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

2. 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. ALGEBRA 1 LESSON 1-4 Adding Real Numbers 1-4 TRY: Use a number line to find each sum. a.-6 + 4 b.4 + (-6) c.-3 + (-8) d.9 + (-3)

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

4. Simplify each expression. a. 12 + (–23) = –11b. –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. ALGEBRA 1 LESSON 1-4 Adding Real Numbers 1-4 TRY:

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

6. 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. = 5.3Simplify. ALGEBRA 1 LESSON 1-4 Adding Real Numbers 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

7. 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 + 37Substitute 37 for r. = – 51Simplify. The scuba diver is 51 ft below sea level. ALGEBRA 1 LESSON 1-4 Adding Real Numbers 1-4

8. ALGEBRA 1 LESSON 1-4 Adding Real Numbers 13.2 9 13.4 8–4 Simplify. = 7–5.4–2 11.1 3–1 –68.611 2.35–3 Add+ 7–5.4–2 11.1 3–1 –68.611 2.3 5–3 + –6 + 78.6 + (–5.4)11 + (–2) 2.3 + 11.15 + 3–3 + (–1) Add corresponding elements. = 1-4

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

10. ALGEBRA 1 LESSON 1-4 Adding Real Numbers 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.– 14 15 8989 3 16 1818 13 18 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 1616 13 14 1-4

11. ALGEBRA 1 LESSON 1-4 Adding Real Numbers 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 –11.4 –2123.2 –18.2 11.6 19.1 0 25 –12 1.822 – 7 1212 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 19 24 22 35 11 120 1313 17 60

12. ALGEBRA 1 LESSON 1-4 Adding Real Numbers 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.+2 100 442 50 221

13. ALGEBRA 1 LESSON 1-4 Adding Real Numbers 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. 201 –130.5 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 8351 10221 4101 521182012101521182012101 13562 18422 6202 82.a. 4 b.–4 1-4

14. ALGEBRA 1 LESSON 1-4 Adding Real Numbers 1-4 83. 84. 85. 86. – 87. 88. – 89. 832–27 20 6 0 1–1 21 1414 1212 1212 1212 1212 w 10 c2c2 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 4 m9m9 58a 21 2b92b9 x 12

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 –4 7 15 5 Adding Real Numbers 3 –5 –2 0 –2 –4 8 –6 + 1 – 9 6 – 6 1-4 1515 4 15