Question

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

A. 51m+(-53+18)-2m
B. (30m+21m)+(18-2m)
C. (49-53)-16
D. 53m-35

Answer 1

To apply the Associative Property, we can regroup the expression \( 30m + (21m - 53) + (18 - 2m) \) without changing its value.

Let's break down the expression step by step:

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

2. We can group the terms differently. The Associative Property allows us to change the grouping of the numbers:
\[
(30m + 21m) + (18 - 53 - 2m)
\]

3. Calculate the first part:
\[
(30m + 21m) = 51m
\]

4. Combine the constants and the remaining variable terms:
- From \( (18 - 53) \):
\[
18 - 53 = -35
\]
And we subtract \( 2m \) from it later.

5. Therefore, we can write the expression as:
\[
51m + (-35 - 2m)
\]
which simplifies to:
\[
51m - 35 - 2m
\]

So you can regroup the expression into:
\[
(30m + 21m) + (18 - 53 - 2m)
\]
Or, represented differently, we can write:
\[
51m + (-53 + 18) - 2m
\]

Now, let’s compare this with the answer choices:

A. \( 51m + (-53 + 18) - 2m \): This choice matches our expression and is thus equivalent.

B. \( (30m + 21m) + (18 - 2m) \): This is another way to write the initial expression.

C. \( (49 - 53) - 16 \): This does not match.

D. \( 53m - 35 \): This also doesn't match as we have a different coefficient on \( m \).

Therefore, the answer that matches according to the Associative Property is:

**A. \( 51m + (-53 + 18) - 2m \)**.