Commutative Property of Addition & Its Laws

You are facing a problem in understanding the term “commutative property of addition.” Then do not worry; here, we will explain everything about a commutative property with examples. The commutative property definition states that modifying the order of numbers we add does not change the sum of digits. It means that you do not have to worry about the arrangement of numbers while performing arithmetic operations. Moreover, it is only relevant for addition and multiplication processes. It has two properties: Addition’s commutative and Multiplication’s commutative properties. So we can swap the order of the numbers when adding or multiplying the numbers. So here we will quote an example for you.

For example: 2+3=3+2 =5, LHS=RHS

The above example shows that you can change the order but still get the same answer while adding or multiplying.

Background of Commutative Property

The word first originated from the French, “Commute or Commuter” means to move or switch around, together with the suffix “ative” which means “Tend to.” It was also famous in ancient times. However, the standard use of the commutative property started at the end of the 18th century. So the actual meaning of the word is to tend and switch the order of the numbers. By changing the integers’ order, the answer will remain the same.

What is Commutative Property of Addition

commutative property of addition example
commutative property of addition example

We know that the commutative property states that you can change the order of integers while performing the arithmetic operation and still get the same result. It can be written as a+(b+c) = (a+b)+c.

For example, if you add 5, 4, and 3 together, the property says you will get the same result if you change orders like 3, 4, and 5. The answer will be the same. Put the values in the formula 5 + (4+3) = (5+4) + 3. You can get the same answer by using the property.

Moreover, let’s think that if you have 4 dresses and your sister bought 2 dresses for you, how many dresses do you have? The answer will be 6, and we do not care where the dresses are and in which order they are placed, but we know that the total number of dresses is 6. So it means that you can put the numbers in any order. It does not affect your answer.

Key Facts of Commutative Property

  • The Property is only appropriate for just two arithmetic operations, such as Addition & Multiplication.
  • Modifying the order of numbers does not change the result.
  • Commutative property of *addition: A+B=B+A
  • Commutative Property of Multiplication: A.B=B.A

Some Examples of Commutative Property of Addition

  • A+B= B+A , 2+3= 3+2
  • A+ (B+C)= (A+B)+C, 4+(5+6)= (4+5) + 6

Some Solutions :

  1. You have to prove that a+ b= b+a if a= 9 & b= 3

Solution: so here a= 9 and b=3

A+B=B+A, 9+3=3+9

So, 9+3= 12 &

3+9=12 Hence right hand side is equal to left hand side

  1. Here you can prove that A.B=B.A If a= 2 and b=5

Solution: so here a=2 and B=5

A.B= 2.5= 10

B.A= 5.2= 10

Hence proved that LHS=RHS


  1. What do you mean by commutative Property in maths?

The commutative property says that the result will stay the same if you change the order of numbers while performing the Multiplication or Addition. For example, you can add 2+5 and 5+2. The result will be the same. It is noted that it is only appropriate for Addition and Multiplication.

  1. Can we use the commutative Property for division & subtraction?

You cannot apply the commutative property while subtracting and dividing because it cannot produce the same result. If you subtract 5-3=2 and then 3-5 is not equal, Thus, we cannot use commutative properties in subtraction and division.

  1. What are the Laws of Commutative Property?

Commutative law is the other word of the commutative *Property that applies only to Addition & Multiplication. The law states that the arrangement of the numbers will not change the result. (A+B=B+A). The multiplication law of the commutative property states that multiplying the numbers in any order will not change the outcome (AxB= BxA).

Final Words

We concluded everything about the commutative property of Addition with examples that will help you better understand the term. There are some other properties in mathematics that we will explain some other time. So, if you have any questions or comments about the topic, please leave them in the comments section.