Associative: Difference between revisions
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Revision as of 14:55, 4 October 2015
Maths.
Multiplication and addition are associative
The associative property of multiplication means that the order in which successive multiplications are done makes no difference to the final result.
Example 1
(3 x 4) x 5 gives the same final result as 3 x (4 x 5).
In the first case:
(3 x 4) x 5
= 12 x 5 = 60
In the second case:
3 x (4 x 5)
= 3 x 20 = 60
Example 2
The associative property also applies to addition.
(3 + 4) + 5 gives the same final result as 3 + (4 + 5).
In the first case:
(3 + 4) + 5
= 7 + 5 = 12
In the second case:
3 + (4 + 5)
= 3 + 9 = 12
Division and subtraction are not associative
The associative property does not apply to division. The order of successive divisions does make a difference to the final result.
Example 3
(60 / 4) / 5 gives produces a different result from 60 / (4 / 5).
In the first case:
(60 / 4) / 5
= 15 / 5 = 3
In the second case:
60 / (4 / 5)
= 60 / 0.8 = 75
Example 4
The associative property does not apply to subtraction.
(5 - 4) - 3 gives a different result from 5 - (4 - 3).
In the first case:
(5 - 4) - 3
= 1 - 3 = -2
In the second case:
5 - (4 - 3)
= 5 - 1 = 4
