commutative property


Definition of Commutative Property

    Commutative property is one of the basic properties of numbers. The word “commute” means “exchange” or “swap over”.

    Commutative property states that numbers can be added or multiplied in any order.

    That is:

  • Commutative Property of Addition states that changing the order of addends does not change the sum. That is, a + b = b + a.


  • Commutative Property of Multiplication states that changing the order of factors does not change the product. That is, a × b = b × a.

Examples of Commutative Property

  • 2 + 3 = 3 + 2. Whether you add 3 to 2 or 2 to 3, you get 5 both ways.

  • 4 × 7 = 7 × 4. Whether you multiply 4 by 7 or 7 by 4, the product is the same, i.e. 28.

Commutative Property in real-life

  • Counting a combination of different coins reminds you of commutative property.

    Suppose you have 20 quarters and 10 dimes.

    It doesn’t matter whether you add the quarters first and then the dimes OR add the dimes first and then the quarters OR add a quarter and a dime alternately, finally the total is going to be $6.

More about Commutative Property

  • Commutative property holds for both addition and multiplication. That is: 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.

Solved Example on Commutative Property

(1) Rewrite the expression “4 + m + n” using the commutative property.

Solution:

Commutative property means to exchange or swap things. So, the answer is any of the following.


4 + m + n    =    m + 4 + n    OR    m + n + 4    OR    n + m + 4 OR
                           n + 4 + m    OR    4 + n + m
 


(2) Is 5 (3x) = (3x) 5 true?

Solution:

Yes it is. Because, just the positions of the terms 5 and 3x have been swapped. So, the equation above is true by the commutative property of multiplication.

Related Terms for Commutative Property

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