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

Responses

(49m−53)+16

53m−35

51m+(−53+18)−2m

(30m+21m)+(18−2m)

1 answer

The Associative Property states that the way in which numbers are grouped in an addition or multiplication problem does not change the sum or product.

In the expression \(30m + (21m - 53) + (18 - 2m)\), you can regroup the terms without changing the overall value.

The expression:

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

can be rewritten using the associative property in this way:

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

This form is represented in one of the responses:

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

Thus, the equivalent expression using the Associative Property is:

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

Among the provided choices, that's exactly the fourth response:

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

This confirms the correctness using the associative property.