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According to the Associative Property, which expression is equivalent to 30m+(21m−53)+(18−2m) ?
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
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
Answers
Answered by
GPT-4o mini
To apply the Associative Property, we can group the terms in the expression \(30m + (21m - 53) + (18 - 2m)\). The Associative Property states that the way in which numbers are grouped does not change their sum.
Let's analyze each of the responses:
1. **(30m + 21m) + (18 - 2m)**: This expression groups \(30m\) and \(21m\) together first and then adds the other group. This is an application of the Associative Property.
2. **51m + (-53 + 18) - 2m**: This expression simplifies \(21m\) and \(30m\) to \(51m\) and also groups the constants \(-53\) and \(18\) together. This expression is also valid under the Associative Property.
3. **(49m - 53) + 16**: This tries to combine some of the terms, but it does not follow from the original expression correctly and does not correctly reflect the original values of the terms.
4. **53m - 35**: This simplifies directly, but it does not maintain the original grouping of the components while applying the Associative Property.
From these options, both **(30m + 21m) + (18 - 2m)** and **51m + (-53 + 18) - 2m** represent valid applications of the Associative Property. However, since you seek an expression equivalent to the original, the correct responses that follow the Associative Property logically from the terms given would primarily focus on the groupings as shown in 1 and 2.
Thus, the expressions equivalent to \(30m + (21m − 53) + (18 − 2m)\) based on the Associative Property are:
- **(30m + 21m) + (18 - 2m)**
- **51m + (-53 + 18) - 2m**
Both of these can be considered valid depending on how one prioritizes their view of the associative property in expression evaluation.
Let's analyze each of the responses:
1. **(30m + 21m) + (18 - 2m)**: This expression groups \(30m\) and \(21m\) together first and then adds the other group. This is an application of the Associative Property.
2. **51m + (-53 + 18) - 2m**: This expression simplifies \(21m\) and \(30m\) to \(51m\) and also groups the constants \(-53\) and \(18\) together. This expression is also valid under the Associative Property.
3. **(49m - 53) + 16**: This tries to combine some of the terms, but it does not follow from the original expression correctly and does not correctly reflect the original values of the terms.
4. **53m - 35**: This simplifies directly, but it does not maintain the original grouping of the components while applying the Associative Property.
From these options, both **(30m + 21m) + (18 - 2m)** and **51m + (-53 + 18) - 2m** represent valid applications of the Associative Property. However, since you seek an expression equivalent to the original, the correct responses that follow the Associative Property logically from the terms given would primarily focus on the groupings as shown in 1 and 2.
Thus, the expressions equivalent to \(30m + (21m − 53) + (18 − 2m)\) based on the Associative Property are:
- **(30m + 21m) + (18 - 2m)**
- **51m + (-53 + 18) - 2m**
Both of these can be considered valid depending on how one prioritizes their view of the associative property in expression evaluation.
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