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

Answer 1

To apply the Associative Property, we can reorganize the terms in the expression without changing their sum.

The original expression is: \[ 30m + (21m - 53) + (18 - 2m) \]

We can rearrange and group the expressions.

First, let's simplify:

1. Combine \(30m\) and \(21m\): \[ 30m + 21m = 51m \]

2. Now consider what remains: \[ 51m - 53 + (18 - 2m) \]

3. Combine the constants: \[ -53 + 18 = -35 \]

4. Now combine like terms: \[ 51m - 2m = 49m \]

Thus, the overall expression simplifies to: \[ 49m - 35 \]

Now, let's check the responses. The equivalent expression we found is: \[ (49m - 53) + 16 \] This does not equal \( 49m - 35 \) directly, but can be seen as equal since: \[ 49m - 53 + 16 = 49m - 37 \] (which is not what we have). The option \( (30m + 21m) + (18 - 2m) \) is just grouping in the same way as we did and equals \( 30m + 21m + 18 - 2m = 49m - 35 \).

Therefore, the equivalent expression using associative property is: (30m + 21m) + (18 - 2m)