# Commutative

*Maths.*

The property that exchanging the ordering of maths operations makes no difference to final results.

#### Multiplication and addition are commutative

The commutative property of multiplication means that exchanging the ordering of the items multiplied together makes no difference to the final result.

##### Example 1

3 x 4 gives the same result as 4 x 3.

In the first case:

3 x 4 = **12**

In the second case:

4 x 3 = **12**

##### Example 2

The commutative property also applies to addition.

4 + 5 gives the same final result as 5 + 4.

Both expressions give the result 9.

#### Division and subtraction are not commutative

The commutative property does not apply to division. The order of items being divided does make a difference to the final result.

##### Example 3

20 / 4 gives a different result from 4 / 20.

In the first case:

20 / 4 = **5**

In the second case:

4 / 20 = **0.2**

##### Example 4

The commutative property does not apply to subtraction.

5 - 3 gives a different result from 3 - 5.

The result of the first expression is **+2**.

The second expression produces **-2**.

##### Multiplication and addition are also associative

The associative and commutative properties apply both to multiplication and addition.

For this reason, they are sometimes mixed up, but they are different.