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  
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  
Commutative  
Summary: The distributive property is the only one that applies to subtraction. 
Division
Property  Example with Subtraction  

Distributive Property 


Associative  
Commutative  
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 ) 