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.
 

More about Commutative Property

  • 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

Correct Answer: A

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

  • Addition
  • Subtraction
  • Multiplication
  • Division
  • Addend
  • Factor
  • Sum
  • Product

 

Additional Links for Commutative Property