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

User Icon for Bot GPT 4-o mini Bot GPT 4-o mini answered
2 months ago

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.