The bar graph below shows the average temperature (in degrees Fahrenheit) of the eight planets, excluding the newly classified “dwarf planet,” Pluto. Notice that a nega-tive 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.
Example 8
Which planet has the lowest average temperature?Solution: The planet with the lowest average temperature is the one that corresponds to the bar that extends the furthest in the negative direction (downward). Neptune has the lowest average temperature of
Work Practice 8
- 330°F.
1200
400
0 800 1000
600
200
200
400
600
Degrees Fahrenheit
Planet
800
Average Surface Temperature of Planets*
Mercury
Source: The World Almanac, 2009
* For some planets, the temperature given is the temperature where the atmospheric pressure equals 1 Earth atmosphere.
Venus Earth Mars Jupiter Saturn Uranus Neptune 330
59
ⴚ81 ⴚ162 ⴚ218
ⴚ323 ⴚ330
867
Answer 8. Venus; 867°F
PRACTICE 8
Which planet has the highest average temperature? What is this temperature?
120
C H A P T E R 2 I INTEGERS AND INTRODUCTION TO VARIABLESObjective Represent each quantity by an integer. See Example 1.
2.2 Exercise Set
121
F O R EXTR A H E LP
opposites absolute value right is less than
inequality symbols negative positive left
signed integers is greater than
Vocabulary and Readiness Check
Use the choices below to fill in each blank. Not all choices will be used.
1. The numbers are called .
2. Positive numbers, negative numbers, and zero, together, are called numbers.
3. The symbols “ ” and “ ” are called .
4. Numbers greater than 0 are called numbers, while numbers less than 0 are called numbers.
5. The sign “ ” means and “ ” means .
6. On a number line, the greater number is to the of the lesser number.
7. A number’s distance from 0 on a number line is the number’s . 8. The numbers - 5and 5 are called .
7 6
7 6
Á , - 3, - 2, - 1, 0, 1, 2, 3, Á
1. A worker in a silver mine in Nevada works 1445 feet underground.
2. A scuba diver is swimming 35 feet below the surface of the water in the Gulf of Mexico.
3. The peak of Mount Elbert in Colorado is 14,433 feet above sea level. (Source: U.S.
Geological Survey)
4. The lowest elevation in the United States is found at Death Valley, California, at an elevation of 282 feet below sea level. (Source: U.S. Geological Survey)
5. The record high temperature in Nevada is 118 degrees above zero Fahrenheit. (Source:
National Climatic Data Center)
6. The Minnesota Viking football team lost 15 yards on a play.
7. The average depth of the Atlantic Ocean is 11,730 feet below the surface of the ocean.
(Source: World Almanac)
8. The Dow Jones stock market average fell 317 points in one day.
9. Ford Motor Company posted a 5-year decline rate in sales of almost 8 percent. Write an integer to represent the percent decrease or decline. (Source: Thomson Reuters)
10. Ford Motor Company posted sales of $132 billion over the past 12 months. Write an integer to represent the billions of dollars in sales. (Source:
Thomson Reuters)
Copyright 2012 Pearson Education,Inc.
12. The temperature on one January day in Chicago was 10° below 0° Celsius. Represent this quantity by an integer and tell whether this temperature is cooler or warmer than 5° below 0° Celsius.
11. Two divers are exploring the bottom of a trench in the Pacific Ocean. Joe is at 135 feet below the surface of the ocean and Sara is at 157 feet below the surface. Represent each quantity by an integer and determine who is deeper in the water.
13. In a week in 2009, the number of downloaded music singles decreased by 13 percent over the previous week. Write an integer to represent the percent decrease in the number of downloaded music singles.
(Source: Nielsen Sound Scan)
14. In a recent year, the number of CDs shipped to music retailers reflected an 18 percent decrease from the previous year. Write an integer to represent the percent decrease in CDs shipped. (Source: Recording Industry Association of America)
15. 1, 2, 4, 6 16. 3, 5, 2, 0
17. 1, -1, 2, -2, -4 18. 3, -3, 5, -5, 6
21. 0, -2, -7, -5 22. 0, -7, 3, -6
23. 0 - 7 24. -8 0 25. -7 - 5 26. -12 - 10
27. -30 - 35 28. -27 - 29 29. -26 26 30. 13 - 13
Objective Graph each integer in the list on the same number line. See Example 2.
Objective Insert 6 or 7 between each pair of integers to make a true statement. See Example 3.
31. ƒ 5 ƒ 32. ƒ 7 ƒ 33. ƒ -8 ƒ 34. ƒ -19 ƒ
35. ƒ 0 ƒ 36. ƒ 100 ƒ 37. ƒ -5 ƒ
Objective Simplify. See Example 4.
55. ƒ -14 ƒ 56. -(-14) 57. -(-29) 58. - ƒ -29 ƒ
59. ƒ - x ƒ if x = -8 60. - ƒ x ƒ if x = -8 61. - ƒ - x ƒ if x = 3 62. - ƒ - x ƒ if x = 7 63. ƒx ƒ if x = -23 64. ƒx ƒ if x = 23 65. - ƒ x ƒ if x = 4 66. ƒ - x ƒ if x = 1 Evaluate. See Example 7.
47. ƒ -7 ƒ 48. ƒ -11 ƒ 49. - ƒ 20 ƒ 50. - ƒ 43 ƒ
51. - ƒ -3 ƒ 52. - ƒ -18 ƒ 53. -(-8) 54. -(-7)
Objectives Mixed Practice Simplify. See Example 6.
39. 5 40. 8 41. -4 42. -6
43. 23 44. 123 45. -10 46. -23
Objective Find the opposite of each integer. See Example 5.
1 1
87. Which lake shown has the lowest elevation?
88. Which lake has an elevation at sea level?
89. Which lake shown has the highest elevation?
90. Which lake shown has the second lowest elevation?
67. -3 - 5 68. -17 - 6 69. ƒ -9 ƒ ƒ - 14 ƒ 70. ƒ -8 ƒ ƒ - 4 ƒ
71. ƒ -33 ƒ - ( - 33) 72. - ƒ 17 ƒ - ( - 17) 73. - ƒ -10 ƒ - ( - 10) 74. ƒ -24 ƒ - ( - 24)
91. Which element has a positive boiling temperature closest to that of water?
92. Which element has the lowest boiling temperature?
93. Which element has a boiling temperature closest to
?
94. Which element has an average boiling temperature closest to + 300°C?
- 200°C
Insert 6 , 7 , or = betweeneach pair of numbers to make a true statement. See Examples 3 through 6.
75. 0 - 9 76. -45 0 77. ƒ 0 ƒ ƒ - 9 ƒ 78. ƒ -45 ƒ ƒ 0 ƒ
79. - ƒ -2 ƒ - ƒ - 10 ƒ 80. - ƒ -8 ƒ - ƒ - 4 ƒ 81. -(-12) - ( - 18) 82. -22 - ( - 38) Objectives Mixed Practice Fill in the chart. See Examples 4 through 7.
83.
85.
84.
86.
Objective The bar graph shows the elevations of selected lakes. Use this graph for Exercises 87 through 90.
See Example 8. (Source: U.S. Geological Survey)
The following bar graph represents the boiling temperature, the temperature at which a substance changes from liquid to gas at standard atmospheric pressure. Use this graph to answer Exercises 91 through 94.
700
Feet Above or Below Sea Level
Caspian
Elevations of Selected Lakes
ⴚ34 400
100
100
200 Boiling Temperature in Degrees Celsius 300
400
“Boiling” Temperature of Various Elements
800
Hydrogen Oxygen Chlorine Wa
Absolute Value Opposite of
Number of Number Number
25
- 84
Absolute Value Opposite of
Number of Number Number
2 - 13
S E C T I O N 2 . 2 I INTRODUCTION TO INTEGERS
123
Copyright 2012 Pearson Education,Inc.
95. 0 + 13 96. 9 + 0 97. 15 + 20
98. 20 + 15 99. 47 + 236 + 77 100. 362 + 37 + 90
Review
Add. See Section 1.3.
Concept Extensions
Write the given numbers in order from least to greatest.
101. 22, -ƒ3ƒ, -1-52, -ƒ- 8ƒ 102. ƒ10ƒ, 23, -ƒ- 5ƒ, -1-42
103. ƒ- 1ƒ, -ƒ- 6ƒ, -1-62, -ƒ1ƒ 104. 14, -1-32, -ƒ7ƒ, ƒ- 20ƒ
105. -1-22, 52, -10, -ƒ- 9ƒ, ƒ- 12ƒ 106. 33, -ƒ- 11ƒ, -1-102, -4, -ƒ2ƒ
Choose all numbers for x from each given list that make each statement true.
107.
a. 0 b. - 5 c. 8 d. -12
ƒxƒ 7 8 108.
a. 0 b. 4 c. - 1 d. -100
ƒxƒ 7 4
109. Evaluate: - 1 -ƒ- 5ƒ2 110. Evaluate: - ( -ƒ- 1 - 72ƒ2
Answer true or false for Exercises 111 through 115.
111. If then a 7 b, a must be a positive number. 112. The absolute value of a number is always a positive number.
113. A positive number is always greater than a negative number.
114. Zero is always less than a positive number.
115. The number is always a negative number.
(Hint: Read “ -”as “the opposite of.”)
- a 116. Given the number line
is it true that b 6 a?
117. Write in your own words how to find the absolute value of a signed number.
118. Explain how to determine which of two signed numbers is larger.
1
,
1 0 b a