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3. Lesson 3-1 Integers and Absolute Value
Lesson 3-2 Comparing and Ordering Integers
Lesson 3-3 The Coordinate Plane
Lesson 3-4 Adding Integers
Lesson 3-5 Subtracting Integers
Lesson 3-6 Multiplying Integers
Lesson 3-7 Dividing Integers
Contents

4. Example 1 Write Integers for Real-Life Situations
Example 3 Evaluate Expressions
Example 4 Evaluate Expressions
Lesson 1 Contents

5. Write an integer for the following situation.
The seasonal snowfall for Barrow, Alaska was 3 inches above normal.
Answer: Because it represents above normal, the integer is 3.
Example 1-1a

6. Write an integer for the following situation.
The average monthly temperature in Cleveland, Ohio for the month of January was 4 degrees below normal.
Answer: –4
Example 1-1b

7. Write an integer for the following situation.
The total rainfall this month is 2 inches below normal.
Answer: Because it represents below normal, the integer is –2.
Example 1-2a

8. Write an integer for the following situation.
The total snowfall this month was 5 inches above normal.
Answer: 5
Example 1-2b

9. Evaluate the expression
On the number line, the graph of is 5 units from 0.
Answer: So,
Example 1-3a

10. Evaluate the expression
Answer: 9
Example 1-3b

11. Evaluate the expression
Subtract.
Answer: 1
Example 1-4a

12. Evaluate the expression
Answer: 3
Example 1-4b

13. End of Lesson 1

14. Example 1 Compare Integers Example 2 Order Integers
Lesson 2 Contents

15. Replace the  with < or > to make –9  –5 a true sentence.
Answer: Since –9 is to the left of –5, –9 < –5.
Example 2-1a

16. Replace the  with < or > to make –3  –6 a true sentence.
Answer: –3 > –6
Example 2-1b

17. Record Low Temperature (°F)
MULTIPLE-CHOICE TEST ITEM The lowest temperatures in Europe, Greenland, Oceania, and Antarctica are listed in the table. Order the temperatures from least to greatest.
A –67, –87, 14, –129
B 14, –67, –87, –129
C –129, –87, –67, 14
D –67, –87, –129, 14
–129
Antarctica 14
Oceania
–87
Greenland
–67
Europe
Record Low Temperature (°F)
Continent
Source: The World Almanac
Example 2-2a

18. Read the Test Item To order the integers, graph them on a number line.
Solve the Test Item A G E O
Order the integers from least to greatest by reading from left to right: –129, –87, –67, 14.
Answer: C
Example 2-2a

19. MULTIPLE-CHOICE TEST ITEM The lowest temperatures on a given day in four cities in the United States are listed in the table. Order the temperatures from least to greatest. –3
Newport, RI 7
Denver, CO –6
New York City, NY
–12
Portland, OR
Low Temperature
City
A –3, –6, 7, –12
B –12, –6, –3, 7
C –12, 7, –6, –3
D 7, –3, –6, –12
Answer: B
Example 2-2b

20. End of Lesson 2

21. Example 1 Name an Ordered Pair Example 2 Graph an Ordered Pair
Example 3 Identify Quadrants
Example 4 Identify Quadrants
Lesson 3 Contents

22. Name the ordered pair for point R graphed below.
Start at the origin. R
Move left to find the x-coordinate of point R, which is –2.
Move up to find the y-coordinate, which is 4.
Answer: So, the ordered pair for point R is (–2, 4).
Example 3-1a

23. Name the ordered pair for point M graphed below.
Answer: (3, –1)
Example 3-1b

24. Graph and label the point M(3, 5).
Draw a coordinate plane.
Move 3 units to the right.
Then move 5 units up.
Draw a dot and label it M(3, 5).
Answer:
Example 3-2a

25. Graph and label the point G(–2, –4).
Answer:
Example 3-2b

26. Vernal is located in the upper right quadrant, quadrant I.
GEOGRAPHY Use the map of Utah shown below. In which quadrant is Vernal located?
Vernal is located in the upper right quadrant, quadrant I.
Answer: Quadrant I
Example 3-3a

27. GEOGRAPHY Use the map of Utah shown below
GEOGRAPHY Use the map of Utah shown below. In which quadrant is Tremonton located?
Answer: Quadrant II
Example 3-3b

28. Quadrant IV is the bottom-right quadrant. So, Bluff is in quadrant IV.
Name a city from the map of Utah shown below that is located in quadrant IV.
Quadrant IV is the bottom-right quadrant. So, Bluff is in quadrant IV.
Answer: Bluff
Example 3-4a

29. Name a city from the map of Utah shown below that is located in III.
Answer: Cedar City
Example 3-4b

30. End of Lesson 3

31. Example 1 Add Integers with the Same Sign
Example 3 Add Integers with Different Signs
Example 4 Add Integers with Different Signs
Example 5 Add Integers with Different Signs
Example 6 Add Integers with Different Signs
Example 7 Simplify an Expression with Integers
Example 8 Use Integers to Solve a Problem
Lesson 4 Contents

32. Move 6 units left to show –6.
Find
Use a number line.
Start at 0.
Move 6 units left to show –6.
From there, move 3 units left to show –3.
Answer:
Example 4-1a

33. Find
Answer: –7
Example 4-1b

34. The sum of two negative integers is negative.
Find
The sum of two negative integers is negative.
Answer: –55
Example 4-2a

35. Find
Answer: –46
Example 4-2b

36. Find
Use counters.
Remove all zero pairs.
Answer:
Example 4-3a

37. Find
Answer: 4
Example 4-3b

38. Find Use a number line. Start at 0. Move 5 units left.
Then move 4 units right.
Answer:
Example 4-4a

39. Find
Answer: 2
Example 4-4b

40. Find
Subtract. Keep the sign of the integer with the greater absolute value.
Answer: –5
Example 4-5a

41. Find
Answer: –4
Example 4-5b

42. Find
Subtract. Keep the sign of the integer with the greater absolute value.
Answer: –3
Example 4-6a

43. Find
Answer: 4
Example 4-6b

44. Commutative Property of Addition
ALGEBRA Simplify
Commutative Property of Addition
Add.
Answer:
Example 4-7a

45. ALGEBRA Simplify
Answer:
Example 4-7b

46. OCEANOGRAPHY Oceanographers divide the ocean into three light zones
OCEANOGRAPHY Oceanographers divide the ocean into three light zones. The deeper the water, the less light shines through. The middle zone is called the Twilight Zone. The lowest part of this zone is 1,000 meters below the surface of the water. The top of the zone lies 800 meters above the lowest zone. What is the depth of the top of the zone?
The lowest part of the zone is 1,000 meters below the surface of the water and the top of the zone is 800 meters above that. So, the depth of the top of the zone can be represented by the sentence
Answer: The depth of the top of the zone is 200 meters below the surface of the water.
Example 4-8a

47. FOOTBALL The Bluedale Bobcats lost a total of 27 yards on two successive plays. On the third down, they managed to gain 18 yards. Find their position after the third down, relative to where they started.
Answer: loss of 9 yards
Example 4-8b

48. End of Lesson 4

49. Example 1 Subtract Positive Integers
Example 3 Subtract Negative Integers
Example 4 Subtract Negative Integers
Example 5 Evaluate an Expression
Example 6 Use Integers to Solve a Problem
Lesson 5 Contents

50. Find
To subtract 15, add –15.
Simplify.
Answer: –13
Example 5-1a

51. Find
Answer: –8
Example 5-1b

52. Find
To subtract 8, add –8.
Simplify.
Answer: –21
Example 5-2a

53. Find
Answer: –20
Example 5-2b

54. Find
To subtract –6, add 6.
Simplify.
Answer: 18
Example 5-3a

55. Find
Answer: 13
Example 5-3b

56. Find
To subtract –8, add 8.
Simplify.
Answer: 29
Example 5-4a

57. Find
Answer: 23
Example 5-4b

58. Replace g with –2 and h with –7.
ALGEBRA Evaluate
Replace g with –2 and h with –7.
To subtract –7, add 7.
Simplify.
Answer: 5
Example 5-5a

59. ALGEBRA Evaluate
Answer: –10
Example 5-5b

60. Answer: The range of temperatures is 85C.
GEOGRAPHY In Mongolia, the temperature can dip down to –45C in January. The temperature in July may reach 40C. What is the temperature range in Mongolia?
To find the range, or difference in temperatures, subtract the lowest temperature from the highest temperature.
To subtract –45, add 45.
Simplify.
Answer: The range of temperatures is 85C.
Example 5-6a

61. TEMPERATURE On a particular day in Anchorage, Alaska, the high temperature was 15F and the low temperature was –11F. What is the range of temperatures for that day?
Answer: 26F
Example 5-6b

62. End of Lesson 5

63. Example 1 Multiply Integers with Different Signs
Example 3 Multiply Integers with the Same Sign
Example 4 Multiply Integers with the Same Sign
Example 5 Simplify and Evaluate Expressions
Example 6 Simplify and Evaluate Expressions
Lesson 6 Contents

64. The integers have different signs. The product is negative.
Find
The integers have different signs. The product is negative.
Answer: –20
Example 6-1a

65. Find
Answer: –15
Example 6-1b

66. The integers have different signs. The product is negative.
Find
The integers have different signs. The product is negative.
Answer: –27
Example 6-2a

67. Find
Answer: –35
Example 6-2b

68. The integers have the same sign. The product is positive.
Find
The integers have the same sign. The product is positive.
Answer: 48
Example 6-3a

69. Find
Answer: 28
Example 6-3b

70. There are two factors of –8.
Find
There are two factors of –8.
The product is positive.
Answer: 64
Example 6-4a

71. Find
Answer: 25
Example 6-4b

72. Associative Property of Multiplication
ALGEBRA Simplify
Associative Property of Multiplication
Simplify.
Answer: 35x
Example 6-5a

73. ALGEBRA Simplify
Answer: –48x
Example 6-5b

74. Replace a with –3, b with 5, and c with –8.
ALGEBRA Evaluate
Replace a with –3, b with 5, and c with –8.
Multiply –3 and 5.
Multiply –15 and –8.
Answer: 120
Example 6-6a

75. ALGEBRA Evaluate
Answer: 48
Example 6-6b

76. End of Lesson 6

77. Example 1 Dividing Integers with Different Signs
Example 3 Dividing Integers with the Same Sign
Example 4 Evaluate an Expression
Lesson 7 Contents

78. The integers have different signs. The quotient is negative.
Find
The integers have different signs. The quotient is negative.
Answer: –17
Example 7-1a

79. Find
Answer: –4
Example 7-1b

80. The integers have different signs. The quotient is negative.
Find
The integers have different signs. The quotient is negative.
Answer: –9
Example 7-2a

81. Find
Answer: –5
Example 7-2b

82. The integers have the same sign. The quotient is positive.
Find –12 (–2)
The integers have the same sign. The quotient is positive.
Answer: 6
Example 7-3a

83. Find –24 (–8)
Answer: 3
Example 7-3b

84. Answer: The car’s acceleration is –4 feet per second.
PHYSICS An object’s acceleration is determined by the difference between the final and starting speeds divided by the total time. A car is traveling at 80 feet per second and, after 10 seconds, is traveling at 40 feet per second. What is the car’s acceleration?
Subtract 55 from 15.
Divide.
Answer: The car’s acceleration is –4 feet per second.
Example 7-4a

85. WEATHER The temperature at 4:00 p. m. was 52F. By 8:00 p. m
WEATHER The temperature at 4:00 p.m. was 52F. By 8:00 p.m., the temperature had gone down to 36F. What is the average change in temperature per hour?
Answer: –4
Example 7-4b

86. End of Lesson 7

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