{"id":4866,"date":"2022-03-26T19:51:22","date_gmt":"2022-03-26T14:21:22","guid":{"rendered":"https:\/\/ccssmathanswers.com\/?p=4866"},"modified":"2022-04-07T12:28:21","modified_gmt":"2022-04-07T06:58:21","slug":"go-math-grade-6-answer-key-chapter-3-understand-positive-and-negative-numbers","status":"publish","type":"post","link":"https:\/\/bigideasmathanswers.com\/go-math-grade-6-answer-key-chapter-3-understand-positive-and-negative-numbers\/","title":{"rendered":"Go Math Grade 6 Answer Key Chapter 3 Understand Positive and Negative Numbers"},"content":{"rendered":"<p>Enhance your knowledge by practicing the problems from Go Math Grade 6 Answer Key Chapter 3 Understand Positive and Negative Numbers. You can get the free pdfs of Go Math Grade 6 Chapter 3 Understand Positive and Negative Numbers Solution Key. We have provided the <a href=\"https:\/\/ccssmathanswers.com\/go-math-grade-6-answer-key\/\" target=\"_blank\" rel=\"noopener noreferrer\">Go Math Grade 6 Answer Key<\/a> in pdf format so that you can practice online and offline mode. Take the given resources as references and score well in the exams.<\/p>\n<h2>Go Math Grade 6 Chapter 3 Understand Positive and Negative Numbers Answer Key<\/h2>\n<p>Improve your math skills with the help of Go Math 6th Standard Answer Key Chapter 3 Understand Positive and Negative Numbers. Unlimited practice with all the maths questions and answers along with the practice questions. It is mandatory to practice with the Grade 6 Chapter 3 Solution key to score maximum marks in the exams. Check out the links given the below sections before you start your preparation.<\/p>\n<p><strong>Lesson 1: Understand Positive and Negative Numbers<\/strong><\/p>\n<ul>\n<li><a href=\"#Understand_Positive_and_Negative_Numbers_\u2013_Page_No._141\">Understand Positive and Negative Numbers \u2013 Page No. 141<\/a><\/li>\n<li><a href=\"#Understand_Positive_and_Negative_Numbers_\u2013_Page_No._142\">Understand Positive and Negative Numbers \u2013 Page No. 142<\/a><\/li>\n<li><a href=\"#Understand_Positive_and_Negative_Numbers_\u2013_Page_No._143\">Understand Positive and Negative Numbers \u2013 Page No. 143<\/a><\/li>\n<li><a href=\"#Understand_Positive_and_Negative_Numbers_Lesson_Check_\u2013_Page_No._144\">Understand Positive and Negative Numbers Lesson Check \u2013 Page No. 144<\/a><\/li>\n<\/ul>\n<p><strong>Lesson 2: Compare and Order Integers<\/strong><\/p>\n<ul>\n<li><a href=\"#Compare_and_Order_Integers_\u2013_Page_No._147\">Compare and Order Integers \u2013 Page No. 147<\/a><\/li>\n<li><a href=\"#Compare_and_Order_Integers_\u2013_Page_No._148\">Compare and Order Integers \u2013 Page No. 148<\/a><\/li>\n<li><a href=\"#Compare_and_Order_Integers_\u2013_Page_No._149\">Compare and Order Integers \u2013 Page No. 149<\/a><\/li>\n<li><a href=\"#Compare_and_Order_Integers_Lesson_Check_\u2013_Page_No._150\">Compare and Order Integers Lesson Check \u2013 Page No. 150<\/a><\/li>\n<\/ul>\n<p><strong>Lesson 3: Rational Numbers and the Number Line<\/strong><\/p>\n<ul>\n<li><a href=\"#Rational_Numbers_and_the_Number_Line_\u2013_Page_No._153\">Rational Numbers and the Number Line \u2013 Page No. 153<\/a><\/li>\n<li><a href=\"#Rational_Numbers_and_the_Number_Line_\u2013_Page_No._154\">Rational Numbers and the Number Line \u2013 Page No. 154<\/a><\/li>\n<li><a href=\"#Rational_Numbers_and_the_Number_Line_\u2013_Page_No._155\">Rational Numbers and the Number Line \u2013 Page No. 155<\/a><\/li>\n<li><a href=\"#Rational_Numbers_and_the_Number_Line_Lesson_Check\u2013_Page_No._156\">Rational Numbers and the Number Line Lesson Check\u2013 Page No. 156<\/a><\/li>\n<\/ul>\n<p><strong>Lesson 4: Compare and Order Rational Numbers<\/strong><\/p>\n<ul>\n<li><a href=\"#Compare_and_Order_Rational_Numbers_\u2013_Page_No._159\">Compare and Order Rational Numbers \u2013 Page No. 159<\/a><\/li>\n<li><a href=\"#Compare_and_Order_Rational_Numbers_\u2013_Page_No._160\">Compare and Order Rational Numbers \u2013 Page No. 160<\/a><\/li>\n<li><a href=\"#Compare_and_Order_Rational_Numbers_\u2013_Page_No._161\">Compare and Order Rational Numbers \u2013 Page No. 161<\/a><\/li>\n<li><a href=\"#Compare_and_Order_Rational_Numbers_Lesson_Check_\u2013_Page_No._162\">Compare and Order Rational Numbers Lesson Check \u2013 Page No. 162<\/a><\/li>\n<\/ul>\n<p><strong>Mid-Chapter Checkpoint<\/strong><\/p>\n<ul>\n<li><a href=\"#Mid-Chapter_Checkpoint_\u2013_Page_No._163\">Mid-Chapter Checkpoint \u2013 Page No. 163<\/a><\/li>\n<li><a href=\"#Mid-Chapter_Checkpoint_\u2013_Page_No._164\">Mid-Chapter Checkpoint \u2013 Page No. 164<\/a><\/li>\n<\/ul>\n<p><strong>Lesson 5: Absolute Value<\/strong><\/p>\n<ul>\n<li><a href=\"#Absolute_Value_\u2013_Page_No._167\">Absolute Value \u2013 Page No. 167<\/a><\/li>\n<li><a href=\"#Absolute_Value_\u2013_Page_No._168\">Absolute Value \u2013 Page No. 168<\/a><\/li>\n<li><a href=\"#Absolute_Value_\u2013_Page_No._169\">Absolute Value \u2013 Page No. 169<\/a><\/li>\n<li><a href=\"#Absolute_Value_\u2013_Page_No._170\">Absolute Value \u2013 Page No. 170<\/a><\/li>\n<\/ul>\n<p><strong>Lesson 6: Compare Absolute Values<\/strong><\/p>\n<ul>\n<li><a href=\"#Compare_Absolute_Values_\u2013_Page_No._173\">Compare Absolute Values \u2013 Page No. 173<\/a><\/li>\n<li><a href=\"#Compare_Absolute_Values_\u2013_Page_No._174\">Compare Absolute Values \u2013 Page No. 174<\/a><\/li>\n<li><a href=\"#Compare_Absolute_Values_\u2013_Page_No._175\">Compare Absolute Values \u2013 Page No. 175<\/a><\/li>\n<li><a href=\"#Compare_Absolute_Values_\u2013_Page_No._176\">Compare Absolute Values \u2013 Page No. 176<\/a><\/li>\n<\/ul>\n<p><strong>Lesson 7: Rational Numbers and the Coordinate Plane<\/strong><\/p>\n<ul>\n<li><a href=\"#Rational_Numbers_and_the_Coordinate_Plane_\u2013_Page_No._179\">Rational Numbers and the Coordinate Plane \u2013 Page No. 179<\/a><\/li>\n<li><a href=\"#Rational_Numbers_and_the_Coordinate_Plane_\u2013_Page_No._180\">Rational Numbers and the Coordinate Plane \u2013 Page No. 180<\/a><\/li>\n<li><a href=\"#Rational_Numbers_and_the_Coordinate_Plane_\u2013_Page_No._181\">Rational Numbers and the Coordinate Plane \u2013 Page No. 181<\/a><\/li>\n<li><a href=\"#Rational_Numbers_and_the_Coordinate_Plane_\u2013_Page_No._182\">Rational Numbers and the Coordinate Plane \u2013 Page No. 182<\/a><\/li>\n<\/ul>\n<p><strong>Lesson 8: Ordered Pair Relationships<\/strong><\/p>\n<ul>\n<li><a href=\"#Ordered_Pair_Relationships_\u2013_Page_No._185\">Ordered Pair Relationships \u2013 Page No. 185<\/a><\/li>\n<li><a href=\"#Ordered_Pair_Relationships_\u2013_Page_No._186\">Ordered Pair Relationships \u2013 Page No. 186<\/a><\/li>\n<li><a href=\"#Ordered_Pair_Relationships_\u2013_Page_No._187\">Ordered Pair Relationships \u2013 Page No. 187<\/a><\/li>\n<li><a href=\"#Ordered_Pair_Relationships_\u2013_Page_No._188\">Ordered Pair Relationships \u2013 Page No. 188<\/a><\/li>\n<\/ul>\n<p><strong>Lesson 9: Distance on the Coordinate Plane<\/strong><\/p>\n<ul>\n<li><a href=\"#Distance_on_the_Coordinate_Plane_\u2013_Page_No._191\">Distance on the Coordinate Plane \u2013 Page No. 191<\/a><\/li>\n<li><a href=\"#Distance_on_the_Coordinate_Plane_\u2013_Page_No._192\">Distance on the Coordinate Plane \u2013 Page No. 192<\/a><\/li>\n<li><a href=\"#Distance_on_the_Coordinate_Plane_\u2013_Page_No._193\">Distance on the Coordinate Plane \u2013 Page No. 193<\/a><\/li>\n<li><a href=\"#Distance_on_the_Coordinate_Plane_\u2013_Page_No._194\">Distance on the Coordinate Plane \u2013 Page No. 194<\/a><\/li>\n<\/ul>\n<p><strong>Lesson 10: Problem Solving \u2022 The Coordinate Plane<\/strong><\/p>\n<ul>\n<li><a href=\"#The_Coordinate_Plane_\u2013_Page_No._197\">The Coordinate Plane \u2013 Page No. 197<\/a><\/li>\n<li><a href=\"#The_Coordinate_Plane_\u2013_Page_No._198\">The Coordinate Plane \u2013 Page No. 198<\/a><\/li>\n<li><a href=\"#The_Coordinate_Plane_\u2013_Page_No._199\">The Coordinate Plane \u2013 Page No. 199<\/a><\/li>\n<li><a href=\"#The_Coordinate_Plane_\u2013_Page_No._200\">The Coordinate Plane \u2013 Page No. 200<\/a><\/li>\n<\/ul>\n<p><strong>Chapter 3 Review\/Test<\/strong><\/p>\n<ul>\n<li><a href=\"#Review\/Test_\u2013_Page_No._201\">Review\/Test \u2013 Page No. 201<\/a><\/li>\n<li><a href=\"#Review\/Test_\u2013_Page_No._202\">Review\/Test \u2013 Page No. 202<\/a><\/li>\n<li><a href=\"#Review\/Test_\u2013_Page_No._203\">Review\/Test \u2013 Page No. 203<\/a><\/li>\n<li><a href=\"#Review\/Test_\u2013_Page_No._204\">Review\/Test \u2013 Page No. 204<\/a><\/li>\n<li><a href=\"#Review\/Test_\u2013_Page_No._205\">Review\/Test \u2013 Page No. 205<\/a><\/li>\n<li><a href=\"#Review\/Test_\u2013_Page_No._206\">Review\/Test \u2013 Page No. 206<\/a><\/li>\n<\/ul>\n<h3><a id=\"Understand_Positive_and_Negative_Numbers_\u2013_Page_No._141\"><\/a>Share and Show &#8211; Page No. 141<\/h3>\n<p><strong>Graph the integer and its opposite on a number line.<\/strong><\/p>\n<p>Question 1.<br \/>\n\u22127<br \/>\nType below:<br \/>\n__________<\/p>\n<p>Answer:<br \/>\n7<\/p>\n<p>Explanation:<br \/>\nThe opposite number of -7 is 7<\/p>\n<p>Question 2.<br \/>\n9<br \/>\nType below:<br \/>\n__________<\/p>\n<p>Answer:<br \/>\n-9<\/p>\n<p>Explanation:<br \/>\nThe opposite number of 9 is -9<\/p>\n<p><strong>Name the integer that represents the situation, and tell what 0 represents in that situation.<\/strong><br \/>\n<img loading=\"lazy\" src=\"https:\/\/ccssmathanswers.com\/wp-content\/uploads\/2020\/08\/Go-Math-Grade-6-Answer-Key-Chapter-3-Understand-Positive-and-Negative-Numbers-img-1.jpg\" alt=\"Go Math Grade 6 Answer Key Chapter 3 Understand Positive and Negative Numbers img 1\" width=\"737\" height=\"159\" \/><\/p>\n<p>Question 3.<br \/>\nType below:<br \/>\n__________<\/p>\n<p>Answer:<br \/>\nInteger: 24<br \/>\n0 represents: neither gaining nor losing points<\/p>\n<p>Explanation:<br \/>\nKerri gained 24 pounds during a round of the game show. So, he has a positive integer.<\/p>\n<p>Question 4.<br \/>\nType below:<br \/>\n__________<\/p>\n<p>Answer:<br \/>\nInteger: -5<br \/>\n0 represents: Ben neither gains nor loses during the summer<\/p>\n<p>Explanation:<br \/>\nBen lost 5 points during the summer. He has a negative integer.<\/p>\n<p>Question 5.<br \/>\nType below:<br \/>\n__________<\/p>\n<p>Answer:<br \/>\nInteger: 35<br \/>\n0 represents: No changes in her savings account.<\/p>\n<p>Explanation:<br \/>\nMarcy deposited $35 in her savings account. She has a positive integer.<\/p>\n<p><strong>On Your Own<\/strong><\/p>\n<p><strong>Write the opposite of the integer.<\/strong><\/p>\n<p>Question 6.<br \/>\n\u221298<br \/>\nType below:<br \/>\n__________<\/p>\n<p>Answer:<br \/>\n98<\/p>\n<p>Explanation:<br \/>\nThe integer \u221298 is on the left side of 0.<br \/>\nSo, the opposite of -98 is 98<\/p>\n<p>Question 7.<br \/>\n0<br \/>\nType below:<br \/>\n__________<\/p>\n<p>Answer:<br \/>\n0<\/p>\n<p>Explanation:<br \/>\nOpposite of 0 is 0<\/p>\n<p>Question 8.<br \/>\n\u221253<br \/>\nType below:<br \/>\n__________<\/p>\n<p>Answer:<br \/>\n53<\/p>\n<p>Explanation:<br \/>\nThe integer \u221253 is on the left side of 0.<br \/>\nSo, the opposite of -53 is 53<\/p>\n<p><strong>Name the integer that represents the situation, and tell what 0 represents in that situation.<\/strong><br \/>\n<img loading=\"lazy\" src=\"https:\/\/ccssmathanswers.com\/wp-content\/uploads\/2020\/08\/Go-Math-Grade-6-Answer-Key-Chapter-3-Understand-Positive-and-Negative-Numbers-img-2.jpg\" alt=\"Go Math Grade 6 Answer Key Chapter 3 Understand Positive and Negative Numbers img 2\" width=\"754\" height=\"159\" \/><\/p>\n<p>Question 9.<br \/>\nType below:<br \/>\n__________<\/p>\n<p>Answer:<br \/>\nInteger: $850<br \/>\n0 represents: Desmond neither gains nor loses at his summer job<\/p>\n<p>Question 10.<br \/>\nType below:<br \/>\n__________<\/p>\n<p>Answer:<br \/>\nInteger: -300<br \/>\n0 represents: No change from his checking point<\/p>\n<p>Question 11.<br \/>\nType below:<br \/>\n__________<\/p>\n<p>Answer:<br \/>\nInteger: 2<br \/>\n0 represents: No change of protons than electrons<\/p>\n<p><strong>Write the opposite of the opposite of the integer.<\/strong><\/p>\n<p>Question 12.<br \/>\n\u221223<br \/>\nType below:<br \/>\n__________<\/p>\n<p>Answer:<br \/>\n-23<\/p>\n<p>Explanation:<br \/>\nThe opposite integer of the -23 is 23<br \/>\nThe opposite integer of the 23 is -23.<br \/>\nSo, the opposite of the opposite of the integer -23 is -23.<\/p>\n<p>Question 13.<br \/>\n17<br \/>\nType below:<br \/>\n__________<\/p>\n<p>Answer:<br \/>\n17<\/p>\n<p>Explanation:<br \/>\nThe opposite integer of the 17 is -17<br \/>\nThe opposite integer of the -17 is 17.<br \/>\nSo, the opposite of the opposite of the integer 17 is 17.<\/p>\n<p>Question 14.<br \/>\n\u2212125<br \/>\nType below:<br \/>\n__________<\/p>\n<p>Answer:<br \/>\n-125<\/p>\n<p>Explanation:<br \/>\nThe opposite integer of the -125 is 125<br \/>\nThe opposite integer of the 125 is -125.<br \/>\nSo, the opposite of the opposite of the integer -125 is -125.<\/p>\n<p>Question 15.<br \/>\nSuppose you know a certain number\u2019s distance from zero on the number line. Explain how you could find the number\u2019s distance from its opposite.<br \/>\nType below:<br \/>\n__________<\/p>\n<p>Answer:<br \/>\nThe distance between a number\u2019s place on the number line and 0 is called the number\u2019s [absolute value]. To write the absolute value of a number, use short vertical lines (|) on either side of the number. For example, the absolute value of \u22125 is written |\u22125|<\/p>\n<h3><a id=\"Understand_Positive_and_Negative_Numbers_\u2013_Page_No._142\"><\/a>Problem Solving + Applications &#8211; Page No. 142<\/h3>\n<p><strong>Wind makes the air temperature seem colder. The chart gives the wind chill temperature (what the temperature seems like) at several air temperatures and wind speeds. Use the chart for 16\u201318.<\/strong><br \/>\n<img loading=\"lazy\" src=\"https:\/\/ccssmathanswers.com\/wp-content\/uploads\/2020\/08\/Go-Math-Grade-6-Answer-Key-Chapter-3-Understand-Positive-and-Negative-Numbers-img-3.jpg\" alt=\"Go Math Grade 6 Answer Key Chapter 3 Understand Positive and Negative Numbers img 3\" width=\"294\" height=\"228\" \/><\/p>\n<p>Question 16.<br \/>\nAt 6 a.m., the air temperature was 20\u00b0F and the wind speed was 55 mi\/hr. What was the wind chill temperature at 6 a.m.?<br \/>\nType below:<br \/>\n__________<\/p>\n<p>Answer:<br \/>\nAt 6 a.m., the air temperature was 20\u00b0F and the wind speed was 55 mi\/hr.<br \/>\nThe winds chill temperature at 6 a.m. is -4<\/p>\n<p>Question 17.<br \/>\nAt noon, the air temperature was 15\u00b0F and the wind speed was 45 mi\/hr. At what air temperature and wind speed would the wind chill temperature be the opposite of what it was at noon?<br \/>\nType below:<br \/>\n__________<\/p>\n<p>Answer:<br \/>\nIf the air temperature was 15\u00b0F and the wind speed was 45 mi\/hr, the wind chill temperature is -9. The opposite number of -9 is 9.<br \/>\nSo, at the air temperature was 25\u00b0F and the wind speed was 25 mi\/hr, the wind chill temperature is the opposite of what it was at noon.<\/p>\n<p>Question 18.<br \/>\nThe wind was blowing 35 mi\/hr in both Ashton and Fenton. The wind chill temperatures in the two towns were opposites. If the air temperature in Ashton was 25\u00b0F, what was the air temperature in Fenton?<br \/>\nType below:<br \/>\n__________<\/p>\n<p>Answer:<br \/>\nThe wind was blowing 35 mi\/hr in both Ashton and Fenton.<br \/>\nIf the air temperature in Ashton was 25\u00b0F, the wind chill temperature is 7.<br \/>\nThe wind chill temperatures in the two towns were opposites.<br \/>\nSo, the wind chill temperature in Fenton is -7. So, the air temperature in Fenton was 15\u00b0F.<\/p>\n<p>Question 19.<br \/>\nSense or Nonsense? Claudia states that the opposite of any integer is always a different number than the integer. Is Claudia\u2019s statement sense or nonsense? Explain.<br \/>\nType below:<br \/>\n__________<\/p>\n<p>Answer:<br \/>\nClaudia is correct.<br \/>\nBecause the opposite of any integer is always a different number than the integer.<br \/>\nExample: The opposite of 7 is -7.<\/p>\n<p>Question 20.<br \/>\nFor numbers 20a\u221220d, choose Yes or No to indicate whether the situation can be represented by a negative number.<br \/>\n20a. Death Valley is located 282 feet below sea level.<br \/>\n20b. Austin\u2019s golf score was 3 strokes below par.<br \/>\n20c. The average temperature in Santa Monica in August is 75\u00b0F.<br \/>\n20d. Janai withdraws $20 from her bank account.<br \/>\n20a. __________<br \/>\n20b. __________<br \/>\n20c. __________<br \/>\n20d. __________<\/p>\n<p>Answer:<br \/>\n20a. Yes<br \/>\n20b. Yes<br \/>\n20c. No<br \/>\n20d. Yes<\/p>\n<h3><a id=\"Understand_Positive_and_Negative_Numbers_\u2013_Page_No._143\"><\/a>Understand Positive and Negative Numbers &#8211; Page No. 143<\/h3>\n<p><strong>Graph the integer and its opposite on a number line.<\/strong><\/p>\n<p>Question 1.<br \/>\n\u22126<br \/>\nType below:<br \/>\n__________<\/p>\n<p>Answer:<br \/>\n6<br \/>\n<img loading=\"lazy\" class=\"alignnone size-medium wp-image-7182\" src=\"https:\/\/ccssmathanswers.com\/wp-content\/uploads\/2020\/08\/grade-6-chapter-3-image-1-300x46.jpg\" alt=\"grade 6 chapter 3 image 1\" width=\"300\" height=\"46\" srcset=\"https:\/\/bigideasmathanswers.com\/wp-content\/uploads\/2020\/08\/grade-6-chapter-3-image-1-300x46.jpg 300w, https:\/\/bigideasmathanswers.com\/wp-content\/uploads\/2020\/08\/grade-6-chapter-3-image-1.jpg 322w\" sizes=\"(max-width: 300px) 100vw, 300px\" \/><\/p>\n<p>Explanation:<br \/>\nThe opposite number of -6 is 6<\/p>\n<p>Question 2.<br \/>\n3<br \/>\nType below:<br \/>\n__________<\/p>\n<p>Answer:<br \/>\n-3<br \/>\n<img loading=\"lazy\" class=\"alignnone size-medium wp-image-7183\" src=\"https:\/\/ccssmathanswers.com\/wp-content\/uploads\/2020\/08\/grade-6-chapter-3-image-2-300x48.jpg\" alt=\"grade 6 chapter 3 image 2\" width=\"300\" height=\"48\" srcset=\"https:\/\/bigideasmathanswers.com\/wp-content\/uploads\/2020\/08\/grade-6-chapter-3-image-2-300x48.jpg 300w, https:\/\/bigideasmathanswers.com\/wp-content\/uploads\/2020\/08\/grade-6-chapter-3-image-2.jpg 315w\" sizes=\"(max-width: 300px) 100vw, 300px\" \/><\/p>\n<p>Explanation:<br \/>\nThe opposite number of -3 is 3<\/p>\n<p>Question 3.<br \/>\n10<br \/>\nType below:<br \/>\n__________<\/p>\n<p>Answer:<br \/>\n-10<br \/>\n<img loading=\"lazy\" class=\"alignnone size-medium wp-image-7184\" src=\"https:\/\/ccssmathanswers.com\/wp-content\/uploads\/2020\/08\/grade-6-chapter-3-image-3-300x45.jpg\" alt=\"grade 6 chapter 3 image 3\" width=\"300\" height=\"45\" srcset=\"https:\/\/bigideasmathanswers.com\/wp-content\/uploads\/2020\/08\/grade-6-chapter-3-image-3-300x45.jpg 300w, https:\/\/bigideasmathanswers.com\/wp-content\/uploads\/2020\/08\/grade-6-chapter-3-image-3.jpg 326w\" sizes=\"(max-width: 300px) 100vw, 300px\" \/><\/p>\n<p>Explanation:<br \/>\nThe opposite number of 10 is -10<\/p>\n<p>Question 4.<br \/>\n\u22128<br \/>\nType below:<br \/>\n__________<\/p>\n<p>Answer:<br \/>\n8<br \/>\n<img loading=\"lazy\" class=\"alignnone size-medium wp-image-7185\" src=\"https:\/\/ccssmathanswers.com\/wp-content\/uploads\/2020\/08\/grade-6-chapter-3-image-4-300x46.jpg\" alt=\"grade 6 chapter 3 image 4\" width=\"300\" height=\"46\" srcset=\"https:\/\/bigideasmathanswers.com\/wp-content\/uploads\/2020\/08\/grade-6-chapter-3-image-4-300x46.jpg 300w, https:\/\/bigideasmathanswers.com\/wp-content\/uploads\/2020\/08\/grade-6-chapter-3-image-4.jpg 322w\" sizes=\"(max-width: 300px) 100vw, 300px\" \/><\/p>\n<p>Explanation:<br \/>\nThe opposite number of -8 is 8<\/p>\n<p><strong>Name the integer that represents the situation, and tell what 0 represents in that situation<\/strong><br \/>\n<img loading=\"lazy\" src=\"https:\/\/ccssmathanswers.com\/wp-content\/uploads\/2020\/08\/Go-Math-Grade-6-Answer-Key-Chapter-3-Understand-Positive-and-Negative-Numbers-img-4.jpg\" alt=\"Go Math Grade 6 Answer Key Chapter 3 Understand Positive and Negative Numbers img 4\" width=\"771\" height=\"201\" \/><\/p>\n<p>Question 5.<br \/>\nType below:<br \/>\n__________<\/p>\n<p>Answer:<br \/>\nInteger: -60<br \/>\n0 represents: No changes in the account balance<\/p>\n<p>Explanation:<\/p>\n<p>Question 6.<br \/>\nType below:<br \/>\n__________<\/p>\n<p>Answer:<br \/>\nInteger: 12<br \/>\n0 represents: neither gaining nor losing points<\/p>\n<p>Explanation:<\/p>\n<p><strong>Write the opposite of the opposite of the integer.<\/strong><\/p>\n<p>Question 7.<br \/>\n\u221220<br \/>\nType below:<br \/>\n__________<\/p>\n<p>Answer:<br \/>\n-20<\/p>\n<p>Explanation:<br \/>\nThe opposite integer of the -20 is 20<br \/>\nThe opposite integer of the 20 is -20.<br \/>\nSo, the opposite of the opposite of the integer -20 is -20<\/p>\n<p>Question 8.<br \/>\n4<br \/>\nType below:<br \/>\n__________<\/p>\n<p>Answer:<br \/>\n4<\/p>\n<p>Explanation:<br \/>\nThe opposite integer of the 4 is -4<br \/>\nThe opposite integer of the -4 is 4.<br \/>\nSo, the opposite of the opposite of the integer -4 is 4.<\/p>\n<p>Question 9.<br \/>\n95<br \/>\nType below:<br \/>\n__________<\/p>\n<p>Answer:<br \/>\n95<\/p>\n<p>Explanation:<br \/>\nThe opposite integer of the 95 is -95<br \/>\nThe opposite integer of the -95 is 95.<br \/>\nSo, the opposite of the opposite of the integer 95 is 95.<\/p>\n<p>Question 10.<br \/>\n\u221263<br \/>\nType below:<br \/>\n__________<\/p>\n<p>Answer:<br \/>\n-63<\/p>\n<p>Explanation:<br \/>\nThe opposite integer of the -63 is 63<br \/>\nThe opposite integer of the 63 is -63.<br \/>\nSo, the opposite of the opposite of the integer -63 is -63.<\/p>\n<p><strong>Problem Solving<\/strong><\/p>\n<p>Question 11.<br \/>\nDakshesh won a game by scoring 25 points. Randy scored the opposite number of points as Dakshesh. What is Randy\u2019s score?<br \/>\nType below:<br \/>\n__________<\/p>\n<p>Answer:<br \/>\nRandy\u2019s score -25.<\/p>\n<p>Explanation:<br \/>\nDakshesh won a game by scoring 25 points. Randy scored the opposite number of points as Dakshesh.<br \/>\nThe opposite number of 25 is -25<\/p>\n<p>Question 12.<br \/>\nWhen Dakshesh and Randy played the game again, Dakshesh scored the opposite of the opposite of his first score. What is his score?<br \/>\nType below:<br \/>\n__________<\/p>\n<p>Answer:<br \/>\n25 points<\/p>\n<p>Explanation:<br \/>\nWhen Dakshesh and Randy played the game again, Dakshesh scored the opposite of the opposite of his first score.<br \/>\nThe opposite of the 25 is -25.<br \/>\nThe opposite of the -25 is 25.<br \/>\nThe opposite of the opposite of his first score is 25<\/p>\n<p>Question 13.<br \/>\nGive three examples of when negative numbers are used in daily life.<br \/>\nType below:<br \/>\n__________<\/p>\n<p>Answer:<br \/>\n1) negative numbers in weather reports and on food packaging. The temperature -5\u00b0C is \u2018negative five degrees\u2019 and it means 5 degrees below zero.<br \/>\n2) The floors as you go down in a lift, starting on the third floor you\u2019ll see:<br \/>\n3, 2, 1, 0, -1, -2.<br \/>\nIn this example building, -2 is the second floor underground<br \/>\n3) When you spend more money than you have in your bank account it shows up as a negative number.<\/p>\n<h3><a id=\"Understand_Positive_and_Negative_Numbers_Lesson_Check_\u2013_Page_No._144\"><\/a>Lesson Check &#8211; Page No. 144<\/h3>\n<p><strong>Name the integers that represent each situation.<\/strong><\/p>\n<p>Question 1.<br \/>\nDuring their first round of golf, Imani was 7 strokes over par and Peter was 8 strokes below par.<br \/>\nType below:<br \/>\n__________<\/p>\n<p>Answer:<br \/>\nIn the first round of golf, Imani has scored 7 strokes over par. So, it is represented by 7.<br \/>\nPeter was scored 8 strokes below par. So, it is represented by -8.<br \/>\nTherefore, the answer is 7 and -8.<\/p>\n<p>Question 2.<br \/>\nWyatt earned $15 baby-sitting on Saturday. Wilson spent $12 at the movies.<br \/>\nType below:<br \/>\n__________<\/p>\n<p>Answer:<br \/>\nHe has $3 dollars left because you take 12 from 15 and you get 3<br \/>\n$15 &#8211; $12 = $3<\/p>\n<p><strong>Spiral Review<\/strong><\/p>\n<p>Question 3.<br \/>\nMr. Nolan\u2019s code for his ATM card is a 4-digit number. The digits of the code are the prime factors of 84 listed from least to greatest. What is the code for Mr. Nolan\u2019s ATM card?<br \/>\nType below:<br \/>\n__________<\/p>\n<p>Answer:<br \/>\n2237<\/p>\n<p>Explanation:<br \/>\nMr.Nolan&#8217;s code for his ATM card is a 4- digit number.<br \/>\nThe digits of the code are the prime factors of 84 listed from least to greatest.<br \/>\nIn order to find the code, we have to find the prime factors of 84.<br \/>\nThe prime factors of 84 are 2,2,3 and 7.<br \/>\nTherefore, the code=2237<\/p>\n<p>Question 4.<br \/>\nOver a four-year period, a tree grew 2.62 feet. If the tree grows at a constant rate, how many feet did the tree grow each year?<br \/>\nType below:<br \/>\n__________<\/p>\n<p>Answer:<br \/>\n0.655 feet<\/p>\n<p>Explanation:<br \/>\nEach year the tree grows<br \/>\n( 2.62 \u00f7 4 ) feet<br \/>\n= 0.655 feet<\/p>\n<p>Question 5.<br \/>\nOmarion has \\(\\frac{9}{10}\\) of the pages in a book remaining to read for school. He reads \\(\\frac{2}{3}\\) of the remaining pages over the weekend. What fraction of the book does Omarion read over the weekend?<br \/>\nType below:<br \/>\n__________<\/p>\n<p>Answer:<br \/>\n\\(\\frac{3}{5}\\)<\/p>\n<p>Explanation:<br \/>\nOmarion has 9\/10 of pages in a book remaining to read for school and he reads 2\/3 of the remaining pages over the weekend.<br \/>\nThe fraction of the book trade over the weekend = the fraction of the pages read over the weekend multiplied by the fraction of the book that is remaining to be read.<br \/>\nTherefore, the fraction of the book that Omarion trad over the weekend is 2\/3 \u00d7 9\/10 = 3\/5<br \/>\nThus, the required fraction of the book that Omarion trad over the weekend is 3\/5<\/p>\n<p>Question 6.<br \/>\nMarianne has \\(\\frac{5}{8}\\) pound of peas. She cooks \\(\\frac{2}{3}\\) of those peas for 5 people. If each person is served an equal amount, how much peas did each person get?<br \/>\nType below:<br \/>\n__________<\/p>\n<p>Answer:<br \/>\n\\(\\frac{1}{12}\\) pounds<\/p>\n<p>Explanation:<br \/>\nMarianne has \\(\\frac{5}{8}\\) pound of peas. IShe cooks \\(\\frac{2}{3}\\) of those peas for 5 people.<br \/>\nMarianne cooks 5\/8 \u00d7 2\/3 = 5\/12 pounds.<br \/>\n(5\/12)\/5 = 1\/12 pounds<\/p>\n<p><strong>the answer is<\/strong><\/p>\n<h3><a id=\"Compare_and_Order_Integers_\u2013_Page_No._147\"><\/a>Share and Show &#8211; Page No. 147<\/h3>\n<p><strong>Compare the numbers. Write &lt; or &gt;.<\/strong><\/p>\n<p>Question 1.<br \/>\n<sup>&#8211;<\/sup>8 _____ 6<\/p>\n<p>Answer:<br \/>\n\u20138 &lt; 6<\/p>\n<p>Explanation:<br \/>\n-8 is to the left of 6 on the number line.<br \/>\nSo, -8 is less than 6.<\/p>\n<p>Question 2.<br \/>\n1 _____ <sup>&#8211;<\/sup>8<\/p>\n<p>Answer:<br \/>\n1 &gt; \u20138<\/p>\n<p>Explanation:<br \/>\n1 is to the right of -8 on the number line.<br \/>\nSo, 1 is greater than -8.<\/p>\n<p>Question 3.<br \/>\n<sup>&#8211;<\/sup>4 _____ 0<\/p>\n<p>Answer:<br \/>\n-4 &lt; 0<\/p>\n<p>Explanation:<br \/>\n-4 is to the left of 0 on the number line.<br \/>\nSo, -4 is less than 0.<\/p>\n<p>Question 4.<br \/>\n3 _____ <sup>&#8211;<\/sup>7<\/p>\n<p>Answer:<br \/>\n3 &gt; -7<\/p>\n<p>Explanation:<br \/>\n3 is to the right of -7 on the number line.<br \/>\nSo, 3 is greater than -7.<\/p>\n<p><strong>Order the numbers from least to greatest.<\/strong><\/p>\n<p>Question 5.<br \/>\n4, <sup>&#8211;<\/sup>3, <sup>&#8211;<\/sup>7<br \/>\nType below:<br \/>\n__________<\/p>\n<p>Answer:<br \/>\n-7, -3, 4<\/p>\n<p>Explanation:<br \/>\n-7 is to the left of -3 on the number line. -3 is to the left of 4 on the number line.<br \/>\nSo, -7 &lt; -3 &lt; 4<\/p>\n<p>Question 6.<br \/>\n0, <sup>&#8211;<\/sup>1, 3<br \/>\nType below:<br \/>\n__________<\/p>\n<p>Answer:<br \/>\n-1, 0, 3<\/p>\n<p>Explanation:<br \/>\n-1 is to the left of 0 on the number line. 0 is to the left of 3 on the number line.<br \/>\nSo, -1 &lt; 0 &lt; 3<\/p>\n<p>Question 7.<br \/>\n<sup>&#8211;<\/sup>5, <sup>&#8211;<\/sup>3, <sup>&#8211;<\/sup>9<br \/>\nType below:<br \/>\n__________<\/p>\n<p>Answer:<br \/>\n-9, -5, -3<\/p>\n<p>Explanation:<br \/>\n-9 is to the left of -5 on the number line. -5 is to the left of -3 on the number line.<br \/>\nSo, -9 &lt; -5 &lt; -3<\/p>\n<p><strong>Order the numbers from greatest to least.<\/strong><\/p>\n<p>Question 8.<br \/>\n<sup>&#8211;<\/sup>1, <sup>&#8211;<\/sup>4, 2<br \/>\nType below:<br \/>\n__________<\/p>\n<p>Answer:<br \/>\n2, -1, -4<\/p>\n<p>Explanation:<br \/>\n2 is to the right of -1 on the number line. -1 is to the right of -4 on the number line.<br \/>\nSo, 2 &gt; -1 &gt; -4<\/p>\n<p>Question 9.<br \/>\n5, 0, 10<br \/>\nType below:<br \/>\n__________<\/p>\n<p>Answer:<br \/>\n10, 5, 0<\/p>\n<p>Explanation:<br \/>\n10 is to the right of 5 on the number line. 5 is to the right of 0 on the number line.<br \/>\nSo, 10 &gt; 5 &gt; 0<\/p>\n<p>Question 10.<br \/>\n<sup>&#8211;<\/sup>5, <sup>&#8211;<\/sup>4, <sup>&#8211;<\/sup>3<br \/>\nType below:<br \/>\n__________<\/p>\n<p>Answer:<br \/>\n-3, -4, -5<\/p>\n<p>Explanation:<br \/>\n-3 is to the right of -4 on the number line. -4 is to the right of -5 on the number line.<br \/>\nSo, -3 &gt; -4 &gt; -5<\/p>\n<p><strong>On Your Own<\/strong><\/p>\n<p><strong>Order the numbers from least to greatest.<\/strong><\/p>\n<p>Question 11.<br \/>\n2, 1, <sup>&#8211;<\/sup>1<br \/>\nType below:<br \/>\n__________<\/p>\n<p>Answer:<br \/>\n-1, 1, 2<\/p>\n<p>Explanation:<br \/>\n-1 is to the left of 1 on the number line. 1 is to the left of 2 on the number line.<br \/>\nSo, -1 &lt; 1 &lt; 2<\/p>\n<p>Question 12.<br \/>\n<sup>&#8211;<\/sup>6, <sup>&#8211;<\/sup>12, 30<br \/>\nType below:<br \/>\n__________<\/p>\n<p>Answer:<br \/>\n-12, -6, 30<\/p>\n<p>Explanation:<br \/>\n-12 is to the left of -6 on the number line. -6 is to the left of 30 on the number line.<br \/>\nSo, -12 &lt; -6 &lt; 30<\/p>\n<p>Question 13.<br \/>\n15, <sup>&#8211;<\/sup>9, <sup>&#8211;<\/sup>20<br \/>\nType below:<br \/>\n__________<\/p>\n<p>Answer:<br \/>\n-20, -15, -9<\/p>\n<p>Explanation:<br \/>\n-20 is to the left of -15 on the number line. -15 is to the left of -9 on the number line.<br \/>\nSo, -20 &lt; -15 &lt; -9<\/p>\n<p><strong>Order the number from greatest to least.<\/strong><\/p>\n<p>Question 14.<br \/>\n<sup>&#8211;<\/sup>13, 14, <sup>&#8211;<\/sup>14<br \/>\nType below:<br \/>\n__________<\/p>\n<p>Answer:<br \/>\n14, -13, -14<\/p>\n<p>Explanation:<br \/>\n14 is to the right of -13 on the number line. -13 is to the right of -14 on the number line.<br \/>\nSo, 14 &gt; -13 &gt; -14<\/p>\n<p>Question 15.<br \/>\n<sup>&#8211;<\/sup>20, <sup>&#8211;<\/sup>30, <sup>&#8211;<\/sup>40<br \/>\nType below:<br \/>\n__________<\/p>\n<p>Answer:<br \/>\n-20, -30, -40<\/p>\n<p>Explanation:<br \/>\n-20 is to the right of -30 on the number line. -30 is to the right of -40 on the number line.<br \/>\nSo, -20 &gt; -30 &gt; -40<\/p>\n<p>Question 16.<br \/>\n9, <sup>&#8211;<\/sup>37, 0<br \/>\nType below:<br \/>\n__________<\/p>\n<p>Answer:<br \/>\n9, 0, -37<\/p>\n<p>Explanation:<br \/>\n9 is to the right of 0 on the number line. 0 is to the right of -37 on the number line.<br \/>\nSo, 9 &gt; 0 &gt; -37<\/p>\n<p>Question 17.<br \/>\nSaturday\u2019s low temperature was \u22126\u00b0F. Sunday\u2019s low temperature was 3\u00b0F. Monday\u2019s low temperature was \u22122\u00b0F. Tuesday\u2019s low temperature was 5\u00b0F. Which day\u2019s low temperature was closest to 0\u00b0F?<br \/>\nType below:<br \/>\n__________<\/p>\n<p>Answer:<br \/>\nMonday\u2019s temperature was closest to 0\u00b0F<\/p>\n<p>Explanation:<br \/>\nSaturday\u2019s low temperature was \u22126\u00b0F. Sunday\u2019s low temperature was 3\u00b0F. Monday\u2019s low temperature was \u22122\u00b0F. Tuesday\u2019s low temperature was 5\u00b0F.<br \/>\n-2 is closest to 0. So, Monday\u2019s temperature was closest to 0\u00b0F.<\/p>\n<p>Question 18.<br \/>\nUse Symbols Write a comparison using &lt; or &gt; to show that South America\u2019s Valdes Peninsula (elevation \u2212131 ft) is lower than Europe\u2019s Caspian Sea (elevation \u221292 ft).<br \/>\nType below:<br \/>\n__________<\/p>\n<p>Answer:<br \/>\nSouth America\u2019s Valdes Peninsula &lt; Europe\u2019s Caspian Sea<\/p>\n<p>Explanation:<br \/>\nSouth America\u2019s Valdes Peninsula (elevation \u2212131 ft) is lower than Europe\u2019s Caspian Sea (elevation \u221292 ft).<br \/>\n-131 &lt; -92.<br \/>\nSo, South America\u2019s Valdes Peninsula &lt; Europe\u2019s Caspian Sea<\/p>\n<h3><a id=\"Compare_and_Order_Integers_\u2013_Page_No._148\"><\/a>Problem Solving + Applications &#8211; Page No. 148<\/h3>\n<p><strong>What\u2019s the Error?<\/strong><\/p>\n<p>Question 19.<br \/>\nIn the game of golf, the player with the lowest score wins. Raheem, Erin, and Blake played a game of miniature golf. The table shows their scores compared to par.<br \/>\n<img loading=\"lazy\" src=\"https:\/\/ccssmathanswers.com\/wp-content\/uploads\/2020\/08\/Go-Math-Grade-6-Answer-Key-Chapter-3-Understand-Positive-and-Negative-Numbers-img-5.jpg\" alt=\"Go Math Grade 6 Answer Key Chapter 3 Understand Positive and Negative Numbers img 5\" width=\"389\" height=\"74\" \/><br \/>\nAt the end of the game, they wanted to know who had won.<br \/>\nLook at how they solved the problem. Find their error.<br \/>\nSTEP 1: 0 is greater than both \u22121 and \u22125. Since Raheem had the highest score, he did not win.<br \/>\nSTEP 2: \u22121 is less than \u22125, so Blake\u2019s score was less than Erin\u2019s score. Since Blake had the lowest score, he won the game.<br \/>\nCorrect the error by ordering the scores from least to greatest.<br \/>\nSo, _____ won. _____ came in second. _____ came in third.<br \/>\nDescribe the error that the players made.<br \/>\nType below:<br \/>\n__________<\/p>\n<p>Answer:<br \/>\nStep 2 is wrong.<br \/>\nIn step 2, they mentioned that -1 is less than \u22125. But -1 is greater than -5.<br \/>\nSo, Erin won. Blake came in second. Raheem came in third.<\/p>\n<p>Question 20.<br \/>\nJasmine recorded the low temperatures for 3 cities.<br \/>\n<img loading=\"lazy\" src=\"https:\/\/ccssmathanswers.com\/wp-content\/uploads\/2020\/08\/Go-Math-Grade-6-Answer-Key-Chapter-3-Understand-Positive-and-Negative-Numbers-img-6.jpg\" alt=\"Go Math Grade 6 Answer Key Chapter 3 Understand Positive and Negative Numbers img 6\" width=\"286\" height=\"131\" \/><br \/>\nDraw a dot on the number line to represent the low temperature of each city. Write the letter of the city above the dot.<br \/>\nType below:<br \/>\n__________<\/p>\n<p>Answer:<br \/>\n<img loading=\"lazy\" class=\"alignnone size-medium wp-image-7195\" src=\"https:\/\/ccssmathanswers.com\/wp-content\/uploads\/2020\/08\/grade-6-chapter-3-image-5-300x55.jpg\" alt=\"grade 6 chapter 3 image 5\" width=\"300\" height=\"55\" srcset=\"https:\/\/bigideasmathanswers.com\/wp-content\/uploads\/2020\/08\/grade-6-chapter-3-image-5-300x55.jpg 300w, https:\/\/bigideasmathanswers.com\/wp-content\/uploads\/2020\/08\/grade-6-chapter-3-image-5.jpg 673w\" sizes=\"(max-width: 300px) 100vw, 300px\" \/><\/p>\n<p>Explanation:<br \/>\n6 &gt; 2 &gt; -4<\/p>\n<h3><a id=\"Compare_and_Order_Integers_\u2013_Page_No._149\"><\/a>Compare and Order Integers &#8211; Page No. 149<\/h3>\n<p><strong>Compare the numbers. Write &lt; or &gt;.<\/strong><\/p>\n<p>Question 1.<br \/>\n<sup>&#8211;<\/sup>4 ____ <sup>&#8211;<\/sup>5<\/p>\n<p>Answer:<br \/>\n-4 &gt; -5<\/p>\n<p>Explanation:<br \/>\n-4 is to the right of -5 on the number line.<br \/>\nSo, -4 is greater than -5.<\/p>\n<p>Question 2.<br \/>\n0 ____ <sup>&#8211;<\/sup>1<\/p>\n<p>Answer:<br \/>\n0 &gt; -1<\/p>\n<p>Explanation:<br \/>\n0 is to the right of -1 on the number line.<br \/>\nSo, 0 is greater than -1.<\/p>\n<p>Question 3.<br \/>\n4 ____ <sup>&#8211;<\/sup>6<\/p>\n<p>Answer:<br \/>\n4 &gt; -6<\/p>\n<p>Explanation:<br \/>\n4 is to the right of -6 on the number line.<br \/>\nSo, 4 is greater than -6.<\/p>\n<p>Question 4.<br \/>\n<sup>&#8211;<\/sup>9 ____ <sup>&#8211;<\/sup>8<\/p>\n<p>Answer:<br \/>\n-9 &lt; -8<\/p>\n<p>Explanation:<br \/>\n-9 is to the left of -8 on the number line.<br \/>\nSo, -9 is less than -8.<\/p>\n<p>Question 5.<br \/>\n2 ____ <sup>&#8211;<\/sup>10<\/p>\n<p>Answer:<br \/>\n2 &gt; -10<\/p>\n<p>Explanation:<br \/>\n2 is to the right of -10 on the number line.<br \/>\nSo, 2 is greater than -10.<\/p>\n<p>Question 6.<br \/>\n<sup>&#8211;<\/sup>12 ____ <sup>&#8211;<\/sup>11<\/p>\n<p>Answer:<br \/>\n-12 &lt; -11<\/p>\n<p>Explanation:<br \/>\n-12 is to the left of -11 on the number line.<br \/>\nSo, -12 is less than -11.<\/p>\n<p>Question 7.<br \/>\n1 ____ <sup>&#8211;<\/sup>10<\/p>\n<p>Answer:<br \/>\n1 &gt; -10<\/p>\n<p>Explanation:<br \/>\n1 is to the right of -10 on the number line.<br \/>\nSo, 1 is greater than -10.<\/p>\n<p><strong>Order the numbers from least to greatest.<\/strong><\/p>\n<p>Question 8.<br \/>\n3, <sup>&#8211;<\/sup>2, <sup>&#8211;<\/sup>7<br \/>\nType below:<br \/>\n__________<\/p>\n<p>Answer:<br \/>\n-7, -2, 3<\/p>\n<p>Explanation:<br \/>\n-7 is to the left of -2 on the number line. -2 is to the left of 3 on the number line.<br \/>\nSo, -7 &lt; -2 &lt; 3<\/p>\n<p>Question 9.<br \/>\n0, 2, <sup>&#8211;<\/sup>5<br \/>\nType below:<br \/>\n__________<\/p>\n<p>Answer:<br \/>\n-5, 0, 2<\/p>\n<p>Explanation:<br \/>\n-5 is to the left of 0 on the number line. 0 is to the left of 2 on the number line.<br \/>\nSo, -5 &lt; 0 &lt; 2<\/p>\n<p>Question 10.<br \/>\n<sup>&#8211;<\/sup>9, <sup>&#8211;<\/sup>12, <sup>&#8211;<\/sup>10<br \/>\nType below:<br \/>\n__________<\/p>\n<p>Answer:<br \/>\n-12, -10, -9<\/p>\n<p>Explanation:<br \/>\n-12 is to the left of -10 on the number line. -10 is to the left of -9 on the number line.<br \/>\nSo, -12 &lt; -10 &lt; -9<\/p>\n<p>Question 11.<br \/>\n<sup>&#8211;<\/sup>2, <sup>&#8211;<\/sup>3, <sup>&#8211;<\/sup>4<br \/>\nType below:<br \/>\n__________<\/p>\n<p>Answer:<br \/>\n-4, -3, -2<\/p>\n<p>Explanation:<br \/>\n-4 is to the left of -3 on the number line. -3 is to the left of -2 on the number line.<br \/>\nSo, -4 &lt; -3 &lt; -2<\/p>\n<p>Question 12.<br \/>\n1, <sup>&#8211;<\/sup>6, <sup>&#8211;<\/sup>13<br \/>\nType below:<br \/>\n__________<\/p>\n<p>Answer:<br \/>\n-13, -6, 1<\/p>\n<p>Explanation:<br \/>\n-13 is to the left of -6 on the number line. -6 is to the left of 1 on the number line.<br \/>\nSo, -13 &lt; -6 &lt; 1<\/p>\n<p>Question 13.<br \/>\n5, 7, 0<br \/>\nType below:<br \/>\n__________<\/p>\n<p>Answer:<br \/>\n0, 5, 7<\/p>\n<p>Explanation:<br \/>\n0 is to the left of 5 on the number line. 5 is to the left of 7 on the number line.<br \/>\nSo, 0 &lt; 5 &lt; 7<\/p>\n<p>Question 14.<br \/>\n0, 13, <sup>&#8211;<\/sup>13<br \/>\nType below:<br \/>\n__________<\/p>\n<p>Answer:<br \/>\n-13, 0, 13<\/p>\n<p>Explanation:<br \/>\n-13 is to the left of 0 on the number line. 0 is to the left of 13 on the number line.<br \/>\nSo, -13 &lt; 0 &lt; 13<\/p>\n<p>Question 15.<br \/>\n<sup>&#8211;<\/sup>11, 7, <sup>&#8211;<\/sup>5<br \/>\nType below:<br \/>\n__________<\/p>\n<p>Answer:<br \/>\n-11, -5, 7<\/p>\n<p>Explanation:<br \/>\n-11 is to the left of -5 on the number line. -5 is to the left of 7 on the number line.<br \/>\nSo, -11 &lt; -5 &lt; 7<\/p>\n<p>Question 16.<br \/>\n<sup>&#8211;<\/sup>9, <sup>&#8211;<\/sup>8, 1<br \/>\nType below:<br \/>\n__________<\/p>\n<p>Answer:<br \/>\n-9, -8, 1<\/p>\n<p>Explanation:<br \/>\n-9 is to the left of -8 on the number line. -8 is to the left of 1 on the number line.<br \/>\nSo, -9 &lt; -8 &lt; 1<\/p>\n<p><strong>Problem Solving<\/strong><\/p>\n<p>Question 17.<br \/>\nMeg and Derek played a game. Meg scored <sup>&#8211;<\/sup>11 points, and Derek scored 4 points. Write a comparison to show that Meg\u2019s score is less than Derek\u2019s score.<br \/>\nType below:<br \/>\n__________<\/p>\n<p>Answer:<br \/>\n-11 &lt; 4<\/p>\n<p>Explanation:<br \/>\nMeg and Derek played a game. Meg scored -11 points, and Derek scored 4 points.<br \/>\n-11 &lt; 4<\/p>\n<p>Question 18.<br \/>\nMisha is thinking of a negative integer greater than \u22124. What number could she be thinking of?<br \/>\nType below:<br \/>\n__________<\/p>\n<p>Answer:<br \/>\n-3, -2, -1<\/p>\n<p>Explanation:<br \/>\nMisha is thinking of a negative integer greater than \u22124.<br \/>\n-3, -2, -1<\/p>\n<p>Question 19.<br \/>\nExplain how to use a number line to compare two negative integers. Give an example.<br \/>\nType below:<br \/>\n__________<\/p>\n<p>Answer:<br \/>\n-&gt; On a number line, numbers always increase (become &#8220;more positive&#8221;) to the right and decrease (become &#8220;more negative&#8221;) to the left.<br \/>\n-&gt; Numbers to the right are greater than numbers to the left and numbers to the left are less than numbers to the right.<br \/>\nExample: 2 &gt; -10<br \/>\n2 is to the right of -10 on the number line.<br \/>\nSo, 2 is greater than -10.<\/p>\n<h3><a id=\"Compare_and_Order_Integers_Lesson_Check_\u2013_Page_No._150\"><\/a>Lesson Check &#8211; Page No. 150<\/h3>\n<p><img loading=\"lazy\" src=\"https:\/\/ccssmathanswers.com\/wp-content\/uploads\/2020\/08\/Go-Math-Grade-6-Answer-Key-Chapter-3-Understand-Positive-and-Negative-Numbers-img-7.jpg\" alt=\"Go Math Grade 6 Answer Key Chapter 3 Understand Positive and Negative Numbers img 7\" width=\"756\" height=\"55\" \/><br \/>\n<strong>The chart shows the high temperatures for seven cities on one day in January.<\/strong><\/p>\n<p>Question 1.<br \/>\nWhich city had the lower temperature, Helena or Chicago?<br \/>\nType below:<br \/>\n__________<\/p>\n<p>Answer:<br \/>\nHelena had a lower temperature<\/p>\n<p>Explanation:<br \/>\nHelena = -1<br \/>\nChicago = 2<br \/>\n-1 &lt; 2<br \/>\nSo, Helena had a lower temperature.<\/p>\n<p>Question 2.<br \/>\nWrite the temperatures of the following cities in order from greatest to least: Denver, Helena, Lansing.<br \/>\nType below:<br \/>\n__________<\/p>\n<p>Answer:<br \/>\nLansing, Helena, Denver<\/p>\n<p>Explanation:<br \/>\nDenver = -8<br \/>\nHelena = -1<br \/>\nLansing = 3<br \/>\n3 &gt; -1 &gt; -8<br \/>\nSo, Lansing, Helena, Denver is the answer.<\/p>\n<p><strong>Spiral Review<\/strong><\/p>\n<p>Question 3.<br \/>\nFiona starts at the beginning of a hiking trail and walks \\(\\frac{4}{5}\\) mile. She counts the mileage markers that are placed every \\(\\frac{1}{10}\\) mile along the trail. How many markers does she count?<br \/>\n______ markers<\/p>\n<p>Answer:<br \/>\n8 markers<\/p>\n<p>Explanation:<br \/>\nFiona starts at the beginning of a hiking trail and walks \\(\\frac{4}{5}\\) mile. She counts the mileage markers that are placed every \\(\\frac{1}{10}\\) mile along the trail.<br \/>\nNumber of markers = (4\/5)\/(1\/10) = 4\/5 \u00d7 10 = 8<\/p>\n<p>Question 4.<br \/>\nIf Amanda hikes at an average speed of 2.72 miles per hour, how long will it take her to hike 6.8 miles?<br \/>\n______ hours<\/p>\n<p>Answer:<br \/>\n2.5 hours<\/p>\n<p>Explanation:<br \/>\nspeed times time = distance<br \/>\ndistance = 6.8<br \/>\nspeed = 2.72<br \/>\ntime = s<br \/>\n2.72 times s = 6.8<br \/>\ndivide both sides by 2.72<br \/>\ns = 2.5<br \/>\nThe answer is 2.5 hours<\/p>\n<p>Question 5.<br \/>\nThe area of a rectangle is 5 \\(\\frac{4}{5}\\) square meters. The width of the rectangle is 2 \\(\\frac{1}{4}\\) meter. Which is the best estimate for the length of the rectangle?<br \/>\n______ meters<\/p>\n<p>Answer:<br \/>\n2 \\(\\frac{26}{45}\\) meters<\/p>\n<p>Explanation:<br \/>\nSince the area of a rectangle is, A = l \u00d7 b<br \/>\nA = 5 \\(\\frac{4}{5}\\) square meters<br \/>\nb = 2 \\(\\frac{1}{4}\\) meter<br \/>\n5 \\(\\frac{4}{5}\\) = l \u00d7 2 \\(\\frac{1}{4}\\)<br \/>\nl = \\(\\frac{29 \u00d7 4}{9 \u00d7 5}\\) = \\(\\frac{116}{45}\\) = 2 \\(\\frac{26}{45}\\)<\/p>\n<p>Question 6.<br \/>\nLillian bought 2.52 pounds of tomatoes and 1.26 pounds of lettuce to make a salad for 18 people. If each person got the same amount of salad, how much salad did each person get?<br \/>\n______ pounds per person<\/p>\n<p>Answer:<br \/>\n0.21 pounds per person<\/p>\n<p>Explanation:<br \/>\nLillian bought 2.52 pounds of tomatoes and 1.26 pounds of lettuce to make a salad for 18 people.<br \/>\n2.52 pounds + 1.26 pounds = 3.78 pounds of salad \u00f7 18 people = 0.21 pounds of salad per person<\/p>\n<h3><a id=\"Rational_Numbers_and_the_Number_Line_\u2013_Page_No._153\"><\/a>Share and Show &#8211; Page No. 153<\/h3>\n<p><strong>Graph the number on the horizontal number line.<\/strong><\/p>\n<p>Question 1.<br \/>\n<sup>&#8211;<\/sup>2.25<br \/>\nType below:<br \/>\n__________<\/p>\n<p>Answer:<br \/>\n<img loading=\"lazy\" class=\"alignnone size-medium wp-image-7199\" src=\"https:\/\/ccssmathanswers.com\/wp-content\/uploads\/2020\/08\/grade-6-chapter-3-image-6-300x81.jpg\" alt=\"grade 6 chapter 3 image 6\" width=\"300\" height=\"81\" srcset=\"https:\/\/bigideasmathanswers.com\/wp-content\/uploads\/2020\/08\/grade-6-chapter-3-image-6-300x81.jpg 300w, https:\/\/bigideasmathanswers.com\/wp-content\/uploads\/2020\/08\/grade-6-chapter-3-image-6.jpg 674w\" sizes=\"(max-width: 300px) 100vw, 300px\" \/><\/p>\n<p>Explanation:<br \/>\n-2.25 is in between -2 and -3.<br \/>\n-2.25 is between -2 and -2.5<\/p>\n<p>Question 2.<br \/>\n<sup>&#8211;<\/sup>1 \\(\\frac{5}{8}\\)<br \/>\nType below:<br \/>\n__________<\/p>\n<p>Answer:<br \/>\n<img loading=\"lazy\" class=\"alignnone size-medium wp-image-7200\" src=\"https:\/\/ccssmathanswers.com\/wp-content\/uploads\/2020\/08\/grade-6-chapter-3-image-7-300x88.jpg\" alt=\"grade 6 chapter 3 image 7\" width=\"300\" height=\"88\" srcset=\"https:\/\/bigideasmathanswers.com\/wp-content\/uploads\/2020\/08\/grade-6-chapter-3-image-7-300x88.jpg 300w, https:\/\/bigideasmathanswers.com\/wp-content\/uploads\/2020\/08\/grade-6-chapter-3-image-7.jpg 672w\" sizes=\"(max-width: 300px) 100vw, 300px\" \/><\/p>\n<p>Explanation:<br \/>\n-1 \\(\\frac{5}{8}\\) is in between -1 and -2.<br \/>\n-1 \\(\\frac{5}{8}\\) is closer to -2.<\/p>\n<p>Question 3.<br \/>\n\\(\\frac{1}{2}\\)<br \/>\nType below:<br \/>\n__________<\/p>\n<p>Answer:<br \/>\n<img loading=\"lazy\" class=\"alignnone size-medium wp-image-7201\" src=\"https:\/\/ccssmathanswers.com\/wp-content\/uploads\/2020\/08\/grade-6-chapter-3-image-8-300x114.jpg\" alt=\"grade 6 chapter 3 image 8\" width=\"300\" height=\"114\" srcset=\"https:\/\/bigideasmathanswers.com\/wp-content\/uploads\/2020\/08\/grade-6-chapter-3-image-8-300x114.jpg 300w, https:\/\/bigideasmathanswers.com\/wp-content\/uploads\/2020\/08\/grade-6-chapter-3-image-8.jpg 677w\" sizes=\"(max-width: 300px) 100vw, 300px\" \/><\/p>\n<p>Explanation:<br \/>\n\\(\\frac{1}{2}\\) is in between 0 and 1<br \/>\n\\(\\frac{1}{2}\\) = 0.5<\/p>\n<p><strong>On Your Own<\/strong><\/p>\n<p><strong>Practice: Copy and Solve Graph the number on a vertical number line.<\/strong><\/p>\n<p>Question 4.<br \/>\n0.6<br \/>\nType below:<br \/>\n__________<\/p>\n<p>Answer:<br \/>\n<img loading=\"lazy\" class=\"alignnone size-medium wp-image-7207\" src=\"https:\/\/ccssmathanswers.com\/wp-content\/uploads\/2020\/08\/grade-6-chapter-3-image-13-63x300.jpg\" alt=\"grade 6 chapter 3 image 13\" width=\"63\" height=\"300\" srcset=\"https:\/\/bigideasmathanswers.com\/wp-content\/uploads\/2020\/08\/grade-6-chapter-3-image-13-63x300.jpg 63w, https:\/\/bigideasmathanswers.com\/wp-content\/uploads\/2020\/08\/grade-6-chapter-3-image-13.jpg 102w\" sizes=\"(max-width: 63px) 100vw, 63px\" \/><\/p>\n<p>Explanation:<br \/>\n0.6 is in between 0 and 1.<br \/>\n0.6 is closer to 1<\/p>\n<p>Question 5.<br \/>\n<sup>&#8211;<\/sup>1.25<br \/>\nType below:<br \/>\n__________<\/p>\n<p>Answer:<br \/>\n<img loading=\"lazy\" class=\"alignnone size-medium wp-image-7204\" src=\"https:\/\/ccssmathanswers.com\/wp-content\/uploads\/2020\/08\/grade-6-chapter-3-image-10-70x300.jpg\" alt=\"grade 6 chapter 3 image 10\" width=\"70\" height=\"300\" \/><\/p>\n<p>Explanation:<br \/>\n-1.25 is in between -1 and -2<br \/>\n-1.25 is closer to -1.<\/p>\n<p>Question 6.<br \/>\n<sup>&#8211;<\/sup>1 \\(\\frac{1}{2}\\)<br \/>\nType below:<br \/>\n__________<\/p>\n<p>Answer:<br \/>\n<img loading=\"lazy\" class=\"alignnone size-medium wp-image-7205\" src=\"https:\/\/ccssmathanswers.com\/wp-content\/uploads\/2020\/08\/grade-6-chapter-3-image-11-64x300.jpg\" alt=\"grade 6 chapter 3 image 11\" width=\"64\" height=\"300\" \/><\/p>\n<p>Explanation:<br \/>\n-1 \\(\\frac{1}{2}\\) is in between -1 and -2<br \/>\n-1 \\(\\frac{1}{2}\\) = -1.5<\/p>\n<p>Question 7.<br \/>\n0.3<br \/>\nType below:<br \/>\n__________<\/p>\n<p>Answer:<br \/>\n<img loading=\"lazy\" class=\"alignnone size-medium wp-image-7208\" src=\"https:\/\/ccssmathanswers.com\/wp-content\/uploads\/2020\/08\/grade-6-chapter-3-image-14-67x300.jpg\" alt=\"grade 6 chapter 3 image 14\" width=\"67\" height=\"300\" srcset=\"https:\/\/bigideasmathanswers.com\/wp-content\/uploads\/2020\/08\/grade-6-chapter-3-image-14-67x300.jpg 67w, https:\/\/bigideasmathanswers.com\/wp-content\/uploads\/2020\/08\/grade-6-chapter-3-image-14.jpg 106w\" sizes=\"(max-width: 67px) 100vw, 67px\" \/><\/p>\n<p>Explanation:<br \/>\n0.3 is in between 0 and 1<br \/>\n0.3 is closer to 0<\/p>\n<p>Question 8.<br \/>\n<sup>&#8211;<\/sup>0.7<br \/>\nType below:<br \/>\n__________<\/p>\n<p>Answer:<br \/>\n<img loading=\"lazy\" class=\"alignnone size-medium wp-image-7209\" src=\"https:\/\/ccssmathanswers.com\/wp-content\/uploads\/2020\/08\/grade-6-chapter-3-image-15-62x300.jpg\" alt=\"grade 6 chapter 3 image 15\" width=\"62\" height=\"300\" \/><\/p>\n<p>Explanation:<br \/>\n-0.7 is in between 0 and -1<br \/>\n-0.7 is closer to -1<\/p>\n<p>Question 9.<br \/>\n1.4<br \/>\nType below:<br \/>\n__________<\/p>\n<p>Answer:<br \/>\n<img loading=\"lazy\" class=\"alignnone size-medium wp-image-7210\" src=\"https:\/\/ccssmathanswers.com\/wp-content\/uploads\/2020\/08\/grade-6-chapter-3-image-16-78x300.jpg\" alt=\"grade 6 chapter 3 image 16\" width=\"78\" height=\"300\" srcset=\"https:\/\/bigideasmathanswers.com\/wp-content\/uploads\/2020\/08\/grade-6-chapter-3-image-16-78x300.jpg 78w, https:\/\/bigideasmathanswers.com\/wp-content\/uploads\/2020\/08\/grade-6-chapter-3-image-16.jpg 120w\" sizes=\"(max-width: 78px) 100vw, 78px\" \/><\/p>\n<p>Explanation:<br \/>\n1.4 is in between 1 and 2<br \/>\n1.4 is closer to 1<\/p>\n<p>Question 10.<br \/>\n<sup>\u2212<\/sup>0.5<br \/>\nType below:<br \/>\n__________<\/p>\n<p>Answer:<br \/>\n<img loading=\"lazy\" class=\"alignnone size-medium wp-image-7211\" src=\"https:\/\/ccssmathanswers.com\/wp-content\/uploads\/2020\/08\/grade-6-chapter-3-image-17-79x300.jpg\" alt=\"grade 6 chapter 3 image 17\" width=\"79\" height=\"300\" srcset=\"https:\/\/bigideasmathanswers.com\/wp-content\/uploads\/2020\/08\/grade-6-chapter-3-image-17-79x300.jpg 79w, https:\/\/bigideasmathanswers.com\/wp-content\/uploads\/2020\/08\/grade-6-chapter-3-image-17.jpg 128w\" sizes=\"(max-width: 79px) 100vw, 79px\" \/><\/p>\n<p>Explanation:<br \/>\n\u22120.5 is in between 0 and -1<\/p>\n<p>Question 11.<br \/>\n\u2212 \\(\\frac{1}{4}\\)<br \/>\nType below:<br \/>\n__________<\/p>\n<p>Answer:<br \/>\n<img loading=\"lazy\" class=\"alignnone size-medium wp-image-7212\" src=\"https:\/\/ccssmathanswers.com\/wp-content\/uploads\/2020\/08\/grade-6-chapter-3-image-19-66x300.jpg\" alt=\"grade 6 chapter 3 image 19\" width=\"66\" height=\"300\" srcset=\"https:\/\/bigideasmathanswers.com\/wp-content\/uploads\/2020\/08\/grade-6-chapter-3-image-19-66x300.jpg 66w, https:\/\/bigideasmathanswers.com\/wp-content\/uploads\/2020\/08\/grade-6-chapter-3-image-19.jpg 104w\" sizes=\"(max-width: 66px) 100vw, 66px\" \/><\/p>\n<p>Explanation:<br \/>\n\u2212 \\(\\frac{1}{4}\\) is in between 0 and -1<br \/>\n-0.25 is closer to 0<\/p>\n<p><strong>State whether the numbers are on the same or opposite sides of zero.<\/strong><\/p>\n<p>Question 12.<br \/>\n<sup>\u2212<\/sup>1.38 and 2.9<br \/>\nType below:<br \/>\n__________<\/p>\n<p>Answer:<br \/>\nOpposite<\/p>\n<p>Explanation:<br \/>\n-1.38 is a negative number.<br \/>\n2.9 is a positive number.<br \/>\nSo, both numbers are on opposite sides of zero.<\/p>\n<p>Question 13.<br \/>\n<sup>\u2212<\/sup>3 \\(\\frac{9}{10}\\) and <sup>\u2212<\/sup>0.99<br \/>\nType below:<br \/>\n__________<\/p>\n<p>Answer:<br \/>\nSame<\/p>\n<p>Explanation:<br \/>\n\u22123 \\(\\frac{9}{10}\\) is a negative number.<br \/>\n\u22120.99 is a negative number.<br \/>\nSo, both numbers are on the same sides of zero.<\/p>\n<p>Question 14.<br \/>\n\\(\\frac{5}{6}\\) and <sup>\u2212<\/sup>4.713<br \/>\nType below:<br \/>\n__________<\/p>\n<p>Answer:<br \/>\nOpposite<\/p>\n<p>Explanation:<br \/>\n\u22124.713 is a negative number.<br \/>\n\\(\\frac{5}{6}\\) is a positive number.<br \/>\nSo, both numbers are on opposite sides of zero.<\/p>\n<p><strong>Identify a decimal and a fraction in simplest form for the point.<\/strong><br \/>\n<img loading=\"lazy\" src=\"https:\/\/ccssmathanswers.com\/wp-content\/uploads\/2020\/08\/Go-Math-Grade-6-Answer-Key-Chapter-3-Understand-Positive-and-Negative-Numbers-img-8.jpg\" alt=\"Go Math Grade 6 Answer Key Chapter 3 Understand Positive and Negative Numbers img 8\" width=\"463\" height=\"88\" \/><\/p>\n<p>Question 15.<br \/>\nPoint A<br \/>\nType below:<br \/>\n__________<\/p>\n<p>Answer:<br \/>\n-1.0<\/p>\n<p>Explanation:<br \/>\nThe point A is located at -1.0 = -1<\/p>\n<p>Question 16.<br \/>\nPoint B<br \/>\nType below:<br \/>\n__________<\/p>\n<p>Answer:<br \/>\n0.75 = 3\/4<\/p>\n<p>Explanation:<br \/>\nPoint B is between 0.5 and 1. It is 0.75<\/p>\n<p>Question 17.<br \/>\nPoint C<br \/>\nType below:<br \/>\n__________<\/p>\n<p>Answer:<br \/>\n-0.25 = 1\/4<\/p>\n<p>Explanation:<br \/>\nPoint C is in between 0 and -0.5<br \/>\n-0.25<\/p>\n<p>Question 18.<br \/>\nPoint D<br \/>\nType below:<br \/>\n__________<\/p>\n<p>Answer:<br \/>\n-1.25 = 5\/4<\/p>\n<p>Explanation:<br \/>\nPoint D is in between -1 and -1.5.<br \/>\n-1.25<\/p>\n<p>Question 19.<br \/>\nThe roots of 6 corn plants grew to <sup>\u2212<\/sup>3.54 feet, <sup>\u2212<\/sup>2 \\(\\frac{4}{5}\\) feet, <sup>\u2212<\/sup>3.86 feet, <sup>\u2212<\/sup>4 \\(\\frac{1}{8}\\) feet, <sup>\u2212<\/sup>4.25 feet, and <sup>\u2212<\/sup>2 \\(\\frac{2}{5}\\) feet. How many corn plants had roots between 3 and 4 feet deep?<br \/>\n______ plants<\/p>\n<p>Answer:<br \/>\n2 plants<\/p>\n<p>Explanation:<br \/>\nThe roots of 6 corn plants grew to \u22123.54 feet, \u22122 \\(\\frac{4}{5}\\) feet, \u22123.86 feet, \u22124 \\(\\frac{1}{8}\\) feet, \u22124.25 feet, and \u22122 \\(\\frac{2}{5}\\) feet.<br \/>\n\u22123.54 feet, \u22123.86 feet,<br \/>\n2 corn plants had roots between 3 and 4 feet deep.<\/p>\n<h3><a id=\"Rational_Numbers_and_the_Number_Line_\u2013_Page_No._154\"><\/a>Problem Solving + Applications &#8211; Page No. 154<\/h3>\n<p><strong>A star\u2019s magnitude is a number that measures the star\u2019s brightness. Use the table of star magnitudes for 20\u201322.<\/strong><br \/>\n<img loading=\"lazy\" src=\"https:\/\/ccssmathanswers.com\/wp-content\/uploads\/2020\/08\/Go-Math-Grade-6-Answer-Key-Chapter-3-Understand-Positive-and-Negative-Numbers-img-9.jpg\" alt=\"Go Math Grade 6 Answer Key Chapter 3 Understand Positive and Negative Numbers img 9\" width=\"321\" height=\"262\" \/><\/p>\n<p>Question 20.<br \/>\nBetween what two integers is the magnitude of Canopus?<br \/>\nType below:<br \/>\n__________<\/p>\n<p>Answer:<br \/>\n-0.72 is between -0.04 and -1.46<\/p>\n<p>Explanation:<br \/>\nCanopus = -0.72<br \/>\n-0.72 is between -0.04 and -1.46<\/p>\n<p>Question 21.<br \/>\nModel Mathematics<br \/>\nGraph the magnitude of Betelgeuse on the number line.<br \/>\nType below:<br \/>\n__________<\/p>\n<p>Answer:<br \/>\n<img loading=\"lazy\" class=\"alignnone size-medium wp-image-7223\" src=\"https:\/\/ccssmathanswers.com\/wp-content\/uploads\/2020\/08\/grade-6-chapter-3-image-20-300x81.jpg\" alt=\"grade 6 chapter 3 image 20\" width=\"300\" height=\"81\" srcset=\"https:\/\/bigideasmathanswers.com\/wp-content\/uploads\/2020\/08\/grade-6-chapter-3-image-20-300x81.jpg 300w, https:\/\/bigideasmathanswers.com\/wp-content\/uploads\/2020\/08\/grade-6-chapter-3-image-20.jpg 663w\" sizes=\"(max-width: 300px) 100vw, 300px\" \/><\/p>\n<p>Explanation:<br \/>\nBetelgeuse = 0.7<\/p>\n<p>Question 22.<br \/>\nWhat\u2019s the Error?<br \/>\nJacob graphed the magnitude of Sirius on the number line. Explain his error. Then graph the magnitude correctly.<br \/>\nType below:<br \/>\n__________<\/p>\n<p>Answer:<br \/>\n<img loading=\"lazy\" class=\"alignnone size-medium wp-image-7224\" src=\"https:\/\/ccssmathanswers.com\/wp-content\/uploads\/2020\/08\/grade-6-chapter-3-image-21-300x87.jpg\" alt=\"grade 6 chapter 3 image 21\" width=\"300\" height=\"87\" srcset=\"https:\/\/bigideasmathanswers.com\/wp-content\/uploads\/2020\/08\/grade-6-chapter-3-image-21-300x87.jpg 300w, https:\/\/bigideasmathanswers.com\/wp-content\/uploads\/2020\/08\/grade-6-chapter-3-image-21.jpg 680w\" sizes=\"(max-width: 300px) 100vw, 300px\" \/><\/p>\n<p>Explanation:<br \/>\nSirius = -1.46<\/p>\n<p>Question 23.<br \/>\nThe flag pole is located at point 0 on a map of Orange Avenue. Other points of interest on Orange Avenue are located on the number line based on their distances, in miles to the right of the flag pole (positive numbers) or to the left of the flag pole (negative numbers). Graph and label each location on the number line.<br \/>\n<img loading=\"lazy\" src=\"https:\/\/ccssmathanswers.com\/wp-content\/uploads\/2020\/08\/Go-Math-Grade-6-Answer-Key-Chapter-3-Understand-Positive-and-Negative-Numbers-img-10.jpg\" alt=\"Go Math Grade 6 Answer Key Chapter 3 Understand Positive and Negative Numbers img 10\" width=\"287\" height=\"168\" \/><br \/>\nType below:<br \/>\n__________<\/p>\n<p>Answer:<br \/>\n<img loading=\"lazy\" class=\"alignnone size-medium wp-image-7225\" src=\"https:\/\/ccssmathanswers.com\/wp-content\/uploads\/2020\/08\/grade-6-chapter-3-image-22-300x74.jpg\" alt=\"grade 6 chapter 3 image 22\" width=\"300\" height=\"74\" srcset=\"https:\/\/bigideasmathanswers.com\/wp-content\/uploads\/2020\/08\/grade-6-chapter-3-image-22-300x74.jpg 300w, https:\/\/bigideasmathanswers.com\/wp-content\/uploads\/2020\/08\/grade-6-chapter-3-image-22.jpg 662w\" sizes=\"(max-width: 300px) 100vw, 300px\" \/><\/p>\n<p>Explanation:<br \/>\n0.4 is the right side of the 0.<br \/>\n1.8 is the right side of the 0.<br \/>\n-1 is the left side of the 0.<br \/>\n-1.3 is the left side of the 0.<\/p>\n<h3><a id=\"Rational_Numbers_and_the_Number_Line_\u2013_Page_No._155\"><\/a>Rational Numbers and the Number Line &#8211; Page No. 155<\/h3>\n<p><strong>Graph the number on the number line.<\/strong><\/p>\n<p>Question 1.<br \/>\n<sup>\u2212<\/sup>2 \\(\\frac{3}{4}\\)<br \/>\nType below:<br \/>\n__________<\/p>\n<p>Answer:<br \/>\n<img loading=\"lazy\" class=\"alignnone size-full wp-image-7229\" src=\"https:\/\/ccssmathanswers.com\/wp-content\/uploads\/2020\/08\/grade-6-chapter-3-Page-no.-155-image-1.jpg\" alt=\"grade 6 chapter 3 Page no. 155 image 1\" width=\"293\" height=\"81\" \/><\/p>\n<p>Explanation:<br \/>\nThe number is between the integers -3 and -2.<br \/>\nIt is closer to the integer -3.<\/p>\n<p>Question 2.<br \/>\n\\(\\frac{-1}{4}\\)<br \/>\nType below:<br \/>\n__________<\/p>\n<p>Answer:<br \/>\n<img loading=\"lazy\" class=\"alignnone size-full wp-image-7230\" src=\"https:\/\/ccssmathanswers.com\/wp-content\/uploads\/2020\/08\/grade-6-chapter-3-Page-no.-155-image-2.jpg\" alt=\"grade 6 chapter 3 Page no. 155 image 2\" width=\"233\" height=\"52\" \/><\/p>\n<p>Explanation:<br \/>\nThe number is between the integers -0.3 and -0.2.<br \/>\nIt is closer to the integer -0.25.<\/p>\n<p>Question 3.<br \/>\n<sup>\u2212<\/sup>0.5<br \/>\nType below:<br \/>\n__________<\/p>\n<p>Answer:<br \/>\n<img loading=\"lazy\" class=\"alignnone size-full wp-image-7231\" src=\"https:\/\/ccssmathanswers.com\/wp-content\/uploads\/2020\/08\/grade-6-chapter-3-Page-no.-155-image-3JPG.jpg\" alt=\"grade 6 chapter 3 Page no. 155 image 3JPG\" width=\"48\" height=\"190\" \/><\/p>\n<p>Explanation:<br \/>\nThe number is between integers 0 and -1.<br \/>\nIt is closer to the integer -0.5.<\/p>\n<p>Question 4.<br \/>\n1.75<br \/>\nType below:<br \/>\n__________<\/p>\n<p>Answer:<br \/>\n<img loading=\"lazy\" class=\"alignnone size-full wp-image-7232\" src=\"https:\/\/ccssmathanswers.com\/wp-content\/uploads\/2020\/08\/grade-6-chapter-3-Page-no.-155-image-4.jpg\" alt=\"grade 6 chapter 3 Page no. 155 image 4\" width=\"55\" height=\"200\" \/><\/p>\n<p>Explanation:<br \/>\nThe number is between integers 1 and 2.<br \/>\nIt is closer to the integer 1.75.<\/p>\n<p>Question 5.<br \/>\n1 \\(\\frac{1}{2}\\)<br \/>\nType below:<br \/>\n__________<\/p>\n<p>Answer:<br \/>\n<img loading=\"lazy\" class=\"alignnone size-full wp-image-7233\" src=\"https:\/\/ccssmathanswers.com\/wp-content\/uploads\/2020\/08\/grade-6-chapter-3-Page-no.-155-image-5.jpg\" alt=\"grade 6 chapter 3 Page no. 155 image 5\" width=\"214\" height=\"59\" \/><\/p>\n<p>Explanation:<br \/>\nThe number is between integers 1 and 2.<br \/>\nIt is closer to the integer 1.5.<\/p>\n<p><strong>State whether the numbers are on the same or opposite sides of zero.<\/strong><\/p>\n<p>Question 6.<br \/>\n<sup>\u2212<\/sup>2.4 and 2.3<br \/>\nType below:<br \/>\n__________<\/p>\n<p>Answer:<br \/>\nOpposite<\/p>\n<p>Explanation:<br \/>\n-2.4 is a negative number.<br \/>\n2.3 is a positive number.<br \/>\nSo, both numbers are on opposite sides of zero.<\/p>\n<p>Question 7.<br \/>\n<sup>\u2212<\/sup>2 \\(\\frac{1}{5}\\) and <sup>\u2212<\/sup>1<br \/>\nType below:<br \/>\n__________<\/p>\n<p>Answer:<br \/>\nSame<\/p>\n<p>Explanation:<br \/>\n\u22122 \\(\\frac{1}{5}\\) is a negative number.<br \/>\n-1 is a negative number.<br \/>\nSo, both numbers are on the same sides of zero.<\/p>\n<p>Question 8.<br \/>\n<sup>\u2212<\/sup>0.3 and 0.3<br \/>\nType below:<br \/>\n__________<\/p>\n<p>Answer:<br \/>\nopposite<\/p>\n<p>Explanation:<br \/>\n-0.3 is a negative number.<br \/>\n0.3 is a positive number.<br \/>\nSo, both numbers are on opposite sides of zero.<\/p>\n<p>Question 9.<br \/>\n0.44 and \\(\\frac{2}{3}\\)<br \/>\nType below:<br \/>\n__________<\/p>\n<p>Answer:<br \/>\nSame<\/p>\n<p>Explanation:<br \/>\n0.44 is a positive number.<br \/>\n\\(\\frac{2}{3}\\) is a positive number.<br \/>\nSo, both numbers are on the same sides of zero.<\/p>\n<p><strong>Write the opposite of the number.<\/strong><\/p>\n<p>Question 10.<br \/>\n<sup>\u2212<\/sup>5.23<br \/>\nType below:<br \/>\n__________<\/p>\n<p>Answer:<br \/>\n5.23<\/p>\n<p>Explanation:<br \/>\nThe opposite number of -5.23 is 5.23<\/p>\n<p>Question 11.<br \/>\n\\(\\frac{4}{5}\\)<br \/>\nType below:<br \/>\n__________<\/p>\n<p>Answer:<br \/>\n&#8211;\\(\\frac{4}{5}\\)<\/p>\n<p>Explanation:<br \/>\nThe opposite number of \\(\\frac{4}{5}\\) is &#8211;\\(\\frac{4}{5}\\)<\/p>\n<p>Question 12.<br \/>\n\u22125<br \/>\nType below:<br \/>\n__________<\/p>\n<p>Answer:<br \/>\n5<\/p>\n<p>Explanation:<br \/>\nThe opposite number of -5 is 5<\/p>\n<p>Question 13.<br \/>\n<sup>\u2212<\/sup>2 \\(\\frac{2}{3}\\)<br \/>\nType below:<br \/>\n__________<\/p>\n<p>Answer:<br \/>\n2 \\(\\frac{2}{3}\\)<\/p>\n<p>Explanation:<br \/>\nThe opposite number of \u22122 \\(\\frac{2}{3}\\) is 2 \\(\\frac{2}{3}\\)<\/p>\n<p><strong>Problem Solving<\/strong><\/p>\n<p>Question 14.<br \/>\nThe outdoor temperature yesterday reached a low of \u22124.5\u00b0 F. Between what two integers was the temperature?<br \/>\nType below:<br \/>\n__________<\/p>\n<p>Answer:<br \/>\nAn integer is a whole number. -4.5 is not a whole number.<br \/>\n-4.5 is in between -4 and the integer below it is -5.<\/p>\n<p>Question 15.<br \/>\nJacob needs to graph <sup>\u2212<\/sup>6 \\(\\frac{2}{5}\\) on a horizontal number line. Should he graph it to the left or right of <sup>\u2212<\/sup>6?<br \/>\nType below:<br \/>\n__________<\/p>\n<p>Answer:<br \/>\nleft<\/p>\n<p>Explanation:<br \/>\nIt will on the left because it is negative and on a number line the left side is the least side.<\/p>\n<p>Question 16.<br \/>\nDescribe how to plot <sup>\u2212<\/sup>3 \\(\\frac{3}{4}\\) on a number line.<br \/>\nType below:<br \/>\n__________<\/p>\n<p>Answer:<br \/>\nOn the number line, negative numbers go to the left. Since -3 3\/4 is negative, go 3 spaces to the left.<br \/>\nIf there are half marks in between the numbers, plot the point near the half mark. If it&#8217;s -3 3\/4, count 3 spaces, then go to the half mark of -3 to -4, and plot the 3\/4 in between the -3 and -4 half mark. If there is no half mark, place it near the -4 mark.<br \/>\nThe red line represents the half mark, the blue line represents where the point would go. Notice how when negative, the numbers go higher as they go left.<br \/>\n<img loading=\"lazy\" class=\"alignnone size-full wp-image-7235\" src=\"https:\/\/ccssmathanswers.com\/wp-content\/uploads\/2020\/08\/grade-6-chapter-3-Page-no.-155-image-5-1.jpg\" alt=\"grade 6 chapter 3 Page no. 155 image 5\" width=\"189\" height=\"129\" \/><\/p>\n<h3><a id=\"Rational_Numbers_and_the_Number_Line_Lesson_Check\u2013_Page_No._156\"><\/a>Lesson Check &#8211; Page No. 156<\/h3>\n<p>Question 1.<br \/>\nWhat number is the opposite of 0.2?<br \/>\nType below:<br \/>\n__________<\/p>\n<p>Answer:<br \/>\n-0.2<\/p>\n<p>Explanation:<br \/>\nThe opposite of 0.2 is -0.2<\/p>\n<p>Question 2.<br \/>\nBetween which two integers would you locate \u22123.4 on a number line?<br \/>\nType below:<br \/>\n__________<\/p>\n<p>Answer:<br \/>\n-3.4 is located between -3 and -4<\/p>\n<p>Explanation:<br \/>\nPositive 3.4 lies between 3 and 4 on the number line. It is more than 3 but less than 4. 3.4 is further from 0 than just 3. In the same way and because of the symmetrical arrangement of numbers on the number line, -3.4 lies between -3 and -4.<\/p>\n<p><strong>Spiral Review<\/strong><\/p>\n<p>Question 3.<br \/>\nYemi used these pattern blocks to solve a division problem. He found a quotient of 7. Which division problem was he solving?<br \/>\n<img loading=\"lazy\" src=\"https:\/\/ccssmathanswers.com\/wp-content\/uploads\/2020\/08\/Go-Math-Grade-6-Answer-Key-Chapter-3-Understand-Positive-and-Negative-Numbers-img-11.jpg\" alt=\"Go Math Grade 6 Answer Key Chapter 3 Understand Positive and Negative Numbers img 11\" width=\"325\" height=\"88\" \/><br \/>\nType below:<br \/>\n__________<\/p>\n<p>Answer:<br \/>\n7<\/p>\n<p>Explanation:<br \/>\n3 1\/2 \u00f7 1\/2<br \/>\nFirst, we transform the mixed number into a fraction, 3 1\/2 = 7\/2<br \/>\nThen, we divide<br \/>\n7\/2 \u00f7 1\/2 = 7<br \/>\nThe quotient of the first division is 7.<\/p>\n<p>Question 4.<br \/>\nEric had 2 liters of water. He gave 0.42 liter to his friend and then drank 0.32 liter. How much water does he have left?<br \/>\n______ liters<\/p>\n<p>Answer:<br \/>\n1.26 liters<\/p>\n<p>Explanation:<br \/>\nEric had 2 liters of water. He gave 0.42 liter to his friend and then drank 0.32 liter.<br \/>\n2 &#8211; 0.42 &#8211; 0.32 = 1.26 L<\/p>\n<p>Question 5.<br \/>\nTo pass a math test, students must correctly answer at least 0.6 of the questions. Donald\u2019s score is \\(\\frac{5}{8}\\), Karen\u2019s score is 0.88, Gino\u2019s score is \\(\\frac{3}{5}\\) and Sierra\u2019s score is \\(\\frac{4}{5}\\). How many of the students passed the test?<br \/>\nType below:<br \/>\n__________<\/p>\n<p>Answer:<br \/>\n4<\/p>\n<p>Explanation:<br \/>\nDonald&#8217;s score of 5\/8 is equal to 0.625.<br \/>\nGino scored 3\/5 which is 0.6.<br \/>\nSierra&#8217;s score of 4\/5 equals 0.8.<br \/>\nKaren&#8217;s score is already given, and 0.88 is greater than 0.6.<br \/>\nNone of the students obtained lower than 0.6.<br \/>\nIf at least does not include scores equal to 0.6, and only scores greater than 0.6, then Gino possibly failed this math test.<br \/>\nIf a passing score is equal to or greater than 0.6, then all four students passed the test.<\/p>\n<p>Question 6.<br \/>\nJonna mixes \\(\\frac{1}{4}\\) gallon of orange juice and \\(\\frac{1}{2}\\) gallon of pineapple juice to make punch. Each serving is \\(\\frac{1}{16}\\) gallon. How many servings can Jonna make?<br \/>\n_____ servings<\/p>\n<p>Answer:<br \/>\n12 servings<\/p>\n<p>Explanation:<br \/>\nThe number of a gallon of orange juice is mixed to make punch is given by 1\/4<br \/>\nThe number of a gallon of pineapple juice is mixed to make punch is given by 1\/2<br \/>\nThe number of gallon in each serving is given by 1\/16<br \/>\n1\/4 + 1\/2 = 3\/4<br \/>\n3\/4 \u00f7 1\/16 = 12<br \/>\nSo, there are 12 servings which can be made by Jonna.<\/p>\n<h3><a id=\"Compare_and_Order_Rational_Numbers_\u2013_Page_No._159\"><\/a>Share and Show &#8211; Page No. 159<\/h3>\n<p><strong>Compare the numbers. Write &lt; or &gt;.<\/strong><\/p>\n<p>Question 1.<br \/>\n<sup>\u2212<\/sup>0.3 _____ 0.2<\/p>\n<p>Answer:<br \/>\n-0.3 &lt; 0.2<\/p>\n<p>Explanation:<br \/>\n-0.3 is to the left of 0.2 on the number line.<br \/>\nSo, -0.3 is less than 0.2.<\/p>\n<p>Question 2.<br \/>\n\\(\\frac{1}{3}\\) _____ \\(\\frac{\u22122}{5}\\)<\/p>\n<p>Answer:<br \/>\n\\(\\frac{1}{3}\\) &gt; \\(\\frac{\u22122}{5}\\)<\/p>\n<p>Explanation:<br \/>\n\\(\\frac{1}{3}\\) is to the right of \\(\\frac{\u22122}{5}\\) on the number line.<br \/>\nSo, \\(\\frac{1}{3}\\) is greater than \\(\\frac{\u22122}{5}\\).<\/p>\n<p>Question 3.<br \/>\n<sup>\u2212<\/sup>0.8 _____ <sup>\u2212<\/sup>0.5<\/p>\n<p>Answer:<br \/>\n\u22120.8 &lt; \u22120.5<\/p>\n<p>Explanation:<br \/>\n-0.8 is to the left of -0.5 on the number line.<br \/>\nSo, -0.8 is less than -0.5.<\/p>\n<p>Question 4.<br \/>\n\\(\\frac{\u22123}{4}\\) _____ \u22120.7<\/p>\n<p>Answer:<br \/>\n\\(\\frac{\u22123}{4}\\) &lt; \u22120.7<\/p>\n<p>Explanation:<br \/>\n\\(\\frac{\u22123}{4}\\) is to the left of \u22120.7 on the number line.<br \/>\nSo, \\(\\frac{\u22123}{4}\\) is less than \u22120.7.<\/p>\n<p><strong>Order the numbers from least to greatest.<\/strong><\/p>\n<p>Question 5.<br \/>\n3.6, <sup>\u2212<\/sup>7.1, <sup>\u2212<\/sup>5.9<br \/>\nType below:<br \/>\n__________<\/p>\n<p>Answer:<br \/>\n-7.1, -5.9, 3.6<\/p>\n<p>Explanation:<br \/>\n-7.1 is to the left of -5.9 on the number line. -5.9 is to the left of 3.6 on the number line.<br \/>\nSo, -7.1 &lt; -5.9 &lt; 3.6<\/p>\n<p>Question 6.<br \/>\n\\(\\frac{-6}{7}, \\frac{1}{9}, \\frac{-2}{3}\\)<br \/>\nType below:<br \/>\n__________<\/p>\n<p>Answer:<br \/>\n\\(\\frac{-6}{7}, \\frac{-2}{3}, \\frac{1}{9}\\)<\/p>\n<p>Explanation:<br \/>\n-6\/7 = -0.857<br \/>\n1\/9 = 0.111<br \/>\n-2\/3 = -0.666<br \/>\n-6\/7 is to the left of -2\/3 on the number line. -2\/3 is to the left of 1\/9 on the number line.<br \/>\nSo, -6\/7 &lt; -2\/3 &lt; 1\/9<\/p>\n<p>Question 7.<br \/>\n<sup>\u2212<\/sup>5 \\(\\frac{1}{4}\\), <sup>\u2212<\/sup>6.5, <sup>\u2212<\/sup>5.3<br \/>\nType below:<br \/>\n__________<\/p>\n<p>Answer:<br \/>\n-6.5, -5.3, \u22125 \\(\\frac{1}{4}\\)<\/p>\n<p>Explanation:<br \/>\n\u22125 \\(\\frac{1}{4}\\) = -21\/4 = -5.25<br \/>\n-6.5 is to the left of -5.3 on the number line. -5.3 is to the left of -5 \\(\\frac{1}{4}\\) on the number line.<br \/>\n-6.5 &lt; -5.3 &lt; -5.25<\/p>\n<p><strong>On Your Own<\/strong><\/p>\n<p><strong>Compare the numbers. Write &lt; or &gt;.<\/strong><\/p>\n<p>Question 8.<br \/>\n\\(\\frac{\u22121}{2}\\) _____ \\(\\frac{\u22123}{7}\\)<\/p>\n<p>Answer:<br \/>\n\\(\\frac{\u22121}{2}\\) &lt; \\(\\frac{\u22123}{7}\\)<\/p>\n<p>Explanation:<br \/>\n\\(\\frac{\u22121}{2}\\) = -0.5<br \/>\n\\(\\frac{\u22123}{7}\\) = -0.428<br \/>\n\\(\\frac{\u22121}{2}\\) is to the left of \\(\\frac{\u22123}{7}\\) on the number line.<br \/>\nSo, \\(\\frac{\u22121}{2}\\) is less than \\(\\frac{\u22123}{7}\\).<\/p>\n<p>Question 9.<br \/>\n<sup>\u2212<\/sup>23.7 _____ <sup>\u2212<\/sup>18.8<\/p>\n<p>Answer:<br \/>\n\u221223.7 &lt; \u221218.8<\/p>\n<p>Explanation:<br \/>\n\u221223.7 is to the left of \u221218.8 on the number line.<br \/>\nSo, \u221223.7 is less than \u221218.8.<\/p>\n<p>Question 10.<br \/>\n<sup>\u2212<\/sup>3 \\(\\frac{1}{4}\\) _____ <sup>\u2212<\/sup>4.3<\/p>\n<p>Answer:<br \/>\n\u22123 \\(\\frac{1}{4}\\) &gt; \u22124.3<\/p>\n<p>Explanation:<br \/>\n\u22123 \\(\\frac{1}{4}\\) = -13\/4 = -3.25<br \/>\n\u22123 \\(\\frac{1}{4}\\) is to the right of \u22124.3 on the number line.<br \/>\nSo, \u22123 \\(\\frac{1}{4}\\) is greater than \u22124.3.<\/p>\n<p><strong>Order the numbers from greatest to least.<\/strong><\/p>\n<p>Question 11.<br \/>\n<sup>\u2212<\/sup>2.4, 1.9, <sup>\u2212<\/sup>7.6<br \/>\nType below:<br \/>\n__________<\/p>\n<p>Answer:<br \/>\n1.9, -2.4, -7.6<\/p>\n<p>Explanation:<br \/>\n1.9 is to the right of -2.4 on the number line. -2.4 is to the right of -7.6 on the number line.<br \/>\nSo, 1.9 &gt; -2.4 &gt; -7.6<\/p>\n<p>Question 12.<br \/>\n\\(\\frac{-2}{5}, \\frac{-3}{4}, \\frac{-1}{2}\\)<br \/>\nType below:<br \/>\n__________<\/p>\n<p>Answer:<br \/>\n\\(\\frac{-2}{5}, \\frac{-1}{2}, \\frac{-3}{4}\\)<\/p>\n<p>Explanation:<br \/>\n-2\/5 = -0.4; -3\/4 = -0.75; -1\/2 = -0.5<br \/>\n-2\/5 is to the right of -1\/2 on the number line. -1\/2 is to the right of -3\/4 on the number line.<br \/>\nSo, -2\/5 &gt; -1\/2 &gt; -3\/4<\/p>\n<p>Question 13.<br \/>\n3, <sup>\u2212<\/sup>6 \\(\\frac{4}{5}\\), <sup>\u2212<\/sup>3 \\(\\frac{2}{3}\\)<br \/>\nType below:<br \/>\n__________<\/p>\n<p>Answer:<br \/>\n3, \u22123 \\(\\frac{2}{3}\\), \u22126 \\(\\frac{4}{5}\\)<\/p>\n<p>Explanation:<br \/>\n\u22126 \\(\\frac{4}{5}\\) = -34\/5 = -6.8<br \/>\n\u22123 \\(\\frac{2}{3}\\) = -11\/3 = -3.666<br \/>\n3 is to the right of -3 \\(\\frac{2}{3}\\) on the number line. -3 \\(\\frac{2}{3}\\) is to the right of \u22126 \\(\\frac{4}{5}\\) on the number line.<br \/>\nSo, 3 &gt; \u22123 \\(\\frac{2}{3}\\) &gt; \u22126 \\(\\frac{4}{5}\\)<\/p>\n<p>Question 14.<br \/>\nLast week, Wednesday\u2019s low temperature was \u22124.5\u00b0F, Thursday\u2019s low temperature was \u22121.2\u00b0F, Friday\u2019s low temperature was \u22122.7\u00b0F, and Saturday\u2019s low temperature was 0.5\u00b0F. The average low temperature for the week was \u22121.5\u00b0F. How many of these days had low temperatures less than the average low temperature for the week?<br \/>\n_____ days<\/p>\n<p>Answer:<br \/>\n2 days<\/p>\n<p>Explanation:<br \/>\nLast week, Wednesday\u2019s low temperature was \u22124.5\u00b0F, Thursday\u2019s low temperature was \u22121.2\u00b0F, Friday\u2019s low temperature was \u22122.7\u00b0F, and Saturday\u2019s low temperature was 0.5\u00b0F. The average low temperature for the week was \u22121.5\u00b0F.<br \/>\n-4.5 &lt; -1.5; -2.7 &lt; -1.5<br \/>\n2 days had low temperatures less than the average low temperature for the week.<\/p>\n<p>Question 15.<br \/>\nUse Symbols Write a comparison using &lt; or &gt; to show the relationship between an elevation of <sup>\u2212<\/sup>12 \\(\\frac{1}{2}\\) ft and an elevation of <sup>\u2212<\/sup>16 \\(\\frac{5}{8}\\) ft.<br \/>\nType below:__________<\/p>\n<p>Answer:<br \/>\n\u221212 \\(\\frac{1}{2}\\) ft &gt; \u221216 \\(\\frac{5}{8}\\) ft<\/p>\n<p>Explanation:<br \/>\n\u221212 \\(\\frac{1}{2}\\) = -25\/2 = -12.5<br \/>\n\u221216 \\(\\frac{5}{8}\\) = -133\/8 = -16.625<br \/>\n-12.5 &gt; -16.625<\/p>\n<h3><a id=\"Compare_and_Order_Rational_Numbers_\u2013_Page_No._160\"><\/a>Problem Solving + Applications &#8211; Page No. 160<\/h3>\n<p><strong>Elevations, in miles, are given for the lowest points below sea level for 4 bodies of water. Use the table for 16\u201319.<\/strong><br \/>\n<img loading=\"lazy\" src=\"https:\/\/ccssmathanswers.com\/wp-content\/uploads\/2020\/08\/Go-Math-Grade-6-Answer-Key-Chapter-3-Understand-Positive-and-Negative-Numbers-img-12.jpg\" alt=\"Go Math Grade 6 Answer Key Chapter 3 Understand Positive and Negative Numbers img 12\" width=\"341\" height=\"197\" \/><\/p>\n<p>Question 16.<br \/>\nThe lowest point of which has the greater elevation, the Arctic Ocean or Lake Tanganyika?<br \/>\nType below:<br \/>\n__________<\/p>\n<p>Answer:<br \/>\nArctic Ocean has the greater elevation<\/p>\n<p>Explanation:<br \/>\nArctic Ocean = -0.8<br \/>\nLake Tanganyika = -0.9<br \/>\n-0.8 &gt; -0.9<br \/>\nArctic Ocean has the greater elevation<\/p>\n<p>Question 17.<br \/>\nWhich has a lower elevation, the lowest point of Lake Superior or a point at an elevation of \\(\\frac{2}{5}\\) mi?<br \/>\nType below:<br \/>\n__________<\/p>\n<p>Answer:<br \/>\nLake Superior has a lower elevation<\/p>\n<p>Explanation:<br \/>\nLake Superior = -1\/4 = -0.25<br \/>\n\\(\\frac{2}{5}\\) = 0.4<br \/>\n-0.25 &lt; 0.4<br \/>\nLake Superior has a lower elevation<\/p>\n<p>Question 18.<br \/>\nList the elevations in order from least to greatest.<br \/>\nType below:<br \/>\n__________<\/p>\n<p>Answer:<br \/>\n-0.9, -0.8, -1\/3, -1\/4<\/p>\n<p>Explanation:<br \/>\nArticle Ocean = -0.8<br \/>\nLake Superior = -1\/4 = -0.25<br \/>\nLake Tanganyika = -0.9<br \/>\nRed Sea = -1\/3 = -0.333<br \/>\n-0.9 &lt; -0.8 &lt; -0.333 &lt; -0.25<\/p>\n<p>Question 19.<br \/>\nA shipwreck is found at an elevation of \u2013 0.75 mile. In which bodies of water could the shipwreck have been found?<br \/>\nType below:<br \/>\n__________<\/p>\n<p>Answer:<br \/>\nArticle Ocean<\/p>\n<p>Explanation:<br \/>\n-0.75 is closer to -0.8<br \/>\nArticle Ocean = -0.8<\/p>\n<p>Question 20.<br \/>\nCircle &lt;, &gt;, or =.<br \/>\n20a. \\(\\frac{\u22123}{5}\\) \u039f \\(\\frac{\u22124}{5}\\)<br \/>\n20b. \\(\\frac{\u22122}{5}\\) \u039f \\(\\frac{\u22123}{4}\\)<br \/>\n20c. <sup>\u2212<\/sup>6.5 \u039f <sup>\u2212<\/sup>4.2<br \/>\n20d. <sup>\u2212<\/sup>2.4 \u039f <sup>\u2212<\/sup>3.7<br \/>\n\\(\\frac{\u22123}{5}\\) _____ \\(\\frac{\u22124}{5}\\)<br \/>\n\\(\\frac{\u22122}{5}\\) _____ \\(\\frac{\u22123}{4}\\)<br \/>\n<sup>\u2212<\/sup>6.5 _____ <sup>\u2212<\/sup>4.7<br \/>\n<sup>\u2212<\/sup>2.4 _____ <sup>\u2212<\/sup>3.7<\/p>\n<p>Answer:<br \/>\n\\(\\frac{\u22123}{5}\\) &gt; \\(\\frac{\u22124}{5}\\)<br \/>\n\\(\\frac{\u22122}{5}\\) &gt; \\(\\frac{\u22123}{4}\\)<br \/>\n\u22126.5 &lt; \u22124.7<br \/>\n\u22122.4 &gt; \u22123.7<\/p>\n<p>Explanation:<br \/>\n-3\/5 = -0.6; -4\/5 = -0.8<br \/>\n-0.6 &gt; -0.8<br \/>\n-2\/5 = -0.4; -3\/4 = -0.75<br \/>\n-0.4 &gt; -0.75<br \/>\n-6.5 &lt; -4.7<br \/>\n-2.4 &gt; -3.7<\/p>\n<h3><a id=\"Compare_and_Order_Rational_Numbers_\u2013_Page_No._161\"><\/a>Compare and Order Rational Numbers &#8211; Page No. 161<\/h3>\n<p><strong>Compare the numbers. Write &lt; or &gt;.<\/strong><\/p>\n<p>Question 1.<br \/>\n<sup>\u2212<\/sup>1\\(\\frac{1}{2}\\) _____ \\(\\frac{\u22121}{2}\\)<\/p>\n<p>Answer:<br \/>\n\u22121\\(\\frac{1}{2}\\) &lt; \\(\\frac{\u22121}{2}\\)<\/p>\n<p>Explanation:<br \/>\n\u22121\\(\\frac{1}{2}\\) = -3\/2 = &#8211; 1.5<br \/>\n\\(\\frac{\u22121}{2}\\) = -0.5<br \/>\n-1.5 &lt; -0.5<\/p>\n<p>Question 2.<br \/>\n0.1 _____ <sup>\u2212<\/sup>1.9<\/p>\n<p>Answer:<br \/>\n0.1 &gt; \u22121.9<\/p>\n<p>Explanation:<br \/>\n0.1 is to the right of -1.9 on the number line.<br \/>\nSo, 0.1 is greater than -1.9.<\/p>\n<p>Question 3.<br \/>\n0.4 _____ \\(\\frac{\u22121}{2}\\)<\/p>\n<p>Answer:<br \/>\n0.4 &gt; \\(\\frac{\u22121}{2}\\)<\/p>\n<p>Explanation:<br \/>\n0.4 is to the right of \\(\\frac{\u22121}{2}\\) on the number line.<br \/>\nSo, 0.4 is greater than \\(\\frac{\u22121}{2}\\).<\/p>\n<p>Question 4.<br \/>\n\\(\\frac{2}{5}\\) _____ 0.5<\/p>\n<p>Answer:<br \/>\n\\(\\frac{2}{5}\\) &lt; 0.5<\/p>\n<p>Explanation:<br \/>\n2\/5 = 0.4<br \/>\n0.4 &lt; 0.5<\/p>\n<p><strong>Order the numbers from least to greatest.<\/strong><\/p>\n<p>Question 5.<br \/>\n0.2, <sup>\u2212<\/sup>1.7, <sup>\u2212<\/sup>1<br \/>\nType below:<br \/>\n__________<\/p>\n<p>Answer:<br \/>\n-1.7, -1, 0.2<\/p>\n<p>Explanation:<br \/>\n-1.7 is to the left of -1 on the number line. -1 is to the left of 0.2 on the number line.<br \/>\nSo, -1.7 &lt; -1 &lt; 0.2<\/p>\n<p>Question 6.<br \/>\n\\(2 \\frac{3}{4}, \\frac{-3}{5}, 1 \\frac{3}{4}\\)<br \/>\nType below:<br \/>\n__________<\/p>\n<p>Answer:<br \/>\n\\( \\frac{-3}{5}, 1\\frac{3}{4}, 2 \\frac{3}{4}\\)<\/p>\n<p>Explanation:<br \/>\n2 3\/4 = 11\/4 = 2.75<br \/>\n-3\/5 = &#8211; 0.6<br \/>\n1 3\/4 = 7\/4 = 1.75<br \/>\n-0.6 &lt; 1.75 &lt; 2.75<\/p>\n<p>Question 7.<br \/>\n<sup>\u2212<\/sup>0.5, <sup>\u2212<\/sup>1 \\(\\frac{2}{3}\\), <sup>\u2212<\/sup>2.7<br \/>\nType below:<br \/>\n__________<\/p>\n<p>Answer:<br \/>\n-2.7, \u22121 \\(\\frac{2}{3}\\), -0.5<\/p>\n<p>Explanation:<br \/>\n\u22121 \\(\\frac{2}{3}\\) = -5\/3 = -1.666<br \/>\n-2.7 &lt; -1.66, -0.5<\/p>\n<p><strong>Order the numbers from greatest to least.<\/strong><\/p>\n<p>Question 8.<br \/>\n<sup>\u2212<\/sup>1, \\(\\frac{\u22125}{6}\\), 0<br \/>\nType below:<br \/>\n__________<\/p>\n<p>Answer:<br \/>\n0, \\(\\frac{\u22125}{6}\\), -1<\/p>\n<p>Explanation:<br \/>\n\\(\\frac{\u22125}{6}\\) = -0.8333<br \/>\n0 is to the right of \\(\\frac{\u22125}{6}\\) on the number line. \\(\\frac{\u22125}{6}\\) is to the right of -1 on the number line.<br \/>\nSo, 0 &gt; \\(\\frac{\u22125}{6}\\) &gt; -1<\/p>\n<p>Question 9.<br \/>\n\\(1.82, \\frac{-2}{5}, \\frac{4}{5}\\)<br \/>\nType below:<br \/>\n__________<\/p>\n<p>Answer:<br \/>\n\\(1.82, \\frac{4}{5}, \\frac{-2}{5}\\)<\/p>\n<p>Explanation:<br \/>\n-2\/5 = -0.4<br \/>\n4\/5 = 0.8<br \/>\n1.82<br \/>\n1.82 &gt; 0.8 &gt; -0.4<\/p>\n<p>Question 10.<br \/>\n<sup>\u2212<\/sup>2.19, <sup>\u2212<\/sup>2.5, 1.1<br \/>\nType below:<br \/>\n__________<\/p>\n<p>Answer:<br \/>\n1.1, -2.19, -2.5<\/p>\n<p>Explanation:<br \/>\n1.1 is to the right of -2.19 on the number line. -2.19 is to the right of -2.5 on the number line.<br \/>\nSo, 1.1 &gt; -2.19 &gt; -2.5<\/p>\n<p><strong>Write a comparison using &lt; or &gt; to show the relationship between the two values.<\/strong><\/p>\n<p>Question 11.<br \/>\nan elevation of \u221215 m and an elevation of \u221220.5 m<br \/>\nType below:<br \/>\n__________<\/p>\n<p>Answer:<br \/>\n-15m &gt; -20.5m<\/p>\n<p>Explanation:<br \/>\n-15 is to the right of -20.5 on the number line.<br \/>\n-15m &gt; -20.5m<\/p>\n<p>Question 12.<br \/>\na balance of $78 and a balance of \u2212$42<br \/>\nType below:<br \/>\n__________<\/p>\n<p>Answer:<br \/>\n$42 &lt; $78<\/p>\n<p>Explanation:<br \/>\n$42 is to the left of $78 on the number line.<br \/>\nSo, $42 is less than $78.<\/p>\n<p>Question 13.<br \/>\na score of \u221231 points and a score of \u221230 points<br \/>\nType below:<br \/>\n__________<\/p>\n<p>Answer:<br \/>\n-31 points &lt; -30 points<\/p>\n<p>Explanation:<br \/>\n-31 is to the left of -30 on the number line.<br \/>\nSo, -31 is less than -30.<\/p>\n<p><strong>Problem Solving<\/strong><\/p>\n<p>Question 14.<br \/>\nThe temperature in Cold Town on Monday was 1\u00b0C. The temperature in Frosty Town on Monday was \u22122\u00b0C. Which town was colder on Monday?<br \/>\nType below:<br \/>\n__________<\/p>\n<p>Answer:<br \/>\nFrosty Town<\/p>\n<p>Explanation:<br \/>\nThe temperature in Cold Town on Monday was 1\u00b0C. The temperature in Frosty Town on Monday was \u22122\u00b0C.<br \/>\nFrosty Town town was colder on Monday.<\/p>\n<p>Question 15.<br \/>\nStan\u2019s bank account balance is less than \u2212$20.00 but greater than \u2212$21.00. What could Stan\u2019s account balance be?<br \/>\nType below:<br \/>\n__________<\/p>\n<p>Answer:<br \/>\nFrom -$20.99 to -$20.01<\/p>\n<p>Explanation:<br \/>\nStan\u2019s bank account balance is less than \u2212$20.00 but greater than \u2212$21.00. The possible answer is From -$20.99 to -$20.01<\/p>\n<p>Question 16.<br \/>\nDescribe two situations in which it would be helpful to compare or order positive and negative rational numbers.<br \/>\nType below:<br \/>\n__________<\/p>\n<p>Answer:<br \/>\n1) negative numbers in weather reports and on food packaging. The temperature -5\u00b0C is \u2018negative five degrees\u2019 and it means 5 degrees below zero.<br \/>\n2) When you spend more money than you have in your bank account it shows up as a negative number.<\/p>\n<h3><a id=\"Compare_and_Order_Rational_Numbers_Lesson_Check_\u2013_Page_No._162\"><\/a>Lesson Check &#8211; Page No. 162<\/h3>\n<p>Question 1.<br \/>\nThe low temperature was \u20141.8 \u00b0C yesterday and \u22122.1 \u00b0C today. Use the symbols &lt; or &gt; to show the relationship between the temperatures.<br \/>\nType below:<br \/>\n__________<\/p>\n<p>Answer:<br \/>\nThe low temperature was \u20141.8 \u00b0C yesterday and \u22122.1 \u00b0C today.<br \/>\n-1.8 &gt; -2.1<\/p>\n<p>Question 2.<br \/>\nThe scores at the end of a game are shown. List the scores in order from greatest to least.<br \/>\nVince: \u22120.5<br \/>\nAllison: \\(\\frac{3}{8}\\)<br \/>\nMariah: \\(\\frac{\u22127}{20}\\)<br \/>\nType below:<br \/>\n__________<\/p>\n<p>Answer:<br \/>\n\\(\\frac{3}{8}\\), -0.5, \\(\\frac{\u22127}{20}\\)<\/p>\n<p>Explanation:<br \/>\n\\(\\frac{3}{8}\\) = 0.375<br \/>\n\\(\\frac{\u22127}{20}\\) = -0.35<br \/>\n-0.5<br \/>\n\\(\\frac{3}{8}\\) &gt; -0.5 &gt; -0.35<\/p>\n<p><strong>Spiral Review<\/strong><\/p>\n<p>Question 3.<br \/>\nSimone bought 3.42 pounds of green apples and 2.19 pounds of red apples. She used 3 pounds to make a pie. How many pounds of apples are left?<br \/>\n_____ pounds<\/p>\n<p>Answer:<br \/>\n2.61 pounds<\/p>\n<p>Explanation:<br \/>\nShe bought 3.42 pounds of green apples, then you can subtract 3 lbs off of that, so she bought .42 lbs of green apples and 2.19 lbs red apples<br \/>\nSo now, you just need to add .42 and 2.19<br \/>\n.42 + 2.19 = 2.61, so she has 2.61 lbs of apples left<\/p>\n<p>Question 4.<br \/>\nKwan bought three rolls of regular wrapping paper with 6.7 square meters of paper each. He also bought a roll of fancy wrapping paper containing 4.18 square meters. How much paper did he have altogether?<br \/>\n_____ square meters<\/p>\n<p>Answer:<br \/>\n24.28 square meters<\/p>\n<p>Explanation:<br \/>\nHe bought 3 rolls of regular wrapping paper with 6.7 m\u00b2. Then the total of this paper is: 3 \u00d7 6.7 = 20.1<br \/>\nHe also bought a roll of fancy wrapping with 4.18 m\u00b2. Therefore, to calculate the amount of paper he had together (which you can call\u00a0), you must add 20.1 m\u00b2 and 4.18 m\u00b2,<br \/>\nx = 20.1 + 41.8 = 24.28<\/p>\n<p>Question 5.<br \/>\nEddie needs 223 cups of flour for one batch of pancakes. How much flour does he need for 212 batches?<br \/>\n_____ \\(\\frac{\u25a1}{\u25a1}\\) cups<\/p>\n<p>Answer:<br \/>\n6\\(\\frac{4}{6}\\) cups<\/p>\n<p>Explanation:<br \/>\nFor 1 batch of pancake = 2 2\/3 = 8\/3 cups<br \/>\nFor 2 1\/2 = 5\/2 pancake = 8\/3 \u00d7 5\/2 = 40\/6 cups = 6 4\/6 cups<\/p>\n<p>Question 6.<br \/>\nTommy notices that he reads \\(\\frac{2}{3}\\) page in a minute. At that rate, how long will it take him to read 12 pages?<br \/>\n_____ minutes<\/p>\n<p>Answer:<br \/>\n18 minutes<\/p>\n<p>Explanation:<br \/>\nIt will take him 18 minutes.<br \/>\n2\/3 of a page in 18 minutes= 12 pages read<\/p>\n<h3><a id=\"Mid-Chapter_Checkpoint_\u2013_Page_No._163\"><\/a>Mid-Chapter Checkpoint &#8211; Vocabulary &#8211; Page No. 163<\/h3>\n<p><strong>Choose the best term from the box to complete the sentence.<\/strong><br \/>\n<img loading=\"lazy\" src=\"https:\/\/ccssmathanswers.com\/wp-content\/uploads\/2020\/08\/Go-Math-Grade-6-Answer-Key-Chapter-3-Understand-Positive-and-Negative-Numbers-img-13.jpg\" alt=\"Go Math Grade 6 Answer Key Chapter 3 Understand Positive and Negative Numbers img 13\" width=\"273\" height=\"194\" \/><\/p>\n<p>Question 1.<br \/>\nAny number that can be written as \\(\\frac{a}{b}\\), where a and b are integers and b\u22600 is called a(n) _____.<br \/>\nType below:<br \/>\n__________<\/p>\n<p>Answer:<br \/>\nrational number<\/p>\n<p>Question 2.<br \/>\nThe set of whole numbers and their opposites is the set of _____.<br \/>\nType below:<br \/>\n__________<\/p>\n<p>Answer:<br \/>\nIntegers<\/p>\n<p><strong>Concepts and Skills<\/strong><\/p>\n<p><strong>Write the opposite of the integer.<\/strong><\/p>\n<p>Question 3.<br \/>\n<sup>\u2212<\/sup>72<br \/>\nType below:<br \/>\n__________<\/p>\n<p>Answer:<br \/>\n72<\/p>\n<p>Explanation:<br \/>\nThe integer \u221272 is on the left side of 0.<br \/>\nSo, the opposite of -72 is 72<\/p>\n<p>Question 4.<br \/>\n0<br \/>\nType below:<br \/>\n__________<\/p>\n<p>Answer:<br \/>\n0<\/p>\n<p>Explanation:<\/p>\n<p>Opposite of 0 is 0<\/p>\n<p>Question 5.<br \/>\n<sup>\u2212<\/sup>31<br \/>\nType below:<br \/>\n__________<\/p>\n<p>Answer:<br \/>\n31<\/p>\n<p>Explanation:<br \/>\nThe integer \u221231 is on the left side of 0.<br \/>\nSo, the opposite of -31 is 31<\/p>\n<p>Question 6.<br \/>\n27<br \/>\nType below:<br \/>\n__________<\/p>\n<p>Answer:<\/p>\n<p>Explanation:<br \/>\nThe integer 27 is on the right side of 0.<br \/>\nSo, the opposite of 27 is -27<\/p>\n<p><strong>Name the integer that represents the situation, and tell what 0 represents in that situation.<\/strong><br \/>\n<img loading=\"lazy\" src=\"https:\/\/ccssmathanswers.com\/wp-content\/uploads\/2020\/08\/Go-Math-Grade-6-Answer-Key-Chapter-3-Understand-Positive-and-Negative-Numbers-img-14.jpg\" alt=\"Go Math Grade 6 Answer Key Chapter 3 Understand Positive and Negative Numbers img 14\" width=\"774\" height=\"122\" \/><\/p>\n<p>Question 7.<br \/>\nType below:<br \/>\n__________<\/p>\n<p>Answer:<br \/>\nInteger: 278<br \/>\n0 represents: Neither loses or gains in the video game.<\/p>\n<p>Question 8.<br \/>\nType below:<br \/>\n__________<\/p>\n<p>Answer:<br \/>\nInteger: -8 degrees<br \/>\n0 represents: No change in the temperature.<\/p>\n<p><strong>Compare the numbers. Write &lt; or &gt;.<\/strong><\/p>\n<p>Question 9.<br \/>\n3 _____ <sup>\u2212<\/sup>4<\/p>\n<p>Answer:<br \/>\n3 &gt; \u22124<\/p>\n<p>Explanation:<br \/>\n3 is to the right of -4 on the number line.<br \/>\nSo, 3 is greater than -4.<\/p>\n<p>Question 10.<br \/>\n<sup>\u2212<\/sup>6 _____ <sup>\u2212<\/sup>5<\/p>\n<p>Answer:<br \/>\n\u22126 &lt; \u22125<\/p>\n<p>Explanation:<br \/>\n-6 is to the left of -5 on the number line.<br \/>\nSo, -6 is less than -5.<\/p>\n<p>Question 11.<br \/>\n5 _____ <sup>\u2212<\/sup>6<\/p>\n<p>Answer:<br \/>\n5 &gt; \u22126<\/p>\n<p>Explanation:<br \/>\n5 is to the right of -6 on the number line.<br \/>\nSo, 5 is greater than -6.<\/p>\n<p>Question 12.<br \/>\n\\(\\frac{1}{3}\\) _____ \\(\\frac{1}{2}\\)<\/p>\n<p>Answer:<br \/>\n\\(\\frac{1}{3}\\) &lt; \\(\\frac{1}{2}\\)<\/p>\n<p>Explanation:<br \/>\n\\(\\frac{1}{3}\\) is to the left of \\(\\frac{1}{2}\\) on the number line.<br \/>\nSo, \\(\\frac{1}{3}\\) is less than \\(\\frac{1}{2}\\).<\/p>\n<p>Question 13.<br \/>\n<sup>\u2212<\/sup>3.1 _____ <sup>\u2212<\/sup>4.3<\/p>\n<p>Answer:<br \/>\n\u22123.1 &gt;\u22124.3<\/p>\n<p>Explanation:<br \/>\n-3.1 is to the right of -4.3 on the number line.<br \/>\nSo, -3.1 is greater than -4.3.<\/p>\n<p>Question 14.<br \/>\n1\\(\\frac{3}{4}\\) _____ <sup>\u2212<\/sup>2\\(\\frac{1}{2}\\)<\/p>\n<p>Answer:<br \/>\n1\\(\\frac{3}{4}\\) &gt;\u22122\\(\\frac{1}{2}\\)<\/p>\n<p>Explanation:<br \/>\n1\\(\\frac{3}{4}\\) is to the right of \u22122\\(\\frac{1}{2}\\) on the number line.<br \/>\nSo, 1\\(\\frac{3}{4}\\) is greater than \u22122\\(\\frac{1}{2}\\).<\/p>\n<p><strong>Order the numbers.<\/strong><\/p>\n<p>Question 15.<br \/>\n5, <sup>\u2212<\/sup>2, <sup>\u2212<\/sup>8<br \/>\nType below:<br \/>\n__________<\/p>\n<p>Answer:<br \/>\n-8, -2, 5<\/p>\n<p>Explanation:<br \/>\n-8 is to the left of -2 on the number line. -2 is to the left of 5 on the number line.<br \/>\nSo, -8 &lt; -2 &lt; 5<\/p>\n<p>Question 16.<br \/>\n0, <sup>\u2212<\/sup>3, 1<br \/>\nType below:<br \/>\n__________<\/p>\n<p>Answer:<br \/>\n-3, 0, 1<\/p>\n<p>Explanation:<br \/>\n-3 is to the left of 0 on the number line. 0 is to the left of 1 on the number line.<br \/>\nSo, -3 &lt; 0 &lt; 1<\/p>\n<p>Question 17.<br \/>\n<sup>\u2212<\/sup>7, <sup>\u2212<\/sup>6, <sup>\u2212<\/sup>11<br \/>\nType below:<br \/>\n__________<\/p>\n<p>Answer:<br \/>\n-11, -7, -6<\/p>\n<p>Explanation:<br \/>\n-11 is to the left of -7 on the number line. -7 is to the left of -6 on the number line.<br \/>\nSo, -11 &lt; -7 &lt; -6<\/p>\n<p>Question 18.<br \/>\n2.5, <sup>\u2212<\/sup>1.7, <sup>\u2212<\/sup>4.3<br \/>\nType below:<br \/>\n__________<\/p>\n<p>Answer:<br \/>\n-4.3, -1.7, 2.5<\/p>\n<p>Explanation:<br \/>\n-4.3 is to the left of -1.7 on the number line. -1.7 is to the left of 2.5 on the number line.<br \/>\nSo, -4.3 &lt; -1.7 &lt; 2.5<\/p>\n<p>Question 19.<br \/>\n\\(\\frac{2}{3} \\cdot \\frac{1}{4}, \\frac{5}{12}\\)<br \/>\nType below:<br \/>\n__________<\/p>\n<p>Answer:<br \/>\n\\(\\frac{1}{4} \\cdot \\frac{5}{12}, \\frac{2}{3}\\)<\/p>\n<p>Explanation:<br \/>\n2\/3 = 0.666<br \/>\n1\/4 = 0.25<br \/>\n5\/12 = 0.4166<br \/>\n1\/4 &lt; 5\/12 &lt; 2\/3<\/p>\n<p>Question 20.<br \/>\n<sup>\u2212<\/sup>5.2, <sup>\u2212<\/sup>3.8, <sup>\u2212<\/sup>9.4<br \/>\nType below:<br \/>\n__________<\/p>\n<p>Answer:<br \/>\n\u22129.4, \u22125.2, \u22123.8<\/p>\n<p>Explanation:<br \/>\n-9.4 is to the left of -5.2 on the number line. -5.2 is to the left of -3.8 on the number line.<br \/>\nSo, -9.4 &lt; -5.2 &lt; -3.8<\/p>\n<h3><a id=\"Mid-Chapter_Checkpoint_\u2013_Page_No._164\"><\/a>Page No. 164<\/h3>\n<p>Question 21.<br \/>\nJudy is scuba diving at \u22127 meters, Nelda is scuba diving at \u22129 meters, and Rod is scuba diving at \u22123 meters. List the divers in order from the deepest diver to the diver who is closest to the surface.<br \/>\nType below:<br \/>\n__________<\/p>\n<p>Answer:<br \/>\nJudy is scuba diving at \u22127 meters, Nelda is scuba diving at \u22129 meters, and Rod is scuba diving at \u22123 meters.<br \/>\nthe higher the value of the negative number, the deepest the diver is.<br \/>\nNelda (-9)- Judy (-7) -Rod (-3)<\/p>\n<p>Question 22.<br \/>\nA football team gains 8 yards on their first play. They lose 12 yards on the next play. What two integers represent the two plays?<br \/>\nType below:<br \/>\n__________<\/p>\n<p>Answer:<br \/>\nA football team gains 8 yards on their first play. +8<br \/>\nThey lose 12 yards on the next play. -12<br \/>\nThe 2 integers are positive 8 and negative 12<\/p>\n<p>Question 23.<br \/>\nThe player who scores the closest to 0 points wins the game. The scores of four players are given in the table. Who won the game?<br \/>\n<img loading=\"lazy\" src=\"https:\/\/ccssmathanswers.com\/wp-content\/uploads\/2020\/08\/Go-Math-Grade-6-Answer-Key-Chapter-3-Understand-Positive-and-Negative-Numbers-img-15.jpg\" alt=\"Go Math Grade 6 Answer Key Chapter 3 Understand Positive and Negative Numbers img 15\" width=\"276\" height=\"237\" \/><br \/>\nType below:<br \/>\n__________<\/p>\n<p>Answer:<br \/>\nDonovan won the game<\/p>\n<p>Explanation:<br \/>\nDonovan because he has-1.5<br \/>\nMyra has -1.93<br \/>\nAmari has -1.66666666<br \/>\nJustine has -1.8<br \/>\n-1.5 is the closest to 0<\/p>\n<p>Question 24.<br \/>\nWhich point on the graph represents <sup>\u2212<\/sup>3 \\(\\frac{3}{4}\\) ? What number does point C represent?<br \/>\n<img loading=\"lazy\" src=\"https:\/\/ccssmathanswers.com\/wp-content\/uploads\/2020\/08\/Go-Math-Grade-6-Answer-Key-Chapter-3-Understand-Positive-and-Negative-Numbers-img-16.jpg\" alt=\"Go Math Grade 6 Answer Key Chapter 3 Understand Positive and Negative Numbers img 16\" width=\"650\" height=\"100\" \/><br \/>\nType below:<br \/>\n__________<\/p>\n<p>Answer:<br \/>\nA<\/p>\n<p>Explanation:<br \/>\n\u22123 \\(\\frac{3}{4}\\) = -15\/4 = -3.75<br \/>\n-3.75 is in between -3 and -4.<br \/>\nSo, point A is the correct answer<\/p>\n<h3><a id=\"Absolute_Value_\u2013_Page_No._167\"><\/a>Share and Show &#8211; Page No. 167<\/h3>\n<p><strong>Find the absolute value.<\/strong><\/p>\n<p>Question 1.<br \/>\n|<sup>\u2212<\/sup>2|<br \/>\nType below:<br \/>\n__________<\/p>\n<p>Answer:<br \/>\n2<\/p>\n<p>Explanation:<br \/>\nThe distance from 0 to the point I graphed is 2 units.<br \/>\n|\u22122| = 2<\/p>\n<p>Question 2.<br \/>\n|6|<br \/>\nType below:<br \/>\n__________<\/p>\n<p>Answer:<br \/>\n6<\/p>\n<p>Explanation:<br \/>\nThe distance from 0 to the point I graphed is 6 units.<br \/>\n|6| = 6<\/p>\n<p>Question 3.<br \/>\n|<sup>\u2212<\/sup>5|<br \/>\nType below:<br \/>\n__________<\/p>\n<p>Answer:<br \/>\n5<\/p>\n<p>Explanation:<br \/>\nThe distance from 0 to the point I graphed is 6 units.<br \/>\n|-5| = 5<\/p>\n<p>Question 4.<br \/>\n|<sup>\u2212<\/sup>11|<br \/>\nType below:<br \/>\n__________<\/p>\n<p>Answer:<br \/>\n11<\/p>\n<p>Explanation:<br \/>\nThe distance from 0 to the point I graphed is 6 units.<br \/>\n|-11| = 11<\/p>\n<p>Question 5.<br \/>\n|9|<br \/>\nType below:<br \/>\n__________<\/p>\n<p>Answer:<br \/>\n9<\/p>\n<p>Explanation:<br \/>\nThe distance from 0 to the point I graphed is 6 units.<br \/>\n|9| = 9<\/p>\n<p>Question 6.<br \/>\n|<sup>\u2212<\/sup>15|<br \/>\nType below:<br \/>\n__________<\/p>\n<p>Answer:<br \/>\n15<\/p>\n<p>Explanation:<br \/>\nThe distance from 0 to the point I graphed is 6 units.<br \/>\n|-15| = 15<\/p>\n<p><strong>On Your Own<\/strong><\/p>\n<p><strong>Find the absolute value.<\/strong><\/p>\n<p>Question 7.<br \/>\n|<sup>\u2212<\/sup>37|<br \/>\nType below:<br \/>\n__________<\/p>\n<p>Answer:<br \/>\n37<\/p>\n<p>Explanation:<br \/>\nThe distance from 0 to the point I graphed is 6 units.<br \/>\n|-37| = 37<\/p>\n<p>Question 8.<br \/>\n|1.8|<br \/>\nType below:<br \/>\n__________<\/p>\n<p>Answer:<br \/>\n1.8<\/p>\n<p>Explanation:<br \/>\nThe distance from 0 to the point I graphed is 6 units.<br \/>\n|1.8| = 1.8<\/p>\n<p>Question 9.<br \/>\n|\\(\\frac{\u22122}{3}\\)|<br \/>\nType below:<br \/>\n__________<\/p>\n<p>Answer:<br \/>\n|\\(\\frac{2}{3}\\)|<\/p>\n<p>Explanation:<br \/>\nThe distance from 0 to the point I graphed is 6 units.<br \/>\n||\\(\\frac{\u22122}{3}\\)|| = |\\(\\frac{2}{3}\\)|<\/p>\n<p>Question 10.<br \/>\n|<sup>\u2212<\/sup>6.39|<br \/>\nType below:<br \/>\n__________<\/p>\n<p>Answer:<br \/>\n6.39<\/p>\n<p>Explanation:<br \/>\nThe distance from 0 to the point I graphed is 6 units.<br \/>\n|-6.39| = 6.39<\/p>\n<p>Question 11.<br \/>\n|<sup>\u2212<\/sup>5\\(\\frac{7}{8}\\)|<br \/>\nType below:<br \/>\n__________<\/p>\n<p>Answer:<br \/>\n5\\(\\frac{7}{8}\\)<\/p>\n<p>Explanation:<br \/>\nThe distance from 0 to the point I graphed is 5\\(\\frac{7}{8}\\) units.<br \/>\n|\u22125\\(\\frac{7}{8}\\)| = 5\\(\\frac{7}{8}\\)<\/p>\n<p><strong>Find all numbers with the given absolute value.<\/strong><\/p>\n<p>Question 12.<br \/>\n13<br \/>\nType below:<br \/>\n__________<\/p>\n<p>Answer:<br \/>\n13 and -13<\/p>\n<p>Explanation:<br \/>\n13 and -13 are at the same distance from 0.<\/p>\n<p>Question 13.<br \/>\n\\(\\frac{5}{6}\\)<br \/>\nType below:<br \/>\n__________<\/p>\n<p>Answer:<br \/>\n\\(\\frac{5}{6}\\) and \\(\\frac{-5}{6}\\)<\/p>\n<p>Explanation:<br \/>\n\\(\\frac{5}{6}\\) and \\(\\frac{-5}{6}\\) are at the same distance from 0.<\/p>\n<p>Question 14.<br \/>\n14.03<br \/>\nType below:<br \/>\n__________<\/p>\n<p>Answer:<br \/>\n14.03 and -14.03<\/p>\n<p>Explanation:<br \/>\n14.03 and -14.03 are at the same distance from 0.<\/p>\n<p>Question 15.<br \/>\n0.59<br \/>\nType below:<br \/>\n__________<\/p>\n<p>Answer:<br \/>\n0.59 and -0.59<\/p>\n<p>Explanation:<br \/>\n0.59 and -0.59 are at the same distance from 0.<\/p>\n<p>Question 16.<br \/>\n3\\(\\frac{1}{7}\\)<br \/>\nType below:<br \/>\n__________<\/p>\n<p>Answer:<br \/>\n3\\(\\frac{1}{7}\\) and -3\\(\\frac{1}{7}\\)<\/p>\n<p>Explanation:<br \/>\n3\\(\\frac{1}{7}\\) and -3\\(\\frac{1}{7}\\) are at the same distance from 0.<\/p>\n<p><strong>Use Reasoning Algebra Find the missing number or numbers to make the statement true.<\/strong><\/p>\n<p>Question 17.<br \/>\n|?| = 10<br \/>\nType below:<br \/>\n__________<\/p>\n<p>Answer:<br \/>\n10 and -10<\/p>\n<p>Explanation:<br \/>\n|-10| = 10<br \/>\n|10| = 10<\/p>\n<p>Question 18.<br \/>\n|?| = 1.78<br \/>\nType below:<br \/>\n__________<\/p>\n<p>Answer:<br \/>\n1.78 and -1.78<\/p>\n<p>Explanation:<br \/>\n|-1.78| = 1.78<br \/>\n|1.78| = 1.78<\/p>\n<p>Question 19.<br \/>\n|?| = 0<br \/>\nType below:<br \/>\n__________<\/p>\n<p>Answer:<br \/>\n0<\/p>\n<p>Explanation:<br \/>\n|0| = 0<\/p>\n<p>Question 20.<br \/>\n|?| = \\(\\frac{15}{16}\\)<br \/>\nType below:<br \/>\n__________<\/p>\n<p>Answer:<br \/>\n\\(\\frac{-15}{16}\\) and \\(\\frac{15}{16}\\)<\/p>\n<p>Explanation:<br \/>\n|\\(\\frac{-15}{16}\\)| = \\(\\frac{15}{16}\\)<br \/>\n|\\(\\frac{15}{16}\\)| = \\(\\frac{15}{16}\\)<\/p>\n<p>Question 21.<br \/>\nFind all of the integers whose absolute value is less than |\u20134|.<br \/>\nType below:<br \/>\n__________<\/p>\n<p>Answer:<br \/>\n3, 2, 1, 0<\/p>\n<p>Explanation:<br \/>\nThe absolute value of |\u20134| = 4.<br \/>\n3, 2, 1, 0 are the integers whose absolute value is less than |\u20134|.<\/p>\n<h3><a id=\"Absolute_Value_\u2013_Page_No._168\"><\/a>Unlock The Problem &#8211; Page No. 168<\/h3>\n<p>Question 22.<br \/>\nThe Blue Ridge Trail starts at Park Headquarters in Big Bear Park and goes up the mountain. The Green Creek Trail starts at Park Headquarters and goes down the mountain. The table gives elevations of various points of interest in relation to Park Headquarters. How many points of interest are less than 1 kilometer above or below Park Headquarters?<br \/>\n<img loading=\"lazy\" src=\"https:\/\/ccssmathanswers.com\/wp-content\/uploads\/2020\/08\/Go-Math-Grade-6-Answer-Key-Chapter-3-Understand-Positive-and-Negative-Numbers-img-17.jpg\" alt=\"Go Math Grade 6 Answer Key Chapter 3 Understand Positive and Negative Numbers img 17\" width=\"375\" height=\"318\" \/><br \/>\na. How can you find how far above or below Park Headquarters a given point of interest is located?<br \/>\nType below:<br \/>\n__________<\/p>\n<p>Answer:<br \/>\nBy knowing the values below 1 km can help you to find how far above or below Park Headquarters a given point of interest is located<\/p>\n<p>Question 22.<br \/>\nb. How can you find the number of points of interest that are less than 1 km above or below Park Headquarters?<br \/>\nType below:<br \/>\n__________<\/p>\n<p>Answer:<br \/>\nBy counting the number of points of interest that are less than 1 km, you can find the number of points of interest that are less than 1 km above or below Park Headquarters.<\/p>\n<p>Question 22.<br \/>\nc. Find how far above or below Park Headquarters each point of interest is located.<br \/>\nType below:<br \/>\n__________<\/p>\n<p>Answer:<br \/>\nC, D, E, F, G, H<\/p>\n<p>Question 22.<br \/>\nd. How many points of interest are less than 1 kilometer above or below Park Headquarters?<br \/>\nType below:<br \/>\n__________<\/p>\n<p>Answer:<br \/>\n6<\/p>\n<p>Question 23.<br \/>\nUse Reasoning Name a rational number that can replace ? to make both statements true.<br \/>\n?&gt;<sup>\u2212<\/sup>3\u00a0 \u00a0 \u00a0 \u00a0 \u00a0 \u00a0 \u00a0|?|&lt;|<sup>\u2212<\/sup>3|<br \/>\nType below:<br \/>\n__________<\/p>\n<p>Answer:<br \/>\n-2 or -1 &gt;\u22123\u00a0 \u00a0 \u00a0 \u00a0 \u00a0 1 or 2 &lt; |\u22123|<\/p>\n<p>Explanation:<br \/>\nThe greatest numbers than -3 are -2 or -1.<br \/>\n|\u22123| = 3. So, the fewer numbers than 3 are 1, 2<\/p>\n<p>Question 24.<br \/>\nLaila said |4| equals |\u22124|. Is Laila correct? Use the number line and words to support your answer.<br \/>\nType below:<br \/>\n__________<\/p>\n<p>Answer:<br \/>\nLaila is correct. The absolute value of |\u22124| = 4 = |4|<\/p>\n<h3><a id=\"Absolute_Value_\u2013_Page_No._169\"><\/a>Absolute Value &#8211; Page No. 169<\/h3>\n<p><strong>Find the absolute value.<\/strong><\/p>\n<p>Question 1.<br \/>\n|7|<br \/>\nType below:<br \/>\n__________<\/p>\n<p>Answer:<br \/>\n7<\/p>\n<p>Explanation:<\/p>\n<p>The distance from 0 to the point I graphed is 2 units.<br \/>\n|7| = 7<\/p>\n<p>Question 2.<br \/>\n|<sup>\u2212<\/sup>8|<br \/>\nType below:<br \/>\n__________<\/p>\n<p>Answer:<br \/>\n8<\/p>\n<p>Explanation:<br \/>\nThe distance from 0 to the point I graphed is 2 units.<br \/>\n|\u22128| = 8<\/p>\n<p>Question 3.<br \/>\n|16|<br \/>\nType below:<br \/>\n__________<\/p>\n<p>Answer:<br \/>\n16<\/p>\n<p>Explanation:<br \/>\nThe distance from 0 to the point I graphed is 2 units.<br \/>\n|16| = 16<\/p>\n<p>Question 4.<br \/>\n|8.65|<br \/>\nType below:<br \/>\n__________<\/p>\n<p>Answer:<br \/>\n8.65<\/p>\n<p>Explanation:<br \/>\nThe distance from 0 to the point I graphed is 2 units.<br \/>\n|8.65| = 8.65<\/p>\n<p>Question 5.<br \/>\n|4\\(\\frac{3}{20}\\)|<br \/>\nType below:<br \/>\n__________<\/p>\n<p>Answer:<br \/>\n4\\(\\frac{3}{20}\\)<\/p>\n<p>Explanation:<br \/>\nThe distance from 0 to the point I graphed is 2 units.<br \/>\n|4\\(\\frac{3}{20}\\)| = 4\\(\\frac{3}{20}\\)<\/p>\n<p>Question 6.<br \/>\n|<sup>\u2212<\/sup>5000|<br \/>\nType below:<br \/>\n__________<\/p>\n<p>Answer:<br \/>\n5000<\/p>\n<p>Explanation:<br \/>\nThe distance from 0 to the point I graphed is 2 units.<br \/>\n|\u22125000| = 5000<\/p>\n<p><strong>Find all numbers with the given absolute value.<\/strong><\/p>\n<p>Question 7.<br \/>\n12<br \/>\nType below:<br \/>\n__________<\/p>\n<p>Answer:<br \/>\n12 and -12<\/p>\n<p>Explanation:<br \/>\n12 and -12 are at the same distance from 0.<\/p>\n<p>Question 8.<br \/>\n1.7<br \/>\nType below:<br \/>\n__________<\/p>\n<p>Answer:<br \/>\n1.7 and -1.7<\/p>\n<p>Explanation:<br \/>\n1.7 and -1.7 are at the same distance from 0.<\/p>\n<p>Question 9.<br \/>\n\\(\\frac{3}{5}\\)<br \/>\nType below:<br \/>\n__________<\/p>\n<p>Answer:<br \/>\n\\(\\frac{3}{5}\\) and \\(\\frac{-3}{5}\\)<\/p>\n<p>Explanation:<br \/>\n\\(\\frac{3}{5}\\) and \\(\\frac{-3}{5}\\) are at the same distance from 0.<\/p>\n<p>Question 10.<br \/>\n3\\(\\frac{1}{6}\\)<br \/>\nType below:<br \/>\n__________<\/p>\n<p>Answer:<br \/>\n3\\(\\frac{1}{6}\\) and -3\\(\\frac{1}{6}\\)<\/p>\n<p>Explanation:<br \/>\n3\\(\\frac{1}{6}\\) and -3\\(\\frac{1}{6}\\) are at the same distance from 0.<\/p>\n<p>Question 11.<br \/>\n0<br \/>\nType below:<br \/>\n__________<\/p>\n<p>Answer:<br \/>\n0<\/p>\n<p>Explanation:<br \/>\n0 is same distance from 0.<\/p>\n<p><strong>Find the number or numbers that make the statement true.<\/strong><\/p>\n<p>Question 12.<br \/>\n|?| = 17<br \/>\nType below:<br \/>\n__________<\/p>\n<p>Answer:<br \/>\n17 and -17<\/p>\n<p>Explanation:<br \/>\n|-17| = 17<br \/>\n|17| = 17<\/p>\n<p>Question 13.<br \/>\n|?| = 2.04<br \/>\nType below:<br \/>\n__________<\/p>\n<p>Answer:<br \/>\n2.04 and -2.04<\/p>\n<p>Explanation:<br \/>\n|-2.04| = 2.04<br \/>\n|2.04| = 2.04<\/p>\n<p>Question 14.<br \/>\n|?| = 1\\(\\frac{9}{10}\\)<br \/>\nType below:<br \/>\n__________<\/p>\n<p>Answer:<br \/>\n1\\(\\frac{9}{10}\\) and -1\\(\\frac{9}{10}\\)<\/p>\n<p>Explanation:<br \/>\n|-1\\(\\frac{9}{10}\\)| = 1\\(\\frac{9}{10}\\)<br \/>\n|1\\(\\frac{9}{10}\\)| = 1\\(\\frac{9}{10}\\)<\/p>\n<p>Question 15.<br \/>\n|?| = \\(\\frac{19}{24}\\)<br \/>\nType below:<br \/>\n__________<\/p>\n<p>Answer:<br \/>\n\\(\\frac{19}{24}\\) and \\(\\frac{-19}{24}\\)<\/p>\n<p>Explanation:<br \/>\n|\\(\\frac{-19}{24}\\)| = \\(\\frac{19}{24}\\)<br \/>\n|\\(\\frac{19}{24}\\)| = \\(\\frac{19}{24}\\)<\/p>\n<p><strong>Problem Solving<\/strong><\/p>\n<p>Question 16.<br \/>\nWhich two numbers are 7.5 units away from 0 on a number line?<br \/>\nType below:<br \/>\n__________<\/p>\n<p>Answer:<br \/>\n7.5 and -7.5 are away from 0 on a number line<\/p>\n<p>Explanation:<br \/>\n|7.5| = 7.5<br \/>\n|-7.5| = 7.5<\/p>\n<p>Question 17.<br \/>\nEmilio is playing a game. He just answered a question incorrectly, so his score will change by \u221210 points. Find the absolute value of \u221210.<br \/>\nType below:<br \/>\n__________<\/p>\n<p>Answer:<br \/>\n10<\/p>\n<p>Explanation:<br \/>\nEmilio is playing a game. He just answered a question incorrectly, so his score will change by \u221210 points.<br \/>\n|-10| = 10<\/p>\n<p>Question 18.<br \/>\nWrite two different real-world examples. One should involve the absolute value of a positive number, and the other should involve the absolute value of a negative number.<br \/>\nType below:<br \/>\n__________<\/p>\n<p>Answer:<br \/>\n1) If we have a balance of -$35 dollars in an account, we may also choose to represent that as a debt of $35.<br \/>\n2) The temperature of the human body<\/p>\n<h3><a id=\"Absolute_Value_\u2013_Page_No._170\"><\/a>Lesson Check &#8211; Page No. 170<\/h3>\n<p>Question 1.<br \/>\nWhat is the absolute value of \\(\\frac{8}{9}\\)?<br \/>\nType below:<br \/>\n__________<\/p>\n<p>Answer:<br \/>\n\\(\\frac{8}{9}\\)<\/p>\n<p>Explanation:<br \/>\n|\\(\\frac{8}{9}\\)| = \\(\\frac{8}{9}\\)<\/p>\n<p>Question 2.<br \/>\nWhat two numbers have an absolute value of 21.63?<br \/>\nType below:<br \/>\n__________<\/p>\n<p>Answer:<br \/>\n21.63 and -21.63<\/p>\n<p>Explanation:<br \/>\n|-21.63| = 21.63<br \/>\n|21.63| = 21.63<\/p>\n<p><strong>Spiral Review<\/strong><\/p>\n<p>Question 3.<br \/>\nRachel earned $89.70 on Tuesday. She spent $55.89 at the grocery store. How much money does she have left?<br \/>\n$ ______<\/p>\n<p>Answer:<br \/>\n$33.81<\/p>\n<p>Explanation:<br \/>\nRachel earned $89.70 on Tuesday. She spent $55.89 at the grocery store.<br \/>\n89.70 &#8211; 55.89 = 33.81<br \/>\nRachel has $33.81 left<\/p>\n<p>Question 4.<br \/>\nOne carton contains \\(\\frac{17}{20}\\) liter of juice. Another carton contains 0.87 liter of juice. Which carton contains the most?<br \/>\nType below:<br \/>\n__________<\/p>\n<p>Answer:<br \/>\n0.87 is more because 17\/20 is 0.85<\/p>\n<p>Explanation:<br \/>\nOne carton contains \\(\\frac{17}{20}\\) liter of juice. Another carton contains 0.87 liters of juice.<br \/>\n0.87 is more because 17\/20 is 0.85<\/p>\n<p>Question 5.<br \/>\nMaggie jogged \\(\\frac{7}{8}\\) mile on Monday and \\(\\frac{1}{2}\\) of that distance on Tuesday. How far did she jog on Tuesday?<br \/>\n\\(\\frac{\u25a1}{\u25a1}\\) mile<\/p>\n<p>Answer:<br \/>\n\\(\\frac{7}{4}\\) mile<\/p>\n<p>Explanation:<br \/>\nMaggie jogged \\(\\frac{7}{8}\\) mile on Monday and \\(\\frac{1}{2}\\) of that distance on Tuesday.<br \/>\n\\(\\frac{7}{8}\\) \u00f7 \\(\\frac{1}{2}\\) = 7\/4<br \/>\n7\/4 or as a mixed fraction which is 1 3\/4 mile<\/p>\n<p>Question 6.<br \/>\nTrygg has \\(\\frac{3}{4}\\) package of marigold seeds. He plants \\(\\frac{1}{6}\\) of those seeds in his garden and divides the rest equally into 10 flowerpots. What fraction of a package of seeds is planted in each flowerpot?<br \/>\n\\(\\frac{\u25a1}{\u25a1}\\) package<\/p>\n<p>Answer:<br \/>\n\\(\\frac{1}{16}\\) package<\/p>\n<p>Explanation:<br \/>\nHe has a 3\/4 package and plants 1\/6 of the seeds.<br \/>\n3\/4 \u00d7 1\/6 = 1\/8<br \/>\nHe divides the rest equally into 10 flowerpots.<br \/>\nSubtract 1\/8 from 3\/4.<br \/>\nThe common denominator of 4 and 8 is 8.<br \/>\nMultiply the numerator 3 \u00d7 2= 6 with a denominator of 8.<br \/>\n3\/4 &#8211; 1\/8 = 6\/8 -1\/8 = 5\/8<br \/>\n5\/8 is left to be divided equally into 10 flowerpots.<br \/>\n5\/8 \u00f7 10\/1<br \/>\n= 5\/8 * 1\/10<br \/>\n= 5\/80<br \/>\n= 1\/16<\/p>\n<h3><a id=\"Compare_Absolute_Values_\u2013_Page_No._173\"><\/a>Share and Show &#8211; Page No. 173<\/h3>\n<p>Question 1.<br \/>\nOn Monday, Allie\u2019s bank account balance was \u2013 $24. On Tuesday, her account balance was less than it was on Monday. Use absolute value to describe Allie\u2019s balance on Tuesday as a debt.<br \/>\nType below:<br \/>\n__________<\/p>\n<p>Answer:<br \/>\nOn Tuesday, her account balance is less than -$24 means her debt will be bigger than $24 dollars.<\/p>\n<p>Explanation:<br \/>\nOn Monday, allies&#8217; bank account balance was -$24.<br \/>\nBalance being negative means he is carrying a debt of $24.<br \/>\nOn Tuesday, Allie&#8217;s balance account was less than it was on Monday. It means<br \/>\nHer bank account &lt; -$24<br \/>\nSo, she must be carrying a debit bigger than $24.<br \/>\nTherefore, on Tuesday, her account balance being less than -$24 means her debt will be greater than $24 dollars.<\/p>\n<p>Question 2.<br \/>\nMatthew scored \u221236 points in his turn at a video game. In Genevieve\u2019s turn, she scored fewer points than Matthew. Use absolute value to describe Genevieve\u2019s score as a loss.<br \/>\nType below:<br \/>\n__________<\/p>\n<p>Answer:<br \/>\nGenevieve lost more than 36 points<\/p>\n<p>Explanation:<br \/>\nMatthew scored \u221236 points in his turn at a video game. In Genevieve\u2019s turn, she scored fewer points than Matthew.<br \/>\n-36 &gt; -40<br \/>\n|-36| &lt; |-40|<br \/>\n36 &lt; 40<br \/>\nGenevieve lost more than 36 points<\/p>\n<p><strong>On Your Own<\/strong><\/p>\n<p>Question 3.<br \/>\nOne of the cats shown in the table is a tabby. The tabby had a decrease in weight of more than 3.3 ounces. Which cat is the tabby?<br \/>\n<img loading=\"lazy\" src=\"https:\/\/ccssmathanswers.com\/wp-content\/uploads\/2020\/08\/Go-Math-Grade-6-Answer-Key-Chapter-3-Understand-Positive-and-Negative-Numbers-img-18.jpg\" alt=\"Go Math Grade 6 Answer Key Chapter 3 Understand Positive and Negative Numbers img 18\" width=\"287\" height=\"187\" \/><br \/>\nType below:<br \/>\n__________<\/p>\n<p>Answer:<br \/>\nSpot is tabby<\/p>\n<p>Explanation:<br \/>\n|-3.4| = 3.4<br \/>\nSo, Spot is tabby<\/p>\n<p><strong>Compare. Write &lt;, &gt;, or =.<\/strong><\/p>\n<p>Question 4.<br \/>\n\u22128 _____ |<sup>\u2212<\/sup>8|<\/p>\n<p>Answer:<br \/>\n\u22128 &lt; |\u22128|<\/p>\n<p>Explanation:<br \/>\n|\u22128| = 8<br \/>\n-8 &lt; 8<\/p>\n<p>Question 5.<br \/>\n13 _____ |<sup>\u2212<\/sup>13|<\/p>\n<p>Answer:<br \/>\n13 = |\u221213|<\/p>\n<p>Explanation:<br \/>\n|\u221213| = 13<br \/>\n13 = 13<\/p>\n<p>Question 6.<br \/>\n|<sup>\u2212<\/sup>23| _____ |<sup>\u2212<\/sup>24|<\/p>\n<p>Answer:<br \/>\n|\u221223| &lt; |\u221224|<\/p>\n<p>Explanation:<br \/>\n|\u221223| = 23<br \/>\n|\u221224| = 24<br \/>\n23 &lt; 24<\/p>\n<p>Question 7.<br \/>\n15 _____ |<sup>\u2212<\/sup>14|<\/p>\n<p>Answer:<br \/>\n15 &gt; |\u221214|<\/p>\n<p>Explanation:<br \/>\n|\u221214| = 14<br \/>\n15 &gt; 14<\/p>\n<p>Question 8.<br \/>\n34 _____ |<sup>\u2212<\/sup>36|<\/p>\n<p>Answer:<br \/>\n34 &lt; |\u221236|<\/p>\n<p>Explanation:<br \/>\n|\u221236| = 36<br \/>\n34 &lt; 36<\/p>\n<p>Question 9.<br \/>\n\u22125 _____ |<sup>\u2212<\/sup>6|<\/p>\n<p>Answer:<br \/>\n\u22125 &lt; |\u22126|<\/p>\n<p>Explanation:<br \/>\n|\u22126| = 6<br \/>\n-5 &lt; 6<\/p>\n<p>Question 10.<br \/>\nWrite the values in order from least to greatest.<br \/>\n<img loading=\"lazy\" src=\"https:\/\/ccssmathanswers.com\/wp-content\/uploads\/2020\/08\/Go-Math-Grade-6-Answer-Key-Chapter-3-Understand-Positive-and-Negative-Numbers-img-19.jpg\" alt=\"Go Math Grade 6 Answer Key Chapter 3 Understand Positive and Negative Numbers img 19\" width=\"350\" height=\"68\" \/><br \/>\nType below:<br \/>\n__________<\/p>\n<p>Answer:<br \/>\n1, 2, 3, 6<\/p>\n<p>Explanation:<br \/>\n|-2| = 2<br \/>\n|3| = 3<br \/>\n|-6| = 6<br \/>\n|1| = 1<br \/>\n1 &lt; 2 &lt; 3 &lt; 6<\/p>\n<h3><a id=\"Compare_Absolute_Values_\u2013_Page_No._174\"><\/a>Compare and Contrast &#8211; Page No. 174<\/h3>\n<p>When you compare and contrast, you look for ways that two or more subjects are alike (compare) and ways they are different (contrast). This helps you to discover information about each subject that you might not have known otherwise. As you read the following passage, think about how the main topics are alike and how they are different.<\/p>\n<p>Trevor mows lawns after school to raise money for a new mountain bike. Last week, it rained every day, and he couldn\u2019t work. While waiting for better weather, he spent some of his savings on lawnmower repairs. As a result, his savings balance changed by \u2212$45. This week, the weather was better, and Trevor returned to work. His savings balance changed by +$45 this week.<\/p>\n<p>Question 11.<br \/>\nThe passage has two main parts. Describe them.<br \/>\nType below:<br \/>\n__________<\/p>\n<p>Answer:<br \/>\nLast week, Trevor couldn&#8217;t work, so he spent money to repair the lawnmower!<br \/>\nThis week, he goes back to work and earns money again!<\/p>\n<p>Question 12.<br \/>\nDescribe the two changes in Trevor\u2019s savings balance<br \/>\nType below:<br \/>\n__________<\/p>\n<p>Answer:<br \/>\nHis savings balance changed by \u2212$45 in one week and his savings balance changed by +$45 in another week.<\/p>\n<p>Question 13.<br \/>\nReason Quantitatively Compare the two changes in Trevor\u2019s savings balance. How are they alike?<br \/>\nType below:<br \/>\n__________<\/p>\n<p>Answer:<br \/>\nEach week, Trevor&#8217;s balance changed by $45\u037e or his balance is the same distance from 0 each week.<\/p>\n<p>Question 14.<br \/>\nContrast the two changes in Trevor\u2019s savings balance. How are they different?<br \/>\nType below:<br \/>\n__________<\/p>\n<p>Answer:<br \/>\nThe balances are different because one week the balance had a decrease, while the next week there was an increase in the balance<\/p>\n<h3><a id=\"Compare_Absolute_Values_\u2013_Page_No._175\"><\/a>Compare Absolute Values &#8211; Page No. 175<\/h3>\n<p><strong>Solve.<\/strong><\/p>\n<p>Question 1.<br \/>\nJamie scored \u22125 points on her turn at a trivia game. In Veronica\u2019s turn, she scored more points than Jamie. Use absolute value to describe Veronica\u2019s score as a loss.<br \/>\nType below:<br \/>\n__________<br \/>\nJamie scored \u22125 points on her turn at a trivia game. In Veronica\u2019s turn, she scored more points than Jamie.<\/p>\n<p>Answer:<br \/>\nIn this situation, |-5| represents a loss of 5 points. Veronica lost fewer than 5 points.<\/p>\n<p>Question 2.<br \/>\nThe low temperature on Friday was \u221210\u00b0F. The low temperature on Saturday was colder. Use absolute value to describe the temperature on Saturday as a temperature below zero.<br \/>\nType below:<br \/>\n__________<\/p>\n<p>Answer:<br \/>\nThe temperature on Sunday was more than 10 degrees below zero<\/p>\n<p>Explanation:<br \/>\nThe low temperature on Friday was \u221210\u00b0F. The low temperature on Saturday was colder. The temperature on Sunday was more than 10 degrees below zero<\/p>\n<p>Question 3.<br \/>\nThe table shows changes in the savings accounts of five students. Which student had the greatest increase in money? By how much did the student\u2019s account increase?<br \/>\n<img loading=\"lazy\" src=\"https:\/\/ccssmathanswers.com\/wp-content\/uploads\/2020\/08\/Go-Math-Grade-6-Answer-Key-Chapter-3-Understand-Positive-and-Negative-Numbers-img-20.jpg\" alt=\"Go Math Grade 6 Answer Key Chapter 3 Understand Positive and Negative Numbers img 20\" width=\"368\" height=\"185\" \/><br \/>\nType below:<br \/>\n__________<\/p>\n<p>Answer:<br \/>\nCarissa; an increase of $15<\/p>\n<p><strong>Compare. Write &lt;, &gt;, or =.<\/strong><\/p>\n<p>Question 4.<br \/>\n<sup>\u2212<\/sup>16 _____ |<sup>\u2212<\/sup>16|<\/p>\n<p>Answer:<br \/>\n\u221216 &lt; |\u221216|<\/p>\n<p>Explanation:<br \/>\n|\u221216| = 16<br \/>\n-16 &lt; 16<\/p>\n<p>Question 5.<br \/>\n20 _____ 20<\/p>\n<p>Answer:<br \/>\n20 = 20<\/p>\n<p>Question 6.<br \/>\n3 _____ |<sup>\u2212<\/sup>4|<\/p>\n<p>Answer:<br \/>\n3 &lt; |\u22124|<\/p>\n<p>Explanation:<br \/>\n|\u22124| = 4<br \/>\n3 &lt; 4<\/p>\n<p><strong>Problem Solving<\/strong><\/p>\n<p>Question 7.<br \/>\nOn Wednesday, Miguel\u2019s bank account balance was \u2212$55. On Thursday, his balance was less than that. Use absolute value to describe Miguel\u2019s balance on Thursday as a debt.<br \/>\nType below:<br \/>\n__________<\/p>\n<p>Answer:<br \/>\nIn this situation, -$55 represents a debt of $55. On Thursday, Miguel had a debt of more than $55.<\/p>\n<p>Explanation:<br \/>\nOn Wednesday, Miguel\u2019s bank account balance was \u2212$55. On Thursday, his balance was less than that.<br \/>\nIn this situation, -$55 represents a debt of $55. On Thursday, Miguel had a debt of more than $55.<\/p>\n<p>Question 8.<br \/>\nDuring a game, Naomi lost points. She lost fewer than 3 points. Use an integer to describe her possible score.<br \/>\nType below:<br \/>\n__________<\/p>\n<p>Answer:<br \/>\n-2, -1<\/p>\n<p>Explanation:<br \/>\nDuring a game, Naomi lost points. She lost fewer than 3 points.<br \/>\nIt may be -2, -1<\/p>\n<p>Question 9.<br \/>\nGive two numbers that fit this description: a number is less than another number but has a greater absolute value. Describe how you determined the numbers.<br \/>\nType below:<br \/>\n__________<\/p>\n<p>Answer:<br \/>\nChoose a large negative number and a smaller positive number.<br \/>\nExample: Use -14 and 3, -8392 and 274, -1 and 0.5, etc. Even though the negative numbers are technically less, they would have higher absolute values.<\/p>\n<h3><a id=\"Compare_Absolute_Values_\u2013_Page_No._176\"><\/a>Lesson Check &#8211; Page No. 176<\/h3>\n<p>Question 1.<br \/>\nA temperature of \u20136\u00b0 is colder than a temperature of 5\u00b0F below zero. Is this statement true or false?<br \/>\nType below:<br \/>\n__________<\/p>\n<p>Answer:<br \/>\nTrue<\/p>\n<p>Explanation:<br \/>\n\u20136\u00b0 is colder than a temperature of 5\u00b0F below zero<\/p>\n<p>Question 2.<br \/>\nLong Beach, California has an elevation of \u22127 feet. New Orleans, Louisiana is 8 feet below sea level. Which city has a lower elevation?<br \/>\nType below:<br \/>\n__________<\/p>\n<p>Answer:<br \/>\nNew Orleans, Louisiana has a lower elevation<\/p>\n<p>Explanation:<br \/>\nLong Beach, California has an elevation of \u22127 feet.<br \/>\nNew Orleans, Louisiana is 8 feet below sea level. = -8 feet<br \/>\nSo, New Orleans, Louisiana has a lower elevation.<\/p>\n<p><strong>Spiral Review<\/strong><\/p>\n<p>Question 3.<br \/>\nDawn and Lin took off on skateboards from the same location but traveled in opposite directions. After 20 minutes, Dawn had traveled 6.42 kilometers and Lin had traveled 7.7 kilometers. How far apart were they?<br \/>\n_____ kilometers<\/p>\n<p>Answer:<br \/>\n14.12 kilometers<\/p>\n<p>Explanation:<br \/>\nDistance of Dawn = 6.42 km<br \/>\nDistance from Lin = 7.7 km in the opposite direction.<br \/>\nIf they went in opposite directions then they were moving away from each other.<br \/>\nThe final distance between the two, d = 6.42 + 7.7 = 14.12 km<br \/>\nAfter 20 minutes Dawn and Lin were 14.12 km away.<\/p>\n<p>Question 4.<br \/>\nRico and Josh took off on skateboards going in the same direction. After 20 minutes, Rico had traveled 5.98 kilometers and Josh had gone 8.2 kilometers. How far apart were they?<br \/>\n_____ kilometers<\/p>\n<p>Answer:<br \/>\n2.22 kilometers<\/p>\n<p>Explanation:<br \/>\nRico and Josh took off on skateboards going in the same direction.<br \/>\nAfter 20 minutes, Rico had traveled 5.98 kilometers and Josh had gone 8.2 kilometers.<br \/>\nD = 8.2 &#8211; 5.98 = 2.22 km<br \/>\nHence, Rico and Josh were 2.22 km apart from each other.<\/p>\n<p>Question 5.<br \/>\nEtta bought 11.5 yards of fabric selling for $0.90 per yard. What was the total cost?<br \/>\n$ _____<\/p>\n<p>Answer:<br \/>\n$10.35<\/p>\n<p>Explanation:<br \/>\nMultiply 11.5 times 0.90 and get $10.35<\/p>\n<p>Question 6.<br \/>\nYen calculates the product \\(\\frac{5}{8} \\times \\frac{24}{25}\\). Before he multiplies, he simplifies all factors. What does the problem look like after he simplifies the factors?<br \/>\nType below:<br \/>\n__________<\/p>\n<p>Answer:<br \/>\nYen calculates the product \\(\\frac{5}{8} \\times \\frac{24}{25}\\).<br \/>\n5\/8 = 0.625<br \/>\n24\/25 = 0.96<br \/>\n0.625 \u00d7 0.96 = 0.6<\/p>\n<h3><a id=\"Rational_Numbers_and_the_Coordinate_Plane_\u2013_Page_No._179\"><\/a>Share and Show &#8211; Page No. 179<\/h3>\n<p><img loading=\"lazy\" src=\"https:\/\/ccssmathanswers.com\/wp-content\/uploads\/2020\/08\/Go-Math-Grade-6-Answer-Key-Chapter-3-Understand-Positive-and-Negative-Numbers-img-21.jpg\" alt=\"Go Math Grade 6 Answer Key Chapter 3 Understand Positive and Negative Numbers img 21\" width=\"264\" height=\"261\" \/><\/p>\n<p>Question 1.<br \/>\nWrite the ordered pair for point J.<br \/>\nType below:<br \/>\n__________<\/p>\n<p>Answer:<br \/>\n(-1.5, 2.5)<\/p>\n<p>Explanation:<br \/>\nTo find the x-coordinate, move 1.5 units to the left.<br \/>\nTo find the y-coordinate, move 2.5 units up.<br \/>\nPoint J is located at (-1.5, 2.5)<\/p>\n<p><strong>Write the ordered pair for the point.<\/strong><\/p>\n<p>Question 2.<br \/>\nK<br \/>\nType below:<br \/>\n__________<\/p>\n<p>Answer:<br \/>\n(1, -1.5)<\/p>\n<p>Explanation:<br \/>\nTo find the x-coordinate, move 1 unit to the right.<br \/>\nTo find the y-coordinate, move 1.5 units down.<br \/>\nPoint K is located at (1, -1.5)<\/p>\n<p>Question 3.<br \/>\nL<br \/>\nType below:<br \/>\n__________<\/p>\n<p>Answer:<br \/>\n(-2, -1.75)<\/p>\n<p>Explanation:<br \/>\nTo find the x-coordinate, move 2 units to the left.<br \/>\nTo find y-coordinate, move 1.75 units down.<br \/>\nPoint L is located at (-2, -1.75)<\/p>\n<p>Question 4.<br \/>\nM<br \/>\nType below:<br \/>\n__________<\/p>\n<p>Answer:<br \/>\n(1, 0)<\/p>\n<p>Explanation:<br \/>\nTo find the x-coordinate, move 1 unit to the right.<br \/>\nTo find y-coordinate, move 0 units.<br \/>\nPoint M is located at (1, 0)<\/p>\n<p><strong>Graph and label the point on the coordinate plane.<\/strong><\/p>\n<p>Question 5.<br \/>\nP(-2.5, 2)<br \/>\nType below:<br \/>\n__________<\/p>\n<p>Answer:<br \/>\nThe x-coordinate is negative. Move 2.5 units to the left.<br \/>\ny-coordinate is positive. Move 2 units up<\/p>\n<p>Question 6.<br \/>\nQ(-2, \\(\\frac{1}{4}\\))<br \/>\nType below:<br \/>\n__________<\/p>\n<p>Answer:<br \/>\nThe x-coordinate is negative. Move 2 units to the left.<br \/>\ny-coordinate is positive. Move 0.25 units up<\/p>\n<p>Question 7.<br \/>\nR(0, 1.5)<br \/>\nType below:<br \/>\n__________<\/p>\n<p>Answer:<br \/>\nThe x-coordinate is positive. Move 0 units.<br \/>\ny-coordinate is positive. Move 1.5 units up<\/p>\n<p>Question 8.<br \/>\nS(-1, \\(\\frac{-1}{2}\\))<br \/>\nType below:<br \/>\n__________<\/p>\n<p>Answer:<br \/>\nThe x-coordinate is negative. Move 1 unit to the left.<br \/>\ny-coordinate is negative. Move 0.5 units down<\/p>\n<p>Question 9.<br \/>\nT( 1\\(\\frac{1}{2}\\), -2 )<br \/>\nType below:<br \/>\n__________<\/p>\n<p>Answer:<br \/>\nThe x-coordinate is positive. Move 1.5 units to the right.<br \/>\ny-coordinate is negative. Move 2 units down<\/p>\n<p>Question 10.<br \/>\nU(0.75, 1.25)<br \/>\nType below:<br \/>\n__________<\/p>\n<p>Answer:<br \/>\nThe x-coordinate is positive. Move 0.75 units to the right.<br \/>\ny-coordinate is positive. Move 1.25 units up<\/p>\n<p>Question 11.<br \/>\nV(-0.5, 0)<br \/>\nType below:<br \/>\n__________<\/p>\n<p>Answer:<br \/>\nThe x-coordinate is negative. Move 0.5 units to the left.<br \/>\ny-coordinate is positive. Move 0 units<\/p>\n<p>Question 12.<br \/>\nW(2, 0)<br \/>\nType below:<br \/>\n__________<\/p>\n<p>Answer:<br \/>\nThe x-coordinate is positive. Move 2 units to the right.<br \/>\ny-coordinate is positive. Move 0 units up<\/p>\n<p>Question 13.<br \/>\nX(0, -2)<br \/>\nType below:<br \/>\n__________<\/p>\n<p>Answer:<br \/>\nThe x-coordinate is positive. Move 0 units.<br \/>\ny-coordinate is negative. Move 2 units down<\/p>\n<p><img loading=\"lazy\" class=\"alignnone size-medium wp-image-7282\" src=\"https:\/\/ccssmathanswers.com\/wp-content\/uploads\/2020\/08\/grade-6-chapter-3-Page-no.-175-image-1-300x291.jpg\" alt=\"grade 6 chapter 3 Page no. 175 image 1\" width=\"300\" height=\"291\" srcset=\"https:\/\/bigideasmathanswers.com\/wp-content\/uploads\/2020\/08\/grade-6-chapter-3-Page-no.-175-image-1-300x291.jpg 300w, https:\/\/bigideasmathanswers.com\/wp-content\/uploads\/2020\/08\/grade-6-chapter-3-Page-no.-175-image-1.jpg 452w\" sizes=\"(max-width: 300px) 100vw, 300px\" \/><\/p>\n<p><strong>On Your Own<\/strong><\/p>\n<p><strong>Write the ordered pair for the point. Give approximate coordinates when necessary.<\/strong><br \/>\n<img loading=\"lazy\" src=\"https:\/\/ccssmathanswers.com\/wp-content\/uploads\/2020\/08\/Go-Math-Grade-6-Answer-Key-Chapter-3-Understand-Positive-and-Negative-Numbers-img-22.jpg\" alt=\"Go Math Grade 6 Answer Key Chapter 3 Understand Positive and Negative Numbers img 22\" width=\"306\" height=\"307\" \/><\/p>\n<p>Question 14.<br \/>\nA<br \/>\nType below:<br \/>\n__________<\/p>\n<p>Answer:<br \/>\n(4, 4)<\/p>\n<p>Explanation:<br \/>\nTo find the x-coordinate, move 4 units to the right.<br \/>\nTo find y-coordinate, move 4 units up.<br \/>\nPoint A is located at (4, 4)<\/p>\n<p>Question 15.<br \/>\nB<br \/>\nType below:<br \/>\n__________<\/p>\n<p>Answer:<br \/>\n(-4, 3)<\/p>\n<p>Explanation:<br \/>\nTo find the x-coordinate, move 4 units to the left.<br \/>\nTo find y-coordinate, move 3 units up.<br \/>\nPoint B is located at (-4, 3)<\/p>\n<p>Question 16.<br \/>\nC<br \/>\nType below:<br \/>\n__________<\/p>\n<p>Answer:<br \/>\n(-3, 1)<\/p>\n<p>Explanation:<br \/>\nTo find the x-coordinate, move 3 units to the left.<br \/>\nTo find y-coordinate, move 1 unit up.<br \/>\nPoint C is located at (-3, 1)<\/p>\n<p>Question 17.<br \/>\nD<br \/>\nType below:<br \/>\n__________<\/p>\n<p>Answer:<br \/>\n(-2, -3)<\/p>\n<p>Explanation:<br \/>\nTo find the x-coordinate, move 2 units to the left.<br \/>\nTo find y-coordinate, move 3 units down.<br \/>\nPoint D is located at (-2, -3)<\/p>\n<p>Question 18.<br \/>\nE<br \/>\nType below:<br \/>\n__________<\/p>\n<p>Answer:<br \/>\n(5, -3)<\/p>\n<p>Explanation:<br \/>\nTo find the x-coordinate, move 5 units to the right.<br \/>\nTo find y-coordinate, move 3 units down.<br \/>\nPoint E is located at (5, -3)<\/p>\n<p>Question 19.<br \/>\nF<br \/>\nType below:<br \/>\n__________<\/p>\n<p>Answer:<br \/>\n(2.5, 0)<\/p>\n<p>Explanation:<br \/>\nTo find the x-coordinate, move 2.5 units to the right.<br \/>\nTo find y-coordinate, move 0 units.<br \/>\nPoint F is located at (2.5, 0)<\/p>\n<p>Question 20.<br \/>\nG<br \/>\nType below:<br \/>\n__________<\/p>\n<p>Answer:<br \/>\n(-4, -5)<\/p>\n<p>Explanation:<br \/>\nTo find the x-coordinate, move 4 units to the left.<br \/>\nTo find y-coordinate, move 5 units down.<br \/>\nPoint G is located at (-4, -5)<\/p>\n<p>Question 21.<br \/>\nH<br \/>\nType below:<br \/>\n__________<\/p>\n<p>Answer:<br \/>\n(0, 3.5)<\/p>\n<p>Explanation:<br \/>\nTo find the x-coordinate, move 0 units.<br \/>\nTo find y-coordinate, move 3.5 units up.<br \/>\nPoint H is located at (0, 3.5)<\/p>\n<p>Question 22.<br \/>\nJ<br \/>\nType below:<br \/>\n__________<\/p>\n<p>Answer:<br \/>\n(0.5, 0.5)<\/p>\n<p>Explanation:<br \/>\nTo find the x-coordinate, move 0.5 units to the right.<br \/>\nTo find y-coordinate, move 0.5 units up.<br \/>\nPoint J is located at (0.5, 0.5)<\/p>\n<p><strong>Graph and label the point on the coordinate plane.<\/strong><\/p>\n<p>Question 23.<br \/>\nM(-4, 0)<br \/>\nType below:<br \/>\n__________<\/p>\n<p>Answer:<br \/>\nThe x-coordinate is negative. Move 4 units to the left.<br \/>\ny-coordinate is positive. Move 0 units<\/p>\n<p>Question 24.<br \/>\nN(2, 2)<br \/>\nType below:<br \/>\n__________<\/p>\n<p>Answer:<br \/>\nThe x-coordinate is positive. Move 2 units to the right.<br \/>\ny-coordinate is positive. Move 2 units up<\/p>\n<p>Question 25.<br \/>\nP(-3, 3)<br \/>\nType below:<br \/>\n__________<\/p>\n<p>Answer:<br \/>\nThe x-coordinate is positive. Move 3 units to the left.<br \/>\ny-coordinate is positive. Move 3 units up<\/p>\n<p>Question 26.<br \/>\nQ(0, \u22122\\(\\frac{1}{2}\\))<br \/>\nType below:<br \/>\n__________<\/p>\n<p>Answer:<br \/>\nThe x-coordinate is positive. Move 0 units.<br \/>\ny-coordinate is negative. Move 2.5 units down<\/p>\n<p>Explanation:<\/p>\n<p>Question 27.<br \/>\nR(0.5, 0.5)<br \/>\nType below:<br \/>\n__________<\/p>\n<p>Answer:<br \/>\nThe x-coordinate is positive. Move 0.5 units to the right.<br \/>\ny-coordinate is positive. Move 0.5 units up<\/p>\n<p>Question 28.<br \/>\nS(-5, \\(\\frac{1}{2}\\))<br \/>\nType below:<br \/>\n__________<\/p>\n<p>Answer:<br \/>\nThe x-coordinate is negative. Move 5 units to the left.<br \/>\ny-coordinate is positive. Move 0.5 units up<\/p>\n<p>Question 29.<br \/>\nT(0, 0)<br \/>\nType below:<br \/>\n__________<\/p>\n<p>Answer:<br \/>\nIt is at the origin. T is at the origin<\/p>\n<p>Question 30.<br \/>\nU(3 \\(\\frac{1}{2}\\), 0)<br \/>\nType below:<br \/>\n__________<\/p>\n<p>Answer:<br \/>\nThe x-coordinate is positive. Move 3.5 units to the right.<br \/>\ny-coordinate is positive. Move 0 units<\/p>\n<p>Question 31.<br \/>\nV(-2, -4)<br \/>\nType below:<br \/>\n__________<\/p>\n<p>Answer:<br \/>\nThe x-coordinate is negative. Move 2 units to the left.<br \/>\ny-coordinate is negative. Move 4 units down<\/p>\n<p><img loading=\"lazy\" class=\"alignnone size-medium wp-image-7285\" src=\"https:\/\/ccssmathanswers.com\/wp-content\/uploads\/2020\/08\/grade-6-chapter-3-Page-no.-175-image-2-300x297.jpg\" alt=\"grade 6 chapter 3 Page no. 175 image 2\" width=\"300\" height=\"297\" srcset=\"https:\/\/bigideasmathanswers.com\/wp-content\/uploads\/2020\/08\/grade-6-chapter-3-Page-no.-175-image-2-300x297.jpg 300w, https:\/\/bigideasmathanswers.com\/wp-content\/uploads\/2020\/08\/grade-6-chapter-3-Page-no.-175-image-2-150x150.jpg 150w, https:\/\/bigideasmathanswers.com\/wp-content\/uploads\/2020\/08\/grade-6-chapter-3-Page-no.-175-image-2.jpg 479w\" sizes=\"(max-width: 300px) 100vw, 300px\" \/><\/p>\n<p>Question 32.<br \/>\nLook for Structure A point lies to the left of the y-axis and below the x-axis. What can you conclude about the coordinates of the point?<br \/>\nType below:<br \/>\n__________<\/p>\n<p>Answer:<br \/>\nA point lies to the left of the y-axis. So, the x-coordinate is negative.<br \/>\nA point lies below the x-axis. So, y-coordinate is negative.<br \/>\nBoth coordinates points are negative<\/p>\n<h3><a id=\"Rational_Numbers_and_the_Coordinate_Plane_\u2013_Page_No._180\"><\/a>Problem Solving + Applications &#8211; Page No. 180<\/h3>\n<p><strong>Many of the streets in downtown Philadelphia can be modeled by a coordinate plane, as shown on the map. Each unit on the map represents one block. Use the map for 33 and 34.<\/strong><br \/>\n<img loading=\"lazy\" src=\"https:\/\/ccssmathanswers.com\/wp-content\/uploads\/2020\/08\/Go-Math-Grade-6-Answer-Key-Chapter-3-Understand-Positive-and-Negative-Numbers-img-23.jpg\" alt=\"Go Math Grade 6 Answer Key Chapter 3 Understand Positive and Negative Numbers img 23\" width=\"472\" height=\"348\" \/><\/p>\n<p>Question 33.<br \/>\nAnita works at the Historical Society. She leaves the building and walks 3 blocks north to a restaurant. What ordered pair represents the restaurant?<br \/>\nType below:<br \/>\n__________<\/p>\n<p>Answer:<br \/>\nAnita works at the Historical Society. She leaves the building and walks 3 blocks north to a restaurant.<br \/>\nHistorical Society = (2, 4)<br \/>\nAs she walks 3 blocks north to a restaurant 4-3 = 1<br \/>\n(2, 1) ordered pair represents the restaurant<\/p>\n<p>Question 34.<br \/>\nPose a Problem Write and solve a new problem that uses a location on the map.<br \/>\nType below:<br \/>\n__________<\/p>\n<p>Answer:<br \/>\nAnita is at City Hall. She walked 3 blocks to the East and 2 blocks to the North. What ordered pair represents her present location?<br \/>\nShe is at the Fabric Workshop &amp; Museum. The ordered pair is (3, 2)<\/p>\n<p>Question 35.<br \/>\nThe points A, B, C, and D on a coordinate plane can be connected to form a rectangle. Point A is located at (2, 0), point B is located at (6, 0), and point C is located at (6, \u20132.5). Write the ordered pair for point D.<br \/>\nType below:<br \/>\n__________<\/p>\n<p>Answer:<br \/>\nThe point D is at (2, -2.5)<\/p>\n<p>Explanation:<br \/>\n<img loading=\"lazy\" class=\"alignnone size-medium wp-image-7292\" src=\"https:\/\/ccssmathanswers.com\/wp-content\/uploads\/2020\/08\/grade-6-chapter-3-Page-no.-180-image-1-300x286.jpg\" alt=\"grade 6 chapter 3 Page no. 180 image 1\" width=\"300\" height=\"286\" srcset=\"https:\/\/bigideasmathanswers.com\/wp-content\/uploads\/2020\/08\/grade-6-chapter-3-Page-no.-180-image-1-300x286.jpg 300w, https:\/\/bigideasmathanswers.com\/wp-content\/uploads\/2020\/08\/grade-6-chapter-3-Page-no.-180-image-1.jpg 509w\" sizes=\"(max-width: 300px) 100vw, 300px\" \/><br \/>\nThe points A, B, C, and D on a coordinate plane can be connected to form a rectangle. Point A is located at (2, 0), point B is located at (6, 0), and point C is located at (6, \u20132.5). The point D is at (2, -2.5)<\/p>\n<p>Question 36.<br \/>\nIdentify Relationships Explain how you can tell that the line segment connecting two points is vertical without graphing the points.<br \/>\nType below:<br \/>\n__________<\/p>\n<p>Answer:<br \/>\nThe line segment connecting two points is vertical. By calculating the slope, we can say that the line segment connecting two points is vertical without graphing the points.<\/p>\n<p>Question 37.<br \/>\nFor numbers 37a\u201337d, select True or False for each statement.<br \/>\n37a. Point A (2, \u20131) is to the right of the y-axis and below the x-axis.<br \/>\n37b. Point B (\u2013 5,2) is to the left of the y-axis and below the x-axis.<br \/>\n37c. Point C (3, 2) is to the right of the y-axis and above the x-axis.<br \/>\n37d. Point D (\u20132, \u20131) is to the left of the y-axis and below the x-axis.<br \/>\n37a. __________<br \/>\n37b. __________<br \/>\n37c. __________<br \/>\n37d. __________<\/p>\n<p>Answer:<br \/>\n37a. True<br \/>\n37b. False<br \/>\n37c. True<br \/>\n37d. True<\/p>\n<h3><a id=\"Rational_Numbers_and_the_Coordinate_Plane_\u2013_Page_No._181\"><\/a>Rational Numbers and the Coordinate Plane &#8211; Page No. 181<\/h3>\n<p><strong>Write the ordered pair for the point. Give approximate coordinates when necessary.<\/strong><br \/>\n<img loading=\"lazy\" src=\"https:\/\/ccssmathanswers.com\/wp-content\/uploads\/2020\/08\/Go-Math-Grade-6-Answer-Key-Chapter-3-Understand-Positive-and-Negative-Numbers-img-24.jpg\" alt=\"Go Math Grade 6 Answer Key Chapter 3 Understand Positive and Negative Numbers img 24\" width=\"307\" height=\"303\" \/><\/p>\n<p>Question 1.<br \/>\nA<br \/>\nType below:<br \/>\n__________<\/p>\n<p>Answer:<br \/>\n(1, 0.5)<\/p>\n<p>Explanation:<br \/>\nTo find the x-coordinate, move 1 unit to the right.<br \/>\nTo find y-coordinate, move 0.5 units up.<br \/>\nPoint A is located at (1, 0.5)<\/p>\n<p>Question 2.<br \/>\nB<br \/>\nType below:<br \/>\n__________<\/p>\n<p>Answer:<br \/>\n(-0.75, -2.5)<\/p>\n<p>Explanation:<br \/>\nTo find the x-coordinate, move 0.75 units to the left.<br \/>\nTo find y-coordinate, move 2.5 units down.<br \/>\nPoint B is located at (-0.75, -2.5)<\/p>\n<p>Question 3.<br \/>\nC<br \/>\nType below:<br \/>\n__________<\/p>\n<p>Answer:<br \/>\n(2, -1.5)<\/p>\n<p>Explanation:<br \/>\nTo find the x-coordinate, move 2 units to the right.<br \/>\nTo find y-coordinate, move 1.5 units down.<br \/>\nPoint C is located at (2, -1.5)<\/p>\n<p>Question 4.<br \/>\nD<br \/>\nType below:<br \/>\n__________<\/p>\n<p>Answer:<br \/>\n(-1.5, 0)<\/p>\n<p>Explanation:<br \/>\nTo find the x-coordinate, move 1.5 units to the left.<br \/>\nTo find y-coordinate, move 0 units.<br \/>\nPoint D is located at (-1.5, 0)<\/p>\n<p><strong>Graph and label the point on the coordinate plane.<\/strong><\/p>\n<p>Question 5.<br \/>\nG(\u2212\\(\\frac{1}{2}\\), 1 \\(\\frac{1}{2}\\))<br \/>\nType below:<br \/>\n__________<\/p>\n<p>Answer:<br \/>\nThe x-coordinate is negative. Move 0.5 units to the left.<br \/>\ny-coordinate is positive. Move 1.5 units up<\/p>\n<p>Explanation:<br \/>\n-1\/2 = -0.5<br \/>\n1 1\/2 = 3\/2 = 1.5<\/p>\n<p>Question 6.<br \/>\nH(0, 2.50)<br \/>\nType below:<br \/>\n__________<\/p>\n<p>Answer:<br \/>\nThe x-coordinate is positive. Move 0 units.<br \/>\ny-coordinate is positive. Move 2.5 units up<\/p>\n<p>Question 7.<br \/>\nJ(\u22121 \\(\\frac{1}{2}\\), \\(\\frac{1}{2}\\))<br \/>\nType below:<br \/>\n__________<\/p>\n<p>Answer:<br \/>\nThe x-coordinate is negative. Move 1.5 units to the left.<br \/>\ny-coordinate is positive. Move 0.5 units up<\/p>\n<p>Explanation:<br \/>\n-1 1\/2 = -3\/2 = -1.5<br \/>\n1\/2 = 0.5<\/p>\n<p>Question 8.<br \/>\nK(1, 2)<br \/>\nType below:<br \/>\n__________<\/p>\n<p>Answer:<br \/>\nThe x-coordinate is positive. Move 1 unit to the right.<br \/>\ny-coordinate is positive. Move 2 units up<\/p>\n<p>Question 9.<br \/>\nL(\u22121 \\(\\frac{1}{2}\\), \u22122 \\(\\frac{1}{2}\\))<br \/>\nType below:<br \/>\n__________<\/p>\n<p>Answer:<br \/>\nThe x-coordinate is negative. Move 1.5 units to the left.<br \/>\ny-coordinate is negative. Move 2.5 units down<\/p>\n<p>Explanation:<br \/>\n-1 1\/2 = -3\/2 = -1.5<br \/>\n-2 1\/2 = -5\/2 = -2.5<\/p>\n<p>Question 10.<br \/>\nM(1, -0.5)<br \/>\nType below:<br \/>\n__________<\/p>\n<p>Answer:<br \/>\nThe x-coordinate is positive. Move 1 unit to the up.<br \/>\ny-coordinate is negative. Move 0.5 units down<\/p>\n<p>Question 11.<br \/>\nN(\\(\\frac{1}{4}\\), 1 \\(\\frac{1}{2}\\))<br \/>\nType below:<br \/>\n__________<\/p>\n<p>Answer:<br \/>\nThe x-coordinate is positive. Move 0.25 units to the right.<br \/>\ny-coordinate is positive. Move 1.5 units up<\/p>\n<p>Question 12.<br \/>\nP(1.25, 0)<br \/>\nType below:<br \/>\n__________<\/p>\n<p>Answer:<br \/>\nThe x-coordinate is positive. Move 1.25 units to the right.<br \/>\ny-coordinate is positive. Move 0 units<\/p>\n<p><img loading=\"lazy\" class=\"alignnone size-medium wp-image-7295\" src=\"https:\/\/ccssmathanswers.com\/wp-content\/uploads\/2020\/08\/grade-6-chapter-3-Page-no.-180-image-2-290x300.jpg\" alt=\"grade 6 chapter 3 Page no. 180 image 2\" width=\"290\" height=\"300\" srcset=\"https:\/\/bigideasmathanswers.com\/wp-content\/uploads\/2020\/08\/grade-6-chapter-3-Page-no.-180-image-2-290x300.jpg 290w, https:\/\/bigideasmathanswers.com\/wp-content\/uploads\/2020\/08\/grade-6-chapter-3-Page-no.-180-image-2.jpg 446w\" sizes=\"(max-width: 290px) 100vw, 290px\" \/><\/p>\n<p><strong>Problem Solving<\/strong><\/p>\n<p><strong>Use the map for 13\u201315.<\/strong><br \/>\n<img loading=\"lazy\" src=\"https:\/\/ccssmathanswers.com\/wp-content\/uploads\/2020\/08\/Go-Math-Grade-6-Answer-Key-Chapter-3-Understand-Positive-and-Negative-Numbers-img-25.jpg\" alt=\"Go Math Grade 6 Answer Key Chapter 3 Understand Positive and Negative Numbers img 25\" width=\"310\" height=\"355\" \/><\/p>\n<p>Question 13.<br \/>\nWhat is the ordered pair for the city hall?<br \/>\nType below:<br \/>\n__________<\/p>\n<p>Answer:<br \/>\n(-1, 0.5)<\/p>\n<p>Explanation:<br \/>\nTo find the x-coordinate, move 1 unit to the left.<br \/>\nTo find y-coordinate, move 0.5 units up.<br \/>\nCity Hall is located at (-1, 0.5)<\/p>\n<p>Question 14.<br \/>\nThe post office is located at (\\(\\frac{\u22121}{2}\\), 2). Graph and label a point on the map to represent the post office.<br \/>\nType below:<br \/>\n__________<\/p>\n<p>Answer:<br \/>\n<img loading=\"lazy\" class=\"alignnone size-medium wp-image-7298\" src=\"https:\/\/ccssmathanswers.com\/wp-content\/uploads\/2020\/08\/grade-6-chapter-3-Page-no.-181-image-1-264x300.jpg\" alt=\"grade 6 chapter 3 Page no. 181 image 1\" width=\"264\" height=\"300\" srcset=\"https:\/\/bigideasmathanswers.com\/wp-content\/uploads\/2020\/08\/grade-6-chapter-3-Page-no.-181-image-1-264x300.jpg 264w, https:\/\/bigideasmathanswers.com\/wp-content\/uploads\/2020\/08\/grade-6-chapter-3-Page-no.-181-image-1.jpg 484w\" sizes=\"(max-width: 264px) 100vw, 264px\" \/><\/p>\n<p>Explanation:<br \/>\nThe x-coordinate is negative. Move 0.5 units to the left.<br \/>\ny-coordinate is positive. Move 2 units up<\/p>\n<p>Question 15.<br \/>\nDescribe how to graph the ordered pair (\u22121, 4.5).<br \/>\nType below:<br \/>\n__________<\/p>\n<p>Answer:<br \/>\nThe x-coordinate is negative. Move 1 unit to the left.<br \/>\ny-coordinate is positive. Move 4.5 units up<\/p>\n<h3><a id=\"Rational_Numbers_and_the_Coordinate_Plane_\u2013_Page_No._182\"><\/a>Lesson Check &#8211; Page No. 182<\/h3>\n<p>Question 1.<br \/>\nAn artist uses a coordinate plane to create a design. As part of the design, the artist wants to graph the point (\u22126.5, 2). How should the artist graph this point?<br \/>\nType below:<br \/>\n__________<\/p>\n<p>Answer:<br \/>\nThe Artist should go 6.5 units to the left on the x-axis and then 2 units up on the y-axis giving:<br \/>\ngraph {((x + 6.5)^2 + (y &#8211; 2)^2 &#8211; 0.0125) = 0 [-10, 5, -5, 2.5]}<\/p>\n<p>Question 2.<br \/>\nWhat are the coordinates of the campground?<br \/>\n<img loading=\"lazy\" src=\"https:\/\/ccssmathanswers.com\/wp-content\/uploads\/2020\/08\/Go-Math-Grade-6-Answer-Key-Chapter-3-Understand-Positive-and-Negative-Numbers-img-26.jpg\" alt=\"Go Math Grade 6 Answer Key Chapter 3 Understand Positive and Negative Numbers img 26\" width=\"323\" height=\"312\" \/><br \/>\nType below:<br \/>\n__________<\/p>\n<p>Answer:<br \/>\n(-1, -1.5)<\/p>\n<p>Explanation:<br \/>\nThe x-coordinate is negative. Move 1 unit to the left.<br \/>\ny-coordinate is negative. Move 1.5 units down<\/p>\n<p><strong>Spiral Review<\/strong><\/p>\n<p>Question 3.<br \/>\nFour students volunteer at the hospital. Casey volunteers 20.7 hours, Danielle 20 \\(\\frac{3}{4}\\) hours, Javier 18 \\(\\frac{9}{10}\\) hours, and Forrest, 20 \\(\\frac{18}{25}\\) hours. Who volunteered the greatest number of hours?<br \/>\n__________<\/p>\n<p>Answer:<br \/>\nDanielle volunteered the greatest number of hours<\/p>\n<p>Explanation:<br \/>\nDanielle volunteered the most. She did 20.75 hours while Forest had 20.72, Casey had 20.7 and Javier had the least at 18.90 hours.<\/p>\n<p>Question 4.<br \/>\nDirections for making a quilt say to cut fifteen squares with sides that are 3.625 inches long. What is the side length written as a fraction?<br \/>\n_____ \\(\\frac{\u25a1}{\u25a1}\\)<\/p>\n<p>Answer:<br \/>\n3\\(\\frac{5}{8}\\)<\/p>\n<p>Explanation:<br \/>\n3.625 = 3 0.625<br \/>\n3.625 = 3 0.625(1000)\/1000<br \/>\n3.625 = 3 625\/1000<br \/>\n3.625 = 3 (625\/125) \/ (1000\/125)<br \/>\n3.625 = 3 5\/8<br \/>\nThe decimal length of the side of the squares (3.625 inches long) witten as a fraction is 3 5\/8 inches long.<\/p>\n<p>Question 5.<br \/>\nCam has a piece of plywood that is 6 \\(\\frac{7}{8}\\) feet wide. He is going to cut shelves from the plywood that are each 1 \\(\\frac{1}{6}\\) feet wide. Which is a good estimate for the number of shelves Cam can make?<br \/>\nType below:<br \/>\n__________<\/p>\n<p>Answer:<br \/>\n5 shelves<\/p>\n<p>Explanation:<br \/>\n6 7\/8= 55\/8<br \/>\n6 1\/6= 7\/6<br \/>\nfirst, find common denominators<br \/>\n55\/8 \u00d7 3= 165\/24<br \/>\n7\/6 \u00d7 4= 28\/24<br \/>\n165\/24 divided by 28\/24 is the same as 165\/24 time 24\/28<br \/>\nso that equals 3960\/672 =\u00a05.8928<br \/>\nAbout 5 shelves<\/p>\n<p>Question 6.<br \/>\nZach has \\(\\frac{3}{4}\\) hour to play video games. It takes him \\(\\frac{1}{12}\\) hour to set up the system. Each round of his favorite game takes \\(\\frac{1}{6}\\) hour. How many rounds can he play?<br \/>\n_____ rounds<\/p>\n<p>Answer:<br \/>\n4 rounds<\/p>\n<p>Explanation:<br \/>\nZach has 3\/4 hour to play video games. it takes him 1\/12 hour to set up the system. Each round of his favorite game takes 1\/6 hours.<br \/>\n1) Zach has 3\/4 hour to play video games<br \/>\nConvert to minutes<br \/>\n1 hour = 60 minutes<br \/>\n3\/4 \u00d7 60 = 45 minutes<br \/>\n2) It takes him an hour to set up the system<br \/>\nConvert to minutes<br \/>\n1\/12 \u00d7 60 = 5 minutes<br \/>\n3) 45 minutes &#8211; 5 minutes = 40 minutes<br \/>\n4) Each round of his favorite game takes an hour<br \/>\nConvert to minutes<br \/>\n1\/6 \u00d7 60 = 10 minutes<br \/>\n5) Divide the time available to play video games by the time each round of his favorite game<br \/>\n40\/10 = 4 rounds<\/p>\n<h3><a id=\"Ordered_Pair_Relationships_\u2013_Page_No._185\"><\/a>Share and Show &#8211; Page No. 185<\/h3>\n<p><strong>Identify the quadrant where the point is located.<\/strong><\/p>\n<p>Question 1.<br \/>\n(2, -5)<br \/>\nType below:<br \/>\n__________<\/p>\n<p>Answer:<br \/>\nQuadrant IV<\/p>\n<p>Explanation:<br \/>\nThe x-coordinate is positive. So, the point is 2 units to the right of the origin.<br \/>\nSince the point is to the right of the origin, it must be located in either<br \/>\nQuadrant I or Quadrant IV<br \/>\nThe y-coordinate is negative, so the point is 5 units down from the origin.<br \/>\nSince the point is down the origin, it must be located in Quadrant IV.<br \/>\nCheck by graphing the point (2, -5) on the coordinate plane.<br \/>\nQuadrant IV.<\/p>\n<p>Question 2.<br \/>\n(4, 1)<br \/>\nType below:<br \/>\n__________<\/p>\n<p>Answer:<br \/>\nQuadrant I<\/p>\n<p>Explanation:<br \/>\nThe x-coordinate is positive. So, the point is 4 units to the right of the origin.<br \/>\nSince the point is to the right of the origin, it must be located in either<br \/>\nQuadrant I or Quadrant IV<br \/>\ny-coordinate is positive, so the point is 1 unit up from the origin.<br \/>\nSince the point is up to the origin, it must be located in Quadrant I.<br \/>\nCheck by graphing the point (4, 1) on the coordinate plane.<br \/>\nQuadrant I.<\/p>\n<p>Question 3.<br \/>\n(-6, -2)<br \/>\nType below:<br \/>\n__________<\/p>\n<p>Answer:<br \/>\nQuadrant III<\/p>\n<p>Explanation:<br \/>\nThe x-coordinate is negative. So, the point is 6 units to the left of the origin.<br \/>\nSince the point is to the left of the origin, it must be located in either<br \/>\nQuadrant II or Quadrant III<br \/>\nThe y-coordinate is negative, so the point is 2 units down from the origin.<br \/>\nSince the point is down the origin, it must be located in Quadrant III.<br \/>\nQuadrant III.<\/p>\n<p>Question 4.<br \/>\n(-7, 3)<br \/>\nType below:<br \/>\n__________<\/p>\n<p>Answer:<br \/>\nQuadrant II<\/p>\n<p>Explanation:<br \/>\nThe x-coordinate is negative. So, the point is 7 units to the left of the origin.<br \/>\nSince the point is to the left of the origin, it must be located in either<br \/>\nQuadrant II or Quadrant III<br \/>\nThe y-coordinate is positive, so the point is 3 units up from the origin.<br \/>\nSince the point is up to the origin, it must be located in Quadrant II.<br \/>\nQuadrant II.<\/p>\n<p>Question 5.<br \/>\n(8, 8)<br \/>\nType below:<br \/>\n__________<\/p>\n<p>Answer:<br \/>\nQuadrant I<\/p>\n<p>Explanation:<br \/>\nThe x-coordinate is positive. So, the point is 8 units to the right of the origin.<br \/>\nSince the point is to the right of the origin, it must be located in either<br \/>\nQuadrant I or Quadrant IV<br \/>\nThe y-coordinate is positive, so the point is 8 units up from the origin.<br \/>\nSince the point is up to the origin, it must be located in Quadrant I.<br \/>\nQuadrant I.<\/p>\n<p>Question 6.<br \/>\n(1, -1)<br \/>\nType below:<br \/>\n__________<\/p>\n<p>Answer:<br \/>\nQuadrant IV<\/p>\n<p>Explanation:<br \/>\nThe x-coordinate is positive. So, the point is 1 unit to the right of the origin.<br \/>\nSince the point is to the right of the origin, it must be located in either<br \/>\nQuadrant I or Quadrant IV<br \/>\nThe y-coordinate is negative, so the point is 1 unit down from the origin.<br \/>\nSince the point is down to the origin, it must be located in Quadrant IV.<br \/>\nQuadrant IV.<\/p>\n<p><strong>The two points are reflections of each other across the x- or y-axis. Identify the axis.<\/strong><\/p>\n<p>Question 7.<br \/>\n(-1, 3) and (1, 3)<br \/>\nType below:<br \/>\n__________<\/p>\n<p>Answer:<br \/>\ny-axis<\/p>\n<p>Explanation:<br \/>\nThe given x-axis points are -1 and 1<br \/>\nThe y-axis points are 3 and 3<br \/>\nThe y-axis points are reflections to each other<\/p>\n<p>Question 8.<br \/>\n(4, 4) and (4, -4)<br \/>\nType below:<br \/>\n__________<\/p>\n<p>Answer:<br \/>\nx-axis<\/p>\n<p>Explanation:<br \/>\nThe given x-axis points are 4 and 4<br \/>\nThe y-axis points are 4 and -4<br \/>\nThe x-axis points are reflections to each other<\/p>\n<p>Question 9.<br \/>\n(2, -9) and (2, 9)<br \/>\nType below:<br \/>\n__________<\/p>\n<p>Answer:<br \/>\nx-axis<\/p>\n<p>Explanation:<br \/>\nThe given x-axis points are 2 and 2<br \/>\nThe y-axis points are -9 and 9<br \/>\nThe x-axis points are reflections to each other<\/p>\n<p>Question 10.<br \/>\n(8, 1) and (-8, 1)<br \/>\nType below:<br \/>\n__________<\/p>\n<p>Answer:<br \/>\ny-axis<\/p>\n<p>Explanation:<br \/>\nThe given x-axis points are 8 and -8<br \/>\nThe y-axis points are 1 and 1<br \/>\nThe y-axis points are reflections to each other<\/p>\n<p><strong>On Your Own<\/strong><\/p>\n<p><strong>Identify the quadrant where the point is located.<\/strong><\/p>\n<p>Question 11.<br \/>\n(-8, -9)<br \/>\nType below:<br \/>\n__________<\/p>\n<p>Answer:<br \/>\nQuadrant III<\/p>\n<p>Explanation:<br \/>\nThe x-coordinate is negative. So, the point is 8 units to the left of the origin.<br \/>\nSince the point is to the left of the origin, it must be located in either<br \/>\nQuadrant II or Quadrant III<br \/>\nThe y-coordinate is negative, so the point is 9 units down from the origin.<br \/>\nSince the point is down to the origin, it must be located in Quadrant III.<br \/>\nQuadrant III.<\/p>\n<p>Question 12.<br \/>\n(12, 1)<br \/>\nType below:<br \/>\n__________<\/p>\n<p>Answer:<br \/>\nQuadrant I<\/p>\n<p>Explanation:<br \/>\nThe x-coordinate is positive. So, the point is 12 units to the right of the origin.<br \/>\nSince the point is to the right of the origin, it must be located in either<br \/>\nQuadrant I or Quadrant IV<br \/>\nThe y-coordinate is positive, so the point is 1 unit up from the origin.<br \/>\nSince the point is up to the origin, it must be located in Quadrant I.<br \/>\nQuadrant I.<\/p>\n<p>Question 13.<br \/>\n(-13, 10)<br \/>\nType below:<br \/>\n__________<\/p>\n<p>Answer:<br \/>\nQuadrant II<\/p>\n<p>Explanation:<br \/>\nThe x-coordinate is negative. So, the point is 13 units to the left of the origin. Since the point is to the left of the origin, it must be located in either<br \/>\nQuadrant II or Quadrant III<br \/>\nThe y-coordinate is negative, so the point is 10 units up from the origin.<br \/>\nSince the point is up to the origin, it must be located in Quadrant II.<br \/>\nQuadrant II.<\/p>\n<p>Question 14.<br \/>\n(5, -20)<br \/>\nType below:<br \/>\n__________<\/p>\n<p>Answer:<br \/>\nQuadrant IV<\/p>\n<p>Explanation:<br \/>\nThe x-coordinate is positive. So, the point is 5 units to the right of the origin.<br \/>\nSince the point is to the right of the origin, it must be located in either<br \/>\nQuadrant I or Quadrant IV<br \/>\nThe y-coordinate is negative, so the point is 20 units down from the origin.<br \/>\nSince the point is down to the origin, it must be located in Quadrant IV.<br \/>\nQuadrant IV.<\/p>\n<p><strong>The two points are reflections of each other across the x- or y-axis. Identify the axis.<\/strong><\/p>\n<p>Question 15.<br \/>\n(-9, -10) and (-9, 10)<br \/>\nType below:<br \/>\n__________<\/p>\n<p>Answer:<br \/>\nx-axis<\/p>\n<p>Explanation:<br \/>\nThe given x-axis points are -9 and -9<br \/>\nThe y-axis points are -10 and 10<br \/>\nThe x-axis points are reflections to each other<\/p>\n<p>Question 16.<br \/>\n(21, -31) and (21, 31)<br \/>\nType below:<br \/>\n__________<\/p>\n<p>Answer:<br \/>\nx-axis<\/p>\n<p>Explanation:<br \/>\nThe given x-axis points are 21 and 21<br \/>\nThe y-axis points are -31 and 31<br \/>\nThe x-axis points are reflections to each other<\/p>\n<p>Question 17.<br \/>\n(15, -20) and (-15, -20)<br \/>\nType below:<br \/>\n__________<\/p>\n<p>Answer:<br \/>\ny-axis<\/p>\n<p>Explanation:<br \/>\nThe given x-axis points are 15 and -15<br \/>\nThe y-axis points are -20 and -20<br \/>\nThe y-axis points are reflections to each other<\/p>\n<p><strong>Give the reflection of the point across the given axis.<\/strong><\/p>\n<p>Question 18.<br \/>\n(\u22127, \u22127), y-axis<br \/>\nType below:<br \/>\n__________<\/p>\n<p>Answer:<br \/>\n(7, -7)<\/p>\n<p>Explanation:<br \/>\nThe x-axis point is -7.<br \/>\nSo, the reflection of point 7<\/p>\n<p>Question 19.<br \/>\n(\u221215, 18), x-axis<br \/>\nType below:<br \/>\n__________<\/p>\n<p>Answer:<br \/>\n(-15, -18)<\/p>\n<p>Explanation:<br \/>\nThe y-axis point is 18.<br \/>\nSo, the reflection of a point -18<\/p>\n<p>Question 20.<br \/>\n(11, 9), x-axis<br \/>\nType below:<br \/>\n__________<\/p>\n<p>Answer:<br \/>\n(11, -9)<\/p>\n<p>Explanation:<br \/>\nThe y-axis point is 9.<br \/>\nSo, the reflection of a point -9<\/p>\n<h3><a id=\"Ordered_Pair_Relationships_\u2013_Page_No._186\"><\/a>Problem Solving + Applications &#8211; Page No. 186<\/h3>\n<p><strong>Use the map of Gridville for 21\u201323.<br \/>\n<\/strong><\/p>\n<p>Question 21.<br \/>\nThe library\u2019s location has opposite x- and y-coordinates as City Hall. Across which streets could you reflect City Hall\u2019s location to find the library\u2019s location?<br \/>\nType below:<br \/>\n__________<\/p>\n<p>Answer:<br \/>\nThe library\u2019s location has opposite x- and y-coordinates as City Hall.<br \/>\nCity Hall = (2, -3)<br \/>\nThe opposite x- and y-coordinates of City Hall = (-2, 3)<br \/>\nSo, the library\u2019s location is (-2, 3)<\/p>\n<p>Question 22.<br \/>\nEach unit on the map represents 1 mile. Gregory leaves his house at (\u22125, 4), cycles 4 miles east, 6 miles south, and 1 mile west. In which quadrant of the city is he now?<br \/>\nType below:<br \/>\n__________<\/p>\n<p>Answer:<br \/>\nQuadrant III<\/p>\n<p>Explanation:<br \/>\nGregory leaves his house at (\u22125, 4)<br \/>\ncycles 4 miles east = -5 + 4 = -1; (-1, 4)<br \/>\n6 miles south = (-1, -1)<br \/>\n1 mile west (-2, -1)<br \/>\nSo, he is now in Quadrant III<\/p>\n<p>Question 23.<br \/>\nThe bus station has the same x-coordinate as City Hall but the opposite y-coordinate. In which quadrant of the city is the bus station located?<br \/>\nType below:<br \/>\n__________<\/p>\n<p>Answer:<br \/>\nQuadrant I<\/p>\n<p>Explanation:<br \/>\nThe bus station has the same x-coordinate as City Hall but the opposite y-coordinate.<br \/>\nCity Hall = (2, -3)<br \/>\nThe opposite y-coordinate = 3<br \/>\nBus station located at (2, 3)<br \/>\nBus station located at Quadrant I<\/p>\n<p>Question 24.<br \/>\nDescribe Relationships Describe the relationship between the locations of the points (2, 5) and (2, \u22125) on the coordinate plane.<br \/>\nType below:<br \/>\n__________<\/p>\n<p>Answer:<br \/>\n(2, 5) and (2, \u22125) have the same x-coordinate.<br \/>\nThey have the opposite y-coordinate.<\/p>\n<p>Question 25.<br \/>\nIdentify the quadrant where each point is located. Write each point in the correct box.<br \/>\n(\u22121, 3), (4, \u22122), (\u22123, \u22122), (1, \u22123), (\u22121, 2), (3, 4)<br \/>\nType below:<br \/>\n__________<\/p>\n<p>Answer:<br \/>\n(\u22121, 3) = Quadrant II<br \/>\n(4, \u22122) = Quadrant IV<br \/>\n(\u22123, \u22122) = Quadrant III<br \/>\n(1, \u22123) = Quadrant IV<br \/>\n(\u22121, 2) = Quadrant II<br \/>\n(3, 4) = Quadrant I<\/p>\n<h3><a id=\"Ordered_Pair_Relationships_\u2013_Page_No._187\"><\/a>Problem Solving + Applications &#8211; Page No. 187<\/h3>\n<p><strong>Identify the quadrant where the point is located.<\/strong><\/p>\n<p>Question 1.<br \/>\n(10, -2)<br \/>\nType below:<br \/>\n__________<\/p>\n<p>Answer:<br \/>\nQuadrant IV<\/p>\n<p>Explanation:<br \/>\nThe x-coordinate is positive. So, the point is 10 units to the right of the origin.<br \/>\nSince the point is to the right of the origin, it must be located in either<br \/>\nQuadrant I or Quadrant IV<br \/>\nThe y-coordinate is negative, so the point is 2 units down from the origin.<br \/>\nSince the point is down the origin, it must be located in Quadrant IV.<br \/>\nQuadrant IV<\/p>\n<p>Question 2.<br \/>\n(-5, -6)<br \/>\nType below:<br \/>\n__________<\/p>\n<p>Answer:<br \/>\nQuadrant III<\/p>\n<p>Explanation:<br \/>\nThe x-coordinate is negative. So, the point is 5 units to the left of the origin.<br \/>\nSince the point is to the left of the origin, it must be located in either<br \/>\nQuadrant II or Quadrant III<br \/>\nThe y-coordinate is negative, so the point is 6 units down from the origin.<br \/>\nSince the point is down the origin, it must be located in Quadrant III.<br \/>\nQuadrant III.<\/p>\n<p>Question 3.<br \/>\n(3, 7)<br \/>\nType below:<br \/>\n__________<\/p>\n<p>Answer:<br \/>\nQuadrant I<\/p>\n<p>Explanation:<br \/>\nThe x-coordinate is positive. So, the point is 3 units to the right of the origin.<br \/>\nSince the point is to the right of the origin, it must be located in either<br \/>\nQuadrant I or Quadrant IV<br \/>\ny-coordinate is positive, so the point is 7 units up from the origin.<br \/>\nSince the point is up to the origin, it must be located in Quadrant I.<br \/>\nQuadrant I<\/p>\n<p><strong>The two points are reflections of each other across the x- or y-axis. Identify the axis.<\/strong><\/p>\n<p>Question 4.<br \/>\n(5, 3) and (\u22125, 3)<br \/>\nType below:<br \/>\n__________<\/p>\n<p>Answer:<br \/>\ny-axis<\/p>\n<p>Explanation:<br \/>\nThe given x-axis points are 5 and -5<br \/>\nThe y-axis points are 3 and 3<br \/>\nThe y-axis points are reflections to each other<\/p>\n<p>Question 5.<br \/>\n(\u22127, 1) and (\u22127, \u22121)<br \/>\nType below:<br \/>\n__________<\/p>\n<p>Answer:<br \/>\nx-axis<\/p>\n<p>Explanation:<br \/>\nThe given x-axis points are -7 and -7<br \/>\nThe y-axis points are 1 and -1<br \/>\nThe x-axis points are reflections to each other<\/p>\n<p>Question 6.<br \/>\n(\u22122, 4) and (\u22122, \u22124)<br \/>\nType below:<br \/>\n__________<\/p>\n<p>Answer:<br \/>\nx-axis<\/p>\n<p>Explanation:<br \/>\nThe given x-axis points are -2 and -2<br \/>\nThe y-axis points are 4 and -4<br \/>\nThe x-axis points are reflections to each other<\/p>\n<p><strong>Give the reflection of the point across the given axis.<\/strong><\/p>\n<p>Question 7.<br \/>\n(\u22126, \u221210), y-axis<br \/>\nType below:<br \/>\n__________<\/p>\n<p>Answer:<br \/>\n(6, -10)<\/p>\n<p>Explanation:<br \/>\nThe x-axis point is -6.<br \/>\nSo, the reflection of the point 6<\/p>\n<p>Question 8.<br \/>\n(\u221211, 3), x-axis<br \/>\nType below:<br \/>\n__________<\/p>\n<p>Answer:<br \/>\n(-11, -3)<\/p>\n<p>Explanation:<br \/>\nThe y-axis point is -3.<br \/>\nSo, the reflection of a point 3<\/p>\n<p>Question 9.<br \/>\n(8, 2), x-axis<br \/>\nType below:<br \/>\n__________<\/p>\n<p>Answer:<br \/>\n(8, -2)<\/p>\n<p>Explanation:<br \/>\nThe y-axis point is 2.<br \/>\nSo, the reflection of a point -2<\/p>\n<p><strong>Problem Solving<\/strong><\/p>\n<p>Question 10 .<br \/>\nA town\u2019s post office is located at the point (7, 5) on a coordinate plane. In which quadrant is the post office located?<br \/>\nType below:<br \/>\n__________<\/p>\n<p>Answer:<br \/>\nQuadrant I<\/p>\n<p>Explanation:<br \/>\nA town\u2019s post office is located at the point (7, 5) on a coordinate plane.<br \/>\nThe x-coordinate is positive. So, the point is 7 units to the right of the origin.<br \/>\nSince the point is to the right of the origin, it must be located in either<br \/>\nQuadrant I or Quadrant IV<br \/>\nThe y-coordinate is positive, so the point is 5 units up from the origin.<br \/>\nSince the point is up the origin, it must be located in Quadrant I.<br \/>\nQuadrant I<\/p>\n<p>Question 11.<br \/>\nThe grocery store is located at a point on a coordinate plane with the same y-coordinate as the bank but with the opposite x-coordinate. The grocery store and bank are reflections of each other across which axis?<br \/>\nType below:<br \/>\n__________<\/p>\n<p>Answer:<br \/>\ny-axis<\/p>\n<p>Explanation:<br \/>\nThe grocery store is located at a point on a coordinate plane with the same y-coordinate as the bank but with the opposite x-coordinate.<br \/>\nThe grocery store and bank are reflections of each other across the y-axis.<\/p>\n<p>Question 12.<br \/>\nExplain to a new student how a reflection across the y-axis changes the coordinates of the original point.<br \/>\nType below:<br \/>\n__________<\/p>\n<p>Answer:<br \/>\nThe coordinate plane with the same y-coordinate remains same but with the opposite x-coordinate.<\/p>\n<h3><a id=\"Ordered_Pair_Relationships_\u2013_Page_No._188\"><\/a>Lesson Check &#8211; Page No. 188<\/h3>\n<p>Question 1.<br \/>\nIn which quadrant does the point (\u22124, 15) lie?<br \/>\nType below:<br \/>\n__________<\/p>\n<p>Answer:<br \/>\nQuadrant II<\/p>\n<p>Explanation:<br \/>\nThe x-coordinate is negative. So, the point is 4 units to the left of the origin.<br \/>\nSince the point is to the left of the origin, it must be located in either<br \/>\nQuadrant II or Quadrant III<br \/>\nThe y-coordinate is positive, so the point is 15 units up from the origin.<br \/>\nSince the point is up to the origin, it must be located in Quadrant II.<br \/>\nQuadrant II.<\/p>\n<p>Question 2.<br \/>\nWhat are the coordinates of the point (10, \u22124) if it is reflected across the y\u2013axis?<br \/>\nType below:<br \/>\n__________<\/p>\n<p>Answer:<br \/>\n(-10, -4)<\/p>\n<p>Explanation:<br \/>\ncoordinates of the point (-10, \u22124)<br \/>\nIf it is reflected across the y\u2013axis, coordinates of the point will be (-10, -4)<\/p>\n<p><strong>Spiral Review<\/strong><\/p>\n<p>Question 3.<br \/>\nSmall juice bottles come in packages of 6. Yogurt treats come in packages of 10. Paula wants to have the exact same number of each item. What is the least number of bottles of juice and individual yogurt treats she will have? How many packages of each will she need?<br \/>\nType below:<br \/>\n__________<\/p>\n<p>Answer:<br \/>\n5 packages<\/p>\n<p>Explanation:<br \/>\nNumber of packages of small juice bottles = 6<br \/>\nNumber of packages of yogurt = 10<br \/>\nFor this, we will find the L.C.M. of 6 and 10 =30<br \/>\nSo, there will be 5 packages of small juice bottles and 3 packages of yogurt.<\/p>\n<p>Question 4.<br \/>\nAlison saves $29.26 each month. How many months will it take her to save enough money to buy a stereo for $339.12?<br \/>\n_____ month<\/p>\n<p>Answer:<br \/>\n11 months<\/p>\n<p>Explanation:<br \/>\nRound 29 and 339 to 30 and 340.<br \/>\nDivide 340 by 30<br \/>\nThe answer should be 11.3 repeatings.<br \/>\n11 months<\/p>\n<p>Question 5.<br \/>\nThe library is 1.75 miles directly north of the school. The park is 0.6 miles directly south of the school. How far is the library from the park?<br \/>\nType below:<br \/>\n__________<\/p>\n<p>Answer:<br \/>\n2.35 miles<\/p>\n<p>Explanation:<br \/>\nThe library is 1.75 miles directly north of the school. The park is 0.6 miles directly south of the school.<br \/>\n1.75 + 0.6 would be 2.35 miles, the library to the parking.<\/p>\n<p>Question 6.<br \/>\nTours of the art museum are offered every \\(\\frac{1}{3}\\) hour starting at 10 A.M. The museum closes at 4:00 P.M. How many tours are offered each day?<br \/>\n_____ tours<\/p>\n<p>Answer:<br \/>\n18 tours<\/p>\n<p>Explanation:<br \/>\nStaring time of tours=10 am<br \/>\nClosing time of tours=4 pm<br \/>\nDuration of tours(10 am to 4 pm)=6 hours<br \/>\nTime for each tour= 1\/3 hours<br \/>\nTotal number of tours offered in a day= 6 \u00d7 3 = 18<br \/>\nTherefore, 18 tours offered each day.<\/p>\n<h3><a id=\"Distance_on_the_Coordinate_Plane_\u2013_Page_No._191\"><\/a>Share and Show &#8211; Page No. 191<\/h3>\n<p><strong>Find the distance between the pair of points.<\/strong><br \/>\n<img loading=\"lazy\" src=\"https:\/\/ccssmathanswers.com\/wp-content\/uploads\/2020\/08\/Go-Math-Grade-6-Answer-Key-Chapter-3-Understand-Positive-and-Negative-Numbers-img-27.jpg\" alt=\"Go Math Grade 6 Answer Key Chapter 3 Understand Positive and Negative Numbers img 27\" width=\"310\" height=\"314\" \/><\/p>\n<p>Question 1.<br \/>\n(\u22123, 1) and (2, 1)<br \/>\n_____ units<\/p>\n<p>Answer:<br \/>\n5 units<\/p>\n<p>Explanation:<br \/>\nThe points have the same y-coordinate, so they are located on a horizontal line.<br \/>\nFind the distance between the x-coordinates of the point (-3, 1) and the point (2, 1)<br \/>\n|-3| = 3<br \/>\n3 + 2 = 5<\/p>\n<p>Question 2.<br \/>\n(2, 1) and (2, -4)<br \/>\n_____ units<\/p>\n<p>Answer:<br \/>\n5 units<\/p>\n<p>Explanation:<br \/>\nThe points have the same x-coordinate, so they are located on a vertical line.<br \/>\nFind the distance between the y-coordinates of the point (2, 1) and the point (2, -4)<br \/>\n|-4| = 4<br \/>\n1 + 4 = 5<\/p>\n<p>Question 3.<br \/>\n(2, -4) and (4, -4)<br \/>\n_____ units<\/p>\n<p>Answer:<br \/>\n2 units<\/p>\n<p>Explanation:<br \/>\nThe points have the same y-coordinate, so they are located on a horizontal line.<br \/>\nFind the distance between the x-coordinates of the point (2, -4) and the point (4, -4)<br \/>\n4 &#8211; 2 = 2<\/p>\n<p>Question 4.<br \/>\n(-3, 3) and (-3, 1)<br \/>\n_____ units<\/p>\n<p>Answer:<br \/>\n2 units<\/p>\n<p>Explanation:<br \/>\nThe points have the same x-coordinate, so they are located on a vertical line.<br \/>\nFind the distance between the y-coordinates of the point (-3, 3) and the point (-3, 1)<br \/>\n3 &#8211; 1 = 2<\/p>\n<p><strong>On Your Own<\/strong><\/p>\n<p><strong>Practice: Copy and Solve Graph the pair of points. Then find the distance between them.<\/strong><\/p>\n<p>Question 5.<br \/>\n(0, 5) and (0, -5)<br \/>\n_____ units<\/p>\n<p>Answer:<br \/>\n10 units<\/p>\n<p>Explanation:<br \/>\nThe points have the same x-coordinate, so they are located on a vertical line.<br \/>\nFind the distance between the y-coordinates of the point (0, 5) and the point (0, -5)<br \/>\n|-5| = 5<br \/>\n5 + 5 = 10<\/p>\n<p>Question 6.<br \/>\n(1, 1) and (1, -3)<br \/>\n_____ units<\/p>\n<p>Answer:<br \/>\n4 units<\/p>\n<p>Explanation:<br \/>\nThe points have the same x-coordinate, so they are located on a vertical line.<br \/>\nFind the distance between the y-coordinates of the point (1, 1) and the point (1, -3)<br \/>\n|-3| = 3<br \/>\n1 + 3 = 4<\/p>\n<p>Question 7.<br \/>\n(-2, -5) and (-2, -1)<br \/>\n_____ units<\/p>\n<p>Answer:<br \/>\n4 units<\/p>\n<p>Explanation:<br \/>\nThe points have the same x-coordinate, so they are located on a vertical line.<br \/>\nFind the distance between the y-coordinates of the point (-2, -5) and the point (-2, -1)<br \/>\n|-5| = 5<br \/>\n|-1| = 1<br \/>\n5 &#8211; 1 = 4<\/p>\n<p>Question 8.<br \/>\n(-7, 3) and (5, 3)<br \/>\n_____ units<\/p>\n<p>Answer:<br \/>\n12 units<\/p>\n<p>Explanation:<br \/>\nThe points have the same y-coordinate, so they are located on a horizontal line.<br \/>\nFind the distance between the x-coordinates of the point (-7, 3) and the point (5, 3)<br \/>\n|-7| = 7<br \/>\n7 + 5 = 12<\/p>\n<p>Question 9.<br \/>\n(3, -6) and (3, -10)<br \/>\n_____ units<\/p>\n<p>Answer:<br \/>\n4 units<\/p>\n<p>Explanation:<br \/>\nThe points have the same x-coordinate, so they are located on a vertical line.<br \/>\nFind the distance between the y-coordinates of the point (3, -6) and the point (3, -10)<br \/>\n|-6| = 6<br \/>\n|-10| = 10<br \/>\n10 &#8211; 6 = 4<\/p>\n<p>Question 10.<br \/>\n(8, 0) and (8, -8)<br \/>\n_____ units<\/p>\n<p>Answer:<br \/>\n8 units<\/p>\n<p>Explanation:<br \/>\nThe points have the same x-coordinate, so they are located on a vertical line.<br \/>\nFind the distance between the y-coordinates of the point (8, 0) and the point (8, -8)<br \/>\n|-8| = 8<br \/>\n0 + 8 = 8<\/p>\n<p><strong>Use Reasoning Algebra Write the coordinates of a point that is the given distance from the given point.<\/strong><\/p>\n<p>Question 11.<br \/>\n4 units from (3, 5)<br \/>\nType below:<br \/>\n__________<\/p>\n<p>Answer:<br \/>\n1 or 9<\/p>\n<p>Explanation:<br \/>\n4 units from (3, 5)<br \/>\n(3, 9) or (3, 1)<\/p>\n<p>Question 12.<br \/>\n6 units from (2, 1)<br \/>\nType below:<br \/>\n__________<\/p>\n<p>Answer:<br \/>\n8 or -4<\/p>\n<p>Explanation:<br \/>\n6 units from (2, 1)<br \/>\n(8, 1) or (-4, 1)<\/p>\n<p>Question 13.<br \/>\n7 units from (\u22124, \u22121)<br \/>\nType below:<br \/>\n__________<\/p>\n<p>Answer:<br \/>\n-8 or 6<\/p>\n<p>Explanation:<br \/>\n7 units from (\u22124, \u22121)<br \/>\n(-8, -1) or (-8, 6)<\/p>\n<h3><a id=\"Distance_on_the_Coordinate_Plane_\u2013_Page_No._192\"><\/a>Problem Solving + Applications &#8211; Page No. 192<\/h3>\n<p><strong>An archaeologist is digging at an ancient city. The map shows the locations of several important finds. Each unit represents 1 kilometer. Use the map for 14\u201318.<\/strong><\/p>\n<p>Question 14.<br \/>\nHow far is it from the stadium to the statue?<br \/>\n<img loading=\"lazy\" src=\"https:\/\/ccssmathanswers.com\/wp-content\/uploads\/2020\/08\/Go-Math-Grade-6-Answer-Key-Chapter-3-Understand-Positive-and-Negative-Numbers-img-28.jpg\" alt=\"Go Math Grade 6 Answer Key Chapter 3 Understand Positive and Negative Numbers img 28\" width=\"308\" height=\"352\" \/><br \/>\n_____ km<\/p>\n<p>Answer:<br \/>\n8 km<\/p>\n<p>Explanation:<br \/>\nStadium = (4, 5)<br \/>\nstatue = (4, -3)<br \/>\nThe points have the same x-coordinate, so they are located on a vertical line.<br \/>\nFind the distance between the y-coordinates of the point (4, 5) and the point (4, -3)<br \/>\n|-3| = 3<br \/>\n5 + 3 = 8<\/p>\n<p>Question 15.<br \/>\nThe archaeologist drives 3 km south from the palace. How far is he from the market?<br \/>\n_____ km<\/p>\n<p>Answer:<br \/>\n3 km<\/p>\n<p>Explanation:<br \/>\nThe palace is at the origin (0, 0)<br \/>\nSo, the answer is 3 km<\/p>\n<p>Question 16.<br \/>\nThe archaeologist\u2019s campsite is located at (\u22129, \u22123). How far is it from the campsite to the market?<br \/>\n_____ km<\/p>\n<p>Answer:<br \/>\n11 km<\/p>\n<p>Explanation:<br \/>\nthe campsite is located at (\u22129, \u22123)<br \/>\nthe market is located at (-2, -3)<br \/>\nThe points have the same y-coordinate, so they are located on a horizontal line.<br \/>\nFind the distance between the x-coordinates of the point (\u22129, \u22123) and the point (-2, -3)<br \/>\n|-9| = 9<br \/>\n|-2| = 2<br \/>\n9 + 2 = 11<br \/>\ncampsite is 11 km far to the market<\/p>\n<p>Question 17.<br \/>\nThe archaeologist rode east on a donkey from the Great Gate, at (\u221211, 4), to the Royal Road. Then he rode south to the palace. How far did the archaeologist ride?<br \/>\n_____ km<\/p>\n<p>Answer:<br \/>\n15 km<\/p>\n<p>Explanation:<br \/>\nThe archaeologist rode east on a donkey from the Great Gate, at (\u221211, 4), to the Royal Road. Then he rode south to the palace.<br \/>\nFirst, he needs to move |-11| = 11 km<br \/>\nThen, he needs to move 4 km<br \/>\n4 + 11 = 15 km<\/p>\n<p>Question 18.<br \/>\nGeneralize Explain how you could find the distance from the palace to any point on the Imperial Highway.<br \/>\nType below:<br \/>\n__________<\/p>\n<p>Answer:<br \/>\nThe distance varies according to the points on the Imperial Highway<\/p>\n<p>Question 19.<br \/>\nSelect the pairs of points that have a distance of 10 between them. Mark all that apply.<br \/>\n(3, \u22126) and (3, 4)<br \/>\n( \u22123, 8) and (7, 8)<br \/>\n(4, 5) and (6, 5)<br \/>\n(4, 1) and (4, 11)<br \/>\nType below:<br \/>\n__________<\/p>\n<p>Answer:<br \/>\n(3, \u22126) and (3, 4)<br \/>\n( \u22123, 8) and (7, 8)<br \/>\n(4, 5) and (6, 5)<\/p>\n<p>Explanation:<br \/>\n6 + 4 = 10<br \/>\n3 + 7 = 10<br \/>\n4 + 6 = 10<\/p>\n<h3><a id=\"Distance_on_the_Coordinate_Plane_\u2013_Page_No._193\"><\/a>Distance on the Coordinate Plane &#8211; Page No. 193<\/h3>\n<p><strong>Find the distance between the pair of points.<\/strong><\/p>\n<p>Question 1.<br \/>\n(1, 4) and (\u22123, 4)<br \/>\n_____ units<\/p>\n<p>Answer:<br \/>\n4 units<\/p>\n<p>Explanation:<br \/>\nThe points have the same y-coordinate, so they are located on a horizontal line.<br \/>\nFind the distance between the x-coordinates of the point (1, 4) and the point (\u22123, 4)<br \/>\n|-3| = 3<br \/>\n1 + 3 = 4<\/p>\n<p>Question 2.<br \/>\n(7, \u22122) and (11, \u22122)<br \/>\n_____ units<\/p>\n<p>Answer:<br \/>\n3 units<\/p>\n<p>Explanation:<br \/>\nThe points have the same y-coordinate, so they are located on a horizontal line.<br \/>\nFind the distance between the x-coordinates of the point (7, \u22122) and the point (11, \u22122)<br \/>\n11 &#8211; 7 = 3<\/p>\n<p>Question 3.<br \/>\n(6, 4) and (6, \u22128)<br \/>\n_____ units<\/p>\n<p>Answer:<br \/>\n12 units<\/p>\n<p>Explanation:<br \/>\nThe points have the same x-coordinate, so they are located on a vertical line.<br \/>\nFind the distance between the y-coordinates of the point (6, 4) and the point (6, \u22128)<br \/>\n|-8| = 8<br \/>\n4 + 8 = 12<\/p>\n<p>Question 4.<br \/>\n(8, \u221210) and (5, \u221210)<br \/>\n_____ units<\/p>\n<p>Answer:<br \/>\n3 units<\/p>\n<p>Explanation:<br \/>\nThe points have the same y-coordinate, so they are located on a horizontal line.<br \/>\nFind the distance between the x-coordinates of the point (8, \u221210) and the point (5, \u221210)<br \/>\n8 &#8211; 5 = 3<\/p>\n<p>Question 5.<br \/>\n(\u22122, \u22126) and (\u22122, 5)<br \/>\n_____ units<\/p>\n<p>Answer:<br \/>\n11 units<\/p>\n<p>Explanation:<br \/>\nThe points have the same x-coordinate, so they are located on a vertical line.<br \/>\nFind the distance between the y-coordinates of the point (\u22122, \u22126)and the point (\u22122, 5)<br \/>\n|-6| = 6<br \/>\n6 + 5 = 11<\/p>\n<p>Question 6.<br \/>\n(\u22125, 2) and (\u22125, \u22124)<br \/>\n_____ units<\/p>\n<p>Answer:<br \/>\n6 units<\/p>\n<p>Explanation:<br \/>\nThe points have the same x-coordinate, so they are located on a vertical line.<br \/>\nFind the distance between the y-coordinates of the point (\u22125, 2) and the point (\u22125, \u22124)<br \/>\n|-4| = 4<br \/>\n2 + 4 = 6<\/p>\n<p><strong>Write the coordinates of a point that is the given distance from the given point.<\/strong><\/p>\n<p>Question 7.<br \/>\n5 units from (\u22121, \u22122)<br \/>\nType below:<br \/>\n__________<\/p>\n<p>Answer:<br \/>\n-6 or 4<\/p>\n<p>Explanation:<br \/>\n5 units from (\u22121, \u22122)<br \/>\n(-6, -2) or (4, -2)<\/p>\n<p>Question 8.<br \/>\n8 units from (2, 4)<br \/>\nType below:<br \/>\n__________<\/p>\n<p>Answer:<br \/>\n12 or -4<\/p>\n<p>Explanation:<br \/>\n8 units from (2, 4)<br \/>\n(2, 12) or (2, -4)<\/p>\n<p>Question 9.<br \/>\n3 units from (\u22127, \u22125)<br \/>\nType below:<br \/>\n__________<\/p>\n<p>Answer:<br \/>\n-2 or -8<\/p>\n<p>Explanation:<br \/>\n3 units from (\u22127, \u22125)<br \/>\n(-7, -2) or (-7, -8)<\/p>\n<p><strong>Problem Solving<\/strong><\/p>\n<p><strong>The map shows the locations of several areas in an amusement park. Each unit represents 1 kilometer.<\/strong><br \/>\n<img loading=\"lazy\" src=\"https:\/\/ccssmathanswers.com\/wp-content\/uploads\/2020\/08\/Go-Math-Grade-6-Answer-Key-Chapter-3-Understand-Positive-and-Negative-Numbers-img-29.jpg\" alt=\"Go Math Grade 6 Answer Key Chapter 3 Understand Positive and Negative Numbers img 29\" width=\"347\" height=\"344\" \/><\/p>\n<p>Question 10.<br \/>\nHow far is the Ferris wheel from the rollercoaster?<br \/>\n_____ km<\/p>\n<p>Answer:<br \/>\n4 km<\/p>\n<p>Explanation:<br \/>\nFerris wheel = (5, 6)<br \/>\nrollercoaster = (5, 2)<br \/>\n6 &#8211; 2 = 4<\/p>\n<p>Question 11.<br \/>\nHow far is the water slide from the restrooms?<br \/>\n_____ km<\/p>\n<p>Answer:<br \/>\n7 km<\/p>\n<p>Explanation:<br \/>\nwater slide = (-3, -4)<br \/>\nrestrooms = (4, -4)<br \/>\n3 + 4 = 7<\/p>\n<p>Question 12.<br \/>\nGraph the points (23, 3), (23, 7), and (4, 3) on a coordinate plane. Explain how to find the distance from (23, 3) to (23, 7) and from (23, 3) and (4, 3).<br \/>\nType below:<br \/>\n__________<\/p>\n<p>Answer:<\/p>\n<p>Explanation:<br \/>\n(23, 3) to (23, 7)<br \/>\nThe points have the same x-coordinate, so they are located on a vertical line.<br \/>\nFind the distance between the y-coordinates of the point (23, 3) and the point (23, 7)<br \/>\n7 &#8211; 3 = 4<br \/>\n(23, 3) and (4, 3).<br \/>\nThe points have the same y-coordinate, so they are located on a horizontal line.<br \/>\nFind the distance between the x-coordinates of the point (23, 3) and the point (4, 3)<br \/>\n4 &#8211; 3 = 1<\/p>\n<h3><a id=\"Distance_on_the_Coordinate_Plane_\u2013_Page_No._194\"><\/a>Lesson Check &#8211; Page No. 194<\/h3>\n<p>Question 1.<br \/>\nWhat is the distance between (4, \u22127) and (\u22125, \u22127)?<br \/>\n_____ units<\/p>\n<p>Answer:<br \/>\n9 units<\/p>\n<p>Explanation:<br \/>\n(4, \u22127) and (\u22125, \u22127)<br \/>\nThe points have the same y-coordinate, so they are located on a horizontal line.<br \/>\nFind the distance between the x-coordinates of the point (4, \u22127) and the point (\u22125, \u22127)<br \/>\n|-5| = 5<br \/>\n5 + 4 = 9<\/p>\n<p>Question 2.<br \/>\nPoint A and point B are 5 units apart. The coordinates of point A are (3, \u22129). The y\u2013coordinate of point B is \u22129. What is a possible x\u2013coordinate for point B?<br \/>\nType below:<br \/>\n__________<\/p>\n<p>Answer:<br \/>\n8 or -2<\/p>\n<p>Explanation:<br \/>\nPoint A and point B are 5 units apart. The coordinates of point A are (3, \u22129). The y\u2013coordinate of point B is \u22129.<br \/>\nThe points have the same y-coordinate, so they are located on a horizontal line.<br \/>\nthe distance between the x-coordinates = 5<br \/>\nSo, 8 or -2<\/p>\n<p><strong>Spiral Review<\/strong><\/p>\n<p>Question 3.<br \/>\nAn apple is cut into 10 pieces. 0.8 of the apple is eaten. Which fraction, in simplest form, represents the amount of apple that is left?<br \/>\n\\(\\frac{\u25a1}{\u25a1}\\)<\/p>\n<p>Answer:<br \/>\n\\(\\frac{1}{5}\\)<\/p>\n<p>Explanation:<br \/>\nAn apple is cut into 10 pieces. 0.8 of the apple is eaten.<br \/>\n10\/10 &#8211; 8\/10 = 2\/10 = 1\/5 amount of apple left.<\/p>\n<p>Question 4.<br \/>\nA carton contains soup cans weighing a total of 20 pounds. Each can weighs 1 \\(\\frac{1}{4}\\) pounds. How many cans does the carton contain?<br \/>\n_____ cans<\/p>\n<p>Answer:<br \/>\n16 cans<\/p>\n<p>Explanation:<br \/>\nDivide 20 with 5\/4 (=1 1\/4)<br \/>\nSo, 20 \u00d7 4\/5 which would be 80\/5 = 16 cans<\/p>\n<p>Question 5.<br \/>\nList \u22121, \\(\\frac{1}{4}\\), and \u22121 \\(\\frac{2}{3}\\) in order from greatest to least.<br \/>\nType below:<br \/>\n__________<\/p>\n<p>Answer:<br \/>\n\\(\\frac{1}{4}\\), -1, \u22121 \\(\\frac{2}{3}\\)<\/p>\n<p>Explanation:<br \/>\n\\(\\frac{1}{4}\\) &gt; -1 &gt; \u22121 \\(\\frac{2}{3}\\)<\/p>\n<p>Question 6.<br \/>\nThe point located at (3, \u22121) is reflected across the y\u2212axis. What are the coordinates of the reflected point?<br \/>\nType below:<br \/>\n__________<\/p>\n<p>Answer:<br \/>\n(-3, -1)<\/p>\n<p>Explanation:<br \/>\nThe point located at (3, \u22121) is reflected across the y\u2212axis.<br \/>\n(-3, -1)<\/p>\n<h3><a id=\"The_Coordinate_Plane_\u2013_Page_No._197\"><\/a>Share and Show &#8211; Page No. 197<\/h3>\n<p>Question 1.<br \/>\nBusby County is rectangular. A map of the county on a coordinate plane shows the vertices of the county at (\u22125, 8), (8, 8), (8, \u221210), and (\u22125, \u221210). Each unit on the map represents 1 mile. What is the county\u2019s perimeter?<br \/>\n_____ miles<\/p>\n<p>Answer:<br \/>\n62 miles<\/p>\n<p>Explanation:<br \/>\nBusby County is rectangular. A map of the county on a coordinate plane shows the vertices of the county at (\u22125, 8), (8, 8), (8, \u221210), and (\u22125, \u221210).<br \/>\nThe distance of (\u22125, 8) is 8<br \/>\nThe distance of (8, 8) is 8<br \/>\nThe distance between -5 to 8 is 5 + 8 = 13<br \/>\nThe distance of (8, \u221210) is 10<br \/>\nThe distance of (\u22125, \u221210) is 10<br \/>\nThe distance between -5 to 8 is 5 + 8 = 13<br \/>\n8 + 8 + 13 + 10 + 10 + 13 = 62<\/p>\n<p>Question 2.<br \/>\nWhat if the vertices of the county were (\u22125, 8), (8, 8), (8, \u22126), and (\u22125, \u22126)? What would the perimeter of the county be?<br \/>\n_____ miles<\/p>\n<p>Answer:<br \/>\n54 miles<\/p>\n<p>Explanation:<br \/>\nThe distance from &#8211; 5 to 8 is 5 + 8 = 13<br \/>\nThe distance from &#8211; 5 to 8 is 5 + 8 = 13<br \/>\nThe distance from 8 to -6 is 8 + 6 = 14<br \/>\nThe distance from 8 to -6 is 8 + 6 = 14<br \/>\n13 + 14 + 13 + 14 = 54<\/p>\n<p>Question 3.<br \/>\nOn a coordinate map of Melville, a restaurant is located at (\u22129, \u22125). A laundry business is located 3 units to the left of the restaurant on the map. What are the map coordinates of the laundry business?<br \/>\nType below:<br \/>\n__________<\/p>\n<p>Answer:<br \/>\n(-12, -5)<\/p>\n<p>Explanation:<br \/>\nOn a coordinate map of Melville, a restaurant is located at (\u22129, \u22125).<br \/>\nA laundry business is located 3 units to the left of the restaurant on the map.(-12, -5) is the answer<\/p>\n<p>Question 4.<br \/>\nThe library is 4 blocks north and 9 blocks east of the school. The museum is 9 blocks east and 11 blocks south of the school. How far is it from the library to the museum?<br \/>\n_____ blocks<\/p>\n<p>Answer:<br \/>\n15 blocks<\/p>\n<p>Explanation:<br \/>\nthe library is 4 blocks north = (0, 4)<br \/>\n9 blocks east = (9, 4)<br \/>\nThe museum is 9 blocks east = (9, 0)<br \/>\n11 blocks south = (9, -11)<br \/>\n4 + 11 = 15<\/p>\n<h3><a id=\"The_Coordinate_Plane_\u2013_Page_No._198\"><\/a>Problem Solving + Applications &#8211; Page No. 198<\/h3>\n<p>Question 5.<br \/>\nMake Sense of Problems Diana left her campsite at (2, 6) on a map of Big Trees Park, hiked to Redwood Grove at (\u22125, 6), and continued on to Bass Lake at (\u22125, \u22123). Each unit on the map represents 1 kilometer. How far did Diana hike?<br \/>\n_____ km<\/p>\n<p>Answer:<br \/>\n16 km<\/p>\n<p>Explanation:<br \/>\nDiana left her campsite at (2, 6) on a map of Big Trees Park, hiked to Redwood Grove at (\u22125, 6), 2 + 5 = 7<br \/>\nand continued on to Bass Lake at (\u22125, \u22123), 6 + 3 = 9<br \/>\n7 + 9 = 16 km<\/p>\n<p>Question 6.<br \/>\nHector left his house at (\u22126, 13) on a map of Coleville and walked to the zoo at (\u22126, 2). From there he walked east to his friend\u2019s house. He walked a total distance of 25 blocks. If each unit on the map represents one block, what are the coordinates of Hector\u2019s friend\u2019s house?<br \/>\nType below:<br \/>\n__________<\/p>\n<p>Answer:<br \/>\n(19,2) should be the answer. He was -6 above the x-axis. Going east for 25 unit means he walked horizontally keeping the y-axis same<\/p>\n<p>Question 7.<br \/>\nIn November, the price of a cell phone was double the price in March. In December, the price was $57, which was $29 less than the price in November. What was the price of the cell phone in March?<br \/>\n$ _____<\/p>\n<p>Answer:<br \/>\n$172<\/p>\n<p>Explanation:<br \/>\nIn November, the price of a cell phone was double the price in March. In December, the price was $57, which was $29 less than the price in November.<br \/>\n29 + 57 = 86<br \/>\n86 \u00d7 2 = $172<\/p>\n<p>Question 8.<br \/>\nA map of the city holding the Olympics is placed on a coordinate plane. Olympic Stadium is located at the origin of the map. Each unit on the map represents 2 miles.<br \/>\n<img loading=\"lazy\" src=\"https:\/\/ccssmathanswers.com\/wp-content\/uploads\/2020\/08\/Go-Math-Grade-6-Answer-Key-Chapter-3-Understand-Positive-and-Negative-Numbers-img-30.jpg\" alt=\"Go Math Grade 6 Answer Key Chapter 3 Understand Positive and Negative Numbers img 30\" width=\"344\" height=\"166\" \/><br \/>\nGraph the locations of four other Olympic buildings.<\/p>\n<p>Max said the distance between the Aquatics Center and the Olympic Village is greater than the distance between the Media Center and the Basketball Arena. Do you agree with Max? Use words and numbers to support your answer<br \/>\nType below:<br \/>\n__________<\/p>\n<p>Answer:<br \/>\nMax said is correct<br \/>\nAquatics Center = (8, 4)<br \/>\nOlympic Village = (-8, 4)<br \/>\nThe distance = 8 + 8 = 16<br \/>\nMedia Center = (4, -5)<br \/>\nBasketball Arena = (-8, -5)<br \/>\nThe distance = 4 + 8 = 12<\/p>\n<h3><a id=\"The_Coordinate_Plane_\u2013_Page_No._199\"><\/a>Problem Solving The Coordinate Plane &#8211; Page No. 199<\/h3>\n<p><strong>Read each problem and solve.<\/strong><\/p>\n<p>Question 1.<br \/>\nOn a coordinate map of Clifton, an electronics store is located at (6, \u22127). A convenience store is located 7 units north of the electronics store on the map. What are the map coordinates of the convenience store?<br \/>\nType below:<br \/>\n__________<\/p>\n<p>Answer:<br \/>\n(6, 0)<\/p>\n<p>Explanation:<br \/>\nOn a coordinate map of Clifton, an electronics store is located at (6, \u22127). A convenience store is located 7 units north of the electronics store on the map.<br \/>\nThe map coordinates of the convenience store is (6, 0)<\/p>\n<p>Question 2.<br \/>\nSonya and Lucas walk from the school to the library. They walk 5 blocks south and 4 blocks west to get to the library. If the school is located at a point (9, \u22121) on a coordinate map, what are the map coordinates of the library?<br \/>\nType below:<br \/>\n__________<\/p>\n<p>Answer:<br \/>\n(5, -6)<\/p>\n<p>Explanation:<br \/>\nThe school is at (9, \u22121)<br \/>\n5 blocks South mean that you subtract 5 from the y coordinate:<br \/>\n(9, -1-5) = (9, -6)<br \/>\n4 blocks West means that you subtract 4 from the x coordinate:<br \/>\n(9-4, -6) = (5, -6)<br \/>\nThe library is at (5, -6)<\/p>\n<p>Question 3.<br \/>\nOn a coordinate map, Sherry\u2019s house is at the point (10, \u22122) and the mall is at point (\u22124, \u22122). If each unit on the map represents one block, what is the distance between Sherry\u2019s house and the mall?<br \/>\n_____ blocks<\/p>\n<p>Answer:<br \/>\n14 blocks<\/p>\n<p>Explanation:<br \/>\n(10,-2)<br \/>\n(-4,-2)<br \/>\nx value- 10-(-4)=14<br \/>\ny value- Since both y values are the same, you don&#8217;t do anything.<\/p>\n<p>Question 4.<br \/>\nArthur left his job at (5, 4) on a coordinate map and walked to his house at (5, \u22126). Each unit on the map represents 1 block. How far did Arthur walk?<br \/>\n_____ blocks<\/p>\n<p>Answer:<br \/>\n10 blocks<\/p>\n<p>Explanation:<br \/>\nHe walked 10 blocks. 4 to -6 is 10. 4, 3, 2, 1, 0, -1, -2, -3, -4, -5, -6.<\/p>\n<p>Question 5.<br \/>\nA fire station is located 2 units east and 6 units north of a hospital. If the hospital is located at a point (\u22122, \u22123) on a coordinate map, what are the coordinates of the fire station?<br \/>\nType below:<br \/>\n__________<\/p>\n<p>Answer:<br \/>\n(0, 3)<\/p>\n<p>Explanation:<br \/>\nthe hospital is located at a point (\u22122, \u22123).<br \/>\nA fire station is located 2 units east and 6 units north of a hospital.<br \/>\n(-2 +2, -3+6) = (0,3)<\/p>\n<p>Question 6.<br \/>\nXavier\u2019s house is located at the point (4, 6). Michael\u2019s house is 10 blocks west and 2 blocks south of Xavier\u2019s house. What are the coordinates of Michael\u2019s house?<br \/>\nType below:<br \/>\n__________<\/p>\n<p>Answer:<br \/>\n(-6, 4)<\/p>\n<p>Explanation:<br \/>\nthe coordinates are -6,4. (x-10,y-2)<\/p>\n<p>Question 7.<br \/>\nWrite a problem that can be solved by drawing a diagram on a coordinate plane.<br \/>\nType below:<br \/>\n__________<\/p>\n<p>Answer:<br \/>\nOn a coordinate map, Sherry\u2019s house is at the point (10, \u22122) and the mall is at point (\u22124, \u22122). If each unit on the map represents one block, what is the distance between Sherry\u2019s house and the mall?<\/p>\n<h3><a id=\"The_Coordinate_Plane_\u2013_Page_No._200\"><\/a>Lesson Check &#8211; Page No. 200<\/h3>\n<p>Question 1.<br \/>\nThe points (\u22124, \u22124), (\u22124, 4), (4, 4), and (4, \u22124) form a square on a coordinate plane. How long is a side length of the square?<br \/>\n_____ units<\/p>\n<p>Answer:<br \/>\n8 units<\/p>\n<p>Explanation:<br \/>\n-4 + 4 = 8 units<br \/>\nside length of the square is 8 units<\/p>\n<p>Question 2.<br \/>\nOn a coordinate map, the museum is located at (\u22125, 7). A park is located 6 units to the right of the museum on the map. What are the coordinates of the park?<br \/>\nType below:<br \/>\n__________<\/p>\n<p>Answer:<br \/>\n(1, 7)<\/p>\n<p>Explanation:<br \/>\nOn a coordinate map, the museum is located at (\u22125, 7). A park is located 6 units to the right of the museum on the map.<br \/>\n(1,7)<\/p>\n<p><strong>Spiral Review<\/strong><\/p>\n<p>Question 3.<br \/>\nOn a grid Joe\u2019s house is marked at (\u22125, \u22123) and Andy\u2019s house is marked at (1, \u22123). What is the distance, on the grid, between Joe\u2019s house and Andy\u2019s house?<br \/>\n_____ units<\/p>\n<p>Answer:<br \/>\n6 units<\/p>\n<p>Explanation:<br \/>\nOn a grid Joe\u2019s house is marked at (\u22125, \u22123) and Andy\u2019s house is marked at (1, \u22123).<br \/>\n|-5| = 5<br \/>\n5 + 0 = 5<br \/>\n0 + 1 = 1<br \/>\n5 + 1 = 6<\/p>\n<p>Question 4.<br \/>\nIn the last two years, Mari grew 2 \\(\\frac{1}{4}\\) inches, Kim grew 2.4 inches, and Kate grew 2 \\(\\frac{1}{8}\\) inches. Write the amounts they grew in order from least to greatest.<br \/>\nType below:<br \/>\n__________<\/p>\n<p>Answer:<br \/>\n2 \\(\\frac{1}{8}\\), 2 \\(\\frac{1}{4}\\), 2.4<\/p>\n<p>Explanation:<br \/>\nIn the last two years, Mari grew 2 \\(\\frac{1}{4}\\) inches, Kim grew 2.4 inches, and Kate grew 2 \\(\\frac{1}{8}\\) inches.<br \/>\n2 \\(\\frac{1}{4}\\) = 9\/4 = 2.25<br \/>\n2 \\(\\frac{1}{8}\\) = 17\/8 = 2.125<br \/>\n2.125, 2.25, 2.4<\/p>\n<p>Question 5.<br \/>\nA jar of jelly that weighs 4.25 ounces costs $2.89. What is the cost of one ounce of jelly?<br \/>\n$ _____<\/p>\n<p>Answer:<br \/>\n$0.68<\/p>\n<p>Explanation:<br \/>\nA jar of jelly that weighs 4.25 ounces costs $2.89.<br \/>\n$2.89\/4.25 = $0.68<\/p>\n<p>Question 6.<br \/>\nJan began with \\(\\frac{5}{6}\\) pound of modeling clay. She used \\(\\frac{1}{5}\\) of the clay to make decorative magnets. She divided the remaining clay into 8 equal portions. What is the weight of the clay in each portion?<br \/>\n\\(\\frac{\u25a1}{\u25a1}\\) pounds<\/p>\n<p>Answer:<br \/>\n\\(\\frac{1}{12}\\) pounds<\/p>\n<p>Explanation:<br \/>\nWeight of modelling clay is = 5\/6 pounds<br \/>\nPart of clay used to make decorative magnets is = 1\/5<br \/>\nRemaining part of clay = 1 &#8211; 1\/5 = 4\/5<br \/>\nSo, Remaining part of clay is divided into 8 equal parts so, Weight of each clay is given by 4\/5 \u00d7 5\/6 \u00d7 1\/8 = 1\/12 pounds<br \/>\nSo, weight of the clay in each portion is 1\/12 pounds<\/p>\n<h3><a id=\"Review\/Test_\u2013_Page_No._201\"><\/a>Chapter 3 Review\/Test &#8211; Page No. 201<\/h3>\n<p>Question 1.<br \/>\nFor numbers 1a\u20131d, choose Yes or No to indicate whether the situation can be represented by a negative number.<br \/>\n1a. Sherri lost 100 points answering a question wrong. Yes No<br \/>\n1b. The peak of a mountain is 2,000 feet above sea level. Yes No<br \/>\n1c. Yong paid $25 for a parking ticket. Yes No<br \/>\n1d. A puppy gained 3 pounds. Yes No<br \/>\n1a. __________<br \/>\n1b. __________<br \/>\n1c. __________<br \/>\n1d. __________<\/p>\n<p>Answer:<br \/>\n1a. Yes<br \/>\n1b. No<br \/>\n1c. No<br \/>\n1d. No<\/p>\n<p>Question 2.<br \/>\nThe low weekday temperatures for a city are shown.<br \/>\n<img loading=\"lazy\" src=\"https:\/\/ccssmathanswers.com\/wp-content\/uploads\/2020\/08\/Go-Math-Grade-6-Answer-Key-Chapter-3-Understand-Positive-and-Negative-Numbers-img-31.jpg\" alt=\"Go Math Grade 6 Answer Key Chapter 3 Understand Positive and Negative Numbers img 31\" width=\"289\" height=\"216\" \/><br \/>\nPart A<br \/>\nUsing the information in the table, order the temperatures from lowest to highest.<br \/>\nType below:<br \/>\n__________<\/p>\n<p>Answer:<br \/>\n-7, -5, -3, 2, 3<\/p>\n<p>Explanation:<br \/>\nMonday = -5<br \/>\nTuesday = -3<br \/>\nWednesday = 2<br \/>\nThursday = -7<br \/>\nFriday = 3<br \/>\n-7, -5, -3, 2, 3<\/p>\n<p>Question 2.<br \/>\nPart B<br \/>\nExplain how to use a vertical number line to determine the order.<br \/>\nType below:<br \/>\n__________<\/p>\n<p>Answer:<br \/>\nPlace the -3, -5, -7, are below the 0. And place 2 and 3 are above the 0.<\/p>\n<h3><a id=\"Review\/Test_\u2013_Page_No._202\"><\/a>Page No. 202<\/h3>\n<p>Question 3.<br \/>\nFor numbers 3a\u20133e, choose Yes or No to indicate whether the number is between \u20131 and \u20132.<br \/>\n3a. \\(\\frac{-4}{5}\\) Yes No<br \/>\n3b. 1 \\(\\frac{2}{3}\\) Yes No<br \/>\n3c. \u22121.3 Yes No<br \/>\n3d. \u22121 \\(\\frac{1}{4}\\) Yes No<br \/>\n3e. \u22122 \\(\\frac{1}{10}\\) Yes No<br \/>\n3a. __________<br \/>\n3b. __________<br \/>\n3c. __________<br \/>\n3d. __________<br \/>\n3e. __________<\/p>\n<p>Answer:<br \/>\n3a. No<br \/>\n3b. No<br \/>\n3c. Yes<br \/>\n3d. Yes<br \/>\n3e. No<\/p>\n<p>Explanation:<br \/>\n3a. \\(\\frac{-4}{5}\\) = -0.8<br \/>\n3b. 1 \\(\\frac{2}{3}\\) = 1.666<br \/>\n3c. -1.3<br \/>\n3d. \u22121 \\(\\frac{1}{4}\\) = -1.25<br \/>\n3e. \u22122 \\(\\frac{1}{10}\\) = -21\/10 = -2.1<\/p>\n<p>Question 4.<br \/>\nCompare \\(\\frac{-1}{5}\\) and \u20130.9. Use numbers and words to explain your answer<br \/>\nType below:<br \/>\n__________<\/p>\n<p>Answer:<br \/>\n\\(\\frac{-1}{5}\\) = -0.2<br \/>\n-0.9<br \/>\n-0.2 and -0.9 both are negative numbers. They lies between 0 and -1<\/p>\n<p>Question 5.<br \/>\nJeandre said |3| equals |\u20133|. Is Jeandre correct? Use a number line and words to support your answer.<br \/>\nType below:<br \/>\n__________<\/p>\n<p>Answer:<br \/>\n<img loading=\"lazy\" class=\"alignnone size-medium wp-image-7357\" src=\"https:\/\/ccssmathanswers.com\/wp-content\/uploads\/2020\/08\/grade-6-chapter-3-Page-no.-202-image-1-300x92.jpg\" alt=\"grade 6 chapter 3 Page no. 202 image 1\" width=\"300\" height=\"92\" srcset=\"https:\/\/bigideasmathanswers.com\/wp-content\/uploads\/2020\/08\/grade-6-chapter-3-Page-no.-202-image-1-300x92.jpg 300w, https:\/\/bigideasmathanswers.com\/wp-content\/uploads\/2020\/08\/grade-6-chapter-3-Page-no.-202-image-1.jpg 646w\" sizes=\"(max-width: 300px) 100vw, 300px\" \/><\/p>\n<p>Explanation:<br \/>\nYes, he is correct and he is referring to the absolute values of number 3 and -3. And by absolute value, this is the distance of the number from the origin zero (0) which is symbolized by two vertical lines, as |3| or |-3| is equal to 3.<br \/>\nThe picture shows a number line where green is the origin zero (0). The purple line is the distance between 0 and 3 which is 3. The pink one is the distance of -3 from 0 which is also 3. Therefore, |3| equals |-3|<\/p>\n<p>Question 6.<br \/>\nWrite the values in order from least to greatest.<br \/>\n<img loading=\"lazy\" src=\"https:\/\/ccssmathanswers.com\/wp-content\/uploads\/2020\/08\/Go-Math-Grade-6-Answer-Key-Chapter-3-Understand-Positive-and-Negative-Numbers-img-32.jpg\" alt=\"Go Math Grade 6 Answer Key Chapter 3 Understand Positive and Negative Numbers img 32\" width=\"471\" height=\"63\" \/><br \/>\nType below:<br \/>\n__________<\/p>\n<p>Answer:<br \/>\n|2| |-4| |8| |-12|<\/p>\n<p>Explanation:<br \/>\n|-4| = 4<br \/>\n|2| = 2<br \/>\n|-12| = 12<br \/>\n|8| = 8<br \/>\n2, 4, 8, 12<\/p>\n<p>Question 7.<br \/>\nFor numbers 7a\u20137d, select True or False for each statement.<br \/>\n7a. The x-coordinate of any point on the y-axis is 0. True False<br \/>\n7b. Point D(\u20132, 1) is to the left of the y-axis and below the x-axis. True False<br \/>\n7c. The point where the axes intersect is the origin. True False<br \/>\n7d. If both the x- and y- coordinates are positive, the point is to the right of the y-axis and below the x-axis. True False<br \/>\n__________<br \/>\n__________<br \/>\n__________<br \/>\n__________<\/p>\n<p>Answer:<br \/>\n7a. True<br \/>\n7b. False<br \/>\n7c. True<br \/>\n7d. False<\/p>\n<h3><a id=\"Review\/Test_\u2013_Page_No._203\"><\/a>Page No. 203<\/h3>\n<p>Question 8.<br \/>\nMia\u2019s house is located at point (3, 4) on a coordinate plane. The location of Keisha\u2019s house is the reflection of the location of Mia\u2019s house across the y-axis. In what quadrant is Keisha\u2019s house in?<br \/>\nType below:<br \/>\n__________<\/p>\n<p>Answer:<br \/>\nquadrant II<\/p>\n<p>Explanation:<br \/>\nMia\u2019s house is located at point (3, 4) on a coordinate plane. The location of Keisha\u2019s house is the reflection of the location of Mia\u2019s house across the y-axis.<br \/>\nquadrant II is the answer.<\/p>\n<p>Question 9.<br \/>\nPoints A(3, 8) and B(\u20134, 8) are located on a coordinate plane. Graph the pair of points. Then find the distance between them. Use numbers and words to explain your answer.<br \/>\nType below:<br \/>\n__________<\/p>\n<p>Answer:<\/p>\n<p>Explanation:<br \/>\nPoints A(3, 8) and B(\u20134, 8) are located on a coordinate plane.<br \/>\n3 + 0 = 3<br \/>\n|-4| = 4<br \/>\n4 + 0 = 4<br \/>\n3 + 4 = 7<br \/>\n7 units<\/p>\n<h3><a id=\"Review\/Test_\u2013_Page_No._204\"><\/a>Page No. 204<\/h3>\n<p>Question 10.<br \/>\nThe map shows the location J of Jose\u2019s house and the location F of the football field. Jose is going to go to Tyrell\u2019s house and then the two of them are going to go to the football field for practice.<br \/>\n<img loading=\"lazy\" src=\"https:\/\/ccssmathanswers.com\/wp-content\/uploads\/2020\/08\/Go-Math-Grade-6-Answer-Key-Chapter-3-Understand-Positive-and-Negative-Numbers-img-33.jpg\" alt=\"Go Math Grade 6 Answer Key Chapter 3 Understand Positive and Negative Numbers img 33\" width=\"359\" height=\"357\" \/><br \/>\nPart A<br \/>\nTyrell\u2019s house is located at point T, the reflection of point J across the y-axis. What are the coordinates of points T, J, and F?<br \/>\nType below:<br \/>\n__________<\/p>\n<p>Answer:<br \/>\ncoordinates of points T (6, 8)<br \/>\ncoordinates of points J (-6, 8), and<br \/>\ncoordinates of points F(-5, 6)<\/p>\n<p>Question 10.<br \/>\nPart B<br \/>\nIf each unit on the map represents 1 block, what was the distance Tyrell traveled to the football field and what was the distance Jose traveled to the football field? Use numbers and words to explain your answer<br \/>\nType below:<br \/>\n__________<\/p>\n<p>Answer:<br \/>\nIf each unit on the map represents 1 block, the distance Jose traveled to the football field<br \/>\ncoordinates of points T (6, 8)<br \/>\ncoordinates of points J (-6, 8)<br \/>\n|-6| = 6<br \/>\n6 + 6 = 12 units.<br \/>\nthe distance Tyrell traveled to the football field<br \/>\ncoordinates of points T (6, 8)<br \/>\ncoordinates of points F(-5, 6)<br \/>\n6 + 5 = 11 units<\/p>\n<p>Question 11.<br \/>\nFor numbers 11a\u201311d, choose Yes or No to indicate whether the situation could be represented by the integer +3.<br \/>\n11a. A football team gains 3 yards on a play. Yes No<br \/>\n11b. A golfer\u2019s score is 3 over par. Yes No<br \/>\n11c. A student answers a Yes No 3-point question correctly. Yes No<br \/>\n11d. A cat loses 3 pounds. Yes No<br \/>\n11a. __________<br \/>\n11b. __________<br \/>\n11c. __________<br \/>\n11d. __________<\/p>\n<p>Answer:<br \/>\n11a. Yes<br \/>\n11b. Yes<br \/>\n11c. Yes<br \/>\n11d. No<\/p>\n<h3><a id=\"Review\/Test_\u2013_Page_No._205\"><\/a>Page No. 205<\/h3>\n<p>Question 12.<br \/>\nJason used a map to record the elevations of five locations.<br \/>\n<img loading=\"lazy\" src=\"https:\/\/ccssmathanswers.com\/wp-content\/uploads\/2020\/08\/Go-Math-Grade-6-Answer-Key-Chapter-3-Understand-Positive-and-Negative-Numbers-img-34.jpg\" alt=\"Go Math Grade 6 Answer Key Chapter 3 Understand Positive and Negative Numbers img 34\" width=\"290\" height=\"214\" \/><br \/>\nJason wrote the elevations in order from lowest to highest : -3, 5, 8 -18, -20.<br \/>\nIs Jason correct? Use words and numbers to explain why or why not. If Jason is incorrect, what is the correct order?<br \/>\nType below:<br \/>\n__________<\/p>\n<p>Answer:<br \/>\nJason is incorrect.<br \/>\nthe elevations in order from lowest to highest: -20, -18, -3, 5, 8<\/p>\n<p>Question 13.<br \/>\nFor numbers 13a\u201313d, select True or False for each statement.<br \/>\n13a. \\(\\frac{1}{5}\\) is between 0 and 1. True False<br \/>\n13b. \u22122 \\(\\frac{2}{3}\\) is between -1 and -2. True False<br \/>\n13c. \u22123 \\(\\frac{5}{8}\\) is between -3 and -4. True False<br \/>\n13d. 4 \\(\\frac{3}{4}\\) is between 3 and 4. True False<br \/>\n13a. __________<br \/>\n13b. __________<br \/>\n13c. __________<br \/>\n13d. __________<\/p>\n<p>Answer:<br \/>\n13a. True<br \/>\n13b. False<br \/>\n13c. True<br \/>\n13d. False<\/p>\n<p>Question 14.<br \/>\nChoose &lt;, &gt;, or =.<br \/>\n14a. 0.25 \u03bf \\(\\frac{3}{4}\\)<br \/>\n14b. 2 \\(\\frac{7}{8}\\) \u03bf 2.875<br \/>\n14c. \\(\\frac{1}{3}\\) \u03bf 0.325<br \/>\n14d. \\(\\frac{-3}{4}\\) \u03bf \\(\\frac{-1}{2}\\)<br \/>\n0.25 ____ \\(\\frac{3}{4}\\)<br \/>\n2 \\(\\frac{7}{8}\\) _____ 2.875<br \/>\n\\(\\frac{1}{3}\\) _____ 0.325<br \/>\n\\(\\frac{-3}{4}\\) _____ \\(\\frac{-1}{2}\\)<\/p>\n<p>Answer:<br \/>\n0.25 &lt; \\(\\frac{3}{4}\\)<br \/>\n2 \\(\\frac{7}{8}\\) = 2.875<br \/>\n\\(\\frac{1}{3}\\) &gt; 0.325<br \/>\n\\(\\frac{-3}{4}\\) &lt; \\(\\frac{-1}{2}\\)<\/p>\n<p>Explanation:<br \/>\n\\(\\frac{3}{4}\\) = 0.75<br \/>\n0.25 &lt; \\(\\frac{3}{4}\\)<br \/>\n2 \\(\\frac{7}{8}\\) = 23\/8 = 2.875<br \/>\n2 \\(\\frac{7}{8}\\) = 2.875<br \/>\n\\(\\frac{-3}{4}\\) = -0.75<br \/>\n\\(\\frac{-1}{2}\\) = -0.5<\/p>\n<h3><a id=\"Review\/Test_\u2013_Page_No._206\"><\/a>Page No. 206<\/h3>\n<p>Question 15.<br \/>\nGraph 4 and \u22124 on the number line.<br \/>\n<img loading=\"lazy\" src=\"https:\/\/ccssmathanswers.com\/wp-content\/uploads\/2020\/08\/Go-Math-Grade-6-Answer-Key-Chapter-3-Understand-Positive-and-Negative-Numbers-img-35.jpg\" alt=\"Go Math Grade 6 Answer Key Chapter 3 Understand Positive and Negative Numbers img 35\" width=\"299\" height=\"63\" \/><br \/>\nTyler says both 4 and \u22124 have an absolute value of 4. Is Tyler correct? Use the number line and words to explain why or why not.<br \/>\nType below:__________<\/p>\n<p>Answer:<br \/>\nTyler is correct.<br \/>\n|-4| = 4<br \/>\n|4| = 4<\/p>\n<p>Question 16.<br \/>\nLindsay and Will have online accounts for buying music. Lindsay&#8217;s account balance is \u2212$20 and Will&#8217;s account balance is \u2212$15. Express each account balance as a debt and explain whose debt is greater.<br \/>\nType below:<br \/>\n__________<\/p>\n<p>Answer:<br \/>\nLindsey is 5$ more in dept than Will.<br \/>\nLindsey= -20$<br \/>\nWill= -15$<\/p>\n<p>Question 17.<br \/>\nExplain how to graph points A(\u20133, 0), B(0, 0), and C(0, \u20133) on the coordinate plane. Then, explain how to graph point D, so that ABCD is a square.<br \/>\nType below:<br \/>\n__________<\/p>\n<p>Answer:<br \/>\nFirst place the points A(\u20133, 0), B(0, 0), and C(0, \u20133) on the coordinate plane.<br \/>\nThe length from point A to point B is 3.<br \/>\nA square has equal lengths on each side.<br \/>\nSo, to find D, Add 3 units to the left to C or down to A.<br \/>\nD(-3, -3)<\/p>\n<p>Question 18.<br \/>\nPoint A(2, \u20133) is reflected across the x-axis to point B. Point B is reflected across the y-axis to point C. What are the coordinates of point C? Use words and numbers to explain your answer.<br \/>\nType below:<br \/>\n__________<\/p>\n<p>Answer:<br \/>\nQuadrant III<\/p>\n<p>Explanation:<br \/>\nPoint A(2, \u20133) is reflected across the x-axis to point B. Point B is reflected across the y-axis to point C.<br \/>\nSo, Point B is (2,3)<br \/>\nPoint C is (-2, 3)<br \/>\nC is in Quadrant III<\/p>\n<h3>Conclusion:<\/h3>\n<p>We believe that the details provided in the HMH Go Math 6th Grade Answer Key for Chapter 3 Understand Positive and Negative Numbers made you happy. All the explanations are prepared by the math experts as per the latest syllabus. Compare the questions in real-time so that you can understand concepts easily. Stay with us to get the answer keys for all the chapters of grade 6.<\/p>\n","protected":false},"excerpt":{"rendered":"<p>Enhance your knowledge by practicing the problems from Go Math Grade 6 Answer Key Chapter 3 Understand Positive and Negative Numbers. You can get the free pdfs of Go Math Grade 6 Chapter 3 Understand Positive and Negative Numbers Solution Key. 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