Question

According to the Associative Property, which expression is equivalent to 30m + (21m - 53) + (18 - 2m)? (1 point)
• (49m - 53) + 16
• 53m — 35
• (30m + 21m) + (18 - 2m)
• 51m + (-53 + 18) - 2m

Answer 1

The Associative Property states that the way we group numbers in addition or multiplication does not change their sum or product. To simplify the expression \(30m + (21m - 53) + (18 - 2m)\), we can rearrange the grouping of the terms.

Let's analyze the given options:

1. **\((49m - 53) + 16\)**: This is not equivalent because it doesn't represent the same individual parts of the original expression.
2. **\(53m - 35\)**: This doesn't match the original expression as it has been altered in terms of coefficients and constants.
3. **\((30m + 21m) + (18 - 2m)\)**: This option is equivalent as it simply groups \(30m\) and \(21m\) together while leaving the rest of the expression unchanged.
4. **\(51m + (-53 + 18) - 2m\)**: This option also doesn't match directly as it has changed the arrangement too much.

Thus, the correct answer that uses the Associative Property correctly is:

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