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# Adding Real Numbers - PowerPoint PPT Presentation

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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ALGEBRA 1 LESSON 1-4

1-4

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

ALGEBRA 1 LESSON 1-4

1-4

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.

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

The sum is negative.

TRY:

1-4

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

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

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.

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

–6 8.6 11

2.3 5 –3

7 –5.4 –2

11.1 3 –1

–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)

=

1 3.2 9

13.4 8 –4

Simplify.

=

ALGEBRA 1 LESSON 1-4

1-4

ALGEBRA 1 LESSON 1-4

TRY:

1-4

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

17

60

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

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.

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

numbers in each column.

59. a. =

b. 0.23

60. 0

61. –2

62. 1

63. –5

64. 7

100

442

50

221

ALGEBRA 1 LESSON 1-4

1-4

ALGEBRA 1 LESSON 1-4

78. The matrices are not the

same size, so they can’t

79. No; time and temperature

are different quantities and

80.a.

82.a. 4

b. –4

80. (continued)

b.

c. 4 employees

d. 10 employees

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

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

ALGEBRA 1 LESSON 1-4

1-4

4

15

1

5

–2 –4

8 –6

3 –5

–2 0

1 – 9

6 – 6

+

–4

7

15

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