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Exercises: Integers (1.3)

Exercises: Multiply Integers

Instructions: For questions 1-8, multiply.

1. −4⋅8

Solution

−32

2. −3⋅9

3. 9(−7)

Solution

−63

4. 13(−5)

5. −1⋅6

Solution

−6

6. −1⋅3

7. −1(−14)

Solution

14

8. −1(−19)

Exercises: Divide Integers

Instructions: For questions 9-14, divide.

9. −24∇⋅6

Solution

−4

10. 35∇⋅(−7)

11. −52∇⋅(−4)

Solution

13

12. −84∇⋅(−6)

13. −180∇⋅15

Solution

−12

14. −192∇⋅12

Exercises: Simplify Expressions with Integers

Instructions: For questions 15-32, simplify each expression.

15. 5(−6)+7(−2)−3

Solution

−47

16. 8(−4)+5(−4)−6

17. (−2)6

Solution

64

18. (−3)5

19. −42

Solution

−16

20. −62

21. −3(−5)(6)

Solution

90

22. −4(−6)(3)

23. (8−11)(9−12)

Solution

9

24. (6−11)(8−13)

25. 26−3(2−7)

Solution

41

26. 23−2(4−6)

27. 65∇⋅(−5)+(−28)∇⋅(−7)

Solution

−9

28. 52∇⋅(−4)+(−32)∇⋅(−8)

29. 9−2[3−8(−2)]

Solution

−29

30. 11−3[7−4(−2)]

31. (−3)2−24∇⋅(8−2)

Solution

5

32. (−4)2−32∇⋅(12−4)

Exercises: Evaluate Variable Expressions with Integers

Instructions: For questions 33-50, evaluate each expression.

33. y+(−14) when

a. y=−33
b. y=30

Solution

a.−47
b. 16

34. x+(−21) when

a. x=−27
b. x=44

35.

a. a+3 when a=−7
b. −a+3 when a=−7

Solution

a.−4
b. 10


36.

a. d+(−9) when d=−8
b. −d+(−9) when d=−8

37. m+n when
m=−15,n=7

Solution

−8

38. p+q when
p=−9,q=17

39. r+s when
r=−9,s=−7

Solution

−16

40. t+u when
t=−6,u=−5

41. (x+y)2 when
x=−3,y=14

Solution

121

42. (y+z)2 when
y=−3,z=15

43. −2x+17 when

a. x=8
b. x=−8

Solution

a. 1
b. 33

44. −5y+14 when

a. y=9
b. y=−9

45. 10−3m when

a. m=5
b. m=−5

Solution

a.−5
b. 25

46. 18−4n when

a. n=3
b. n=−3

47. 2w2−3w+7 when w=−2

Solution

21

48. 3u2−4u+5 when u=−3

49. 9a−2b−8 when
a=−6,b=−3

Solution

−56

50. 7m−4n−2 when
m=−4,n=−9

Exercises: Translate English Phrases to Algebraic Expressions

Instructions: For questions 51-64, translate to an algebraic expression and simplify if possible.

51. the sum of 3 and −15, increased by 7

Solution

(3+(−15))+7
(3+(−15))+7=−5

52. the sum of −8 and −9, increased by 23

53. the difference of 10 and −18

Solution

10−(−18)
10−(−18)=28

54. subtract 11 from −25

55. the difference of −5 and −30

Solution

−5−(−30)
−5−(−30)=25

56. subtract −6 from −13

57. the product of −3 and 15

Solution

−3⋅15
−3⋅15=−45

58. the product of −4 and 16

59. the quotient of −60 and −20

Solution

−60∇⋅(−20)
−60∇⋅(−20)=3

60. the quotient of −40 and −20

61. the quotient of −6 and the sum of a and b

Solution

−6a+b

62. the quotient of −7 and the sum of m and n

63. the product of −10 and the difference of p and q

Solution

−10(p−q)

64. the product of −13 and the difference of c and d

Exercises: Use Integers in Applications

Instructions: For questions 65-72, solve the given word problems.

65. Temperature. On January 15, the high temperature in Anaheim, California, was 84∘. That same day, the high temperature in Embarrass, Minnesota was −12∘. What was the difference between the temperature in Anaheim and the temperature in Embarrass?

Solution

96∘

66. Temperature. On January 21, the high temperature in Palm Springs, California, was 89∘, and the high temperature in Whitefield, New Hampshire was −31∘. What was the difference between the temperature in Palm Springs and the temperature in Whitefield?

67. Football. At the first down, the Chargers had the ball on their 25 yard line. On the next three downs, they lost 6 yards, gained 10 yards, and lost 8 yards. What was the yard line at the end of the fourth down?

Solution

21

68. Football. At the first down, the Steelers had the ball on their 30 yard line. On the next three downs, they gained 9 yards, lost 14 yards, and lost 2 yards. What was the yard line at the end of the fourth down?

69. Checking Account. Mayra has $124 in her checking account. She writes a check for $152. What is the new balance in her checking account?

Solution

−$28

70. Checking Account. Selina has $165 in her checking account. She writes a check for $207. What is the new balance in her checking account?

71. Checking Account. Diontre has a balance of −$38 in his checking account. He deposits $225 to the account. What is the new balance?

Solution

$187

72. Checking Account. Reymonte has a balance of −$49 in his checking account. He deposits $281 to the account. What is the new balance?

Exercises: Everyday Math

Instructions: For questions 73-74, solve the given everyday math word problems.

73. Stock market. Javier owns 300 shares of stock in one company. On Tuesday, the stock price dropped $12 per share. What was the total effect on Javier’s portfolio?

Solution

−$3600

74. Weight loss. In the first week of a diet program, eight women lost an average of 3 pounds each. What was the total weight change for the eight women?

Exercises: Writing Exercises

Instructions: For questions 75-78, answer the given writing exercises.

75. In your own words, state the rules for multiplying integers.

Solution

Answers may vary

76. In your own words, state the rules for dividing integers.

77. Why is −24≠(−2)4?

Solution

Answers may vary

78. Why is −43=(−4)3?

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Fanshawe Pre-Health Sciences Mathematics 1 Copyright © 2022 by Domenic Spilotro, MSc is licensed under a Creative Commons Attribution-ShareAlike 4.0 International License, except where otherwise noted.

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