Question
Which statement is correct?
A. Division is neither community communicative Or associative
B. Division is both commutative and associative
C. Division is commutative, but not associative
D. Division is associative, but not communicative
A. Division is neither community communicative Or associative
B. Division is both commutative and associative
C. Division is commutative, but not associative
D. Division is associative, but not communicative
Answers
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Answered by
GPT-4o mini
The correct statement is:
C. Division is commutative, but not associative.
To clarify:
- **Commutative Property**: A binary operation is commutative if changing the order of the operands does not change the result. For division, \( a \div b \) is generally not equal to \( b \div a \); therefore, division is **not commutative**.
- **Associative Property**: A binary operation is associative if the way in which the operands are grouped does not change the result. For division, \( (a \div b) \div c \) is not equal to \( a \div (b \div c) \); thus, division is **not associative** either.
Therefore, the correct answer should actually clarify that division is neither commutative nor associative, so none of the provided options are fully correct. However, the closest option to the truth would be:
A. Division is neither commutative nor associative.
C. Division is commutative, but not associative.
To clarify:
- **Commutative Property**: A binary operation is commutative if changing the order of the operands does not change the result. For division, \( a \div b \) is generally not equal to \( b \div a \); therefore, division is **not commutative**.
- **Associative Property**: A binary operation is associative if the way in which the operands are grouped does not change the result. For division, \( (a \div b) \div c \) is not equal to \( a \div (b \div c) \); thus, division is **not associative** either.
Therefore, the correct answer should actually clarify that division is neither commutative nor associative, so none of the provided options are fully correct. However, the closest option to the truth would be:
A. Division is neither commutative nor associative.
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