Table of Contents

Last modified on August 3rd, 2023

The commutative property of addition says any change in the order of the numbers being added (addends) does not change the sum. Also known as the order property of addition, it says the addition is commutative. Those two numbers being added are called addends.

For two numbers a and b, the generic formula for the commutative property of addition is given by:

**a + b = b + a**

For example, adding 6 orange balls to 4 blue balls is the same as adding 4 blue balls to 6 orange balls. Both will give a total of 10 balls.

Let us solve some more examples involving the commutative property of addition.

**Verify the commutative property of addition if a = 22 and b = 11**

Solution:

As we know, according to the commutative property of addition:

a + b = b + a

L.H.S

a + b

=> 22 + 11 => 33

R.H.S

b + a

=> 11 + 22

=> 33

Since a + b = b + a the commutative property of addition is verified.

**Find the value of x using the commutative property of addition.****a) 15 + 9 = x + 15****b) x + 20 = 10 + 20****c) (-2) + 5 = 5 + x****d) 0.2 + x = 0.9 + 0.2****If the commutative property of addition holds, then****a + b = b + a**

Solution:

a) Here, a = 15, b = 9

Since 15 + 9 = 24 and addition is satisfied by the commutative property, thus

x + 15 = 24

=> x = 9

b) Here, a = 20, b = 10

Since 20 + 10 = 30 and addition is satisfied by the commutative property, thus

x + 20 = 20

=> x = 10

c) Here, a = -2, b = 5

Since (-2) + 5 = 3 and addition is satisfied by the commutative property, thus

5 + x = 3

=> x = -2

d) Here, a = 0.2, b = 0.9

Since 0.9 + 0.2 = 1.1 and addition is satisfied by the commutative property, thus

0.2 + x = 1.1

=> x = 0.9

Last modified on August 3rd, 2023