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Fun Games
Geometry
Interactive
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Scientific Calc
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Algebra
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Trigonometry
Scientific Calc


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.
Distributive Property
picture of distributive rule
Associative Property

Commutative Property



Properies 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

Multipliction

Property
Example with Multiplication.
Distributive Property The distributive propert is an applicaiton 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 proprety 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 proprety 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 )