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- 1. Chapter 6 Algebra: Use Multiplication and Division Click the mouse or press the space bar to continue.
- 2. Algebra: Use Multiplication and Division 6 Lesson 6-1 Multiplication and Division Expressions Lesson 6-2 Problem-Solving Strategy: Work Backward Lesson 6-3 Order of Operations Lesson 6-4 Algebra: Solve Equations Mentally Lesson 6-5 Problem-Solving Investigation: Choose a Strategy Lesson 6-6 Algebra: Find a Rule Lesson 6-7 Balanced Equations
- 3. 6-1 Multiplication and Division Expressions Five-Minute Check (over Chapter 5) Main Idea California Standards Example 1 Example 2 Example 3
- 4. 6-1 Multiplication and Division Expressions • I will write and find the value of multiplication and division expressions.
- 5. 6-1 Multiplication and Division Expressions Standard 4AF1.1 Use letters, boxes, or other symbols to stand for any number in simple expressions or equations (e.g., demonstrate an understanding and the use of the concept of a variable).
- 6. 6-1 Multiplication and Division Expressions Jake had 4 boxes of apples. There are 6 apples in each box. Find the value of 4 × n if n = 6. 4×n Write the expression.
- 7. 6-1 Multiplication and Division Expressions 4×6 Replace n with 6. 24 Multiply 4 and 6.
- 8. 6-1 Multiplication and Division Expressions Marian has 5 CD cases. Each CD case has 2 CDs inside. Find the value of 5 × n if n = 2. A. 7 B. 10 C. 5 D. 2
- 9. 6-1 Multiplication and Division Expressions Find the value of x ÷ (3 × 2) if x = 30. In Lesson 3-1, you learned that you need to perform the operations inside parentheses first. x ÷ (3 × 2) Write the expression. 30 ÷ (3 × 2) Replace x with 30. 30 ÷ 6, or 5 Find (3 × 2) first. Then find 30 6. Answer: So, the value of x (3 2) if x = 30 is 5.
- 10. 6-1 Multiplication and Division Expressions Find the value of 45 (x × 1) if x = 5. A. 9 B. 45 C. 5 D. 1
- 11. 6-1 Multiplication and Division Expressions Judy has d dollars to buy bottles of water that cost $2 each. Write an expression for the number of bottles of water she can buy. Words Dollars divided by cost Variable Let d = dollars. Expression dollars divided by cost d ÷ $7 Answer: So the number of bottles of water Judy can buy is d 2.
- 12. 6-1 Multiplication and Division Expressions Toby has d dollars to spend on discounted books that cost $3 a piece. Write an expression for the number of books he can buy. A. d ÷ 3 B. d – 3 C. d + 3 D. d × 3
- 13. 6-2 Problem-Solving Strategy: Work Backward Five-Minute Check (over Lesson 6-1) Main Idea California Standards Example 1: Problem-Solving Strategy
- 14. 6-2 Problem-Solving Strategy: Work Backward • I will solve problems by working backward.
- 15. 6-2 Problem-Solving Strategy: Work Backward Standard 4MR1.1 Analyze problems by identifying relationships, distinguishing relevant from irrelevant information, sequencing and prioritizing information, and observing patterns.
- 16. 6-2 Problem-Solving Strategy: Work Backward Standard 4NS3.0 Students solve problems involving addition, subtraction, multiplication, and division of whole numbers and understand the relationships among the operations.
- 17. 6-2 Problem-Solving Strategy: Work Backward Currently, there are 25 students in the chess club. Last October, 3 students joined. Two months before that, in August, 8 students joined. How many students were in the club originally?
- 18. 6-2 Problem-Solving Strategy: Work Backward Understand What facts do you know? • Currently, there are 25 students in the club. • 3 students joined in October. • 8 students joined in August. What do you need to find? • The number of students that were in the club originally.
- 19. 6-2 Problem-Solving Strategy: Work Backward Plan Work backward to solve the problem.
- 20. 6-2 Problem-Solving Strategy: Work Backward Solve Work backward and use inverse operations. Start with the end result and subtract the students who joined the club. 25 – 3 22
- 21. 6-2 Problem-Solving Strategy: Work Backward Solve 22 – 8 14 Answer: So, there were 14 students in the club originally.
- 22. 6-2 Problem-Solving Strategy: Work Backward Check Look back at the problem. A total of 3 + 8 or 11 students joined the club. So, if there were 14 students originally, there would be 14 + 11 or 25 students in the club now. The answer is correct.
- 23. 6-3 Order of Operations Five-Minute Check (over Lesson 6-2) Main Idea and Vocabulary California Standards Key Concept: Order of Operations Example 1 Example 2
- 24. 6-3 Order of Operations • I will use the order of operations to find the value of expressions. • order of operations
- 25. 6-3 Order of Operations Standard 4AF1.2 Interpret and evaluate mathematical expressions that now use parentheses. Standard 4AF1.3 Use parentheses to indicate which operation to perform first when writing expressions containing more than two terms and different operations.
- 26. 6-3 Order of Operations
- 27. 6-3 Order of Operations Find the value of 12 – (4 + 2) ÷ 3. 12 – (4 + 2) ÷ 3 Write the expression. 12 – 6 ÷3 Parentheses first. (2 + 4) = 6 12 – 2 Multiply and divide from left to right. 6÷3=2 10 Add and subtract from left to right. 12 – 2 = 10
- 28. 6-3 Order of Operations Find the value of 21 (3 + 4) + 5. A. 16 B. 1 C. 8 D. 12
- 29. 6-3 Order of Operations Find the value of 4x + 3y ÷ 2, when x = 7 and y = 2. Follow the order of operations. 4x + 3y ÷ 2 = 4 7+3×2÷2 Replace x with 7 and y with 2. = 28 + 3 Multiply and divide from left to right. = 31 Add. Answer: 31
- 30. 6-3 Order of Operations Find the value of 3x – 2y + 12 when x = 5 and y = 3. A. 19 B. 11 C. 21 D. 12
- 31. 6-4 Algebra: Solve Equations Mentally Five-Minute Check (over Lesson 6-3) Main Idea California Standards Example 1 Example 2 Example 3 Multiplication and Division Equations
- 32. 6-4 Algebra: Solve Equations Mentally • I will solve multiplication and division equations mentally.
- 33. 6-4 Algebra: Solve Equations Mentally Standard 4AF1.1 Use letters, boxes, or other symbols to stand for any number in simple expressions or equations (e.g., demonstrate an understanding and the use of the concept of a variable).
- 34. 6-4 Algebra: Solve Equations Mentally Mansis’s Used Car Lot has 8 rows of cars with a total of 32 cars. Solve 8 × c = 32 to find how many cars are in each row.
- 35. 6-4 Algebra: Solve Equations Mentally One Way: Use Models Step 1 Model the equation.
- 36. 6-4 Algebra: Solve Equations Mentally One Way: Use Models Step 2 Find the value of c. 8 × c = 32 Answer: So, c = 4.
- 37. 6-4 Algebra: Solve Equations Mentally Another Way: Mental Math 8 × c = 32 8 × 4 = 32 You know that 8 × 4 = 32. Answer: So, c = 4.
- 38. 6-4 Algebra: Solve Equations Mentally Kyung has just planted a garden. He has a total of 49 vegetables with 7 vegetables in each row. Solve 7 x = 49 to find how many rows of vegetables there are. A. 6 B. 7 C. 8 D. 49
- 39. 6-4 Algebra: Solve Equations Mentally Solve 16 ÷ s = 8. 16 ÷ s = 8 16 ÷ 2 = 8 s=2 You know that 16 2 = 8. Answer: So, the value of s is 2.
- 40. 6-4 Algebra: Solve Equations Mentally Solve 36 p = 6. A. 6 B. 7 C. 8 D. 9
- 41. 6-4 Algebra: Solve Equations Mentally Six friends went shopping. They each bought the same number of t-shirts. A total of 24 t-shirts were bought. Write and solve an equation to find out how many t-shirts each person bought. Write the equation. Words 6 friends bought 24 t-shirts Variable Let t = the number of t-shirts bought per person. Expression 6 t = 24
- 42. 6-4 Algebra: Solve Equations Mentally Solve the equation. 6 t = 24 6 4 = 24 t=4 Answer: So each person bought 4 t-shirts.
- 43. 6-4 Algebra: Solve Equations Mentally Six friends went to a driving range and hit a total of 54 golf balls. If they all hit the same number of golf balls, how many did each one hit? A. 7 B. 8 C. 9 D. 10
- 44. 6-5 Problem-Solving Investigation: Choose a Strategy Five-Minute Check (over Lesson 6-4) Main Idea California Standards Example 1: Problem-Solving Investigation
- 45. 6-5 Problem-Solving Investigation: Choose a Strategy • I will choose the best strategy to solve a problem.
- 46. 6-5 Problem-Solving Investigation: Choose a Strategy Standard 4MR1.1 Analyze problems by identifying relationships, …, and observing patterns.
- 47. 6-5 Problem-Solving Investigation: Choose a Strategy 4NS3.0 Students solve problems involving addition, subtraction, multiplication, and division of whole numbers and understand the relationships among the operations.
- 48. 6-5 Problem-Solving Investigation: Choose a Strategy MATT: I take 30-minute guitar lessons two times a week. There are four weeks in a month. How many minutes do I have guitar lessons each month? YOUR MISSION: Find how many minutes Matt has guitar lessons each month.
- 49. 6-5 Problem-Solving Investigation: Choose a Strategy Understand What facts do you know? • Each lesson Matt takes is 30 minutes long. • He takes lessons two times a week. • There are four weeks in a month. What do you need to find? • Find how many minutes Matt has guitar lessons each month.
- 50. 6-5 Problem-Solving Investigation: Choose a Strategy Plan You can use the four-step plan along with addition and multiplication to solve the problem.
- 51. 6-5 Problem-Solving Investigation: Choose a Strategy Solve Find how many minutes Matt has lessons each week. 30 lesson 1 + 30 lesson 2 60 minutes per week
- 52. 6-5 Problem-Solving Investigation: Choose a Strategy Solve Find how many minutes Matt has lessons each week. 60 minutes per week × 4 weeks per month 240 minutes per month Answer: So, Matt has lessons 240 minutes each month.
- 53. 6-5 Problem-Solving Investigation: Choose a Strategy Check Matt has lessons 30 + 30 or 60 minutes each week. This means he has 60 + 60 + 60 + 60 or 240 minutes of lessons each month. So, the answer is correct.
- 54. 6-6 Algebra: Find a Rule Five-Minute Check (over Lesson 6-5) Main Idea California Standards Example 1 Example 2 Example 3
- 55. 6-6 Algebra: Find a Rule • I will find and use a rule to write an equation.
- 56. 6-6 Algebra: Find a Rule Standard 4AF1.5 Understand that an equation such as y = 3x + 5 is a prescription for determining a second number when a first number is given.
- 57. 6-6 Algebra: Find a Rule Mike earns $10 when he babysits for 2 hours. He earns $20 when he babysits for 4 hours. If he babysits for 6 hours, he earns $30. Write a rule that describes the money Mike earns. Put the information in a table. Then look for a pattern to describe the rule.
- 58. 6-6 Algebra: Find a Rule Pattern: 2 × 5 = 10 4 × 5 = 20 6 × 5 = 30 Rule: Multiply by 5. Equation: x × 5 = y
- 59. 6-6 Algebra: Find a Rule Ricardo earns $16 dollars when he mows 2 lawns of grass. He earns $32 when he mows 4 lawns, and $48 when he mows 6 lawns. Write a rule that describes the money Ricardo earns. A. 8x = y B. x+y=8 C. 2x + 8 = y D. x×8=y
- 60. 6-6 Algebra: Find a Rule Use the equation from Additional Example 1 to find how much money Mike earns for babysitting for 8, 9, or 10 hours.
- 61. 6-6 Algebra: Find a Rule x×5=y 8 × 5 = $40 40 x×5=y x×5=y 45 9 × 5 = $45 10 × 5 = $50 50 Answer: So, Mike will earn $40, $45, or $50 if he babysits for 8, 9, or 10 hours.
- 62. 6-6 Algebra: Find a Rule Use the equation x 8 = y to find how much money Ricardo earns for mowing 7 or 8 lawns. A. $49, $64 B. $15, $16 C. $56, $64 D. $63, $72
- 63. 6-6 Algebra: Find a Rule The cost of admission into a water park is shown in the table to the right. Find a rule that describes the number pattern. Then use the rule to write an equation.
- 64. 6-6 Algebra: Find a Rule Pattern: 6÷6=1 12 ÷ 6 = 2 18 ÷ 6 = 3 Rule: Divide by 6. Equation: c ÷ 6 = n
- 65. 6-6 Algebra: Find a Rule The cost of admission into a basketball game is shown in the table below. Find a rule that describes the number pattern. Then use the rule to write an equation. A. c÷9=n B. c+9=n C. c+n=9 D. c–9=n
- 66. 6-6 Algebra: Find a Rule Use the equation from Additional Example 3 to find how many people will be admitted to the park for $24, $30, and $36.
- 67. 6-6 Algebra: Find a Rule c÷6=n 24 ÷ 6 = 4 c÷6=n c÷6=n 4 30 ÷ 6 = 5 36 ÷ 6 = 6 5 6 Answer: So, $24, $30, and $36 will by 4, 5, and 6 people tickets.
- 68. 6-6 Algebra: Find a Rule Use the equation c 9 = n to find how many people will be admitted to the basketball game for $45 and $63. A. 4, 5 B. 5, 6 C. 7,8 D. 5, 7
- 69. 6-7 Balanced Equations Five-Minute Check (over Lesson 6-6) Main Idea California Standards Example 1 Example 2 Example 3
- 70. 6-7 Balanced Equations • I will balance multiplication and division equations.
- 71. 6-7 Balanced Equations Standard 4AF2.2 Know and understand that equals multiplied by equals are equal.
- 72. 6-7 Balanced Equations Show that the equality of 6r = 24 does not change when each side of the equation is divided by 6. 6r = 24 Write the equation. 6r ÷ 6 = 24 ÷ 6 Divide each side by 6. r=4 So, r = 4.
- 73. 6-7 Balanced Equations Check 6r = 24 6 × 4 = 24 24 = 24
- 74. 6-7 Balanced Equations Show that the equality of 3y = 9 does not change when each side of the equation is divided by 3. A. 3y ÷ 3 = 9 ÷ 3; 6 = 6 B. 3y ÷ 3 = 9 ÷ 3; 3 = 3 C. 3y ÷ 3 = 9; 9 = 9 D. 3y = 9 ÷ 3; 3 = 9
- 75. 6-7 Balanced Equations Show that the equality of q ÷ 7 = 4 does not change when each side of the equation is multiplied by 7. q÷7=4 Write the equation. q÷7×7=4×7 Multiply each side by 4. q = 28 So, q = 28.
- 76. 6-7 Balanced Equations Check q÷7=4 28 ÷ 7 = 4 4=4
- 77. 6-7 Balanced Equations Show that the equality v 5 = 5 does not change when each side of the equation is multiplied by 5. A. v 5 5 = 5; 10 = 10 B. v 5 5=5 5; 25 = 25 C. v 5 = 5; 5 = 5 D. v 5 5=5 5; 10 = 10
- 78. 6-7 Balanced Equations Find the missing number in 5 × 10 × 4 = 50 × . 5 × 10 × 4 = 50 × Write the equation. 5 × 10 × 4 = 50 × You know that 5 × 10 = 50. Each side of the equation must be multiplied by the same number to keep the equation balanced. Answer: So, the missing number is 4.
- 79. 6-7 Balanced Equations Find the missing number in 8 5 3 = 40 . A. 8 B. 5 C. 3 D. 40
- 80. 6-7 Balanced Equations Find the missing number in 2 × 12 ÷ 4 = 24 × . 2 × 12 ÷ 4 = 24 × Write the equation. 2 × 12 ÷ 4 = 24 × You know that 2 × 12 = 24. Each side of the equation must be divided by the same number to keep the equation balanced. Answer: So, the missing number is 4.
- 81. 6-7 Balanced Equations Find the missing number in 4 11 2 = 44 . A. 4 B. 11 C. 44 D. 2
- 82. Algebra: Use Multiplication and Division 6 Five-Minute Checks Multiplication and Division Equations
- 83. Algebra: Use Multiplication and Division 6 Lesson 6-1 (over Chapter 5) Lesson 6-2 (over Lesson 6-1) Lesson 6-3 (over Lesson 6-2) Lesson 6-4 (over Lesson 6-3) Lesson 6-5 (over Lesson 6-4) Lesson 6-6 (over Lesson 6-5) Lesson 6-7 (over Lesson 6-6)
- 84. Algebra: Use Multiplication and Division 6 (over Chapter 5) Tell whether 13 is composite, prime, or neither. A. composite B. prime C. neither
- 85. Algebra: Use Multiplication and Division 6 (over Chapter 5) Tell whether 26 is composite, prime, or neither. A. composite B. prime C. neither
- 86. Algebra: Use Multiplication and Division 6 (over Chapter 5) Tell whether 37 is composite, prime, or neither. A. composite B. prime C. neither
- 87. Algebra: Use Multiplication and Division 6 (over Chapter 5) Tell whether 1 is composite, prime, or neither. A. composite B. prime C. neither
- 88. Algebra: Use Multiplication and Division 6 (over Chapter 5) Tell whether 21 is composite, prime, or neither. A. composite B. prime C. neither
- 89. Algebra: Use Multiplication and Division 6 (over Lesson 6-1) Find the value of each expression if m = 4 and n = 8. m 10 A. 18 B. 14 C. 40 D. 80
- 90. Algebra: Use Multiplication and Division 6 (over Lesson 6-1) Find the value of each expression if m = 4 and n = 8. 3 (n m) A. 1.5 B. 6 C. 12 D. 36
- 91. Algebra: Use Multiplication and Division 6 (over Lesson 6-1) Find the value of each expression if m = 4 and n = 8. (12 m) n A. 6 B. 16 C. 24 D. 64
- 92. Algebra: Use Multiplication and Division 6 (over Lesson 6-1) Find the value of each expression if m = 4 and n = 8. (n m) 2 A. 6 B. 16 C. 24 D. 64
- 93. Algebra: Use Multiplication and Division 6 (over Lesson 6-2) Work backward to solve the problem. Lance had 4 granola bars left from his weekend hike. On Saturday, he ate 2 bars. Before he left for the trip on Friday, his mother added 5 bars to what he had. How many bars did he have to start with? A. 7 bars B. 5 bars C. 3 bars D. 1 bar
- 94. Algebra: Use Multiplication and Division 6 (over Lesson 6-3) Find the value of each expression. 4 + (5 2) – 1 A. 6 B. 11 C. 13 D. 14
- 95. Algebra: Use Multiplication and Division 6 (over Lesson 6-3) Find the value of each expression. 6+6 3 A. 12 B. 15 C. 24 D. 36
- 96. Algebra: Use Multiplication and Division 6 (over Lesson 6-3) Find the value of each expression. (17 – 3) – (2 4) A. 6 B. 7 C. 8 D. 22
- 97. Algebra: Use Multiplication and Division 6 (over Lesson 6-3) Find the value of each expression. (21 3) + 3 A. 9 B. 10 C. 21 D. 22
- 98. Algebra: Use Multiplication and Division 6 (over Lesson 6-4) Solve each equation mentally. 5 x = 25 A. 4 B. 20 C. 5 D. 6
- 99. Algebra: Use Multiplication and Division 6 (over Lesson 6-4) Solve each equation mentally. 56 m=8 A. 8 B. 48 C. 49 D. 7
- 100. Algebra: Use Multiplication and Division 6 (over Lesson 6-4) Solve each equation mentally. r 7=3 A. 21 B. 3 C. 24 D. 7
- 101. Algebra: Use Multiplication and Division 6 (over Lesson 6-4) Solve each equation mentally. k 9 = 36 A. 3 B. 45 C. 4 D. 36
- 102. Algebra: Use Multiplication and Division 6 (over Lesson 6-5) Use any strategy to solve. Tell which strategy you used. Jacobo is 6 years old and his brother is 2 years old. How old will each of them be when Jacobo is twice his brother’s age? A. Jacobo will be 12 and his brother will be 6. B. Jacobo will be 8 and his brother will be 4. C. Jacobo will be 7 and his brother will be 3. D. Jacobo will be 10 and his brother will be 6.
- 103. Algebra: Use Multiplication and Division 6 (over Lesson 6-6) Find a rule and equation that describes the pattern. Then use the equation to find the missing number. A. multiply by 4; x 4 = y; 18 B. add 8; x + 8 = y; 14 C. multiply by 3; x 3 = y; 18 D. multiply by 3; y 3 = x; 18
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