Associative
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 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 either.
(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
