If you're seeing this message, it means we're having trouble loading external resources on our website.

If you're behind a web filter, please make sure that the domains *.kastatic.org and *.kasandbox.org are unblocked.

## Arithmetic (all content)

### Course: Arithmetic (all content)>Unit 3

Lesson 3: Properties of multiplication

# Distributive property review

Review the basics of the distributive property, and try some practice problems.

### What is the distributive property?

The distributive property says that in a multiplication problem, when one factor is rewritten as the sum of two numbers, the product doesn't change.
Using the distributive property allows us to solve two simpler multiplication problems.
Example:
We can change 4, times, 12 into 4, times, left parenthesis, start color #01a995, 10, end color #01a995, plus, start color #74cf70, 2, end color #74cf70, right parenthesis.
The 4 gets distributed to the start color #01a995, 10, end color #01a995 and start color #74cf70, 2, end color #74cf70 and the problem changes to:
left parenthesis, 4, times, start color #01a995, 10, end color #01a995, right parenthesis, plus, left parenthesis, 4, times, start color #74cf70, 2, end color #74cf70, right parenthesis
The array of dots on the left shows left parenthesis, start color #01a995, 4, times, 10, end color #01a995, right parenthesis. The array of dots on the right shows left parenthesis, start color #74cf70, 4, times, 2, end color #74cf70, right parenthesis.
Now we can add the expressions to find the total.
left parenthesis, start color #01a995, 4, times, 10, end color #01a995, right parenthesis, plus, left parenthesis, start color #74cf70, 4, times, 2, end color #74cf70, right parenthesis
equals, start color #01a995, 40, end color #01a995, plus, start color #74cf70, 8, end color #74cf70
equals, 48

## Practice

Problem 1
• Current
The dots below represent 12, times, 2. They are broken up into two groups.
Which expression can we use to calculate the total number of dots?

Want to try more problems like this? Check out this exercise.

## Want to join the conversation?

• Is the commutative property or the associative property related to the distributive property I dont really Know?
• They're each their own property and they are all related to each other. They're all used together in some ways when simplifying expressions.
• What if your math teacher teaches you, a different way, and she can't even tell me what to do if the sentence says 7+2n=? or 2(7+n)=? What can i do?
• Eyal Meltser is correct, however I believe the answer is 14 + 2n because you multiply both 7 and n by 2. Perhaps if I am mistaken please correct me and explain why that is so. Thanks! :D
• what is really different between communtive and associative property
• COMMUTATIVE property states that two numbers can be added or multiplied in any order which will have no effect on the sum or the product of the number.For ex. 2*5=10 and 5*2 also equals 10. and
ASSOCIATIVE property states that while adding or multiplying three numbers they can be grouped in any order without having any effect on the answer. For ex.2*(5*6)=60 and also (2*5)*6=60.
• Why is there something called distributive property in math? Why is it important?
• When you 1st learn the distributive property working with just numbers, it may appear like it isn't needed. If you had something like "3 (5 + 2)", it is just as easy to add, then multiply as to apply the distributive property. However, when you start working with variables and numbers in algebra, the distributive property is often the only way to eliminate parentheses and satisfy PEMDAS requirements. You'll learn more about this when you get into algebra.
• How distributive property help??