1.3E: Exercises
Practice Makes Perfect
Simplify Expressions with Absolute Value
In the following exercises, fill in \(<,>,\) or \(=\) for each of the following pairs of numbers.
1. ⓐ \(|−7| \text{ ___ }−|−7|\)
ⓑ \(6 \text{ ___ }−|−6|\)
ⓒ \(|−11|\text{ ___ }−11\)
ⓓ \(−(−13)\text{ ___ }−|−13|\)
- Answer
-
ⓐ \(>\) ⓑ \(>\) ⓒ \(>\) ⓓ \(>\)
2. ⓐ \(−|−9| \text{ ___ } |−9|\)
ⓑ \(−8 \text{ ___ } |−8| \)
ⓒ \(|−1| \text{ ___ } −1 \)
ⓓ \(−(−14) \text{ ___ } −|−14|\)
3. ⓐ \(−|2| \text{ ___ }−|−2|\)
ⓑ \(−12 \text{ ___ }−|−12|\)
ⓒ \(|−3| \text{ ___ }−3\)
ⓓ \(|−19| \text{ ___ }−(−19) \)
- Answer
-
ⓐ \(=\) ⓑ \(=\) ⓒ \(>\) ⓓ \(=\)
4. ⓐ \(−|−4| \text{ ___ } −|4| \)
ⓑ \(5 \text{ ___ } −|−5| \)
ⓒ \( −|−10| \text{ ___ } −10 \)
ⓓ \(−|−0| \text{ ___ } −(−0) \)
In the following exercises, simplify.
5. \(|15−7|−|14−6|\)
- Answer
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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
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15
10. \(27−|19+4(3−1)−7|\)
11. \(10−3|9−3(3−1)|\)
- Answer
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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
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ⓐ \(−11\) ⓑ \(−3\) ⓒ \(3\)
ⓑ \(−5+9\)
ⓒ \(5+(−9)\)
15. \(48+(−16)\)
- Answer
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32
16. \(34+(−19)\)
17. \(−14+(−12)+4\)
- Answer
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\(-22\)
18. \(−17+(−18)+6\)
19. \(19+2(−3+8)\)
- Answer
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\(29\)
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
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22
26. \(64+(−17)−9\)
27. ⓐ \(44−28\) ⓑ \(44+(−28)\)
- Answer
-
ⓐ 16 ⓑ 16
28. ⓐ \(35−16\) ⓑ \(35+(−16)\)
29. ⓐ \(27−(−18)\) ⓑ \(27+18\)
- Answer
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ⓐ 45 ⓑ 45
30. ⓐ \(46−(−37)\) ⓑ \(46+37\)
31. \((2−7)−(3−8)\)
- Answer
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0
32. \((1−8)−(2−9)\)
33. \(−(6−8)−(2−4)\)
- Answer
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4
34. \(−(4−5)−(7−8)\)
35. \(25−[10−(3−12)]\)
- Answer
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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
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ⓐ \(−4\) ⓑ \(−12\) ⓒ \(−39\) ⓓ \(14\)
ⓑ \(−192÷12\)
ⓒ \(9(−7)\)
ⓓ \(−1(−19)\)
Simplify and Evaluate Expressions with Integers
In the following exercises , simplify each expression.
41. ⓐ \((−2)^6\) ⓑ \(−2^6\)
- Answer
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ⓐ \(64\) ⓑ \(−64\)
42. ⓐ \((−3)^5\) ⓑ \(−3^5\)
43. \(5(−6)+7(−2)−3\)
- Answer
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\(−47\)
44. \(8(−4)+5(−4)−6\)
45. \(−3(−5)(6)\)
- Answer
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\(90\)
46. \(−4(−6)(3)\)
47. \((8−11)(9−12)\)
- Answer
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\(9\)
48. \((6−11)(8−13)\)
49. \(26−3(2−7)\)
- Answer
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\(41\)
50. \(23−2(4−6)\)
51. \(65÷(−5)+(−28)÷(−7)\)
- Answer
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\(-9\)
52. \(52÷(−4)+(−32)÷(−8)\)
53. \(9−2[3−8(−2)]\)
- Answer
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\(-29\)
54. \(11−3[7−4(−2)]\)
55. \(8−|2−4(4−1)+3|\)
- Answer
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\(1\)
56. \(7−|5−3(4−1)−6|\)
57. \(9−3|2(2−6)−(3−7)|\)
- Answer
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\(-3\)
58. \(5−2|2(1−4)−(2−5)|\)
59. \((−3)^2−24÷(8−2)\)
- Answer
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\(5\)
60. \((−4)^2−32÷(12−4)\)
In the following exercises , evaluate each expression.
61. \(y+(−14)\) when ⓐ \(y=−33\) ⓑ \(y=30\)
- Answer
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ⓐ \(−47\) ⓑ \(16\)
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
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\(6\)
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 \(23\)
ⓑ 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
-
\(\dfrac{−6}{a+b}\)
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
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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
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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.
ⓑ After reviewing this checklist, what will you do to become confident for all objectives?