1.2E: 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. ⓐ $|−7| \text{ ___ }−|−7|$

ⓑ $6 \text{ ___ }−|−6|$

ⓓ $−(−13)\text{ ___ }−|−13|$

Answer: ⓐ $>$ ⓑ $>$ ⓒ $>$ ⓓ $>$

2. ⓐ $−|−9| \text{ ___ } |−9|$

ⓑ $−8 \text{ ___ } |−8| $

ⓓ $−(−14) \text{ ___ } −|−14|$

3. ⓐ $−|2| \text{ ___ }−|−2|$

ⓑ $−12 \text{ ___ }−|−12|$

ⓓ $|−19| \text{ ___ }−(−19) $

Answer: ⓐ $=$ ⓑ $=$ ⓒ $>$ ⓓ $=$

4. ⓐ $−|−4| \text{ ___ } −|4| $

ⓑ $5 \text{ ___ } −|−5| $

ⓓ $−|−0| \text{ ___ } −(−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. ⓐ $−7+(−4)$

ⓑ $−7+4$

Answer: ⓐ $−11$ ⓑ $−3$ ⓒ $3$

14. ⓐ $−5+(−9)$

ⓑ $−5+9$

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. ⓐ $13−7$

ⓑ $−13−(−7)$

ⓓ $13−(−7)$

Answer: ⓐ 6 ⓑ −6 ⓒ −20 ⓓ 20

22. ⓐ $15−8$

ⓑ $−15−(−8)$

ⓓ $15−(−8)$

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. ⓐ $−4⋅8$

ⓑ $13(−5)$

ⓓ $−52÷(−4)$

Answer: ⓐ $−32$ ⓑ $−65$ ⓒ $−4$ ⓓ $13$

38. ⓐ $−3⋅9$

ⓑ $9(−7)$

ⓓ $−84÷(−6)$

39. ⓐ $−28÷7$

ⓑ $−180÷15$

ⓓ $−1(−14)$

Answer: ⓐ $−4$ ⓑ $−12$ ⓒ $−39$ ⓓ $14$

40. ⓐ $−36÷4$

ⓑ $−192÷12$

ⓓ $−1(−19)$

Simplify and Evaluate Expressions with Integers

In the following exercises , simplify each expression.

41. ⓐ $(−2)^6$ ⓑ $−2^6$

Answer: ⓐ $64$ ⓑ $−64$

42. ⓐ $(−3)^5$ ⓑ $−3^5$

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

Answer: $6$

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

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

ⓐ $10−(−18);28$

ⓑ$−25−11;−36$

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

ⓑ subtract $−6$ from $−13$

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

Answer: $\dfrac{−6}{a+b}$

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?

Answer: $96^\circ$

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?

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 $−4^3=(−4)^3$?

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?