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. |15−7|−|14−6|
- Answer
-
0
6. |17−8|−|13−4|
7. 18−|2(8−3)|
- Answer
-
8
8. 15−|3(8−5)|
9. 18−|12−4(4−1)+3|
- Answer
-
15
10. 27−|19+4(3−1)−7|
11. 10−3|9−3(3−1)|
- Answer
-
1
12. 13−2|11−2(5−2)|
Add and Subtract Integers
In the following exercises, simplify each expression.
13. ⓐ −7+(−4)
ⓑ −7+4
ⓒ 7+(−4).
- Answer
-
ⓐ −11 ⓑ −3 ⓒ 3
ⓑ −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. ⓐ 13−7
ⓑ −13−(−7)
ⓒ −13−7
ⓓ 13−(−7)
- Answer
-
ⓐ 6 ⓑ −6 ⓒ −20 ⓓ 20
22. ⓐ 15−8
ⓑ −15−(−8)
ⓒ −15−8
ⓓ 15−(−8)
23. −17−42
- Answer
-
−59
24. −58−(−67)
25. −14−(−27)+9
- Answer
-
22
26. 64+(−17)−9
27. ⓐ 44−28 ⓑ 44+(−28)
- Answer
-
ⓐ 16 ⓑ 16
28. ⓐ 35−16 ⓑ 35+(−16)
29. ⓐ 27−(−18) ⓑ 27+18
- Answer
-
ⓐ 45 ⓑ 45
30. ⓐ 46−(−37) ⓑ 46+37
31. (2−7)−(3−8)
- Answer
-
0
32. (1−8)−(2−9)
33. −(6−8)−(2−4)
- Answer
-
4
34. −(4−5)−(7−8)
35. 25−[10−(3−12)]
- Answer
-
6
36. 32−[5−(15−20)]
Multiply and Divide Integers
In the following exercises, multiply or divide.
37. ⓐ −4⋅8
ⓑ 13(−5)
ⓒ −24÷6
ⓓ −52÷(−4)
- Answer
-
ⓐ −32 ⓑ −65 ⓒ −4 ⓓ 13
ⓑ 9(−7)
ⓒ 35÷(−7)
ⓓ −84÷(−6)
ⓑ −180÷15
ⓒ 3(−13)
ⓓ −1(−14)
- Answer
-
ⓐ −4 ⓑ −12 ⓒ −39 ⓓ 14
ⓑ −192÷12
ⓒ 9(−7)
ⓓ −1(−19)
Simplify and Evaluate Expressions with Integers
In the following exercises , simplify each expression.
41. ⓐ (−2)6 ⓑ −26
- Answer
-
ⓐ 64 ⓑ −64
42. ⓐ (−3)5 ⓑ −35
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. (8−11)(9−12)
- Answer
-
9
48. (6−11)(8−13)
49. 26−3(2−7)
- Answer
-
41
50. 23−2(4−6)
51. 65÷(−5)+(−28)÷(−7)
- Answer
-
−9
52. 52÷(−4)+(−32)÷(−8)
53. 9−2[3−8(−2)]
- Answer
-
−29
54. 11−3[7−4(−2)]
55. 8−|2−4(4−1)+3|
- Answer
-
1
56. 7−|5−3(4−1)−6|
57. 9−3|2(2−6)−(3−7)|
- Answer
-
−3
58. 5−2|2(1−4)−(2−5)|
59. (−3)2−24÷(8−2)
- Answer
-
5
60. (−4)2−32÷(12−4)
In the following exercises , evaluate each expression.
61. y+(−14) when ⓐ y=−33 ⓑ y=30
- Answer
-
ⓐ −47 ⓑ 16
62. x+(−21) when ⓐ x=−27 ⓑ x=44
63. (x+y)2 when x=−3 and y=14
- Answer
-
121
64. (y+z)2 when y=−3 and z=15
65. 9a−2b−8 when a=−6 and b=−3
- Answer
-
−56
66. 7m−4n−2 when m=−4 and n=−9
67. 3x2−4xy+2y2 when x=−2 and y=−3
- Answer
-
6
68. 4x2−xy+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
ⓑ subtract 11 from −25
- Answer
-
ⓐ 10−(−18);28
ⓑ−25−11;−36
ⓑ 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.

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