{"id":74540,"date":"2022-06-15T19:59:54","date_gmt":"2022-06-15T14:29:54","guid":{"rendered":"https:\/\/ccssanswers.com\/?p=74540"},"modified":"2022-05-10T12:59:14","modified_gmt":"2022-05-10T07:29:14","slug":"eureka-math-grade-7-module-2-lesson-7","status":"publish","type":"post","link":"https:\/\/ccssanswers.com\/eureka-math-grade-7-module-2-lesson-7\/","title":{"rendered":"Eureka Math Grade 7 Module 2 Lesson 7 Answer Key"},"content":{"rendered":"

Engage NY Eureka Math 7th Grade Module 2 Lesson 7 Answer Key<\/h2>\n

Eureka Math Grade 7 Module 2 Lesson 7 Example Answer Key<\/h3>\n

Example 1.
\nRepresenting Sums of Rational Numbers on a Number Line
\na. Place the tail of the arrow on 12.
\nb. The length of the arrow is the absolute value of -3\\(\\frac{1}{2}\\) , |-3 \\(\\frac{1}{2}\\) | = 3 \\(\\frac{1}{2}\\) .
\nc. The direction of the arrow is to the left since you are adding a negative number to 12.
\nDraw the number line model in the space below.
\n\"Engage
\nAnswer:
\n\"Engage
\n12 + ( -3\\(\\frac{1}{2}\\) ) = 8\\(\\frac{1}{2}\\) or 12 – 3\\(\\frac{1}{2}\\) = 8\\(\\frac{1}{2}\\)<\/p>\n

Example 2.
\nRepresenting Differences of Rational Numbers on a Number Line
\nFind the following difference, and represent it on a number line: 1 – 2\\(\\frac{1}{4}\\) .
\na.
\nAnswer:
\nRewrite the difference 1 – 2\\(\\frac{1}{4}\\) as a sum: 1 + (-2 \\(\\frac{1}{4}\\)).
\nNow follow the steps to represent the sum<\/u>:
\nb.
\nAnswer:
\nPlace the tail of the arrow on 1.<\/p>\n

c.
\nAnswer:
\nThe length of the arrow is the absolute value of -2 \\(\\frac{1}{4}\\) ; | -2 \\(\\frac{1}{4}\\) |= 2\\(\\frac{1}{4}\\) .<\/p>\n

d.
\nAnswer:
\nThe direction of the arrow is to the left since you are adding a negative number to 1.<\/p>\n

Draw the number line model in the space below.
\n\"Engage
\nAnswer:
\n\"Engage<\/p>\n

Eureka Math Grade 7 Module 2 Lesson 7 Exercise Answer Key<\/h3>\n

Exercise 1.
\nReal-World Connection to Adding and Subtracting Rational Numbers
\nSuppose a seventh grader\u2019s birthday is today, and she is 12 years old. How old was she 3\\(\\frac{1}{2}\\) years ago? Write an equation, and use a number line to model your answer.
\nAnswer:
\n12 + ( -3\\(\\frac{1}{2}\\)) = 8\\(\\frac{1}{2}\\) or 12 – 3\\(\\frac{1}{2}\\) = 8\\(\\frac{1}{2}\\)
\n\"Eureka<\/p>\n

Exercise 2.
\nFind the following sum using a number line diagram: -2\\(\\frac{1}{2}\\) + 5.
\nAnswer:
\n\"Eureka
\n(-2\\(\\frac{1}{2}\\)) + 5 = 2\\(\\frac{1}{2}\\)<\/p>\n

Exercise 3.
\nFind the following difference, and represent it on a number line: -5\\(\\frac{1}{2}\\) – (-8).
\n\"Eureka
\nAnswer:
\n\"Eureka
\n(-5\\(\\frac{1}{2}\\) ) + 8 = 2 \\(\\frac{1}{2}\\)<\/p>\n

Exercise 4.
\nFind the following sums and differences using a number line model.<\/p>\n

a. -6 + 5\\(\\frac{1}{4}\\)
\nAnswer:
\n\"Eureka
\n-6 + 5 \\(\\frac{1}{4}\\) = –\\(\\frac{3}{4}\\)<\/p>\n

b. 7-(-0.9)
\nAnswer:
\n\"Eureka
\n7 + (0.9) = 7.9<\/p>\n

c. 2.5 + (-\\(\\frac{1}{2}\\) )
\nAnswer:
\n\"Eureka
\n2.5 + (-0.5) = 2<\/p>\n

d. –\\(\\frac{1}{4}\\) + 4
\nAnswer:
\n\"Eureka
\n–\\(\\frac{1}{4}\\) + 4 = 3\\(\\frac{3}{4}\\)<\/p>\n

e. –\\(\\frac{1}{2}\\) – (-3)
\nAnswer:
\n\"Eureka
\n\\(\\frac{1}{2}\\) + 3 = 3 \\(\\frac{1}{2}\\)<\/p>\n

Exercise 5.
\nCreate an equation and number line diagram to model each answer.
\na. Samantha owes her father $7. She just got paid $5.50 for babysitting. If she gives that money to her dad, how much will she still owe him?
\nAnswer:
\n-7 + 5.50 = -1.50. She still owes him $1.50.
\n\"Eureka<\/p>\n

b. At the start of a trip, a car\u2019s gas tank contains 12 gallons of gasoline. During the trip, the car consumes 10\\(\\frac{1}{8}\\) gallons of gasoline. How much gasoline is left in the tank?
\nAnswer:
\n12 + (-10\\(\\frac{1}{8}\\) ) = 1\\(\\frac{7}{8}\\) or 12-10\\(\\frac{1}{8}\\) =1 \\(\\frac{7}{8}\\) ,There are 1\\(\\frac{7}{8}\\) gallons of gas left in the tank.
\n\"Eureka<\/p>\n

c. A fish was swimming 3\\(\\frac{1}{2}\\) feet below the water\u2019s surface at 7:00 a.m. Four hours later, the fish was at a depth that is 5\\(\\frac{1}{4}\\) feet below where it was at 7:00 a.m. What rational number represents the position of the fish with respect to the water\u2019s surface at 11:00 a.m.?
\nAnswer:
\n-3\\(\\frac{1}{2}\\) +(-5\\(\\frac{1}{4}\\) )= -8\\(\\frac{3}{4}\\) . The fish is 8\\(\\frac{3}{4}\\) feet below the water\u2019s surface.
\n\"Eureka<\/p>\n

Eureka Math Grade 7 Module 2 Lesson 7 Problem Set Answer Key<\/h3>\n

Represent each of the following problems using both a number line diagram and an equation.<\/p>\n

Question 1.
\nA bird that was perched atop a 15\\(\\frac{1}{2}\\) -foot tree dives down six feet to a branch below. How far above the ground is the bird\u2019s new location?
\nAnswer:
\n15\\(\\frac{1}{2}\\) + (-6) = 9\\(\\frac{1}{2}\\)
\nThe bird is 9\\(\\frac{1}{2}\\) feet above the ground.
\n\"Eureka<\/p>\n

Question 2.
\nMariah owed her grandfather $2.25 but was recently able to pay him back $1.50. How much does Mariah currently owe her grandfather?
\nAnswer:
\n-2.25 + 1.50 = -0.75
\nMariah owes her grandfather 75 cents.
\n\"Eureka<\/p>\n

Question 3.
\nJake is hiking a trail that leads to the top of a canyon. The trail is 4.2 miles long, and Jake plans to stop for lunch after he completes 1.6 miles. How far from the top of the canyon will Jake be when he stops for lunch?
\nAnswer:
\n4.2 – 1.6 = 2.6
\nJake will be 2.6 miles from the top of the canyon.
\n\"Eureka<\/p>\n

Question 4.
\nSonji and her friend Rachel are competing in a running race. When Sonji is 0.4 miles from the finish line, she notices that her friend Rachel has fallen. If Sonji runs one-tenth of a mile back to help her friend, how far will she be from the finish line?
\nAnswer:
\n-0.4 + (-0.1) = -0.5 or -0.4 – 0.1 = -0.5
\nSonji will be 0.5 miles from the finish line.
\n\"Eureka<\/p>\n

Question 5.
\nMr. Henderson did not realize his checking account had a balance of $200 when he used his debit card for a $317.25 purchase. What is his checking account balance after the purchase?
\nAnswer:
\n200 + (-317.25) = -117.25 or 200 – 317.25 = -117.25
\nMr. Henderson\u2019s checking account balance will be -$117.25.
\n\"Eureka<\/p>\n

Question 6.
\nIf the temperature is -3\u00b0F at 10:00 p.m., and the temperature falls four degrees overnight, what is the resulting temperature?
\nAnswer:
\n-3 – 4 = -3 + (-4) = -7
\nThe resulting temperature is -7\u00b0F.
\n\"Eureka<\/p>\n

Eureka Math Grade 7 Module 2 Lesson 7 Exit Ticket Answer Key<\/h3>\n

At the beginning of the summer, the water level of a pond is 2 feet below its normal level. After an unusually dry summer, the water level of the pond dropped another 1\\(\\frac{1}{3}\\) feet.<\/p>\n

Question 1.
\nUse a number line diagram to model the pond\u2019s current water level in relation to its normal water level.
\nAnswer:
\nMove 1\\(\\frac{1}{3}\\) units to the left of -2. -3\\(\\frac{1}{3}\\)
\n\"Engage<\/p>\n

Question 2.
\nWrite an equation to show how far above or below the normal water level the pond is at the end of the summer.
\nAnswer:
\n-2 – 1\\(\\frac{1}{3}\\) = -3\\(\\frac{1}{3}\\) or -2 + (-1\\(\\frac{1}{3}\\)) = -3\\(\\frac{1}{3}\\)<\/p>\n","protected":false},"excerpt":{"rendered":"

Engage NY Eureka Math 7th Grade Module 2 Lesson 7 Answer Key Eureka Math Grade 7 Module 2 Lesson 7 Example Answer Key Example 1. Representing Sums of Rational Numbers on a Number Line a. Place the tail of the arrow on 12. b. The length of the arrow is the absolute value of -3 … Read more<\/a><\/p>\n","protected":false},"author":3,"featured_media":0,"comment_status":"open","ping_status":"open","sticky":false,"template":"","format":"standard","meta":{"footnotes":""},"categories":[6],"tags":[],"jetpack_sharing_enabled":true,"jetpack_featured_media_url":"","_links":{"self":[{"href":"https:\/\/ccssanswers.com\/wp-json\/wp\/v2\/posts\/74540"}],"collection":[{"href":"https:\/\/ccssanswers.com\/wp-json\/wp\/v2\/posts"}],"about":[{"href":"https:\/\/ccssanswers.com\/wp-json\/wp\/v2\/types\/post"}],"author":[{"embeddable":true,"href":"https:\/\/ccssanswers.com\/wp-json\/wp\/v2\/users\/3"}],"replies":[{"embeddable":true,"href":"https:\/\/ccssanswers.com\/wp-json\/wp\/v2\/comments?post=74540"}],"version-history":[{"count":1,"href":"https:\/\/ccssanswers.com\/wp-json\/wp\/v2\/posts\/74540\/revisions"}],"predecessor-version":[{"id":137877,"href":"https:\/\/ccssanswers.com\/wp-json\/wp\/v2\/posts\/74540\/revisions\/137877"}],"wp:attachment":[{"href":"https:\/\/ccssanswers.com\/wp-json\/wp\/v2\/media?parent=74540"}],"wp:term":[{"taxonomy":"category","embeddable":true,"href":"https:\/\/ccssanswers.com\/wp-json\/wp\/v2\/categories?post=74540"},{"taxonomy":"post_tag","embeddable":true,"href":"https:\/\/ccssanswers.com\/wp-json\/wp\/v2\/tags?post=74540"}],"curies":[{"name":"wp","href":"https:\/\/api.w.org\/{rel}","templated":true}]}}