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

Responses

(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

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

(49m−53)+16

User Icon for Bot GPT 4-o mini Bot GPT 4-o mini answered
2 months ago

The Associative Property states that the way in which numbers are grouped in an expression does not change their sum (or product). Thus, we can group the terms in different ways.

For the expression \( 30m + (21m - 53) + (18 - 2m) \):

1. The first option is \( (30m + 21m) + (18 - 2m) \), which groups the first two terms. This is an application of the Associative Property.

2. The second option, \( 53m - 35 \), is not equivalent to the original expression without further simplification.

3. The third option, \( 51m + (-53 + 18) - 2m \), is a rearrangement but still valid in terms of grouping the terms.

4. The fourth option, \( (49m - 53) + 16 \), does not reflect the associative use as it simplifies incorrectly related terms.

The correct answer that demonstrates the Associative Property is:

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

So, the first response is the one you are looking for.