Which of the following expressions could you rewrite using the Associative Property?(1 point)
Responses
(5+8)⋅3
left parenthesis 5 plus 8 right parenthesis times 3
(9⋅5)⋅(8⋅3)
left parenthesis 9 times 5 right parenthesis times left parenthesis 8 times 3 right parenthesis
(5⋅8)+3
left parenthesis 5 times 8 right parenthesis plus 3
(9⋅5)+8+3
left parenthesis 9 times 5 right parenthesis plus 8 plus 3
The expression that can be rewritten using the Associative Property is:
(9⋅5)⋅(8⋅3) which can be rewritten as (9⋅5)⋅(8⋅3)
To identify which expressions could be rewritten using the Associative Property, we need to understand what this property states. The Associative Property states that the grouping of numbers does not affect the result when adding or multiplying.
Let's go through each expression and see if we can apply the Associative Property:
1. (5+8)⋅3
The expression involves addition and multiplication. According to the Associative Property, we can rearrange the grouping of the numbers without changing the result. In this case, we can rewrite it as:
5 + (8⋅3)
So, this expression can be rewritten using the Associative Property.
2. (9⋅5)⋅(8⋅3)
Here, we have two multiplications that are already in parentheses. The Associative Property applies to addition and multiplication, not to multiple levels of parentheses. Therefore, we cannot apply the Associative Property in this case.
3. (5⋅8)+3
Similar to the first expression, this involves multiplication and addition. The Associative Property allows us to rearrange the grouping. We can rewrite it as:
5⋅(8+3)
Hence, this expression can be rewritten using the Associative Property.
4. (9⋅5)+8+3
Again, we have addition involved, and we can rearrange the grouping. We can rewrite it as:
(9⋅5)+(8+3)
So, this expression can also be rewritten using the Associative Property.
In conclusion, the expressions that can be rewritten using the Associative Property are:
(5+8)⋅3 and (5⋅8)+3.