Main content

## Arithmetic (all content)

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

Lesson 3: Properties of multiplication- Properties of multiplication
- Properties and patterns for multiplication
- Commutative property of multiplication
- Associative property of multiplication
- Associative property of multiplication
- Distributive property
- Commutative property of multiplication review
- Associative property of multiplication review
- Distributive property review

© 2023 Khan AcademyTerms of usePrivacy PolicyCookie Notice

# 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

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

*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

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

*Want to learn more about the distributive property? Check out this video.*

*Want to know why the distributive property is helpful? Check out this article.*

## Want to join the conversation?

- Is the commutative property or the associative property related to the distributive property I dont really Know?(9 votes)
- 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.(15 votes)

- 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?(4 votes)
- 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(2 votes)

- what is really different between communtive and associative property(4 votes)
**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.(6 votes)

- Why is there something called distributive property in math? Why is it important?(0 votes)
- 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.(15 votes)

- How distributive property help??(2 votes)
- It makes algebra much easier, because one can factor everything out much more easily.(8 votes)

- Distributive property for 50x50(5 votes)
- the formatting of these questions makes a lot sense to me but the thing i am confused on is and adding the equal sign with the two answers of the numbers. I juts usually end up winding the answer without the format(4 votes)
- what if you knew all the problems do you still have to use the distributive property(3 votes)
- can we do more this is fun(3 votes)
- Okay so I found out that I just clicked the wrong one it would be multiplied I clicked addition not reading it right(3 votes)