Chapter 2 Multiplying and Dividing Rational Numbers 85\" width=\"167\" height=\"422\" srcset=\"https:\/\/ccssanswers.com\/wp-content\/uploads\/2021\/01\/big-ideas-math-answers-grade-7-chapter-2-multiplying-and-dividing-rational-numbers-85.jpg 167w, https:\/\/ccssanswers.com\/wp-content\/uploads\/2021\/01\/big-ideas-math-answers-grade-7-chapter-2-multiplying-and-dividing-rational-numbers-85-119x300.jpg 119w\" sizes=\"(max-width: 167px) 100vw, 167px\" \/><\/p>\n<p>Question 9.<br \/>\n-1\\(\\frac{5}{16}\\)<\/p>\n<p>Answer:<br \/>\n-1\\(\\frac{5}{16}\\) = -1.3125<\/p>\n<p>Explanation:<br \/>\n-1\\(\\frac{5}{16}\\) = -21\/16<br \/>\n<img decoding=\"async\" loading=\"lazy\" class=\"alignnone size-full wp-image-43523\" src=\"https:\/\/ccssanswers.com\/wp-content\/uploads\/2021\/01\/big-ideas-math-answers-grade-7-chapter-2-multiplying-and-dividing-rational-numbers-86.jpg\" alt=\"Big Ideas Math Answers Grade 7 Chapter 2 Multiplying and Dividing Rational Numbers 86\" width=\"255\" height=\"587\" srcset=\"https:\/\/ccssanswers.com\/wp-content\/uploads\/2021\/01\/big-ideas-math-answers-grade-7-chapter-2-multiplying-and-dividing-rational-numbers-86.jpg 255w, https:\/\/ccssanswers.com\/wp-content\/uploads\/2021\/01\/big-ideas-math-answers-grade-7-chapter-2-multiplying-and-dividing-rational-numbers-86-130x300.jpg 130w\" sizes=\"(max-width: 255px) 100vw, 255px\" \/><\/p>\n<p><strong>Write the decimal as a fraction or mixed number in simplest form.<\/strong><\/p>\n<p>Question 10.<br \/>\n-0.122<\/p>\n<p>Answer:<br \/>\n-0.122 = -61\/500<\/p>\n<p>Explanation:<br \/>\n-0.122 = -122\/1000<br \/>\n= (-2 x 61) \/ (2 x 500)<br \/>\n= -61\/500<\/p>\n<p>Question 11.<br \/>\n0.33<\/p>\n<p>Answer:<br \/>\n0.33 = 33\/100<\/p>\n<p>Explanation:<br \/>\n0.33 = 33\/100<\/p>\n<p>Question 12.<br \/>\n-7.09<\/p>\n<p>Answer:<br \/>\n-7.09 = -709\/100<\/p>\n<p>Explanation:<br \/>\n-7.09 = -709\/100<\/p>\n<p><strong>Evaluate the expression when x = 5, y = -3, and z = -2.<\/strong><\/p>\n<p>Question 13.<br \/>\n<img decoding=\"async\" loading=\"lazy\" class=\"alignnone size-full wp-image-30244\" src=\"https:\/\/ccssanswers.com\/wp-content\/uploads\/2021\/01\/Big-Ideas-Math-Solutions-Grade-7-Chapter-2-Multiplying-and-Dividing-Rational-Numbers-138.png\" alt=\"Big Ideas Math Solutions Grade 7 Chapter 2 Multiplying and Dividing Rational Numbers 138\" width=\"60\" height=\"49\" \/><\/p>\n<p>Answer:<br \/>\n-6\/5<\/p>\n<p>Explanation:<br \/>\nThe given expression is (y + z)\/x<br \/>\nPut x = 5, y = -3, and z = -2<br \/>\n= (-3 + (-2)) \/ 5<br \/>\n= (-3 &#8211; 2)\/5<br \/>\n= -6\/5<\/p>\n<p>Question 14.<br \/>\n<img decoding=\"async\" loading=\"lazy\" class=\"alignnone size-full wp-image-30245\" src=\"https:\/\/ccssanswers.com\/wp-content\/uploads\/2021\/01\/Big-Ideas-Math-Solutions-Grade-7-Chapter-2-Multiplying-and-Dividing-Rational-Numbers-139.png\" alt=\"Big Ideas Math Solutions Grade 7 Chapter 2 Multiplying and Dividing Rational Numbers 139\" width=\"58\" height=\"48\" \/><\/p>\n<p>Answer:<br \/>\n-5<\/p>\n<p>Explanation:<br \/>\nThe given expression is (x &#8211; 5z)\/y<br \/>\nPut x = 5, y = -3, and z = -2<br \/>\n= (5 &#8211; 5(-2))\/-3<br \/>\n= (5 + 10)\/-3<br \/>\n= 15\/-3 = -5<\/p>\n<p>Question 15.<br \/>\n<img decoding=\"async\" loading=\"lazy\" class=\"alignnone size-full wp-image-30246\" src=\"https:\/\/ccssanswers.com\/wp-content\/uploads\/2021\/01\/Big-Ideas-Math-Solutions-Grade-7-Chapter-2-Multiplying-and-Dividing-Rational-Numbers-140.png\" alt=\"Big Ideas Math Solutions Grade 7 Chapter 2 Multiplying and Dividing Rational Numbers 140\" width=\"39\" height=\"81\" \/><\/p>\n<p>Answer:<br \/>\n10\/9<\/p>\n<p>Explanation:<br \/>\nThe given expression is 1\/3 x \/ y\/z<br \/>\nPut x = 5, y = -3, and z = -2<br \/>\n= [1\/3 (5)]\/[-3\/-2]<br \/>\n= 5\/3 \/ 3\/2<br \/>\n= 5\/3 . 2\/3<br \/>\n= 10\/9<\/p>\n<p>Question 16.<br \/>\nFind the mean of 11, -7, -14, 10, and -5.<\/p>\n<p>Answer:<br \/>\nMean = -1<\/p>\n<p>Explanation:<br \/>\nMean = (11 &#8211; 7 &#8211; 14 + 10 &#8211; 5)\/5<br \/>\n= -5\/5<br \/>\n= -1<\/p>\n<p>Question 17.<br \/>\nA driver receives -25 points for each rule violation. What integer represents the change in points after 4 rule violations?<br \/>\n<img decoding=\"async\" loading=\"lazy\" class=\"alignnone size-full wp-image-30247\" src=\"https:\/\/ccssanswers.com\/wp-content\/uploads\/2021\/01\/Big-Ideas-Math-Solutions-Grade-7-Chapter-2-Multiplying-and-Dividing-Rational-Numbers-141.png\" alt=\"Big Ideas Math Solutions Grade 7 Chapter 2 Multiplying and Dividing Rational Numbers 141\" width=\"327\" height=\"171\" srcset=\"https:\/\/ccssanswers.com\/wp-content\/uploads\/2021\/01\/Big-Ideas-Math-Solutions-Grade-7-Chapter-2-Multiplying-and-Dividing-Rational-Numbers-141.png 327w, https:\/\/ccssanswers.com\/wp-content\/uploads\/2021\/01\/Big-Ideas-Math-Solutions-Grade-7-Chapter-2-Multiplying-and-Dividing-Rational-Numbers-141-300x157.png 300w\" sizes=\"(max-width: 327px) 100vw, 327px\" \/><\/p>\n<p>Answer:<br \/>\nThe change in points after 4 rule violations is -100 points<\/p>\n<p>Explanation:<br \/>\nA driver receives -25 points for each rule violation.<br \/>\nThe change in points after 4 rule violations = 4(-25)<br \/>\n= -100<\/p>\n<p>Question 18.<br \/>\nHow many 2.25-pound containers can you \ufb01ll with 24.75 pounds of almonds?<\/p>\n<p>Answer:<br \/>\nThe number of containers = 11<\/p>\n<p>Explanation:<br \/>\nThe number of containers = 24.75 \/ 2.25<br \/>\n= 2475\/225 = (495 . 5)\/(45 . 5)<br \/>\n= (99 . 5) \/ (9 . 5)<br \/>\n= 11<\/p>\n<p>Question 19.<br \/>\nIn a recent 10-year period, the change in the number of visitors to U.S.national parks was about 11,150,000 visitors.<br \/>\na. What was the mean yearly change in the number of visitors?<br \/>\nb. During the seventh year, the change in the number of visitors was about 10,800,000. Explain how the change for the 10-year period can be negative.<br \/>\n<img decoding=\"async\" loading=\"lazy\" class=\"alignnone size-full wp-image-30248\" src=\"https:\/\/ccssanswers.com\/wp-content\/uploads\/2021\/01\/Big-Ideas-Math-Solutions-Grade-7-Chapter-2-Multiplying-and-Dividing-Rational-Numbers-142.png\" alt=\"Big Ideas Math Solutions Grade 7 Chapter 2 Multiplying and Dividing Rational Numbers 142\" width=\"304\" height=\"203\" srcset=\"https:\/\/ccssanswers.com\/wp-content\/uploads\/2021\/01\/Big-Ideas-Math-Solutions-Grade-7-Chapter-2-Multiplying-and-Dividing-Rational-Numbers-142.png 304w, https:\/\/ccssanswers.com\/wp-content\/uploads\/2021\/01\/Big-Ideas-Math-Solutions-Grade-7-Chapter-2-Multiplying-and-Dividing-Rational-Numbers-142-300x200.png 300w\" sizes=\"(max-width: 304px) 100vw, 304px\" \/><\/p>\n<p>Answer:<br \/>\na. Mean yearly change in the number of visitors = 1,15,000<br \/>\nb. The change is -35000<\/p>\n<p>Explanation:<br \/>\na. Mean yearly change in the number of visitors = 11,150,000\/10<br \/>\n= 1,15,000<br \/>\nb. During the seventh year, the change in the number of visitors was about 10,800,000<br \/>\nThe change in the number of visitors to U.S.national parks was about 11,150,000 visitors<br \/>\n(10,800,000 &#8211; 11,150,000)\/10 = -350000\/10 = -35000<\/p>\n<p>Question 20.<br \/>\nYou have a $50 gift card to go shopping for school supplies. You buy 2 packs of pencils, 5 notebooks, 6 folders, 1 pack of pens, 3 packs of paper, 1 pack of highlighters, and 2 binders.<br \/>\n<img decoding=\"async\" loading=\"lazy\" class=\"alignnone size-full wp-image-30249\" src=\"https:\/\/ccssanswers.com\/wp-content\/uploads\/2021\/01\/Big-Ideas-Math-Solutions-Grade-7-Chapter-2-Multiplying-and-Dividing-Rational-Numbers-143.png\" alt=\"Big Ideas Math Solutions Grade 7 Chapter 2 Multiplying and Dividing Rational Numbers 143\" width=\"244\" height=\"195\" \/><br \/>\na. What number represents the change in the value of the gift card after buying your school supplies?<br \/>\nb. What percentage of the value remains on your gift card?<\/p>\n<p>Answer:<br \/>\na. The change in the value of the gift card after buying your school supplies = $12.06<br \/>\nb. The percentage of the value that remains on your gift card = 24.12%<\/p>\n<p>Explanation:<br \/>\nYou buy 2 packs of pencils, 5 notebooks, 6 folders, 1 pack of pens, 3 packs of paper, 1 pack of highlighters, and 2 binders.<br \/>\na. The change in the value of the gift card after buying your school supplies = 50 &#8211; [2(1.98) + 5(2.95) + 6(0.75) + 1(1.57) + 3(0.89) + 1(3.45) + 2(3.55)]<br \/>\n= 50 &#8211; [3.9 + 14.75 + 4.5 + 1.57 + 2.67 + 3.45 + 7.1]<br \/>\n= 50 &#8211; 37.94<br \/>\n= 12.06<br \/>\nb. The amount remains on the gift card = $12.06<br \/>\nThe percentage of the value that remains on your gift card = (100 x 12.06)\/50<br \/>\n= 2 x 12.06 = 24.12%<\/p>\n<h3><a id=\"Multiplying_and_Dividing_Rational_Numbers_Cumulative_Practice\"><\/a>Multiplying and Dividing Rational Numbers Cumulative Practice<\/h3>\n<p>Question 1.<br \/>\nWhen Jos\u00e9 and Sean were each 5 years old, Jos\u00e9 was 1\\(\\frac{1}{2}\\) inches taller than Sean. Then Jos\u00e9 grew at an average rate of 2\\(\\frac{3}{4}\\) inches per year until he was 13 years old. Jos\u00e9 was 63 inches tall when he was 13 years old. How tall was Sean when he was 5 years old?<br \/>\n<img decoding=\"async\" loading=\"lazy\" class=\"alignnone size-full wp-image-30251\" src=\"https:\/\/ccssanswers.com\/wp-content\/uploads\/2021\/01\/Big-Ideas-Math-Solutions-Grade-7-Chapter-2-Multiplying-and-Dividing-Rational-Numbers-146.png\" alt=\"Big Ideas Math Solutions Grade 7 Chapter 2 Multiplying and Dividing Rational Numbers 146\" width=\"305\" height=\"94\" srcset=\"https:\/\/ccssanswers.com\/wp-content\/uploads\/2021\/01\/Big-Ideas-Math-Solutions-Grade-7-Chapter-2-Multiplying-and-Dividing-Rational-Numbers-146.png 305w, https:\/\/ccssanswers.com\/wp-content\/uploads\/2021\/01\/Big-Ideas-Math-Solutions-Grade-7-Chapter-2-Multiplying-and-Dividing-Rational-Numbers-146-300x92.png 300w\" sizes=\"(max-width: 305px) 100vw, 305px\" \/><\/p>\n<p><img decoding=\"async\" loading=\"lazy\" class=\"alignnone size-full wp-image-30250\" src=\"https:\/\/ccssanswers.com\/wp-content\/uploads\/2021\/01\/Big-Ideas-Math-Solutions-Grade-7-Chapter-2-Multiplying-and-Dividing-Rational-Numbers-145.png\" alt=\"Big Ideas Math Solutions Grade 7 Chapter 2 Multiplying and Dividing Rational Numbers 145\" width=\"338\" height=\"391\" srcset=\"https:\/\/ccssanswers.com\/wp-content\/uploads\/2021\/01\/Big-Ideas-Math-Solutions-Grade-7-Chapter-2-Multiplying-and-Dividing-Rational-Numbers-145.png 338w, https:\/\/ccssanswers.com\/wp-content\/uploads\/2021\/01\/Big-Ideas-Math-Solutions-Grade-7-Chapter-2-Multiplying-and-Dividing-Rational-Numbers-145-259x300.png 259w\" sizes=\"(max-width: 338px) 100vw, 338px\" \/><\/p>\n<p>Answer:<br \/>\nA. 39(1\/2)<\/p>\n<p>Explanation:<br \/>\nJos\u00e9 grew at an average rate of 2\\(\\frac{3}{4}\\) inches per year until he was 13 years old.<br \/>\n2.75 * (13 &#8211; 5) = 2.75 (8) =\u00a0 22<br \/>\nJos\u00e9 was 63 inches<br \/>\n= 63 &#8211; 22 = 41<br \/>\n41 &#8211; 1.5 = 39.5 = 39(1\/2)<br \/>\nsean was only 39.5 inches tall when he was 5.<\/p>\n<p>Question 2.<br \/>\nWhatis the value of -5 + (-7) ?<br \/>\nF. -12<br \/>\nG. -2<br \/>\nH. 2<br \/>\nI. 12<\/p>\n<p>Answer:<br \/>\nF. -12<\/p>\n<p>Explanation:<br \/>\n-5 + (-7) = -5 &#8211; 7<br \/>\n= -12<\/p>\n<p>Question 3.<br \/>\nWhat is the value of the expression?<br \/>\n<img decoding=\"async\" loading=\"lazy\" class=\"alignnone size-full wp-image-30252\" src=\"https:\/\/ccssanswers.com\/wp-content\/uploads\/2021\/01\/Big-Ideas-Math-Solutions-Grade-7-Chapter-2-Multiplying-and-Dividing-Rational-Numbers-147.png\" alt=\"Big Ideas Math Solutions Grade 7 Chapter 2 Multiplying and Dividing Rational Numbers 147\" width=\"215\" height=\"65\" \/><\/p>\n<p>Answer:<br \/>\n9\/16<\/p>\n<p>Explanation:<br \/>\n-9\/16 + 9\/8 = (-9 + 18)\/16<br \/>\n= 9\/16<\/p>\n<p>Question 4.<br \/>\nWhat is the value of <img decoding=\"async\" loading=\"lazy\" class=\"alignnone size-full wp-image-30310\" src=\"https:\/\/ccssanswers.com\/wp-content\/uploads\/2021\/01\/Big-Ideas-Math-Solutions-Grade-7-Chapter-2-Multiplying-and-Dividing-Rational-Numbers-158.png\" alt=\"Big Ideas Math Solutions Grade 7 Chapter 2 Multiplying and Dividing Rational Numbers 158\" width=\"110\" height=\"37\" \/> when a = -2, b = 3, and c = -5?<br \/>\nA. -9<br \/>\nB. -1<br \/>\nC. 1<br \/>\nD. 9<\/p>\n<p>Answer:<br \/>\nC. 1<\/p>\n<p>Explanation:<br \/>\n| a\u00b2 &#8211; 2ac + 5b |<br \/>\nPut a = -2, b = 3, and c = -5<br \/>\n= | (-2)\u00b2 &#8211; 2(-2)(-5) + 5(3) |<br \/>\n= | 4 &#8211; 20 + 15 |<br \/>\n= | -1 |<br \/>\n= 1<\/p>\n<p>Question 5.<br \/>\nYour friend evaluated the expression.<br \/>\n<img decoding=\"async\" loading=\"lazy\" class=\"alignnone size-full wp-image-30253\" src=\"https:\/\/ccssanswers.com\/wp-content\/uploads\/2021\/01\/Big-Ideas-Math-Solutions-Grade-7-Chapter-2-Multiplying-and-Dividing-Rational-Numbers-148.png\" alt=\"Big Ideas Math Solutions Grade 7 Chapter 2 Multiplying and Dividing Rational Numbers 148\" width=\"227\" height=\"116\" \/><br \/>\nWhat should your friend do to correct the error that he made?<br \/>\nF. Subtract 5 from -5 instead of adding.<br \/>\nG. Rewrite 2 &#8211; 3 as -1.<br \/>\nH. Subtract -5 from 3 before subtracting 3 from 2.<br \/>\nI. Rewrite -5 + 5 as -10<\/p>\n<p>Answer:<br \/>\nH. Subtract -5 from 3 before subtracting 3 from 2.<\/p>\n<p>Explanation:<br \/>\n2 &#8211; 3 &#8211; (-5) = 2 &#8211; 3 + 5<br \/>\n= -1 + 5<br \/>\n= 4<\/p>\n<p>Question 6.<br \/>\nWhat is the value of <img decoding=\"async\" loading=\"lazy\" class=\"alignnone size-full wp-image-30255\" src=\"https:\/\/ccssanswers.com\/wp-content\/uploads\/2021\/01\/Big-Ideas-Math-Solutions-Grade-7-Chapter-2-Multiplying-and-Dividing-Rational-Numbers-149.png\" alt=\"Big Ideas Math Solutions Grade 7 Chapter 2 Multiplying and Dividing Rational Numbers 149\" width=\"100\" height=\"51\" \/>?<br \/>\n<img decoding=\"async\" loading=\"lazy\" class=\"alignnone size-full wp-image-30254\" src=\"https:\/\/ccssanswers.com\/wp-content\/uploads\/2021\/01\/Big-Ideas-Math-Solutions-Grade-7-Chapter-2-Multiplying-and-Dividing-Rational-Numbers-149.1.png\" alt=\"Big Ideas Math Solutions Grade 7 Chapter 2 Multiplying and Dividing Rational Numbers 149.1\" width=\"340\" height=\"96\" srcset=\"https:\/\/ccssanswers.com\/wp-content\/uploads\/2021\/01\/Big-Ideas-Math-Solutions-Grade-7-Chapter-2-Multiplying-and-Dividing-Rational-Numbers-149.1.png 340w, https:\/\/ccssanswers.com\/wp-content\/uploads\/2021\/01\/Big-Ideas-Math-Solutions-Grade-7-Chapter-2-Multiplying-and-Dividing-Rational-Numbers-149.1-300x85.png 300w\" sizes=\"(max-width: 340px) 100vw, 340px\" \/><\/p>\n<p>Answer:<br \/>\nB. 1\/4<\/p>\n<p>Explanation:<br \/>\n-1(1\/2) &#8211; (-1(3\/4)) = -3\/2 + 7\/4<br \/>\n= (-6 + 7)\/4<br \/>\n= 1\/4<\/p>\n<p>Question 7.<br \/>\nWhat is the value of the expression when q = -2, r = -12, and s = 8?<br \/>\n<img decoding=\"async\" loading=\"lazy\" class=\"alignnone size-full wp-image-30256\" src=\"https:\/\/ccssanswers.com\/wp-content\/uploads\/2021\/01\/Big-Ideas-Math-Solutions-Grade-7-Chapter-2-Multiplying-and-Dividing-Rational-Numbers-150.png\" alt=\"Big Ideas Math Solutions Grade 7 Chapter 2 Multiplying and Dividing Rational Numbers 150\" width=\"81\" height=\"47\" \/><br \/>\nF. -2<br \/>\nG. -1<br \/>\nH. 1<br \/>\nI. 2<\/p>\n<p>Answer:<br \/>\nH. 1<\/p>\n<p>Explanation:<br \/>\nThe given expression is (-q\u00b2 &#8211; r)\/s<br \/>\nPut q = -2, r = -12, and s = 8<br \/>\n= (-(-2)\u00b2 &#8211; (-12))\/8<br \/>\n= (-4 + 12)\/8<br \/>\n= 8\/8 = 1<\/p>\n<p>Question 8.<br \/>\nYou are stacking wooden blocks with the dimensions shown. How many blocks do you need to stack vertically to build a block tower that is 7\\(\\frac{1}{2}\\) inches tall?<br \/>\n<img decoding=\"async\" loading=\"lazy\" class=\"alignnone size-full wp-image-30257\" src=\"https:\/\/ccssanswers.com\/wp-content\/uploads\/2021\/01\/Big-Ideas-Math-Solutions-Grade-7-Chapter-2-Multiplying-and-Dividing-Rational-Numbers-151.png\" alt=\"Big Ideas Math Solutions Grade 7 Chapter 2 Multiplying and Dividing Rational Numbers 151\" width=\"192\" height=\"152\" \/><br \/>\n<img decoding=\"async\" loading=\"lazy\" class=\"alignnone size-full wp-image-30258\" src=\"https:\/\/ccssanswers.com\/wp-content\/uploads\/2021\/01\/Big-Ideas-Math-Solutions-Grade-7-Chapter-2-Multiplying-and-Dividing-Rational-Numbers-152.png\" alt=\"Big Ideas Math Solutions Grade 7 Chapter 2 Multiplying and Dividing Rational Numbers 152\" width=\"92\" height=\"69\" \/><\/p>\n<p>Answer:<br \/>\nWe need 6 blocks to stack vertically to build a block tower.<\/p>\n<p>Explanation:<br \/>\nThe length of block tower = 7(1\/2) = 15\/2 inches<br \/>\nThe length of each block = 1(1\/4) = 5\/4 inches<br \/>\nSo, 5\/4 x = 15\/2<br \/>\nx = 15\/2 . 4\/5<br \/>\nx = 6<br \/>\nTherefore, we need 6 blocks to stack vertically to build a block tower.<\/p>\n<p>Question 9.<br \/>\nYour friend evaluated an expression.<br \/>\n<img decoding=\"async\" loading=\"lazy\" class=\"alignnone size-full wp-image-30259\" src=\"https:\/\/ccssanswers.com\/wp-content\/uploads\/2021\/01\/Big-Ideas-Math-Solutions-Grade-7-Chapter-2-Multiplying-and-Dividing-Rational-Numbers-153.png\" alt=\"Big Ideas Math Solutions Grade 7 Chapter 2 Multiplying and Dividing Rational Numbers 153\" width=\"204\" height=\"241\" \/><br \/>\nWhat should your friend do to correct the error that she made?<br \/>\n<img decoding=\"async\" loading=\"lazy\" class=\"alignnone size-full wp-image-30260\" src=\"https:\/\/ccssanswers.com\/wp-content\/uploads\/2021\/01\/Big-Ideas-Math-Solutions-Grade-7-Chapter-2-Multiplying-and-Dividing-Rational-Numbers-154.png\" alt=\"Big Ideas Math Solutions Grade 7 Chapter 2 Multiplying and Dividing Rational Numbers 154\" width=\"260\" height=\"194\" \/><\/p>\n<p>Answer:<br \/>\nC.<\/p>\n<p>Explanation:<br \/>\n-4(3\/4) + 2(1\/5) = -19\/4 + 11\/5<br \/>\n= (-95 + 44)\/20<br \/>\n= -51\/20<\/p>\n<p>Question 10.<br \/>\nWhich expression has the greatest value when x = 2 and y = -3?<br \/>\nF. -xy<br \/>\nG. xy<br \/>\nH. x &#8211; y<br \/>\nI. -x &#8211; y<\/p>\n<p>Answer:<br \/>\nF. -xy<\/p>\n<p>Explanation:<br \/>\nPut x = 2 and y = -3<br \/>\nF. -xy<br \/>\n= -2(-3) = 6<br \/>\nG. xy = 2(-3) = -6<br \/>\nH. x &#8211; y = 2 &#8211; (-3) = 2 + 3 = 5<br \/>\nI. -x &#8211; y = -2 &#8211; (-3) = -2 + 3 = 1<\/p>\n<p>Question 11.<br \/>\nFour points are graphed on the number line.<br \/>\n<img decoding=\"async\" loading=\"lazy\" class=\"alignnone size-full wp-image-30261\" src=\"https:\/\/ccssanswers.com\/wp-content\/uploads\/2021\/01\/Big-Ideas-Math-Solutions-Grade-7-Chapter-2-Multiplying-and-Dividing-Rational-Numbers-155.png\" alt=\"Big Ideas Math Solutions Grade 7 Chapter 2 Multiplying and Dividing Rational Numbers 155\" width=\"573\" height=\"84\" srcset=\"https:\/\/ccssanswers.com\/wp-content\/uploads\/2021\/01\/Big-Ideas-Math-Solutions-Grade-7-Chapter-2-Multiplying-and-Dividing-Rational-Numbers-155.png 573w, https:\/\/ccssanswers.com\/wp-content\/uploads\/2021\/01\/Big-Ideas-Math-Solutions-Grade-7-Chapter-2-Multiplying-and-Dividing-Rational-Numbers-155-300x44.png 300w\" sizes=\"(max-width: 573px) 100vw, 573px\" \/><br \/>\n<strong>Part A<\/strong><br \/>\nChoose the two points whose values have the greatest sum. Approximate this sum. Explain your reasoning.<br \/>\n<strong>Part B<\/strong><br \/>\nChoose the two points whose values have the greatest difference. Approximate this difference. Explain your reasoning.<br \/>\n<strong>Part C<\/strong><br \/>\nChoose the two points whose values have the greatest product. Approximate this product. Explain your reasoning.<br \/>\n<strong>Part D<\/strong><br \/>\nChoose the two points whose values have the greatest quotient. Approximate this quotient. Explain your reasoning.<\/p>\n<p>Answer:<br \/>\nA. T + U<br \/>\nB. R &#8211; S<br \/>\nC. R . S<br \/>\nD. U\/T<\/p>\n<p>Explanation:<br \/>\nValues of the points are R = -2.75, S = -1.25, T = 0.4, U = 2.1<br \/>\nA. T + U = 0.4 + 2.1 = 2.5<br \/>\nB. R &#8211; S = -2.75 &#8211; (-1.25) = -2.75 + 1.25 = -1.5<br \/>\nS &#8211; T = -1.25 &#8211; 0.4 = -1.65<br \/>\nT &#8211; U = 0.4 &#8211; 2.1 = -1.7<br \/>\nS &#8211; U = -1.25 &#8211; 2.1 = -3.35<br \/>\nR &#8211; T = -2.75 &#8211; 0.4 = -3.15<br \/>\nR &#8211; U = -2.75 &#8211; 2.1 = -4.85<br \/>\nOut of all R &#8211; S has the greatest difference.<br \/>\nC. R . S = -2.75 . -1.25 = 3.4375<br \/>\nT. U = 0.4 . 2.1 = 0.84<br \/>\nD. R\/s = -2.75\/1.25 = 2.2<br \/>\nT\/U = 0.4\/2.1 = 0.19<br \/>\nU\/T = 2.1\/0.4 = 5.25<\/p>\n<p>Question 12.<br \/>\nWhat number belongs in the box to make the equation true?<br \/>\n<img decoding=\"async\" loading=\"lazy\" class=\"alignnone size-full wp-image-30262\" src=\"https:\/\/ccssanswers.com\/wp-content\/uploads\/2021\/01\/Big-Ideas-Math-Solutions-Grade-7-Chapter-2-Multiplying-and-Dividing-Rational-Numbers-156.png\" alt=\"Big Ideas Math Solutions Grade 7 Chapter 2 Multiplying and Dividing Rational Numbers 156\" width=\"145\" height=\"68\" \/><br \/>\nA. -1<br \/>\nB. -0.2<br \/>\nC. 0.2<br \/>\nD. 1<\/p>\n<p>Answer:<br \/>\nA. -1<\/p>\n<p>Explanation:<br \/>\n-0.4\/-1 + 0.8 = 0.4 + 0.8 = 1.2<br \/>\n-0.4\/1 + 0.8 = -0.4 + 0.8 = 0.4<br \/>\n-0.4\/0.2 + 0.8 = -2<\/p>\n<p>Question 13.<br \/>\nWhich expression has a negative value when x = -4 and y = 2?<br \/>\nF. -x + y<br \/>\nG. y &#8211; x<br \/>\nH. x &#8211; y<br \/>\nI. -x &#8211; y<\/p>\n<p>Answer:<br \/>\nH. x &#8211; y<\/p>\n<p>Explanation:<br \/>\nPut x = -4 and y = 2<br \/>\nF. -x + y = -(-4) + 2 = 4 + 2 = 6<br \/>\nG. y &#8211; x = 2 &#8211; (-4) = 6<br \/>\nH. x &#8211; y = -4 &#8211; 2 = -6<br \/>\nI. -x &#8211; y = -(-4) &#8211; 2 = 4 &#8211; 2 = 2<\/p>\n<p>Question 14.<br \/>\nWhat is the area of a triangle with a base of 2\\(\\frac{1}{2}\\) inches and a height of 2 inches?<br \/>\n<img decoding=\"async\" loading=\"lazy\" class=\"alignnone size-full wp-image-30263\" src=\"https:\/\/ccssanswers.com\/wp-content\/uploads\/2021\/01\/Big-Ideas-Math-Solutions-Grade-7-Chapter-2-Multiplying-and-Dividing-Rational-Numbers-157.png\" alt=\"Big Ideas Math Solutions Grade 7 Chapter 2 Multiplying and Dividing Rational Numbers 157\" width=\"357\" height=\"91\" srcset=\"https:\/\/ccssanswers.com\/wp-content\/uploads\/2021\/01\/Big-Ideas-Math-Solutions-Grade-7-Chapter-2-Multiplying-and-Dividing-Rational-Numbers-157.png 357w, https:\/\/ccssanswers.com\/wp-content\/uploads\/2021\/01\/Big-Ideas-Math-Solutions-Grade-7-Chapter-2-Multiplying-and-Dividing-Rational-Numbers-157-300x76.png 300w\" sizes=\"(max-width: 357px) 100vw, 357px\" \/><\/p>\n<p>Answer:<br \/>\nB<\/p>\n<p>Explanation:<br \/>\nArea of triangle = 1\/2 . base . height<br \/>\n= 1\/2 . 2(1\/2) . 2<br \/>\n= 2(1\/2)<\/p>\n<p>Question 15.<br \/>\nWhich decimal is equivalent to \\(\\frac{2}{9}\\)?<br \/>\nF. 0.2<br \/>\nG. \\(0 . \\overline{2}\\)<br \/>\nH. 0.29<br \/>\nI. 4.5<\/p>\n<p>Answer:<br \/>\nF. 0.2<\/p>\n<p>Explanation:<br \/>\n2\/9 = 0.222<br \/>\n<img decoding=\"async\" loading=\"lazy\" class=\"alignnone size-full wp-image-43610\" src=\"https:\/\/ccssanswers.com\/wp-content\/uploads\/2021\/01\/big-ideas-math-answers-grade-7-chapter-2-multiplying-and-dividing-rational-numbers-87.jpg\" alt=\"Big Ideas Math Answers Grade 7 Chapter 2 Multiplying and Dividing Rational Numbers 87\" width=\"196\" height=\"504\" srcset=\"https:\/\/ccssanswers.com\/wp-content\/uploads\/2021\/01\/big-ideas-math-answers-grade-7-chapter-2-multiplying-and-dividing-rational-numbers-87.jpg 196w, https:\/\/ccssanswers.com\/wp-content\/uploads\/2021\/01\/big-ideas-math-answers-grade-7-chapter-2-multiplying-and-dividing-rational-numbers-87-117x300.jpg 117w\" sizes=\"(max-width: 196px) 100vw, 196px\" \/><\/p>\n<p><em>Conclusion:<\/em><\/p>\n<p>All the answers to the above questions are prepared by the math experts. We have provided the solutions in pdf format so that you can practice through offline mode also. Go through all the topics and feel free to clarify your doubts by posting the comments in the below comment box.<\/p>\n","protected":false},"excerpt":{"rendered":"<p>The best Big Ideas Math Grade 7 Chapter 2 Multiplying and Dividing Rational Numbers Answer Key PDF is available here. The students who are seeking help in math learning in an easy way can refer to this page. You can find the professionals suggested ways of solving Multiplying and Dividing Rational Numbers questions and learn &#8230; <a title=\"Big Ideas Math Answers Grade 7 Chapter 2 Multiplying and Dividing Rational Numbers\" class=\"read-more\" href=\"https:\/\/ccssanswers.com\/big-ideas-math-answers-grade-7-chapter-2\/\" aria-label=\"More on Big Ideas Math Answers Grade 7 Chapter 2 Multiplying and Dividing Rational Numbers\">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\/29847"}],"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=29847"}],"version-history":[{"count":1,"href":"https:\/\/ccssanswers.com\/wp-json\/wp\/v2\/posts\/29847\/revisions"}],"predecessor-version":[{"id":138555,"href":"https:\/\/ccssanswers.com\/wp-json\/wp\/v2\/posts\/29847\/revisions\/138555"}],"wp:attachment":[{"href":"https:\/\/ccssanswers.com\/wp-json\/wp\/v2\/media?parent=29847"}],"wp:term":[{"taxonomy":"category","embeddable":true,"href":"https:\/\/ccssanswers.com\/wp-json\/wp\/v2\/categories?post=29847"},{"taxonomy":"post_tag","embeddable":true,"href":"https:\/\/ccssanswers.com\/wp-json\/wp\/v2\/tags?post=29847"}],"curies":[{"name":"wp","href":"https:\/\/api.w.org\/{rel}","templated":true}]}}