ALGEBRA 1 LESSON 1-4 Adding Real Numbers 1-4. Start at –3. Move right 5 units. Start at –3. Move...

ALGEBRA 1 LESSON 1-4ALGEBRA 1 LESSON 1-4

Adding Real NumbersAdding Real Numbers

1-4

Start at –3.

Move right 5 units.

Start at –3.

Move left 5 units.

Start at 3.

Use a number line to simplify each expression.

a. 3 + (–5) b. –3 + 5

c. –3 + (–5)

3 + (–5) = –2 –3 + 5 = 2

–3 + (–5) = –8

Use a number line to simplify each expression.

Move left 5 units.



1-4

TRY:Use a number lineto find each sum.a. -6 + 4 b. 4 + (-6) c. -3 + (-8) d. 9 + (-3)



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.

Since both addends are negative, add their absolute values.

The sum is negative.



1-4

TRY:

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

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.



1-4

TRY: Evaluate each expression for t = -7.1.a. t + (-4.3) b. -2 + t c. 8.5 + (-t) d. -t + 7.49

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

to the surface.

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

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

Relate: 88 ft below sea level plus feet diver rises

Write: –88 + r

–88 + r

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

–88 + r = –88 + 37 Substitute 37 for r.= – 51 Simplify.

The scuba diver is 51 ft below sea level.



1-4



1 3.2 913.4 8 –4

Simplify.=

7 –5.4 –2

11.1 3 –1

–6 8.6 11

2.3 5 –3Add +

7 –5.4 –2

11.1 3 –1

–6 8.6 11

2.3 5 –3+

–6 + 7 8.6 + (–5.4) 11 + (–2)2.3 + 11.1 5 + 3 –3 + (–1)

Add corresponding elements.=

1-4



1-4

TRY:



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

12. –42

13. 2.2

14. –0.65

15. –7.49

16. 1.33

17.

18. –

19. 6

20. –6

21. 0

22. –

1415

89 3 16

18

1318

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

161314

1-4



1-4

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

38.

39.

40.

41.

42. –2.7

43. –13

44. 6.6

–1 1.4–21 23.2

–18.211.619.1

025

–12

1.8 22

– 712

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

1924

2235

11 120

13

1760



1-4

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

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

100442

50 221



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.

2 0 1–1 3 0.5

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

8 3 5 110 2 2 1

4 1 0 1

5 2 1 18 2 0 12 1 0 1

13 5 6 218 4 2 2

6 2 0 2

82. a. 4

b. –4

1-4



1-4

83.

84.

85.

86. –

87.

88. –

89.

8 32 –27

20 6 0

1 –1

2 1

1412

12

12

12

w 10

c2

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

99. B

100. F

101. D

102. F

103. C

104. H

105. <

106. =

111. 9

112. 2.2

113. 18

114. 21

107. <

108. >

109. >

110. =

x 12

t 6 –3m + 1

4m9

58a212b9

x 12


Simplify.

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

4. – 1 + (– 3 ) 5.

6. Evaluate 25 + 4x for x = – 5.

5 –68 –23

–4 715

5


3 –5–2 0

–2 –4 8 –6+

1 – 96 – 6

1-4

15

4 15

ALGEBRA 1 LESSON 1-4 Adding Real Numbers 1-4. Start at –3. Move right 5 units. Start at –3. Move...

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Transcript of ALGEBRA 1 LESSON 1-4 Adding Real Numbers 1-4. Start at –3. Move right 5 units. Start at –3. Move...