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:
- Group \(30m\) and \(21m\) together: \((30m + 21m) + (18 - 2m - 53)\)
- Another valid regrouping could be \( (30m + (18 - 2m)) + (21m - 53)\)
Since we know \(30m + 21m\) can be grouped, let's check the options given:
- \((30m + 21m) + (18 - 2m)\) - This is valid as it combines the first two terms with the remainder correctly.
- \(51m + (-53 + 18) - 2m\) - This also works because it correctly states the sum of the first and last groups in a different order.
- \((49m - 53) + 16\) - This does not work; there's a mismatch in the grouping.
- \(53m - 35\) - 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.