Question

According to the Associative Property, which expression is equivalent to 30m+(21m−53)+(18−2m) ?(1 point) Responses (49m−53)+16 left parenthesis 49 m minus 53 right parenthesis plus 16 (30m+21m)+(18−2m) left parenthesis 30 m plus 21 m right parenthesis plus left parenthesis 18 minus 2 m right parenthesis 51m+(−53+18)−2m 51 m plus left parenthesis negative 53 plus 18 right parenthesis minus 2 m 53m−35

Answer 1

To apply the Associative Property, we need to regroup the terms in the expression \(30m + (21m - 53) + (18 - 2m)\).

First, we can simplify the original expression:

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

2. We can rearrange and group the terms (using the Associative Property): \[ (30m + 21m) + (18 - 2m - 53) \]

3. Now we calculate:

   • \(30m + 21m = 51m\)
   • Combine \(18 - 53\) first: \(18 - 53 = -35\)
   • Then simplify \(-35 - 2m = -2m - 35\)

Combining gives us: \[ 51m + (-2m - 35) = (51m - 2m) - 35 = 49m - 35 \]

Thus, the rearranged and simplified expression according to the Associative Property is: \[ 49m - 35 \]

Looking at the responses provided, the equivalent expression is: \[ 49m - 35 \]