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1 Module 2 Review Name: Period: Read each of the directions carefully. You must show ALL of your work to earn credit. 1. Margie gained 3 pounds, then started exercising and lost 7 pounds. Draw a chip/tile model of Margie s weight change involving subtraction (not addition). How much is her net weight change from the start? How many zero pairs are involved? Chip/Tile Model Net Weight Change Zero Pairs Based on the number line above. Decide whether each of the following values is positive or negative and circle your choice. Explain your reasoning. a.) a 2 Pos/Neg Explain: Negative because a is less than two units to the right of 0. b.) b c.) ab + 1 Pos/Neg Explain: Positive because b is negative and the opposite of b is positive. Pos/Neg Explain: Negative because the product ab will be further from the 0 than one unit. 3. x, y, and z are nonzero rational numbers and. Use the values x, y, z, -x, -y, or z to fill in the missing values to make each statement true. a. b. -z top: -z bottom: y OR top: z and bottom: -y 4. Is the following statement true or false? For any integer n, the sum of 3 + n is located to the right of 3 on a number line. Explain. False. If n = -2, then 3 + (-2) equals 1 which is to the left of the 3 on a number line 5. Which of the following options result in a final value of -5? Select all that apply. Show your work. a. Start with. Multiply by -1.5 and then add 4. 3 b. Start with -2. Multiply by and then add c. Start with 6. Divide by and then subtract d. Start with Divide by -4 and then subtract e. Start with. Subtract and then divide by 4. 7/4

2 For #6-8, draw a chip model and a horizontal or vertical number line for each problem, and state answer. Chips/Tiles Number Line ( 3) ( 3) ( 7) = 5 2 ( 7) For #9-11, draw a number line model and write your answer in a complete sentence. 9. Adam owes his brother eight dollars. His brother forgives 5 dollars of the debt. How much does Adam owe his brother? Adam owes his brother $ A submarine dives 8 feet below the surface of the water where it remains for 5 hours. It then dives 5 feet deeper. How many feet below the surface of the water is the submarine at this point? The submarine is 13 feet below the surface of the water.

3 11. Sammy the seal is sitting on a cliff that is 5 feet above the surface of the sea. He then dives into the sea to catch a fish that is 3 feet below the surface of the water, then he comes back up to the surface of the water. How many total feet has Sammy traveled? Sammy has traveled a total of 11 feet. For #12 20, write an expression and solve the word problem. Write your answer in a complete sentence. 12. Brandon has $76 in his bank account. After a shopping spree, he looked at his account again and he had - $11. How much did he spend shopping? Brandon spent $ Last week you rode your bicycle for hours and ran for hours. How many hours did you exercise? I exercised hrs. 14. A toy maker cuts a piece of fabric inches long from a piece that is inches long. How much fabric is left? in fabric is left. 15. There were three rainstorms last February. The storms dropped inches, inches, and inches of rain. What was the combined rainfall of the three storms? The combined rainfall of the three storms was in. 16. Roy is hiking along a trail that is miles long. He plans to rest every miles. How many rest stops will he make? He will make 6 rest stops on the trail. 17. A bread recipe calls for cup of chocolate chips. Marla wants to triple the recipe. How many cups of chocolate chips will she need? She needs 2 ¼ cups of chocolate chips. 18. Of the students on the track team, do jumping events. Of the students who do jumping events, do the long jump. What fraction of the students on the track team do the long jump? of the track team do the long jump. 19. Only of the students attending the party like just pepperoni on their pizza. Of those who do not like pepperoni, like only sausage on their pizza. What fraction of the students like only sausage on their pizza? of the students like only sausage on their pizza.

4 20. Mrs. Sanchez wants to buy pizza for the team after the big game. Each pizza comes with 10 slices. When asked, one-third of the team said that they could eat of a pizza; one third of the team said they could eat 50% of a pizza; one-sixth said that they could eat a whole pizza; and one sixth said that they only wanted one slice. How many pizzas need to be ordered if there are 60 players on the team? 36 pizzas will need to be ordered if there are 60 players on the team. For #21 26, simplify each expression. Write your answer in simplest form For #27 28, read the question carefully and answer. 27. Hiram believes that the quantity 5.1 x is sometimes smaller than 5.1 and sometimes larger than 5.1 a. Provide an integer of x for which 5.1 x is smaller than 5.1. Determine the difference of 5.1 x. x = 3 Difference: 2.1 b. Provide an integer of x for which 5.1 x is larger than 5.1. Determine the difference of 5.1 x. x = -5 Difference: The temperature at noon on a cold winter day was degrees Fahrenheit. By evening, the temperature had dropped by 3.2 degrees Fahrenheit. Mary thinks that the temperature for the evening could be found by subtracting 3.2 from Mollie thinks that -3.2 should be added to Their methods are shown in the expressions below. Mary: Mollie: (-3.2) a. Are these two expressions equivalent? Explain. Yes because taking away 3.2 is the same as adding negative 3.2 tiles. b. What does this mean in terms of the methods outlined by Mary and Mollie? Subtracting is the same as adding the opposite. c. What is the actual evening temperature? F 29. What is two-thirds of the way between A and B on the number line?

5 30. Find two fractions whose product is. Show your work to support your answer. 31. Find two fractions whose sum is. Show your work to support your answer.

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