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 (49m-53)+16 left parenthesis 49 m minus 53 right parenthesis plus 16 53m-35 53 m minus 35 51m+\left(-53+18\right)-2m

Answer 1

According to the Associative Property, which states that the grouping of numbers does not change their sum, the expression \( 30m + (21m - 53) + (18 - 2m) \) can be rearranged for clarity.

Let's simplify the original expression step-by-step:

1. Combine the constants and similar terms:

   • First, simplify the terms inside the parentheses:
     • \( 21m - 53 \) and \( 18 - 2m \).
   • The constants can be grouped:
     • \( -53 + 18 = -35 \).

2. Combine like terms:

   • With the main terms:
     • \( 30m + 21m - 2m = 49m \).
   • The constant terms combined:
     • So, \( 30m + 21m + (18 - 2m) - 53 = 49m - 35 \).

Therefore, the expression \( (30m + 21m) + (18 - 2m) \) rearranged is \( 49m - 35 \).

So, the equivalent expression according to the Associative Property is:

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