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 ) |