Question

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)
left parenthesis 30 m plus 21 m right parenthesis plus left parenthesis 18 minus 2 m right parenthesis
51m+(−53+18)−2m

Answer 1

The associative property states that the way in which numbers are grouped in addition does not affect the sum. This means that when adding, the grouping of the addends can be rearranged.

Starting with the original expression:

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

We can use the associative property to regroup the terms. The expression can be rearranged as follows:

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

This shows that we are grouping \(30m\) and \(21m\) together. Then, we can also rearrange the entire expression without changing its value:

The given options include:

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

This aligns with the associative property since it correctly groups the terms for addition.

Therefore, the answer that is equivalent to the original expression according to the associative property is:

\[
\text{(30m + 21m) + (18 - 2m)}
\]

So, the correct response is:

\[
\text{(30 m + 21 m) + (18 - 2 m)}
\]