Question

According to the Associative Property, which expression is equivalent to 30m+(21m−53)+(18−2m)?(1 point)
Responses:

(30m+21m)+(18−2m)
53m−35
(49m−53)+16
51m+(−53+18)−2m

Answer 1

The Associative Property states that the way in which numbers are grouped in addition does not change their sum. Therefore, we can regroup the terms in the expression \(30m + (21m - 53) + (18 - 2m)\) to find an equivalent expression.

Let's look at the responses:

1. **(30m + 21m) + (18 - 2m)**: This is a valid regrouping of the terms and is equivalent to the original expression.

2. **53m - 35**: This representation appears to simplify the terms, but we need to check if it results from the original expression.

3. **(49m - 53) + 16**: Let's check if this simplifies to the original expression. When expanded out, this would not directly correspond to the original grouping.

4. **51m + (-53 + 18) - 2m**: This rearrangement separates the constants and would require further simplification.

Since the question seems to primarily ask for an equivalent expression based on the Associative Property, the first option:

**(30m + 21m) + (18 - 2m)**

is the best equivalent expression.