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Adding Real Numbers. ALGEBRA 1 LESSON 1-4. 1-4. Adding Real Numbers. Start at –3. Start at 3. Move right 5 units. Move left 5 units. Start at –3. Move left 5 units. ALGEBRA 1 LESSON 1-4. Use a number line to simplify each expression. Use a number line to simplify each expression.

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adding real numbers
Adding Real Numbers

ALGEBRA 1 LESSON 1-4

1-4

adding real numbers1
Adding Real Numbers

Start at –3.

Start at 3.

Move right 5 units.

Move left 5 units.

Start at –3.

Move left 5 units.

ALGEBRA 1 LESSON 1-4

Use a number line to simplify each expression.

Use a number line to simplify each expression.

a. 3 + (–5)

b. –3 + 5

3 + (–5) = –2

–3 + 5 = 2

  • TRY:
  • Use a number line
  • to find each sum.
  • -6 + 4
  • 4 + (-6)
  • -3 + (-8)
  • 9 + (-3)

c. –3 + (–5)

–3 + (–5) = –8

1-4

adding real numbers2
Adding Real Numbers

ALGEBRA 1 LESSON 1-4

1-4

adding real numbers3
Adding Real Numbers

ALGEBRA 1 LESSON 1-4

Simplify each expression.

a. 12 + (–23) = –11

b. –6.4 + (–8.6) = –15.0

The difference of the absolute values is 11.

Since both addends are negative, add their absolute values.

The negative addend has the greater absolute value, so the sum is negative.

The sum is negative.

TRY:

1-4

adding real numbers4
Adding Real Numbers

ALGEBRA 1 LESSON 1-4

The water level in a lake rose 6 inches and then fell 11 inches. Write an addition statement to find the total change in water level.

6 + (–11) = –5   The water level fell 5 inches.

1-4

adding real numbers5
Adding Real Numbers

ALGEBRA 1 LESSON 1-4

Evaluate 3.6 + (–t) for t = –1.7.

3.6 + (–t) = 3.6 + [–(–1.7)] Substitute –1.7 for t.

= 3.6 + [1.7] –(–1.7) means the opposite of –1.7, which is 1.7.

= 5.3 Simplify.

TRY: Evaluate each expression for t = -7.1.

a. t + (-4.3) b. -2 + t c. 8.5 + (-t) d. -t + 7.49

1-4

adding real numbers6

Relate: 88 ft below sea level plus  feet diver rises  

Define: Let r = the number of feet the diver rises.

Write: –88 + r

–88 + r = –88 + 37Substitute 37 for r.

= – 51 Simplify.

Adding Real Numbers

ALGEBRA 1 LESSON 1-4

A scuba diver who is 88 ft below sea level begins to ascend to the surface.

a.  Write an expression to represent the diver’s depth below sea level after rising any number of feet.

–88 + r

b.  Find the new depth of the scuba diver after rising 37 ft.

The scuba diver is 51 ft below sea level.

1-4

adding real numbers7

–6 8.6 11

2.3 5 –3

7 –5.4 –2

11.1 3 –1

Add +

–68.611

2.3 5 –3

7–5.4–2

11.1 3 –1

+

–6 + 78.6 + (–5.4)11 + (–2)

2.3 + 11.1 5 + 3 –3 + (–1)

Add corresponding elements.

=

1 3.2 9

13.4 8 –4

Simplify.

=

Adding Real Numbers

ALGEBRA 1 LESSON 1-4

1-4

adding real numbers8
Adding Real Numbers

ALGEBRA 1 LESSON 1-4

TRY:

1-4

adding real numbers9
Adding Real Numbers

ALGEBRA 1 LESSON 1-4

pages 27–30  Exercises

1. 6 + (–3); 3

2. –1 + (–2); –3

3. –5 + 7; 2

4. 3 + (–4); –1

5. 15

6. –11

7. –19

8. 12.14

9. –4

10. 5

11. –8

1

6

12. –42

13. 2.2

14. –0.65

15. –7.49

16. 1.33

17.

18. –

19. 6

20. –6

21. 0

22. –

23. 5

24. –

25. –47 + 12 = –35, 35 ft

below the surface

26. 8 + (–5) = 3, 3 yd gain

27. –6 + 13 = 7, 7°F

28. 8.7

29. –1.7

30. 1.7

31. –8.7

32. 12.6

13

14

14

15

8

9

3

16

1

8

13

18

1-4

adding real numbers10

17

60

Adding Real Numbers

ALGEBRA 1 LESSON 1-4

38.

39.

40.

41.

42. –2.7

43. –13

44. 6.6

33. –5.6

34. 5.6

35. –12.6

36–37. Choices of variable may vary.

36.c = change in temp., –8 + c

a. –1°F

b. –11°F

c. 11°F

37. c = change in amount

of money, 74 + c

a. $92

b. $45

c. $27

19

24

–1 1.4

–21 23.2

45. 11

46. 4

47. –3

48. –18.53

49. –20.83

50. –1.72

51. –

52. –5

53. 0.8

54. 4

55. –8.8

22

35

–18.2

11.6

19.1

0

25

–12

1.8 22

– 7

11

120

1

2

1

3

1-4

adding real numbers11

65. 5

66. –1

67. 1

68. The sum of –227 and 319;

the sum of –227 and 319

is positive, while the sum

of 227 and –319 is negative.

69. Answers may vary. Sample:

Although 20 and –20 are

opposite numbers, there is

no such thing as opposite

temperatures.

70. –0.3

71. –13.7

72. –0.6

73. 8.7

74. 0.1

75. –1.9

76. +2

56. 13.8 million people

57. 6.3 million people

58. Weaving; add the

numbers in each column.

59. a. =

b. 0.23

c. about 23%

60. 0

61. –2

62. 1

63. –5

64. 7

100

442

50

221

Adding Real Numbers

ALGEBRA 1 LESSON 1-4

1-4

adding real numbers12
Adding Real Numbers

ALGEBRA 1 LESSON 1-4

77. Answers may vary. Sample:

78. The matrices are not the

same size, so they can’t

be added.

79. No; time and temperature

are different quantities and

can’t be added.

80.a.

82.a. 4

b. –4

80. (continued)

b.

c. 4 employees

d. 10 employees

e. Answers may vary. Sample:

Multiply the entries in each

column by the appropriate

hourly wage, then by 8, and

then add all entries to find

the total wages.

f. $3230

81. $7

2 0 1

–1 3 0.5

13 5 6 2

18 4 2 2

6 2 0 2

8 3 5 1

10 2 2 1

4 1 0 1

5 2 1 1

8 2 0 1

2 1 0 1

1-4

adding real numbers13

90. –

91.

92.

93.

94. Pos.; if m is neg.,

–m is pos. and the

sum of two pos.

is pos.

95. Neg.; if n is pos.,

–n is neg. and the

sum of two neg.

is neg.

96. Pos.; if m is neg.,

–m is pos. and the

sum of two pos.

is pos.

97. Zero; sum of neg.

and pos. is the

difference of the

abs. values.

|n| = |m| so |n| – |m| = 0.

98. zero; n + (–m) = n + (–n) = 0

x

12

83.

84.

85.

86. –

87.

88. –

89.

1

2

1

4

1 –1

2 1

t

6

1

2

–3m + 1

4

m

9

1

2

8 32 –27

20 6 0

1

2

w

10

c

2

107. <

108. >

109. >

110. =

111. 9

112. 2.2

113. 18

114. 21

99. B

100. F

101. D

102. F

103. C

104. H

105. <

106. =

58a

21

2b

9

x

12

Adding Real Numbers

ALGEBRA 1 LESSON 1-4

1-4

adding real numbers14

4

15

1

5

–2 –4

8 –6

3 –5

–2 0

1 – 9

6 – 6

+

–4

7

15

Adding Real Numbers

ALGEBRA 1 LESSON 1-4

Simplify.

1. 15 + (– 10) 2. – 57 + (– 11) 3. – 42 + 19

4. – 1 + (– 3 ) 5.

6. Evaluate 25 + 4x for x = – 5.

5

–68

–23

5

1-4