Associative, Distributive and Commutative Properties

To learn more about any of the properties below, visit that property's individual page.

Properties and Operations

Let's look at how (and if) these properties work with addition, multiplication, subtraction and division.

Addition

Property Example with Addition
Distributive Property picture of distributive rule
Associative associative property
Commutative commutative icon
Summary: All 3 of these properties apply to addition.

Multiplication

Property Example with Multiplication
Distributive Property The distributive property is an application of multiplication (so there is nothing to show here).
Associative associative icon
Commutative commutative icon
Summary: All 3 of these properties apply to multiplication.

Subtraction

Property Example with Subtraction
Distributive Property distributive over subtraction
Associative Associative Property of Subtraction
Commutative Commutative Property and Subtraction
Summary: The distributive property is the only one that applies to subtraction.

Division

Property Example with Subtraction
Distributive Property distributive over division
Associative Associative Property of Division
Commutative Commutative Property and Division
Summary: None of these properties applies to division.

Practice Problems

Which of the following statements illustrate the distributive, associate and the commutative property?

Directions: Click on each answer button to see what property goes with the statement on the left.

All three of these properties can also be applied to Algebraic Expressions.

Which of the following statements illustrate the distributive, associate and the commutative property?

Directions: Click on each answer button to see what property goes with the statement on the left.