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

Question

Responses

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

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

53m−35
53 m minus 35

51m+(−53+18)−2m

Answer 1

The Associative Property states that the way in which numbers are grouped in addition (or multiplication) does not change their sum (or product). In this case, we want to group the terms of the expression \(30m + (21m - 53) + (18 - 2m)\).

Let's break down the expression:

1. Combine like terms:
   • The terms \(30m\), \(21m\), and \(-2m\) can be grouped together.
   • The constant terms \(-53\) and \(18\) can also be grouped together.

Thus, we can express it as:

\[ (30m + 21m + (-2m)) + (-53 + 18) \]

Now, checking the provided options:

1. \((30m + 21m) + (18 - 2m)\) - This matches our grouping of \(30m + 21m\) and \(18 - 2m\). This one is correct.

2. \((49m - 53) + 16\) - This is not equivalent.

3. \(53m - 35\) - This is not correct.

4. \(51m + (-53 + 18) - 2m\) - While it has the correct variable group, it's not clearly stated or grouped as per the associative property.

So, the correct answer that follows the Associative Property is:

(30m + 21m) + (18 - 2m).