Which of the following expressions could you rewrite using the Associative Property?(1 point) Responses (5⋅8)+3 left parenthesis 5 times 8 right parenthesis plus 3 (5+8)⋅3 left parenthesis 5 plus 8 right parenthesis times 3 (9⋅5)⋅(8⋅3)

1 answer

The Associative Property states that the way in which numbers are grouped in addition or multiplication does not change the sum or product. In other words, for addition, \( (a + b) + c = a + (b + c) \), and for multiplication, \( (a \cdot b) \cdot c = a \cdot (b \cdot c) \).

Let's analyze each of the expressions given:

  1. \( (5 \cdot 8) + 3 \): This expression involves addition and multiplication but doesn't involve a situation where we can regroup multiplication.

  2. \( (5 + 8) \cdot 3 \): This expression is a multiplication of the sum, but it does not have multiple factors to apply the associative property to.

  3. \( (9 \cdot 5) \cdot (8 \cdot 3) \): This could potentially use the Associative Property since it involves products and we can rearrange the grouping of multiplication.

Based on this analysis, the expression that could be rewritten using the Associative Property is:

(9⋅5)⋅(8⋅3)

This expression can be grouped in a different way, for instance, you can regroup it as \( 9 \cdot (5 \cdot (8 \cdot 3)) \) or \( (9 \cdot 5) \cdot 8 \cdot 3 \).