Commutative Property Definition

Definition: The Commutative property states that order does not matter. Multiplication and addition are commutative.

Examples

of the Commutative Property for Addition

• 4 + 2 = 2 + 4
• 5 + 3 + 2 = 5 + 2 + 3
• b + a = a + b (Yes, algebraic expressions are also commutative for addition)

Examples

of the Commutative Property for Multiplication

• 4 • 2 = 2 • 4
• 5 • 3 • 2 = 5 • 2 • 3
• a • b = b • a(Yes, algebraic expressions are also commutative for multiplication)

Examples

of the Commutative Property

Subtraction (Not Commutative)

Subtraction is probably an example that you know, intuitively, is not commutative .

• 4 − 2 $$ \color{red}{ \ne } $$ 2 − 4
• 4 −3 $$ \color{red}{ \ne } $$ 3 − 4
• a − b $$ \color{red}{ \ne } $$ b − a

In addition, division, compositions of functions and matrix multiplication are two well known examples that are not commutative..

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Division (Not Commutative)

Division is probably an example that you know, intuitively, is not commutative.

• 4 ÷ 2 $$ \color{red}{ \ne } $$ 2 ÷ 4
• 4 ÷ 3 $$ \color{red}{ \ne } $$ 3 ÷ 4
• a ÷ b $$ \color{red}{ \ne } $$ b ÷ a

In addition, division, compositions of functions and matrix multiplication are two well known examples that are not commutative..