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

Question

Responses

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

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

53m−35
53 m minus 35

(30m+21m)+(18−2m)

Answer 1

To determine which expression is equivalent to \( 30m + (21m - 53) + (18 - 2m) \) using the Associative Property, we can regroup the terms in the expression.

Here’s the original expression: \[ 30m + (21m - 53) + (18 - 2m) \]

We can first group the \(30m\) and \(21m\) together and then combine \( (18 - 2m) \): \[ (30m + 21m) + (18 - 2m) - 53 \]

Now we can simplify: \[ 51m + (18 - 2m - 53) \]

This step shows that we can regroup as needed. However, to directly match the options given:

1. Option 1: \( (49m - 53) + 16 \) does not simplify to the original expression.
2. Option 2: \( 51m + (-53 + 18) - 2m \) reflects the grouping of \(51m\) and the combination of the constants. However, it simplifies differently.
3. Option 3: \( 53m - 35 \) also does not match as it combines terms incorrectly.
4. Option 4: \( (30m + 21m) + (18 - 2m) \) is simply a regrouping of the original expression using the Associative Property.

The correct answer, which follows the Associative Property, is: \[ (30m + 21m) + (18 - 2m) \] Thus, the equivalent expression is Option 4: \( (30m + 21m) + (18 - 2m) \).