Associative: Difference between revisions
imported>Doug Williamson (Create the page. Source: Oxford English Dictionary, accessed 04 Oct 2015.) |
imported>Doug Williamson (Classify page.) |
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''Maths.'' | ''Maths.'' | ||
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(3 x 4) x 5 | (3 x 4) x 5 | ||
= 12 x 5 = 60 | = 12 x 5 = '''60''' | ||
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3 x (4 x 5) | 3 x (4 x 5) | ||
= 3 x 20 = 60 | = 3 x 20 = '''60''' | ||
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(3 + 4) + 5 | (3 + 4) + 5 | ||
= 7 + 5 = 12 | = 7 + 5 = '''12''' | ||
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3 + (4 + 5) | 3 + (4 + 5) | ||
= 3 + 9 = 12 | = 3 + 9 = '''12''' | ||
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===Division and subtraction are not associative=== | ===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. | The associative property does ''not'' apply to division. The order of successive divisions does make a difference to the final result. | ||
====Example 3==== | ====Example 3==== | ||
(60 / 4) / 5 | (60 / 4) / 5 produces a different result from 60 / (4 / 5). | ||
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(60 / 4) / 5 | (60 / 4) / 5 | ||
= 15 / 5 = 3 | = 15 / 5 = '''3''' | ||
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60 / (4 / 5) | 60 / (4 / 5) | ||
= 60 / 0.8 = 75 | = 60 / 0.8 = '''75''' | ||
====Example 4==== | ====Example 4==== | ||
The associative property does not apply to subtraction. | The associative property does not apply to subtraction either. | ||
(5 - 4) - 3 gives a different result from 5 - (4 - 3). | (5 - 4) - 3 gives a different result from 5 - (4 - 3). | ||
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(5 - 4) - 3 | (5 - 4) - 3 | ||
= 1 - 3 = -2 | = 1 - 3 = '''-2''' | ||
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5 - (4 - 3) | 5 - (4 - 3) | ||
= 5 - 1 = 4 | = 5 - 1 = '''4''' | ||
== See also == | == See also == | ||
* [[Commutative]] | * [[Commutative]] | ||
* [[Distributive]] | * [[Distributive]] | ||
[[Category:The_business_context]] | |||
Latest revision as of 09:58, 27 June 2022
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
