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

Question

Responses

(49m−53)+16
left parenthesis 49 m minus 53 right parenthesis plus 16

51m+(−53+18)−2m
51 m plus left parenthesis negative 53 plus 18 right parenthesis minus 2 m

(30m+21m)+(18−2m)
left parenthesis 30 m plus 21 m right parenthesis plus left parenthesis 18 minus 2 m right parenthesis

53m−35

Answer 1

To simplify the expression \(30m + (21m - 53) + (18 - 2m)\) using the Associative Property, we can rearrange and regroup the terms in any way we wish.

Let's break it down step-by-step:

1. Start with the original expression: \[ 30m + (21m - 53) + (18 - 2m) \]

2. Distribute the terms inside the parentheses: \[ = 30m + 21m - 53 + 18 - 2m \]

3. Now, rearranging and combining like terms:

   • Combine all \(m\) terms: \[ (30m + 21m - 2m) = 49m \]
   • Combine the constant terms: \[ (-53 + 18) = -35 \]

4. Therefore, we obtain: \[ 49m - 35 \]

Now, let's compare this with the provided responses:

1. \( (49m - 53) + 16 \) → This is not equivalent.
2. \( 51m + (-53 + 18) - 2m \) → This simplifies to \( 51m - 35 - 2m = 49m - 35 \), which is equivalent.
3. \( (30m + 21m) + (18 - 2m) \) → This is equivalent as it maintains the grouping.
4. \( 53m - 35 \) → This is not equivalent.

Thus, the correct equivalent expression according to the Associative Property is: \[ (30m + 21m) + (18 - 2m) \] This confirms that the associativity allows us to regroup terms, leading to the same final expression of \(49m - 35\).