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1.3E: Exercises

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Practice Makes Perfect

Simplify Expressions with Absolute Value

In the following exercises, fill in <,>, or = for each of the following pairs of numbers.

1. ⓐ |7| ___ |7|

6 ___ |6|

|11| ___ 11

(13) ___ |13|

Answer

>>>>

2. ⓐ |9| ___ |9|

8 ___ |8|

|1| ___ 1

(14) ___ |14|

3. ⓐ |2| ___ |2|

12 ___ |12|

|3| ___ 3

|19| ___ (19)

Answer

==>=

4. ⓐ |4| ___ |4|

5 ___ |5|

|10| ___ 10

|0| ___ (0)

In the following exercises, simplify.

5. |157||146|

Answer

0

6. |178||134|

7. 18|2(83)|

Answer

8

8. 15|3(85)|

9. 18|124(41)+3|

Answer

15

10. 27|19+4(31)7|

11. 103|93(31)|

Answer

1

12. 132|112(52)|

Add and Subtract Integers

In the following exercises, simplify each expression.

13. ⓐ 7+(4)

7+4

7+(4).

Answer

1133

14. ⓐ 5+(9)

5+9

5+(9)

15. 48+(16)

Answer

32

16. 34+(19)

17. 14+(12)+4

Answer

22

18. 17+(18)+6

19. 19+2(3+8)

Answer

29

20. 24+3(5+9)

21. ⓐ 137

13(7)

137

13(7)

Answer

ⓐ 6 ⓑ −6 ⓒ −20 ⓓ 20

22. ⓐ 158

15(8)

158

15(8)

23. 1742

Answer

59

24. 58(67)

25. 14(27)+9

Answer

22

26. 64+(17)9

27. ⓐ 442844+(28)

Answer

ⓐ 16 ⓑ 16

28. ⓐ 351635+(16)

29. ⓐ 27(18)27+18

Answer

ⓐ 45 ⓑ 45

30. ⓐ 46(37)46+37

31. (27)(38)

Answer

0

32. (18)(29)

33. (68)(24)

Answer

4

34. (45)(78)

35. 25[10(312)]

Answer

6

36. 32[5(1520)]

Multiply and Divide Integers

In the following exercises, multiply or divide.

37. ⓐ 48

13(5)

24÷6

52÷(4)

Answer

3265413

38. ⓐ 39

9(7)

35÷(7)

84÷(6)

39. ⓐ 28÷7

180÷15

3(13)

1(14)

Answer

4123914

40. ⓐ 36÷4

192÷12

9(7)

1(19)

Simplify and Evaluate Expressions with Integers

In the following exercises , simplify each expression.

41. ⓐ (2)626

Answer

6464

42. ⓐ (3)535

43. 5(6)+7(2)3

Answer

47

44. 8(4)+5(4)6

45. 3(5)(6)

Answer

90

46. 4(6)(3)

47. (811)(912)

Answer

9

48. (611)(813)

49. 263(27)

Answer

41

50. 232(46)

51. 65÷(5)+(28)÷(7)

Answer

9

52. 52÷(4)+(32)÷(8)

53. 92[38(2)]

Answer

29

54. 113[74(2)]

55. 8|24(41)+3|

Answer

1

56. 7|53(41)6|

57. 93|2(26)(37)|

Answer

3

58. 52|2(14)(25)|

59. (3)224÷(82)

Answer

5

60. (4)232÷(124)

In the following exercises , evaluate each expression.

61. y+(14) when ⓐ y=33y=30

Answer

4716

62. x+(21) when ⓐ x=27x=44

63. (x+y)2 when x=3 and y=14

Answer

121

64. (y+z)2 when y=3 and z=15

65. 9a2b8 when a=6 and b=3

Answer

56

66. 7m4n2 when m=4 and n=9

67. 3x24xy+2y2 when x=2 and y=3

Answer

6

68. 4x2xy+3y2 when x=3 and y=2

Translate English Phrases to Algebraic Expressions

In the following exercises, translate to an algebraic expression and simplify if possible.

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

Answer

(3+(15))+7;5

70. the sum of 8 and 9, increased by 23

71. ⓐ the difference of 10 and 18

ⓑ subtract 11 from 25

Answer

10(18);28

2511;36

72. ⓐ the difference of 5 and 30

ⓑ subtract 6 from 13

73. the quotient of 6 and the sum of a and b

Answer

6a+b

74. the product of 13 and the difference of c and d

Use Integers in Applications

In the following exercises, solve.

75. 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?

Answer

96

76. 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?

77. Football On 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?

Answer

21

78. Football On 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?

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

Answer

$28

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

Writing Exercises

81. Explain why the sum of −8 and 2 is negative, but the sum of 8 and −2 is positive.

Answer

Answers will vary.

82. Give an example from your life experience of adding two negative numbers.

83. In your own words, state the rules for multiplying and dividing integers.

Answer

Answers will vary.

84. Why is 43=(4)3?

Self Check

ⓐ After completing the EXAMPLEs, use this checklist to evaluate your mastery of the objectives of this section.

This table has 4 columns, 6 rows and a header row. The header row labels each column I can, confidently, with some help and no, I don’t get it. The first column has the following statements: simplify expressions with absolute value, add and subtract integers, multiply and divide integers, simplify and evaluate expressions with integers, translate English phrases to algebraic expressions, use integers in applications. The remaining columns are blank.

ⓑ After reviewing this checklist, what will you do to become confident for all objectives?


This page titled 1.3E: Exercises is shared under a CC BY 4.0 license and was authored, remixed, and/or curated by OpenStax via source content that was edited to the style and standards of the LibreTexts platform.

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