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
left parenthesis 9 times 5 right parenthesis plus 8 plus 3
(9⋅5)⋅(8⋅3)
The Associative Property applies to both addition and multiplication and states that the way in which numbers are grouped does not change their sum or product. This means that you can change the grouping of the numbers in an expression without altering its value.
Here's how the Associative Property can be used with the given expressions:
1. (5⋅8)+3
This expression involves multiplication and addition. The Associative Property can be applied only to addition or multiplication, not both simultaneously in a single step.
2. (5+8)⋅3
Similar to expression 1, this expression also contains both addition and multiplication. While you can apply the Distributive Property to this expression, the Associative Property is not applicable here as it involves different operations.
3. (9⋅5)+8+3
The Associative Property can be applied to this expression for the addition part. You can rewrite it by changing the grouping of the addition as such: 9⋅5+(8+3), which does not change the overall sum.
4. (9⋅5)⋅(8⋅3)
This expression is a pure multiplication example. You can apply the Associative Property to the multiplication:
9⋅(5⋅(8⋅3)) or ((9⋅5)⋅8)⋅3
either way, the result of the multiplication does not change.
The expressions that can be properly rewritten using the Associative Property to show a different grouping without changing the expression's value are:
- (9⋅5)+8+3
- (9⋅5)⋅(8⋅3)