Carve-out

Maths.

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,

See also

• Associative
• Distributive
• Denominator
• Numerator