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# 1.3E: Exercises

• • OpenStax
• OpenStax
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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. ⓐ $$|−7| \text{ ___ }−|−7|$$

ⓑ $$6 \text{ ___ }−|−6|$$

ⓒ $$|−11|\text{ ___ }−11$$

ⓓ $$−(−13)\text{ ___ }−|−13|$$

ⓐ $$>$$ ⓑ $$>$$ ⓒ $$>$$ ⓓ $$>$$

2. ⓐ $$−|−9| \text{ ___ } |−9|$$

ⓑ $$−8 \text{ ___ } |−8|$$

ⓒ $$|−1| \text{ ___ } −1$$

ⓓ $$−(−14) \text{ ___ } −|−14|$$

3. ⓐ $$−|2| \text{ ___ }−|−2|$$

ⓑ $$−12 \text{ ___ }−|−12|$$

ⓒ $$|−3| \text{ ___ }−3$$

ⓓ $$|−19| \text{ ___ }−(−19)$$

ⓐ $$=$$ ⓑ $$=$$ ⓒ $$>$$ ⓓ $$=$$

4. ⓐ $$−|−4| \text{ ___ } −|4|$$

ⓑ $$5 \text{ ___ } −|−5|$$

ⓒ $$−|−10| \text{ ___ } −10$$

ⓓ $$−|−0| \text{ ___ } −(−0)$$

In the following exercises, simplify.

5. $$|15−7|−|14−6|$$

0

6. $$|17−8|−|13−4|$$

7. $$18−|2(8−3)|$$

8

8. $$15−|3(8−5)|$$

9. $$18−|12−4(4−1)+3|$$

15

10. $$27−|19+4(3−1)−7|$$

11. $$10−3|9−3(3−1)|$$

1

12. $$13−2|11−2(5−2)|$$

In the following exercises, simplify each expression.

13. ⓐ $$−7+(−4)$$

ⓑ $$−7+4$$

ⓒ $$7+(−4).$$

ⓐ $$−11$$ ⓑ $$−3$$ ⓒ $$3$$

14. ⓐ $$−5+(−9)$$

ⓑ $$−5+9$$

ⓒ $$5+(−9)$$

15. $$48+(−16)$$

32

16. $$34+(−19)$$

17. $$−14+(−12)+4$$

$$-22$$

18. $$−17+(−18)+6$$

19. $$19+2(−3+8)$$

$$29$$

20. $$24+3(−5+9)$$

21. ⓐ $$13−7$$

ⓑ $$−13−(−7)$$

ⓒ $$−13−7$$

ⓓ $$13−(−7)$$

ⓐ 6 ⓑ −6 ⓒ −20 ⓓ 20

22. ⓐ $$15−8$$

ⓑ $$−15−(−8)$$

ⓒ $$−15−8$$

ⓓ $$15−(−8)$$

23. $$−17−42$$

$$-59$$

24. $$−58−(−67)$$

25. $$−14−(−27)+9$$

22

26. $$64+(−17)−9$$

27. ⓐ $$44−28$$ ⓑ $$44+(−28)$$

ⓐ 16 ⓑ 16

28. ⓐ $$35−16$$ ⓑ $$35+(−16)$$

29. ⓐ $$27−(−18)$$ ⓑ $$27+18$$

ⓐ 45 ⓑ 45

30. ⓐ $$46−(−37)$$ ⓑ $$46+37$$

31. $$(2−7)−(3−8)$$

0

32. $$(1−8)−(2−9)$$

33. $$−(6−8)−(2−4)$$

4

34. $$−(4−5)−(7−8)$$

35. $$25−[10−(3−12)]$$

6

36. $$32−[5−(15−20)]$$

Multiply and Divide Integers

In the following exercises, multiply or divide.

37. ⓐ $$−4⋅8$$

ⓑ $$13(−5)$$

ⓒ $$−24÷6$$

ⓓ $$−52÷(−4)$$

ⓐ $$−32$$ ⓑ $$−65$$ ⓒ $$−4$$ ⓓ $$13$$

38. ⓐ $$−3⋅9$$

ⓑ $$9(−7)$$

ⓒ $$35÷(−7)$$

ⓓ $$−84÷(−6)$$

39. ⓐ $$−28÷7$$

ⓑ $$−180÷15$$

ⓒ $$3(−13)$$

ⓓ $$−1(−14)$$

ⓐ $$−4$$ ⓑ $$−12$$ ⓒ $$−39$$ ⓓ $$14$$

40. ⓐ $$−36÷4$$

ⓑ $$−192÷12$$

ⓒ $$9(−7)$$

ⓓ $$−1(−19)$$

Simplify and Evaluate Expressions with Integers

In the following exercises , simplify each expression.

41. ⓐ $$(−2)^6$$ ⓑ $$−2^6$$

ⓐ $$64$$ ⓑ $$−64$$

42. ⓐ $$(−3)^5$$ ⓑ $$−3^5$$

43. $$5(−6)+7(−2)−3$$

$$−47$$

44. $$8(−4)+5(−4)−6$$

45. $$−3(−5)(6)$$

$$90$$

46. $$−4(−6)(3)$$

47. $$(8−11)(9−12)$$

$$9$$

48. $$(6−11)(8−13)$$

49. $$26−3(2−7)$$

$$41$$

50. $$23−2(4−6)$$

51. $$65÷(−5)+(−28)÷(−7)$$

$$-9$$

52. $$52÷(−4)+(−32)÷(−8)$$

53. $$9−2[3−8(−2)]$$

$$-29$$

54. $$11−3[7−4(−2)]$$

55. $$8−|2−4(4−1)+3|$$

$$1$$

56. $$7−|5−3(4−1)−6|$$

57. $$9−3|2(2−6)−(3−7)|$$

$$-3$$

58. $$5−2|2(1−4)−(2−5)|$$

59. $$(−3)^2−24÷(8−2)$$

$$5$$

60. $$(−4)^2−32÷(12−4)$$

In the following exercises , evaluate each expression.

61. $$y+(−14)$$ when ⓐ $$y=−33$$ ⓑ $$y=30$$

ⓐ $$−47$$ ⓑ $$16$$

62. $$x+(−21)$$ when ⓐ $$x=−27$$ ⓑ $$x=44$$

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

$$121$$

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

65. $$9a−2b−8$$ when $$a=−6$$ and $$b=−3$$

$$-56$$

66. $$7m−4n−2$$ when $$m=−4$$ and $$n=−9$$

67. $$3x^2−4xy+2y^2$$ when $$x=−2$$ and $$y=−3$$

$$6$$

68. $$4x^2−xy+3y^2$$ 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

$$(3+(−15))+7;−5$$

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

71. ⓐ the difference of $$10$$ and $$−18$$

ⓑ subtract $$11$$ from $$−25$$

ⓐ $$10−(−18);28$$

ⓑ$$−25−11;−36$$

72. ⓐ the difference of $$−5$$ and $$−30$$

ⓑ subtract $$−6$$ from $$−13$$

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

$$\dfrac{−6}{a+b}$$

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?

$$96^\circ$$

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?

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?

$$−\ 28$$

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.

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.

84. Why is $$−4^3=(−4)^3$$?

## 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?

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 conform to the style and standards of the LibreTexts platform; a detailed edit history is available upon request.