Use the Distributive Property. Multiply. Then
simplify.
5-4 The Distributive Property
Use the Distributive Property to evaluate the
expression.
26. (3 + 6)(–8)
SOLUTION: Use the Distributive Property. Multiply. Then add.
27. 4(11 – 5)
SOLUTION: Use the Distributive Property. Multiply. Then
subtract.
28. (12 – 4)(–5)
SOLUTION: Use the Distributive Property. Multiply. Then add.
Use the Distributive Property to rewrite the
expression.
29. –8(a + b)
SOLUTION: Use the Distributive Property. Multiply. Then
simplify.
30. (2b + 8)5
SOLUTION: Use the Distributive Property. Multiply. Then
simplify.
31. (p + 7)(–2)
31. (p + 7)(–2)
SOLUTION: Use the Distributive Property. Multiply. Then
simplify.
32. Justify Conclusions Theresa is planning on making
a fleece blanket for her nephew. She learns that the
fabric she wants to use is $7.99 per yard. Find the
total cost of 4 yards of fabric. Justify your answer by
using the Distributive Property.
SOLUTION: Rename $7.99 as $8.00 – $0.01. Then use the
Distributive Property. Multiply. Then subtract.
Theresa will pay $31.96 for 4 yards of fabric.
33. You are ordering T-shirts with your school’s mascot
printed on them. Each T-shirt costs $4.75. The
printer charges a setup fee of $30 and $2.50 to print
each shirt. Write two expressions that you could use
to represent the total cost of printing n T-shirts.
SOLUTION: Each T-shirt costs $4.75 plus $2.50 for printing.
There is a one-time charge of $30. Let n represent
the number of T-shirts to be printed.
Use the Distributive Property to determine an
equivalent expression. Multiply. Simplify.
Two expressions that represent the total cost of
printing n T-shirts are
.
and Use the Distributive Property to rewrite the
expression.
34. 0.5x(y – z)
SOLUTION: Rewrite y – z as y + (–z). Use the Distributive
Property. Multiply. Then simplify.
SOLUTION: Use the Distributive Property. Multiply. Then
simplify.
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35. –6a(2b + 5c)
Property. Multiply. Then simplify.
Two expressions that represent the total cost of
printing
n T-shirts Property
are
5-4 The
Distributive
.
and Use the Distributive Property to rewrite the
expression.
34. 0.5x(y – z)
SOLUTION: Rewrite y – z as y + (–z). Use the Distributive
Property. Multiply. Then simplify.
39. –6(12 p – 8n)
SOLUTION: Rewrite 12 p – 8n as 12 p + (–8n). Use the
Distributive Property. Multiply. Then simplify.
40. Write two equivalent expressions for the area of the
figure.
35. –6a(2b + 5c)
SOLUTION: Use the Distributive Property. Multiply. Then
simplify.
SOLUTION: The figure is a triangle. The area of a triangle is
36. –4m(3n – 6 p )
SOLUTION: Rewrite 3n – 6 p as 3n + (–6 p ). Use the
Distributive Property. Multiply. Then simplify.
. Replace b with 16 and h with x + 4. Use
the Distributive Property. Multiply. Simplify.
37. 3(2y + 4z)
SOLUTION: Use the Distributive Property. Multiply. Then
simplify.
41. A group of 3 seniors, 3 adults, and 3 children bought
tickets to the aquarium. 38. –2(3a – 2b)
SOLUTION: Rewrite 3a – 2b as 3a + (–2b). Use the Distributive
Property. Multiply. Then simplify.
Fill in the boxes to model the total amount spent with
an expression.
______ × ( ______ + ______ + ______)
How much did the group spend on tickets altogether?
How does applying the Distributive Property make it
easier to find this amount?
39. –6(12 p – 8n)
SOLUTION: Rewrite 12 p – 8n as 12 p + (–8n). Use the
Distributive Property. Multiply. Then simplify.
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SOLUTION: Write an expression for the situation:
3 seniors + 3 adults + 3 children
3($14.95) + 3($18.95) + 3($9.95)
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Since the Distributive Property is is defined to be a(b
+ c) = ab + ac, it can be used to rewrite the
expression as:
5-4 The Distributive Property
and then the sum can be multiplied by 3. This
requires fewer steps and easier computations than
multiplying each price by 3 and then adding the
resulting products.
41. A group of 3 seniors, 3 adults, and 3 children bought
tickets to the aquarium. Fill in the boxes to model the total amount spent with
an expression.
______ × ( ______ + ______ + ______)
How much did the group spend on tickets altogether?
How does applying the Distributive Property make it
easier to find this amount?
SOLUTION: Write an expression for the situation:
3 seniors + 3 adults + 3 children
3($14.95) + 3($18.95) + 3($9.95)
Since the Distributive Property is is defined to be a(b
+ c) = ab + ac, it can be used to rewrite the
expression as:
or
.
Evaluate the expression to determine how much was
spent altogether:
42. Celeste is going to summer camp. The table below
shows the cost of items she will need to purchase
with the camp logo.
Celeste needs to buy four of each item. Which of the
following expressions represents the total cost of the
items? Select all that apply.
4(14.75)
4(8.00) + 4.50 + 2.25
4(8) + 4(4.50) + 4(2.25)
4(8.00 + 4.50 + 2.25)
SOLUTION: Determine the expression needed and compare it to
the given expression.
First Expression: A T-shirt costs $8.00, a pair of
shorts costs $4.50, and a pair of socks costs $2.25.
All three items cost a total of
or $14.75. Since Celeste needs to buy 4 of each item,
4(14.75) can be used to find the total cost. This is an
expression that can be used.
So, the total cost was $131.55.
Sample answer: The ticket prices can be added first
and then the sum can be multiplied by 3. This
requires fewer steps and easier computations than
multiplying each price by 3 and then adding the
resulting products.
42. Celeste is going to summer camp. The table below
shows the cost of items she will need to purchase
with the camp logo.
Second Expression: A T-shirt costs $8.00, a pair of
shorts costs $4.50, and a pair of socks costs $2.25.
Celeste needs to buy 4 of each item, so
can be used to find the
total cost. This is an expression that can be used.
Third Expression: A T-shirt costs $8.00, a pair of
shorts costs $4.50, and a pair of socks costs $2.25.
Celeste needs to buy 4 of each item.
cannot be used to find the
total cost because only one item is multiplied by 4.
This is an expression that cannot be used.
Celeste needs to buy four of each item. Which of the
following expressions represents the total cost of the
items? Select all that apply.
Fourth Expression: A T-shirt costs $8.00, a pair of
shorts costs $4.50, and a pair of socks costs $2.25.
Celeste needs to buy 4 of each item, so
can be used to find the
total cost. This is an expression that can be used.
4(14.75)
4(8.00)- Powered
+ 4.50 +
eSolutions Manual
by2.25
Cognero
4(8) + 4(4.50) + 4(2.25)
4(8.00 + 4.50 + 2.25)
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