1. 1-1 Variables and Expressions PRE-ALGEBRA LESSON 1-1 Complete each equation. 1.1 week = days2.1 foot = inches 3.1 nickel = cents4.1 gallon = quarts 5.1 yard = feet

2. Solutions 1.1 week = days2.1 foot = inches 3.1 nickel = cents4.1 gallon = quarts 5.1 yard = feet Variables and Expressions PRE-ALGEBRA LESSON 1-1 1-1 712 54 3

3. Identify each expression as a numerical expression or a variable expression. For a variable expression, name the variable. Variables and Expressions PRE-ALGEBRA LESSON 1-1 numerical expression Variable expression; t is the variable. a. 7  3 b. 4t 1-1

4. Variables and Expressions PRE-ALGEBRA LESSON 1-1 Write a variable expression for the cost of p pens priced at 29¢ each. = number of pens. Words times Let 29¢ number of pens p The variable expression 29 p, or 29p, describes the cost of p pens. Expression29 p 1-1

5. Variables and Expressions PRE-ALGEBRA LESSON 1-1 Pages 6–7 Exercises 16.z – 8 17.2 12 18.d 12 19.5 7 20.5n 21.4 3 22.4g 23.Variable expression; d is the variable. 1.Variable expression; b is the variable. 2.numerical expression 3.Variable expression; n is the variable. 4.numerical expression 5.Variable expression; x is the variable. 6.numerical expression 7.m + 16 8. 9.3c 10.p – 2 11.3b 12.j – 4 13. 14. 15.2 – x 6z6z 3n3n n3n3 1-1

6. Variables and Expressions PRE-ALGEBRA LESSON 1-1 24.numerical expression 25.Variable expression; g is the variable. 26.numerical expression 27.7 4 28.7w 29. 30. 31. 32. 33.d – 20 34.110e + 55 35.70a + 100b 36.B 37.C 38.D 39.A 40.Both use numbers and operation symbols; only variable expressions use variables. 41.Answers may vary. Sample: The student confused the positions of n and 5. 42.B 43.I 44.C 160 16 z 16 100 12 i 12 1-1

7. Variables and Expressions PRE-ALGEBRA LESSON 1-1 45.H 46.225 47.72 48.8 49.75 50.13 51.9,563 52.$2.95 53.a. 500 b. 400 1-1

8. Variables and Expressions PRE-ALGEBRA LESSON 1-1 Write a variable expression for each word phrase. 1.the total of h and 56 2.three less than d 3.p decreased by three4.a divided by 7 p – 3 h + 56d – 3 a ÷ 7 1-1

9. 1-2 The Order of Operations PRE-ALGEBRA LESSON 1-2 (For help, go to Skills Handbook p. 760.) Find each quotient. 1.164 ÷ 22.344 ÷ 83.284 ÷ 4 4.133 ÷ 75.182 ÷ 136.650 ÷ 25

10. The Order of Operations PRE-ALGEBRA LESSON 1-2 Solutions 1.Estimate:2.Estimate:3.Estimate: 160 ÷ 2 = 80360 ÷ 8 = 45280 ÷ 4 = 70 82 43 71 2 1648 3444 284 –16 –32 –28 4 24 4 – 4 – 24 – 4 0 0 0 4.Estimate:5.Estimate:6.Estimate: 140 ÷ 7 = 20195 ÷ 13 = 15625 ÷ 25 = 25 19 14 26 7 13313 18225 650 –7 –13 –50 63 52 150 –63 – 52 –150 0 0 0 1-2

11. The Order of Operations PRE-ALGEBRA LESSON 1-2 Simplify 8 – 2 2. 8 – 2 2 8 – 4 First multiply. Then subtract. 4 1-2

12. The Order of Operations PRE-ALGEBRA LESSON 1-2 Simplify 12 ÷ 3 – 1 2 + 1. 12 ÷ 3 – 1 2 + 1 Add and subtract from left to right. 2 + 1 4 – 2 + 1 Multiply and divide from left to right. 3 Add. 1-2

13. The Order of Operations PRE-ALGEBRA LESSON 1-2 Simplify 20 – 3[(5 + 2) – 1]. 20 – 3[(5 + 2) – 1] 20 – 3[ 7 – 1] Add within parentheses. Subtract within brackets. 20 – 3 [6] 20 – 18 Multiply from left to right. Subtract. 2 1-2

14. The Order of Operations PRE-ALGEBRA LESSON 1-2 Pages 11–12 Exercises 17.33 18.13 19.8 20.4 21.3 22.The student subtracted 1 from 6 before dividing, instead of dividing and then subtracting. 1.27 2.3 3.2 4.4 5.16 6.16 7.11 8.31 9.4 10.6 11.14 12.4 13.13 14.108 15.49 16.17 1-2

15. The Order of Operations PRE-ALGEBRA LESSON 1-2 23.We must agree on an order of operations to ensure that everyone gets the same value for an expression. 24.3 25.24 26.12 27.16 28.33 29.25 30.24 31.22 32.4 33.> 34.> 35.> 36.< 37.> 38.< 39.(7 + 4) 6 = 66 40.[7 (8 – 6)] + 3 = 17 41.(3 + 8 – 2) 5 = 45 42.(6 3) + (9 – 4) = 23 43.4 9 + 5; 41 44.21 – (15 + 5); 1 45.17 – (25 ÷ 5); 12 46.4 + 7 3; 25 hours 1-2

16. The Order of Operations PRE-ALGEBRA LESSON 1-2 47–49. Answers may vary. Samples are given. 47.(6  5) – (4  2) and (6  3) + (2  2); 22 in. 2 48.(6  6) – (2  2) and (2  6) + (2  6) + (2  2) + (2  2); 32 m 2 49.(5  4) – (3  3) and (4  1) + (4  1) + (3  1); 11 ft 2 50.Answers may vary. Sample: Payton bought 4 pairs of blue socks and 3 pairs of red socks at $3 a pair. She also bought a hat for $2. What was the total cost of her purchases? $23 51.Answers may vary. Sample: 1 + 2 + 3 + 4 + 5 + 6 + 7 + (8 9) k 20 52.D 53.G 54.D 55.F 56.8n 57. 58.h – 6 59.10d 60.15c 1-2

17. The Order of Operations PRE-ALGEBRA LESSON 1-2 Simplify each expression. 1.7(3) – 2 4 2.6 ÷ 2 + 1 5 3.10 ÷ (4 + 1)4.3[9 2 ÷ (10 – 4)] 2 138 9 1-2

18. 1-3 Evaluating Expressions PRE-ALGEBRA LESSON 1-3 (For help, go to Lesson 1-2.) Simplify each expression. 1.6(9 + 1)2.17 – 2 + 3 3.9 + 8 2 + 44.[3(5) + 1] 2

19. Evaluating Expressions PRE-ALGEBRA LESSON 1-3 Solutions 1. 6(9 + 1) 2.17 – 2 + 3 6(10) 15 + 3 60 18 3.9 + 8 2 + 4 4.[3(5) + 1] 2 9 + 16 + 4 [15 + 1] 2 29 16 2 32 1-3

20. Evaluating Expressions PRE-ALGEBRA LESSON 1-3 Evaluate 18 + 2g for g = 3. 18 + 2g = 18 + 2(3)Replace g with 3. = 18 + 6Multiply. = 24Add. 1-3

21. Evaluating Expressions PRE-ALGEBRA LESSON 1-3 Evaluate 2ab – for a = 3, b = 4, and c = 9. = 2 3 4 – 3Work within grouping symbols. = 6 4 – 3Multiply from left to right. = 24 – 3Multiply. = 21 Subtract. c3c3 2ab – = 2 3 4 –Replace the variables. c3c3 9393 1-3

22. Evaluating Expressions PRE-ALGEBRA LESSON 1-3 The Omelet Café buys cartons of 36 eggs. a.Write a variable expression for the number of cartons the Café should buy for x eggs. b.Evaluate the expression for 180 eggs. a. x eggs b. 180 eggs x 36 = Evaluate for x = 180. 180 36 x 36 = 5Divide. The Omelet Café should buy 5 cartons to get 180 eggs. 1-3

23. Evaluating Expressions PRE-ALGEBRA LESSON 1-3 The One Pizza restaurant makes only one kind of pizza, which costs $16. The delivery charge is $2. Write a variable expression for the cost of having pizzas delivered. Evaluate the expression to find the cost of having two pizzas delivered. $2 delivery charge = number of pizzas. Words for each Let $16 p pizzaplus Evaluate the expression for p = 2. 16 p + 2 = 16 2 + 2 = 32 + 2 = 34 It costs $34 to have two pizzas delivered. Expression 16 p2+ 1-3

24. Evaluating Expressions PRE-ALGEBRA LESSON 1-3 Pages 16–17 Exercises 16.a. 24d + 4 b. $76 17.15 18.735 19.11 20.15 21.91 22.16 23.99 1.35 2.2 3.5 4.23 5.1 6.107 7.60 8.12 9.4 10.10 11.26 12.6 13.14 14.65 15.a. 55m b. 1,100 words 1-3

25. Evaluating Expressions PRE-ALGEBRA LESSON 1-3 24.125 25.2 26.10 27.8d; 24 km 28.a. 153w b. 306 calories 29.Answers may vary. Sample: You did not work within the grouping symbols first. 30.10 31.100 + 25n; $400 32.a. 5 + 2r b. $17 c. 5 rides 33.Answers may vary. Sample: Liam has 5 fewer than 3 times the number of cards that Jamie has. Jamie has 5 cards. How many cards does Liam have? 34.D 35.H 36.D 37.F 38.6 39.53 40.0 41.19 – t 42. 43.8 + n d 20 1-3

26. Evaluating Expressions PRE-ALGEBRA LESSON 1-3 44.No; Valerie’s average grade should be in the 80s. Valerie evaluated 96 + 82 + 78 + 76 ÷ 4 on her calculator instead of. 96 + 82 + 78 + 76 4 1-3

27. Evaluating Expressions PRE-ALGEBRA LESSON 1-3 Evaluate. 1.7(b) – 4 for b = 3 2.h ÷ 2 + 1 for h = 12 3.3c + 4 ÷ d for c = 8, d = 24.fg – g for f = 5, g = 7 26 177 28 1-3

28. 1-4 Integers and Absolute Value PRE-ALGEBRA LESSON 1-4 (For help, go to Skills Handbook p. 775.) Write an integer for each situation. 1.lose $72.find $9 3.8 steps forward4.3 yards gained 5.5 floors down

29. Integers and Absolute Value PRE-ALGEBRA LESSON 1-4 Solutions 1.lose $72.find $9 –79 3.8 steps forward4.3 yards gained 83 5.5 floors down –5 1-4

30. Integers and Absolute Value PRE-ALGEBRA LESSON 1-4 Write a number to represent the temperature shown by the thermometer. The thermometer shows 2 degrees Celsius below zero, or –2°C. 1-4

31. Integers and Absolute Value PRE-ALGEBRA LESSON 1-4 Graph 2, –2, and –3 on a number line. Order the numbers from least to greatest. The numbers from least to greatest are –3, –2, and 2. 1-4

32. Integers and Absolute Value PRE-ALGEBRA LESSON 1-4 Use a number line to find |–5| and |5|. |–5| = 5 |5| = 5 1-4

33. Integers and Absolute Value PRE-ALGEBRA LESSON 1-4 Pages 20–22 Exercises 16.1, 1 17.2, 2 18.8, 8 19.7, 7 20.6, 6 21.4, 4 1.250 2.–18 3.–45 4.110 5.–50 6.7 7.–300 8.–8 9.3,400 10.2 11.5 12.–4 13.–9, –2, 8 14.–12, –9, –3 15.–6, 0, 6 1-4

34. Integers and Absolute Value PRE-ALGEBRA LESSON 1-4 22.18 23.9 24.3 25.6 26.7 27.2 28.Answers may vary. Sample: loss of 1,000 points in a board game 29.Answers may vary. Sample: 28 golf strokes over par 30.Answers may vary. Sample: checkbook balance for checks totalling $126 more than is in the account 31.6 32.–2 33.2 34.–8 35.0 36.1,000 37.–13 38.56 39.–23 40.–12 41.< 42.> 43.< 1-4

35. Integers and Absolute Value PRE-ALGEBRA LESSON 1-4 44.< 45.< 46.= 47.10h 48.– d 49.r + n 50.–12,500; –15,617 51.Answers may vary. Sample: My friend did not take into account 51.(continued) the signs of the numbers. 52.zero 53.negative 54.positive 55.negative 56–58. Answers may vary. Samples are given. 56.–3, –2 57.–2, –1 58.–11, –10 59.a. b. Nevada 60.Answers may vary. Sample: If sea level is zero, then water levels above sea level can be 1313 1-4

36. Integers and Absolute Value PRE-ALGEBRA LESSON 1-4 60.(continued) described by positive integers, and water levels below sea level can be described by negative integers. 61.No. Explanations may vary. Sample: If x and y have opposite signs, | x + y | | x | + | y |. For x = –1 and y = 3, | –1 + 3 | = 2 while | –1 | + | 3 | = 4. 62.B 63.I 64.B 65.F 66.14 67.24 68.440 69.> 70.< 71.c + 6 =/ 1-4

37. Integers and Absolute Value PRE-ALGEBRA LESSON 1-4 Write an integer to represent each situation. 1.A debt of $50 2.A dive of 23 feet below the surface Simplify. 3.| –12 |4.| 8 | 12 –50 –23 8 1-4

38. 1-5 Adding Integers PRE-ALGEBRA LESSON 1-5 (For help, go to Lesson 1-4.) Compare. Use >, <, or = to complete each statement. 1.–6 –32.2 –15 3.–5 | 5 |4.| 10 | | –10 | 5.| 9 | | –2 |6.| –8 | | 0 |

39. Adding Integers PRE-ALGEBRA LESSON 1-5 Solutions 1.–6 –15 3.–5 < | 5 |4.| 10 | = | –10 | 5.| 9 | > | –2 |6.| –8 | > | 0 | 1-5

40. (–7) + 3Model the sum. – 4Group and remove zero pairs. There are four negative tiles left. Adding Integers PRE-ALGEBRA LESSON 1-5 Use tiles to find (–7) + 3. (–7) + 3 = – 4 1-5

41. Adding Integers PRE-ALGEBRA LESSON 1-5 From the surface, a diver goes down 20 feet and then comes back up 4 feet. Find –20 + 4 to find where the diver is. The diver is 16 feet below the surface. –20 + 4 = –16 1-5 Start at 0. To represent –20, move left 20 units. To add positive 4, move right 4 units to –16.

42. Adding Integers PRE-ALGEBRA LESSON 1-5 Find each sum. b. 13 + (–17) a. –20 + (–15) Since –17 has the greater absolute value, the sum is negative. 13 + (–17) = – 4 Since both integers are negative, the sum is negative. –20 + (–15) = –35 Find the difference of the absolute values. |–17| – |13| = 17 – 13= 4 Simplify. 1-5

43. Adding Integers PRE-ALGEBRA LESSON 1-5 A player scores 22 points. He then gets a penalty of 30 points. What is the player’s score after the penalty? Write an expression. 22 + (–30) Find the difference of the absolute values. |–30| – |22| = 30 – 22 Since –30 has the greater absolute value, the sum is negative. 22 + (–30) = – 8 The player’s score is – 8. = 8 Simplify. 1-5

44. Adding Integers PRE-ALGEBRA LESSON 1-5 Find –7 + (– 4) + 13 + (–5). Add from left to right. –7 + (– 4) + 13 + (–5) –7 + (– 4) + 13 + (–5) = –3 –3 |5| – |2| = 3. Since –5 has the greater absolute value, the sum is negative. The sum of the two negative integers is negative. –11 + 13 + (–5) |13| – |11| = 2. Since 13 has the greater absolute value, the sum is positive. 2 + (–5) 1-5

45. Adding Integers PRE-ALGEBRA LESSON 1-5 Pages 27–29 Exercises 17.53 18.–65 19.100 20.0 21.–185 22.2,620 m 23.23 24.12 1.–4 + 7; 3 2.5 + 0; 5 3.–4 + (–2); –6 4.3 + (–8); –5 5.–3 6.–3 7.3 8.–7 9.–5 10.–9 11.–1 12.1 13.3 14.–9 15.–13 16.–14 1-5

46. Adding Integers PRE-ALGEBRA LESSON 1-5 25.–61 26.12 27.Negative; both numbers are negative. 28.Positive; the number with greater absolute value is positive. 29.Zero; the numbers are opposites. 30.15 31.0 32.–8 33.7 34.16 35.–40 36.< 37.> 38.= 39.> 40.> 41.> 42.–7 43.–8 44.–45 45.–20 + 18; –2 46.200 + (–75); 125 47.120 + (–25); 95 48.–35 + 10; –25 49.1 1-5

47. Adding Integers PRE-ALGEBRA LESSON 1-5 50.–3 51.–60 52.4 yd loss 53.$158 54.Answers may vary. Sample: My friend subtracted 5 instead of adding 5. 55.Answers may vary. Sample: First find the difference of the absolute values of the 55.(continued) two numbers. Then give the answer the sign of the number with the greater absolute value. 56.negative 57.positive 58.negative 59.positive 60.B 61.H 62.B 63.G 64.< 65.> 66.> 67.> 68.< 69.< 1-5

48. Adding Integers PRE-ALGEBRA LESSON 1-5 70.(116 – 8) + 130, or 130 + (116 – 8); 238 71.25 + 10n; $55 1-5

49. Find each sum. 1.–37 + (–5)2.14 + (–4) 3.–100 + 5 + (–3)4.Evaluate 33 + t for t = –11. Adding Integers PRE-ALGEBRA LESSON 1-5 –98 –4210 22 1-5

50. 1-6 Subtracting Integers PRE-ALGEBRA LESSON 1-6 (For help, go to Lesson 1-5.) Find each sum. 1.8 + (–9)2.–11 + (–18)3.–4 + (–6) 4.14 + (–3)5.6 + (–6)6.–13 + (–10)

51. Subtracting Integers PRE-ALGEBRA LESSON 1-6 Solutions 1.8 + (–9)4.14 + (–3) | –9 | – | 8 | = 9 – 8| 14 | – | –3 | = 14 – 3 = 1 = 11 8 + (–9) = –1 14 + (–3) = 11 2.–11 + (–18)5.6 + (–6) –11 + (–18) = –29| –6 | – | 6 | = 6 – 6 = 0 6 + (–6) = 0 3.–4 + (–6)6.–13 + (–10) –4 + (–6) = –10–13 + (–10) = –23 1-6

52. Start with 7 negative tiles. Take away 5 negative tiles. There are 2 negative tiles left. Subtracting Integers PRE-ALGEBRA LESSON 1-6 Find –7 – (–5). –7 – (–5) = –2 1-6

53. Start with 2 positive tiles. There are not enough positive tiles to take away 8. Add 6 zero pairs. Take away 8 positive tiles. There are 6 negative tiles left. Subtracting Integers PRE-ALGEBRA LESSON 1-6 Find 2 – 8. 2 – 8 = –6 1-6

54. Subtracting Integers PRE-ALGEBRA LESSON 1-6 An airplane left Houston, Texas, where the temperature was 42°F. When the airplane landed in Anchorage, Alaska, the temperature was 50°F lower. What was the temperature in Anchorage? The temperature in Anchorage was –8°F. Write an expression. 42 – 50 To subtract 50, add its opposite. 42 – 50= 42 + (–50) = –8Simplify. 1-6

55. Subtracting Integers PRE-ALGEBRA LESSON 1-6 Pages 32–34 Exercises 17.–12 18.6 + (–2); 4 19.6 + 2; 8 20.–6 + (–2); –8 21.2 + (–6); –4 22.2 + 6; 8 23.–2 + (–6); –8 24.5 + (–11); –6 1.–9 – (–2) = –7 2.3 + (–8) = –5 or 3 – 8 = –5 3.–4 4.–8 5.1 6.–2 7.2 8.–7 9.–5 10.2 11.15 12.17 13.–6 14.0 15.–1 16.–5 1-6

56. Subtracting Integers PRE-ALGEBRA LESSON 1-6 25.75 + 25; 100 26.22 + 7; 29 27.87 + 9; 96 28.35 + (–15); 20 29.100 + 91; 191 30.–$19 31.–15 32.–124 33.–80 34.19 35.170 36.913 37.–60 38.–83 39.–68 40.–52 41.–30 42.850 43.10 44.66 45–50. Answers may vary. Samples are given. 45.3 – 3 = 0; (–4) – (–4) = 0 46.15 – 5 = 10; –5 – (–15) = 10 47.1 – 7 = –6; –10 – (–4) = –6 1-6

57. Subtracting Integers PRE-ALGEBRA LESSON 1-6 48.5 – 20 = –15; –20 – (–5) = –15 49.7 – 4 = | –3 |; –2 – (–5) = | –3 | 50.12 – 1 = | 11 |; –5 – (–16) = | 11 | 51.It decreases. 52.–24°C 53.–8°C 54.2 55.–60 56.–7 57.150 58.10 59.66 60.12 61.–40 62.0 63.18 64.–30 65.–20 66.–2 – 4; –6; $6 67.3,000 – 600; 2,400; 2,400 ft 68.0 + 15 – 25; –10; – 10°F 69–74. Answers may vary. Samples are given. 69.50 1-6

58. Subtracting Integers PRE-ALGEBRA LESSON 1-6 70.–280 71.–470 72.–110 73.230 74.80 75.a.Answers may vary. Sample: The temp- erature at 5:00 P.M. was 5°C, but it dropped 7 degrees after sundown. What is the temperature 75.(continued) after sundown? b. 5 + (–7); –2°C 76.a. 16, 20, 24, 28 b. 28 c. 24 77.a. a 5 Example: When a = 6, | 6 – 5 | = | 6 | – 5. b. a | 4 | – 5. c. none 78.–3; 79.–15; 80.6; > – 1-6

59. Subtracting Integers PRE-ALGEBRA LESSON 1-6 81.–6; 82.D 83.H 84.D 85.G 86.–5 87.7 88.–6 89–92. Answers may vary. Samples are given. 89.–7 90.3 91.0 92.–6 93.100 + 6 9; 154 1-6

60. Find each difference. 1.–24 – (–5) 2.19 – (–4)3.–33 – 11 4.14 – 465.–200 – 50 – (–10) Subtracting Integers PRE-ALGEBRA LESSON 1-6 –44–1923 –32–240 1-6

61. 1-7 Inductive Reasoning PRE-ALGEBRA LESSON 1-7 (For help, go to Skills Handbook.) Find each difference. 1.–3 – 42.–7 – 4 3.–11 – 44.–15 – 4

62. Inductive Reasoning PRE-ALGEBRA LESSON 1-7 Solutions 1.–3 – 42.–7 – 4 –3 – 4 = –3 + (–4)–7 – 4 = –7 + (–4) = –7 = –11 3.–11 – 44.–15 – 4 –11 – 4 = –11 + (–4)–15 – 4 = –15 + (–4) = –15 = –19 1-7

63. Inductive Reasoning PRE-ALGEBRA LESSON 1-7 Use inductive reasoning. Make a conjecture about the next figure in the pattern. Then draw the figure. Observation: The circles are rotating counterclockwise within the square. Conjecture: The next figure will have a shaded circle at the top right. 1-7

64. Inductive Reasoning PRE-ALGEBRA LESSON 1-7 Write a rule for each number pattern. a. 0, – 4, – 8, –12,... b. 4, – 4, 4, – 4,... c. 1, 2, 4, 8, 10,... Start with 0 and subtract 4 repeatedly. Alternate 4 and its opposite. Start with 1. Alternate multiplying by 2 and adding 2. 1-7

65. Inductive Reasoning PRE-ALGEBRA LESSON 1-7 Write a rule for the number pattern 110, 100, 90, 80,... Find the next two numbers in the pattern. The rule is Start with 110 and subtract 10 repeatedly. The next two numbers in the pattern are 80 – 10 = 70 and 70 – 10 = 60. The next numbers are found by subtracting 10. – 10 The first number is 110. 110,100,90,80 1-7

66. Inductive Reasoning PRE-ALGEBRA LESSON 1-7 A child grows an inch a year for three years in a row. Is it a reasonable conjecture that this child will grow an inch in the year 2015? No; children grow at an uneven rate, and eventually they stop growing. 1-7

67. Inductive Reasoning PRE-ALGEBRA LESSON 1-7 Is each conjecture correct or incorrect? If it is incorrect, give a counterexample. a. Every triangle has three sides of equal length. b. The opposite of a number is negative. The conjecture is incorrect. The figure below is a triangle, but it does not have three equal sides. The conjecture is incorrect. The opposite of –2 is 2. 1-7

68. (continued) Inductive Reasoning PRE-ALGEBRA LESSON 1-7 c. The next figure in the pattern below has 16 dots. The conjecture is correct. The diagram below shows the next figure in the pattern. 1-7

69. Inductive Reasoning PRE-ALGEBRA LESSON 1-7 Pages 38–39 Exercises 8.Start with 1 and alternately add 1 and 3; 10, 13 9.Answers may vary. Sample: No. Mario’s catching a cold could be due to many different reasons. 10.Incorrect; an ostrich cannot fly. 11.correct 1. a square with four corners shaded 2. a six-sided figure with a six-sided figure inside it 3.Start with 100 and subtract 15 repeatedly; 40, 25 4.Start with 5 and multiply by 4 repeatedly; 1,280, 5,120 5.Start with 2 and add 5 repeatedly; 22, 27 6.Start with –10 and add 6 repeatedly; 14, 20 7.Start with 1 and add 3 repeatedly; 13, 16 1-7

70. Inductive Reasoning PRE-ALGEBRA LESSON 1-7 12.Incorrect; =, which is less than. 13. an eight-sided figure with bottom right eighth shaded 14. a square inside a circle inside a 14.(continued) triangle inside a diamond 15.Start with 1 and add 0.5 repeatedly; 3.5, 4, 4.5 16.Start with –1 and alternate between finding the opposite and the next negative integer. –4, 4, –5 17.Start with 6 and add –2 repeatedly; –2, –4, –6 18.Incorrect; some have 4. 19.Incorrect; 8 + (–6) is 2, 2 < 8. 20.correct 21.Start with 1, and then double and add 2, repeatedly; 190, 382, 766 22.Start with 1 and alternately subtract and add consecutive multiples of 3; 10, –11, 13 1212 1212 1414 1212 1-7

71. Inductive Reasoning PRE-ALGEBRA LESSON 1-7 23.a.Answers may vary. Sample: The unemployment rate will decrease; it has decreased every year shown in the graph. b. Answers may vary. Sample: Look up unemployment records for 2001. 24.C 25.G 26.C 27.–7 28.5 29.103 30.–4 31.–2 32.20 33.1,500n; 36,000 gallons 1-7

72. Inductive Reasoning PRE-ALGEBRA LESSON 1-7 Find the next three numbers in each pattern. 1.1, –1, 2, –2, 3,... 2.1, 3, 7, 15, 31,... 3.–11, –8, –5, –2,... 1, 4, 7 –3, 4, –463, 127, 255 1-7

73. 1-8 Look for a Pattern PRE-ALGEBRA LESSON 1-8 (For help, go to Lesson 1-7.) Write a rule for each pattern. Find the next three numbers. 1.8, 11, 14, 17,...2.1, 5, 4, 8, 7,... 3.3, 5, 10, 12, 24,...4.1, 4, 7, 10,...

74. Look for a Pattern PRE-ALGEBRA LESSON 1-8 Solutions 1.8 11 14 17 20 23 26 +3 +3 +3 +3 +3 +3 Start with 8 and add 3 repeatedly. 2.1 5 4 8 7 11 10 14 +4 –1 +4 –1 +4 –1 +4 Start with 1. Alternate adding 4 and subtracting 1. 3.3 5 10 12 24 26 52 54 +2  2 +2  2 +2  2 +2 Start with 3. Alternate adding 2 and multiplying by 2. 4.1 4 7 10 13 16 19 +3 +3 +3 +3 +3 +3 Start with 1 and add 3 repeatedly. 1-8

75. Each student on a committee of five students shakes hands with every other committee member. How many handshakes will there be in all? Look for a Pattern PRE-ALGEBRA LESSON 1-8 The pattern is to add the number of new handshakes to the number of handshakes already made. 4the number of handshakes by 1 student 4 + 3 = 7the number of handshakes by 2 students 1-8

76. Look for a Pattern PRE-ALGEBRA LESSON 1-8 (continued) There will be 10 handshakes in all. Make a table to extend the pattern to 5 students. Student Number of original handshakes Total number of handshakes 1 4 4 2 3 4 + 3 3 2 7 + 2 4 1 9 + 1 5 0 10 + 0 = 7= 9= 10 1-8

77. Look for a Pattern PRE-ALGEBRA LESSON 1-8 Pages 42–43 Exercises 12.(continued) a 4  4 square 13. a circle divided into 5 pieces 14.9°F 15.0 16.17 17.25 1.36 laps/day 2.78 students 3.$10.23 4.365 min, or 6 h and 5 min; 10 min 5.11 pieces; 16 pieces 6.a. 4, 3, 1; 9, 8, 1; 16, 15, 1; 25, 24, 1. The differences are all 1. b. 11 11; 1 c. 2,208 6.(continued) d. 4,225 7.a. $59; $21 b. 10 people 8.3 mi 9.C 10.I 11.B 12. 1-8

78. Look for a Pattern PRE-ALGEBRA LESSON 1-8 Solve using any strategy. 1.You have a penny, a nickel, a dime, and a quarter. You give away three coins. How many different amounts of money can you give away? Name the values. 4; 16¢, 31¢, 36¢, 40¢ 1-8

79. 1-9 Multiplying and Dividing Integers PRE-ALGEBRA LESSON 1-9 (For help, go to Skills Handbook p. 759.) Simplify each expression. 1.5  42.3  83.5  5 4.14  25.6  56.20  7

80. Multiplying and Dividing Integers PRE-ALGEBRA LESSON 1-9 Solutions 1. 52. 33. 5  4  8  5 20 24 25 4. 145. 66. 20  2  5  7 28 30 140 1-9

81. Multiplying and Dividing Integers PRE-ALGEBRA LESSON 1-9 A diver is descending from the surface of the water at a rate of 5 ft/s. Write an expression with repeated addition to show how far the diver is from the surface of the water after four seconds. 4 (–5) = (–5) + (–5) + (–5) + (–5) = –20 The diver is 20 feet below the surface of the water. Use a number line to show repeated addition. 1-9

82. Multiplying and Dividing Integers PRE-ALGEBRA LESSON 1-9 a. –2(7) Use a pattern to find each product. 2(7) = 14Start with products you know. 1(7) = 7 0(7) = 0 –1(7) = –7Continue the pattern. –2(7) = –14 1-9

83. Multiplying and Dividing Integers PRE-ALGEBRA LESSON 1-9 b. –2(–7) (continued) 2(–7) = –14Start with products you know. 1(–7) = –7 0(–7) = 0 –1(–7) = 7Continue the pattern. –2(–7) = 14 1-9

84. Multiplying and Dividing Integers PRE-ALGEBRA LESSON 1-9 Multiply 6(–2)(–3). 6(–2)(–3) = (–12)(–3)Multiply from left to right. The product of a positive integer and a negative integer is negative. = 36Multiply. The product of two negative integers is positive. 1-9

85. Multiplying and Dividing Integers PRE-ALGEBRA LESSON 1-9 Use the table to find the average of the differences in the values of a Canadian dollar and a U.S. dollar for 1994–1997. Write an expression for the average. –27 + (–27) + (–26) + (–28) 4 1-9

86. Multiplying and Dividing Integers PRE-ALGEBRA LESSON 1-9 (continued) The quotient of a negative integer and a positive integer is negative. = –27 For 1994–1997, the average difference was –27¢. Use the order of operations. The fraction bar acts as a grouping symbol. –108 4 = 1-9

87. Multiplying and Dividing Integers PRE-ALGEBRA LESSON 1-9 Pages 47–49 Exercises 16.0 17.–360 18.0 19.–96 20.–1 21.–18 22.–10 23.–7 1.5 (–2) = –10 2.4(–9); –36 3.5(–5); –25 4.–35 5.–9 6.–44 7.–24 8.–50 9.–18 10.–30 11.–81 12.–72 13.–48 14.15 15.–60 1-9

88. Multiplying and Dividing Integers PRE-ALGEBRA LESSON 1-9 24.–6 25.10 26.19 27.–12 28.–3 29.–2°C 30.2 yd 31.0 32.$92 33.Positive; the integers have the same sign. 34.Negative; the integers have opposite signs. 35.Negative; the integers have opposite signs. 36.Positive; the first product is negative, so the second is a product of integers with the same sign. 37.A 38.D 39.C 40.B 41.–15 42.–14 43.4,661 44.–21,384 45.8 46.216 1-9

89. Multiplying and Dividing Integers PRE-ALGEBRA LESSON 1-9 47.–76 48.–20 49.12,288 50.a. –3 b. $40 per share 51.> 52.< 53.> 54.< 55.= 56.< 57.12 58.–15 59.–27 60.–15, 5 61–64. Answers may vary. Samples are given. 61.4 and 8; 7 62.3 and –2; –1 63.2 and –4; 1 64.–11 and 0; –6 65.a. negative; positive; negative b. If there are an even number of negative integers, the sign of the product will be positive; otherwise, the sign will be negative. 1-9

90. Multiplying and Dividing Integers PRE-ALGEBRA LESSON 1-9 66.Negative; the numerator is positive, and the denominator is negative, so the quotient is negative. 67.$.60; $520 68.C 69.F 70.C 71.G 72.37 73.< 74.> 75.< 76.50 – n 77.60y 78.x + y 79. d5d5 1-9

91. Find each product or quotient. 1.–7(–3)2.–36 ÷ (–9) 3.–12 24.7(–3) 5.–6 (–2) (–1) Multiplying and Dividing Integers PRE-ALGEBRA LESSON 1-9 –24 214 –21 –12 1-9

92. 1-10 The Coordinate Plane PRE-ALGEBRA LESSON 1-10 (For help, go to Lesson 1-4.) Graph numbers on a number line. 1.–2, 1, –52.0, 2, –4 3.–3, 3, –24.–1, –5, –8

93. The Coordinate Plane PRE-ALGEBRA LESSON 1-10 Solutions 1.–2, 1, –5 2.0, 2, –4 3. –3, 3, –24.–1, –5, –8 1-10

94. The Coordinate Plane PRE-ALGEBRA LESSON 1-10 Write the coordinates of point G. In which quadrant is point G located? Point G is located 2 units to the left of the y-axis. So the x-coordinate is –2. The point is 3 units below the x-axis. So the y-coordinate is –3. 1-10 The coordinates of point G are (–2, –3). Point G is located in Quadrant III.

95. The Coordinate Plane PRE-ALGEBRA LESSON 1-10 Graph point M(–3, 3). 1-10

96. The Coordinate Plane PRE-ALGEBRA LESSON 1-10 1.III 2.II 3.IV 4.I 5.II 6.III 7.(0, –7) 8.(3, 0) 9.(–2, 4) 10.(–4, –2) 11.(–8, 3) 12.(1, –4) 13–28. 29.(0, 0) 30.Q 31.F 32.M 33.P 34.(2, –3) 35.(–2, 3) 36.(–5, 0) 37.(6, 6) 1-10 Pages 52–54 Exercises

97. The Coordinate Plane PRE-ALGEBRA LESSON 1-10 38.(–5, –2) 39.(0, –4) 40.(3, 0) 41.IV 42.I 43.II 44.III 45.I 46.y-axis 47.III 48.IV 49.y-axis 50.II 51.triangle 52.rectangle 53.parallelogram 1-10

98. The Coordinate Plane PRE-ALGEBRA LESSON 1-10 54.square59.Frankfort, Kentucky 60.Santa Fe, New Mexico 61. 62.(continued) b. 55.(0, –5) 56.(–1, –2) 57.about 90° W, 32° N 58.about 96° W, 39° N 62.a. c. 1-10

99. The Coordinate Plane PRE-ALGEBRA LESSON 1-10 62.(continued) d. 64.Check students’ work. 65.Explanations may vary. Sample: No; since a and b describe positions on two number lines, (a, b) and (b, a) describe different points (unless a = b). 66.A(3, 0), B(0, 3), C(–3, 0), D(0, –3) 67.D 68.I 69.A 70.H 71.A 72.–121 73.–9 74.0 75.–925 ft 63.Answers may vary. Sample: 62a flips the figure across the y- axis. 62b flips the figure across the x- axis. 62c flips the figure across one axis and then the other. 62d doubles the lengths of the sides. 1-10

100. The Coordinate Plane PRE-ALGEBRA LESSON 1-10 76.8 77.–95 78.–12 79.20 80.4 81.3 1-10

101. The Coordinate Plane PRE-ALGEBRA LESSON 1-10 Draw a coordinate grid. Graph each point. 1.S(2, 3) 2. T(2, –3) 3.U(–2, 3)4. K(0, –3) 5. L(3, 0) 1-10

102. 1-A Algebraic Expressions and Integers PRE-ALGEBRA CHAPTER 1 1.n + 19 2.–3 –10 3.–5x 4.–y + 5 5.–10 6.56 7.22 8.18 9.5 10.9 11.–7 12.15 13.< 14.> 15.< 16.> 17.8 18.4 19.63 20.–9 21.–288 22.8 23.143 24.–68 25.–66 26.–180 27.46

103. Algebraic Expressions and Integers PRE-ALGEBRA CHAPTER 1 28.16 29.26 30.0 31.II 32.y-axis 33.III 34.(–3, 2) 35.(1, –2) 36.(2, 0) 37.(–2, –2) 38.a. 25j + 15s b. $150 c. 2 39.D 40.–175 41.Start with 100 and alternately subtract 10 and 5; 55, 45, 40. 42.15th floor 43.Place them on a number line and write them as they appear from left to right. 1-A