Commutative: Difference between revisions
imported>Doug Williamson (Added "exchanging" explicitly) |
imported>Doug Williamson (Distinguish from associative) |
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The second expression produces '''-2'''. | The second expression produces '''-2'''. | ||
====Multiplication and additions are also associative==== | |||
The [[associative]] and commutative properties apply both to multiplications and additions. | |||
For this reason, they are sometimes mixed-up but they are different, | |||
Revision as of 15:08, 7 October 2015
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 additions are also associative
The associative and commutative properties apply both to multiplications and additions.
For this reason, they are sometimes mixed-up but they are different,
