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Apply the associative property

The associative property states that regrouping three or more whole numbers does not change the sum or product: (a+b)+c=a+(b+c)(a+b)+c=a+(b+c) and (a×b)×c=a×(b×c)(a\times b)\times c=a\times(b\times c). It supports choosing convenient groupings to compute efficiently and distinguishes regrouping from changing the order of numbers, which is the commutative property; more general treatment with other number systems is not included here.

Detailed Explanation: Apply the associative property

The associative property lets you regroup three or more whole numbers without changing the answer. The numbers stay in the same order; only the parentheses change.

For addition:

(a+b)+c=a+(b+c)(a+b)+c=a+(b+c)

Example

Find:

18+25+7518+25+75

Group the numbers that are easy to add. Since 25+75=10025+75=100, regroup the expression:

18+(25+75)18+(25+75)

Add inside the parentheses first:

18+100=11818+100=118

So,

18+25+75=11818+25+75=118

The grouping changed, but the order of the numbers did not. Changing the order would use the commutative property, not the associative property.

Learn by doing: Apply the associative property

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Multiplication - Commutative Property


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