The Distributive Property
The distributive property is mental math strategy that can be used when
multiplying.
43 x 5 =?
Break apart the double-digit number.
43 x 5 =?
40 3+
Then multiply each part by 5.
43 x 5 =?
40 3 x 5 x 5
+
Then multiply each part by 5.
43 x 5 =?
40 3 x 5 x 5 200 15
+
Finally, sum your two products
43 x 5 =215
40 3 x 5 x 5 200 15+ = 215
+
Let’s look at another example.
53 x 6 = ?
Break apart the double-digit number.
53 x 6 = ?
Break apart the double-digit number.
53 x 6 = ?
50 3+
Multiply each part by 6.
53 x 6 = ?
50 3 x 6 x 6
+
Multiply each part by 6.
53 x 6 = ?
50 3 x 6 x 6 300 18
+
Sum the two products.
53 x 6 = 318
50 3 x 6 x 6 300 + 18 = 318
+
Example 1
5(3 + 2)
Proof: 5(3+2) = 5(5) = 25
15 + 10 = 25
D.P. with Addition
3(x + 2) =
Use the Distributive Property:
3(x) + 3(2)=
Now multiple:
3x + 6
This your answer
Practice
2(x + 5)=
2(5 + x)=
x(2 +5)=
Answers
2(x + 5)= 2x + 10
2(5 + x)= 10 + 2x
x(2 +5)= 2x + 10
D.P. with Subtraction
Example:
Apply the Distributive Property
3(1 –y)=
Multiply, and keep the subtraction sign
3(1) – 3(y)
Your answer
3 – 3y
Practice
2(x –5) =
3(5 –x) =
(x –5)3 =
Answers
2(x –5) = 2x -10
3(5 –x) = 15 -3x
(x –5)3 = 3x -15
Your Turn
• Use the distributive property to rewrite the expression without parenthesis
1. 3(x + 4)
2. - (y – 9)
3. x(x + 1)
4. 2(3x – 1)
5. (2x – 4)(-3)