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

Question

Responses

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

(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

53m−35

Answer 1

To find an expression equivalent to \(30m + (21m - 53) + (18 - 2m)\) using the Associative Property, we need to group the terms appropriately.

The Associative Property allows us to group terms in different ways without changing the result. Here, we can group the terms as follows:

1. First, we can combine like terms:

   • Start with \(30m + 21m + (-2m) + (-53) + 18\)

2. Combine \(30m\), \(21m\), and \(-2m\): \[ 30m + 21m - 2m = (30 + 21 - 2)m = 49m \]

3. Now add \(-53\) and \(18\): \[ -53 + 18 = -35 \]

So, we have: \[ 49m - 35 \]

From the options given, the correct equivalent expression is: \[ (49m - 53) + 16 \]

This matches the form \(49m - 35\) as \(49m - 53 + 16 = 49m - 35\).

So the correct answer is: \((49m - 53) + 16\)