SOL 5.19 Study Guide
Distributive Property
Learning Goals
5.19
The student will investigate and recognize the distributive property of multiplication over addition.
Distributive Property – Multiplying a sum by a number gives the same result as multiplying each
addend by the number and then adding the products.
(Yes, it sounds complicated. But if you study the example below, it will seem easier.
Examples and Explanations
8 x 23
= 8 x (20 + 3)
First, break apart one factor using expanded form
We’ve taken 23 and written it as the sum of two addends.
= (8 x 20) + (8 x 3)
Second, “distribute” the 8 over each addend
The factor 8 is multiplied by both 20 and 3
This is what the Distributive Property says is always true: that you will get
the same answer if you multiply 8 x 23 as you would when you multiply
8 x 20 and 8 x 3 and then add the two answers together.
= 160 + 24
Third, solve each equation in the parentheses
= 184
Finally, add the products
Additional examples:
6 x 53
6(50 + 3)
(6 x 50) + (6 x 3)
74 x 9
(70 + 4) x 9
(70 x 9) + (4 x 9)
See how one of the factors (53) is
split up into two addends (numbers
that are added together).
The only difference here is the
larger number (74) is written
first.
We usually split a number up into its expanded form to make the multiplication easier. But the number
can be split any way you want and the answer will be the same.
59 x 8
=
59 x 8 =
(50 x 8) + (9 x 8)
or
(40 x 8) + (19 x 8)
or
(20 x 8) + (39 x 8)
And it can be either factor that is split apart:
(59 x 4) + (59 x 4)
or (59 x 6) + (59 x 2)
Sample Questions
1. Which of the following makes the statement below true?
9 x 67 =
A
B
C
D
(9 x 60) + (9 x 7)
9 + (60 + 7)
(9 x 60) + 7
9 (60 x 7)
Look carefully to see in which example has one of the factors been split part into two addends,
and then each addend is multiplied by the other factor? It looks like A.
2. Which does NOT show the distributive property?
A
B
C
D
8(n + 6) = (8 x n) + (8 x 6)
(5 x 6 ) x 4 = 5 x (6 x 4)
7 x (50 + 3) = (7 x 50) + ( 7 x 3)
(5 + 4) x 7 = (5 x 7) + (4 x 7)
All of these, except one, is an example of a multiplication expression where one factor has been split up into
two addends and then multiplied by the other factor. The one example that does not show this, shows a
different property. Example B shows the associative property.
3. Which of the following shows the distributive property?
A
B
C
D
7 x 32 = 7 + 32
5+6=6+5
3 x 92 = 3 (90 + 2)
(3 + 4) + 9 = 3 + (4 + 9)
One of these shows that distributive property, one shows the commutative property of addition, (that’s
example B), one shows the associative property of addition (that’s example D), and one shows no property
at all. In fact, it’s downright wrong because the left side of the equation does not equal the right side at all.
That would be A.
And finally, a model to show that the Distributive Property works.
3 sets of (2+4) is the same as 3 sets of 2 added to 3 sets of 4