L
esson
The D
1
.7
istribu
tive P
roper
ty
Essential Question: How do you use
the distributive property?
Before we
start…
Match the following:
1. 20 (3 + 14 ) = ?
A. 15 ⋅14 − 15 ⋅ 3
2. 15 (14 − 3) = ?
3. 12 (23 + 6 ) = ?
B. 12 ⋅ 23 + 12 ⋅ 6
C. 20 ⋅ 3 + 20 ⋅14
Camping You and a friend are going on a camping trip.
You each buy a backpack that costs $90 and a sleeping
bag that costs $60. What is the total cost of the camping
trip?
What are equivalent numerical
expressions?
2 (90 + 60 )
2 (90 ) + 2 (60 )
Numerical
expressions that
have the same
value.
What is the distributive property?
It allows you to rewrite an
expression as an equivalent
expression to find the product
of a number and a sum or
difference.
This combines
multiplication and
addition.
When you use the distributive property, you
distribute, or multiply, the number outside the
parentheses to each number inside the
parentheses:
The Distributive Property
a (b + c ) = ab + ac
a (b − c ) = ab − ac
Another Way to Look at Distributive
Property
(b + c )a = ba + ca
(b − c )a = ba − ca
How do you use the distributive property?
• You multiply the term on the outside with each
term on the inside.
• Then simplify if necessary.
Use the distributive property to evaluate the
expression.
3(8 + 5)
(2 + 9)2
Use the distributive property to evaluate the
expression.
6(11 − 4)
(3 − 14)(−5)
Use the distributive property to evaluate the
expression.
4(105)
3(97)
Use the distributive property to evaluate the
expression.
5(2.9)
3(5.95)
What are equivalent variable expressions?
Two variable
expressions that have
the same value
You can use the
distributive property to
write equivalent variable
expressions.
Write an equivalent expression.
4 ( y + 3)
(n + 4 )(−2 )
Write an equivalent expression.
3 (x + 7 )
(2 − n )8
Write an equivalent expression.
−5 (x − 6 )
(x − 7 )(−3)
Write an equivalent expression.
−5 (2 y − 3)
(4 x + 2 )(7 )
Simplify
8(𝑥 + 2)
(7 − 𝑡)(−4)
Simplify
9(3𝑚 + 5)
−2(6𝑦 − 4)
Find the area of the figure below.
Find the area of the figure below.
Find the area of the figure below.
Find the area of the figure below.
• How do you use the distributive property?
Ticket Out the Door
Simplify the expression.
5 (x − 8 )