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

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

53m−35
53 m minus 35

(49m−53)+16

Answer 1

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

Let's start by simplifying the original expression:

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

First, we can combine like terms. Rearranging and grouping accordingly gives us:

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

Now, we can combine:

1. For the \(m\) terms: \[ 30m + 21m - 2m = 49m \]

2. For the constants: \[ -53 + 18 = -35 \]

Putting it all together, we get:

\[ 49m - 35 \]

Let's compare this with the provided options:

1. 51m + (−53 + 18) - 2m

   • Not equivalent.

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

   • This is equivalent based on the Associative Property, as it simply rearranges the terms.

3. 53m - 35

   • Not equivalent.

4. (49m - 53) + 16

   • Not equivalent.

Thus, the expression (30m + 21m) + (18 - 2m) is equivalent to the original expression using the Associative Property.