Associative

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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

See also