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E#19
Name _______________________________ Date __________ Class____
SOL 5.19 - Distributive Property
The distributive property states that you can multiply a sum by multiplying each addend separately,
then adding their products.
So…
8 x 23
= 8 x (20 + 3)
= (8 x 20) + (8 x 3)
= 160 + 24
= 184
Use the distributive property to solve the following equations.
1.
4 x 53
= __ x (__ + __)
2.
6 x 98
= __ x (__ + __)
3.
5 x 39
= __ x (__ + __)
= (__ x __) + (__ x __)
= (__ x __) + (__ x __)
= (__ x __) + (__ x __)
= ____ + ____
= ____ + ____
= ____ + ____
=
=
=
4.
7 x 26
5.
35 x 2
6.
29 x 6
7.
84 x 5
8.
73 x 7
9.
17 x 8
E#19
Simplifying with Parentheses
When simplifying expressions with parentheses, you will be applying the Distributive Property. That
is, you will be distributing over (multiplying through) a set of parentheses in order to simplify a given
expression.
The expression 3(5 + 7) is simplified as (3 x 5) + (3 x 7)
When a number is next to a set of parentheses, multiply. No “x” is needed.
Variables can also be used when simplifying expressions. For example:
6(n + 2) is simplified as (6 x n) + (6 x 2)
TRY THESE:
8(4 + 9) = (8 x ___) + (8 x ___)
7(k + 2) = (7 x ___) + (7 x ___)
Simplify the following expressions using the distributive property.
6(5 + 8) = _____________________
2(s + 6) = _____________________
9(n + 3) = _____________________
4(5 + 5) = _____________________
3(4 + 2) = _____________________
7(t + 4) = _____________________
5(8 + r) = _____________________
8(5 + 3) = _____________________
E#19
Breaking Up Numbers
When using the distributive property, break apart larger numbers to simplify them.
For example:
6 x 53
5 x 98
6 x (50 + 3)
74 x 9
5(90 + 8)
(70 + 4) x 9
TRY THESE:
8 x 56
3 x 87
4 x 23
65 x 2
8 x (___ + ___)
3(___ + ___)
4 x (___ + ___)
(___ + ___) x 2
Now, simplify these equations using the distributive property. The first one is done for
you!
4 x 78
3 x 87
9 x 62
8 x 34
76 x 2
32 x 5
99 x 5
53 x 4
22 x 9
= 4(70 x 8)
= (4 x 70) + (4 x 8)