2-4 Multiplying Integers

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1 Find each product ( 8) ( 3)( 5) ( 9)( 5) Financial Literacy Mr. Heppner bought lunch with his debit card every day for 5 days. Each day he spent $8. If these were his only transactions this week, what was the change in his account balance? Write a multiplication expression. Then find and interpret the product. 8(5); $40; Mr. Heppner's account balance is $40 less after 5 days. Simplify each expression m 18m 7. 3a(7b) 21ab 8. 6e( 4f ) 24ef Evaluate each expression. 9. 8j, if j = cd, if c = 3 and d = Find each product ( 9) ( 9) ( 8) ( 7) ( 11)(5) ( 7)( 6) ( 20)(5) The temperature dropped 2 F every hour for the last 6 hours. What is the total change in temperature? Write a multiplication expression. Then find and interpret the product. 2(6); 12 F; The temperature dropped 12 F after 6 hours. esolutions Manual - Powered by Cognero Page 1

2 20. An elevator takes passengers from the ground floor down to an underground parking garage. Where will the elevator be in relation to the ground floor after 5 seconds if it travels at a rate of 3 feet per second? Write a multiplication expression. Then find and interpret the product. 5( 3); 15 ft; The elevator is 15 feet below ground after 15 seconds. Simplify each expression ( 6m) 30m s 50s 23. 9m( 9n) 81mn a(7c) 77ac 25. 4a(b)( 9) 36ab ( j )( 3k) 36jk Evaluate each expression n, if n = m, if m = xy if x = 6 and y = st, if s = 4 and t = Model with Mathematics Diego borrowed $780 from his father to buy a new saddle for his horse. He earns $65 each weekend cleaning stables and uses his earnings to pay off his debt. Write an expression Diego can use to determine how much he owes each week. Then make a table to show how much he owes after 2, 4, 6, and 8 weeks. Based on the pattern in the table, predict how long it will take Diego to repay his father w Week w Amount Owed ($) (2) (4) (6) (8) 260 It will take Diego 12 weeks to repay his father e( 2f )(9g) 54efg 28. 3r(7s)(5t) 105rst esolutions Manual - Powered by Cognero Page 2

3 34. The table shows the number of Calories burned per minute for a 120-pound person during different activities. What is the change in the number of Calories in a 120-pound person s body if he runs for 20 minutes and swims for 25 minutes? Interpret the product. 39. Reason Abstractly Two teams of students played a trivia game. Each team earned 5 points for every correct answer, lost 8 points for every incorrect answer, and lost 2 points for every passed question. For each team, write an expression to determine the number of points they earned. Which team won? 560 Calories; There are 560 fewer Calories. Replace each _ with <, >, or = to make a true sentence (6) _ 3(8) < 36. 3( 2) _ 4( 1) < Team 1 answered 12 questions correctly, 3 questions incorrectly, and passed on 1 question, so Team 1 earned 12(5) + 3( 8) + 1( 2) or 34 points. Team 2 answered 13 questions correctly, 2 questions incorrectly, and passed on 7 questions, so Team 2 earned 13(5) + 2( 8) + 7( 2) or 35 points. Since 34 < 35, Team 2 won. 40. Financial Literacy The price of stock fell $2 each day for 14 consecutive days. The original price of the stock was $41. Write an expression that you could use to find the price of the stock on any day. 2d ( 11)( 3)(6)( 2) _ 24(18) > 38. ( 5)( 2)(9) _ (4)(10)( 9) > esolutions Manual - Powered by Cognero Page 3

4 41. Multiple Representations In this problem, you will investigate the relationship between time and altitude. A hot air balloon is at an altitude of 600 feet. It begins descending at a constant rate of 15 feet per minute. a. Table Complete the table below that shows the altitude every 5 minutes. b. Words What does 0 minutes represent? c. Graph Graph the ordered pairs. d. Symbols Determine the time it will take for the balloon to reach the ground. Explain how you solved. a. Minutes 15x Altitude (ft) 0 15(0) (5) (10) (15) b. the time the balloon began descending c. d. 40 minutes; Sample answer: If you continue the pattern in the table, for every 10 minutes, the balloon drops 150 feet = 600, so 10 4 = 40 minutes. 42. Identify Structure Name two integers that have a product between 10 and 15. Sample answer: 2 and Identify Structure Name all of the values of x if 7 x = and Persevere with Problems Positive integers A and C satisfy A(A C) = 23. What is the value of C? Identify Structure Calculate ( 10)(5)(18)[7 + ( 7)] mentally. Justify your answer. 0; Multiplicative Property of Zero Use a Counterexample Determine whether each of the following is true or false. If false, give a counterexample 46. The product of three negative integers is positive. false; Sample answer: 3( 2)( 2) = The product of four negative integers is positive. true 48. Building on the Essential Question When multiplying more than two integers, how can you determine the sign of the product? Sample answer: The sign of the product will be negative if there is an odd number of negative integers; otherwise the sign will be positive. esolutions Manual - Powered by Cognero Page 4

5 49. A submarine descends at a constant rate of 300 feet per minute. Which of the following equations best represents how to find the change in altitude of the submarine after 5 minutes? A 5( 300) = 1500 B 5(300) = 1500 C 5(300) = 1500 D 5( 300) = Short Response The distance from the water line to the bottom of a cargo ship changes based on the weight of the cargo. A 50. Which of the following equations is modeled by the number line below? F 2( 6) = 12 G 2(6) = 12 H 2(6) = 12 J 2( 6) = 12 J 51. Simplify 14( 2)( 12). A 336 B 168 C 168 D 288 A If the pattern in the table continues, find the depth of the ship, in feet, if the ship is carrying 100 tons of cargo The highest point in California is Mount Whitney, with an elevation of 14,494 feet. The lowest point is Death Valley, with an elevation of 282 feet. How much greater is the elevation of Mount Whitney than Death Valley? 14,776 ft Find each sum ( 9) ( 13) ( 10) ( 12) 6 esolutions Manual - Powered by Cognero Page 5

6 58. The table shows the lowest recorded temperatures for certain states. a. Compare the lowest temperature in Montana and the lowest temperature in Wisconsin using an inequality. b. Write the temperatures in order from greatest to least. a. 54 > 70 b. 54, 70, 80 Find the difference ( 50) ( 5) Challenger Deep is 10,924 meters below sea level. Write an integer to represent this depth of Challenger Deep. Then identify its opposite and describe the meaning. 10,924; 10,924 or +10,924; The meaning of the opposite is 10,924 meters above sea level. esolutions Manual - Powered by Cognero Page 6