What is the Commutative Property of Addition?
The commutative property of addition states that the sum of two addends does not change based on the order of adding the addends.
If A and B are two addends then according to the commutative property of addition, the following condition applies:
A + B = B + A
Let’s consider an example in which the addends are 7 and 8.
According to the commutative property:
7 + 8 = 8 + 7
Let us verify this:
7 + 8 = 15
8 + 7 = 15
So the sum of 7 and 8 remains the same which is 15 irrespective of the order in which they are added.
The same rule applies for multiplication operations as well. However, the commutative property cannot be applied to division and subtraction operations.
Rapid Recall
Solved Examples
Verify if the following condition holds true or not when a= 45 and b= 54.
a + b = b + a.
Solution:
Use the commutative property of addition to verify.
a + b = b + a
45 + 54 = 54 + 45 [Substitute the given values]
99 = 99 [Add]
So, the left side of the equation is equal to the right side of the equation. Therefore the condition ‘a + b = b + a’ holds true.
Example 2:
Write two addition equations using the commutative property of addition using 7 and 8 as the addends.
Answer:
According to the commutative property of addition,
A + B = B + A
7 + 8 = 8 + 7 [Substitute 7 for A and 8 for B]
7 + 8 = 15 [Add]
8 + 7 = 15 [Add]
Therefore 7 + 8 = 15 and 8 + 7 = 15 are the two equations formed with addends 7 and 8 using the commutative property of addition.
Example 3:
Which of the following represents the commutative property of addition:
2 + 3 = 3 + 2
3 + 1 = 4 + 2
10 + 1 = 1 + 10
Answer:
According to the commutative property of addition,
A + B = B + A
Among the given equations the following two equations represent this property:
2 + 3 = 3 + 2
10 + 1 = 1 + 10
Therefore the equations, 2 + 3 = 3 + 2 and 10 + 1 = 1 + 10 represent the commutative property of addition.
What are the basic properties used for adding, subtracting, multiplying or dividing natural numbers?
The basic properties used to add, subtract, multiply or divide natural numbers are as follows:
- Associative Property
- Commutative Property
- Distributive Property
- Identity Property
Commutative property does not apply to division and subtraction operations.
Yes, the commutative property of addition is applicable to all types of numbers.