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4. Contents Lesson 1-1A Plan for Problem Solving Lesson 1-2Powers and Exponents Lesson 1-3Order of Operations Lesson 1-4Algebra: Variables and Expressions Lesson 1-5Algebra: Equations Lesson 1-6Algebra: Properties Lesson 1-7Sequences Lesson 1-8Measurement: The Metric System Lesson 1-9Scientific Notation

5. Lesson 1 Contents Example 1Use the Four-Step Plan Example 2Use a Strategy in the Four-Step Plan

6. Example 1-1a SPENDING A can of soda holds 12 fluid ounces. A 2-liter bottle holds about 67 fluid ounces. If a pack of six cans costs the same as a 2-liter bottle, which is the better buy? ExploreWhat are you trying to find? The number of fluid ounces of soda in a pack of six cans. This number can then be compared to the number of fluid ounces in a 2-liter bottle to determine which is the better buy. What information do you need to solve the problem? You need to know the number of fluid ounces in each can of soda.

7. Example 1-1b PlanYou can find the number of fluid ounces of soda in a pack of six cans by multiplying the number of fluid ounces in one can by six. Solve There are 72 fluid ounces of soda in a pack of six cans. The number of fluid ounces of soda in a 2-liter bottle is about 67. Therefore, the pack of six cans is the better buy because you get more soda for the same price.

8. Example 1-1c Examine Is your answer reasonable? Answer: The pack of six cans is the better buy. The answer makes sense based on the facts given in the problem.

9. Example 1-1d FIELD TRIP The sixth grade class at Meadow Middle School is taking a field trip to the local zoo. There will be 142 students plus 12 adults going on the trip. If each school bus can hold 48 people, how many buses will be needed for the field trip? Answer: 4 buses

10. Example 1-2a POPULATION For every 100,000 people in the United States, there are 5,750 radios. For every 100,000 people in Canada, there are 323 radios. Suppose Sheamus lives in Des Moines, Iowa and Alex lives in Windsor, Ontario. Both cities have about 200,000 residents. About how many more radios are there in Sheamus’s city than in Alex’s city? ExploreYou know the approximate number of radios per 100,000 people in both Sheamus’s city and Alex’s city.

11. Example 1-2b PlanYou can find the approximate number of radios in each city by multiplying the estimate per 100,000 people by two to get an estimate per 200,000 people. Then, subtract to find how many more radios there are in Des Moines than in Windsor. SolveDes Moines: 5,750  2 = 11,500 Windsor: 323  2 = 646 11,500 – 646 = 10,854 So, Des Moines has about 10,854 more radios than Windsor.

12. Example 1-2c ExamineBased on the information given in the problem, the answer seems to be reasonable. Answer: So, Des Moines has about 10,854 more radios than Windsor.

13. Example 1-2d READING Ben borrows a 500-page book from the library. On the first day, he reads 24 pages. On the second day, he reads 39 pages and on the third day he reads 54 pages. If Ben follows the same pattern of number of pages read for seven days, will he have finished the book at the end of the week? Answer: No, he will have only read 483 pages.

14. End of Lesson 1

15. Lesson 2 Contents Example 1Write Powers as Products Example 2Write Powers as Products Example 3Write Powers in Standard Form Example 4Write Powers in Standard Form Example 5Write Numbers in Exponential Form

16. Example 2-1a Write as a product of the same factor. The base is 8. The exponent 4 means that 8 is used as a factor four times. Answer:

17. Example 2-1b Answer: Write as a product of the same factor.

18. Example 2-2a The base is 4. The exponent 6 means that 4 is used as a factor six times. Write as a product of the same factor. Answer: = 4  4  4  4  4  4

19. Example 2-2b Answer: Write as a product of the same factor.

20. Example 2-3a Answer: 512 Evaluate the expression.

21. Example 2-3b Answer: 256 Evaluate the expression

22. Example 2-4a Answer: 1,296 Evaluate the expression

23. Example 2-4b Answer: 3,125 Evaluate the expression

24. Example 2-5a 9 is the base. It is used as a factor 6 times. So, the exponent is 6. Answer: Write in exponential form.

25. Example 2-5b Answer: Write in exponential form.

26. End of Lesson 2

27. Lesson 3 Contents Example 1Evaluate Expressions Example 2Evaluate Expressions Example 3Evaluate Expressions with Powers Example 4Evaluate Expressions with Powers Example 5Evaluate an Expression Example 6Use an Expression to Solve a Problem

28. Example 3-1a Answer: 7 Add first since 18 + 2 is in parentheses. Subtract 20 from 27. Evaluate

29. Example 3-1b Answer: 16 Evaluate

30. Example 3-2a Multiply 5 and 3. Subtract 2 from 30. Add 15 and 15. Answer: 28 Evaluate

31. Example 3-2b Answer: 15 Evaluate

32. Example 3-3a Multiply. Answer: 120,000 Find the value of. Evaluate

33. Example 3-3b Answer: 9,000 Evaluate

34. Example 3-4a Subtract 1 from 3 inside the parentheses. Divide. Answer: 7 Find the value of. Evaluate

35. Example 3-4b Answer: 4 Evaluate

36. Example 3-5a Add 4 and 2. Answer: 18 Subtract from left to right, Multiply from left to right, Add 2 and 16. Evaluate.

37. Example 3-5b Answer: 9 Evaluate

38. Example 3-6a Use the table shown below. Taylor is buying two video game stations, five extra controllers, and ten games. What is the total cost? ItemQuantityUnit Cost game station 2$180.00 controller 5 $24.95 game10 $35.99

39. Example 3-6a number of game stations cost of game station number of controllers number of games cost of game cost of controller 2$180510$35.99$24.95 Multiply from left to right. Add.

40. Example 3-6a Check Check the reasonableness of the answer by estimating. The cost is about (2 × 200) + (5 × 25) + (10 × 40) = 400 + 125 + 400, or about $925. The solution is reasonable. Answer: So, the total cost is $844.65.

41. Example 3-6b Use the table shown below. Suzanne is buying a video game station, four extra controllers, and six games. What is the total cost? ItemQuantityUnit Cost game station1$180.00 controller4 $24.95 game6 $35.99 Answer: $495.74

42. End of Lesson 3

43. Lesson 4 Contents Example 1Evaluate an Expression Example 2Evaluate Expressions Example 3Evaluate Expressions Example 4Evaluate Expressions Example 5Use an Expression to Solve a Problem

44. Example 4-1a Answer: 2 Evaluate

45. Example 4-1b Answer: 11 Evaluate

46. Example 4-2a Answer: 62 Replace x with 7 and y with 9. Add 35 and 27. Use the order of operations. Evaluate

47. Example 4-2b Answer: 24 Evaluate

48. Example 4-3a Answer: 21 Replace r with 7 and s with 12. Divide. The fraction bar is like a grouping symbol. Evaluate

49. Example 4-3b Answer: 12 Evaluate

50. Example 4-4a Replace a with 5. Add 5 and 25. Use the order of operations. Answer: 30 Evaluate

51. Example 4-4b Answer: 15 Evaluate

52. Example 4-5a PHYSICS The final speed of a falling object is found by using the expression v + 9.8t, where v is the speed when you begin timing and t is the length of time the object falls. Find the final speed when the object starts falling at 3 meters per second and falls for 2 seconds. Replace v with 3 and t with 2. Add 3 and 19.6. Use the order of operations. Answer: The final speed of the object is 22.6 meters per second.

53. Example 4-5b BOWLING David is going bowling with a group of friends. His cost for bowling can be described by the formula 1.75 + 2.5g, where g is the number of games David bowls. Find the total cost of bowling if David bowls 3 games. Answer: $9.25

54. End of Lesson 4

55. Lesson 5 Contents Example 1Solve an Equation Mentally Example 2Graph the Solution of an Equation Example 3Write an Equation to Solve a Problem Example 4Find a Solution of an Equation

56. Example 5-1a Write the equation. Answer: The solution is 6. Simplify. Solve mentally.

57. Example 5-1b Solve mentally. Answer: 17

58. Example 5-2a Locate the point named by the solution on a number line. Answer: Graph the solution of the equation Then draw a dot at the solution, 6.

59. Example 5-2b Answer: Graph the solution of the equation

60. Example 5-3a ENTERTAINMENT An adult paid $18.50 for herself and two students to see a movie. If the two student tickets cost $11 together, what is the cost of the adult ticket? Words Variable Equation The cost of one adult ticket and two student tickets is $18.50. Let a represent the cost of an adult movie ticket.

61. Example 5-3b Write the equation. Simplify. Replace a with 7.50 to make the equation true. Answer: The number 7.50 is the solution of the equation. So, the cost of an adult movie ticket is $7.50.

62. Example 5-3c ICE CREAM Julie spends $9.50 at the ice cream parlor. She buys a hot fudge sundae for herself and ice cream cones for each of the three friends who are with her. Find the cost of Julie’s sundae if the three ice cream cones together cost $6.30. Answer: $3.20

63. Example 5-4a MULTIPLE- CHOICE TEST ITEM What value of x is a solution of A 5 B 6 C 7 D 8 Read the Test Item Substitute each value for x to determine which makes the left side of the equation equivalent to the right side.

64. Example 5-4b Solve the Test Item false Replace x with 5. Replace x with 6. Replace x with 7. The value 7 makes the equation true. Answer: C true

65. Example 5-4c What value of x is a solution of MULTIPLE- CHOICE TEST ITEM A 34 B 35 C 36 D 9 Answer: B

66. End of Lesson 5

67. Lesson 6 Contents Example 1Use the Distributive Property Example 2Use the Distributive Property Example 3Use the Distributive Property Example 4Identify Properties Example 5Identify Properties Example 6Identify Properties Example 7Identify Properties

68. Example 6-1a Multiply. Add. Answer: 96 Use the Distributive Property to write as an equivalent expression. Then evaluate the expression.

69. Example 6-1b Answer: 4(6)+4(3); 36 Use the Distributive Property to write as an equivalent expression. Then evaluate the expression.

70. Example 6-2a Use the Distributive Property to write as an equivalent expression. Then evaluate the expression. Multiply. Add. Answer: 66

71. Example 6-2b Use the Distributive Property to write as an equivalent expression. Then evaluate the expression. Answer: 5(7)+ 3(7); 56

72. Example 6-3a VACATIONS Mr. Harmon has budgeted $150 per day for his hotel and meals during his vacation. If he plans to spend six days on vacation, how much will he spend? You can find how much Mr. Harmon will spend over the six-day period by finding 6 150. You can use the Distributive Property to multiply mentally.

73. Example 6-3b Rewrite 150 as 100 + 50. Distributive Property Multiply. Add. Answer: Mr. Harmon will spend about $900 on a six-day vacation.

74. Example 6-3c COOKIES Heidi sold cookies for $2.50 per box for a fundraiser. If she sold 60 boxes of cookies, how much money did she raise? Answer: $150

75. Example 6-4a Name the property shown by the statement Answer: Identity Property of Multiplication

76. Example 6-4b Answer: Identity Property of Multiplication Name the property shown by the statement.

77. Example 6-5a Answer: Commutative Property of Addition Name the property shown by the statement

78. Example 6-5b Answer: Commutative Property of Addition Name the property shown by the statement

79. Example 6-6a Answer: Identity Property of Addition Name the property shown by the statement

80. Example 6-6b Answer: Identity Property of Addition Name the property shown by the statement

81. Example 6-7a Answer: Associative Property of Multiplication Name the property shown by the statement

82. Example 6-7b Answer: Associative Property of Addition Name the property shown by the statement

83. End of Lesson 6

84. Lesson 7 Contents Example 1Describe Patterns in Sequences Example 2Describe Patterns in Sequences Example 3Determine Terms in Sequences Example 4Determine Terms in Sequences

85. Example 7-1a Describe the pattern in the sequence and identify the sequence as arithmetic, geometric, or neither. 3, 6, 12, 24, … 3, 6, 12, 24, … Answer: Each term is found by multiplying the previous term by 2. This sequence is geometric.

86. Example 7-1b Describe the pattern in the sequence and identify the sequence as arithmetic, geometric, or neither. 5, 9, 18, 22, 31, … Answer: Add 4, add 9; neither.

87. Example 7-2a Describe the pattern in the sequence and identify the sequence as arithmetic, geometric, or neither. 7, 11, 15, 19, … 7, 11, 15, 19, … Answer: Each term is found by adding 4 to the previous term. This sequence is arithmetic.

88. Example 7-2b Describe the pattern in the sequence and identify the sequence as arithmetic, geometric, or neither. 3, 11, 19, 27, … Answer: Add 8; arithmetic.

89. Example 7-3a Write the next three terms of the sequence. 5, 14, 23, 32,... 5, 14, 23, 32, … Continue the pattern to find the next three terms. Answer: The next three terms are 41, 50, and 59. Each term is 9 greater than the previous term.

90. Example 7-3b Write the next three terms of the sequence. 12, 17, 22, 27, … Answer: 32, 37, 42

91. Example 7-4a Write the next three terms of the sequence. 0.2, 1.2, 7.2, 43.2, … 0.2, 1.2, 7.2, 43.2, Continue the pattern to find the next three terms. Answer: The next three terms are 259.2, 1,555.2, and 9,331.2. Each term is 6 times the previous term. 9,331.2

92. Example 7-4b Write the next three terms of the sequence. 3, 12, 48, 192, … Answer: 768, 3,072, 12,288

93. End of Lesson 7

94. Lesson 8 Contents Example 1Convert Units of Length Example 2Convert Units of Length Example 3Convert Units of Mass Example 4Convert Units of Mass Example 5Convert Units of Capacity Example 6Convert Units of Capacity

95. Example 8-1a Answer: 280 Complete 28 cm mm. To convert from centimeters to millimeters, multiply by 10.

96. Example 8-1b Complete 3,400 mm cm. Answer: 340

97. Example 8-2a Complete 438 cm m. To convert from centimeters to meters, divide by 100. Answer: 4.38

98. Example 8-2b Complete 7.5 m cm. Answer: 750

99. Example 8-3a Complete 72 g mg. To convert from grams to milligrams, multiply by 1,000. Answer: 72,000

100. Example 8-3b Complete 4,550 mg g. Answer: 4.55

101. Example 8-4a Complete 202 g kg. To convert from grams to kilograms, divide by 1,000. Answer: 0.202

102. Example 8-4b Complete 6.25 kg g. Answer: 6,250

103. Example 8-5a Complete 2 L mL. To convert from liters to milliliters, multiply by 1,000. Answer: 2,000

104. Example 8-5b Complete 450 mL L. Answer: 0.45

105. Example 8-6a Complete 2.4 kL L. To convert from kiloliters to liters, multiply by 1,000. Answer: 2,400

106. Example 8-6b Complete 95.3 L kL. Answer: 0.0953

107. End of Lesson 8

108. Lesson 9 Contents Example 1Write a Number in Standard Form Example 2Write a Number in Scientific Notation Example 3Compute with Large Numbers

109. Example 9-1a Write in standard form. Move the decimal point 6 places to the right. Answer: 3,400,000

110. Example 9-1b Answer: 73,000 Write in standard form.

111. Example 9-2a Write 428,000 in scientific notation. Move the decimal point 5 places to find a number between 1 and 10. Answer:

112. Example 9-2b Write 1,750,000 in scientific notation. Answer:

113. Example 9-3a ASTRONOMY Pluto’s maximum distance from Earth is about 4.6 billion miles. One mile is equal to 5,280 feet. Find the approximate maximum distance of Pluto from Earth in feet. To find the approximate maximum distance in feet, multiply 4.6 billion by 5,280. Enter 4600000000 5280. ENTER

114. Example 9-3b The number on the calculator represents. Answer: The approximate maximum distance of Pluto from Earth is feet.

115. Example 9-3c CONSTRUCTION In order to build a new shopping center, 553,000 bricks were used. A new shopping mall built across town used twelve times as many bricks. About how many bricks were used to build the new shopping mall? Answer: about

116. End of Lesson 9

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