Commutative

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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.


See also