Question

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

Answer 1

To apply the Associative Property, we can regroup the terms in the expression \(30m + (21m - 53) + (18 - 2m)\). The Associative Property states that the way in which numbers are grouped in addition does not change their sum.

Let's take a look at the original expression: \[ 30m + (21m - 53) + (18 - 2m) \]

We can regroup it as follows:

1. Group \(30m\) and \(21m\) together: \((30m + 21m) + (18 - 2m - 53)\)
2. Another valid regrouping could be \( (30m + (18 - 2m)) + (21m - 53)\)

Since we know \(30m + 21m\) can be grouped, let's check the options given:

1. \((30m + 21m) + (18 - 2m)\) - This is valid as it combines the first two terms with the remainder correctly.
2. \(51m + (-53 + 18) - 2m\) - This also works because it correctly states the sum of the first and last groups in a different order.
3. \((49m - 53) + 16\) - This does not work; there's a mismatch in the grouping.
4. \(53m - 35\) - This does not work at all due to incorrect terms.

The best equivalent expressions according to the Associative Property are:

• \((30m + 21m) + (18 - 2m)\)
• \(51m + (-53 + 18) - 2m\)

If you can only select one, choose either the first or the second depending on whether you want to show the re-grouping most clearly.