Commutative Property of Addition

The commutative property of addition states that the sum of two or more numbers remains the same irrespective of the way they are grouped. Let us study more about the commutative property of addition in this article.

According to the commutative property of addition, if two or more numbers are added or sum up, we get the same result irrespective of how the numbers are grouped. Here, grouping refers to the representation in which the brackets are placed and arranged in the given addition problem. Observe the following example to understand the concept of the commutative property of addition.

5 + 6 = 6 + 5
11 = 11

Here we can clearly observe when we finally add all the numbers with different arrangments, the resultant sum is the same.

The commutative property says that the order of operands does not change the final result. The commutative property formula for addition is given below.

Commutative Property of Addition Formula

Commutative property formula for addition: The commutative property of addition says that the order in which we add the addends does not change the sum.

A + B = B + A

Commutative law of addition is applicable only when we can get the desired result equal in any required arrangements, i.e., LHS = RHS. Let us try to justify how and why the commutative property is only valid for multiplication as well as addition. We will apply the general commutative property law individually on the four basic operations. Further, we will discuss a real-life application to understand the commutative property of multiplication more clearly.

For Addition: Commutative property for addition is expressed as a + b = b + a. For example, (17 + 4) = (4 + 17) = 21. We say that the addition is commutative for the given set of numbers.

For Multiplication: Commutative property of multiplication is given as A × B = B × A. For example, (17 × 4) = (4 × 17) = 68. Here we find that multiplication is commutative for the given set of numbers.

Let us look at the real-life application based on the commutative property of addition here.

Illustration: There are seven burgers and five pizzas. Find the total of the items using the commutative property of addition for the reverse combinations you can purchase.

Solution: With 7 burgers, you can choose 5 pizzas that give you a combination as 7 + 5 = 12 items.
Also with 5 pizzas, you can choose 7 burgers this combination gives you 5 + 7 = 12 items.
Both the combination describes the commutative property of addition between 7 burgers and 5 pizzas.

Let us take a look at a few examples to better understand the commutative property of addition.

What is the Commutative Property Law of Addition?

The commutative property formula for addition is defined as the sum of two or more numbers that remain the same, irrespective of the order of the operands and addends. For addition, the commutative property formula is expressed as (A + B) = (B + A).

How Do You Find the Commutative Property of Addition?

The commutative property of addition states that if 'a' and 'b' are two numbers, then a + b = b + a. It can be verified if the LHS and RHS terms are equal after solving the given numerical values.

What is an Example of Commutative Property of Addition?

The example of the commutative property of addition is (A + B) = (B + A). Here A = 8 and B = 9. on solving we get 8 + 9 = 9 + 8 = 17. Hence proved LHS is equal to RHS.

What will be the Commutative Property of Addition for the Numbers 7 and 6?

Let us arrange the given numbers as per the general equation of commutative law that is (A + B) = (B + A). Here A = 7 and B = 6. on solving we get 7 + 6 = 6 + 7 = 13. Hence proved LHS is equal to RHS.

What is the Commutative Property of Addition for Rational Numbers?

The commutative property of addition for rational numbers can be expressed as (P + Q) = (Q + P). Here the values of P, Q are in form of a/b, where b ≠ 0.

What is the Commutative Property of Addition for Fractions?

The commutative property of addition for fractions can be expressed as (P + Q) = (Q + P). Here the values of P, Q are in form of a/b. For example, let say, P = 7/8 and Q = 5/2 on substituting the values in (P + Q) = (Q + P) we get, (7/8 + 5/2) = (5/2 + 7/8) = 27/8.

What is the Commutative Property of Addition for Integers?

The commutative property of addition for integers can be expressed as (P + Q) = (Q + P). For example, let say, P = -3 and Q = -9 on substituting the value in (-3 + (-9)) = (-9 + (-3)) = -12. Hence LHS = RHS.