To determine which expression is equivalent to \(30m + (21m - 53) + (18 - 2m)\) using the Associative Property, let's simplify the given expression step by step.
1. Start with the original expression:
\[
30m + (21m - 53) + (18 - 2m)
\]
2. Combine the terms inside the parentheses:
\[
30m + 21m - 53 + 18 - 2m
\]
3. Now, combine the like terms:
- For the \(m\) terms: \(30m + 21m - 2m = 49m\)
- For the constant terms: \(-53 + 18 = -35\)
4. Now, we can rewrite the expression:
\[
49m - 35
\]
Now we compare it with the provided options:
1. \((49m - 53) + 16\)
2. \((30m + 21m) + (18 - 2m)\)
3. \(53m - 35\)
4. \(51m + (-53 + 18) - 2m\)
The expression we simplified to is \(49m - 35\).
None of the options produce exactly \(49m - 35\) directly, but the interpretation involves rearranging the expressions.
The closest we have based on associative grouping is the second option:
\[
(30m + 21m) + (18 - 2m) \text{ since it correctly complies with associativity, but needs further simplification.}
\]
However, our final simplified form of \(49m - 35\) is inconsistent with any direct choice as none is perfectly equal to this.
So the answer aligning closest with the associative property would remain:
**Response: (30m + 21m) + (18 - 2m)**.