Math > Year 2

Commutative property of Operations

What is Commutative Property?
Commutative Property tells us if we can swap the numbers around while undertaking a calculation, without making any difference in the answer.

Addition
In addition, the order of the numbers to be added doesn’t matter.

For example,
(£2 + £3) is the same as (£3 + £2).
In addition, we can change the order of the numbers to be added without making any difference to the answer.
Hence, addition is commutative.

Subtraction
In Subtraction, the order of the numbers to be subtracted matters.
For example:
£8 - £5 = £3
If we change the order, £5 - £8 = -£3, we don’t get the same answer.
Hence, Subtraction is not Commutative.

As subtraction cannot be done in any other order, we cannot use the inverse of subtraction(addition) every time to work the missing number.

For example:

7 -? = 3
In this case, we cannot use addition to work the missing number.

Here, we will use subtraction i.e.,
7 – 3 = 4

 

Multiplication                             

In multiplication, the order of numbers can be changed.
For example:
3 × 4 = 12
4 × 3 = 12
In multiplication, changing the order of the numbers doesn’t change the answer.
Hence, multiplication is commutative.

Division

In Division, the order of the numbers to be divided matters.
For example:
10 ÷ 2 = 5
2 ÷ 10 = 0.2

If we change the order, we don’t get the same answer.
Hence, division is not Commutative.


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