According to the Associative Property, Which expression is equivalent to 30m+(21m-53)+(18-2m)

A:(49m-53)+16

B:53m-35

C:51m+(-53+18)-2m

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

1 answer

To find the expression that is equivalent to \(30m + (21m - 53) + (18 - 2m)\) using the Associative Property, we can rearrange and group the terms.

We start with the expression: \[ 30m + (21m - 53) + (18 - 2m) \]

Using the Associative Property of addition, we can rearrange the terms: \[ (30m + 21m + (18 - 2m)) - 53 \]

Now, let's break it down:

  1. Combine the \(m\) terms: \[ 30m + 21m - 2m = 49m \]
  2. Then add the constants: \[ 18 - 53 = -35 \] So we get: \[ 49m - 35 \]

Defining the options:

  • A: \((49m - 53) + 16\)
  • B: \(53m - 35\)
  • C: \(51m + (-53 + 18) - 2m\)
  • D: \((30m + 21m + (18 - 2m))\)

Now comparing our derived expression \(49m - 35\) with the options:

  • Option A evaluates to \(49m - 53 + 16 = 49m - 37\) (not equivalent)
  • Option B gives \(53m - 35\) (not equivalent)
  • Option C simplifies to \(51m - 35 - 2m = 49m - 35\) (equivalent)
  • Option D is just a regrouping of the original expression and does not provide a single simplified equivalent expression.

Thus, the answer is: C: \(51m + (-53 + 18) - 2m\), since it simplifies to \(49m - 35\).