Associative: Difference between revisions
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| Line 14: | Line 14: | ||
(3 x 4) x 5 | (3 x 4) x 5 | ||
= 12 x 5 = 60 | = 12 x 5 = '''60''' | ||
| Line 21: | Line 21: | ||
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''' | ||
| Line 42: | Line 42: | ||
3 + (4 + 5) | 3 + (4 + 5) | ||
= 3 + 9 = 12 | = 3 + 9 = '''12''' | ||
| Line 48: | Line 48: | ||
===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). | ||
| Line 58: | Line 58: | ||
(60 / 4) / 5 | (60 / 4) / 5 | ||
= 15 / 5 = 3 | = 15 / 5 = '''3''' | ||
| Line 65: | Line 65: | ||
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). | ||
| Line 79: | Line 79: | ||
(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
