Adding Real Numbers

1. Adding Real Numbers ALGEBRA 1 LESSON 1-4 1-4

2. 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

3. Adding Real Numbers ALGEBRA 1 LESSON 1-4 1-4

4. 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

5. 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

6. 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

7. 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

8. –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

9. Adding Real Numbers ALGEBRA 1 LESSON 1-4 TRY: 1-4

10. 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

11. 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

12. 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

13. 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

14. 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

15. 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