Home Overview SiteMap Math Dictionary

# Commutative Property

Definition of Commutative Property

• Commutative Property of Addition: It states that changing the order of addends does not change the sum.
That is, a + b = b + a.
• Commutative Property of Multiplication: It states that changing the order of factors does not change the product.
That is, a × b = b × a.

• Addition and multiplication are commutative over the set of real numbers.
That means, for any two real numbers x and y, x + y = y + x and xy = yx.
• Subtraction and Division are not commutative.

### Examples of Commutative Property

• 2 + 3 = 3 + 2. Whether you add 3 to 2 or you add 2 to 3, you get 5 both ways.
• 4 × 7 = 7 × 4, Whether you multiply 4 by 7 or you multiply 7 by 4, the product is the same, 28.

### Solved Example on Commutative Property

Which of the following does not illustrate commutative property?

Choices:

A. ab - 1 = ab

B. a + b = b + a

C. ab = ba

D. Both B and C

Solution:

Step 1: According to commutative property, changing the order of addends or factors does not change the sum or product.

Step 2: Of the given choices, chocie ‘A’ does not illustrate commutative property.

### Related Terms for Commutative Property

• Subtraction
• Multiplication
• Division