4-1 The Distributive Property
MENTAL MATH Find each product mentally. Justify your answer.
31. 8 • 22
SOLUTION: 32. 13 • 39
SOLUTION: 33. 19 • 41
SOLUTION: 34. 29 • 13
SOLUTION: 35. 75 • 40
SOLUTION: 36. 95 • 38
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37. 9 • 49
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4-1 The Distributive Property
36. 95 • 38
SOLUTION: 37. 9 • 49
SOLUTION: 38. 31 • 11
SOLUTION: 39. 121 • 15
SOLUTION: 40. MONEY Sarah charges $6.50 per hour to babysit. She babysat for 3 hours on Friday, and 5 hours on Saturday.
Write two equivalent expressions for her total wages. Then find her total wage.
SOLUTION: To find her total wages, multiply her hourly rate by the total number of hours she babysat. Her total wages can be
expressed as $6.50(3 + 5) or $6.50(3) + $6.50(5).
Sarah made a total of $52.00 babysitting.
41. ENTERTAINMENT Admission to the state fair is $8 for adults and $7 for students. Write two equivalent
expressions if two adults and two students go to the fair. Then find the total admission cost.
SOLUTION: The total admission cost for two students and two adults can be expressed as 2($8 + $7) or 2($8) + 2($7).
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The fair admission will cost $30 for two adults and two students.
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4-1 The Distributive Property
Sarah made a total of $52.00 babysitting.
41. ENTERTAINMENT Admission to the state fair is $8 for adults and $7 for students. Write two equivalent
expressions if two adults and two students go to the fair. Then find the total admission cost.
SOLUTION: The total admission cost for two students and two adults can be expressed as 2($8 + $7) or 2($8) + 2($7).
The fair admission will cost $30 for two adults and two students.
Use the Distributive Property to write each expression as an equivalent expression. Then evaluate the
expression. (Hint:
can be written as a sum of 3 +
.)
43. SOLUTION: 44. SOLUTION: 45. SOLUTION: eSolutions Manual - Powered by Cognero
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4-1 The Distributive Property
45. SOLUTION: 46. SOLUTION: 47. COSTUMES Aiko uses
yards of fabric to make costumes for a play. Use the Distributive Property to find how much fabric she will need if she makes 9 costumes.
SOLUTION: To make 9 costumes, Aiko will need 21 yards of fabric.
Use the Distributive Property to write each expression as an equivalent algebraic expression.
48. 3(a + b)
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4-1 The Distributive Property
To make 9 costumes, Aiko will need 21 yards of fabric.
Use the Distributive Property to write each expression as an equivalent algebraic expression.
48. 3(a + b)
SOLUTION: 49. (e + f )(–5)
SOLUTION: 50. –6(x – y)
SOLUTION: 51. −4( j – k)
SOLUTION: 52. 10(r – s)
SOLUTION: 53. (u – w)(8)
SOLUTION: 56. ERROR ANALYSIS Julia and Catelyn are using the Distributive Property to simplify 3(x + 2). Is either of them
correct? Explain your reasoning.
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4-1 The Distributive Property
56. ERROR ANALYSIS Julia and Catelyn are using the Distributive Property to simplify 3(x + 2). Is either of them
correct? Explain your reasoning.
SOLUTION: Catelyn is correct because each number inside the parentheses should be multiplied by 3.
57. CHALLENGE Is 3 + (x • y) = (3 + x) • (3 + y) a true statement? If so, explain your reasoning. If not, give a
counterexample.
SOLUTION: 3 + (x • y) ? (3 + x) • (3 + y)
Substitute 4 for x and 5 for y, then evaluate to determine if the two expressions are equal.
No, 3 + (x • y) is not equal to (3 + x) • (3 + y).
58. WRITING IN MATH Explain how you can use the Distributive Property and mental math to simplify
.
SOLUTION: Sample answer: You can break up
2(4 +
)+
(4 + to be 2 + ). Distribute 2 • 4 + 2 • + and • 4 +
to be 4 + • . Then set up the multiplication expression
. Add 8 + 1 + 2 +
= .
Find each sum or difference. Write in simplest form.
63. SOLUTION: 64. SOLUTION: eSolutions Manual - Powered by Cognero
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4-1 The Distributive Property
64. SOLUTION: 65. SOLUTION: 66. SOLUTION: 67. SEWING Jessica needs
yards of fabric to make a skirt and yards to make a coat. How much fabric does she need in all?
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4-1 The Distributive Property
67. SEWING Jessica needs
yards of fabric to make a skirt and yards to make a coat. How much fabric does she need in all?
SOLUTION: Jessica needs
yards of fabric.
Write each subtraction expression as an addition expression.
73. 9 – 12
SOLUTION: 9 – 12 = 9 + –12
74. –2 – 6
SOLUTION: –2 – 6 = –2 + –6
75. –10 – (–3)
SOLUTION: –10 – (–3) = –10 + 3
76. –12 – 14
SOLUTION: –12 – 14 = –12 + –14
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