The Associative Property states that the way in which numbers are grouped in addition or multiplication does not change the result. This means you can regroup the numbers without changing the outcome.
The expressions you provided are:
- \((9 \cdot 5) \cdot (8 \cdot 3)\) - This expression uses multiplication and can be regrouped.
- \((9 \cdot 5) + 8 + 3\) - This expression uses addition, and you can change the grouping of the addition terms, but it doesn’t directly demonstrate the Associative Property as it's not fully grouped.
- \(3 (5 + 8)\) - This expression uses addition inside and does not involve the Associative Property as it’s a combination of multiplication and addition.
- \(3 (5 \cdot 8) + 3\) - This involves a multiplication being added to 3, which doesn’t show groupings of the same operation.
The most straightforward expression that can be rewritten using the Associative Property is:
(9⋅5)⋅(8⋅3) because you can regroup the factors in multiplication:
For example: \((9 \cdot 5) \cdot (8 \cdot 3) = 9 \cdot (5 \cdot 8) \cdot 3\)
So, the correct answer is:
(9⋅5)⋅(8⋅3).
8 answers