Distributive Property - What Is the Distributive Property? Video
  1. Education

Your suggestion is on its way!

An email with a link to:


was emailed to:

Thanks for sharing About.com with others!

Video:What Is the Distributive Property?

with Bassem Saad

Want to learn about the distributive property and how it pertains to multiplication? Here, see helping information.See Transcript

Transcript:What Is the Distributive Property?

Hi my name is Bassem Saad. I'm an associate math instructor and a PhD candidate at UC Davis. I'm here today for About.com to answer the questions, what is the distributive property.

What Is the Distributive Property?

The distributive property is a rule that governs how you can multiply and add numbers at the same time. Note that the order of operations is already a way of handling this but the distribution property gives us another way of getting us the same result. So let a, b, and c be real numbers. And say we want to multiply a times the sum of b and c. You put b and c inside the parentheses because we want to add these numbers first. This expression will be equal to a times b + a times c. That's the same thing as distributing a to each summand inside the expression.

Examples of the Distributive Property?

For example, say we want to multiply 5 times the sum of 4 and 8. If we use the order of operations we have to add the four and the eight first because they're inside the parentheses. That gives us 12. And then 5 x 12 is 60. So with the distributive property we want to multiply 5 times each summand. So we distribute 5 to 4, that's 5 x 4. And then we distribute 5 to 8. That's 5 x 8. Then we add those results. So we've got 5 x 4 is 20, plus 5 x 8, which is 40, equals 60. So it agrees with the order of operations. So in another important example, let x be a variable. We can still use the distributive property to simplify and expression like this; x times the sum of 3 and x. Now you can't combine the sum of 3 and x. This is about as simplified as you can make it. But you can distribute this x onto the other two terms. So you distribute onto the 3 term, that's x times 3. And you distribute the x to the x term. That's x times x. So this whole expression equals 3x + x squared. That was the distributive property.

Thanks for watching and to learn more visit us on the web at About.com.
About videos are made available on an "as is" basis, subject to the User Agreement.

©2015 About.com. All rights reserved.