Contributor: Meghan Vestal. Lesson ID: 11703
Here is a twoforone property that includes addition and multiplication! A short, simple video, some practice, and birthday invitations "factor" in to make the distributive property clear!
In the previous Related Lessons, found in the righthand sidebar, you learned about the associative and commutative properties of addition.
Summarize each of these properties to your teacher or parent.
In this lesson, you will learn the final property of addition: the distributive property. The "distributive property of addition" is a little deceiving because it actually has to do with both addition and multiplication.
According to the distributive property, multiplying a number by two or more numbers added together will give you the same answer as multiplying a number by each of the individual numbers and adding the products together. This principle is illustrated in the following equation:
On the left side of the equal sign, B and C are added together first because they are in parentheses. Problems within parentheses are always solved first. Then, the sum is multiplied by A. On the right side of the equal sign, A is multiplied by B and C separately, then, the products are added together. Look at the example below to see how this works when we use numbers.
2 
x 
(3 + 5) 
= 
2 
x 
3 
+ 
2 
x 
5 

3 + 5 = 8  2 x 3 = 6  
8 x 2 = 16  2 x 5 = 10  
16  10 + 6 = 16  
16 
While each side of the equal sign appears to have a different value, they are actually the same. Look at the next example. Explain to your teacher or parent how the two sides of the equal sign are equal.
5 
x 
(4 + 10) 
= 
5 
x 
4 
+ 
5 
x 
10 
You should have told your teacher or parent the following:
5 
x 
(4 + 10) 
= 
5 
x 
4 
+ 
5 
x 
10 

4 + 10 = 14  5 x 4 = 20  
14 x 5 = 70  5 x 10 = 50  
70  20 + 50 = 70  
70 
Look back at the question at the beginning of the lesson. When you are distributing invitations to your birthday party, you are giving each of your friends an invitation.
Tell your teacher or parent.
With the distributive property, you are a simplifying a mathematical process by distributing the number outside the parentheses to each of the numbers inside the parentheses. Think of it like this: The number outside the parentheses is giving each of the numbers inside the parentheses an invitation to his birthday party.
For example, pretend you have four stacks of five invitations that need to be distributed to friends on the east side of town, and ten stacks of five invitations that need to be delivered to a group of friends who live on the west side.
You still deliver the 70 invitations, but you distribute your invitations in a more systematic way.
To review what you have learned about the distributive property, watch Distributive Law by Mathematics is Fun:
When you are finished watching the video, summarize the distributive property for your teacher or parent.
Then, move on to the Got It? section to practice solving problems with the distributive property.