To enter a negative number on a calculator, find the key marked . (Some calculators have a key marked and some calculators have a special key for entering a negative sign.) To enter the number for example, press the keys . The display will read
.
-Use a calculator to perform each indicated operation.
1.
2.
3.
4.
5.
6. -196,662 + 1-129,8562 - 108,650 + 1 - 786,2052 - 129 + 101482
61152 + 1-462 811 + 1-10582
- 256 + 97 PRACTICE 18
If the temperature was
Fahrenheit at 6 a.m., and it rose 4 degrees by 7 a.m. and then rose another 7 degrees in the hour from 7 a.m. to 8 a.m., what was the temperature at 8 a.m.?
- 8°
PRACTICE 17
Evaluate for and y = -6.x + y x = -11 PRACTICE 16
Evaluate for and y = 1.x + 3y x = -4
Answers
16. - 1 17. - 17 18. 3°F
Objective Add using a number line. See Examples 1 through 3.
2.3 Exercise Set
129
F O R EXTR A H E LP
Vocabulary and Readiness Check
Use the choices below to fill in each blank. Not all choices will be used. (Review Section 1.3 if needed.) - a a 0 commutative associative
1. If n is a number, then .
2. Since , we say that addition is .
3. If a is a number, then .
4. Since , we say that addition is .
Add.
n + 1x + a2 = 1n + x2 + a - 1 - a2 = x + n = n + x
- n + n =
5. 5 + 0 6. 1-22 + 0 7. 0 + 1-352 8. 0 + 3
9. - 12 + 12 10. 48 + 1-482 11. 28 + 1-282 12. -9 + 9
1. - 1 + 1 - 62 2. 9 + 1-42
1 1
2
3
4
5
6
7 0 2 3 4 5 6 7 141210 8 6 4 2 0 2 4 6 8 10 12 14
3. - 4 + 7 4. 10 + 1-32
1 1
2
3
4
5
6
7 0 2 3 4 5 6 7 141210 8 6 4 2 0 2 4 6 8 10 12 14
5. - 13 + 7 6. -6 + 1-52
2 2
4
6
8
10
12
14 0 4 6 8 10 12 14
2 2
4
6
8
10
12
14 0 4 6 8 10 12 14
Add. See Examples 4 through 13.
7. 23 + 12 8. 15 + 42 9. - 6 + 1 - 22 10. - 5 + 1 - 42 11. -43 + 43
12. - 62 + 62 13.6 + 1-22 14.8 + 1-32 15. - 6 + 8 16. -8 + 12
17. 3 + 1-52 18.5 + 1-92 19. - 2 + 1 - 72 20. - 6 + 1 - 12 21. -12 + 1-122
22. - 23 + 1 - 232 23. - 25 + 1 - 322 24. - 45 + 1 - 902 25. - 123 + 1 - 1002 26. -500 + 1-2302
27. - 7 + 7 28. - 10 + 10 29. 12 + 1-52 30. 24 + 1-102 31. -6 + 3
130
C H A P T E R 2 I INTEGERS AND INTRODUCTION TO VARIABLESCopyright 2012 Pearson Education,Inc.
32. - 8 + 2 33. - 12 + 3 34. - 15 + 5 35. 56 + 1-262 36. 89 + 1-372
37. - 37 + 57 38. - 25 + 65 39. - 42 + 93 40. - 64 + 164 41. 34 + 1-672
42. 42 + 1-832 43. 124 + 1-1442 44. 325 + 1-3752 45. - 82 + 1 - 432 46. -56 + 1-332
Add. See Examples 14 and 15.
47. - 4 + 2 + 1 - 52 48. - 1 + 5 + 1 - 82 49. -52 + 1-772 + 1-1172
50. - 103 + 1 - 322 + 1 - 272 51.12 + 1-42 + 1-42 + 12 52. 18 + 1-92 + 5 + 1-22
53.1-102 + 14 + 25 + 1-162 54. 34 + 1-122 + 1-112 + 213
Objective Mixed PracticeAdd. See Examples 1 through 15.
55. - 8 + 1 - 142 + 1 - 112 56. - 10 + 1 - 62 + 1 - 12 57. -26 + 5
58. - 35 + 1 - 122 59. 5 + 1-12 + 17 60. 3 + 1-232 + 6
61. - 14 + 1 - 312 62. - 100 + 70 63. 13 + 14 + 1-182
64. 1-452 + 22 + 20 65. - 87 + 87 66. -87 + 0
67. - 3 + 1 - 82 + 12 + 1 - 12 68. -16 + 6 + 1-142 + 1-202
69. 0 + 1-1032 70. 94 + 1-942
Objective Evaluate x + yfor the given replacement values. See Examples 16 and 17.
71.x = -20and y = -50 72.x = -1and y = -29
Evaluate 3x + yfor the given replacement values. See Examples 16 and 17.
73.x = 2and y = -3 74.x = 7and y = -11
75.x = 3and y = -30 76.x = 13and y = -17
Objective TranslatingTranslate each phrase; then simplify. See Example 18.
77. Find the sum of - 8and 25. 78. Find the sum of - 30and 10.
79. Find the sum of - 31, - 9,and 30. 80. Find the sum of - 49, - 2,and 40.
S E C T I O N 2 . 3 I ADDING INTEGERS
131
Solve. See Example 18.
81. Suppose a deep-sea diver dives from the surface to 215 feet below the surface. He then dives down 16 more feet. Use positive and negative numbers to represent this situation. Then find the diver’s present depth.
82. Suppose a diver dives from the surface to 248 meters below the surface and then swims up 6 meters, down 17 meters, down another 24 meters, and then up 23 meters. Use positive and negative numbers to represent this situation. Then find the diver’s depth after these movements.
In golf, it is possible to have positive and negative scores. The following table shows the results of the eighteen-hole Round 3 for Angela Stanford and Michelle Wie at the 2009 SBS Open at Turtle Bay. Use the table to answer Exercises 83 and 84.
Player/Hole 1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18
Stanford 0 0 0 - 1 0 0 0 + 1 0 + 1 0 0 - 1 - 1 - 1 0 0 0
Wie 0 0 0 - 1 0 0 0 0 - 1 0 + 2 0 0 0 0 0 + 1 0
(Source: Ladies’ Professional Golf Association)
83. Find the total score for each of the athletes in the round.
84. In golf, the lower score is the winner. Use the result of Exercise 83 to determine who won Round 3.
The following bar graph shows the yearly net income for Apple, Inc. Net income is one indication of a company’s health.
It measures revenue (money taken in) minus cost (money spent). Use this graph to answer Exercises 85 through 88.
(Source: Apple, Inc.)
85. What was the net income (in dollars) for Apple, Inc.
in 2007?
86. What was the net income (in dollars) for Apple, Inc.
in 2001?
87. Find the total net income for the years 2003 and 2005.
88. Find the total net income for all the years shown.
89. The temperature at 4 p.m. on February 2 was Celsius. By 11 p.m. the temperature had risen 12 degrees. Find the temperature at 11 p.m.
90. In some card games, it is possible to have both positive and negative scores. After four rounds of play, Michelle had scores of 14, , , and 7. What was her total score for the game?
- 8 - 5 - 10°
A small business company reports the following net incomes. Use this table for Exercises 91 and 92.
91. Find the sum of the net incomes for 2007 and 2008.
92. Find the net income sum for all four years shown.
2500 Net Income (in millions of dollars)
500
Apple, Inc. Net Income
3000 3500
2001 2003 2005 2007
Year
Year Net Income (in Dollars)
2006 $75,083
2007 - $10,412
2008 - $1786
2009 $96,398
Copyright 2012 Pearson Education,Inc.Copyright 2012 Pearson Education,Inc.
93. The all-time record low temperature for Wyoming is which was recorded on February 9, 1933.
Kansas’s all-time record low temperature is 26°F higher than Wyoming’s record low. What is Kansas’s record low temperature? (Source: National Climatic Data Center)
94. The all-time record low temperature for New York is which occurred on February 13, 1905. In Mississippi, the lowest temperature ever recorded is 33°F higher than New York’s all-time low temperature. What is the all-time record low temperature for Mississippi? (Source: National Climatic Data Center)
95. The deepest spot in the Pacific Ocean is the Mariana Trench, which has an elevation of 10,924 meters below sea level. The bottom of the Pacific’s Aleutian Trench has an elevation 3245 meters higher than that of the Mariana Trench. Use a negative number to represent the depth of the Aleutian Trench. (Source: Defense Mapping Agency)
96. The deepest spot in the Atlantic Ocean is the Puerto Rico Trench, which has an elevation of 8605 meters below sea level. The bottom of the Atlantic’s Cayman Trench has an elevation 1070 meters above the level of the Puerto Rico Trench. Use a negative number to represent the depth of the Cayman Trench. (Source:
Defense Mapping Agency) - 52°F,
- 66°F,
Review
Subtract. See Section 1.4.
97. 44 - 0 98.91 - 0 99.200 - 59 100. 400 - 18
Concept Extensions
101. Name 2 numbers whose sum is - 17. 102. Name 2 numbers whose sum is -30.
Each calculation below is incorrect. Find the error and correct it. See the Concept Check in this section.
103. 7 + 1-102 ⱨ 17 104. -4 + 14 ⱨ -18
105. - 10 + 1 - 122 ⱨ - 120 106. -15 + 1-172 ⱨ 32
For Exercises 107 through 110, determine whether each statement is true or false.
107. The sum of two negative numbers is always a negative number.
108. The sum of two positive numbers is always a positive number.
109. The sum of a positive number and a negative number is always a negative number.
110. The sum of zero and a negative number is always a negative number.
111. In your own words, explain how to add two negative numbers.
112. In your own words, explain how to add a positive number and a negative number.
Wyoming
Kansas
New York
Mississippi