Question

Vance used the associative property to find the equivalent expression of (4.5 m + StartFraction 7 Over 8 EndFraction) minus 9. His work is shown below.


(4.5 m + StartFraction 7 Over 8 EndFraction) minus 9 mc002-3.jpg 4.5 m (StartFraction 7 Over 8 EndFraction minus 9)


Did Vance apply the associative property correctly? Why or why not?
Yes, the terms with variables should be written first.
Yes, the terms can be regrouped and still be equivalent.
No, the order of the terms should have been changed.
No, the addition symbol was dropped in the second expression.

Answer 1

Vance did not apply the associative property correctly. The associative property allows for the regrouping of terms in addition or multiplication, but it does not apply to subtraction. His expression altered the original operation by changing the structure of the addition and subtraction involved.

To clarify the options:
1. **Yes, the terms with variables should be written first.** - This is not relevant to the correctness of the associative property application.
2. **Yes, the terms can be regrouped and still be equivalent.** - This is incorrect because subtraction does not follow the associative property.
3. **No, the order of the terms should have been changed.** - This suggests a misunderstanding; he didn't change the order, but rather misapplied associative regrouping.
4. **No, the addition symbol was dropped in the second expression.** - This is the main issue; the expression changed the operation incorrectly.

The correct answer is: **No, the addition symbol was dropped in the second expression.**