Can you explain the distributive property?

Question

I really don't understand the distributive property of multiplication and addition. We are learning about it in school (grade 7) but I just don't understand how it works or how to use it properly. I kind of get it, but I really want to fully understand. Please explain in easy terms!

Answer 1

For 3 numbers a, b, and c, the distributive property is:

 

a*(b + c) = a*b + a*c

 

Let's try that with real numbers.  Let a=7, b=4, c=2:

 

7*(4+2)

 

We can solve this two ways.  The normal way is to add the 4 and the 2, then multiply by 7

7*(4+2) = 7*(6) = 42

 

Now let's try it using the distributive property:

 

7*(4+2) = 7*4 + 7*2 = 28 + 14 = 42

 

So using the distributive property gives the same answer.  For an easy introduction to the distributive property, check out the following website:

 

http://coolmath.com/prealgebra/06-properties/05-properties-distributive-01.htm