Solving problems often requires subtraction of integers.
PRACTICE 13
The highest point in Asia is the top of Mount Everest, at a height of 29,028 feet above sea level. The lowest point is the Dead Sea, which is 1312 feet below sea level. How much higher is Mount Everest than the Dead Sea? (Source:
National Geographic Society) PRACTICE 12
Evaluate for and
z = -4. 3y - z y = 9
Answers
12. 31 13. 30,340 ft
e
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Objective Subtract. See Examples 1 through 7.
Vocabulary and Readiness Check
Multiple choice: Select the correct lettered response following each exercise.
1. It is true that .
a. b. c.
2. The opposite of n is .
a. b. c. n
3. To evaluate for and , we replace x with and y with and evaluate .
a. b. c. d.
4. The expression equals .
a. b. c. d.
Subtract.
10 - 5 - 5 + 1 - 102
5 + 10 5 - 10
- 5 - 10
- 10 - 1 - 142 - 14 - 10
- 10 - 14 10 - 14
- 14 y = -14 - 10
x = -10 x - y
- 1 - n2 - n
a + b a + 1-b2
b - a
a - b =
2.4 Exercise Set
F O R EXTR A H E LP
5. 5 - 5 6. 7 - 7 7. 8642 - 8642 8. 9012 - 9012
1. -5 - 1-52 2. -6 - 1-62 3. 8 - 3 4. 5 - 2 5. 3 - 8
6. 2 - 5 7. 7 - 1-72 8. 12 - 1-122 9. -5 - 1-82 10. -25 - 1-252
11. -14 - 4 12. -2 - 42 13. 2 - 16 14. 8 - 9 15. 22 - 55
16. 17 - 63 17. 362 - 1-402 18. 844 - 1-202 19. -4 - 10 20. -5 - 8
21. -7 - 1-32 22. -12 - 1-52 23. 16 - 23 24. 16 - 45
Solve. See Example 8.
25. Subtract 17 from -25. 26. Subtract 10 from -22. 27. Find the difference of and - 3.
- 20 28. Find the difference of and
- 13.
- 8 29. Subtract from - 11 2. 30. Subtract from - 50 - 50.
Mixed Practice (Sections 2.3, 2.4) Add or subtract as indicated.
31. -21 + 1-172 32. -35 + 1-112 33. 9 - 20 34. 7 - 30
35. -49 - 78 36. -105 - 68 37. 48 - 59 38. 86 - 98
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Objective Simplify. See Examples 9 and 10.
39. 7 - 3 - 2 40. 8 - 4 - 1 41. 12 - 5 - 7
42. 30 - 7 - 12 43. - 5 - 8 - 1 - 122 44. -10 - 6 - 1-92
45. - 10 + 1 - 52 - 12 46. - 15 + 1 - 82 - 4 47. 12 - 1-342 + 1-62
48. 23 - 1-172 + 1-92 49. - 1 - 62 - 12 + 1 - 162 50. -1-92 - 7 + 1-232
51. - 9 - 1 - 122 + 1 - 72 - 4 52. - 6 - 1 - 82 + 1 - 122 - 7 53. -3 + 4 - 1-232 - 10
54. 5 + 1-182 - 1-212 - 2
Objective Solve. See Example 13.
The bar graph from Section 2.2 showing the average temperature in Fahrenheit of known planets is reprinted below.
Notice that a negative temperature is illustrated by a bar below the horizontal line representing 0°F, and a positive temperature is illustrated by a bar above the horizontal line representing 0°F.
330 867
59
ⴚ81 ⴚ162
ⴚ323 ⴚ330 ⴚ218
Mercury Venus Earth Mars Jupiter Saturn Uranus Neptune
Degrees Fahrenheit
Average Surface Temperature of Planets*
1000 800 600 400 200 0
200
400
600 1200
*(For some planets, the temperature given is the temperature where the atmosphere pressure equals 1 Earth atmosphere; Source: The World Almanac)
Objective Evaluatex - y for the given replacement values. See Examples 11 and 12.
55. x = -4 and y = 7 56. x = -7 and y = 1
57. x = 8 and y = -23 58. x = 9 and y = -2
59.x = 4 and y = -4 60. x = 8 and y = -10
61.x = 1 and y = -18 62. x = 14 and y = -12
63. Find the difference in temperature between Earth and Neptune.
64. Find the difference in temperature between Venus and Mars.
65. Find the difference in temperature between the two plants with the lowest temperature.
66. Find the difference in temperature between Jupiter and Saturn.
Evaluate 2x - y for the given replacement values. See Examples 11 and 12.
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67. The coldest temperature ever recorded on Earth was in Antarctica. The warmest temperature ever recorded was 136°F in the Sahara Desert.
How many degrees warmer is 136°F than
(Source: Questions Kids Ask, Grolier Limited, 1991, and The World Almanac, 2005)
- 129°F?
- 129°F
68. The coldest temperature ever recorded in the United States was in Alaska. The warmest temperature ever recorded was 134°F in California.
How many degrees warmer is 134°F than (Source: The World Almanac, 2005)
- 80°F?
- 80°F
69. Aaron Aiken has $125 in his checking account. He writes a check for $117, makes a deposit of $45, and then writes another check for $69. Find the balance in his account. (Write the amount as an integer.)
70. A woman received a statement of her charge account at Old Navy. She spent $93 on purchases last month. She returned an $18 top because she didn’t like the color. She also returned a $26 night shirt because it was damaged. What does she actually owe on her account?
Solve.
71. The temperature on a February morning is Celsius at 6 a.m. If the temperature drops 3 degrees by 7 a.m., rises 4 degrees between 7 a.m.
and 8 a.m., and then drops 7 degrees between 8 a.m.
and 9 a.m., find the temperature at 9 a.m.
- 6°
72. Mauna Kea in Hawaii has an elevation of 13,796 feet above sea level. The Mid-America Trench in the Pacific Ocean has an elevation of 21,857 feet below sea level. Find the difference in elevation between those two points. (Source: National Geographic Society and Defense Mapping Agency)
Some places on Earth lie below sea level, which is the average level of the surface of the oceans. Use this diagram to answer Exercises 73 through 76. (Source: Fantastic Book of Comparisons, Russell Ash)
73. Find the difference in elevation between Death Valley and Quattâra Depression.
74. Find the difference in elevation between Danakil and Turfan Depressions.
75. Find the difference in elevation between the two lowest elevations shown.
76. Find the difference in elevation between the highest elevation shown and the lowest elevation shown.
Turfan Depression, Xinjiang, China: 505 ft Qattâra Depression, Egypt: 436 ft Poluostrov Mangyshlak, Kazakhstan: 433 ft Danakil Depression, Ethiopia: 384 ft Death Valley, US: 282 ft Salton Sea, US: 236 ft
The bar graph shows heights of selected lakes. For Exercises 77 through 80, find the difference in elevation for the lakes listed. (Source: U.S. Geological Survey)
77. Lake Superior and Lake Eyre
78. Great Bear Lake and Caspian Sea
79. Lake Maracaibo and Lake Vanern
80. Lake Eyre and Caspian Sea
700
Feet Above or Below Sea Level
Caspian
Elevations of Selected Lakes
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Mixed Practice—Translating (Sections 2.3, 2.4) Translate each phrase to an algebraic expression. Use “x”
to represent “a number.”
Solve.
81. The difference between a country’s exports and imports is called the country’s trade balance. In 2007, the United States had $1646 billion in exports and
$2346 billion in imports. What was the U.S. trade balance in 2007? (Source: U.S. Department of Commerce)
82. In 2007, the United States exported 511 million barrels of petroleum products and imported 1241 million barrels of petroleum products. What was the U.S. trade balance for petroleum products in 2007? (Source: U.S. Energy Information
Administration)
83. The sum of - 5and a number. 84. The difference of - 3and a number.
85. Subtract a number from -20. 86. Add a number and -36.
87. 100
20 88. 96
3 89. 23
* 46 90. 51
* 89
Review
Multiply or divide as indicated. See Sections 1.6 and 1.7.
Concept Extensions
91. Name two numbers whose difference is -3. 92. Name two numbers whose difference is -10.
Each calculation below is incorrect. Find the error and correctly calculate. See the Concept Check in this section.
Simplify. (Hint: Find the absolute values first.)
97. ƒ- 3ƒ - ƒ- 7ƒ 98. ƒ- 12ƒ - ƒ- 5ƒ 100. ƒ- 9ƒ - ƒ9ƒ 101. ƒ- 17ƒ - ƒ- 29ƒ
99. ƒ- 6ƒ - ƒ6ƒ 102. ƒ- 23ƒ - ƒ- 42ƒ
103. ƒ- 8 - 3ƒ = 8 - 3 104. ƒ- 2 - 1 - 62ƒ = ƒ- 2ƒ - ƒ- 6ƒ
105. In your own words, explain how to subtract one signed number from another.
106. A student explains to you that the first step to simplify is to add 8 and 12.
Is the student correct? Explain why or why not.
8 + 12
#
5 - 100 For Exercises 103 and 104, determine whether each statement is true or false.93. 9 - 1-72 ⱨ 2 94. -4 - 8 ⱨ 4
95. 10 - 30 ⱨ 20 96. -3 - 1-102 ⱨ -13
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