Associative, Distributive and Commutative Properties

All together on 1 page!

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
Commutative
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
Commutative
Summary: All 3 of these properties apply to multiplication

Subtraction

Property Example with Subtraction
Distributive Property
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
Associative Associative Property of Division
Commutative Commutative Property and Division
Summary: The distributive property does not apply to any of these 4 properties.

Practice Problems

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

Directions: Click on each question mark to see what property goes with the statement on the left.
Statement Property
7 + 2 = 2 + 7
6 + (2 + 11) = (6 + 2 ) + 11
5 (2 + 4) = 5 • 2 + 5 •4
(12 • 44) • 13 • 5= 12 • 44 • (13 • 5)
5 • 3 • 11 = 11 • 5 • 3
6 (3 +11+4) =6 • 3 + 6 •11+ 6 •4

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 question mark to see what property goes with the statement on the left.
Statement Property
a + c = c + a
a (x + y + z) =a • x + a •y + a •z
(a • y) • x • z= a • y • (x • z )