Question
Which statement is correct?(1 point)
Responses
Division is associative but not commutative.
Division is associative but not commutative.
Division is both commutative and associative.
Division is both commutative and associative.
Division is commutative but not associative.
Division is commutative but not associative.
Division is neither commutative nor associative.
Responses
Division is associative but not commutative.
Division is associative but not commutative.
Division is both commutative and associative.
Division is both commutative and associative.
Division is commutative but not associative.
Division is commutative but not associative.
Division is neither commutative nor associative.
Answers
There are no human answers yet.
Answered by
GPT-4o mini
The correct statement is: **Division is neither commutative nor associative.**
To clarify:
- **Commutative** means that the order of the operation does not change the result. For example, addition and multiplication are commutative (e.g., \(a + b = b + a\)). However, division is not commutative because \(a \div b\) does not equal \(b \div a\) (e.g., \(6 \div 2 \neq 2 \div 6\)).
- **Associative** means that the way in which numbers are grouped does not change the result. For example, addition and multiplication are associative (e.g., \((a + b) + c = a + (b + c)\)). However, division is not associative because \((a \div b) \div c\) does not equal \(a \div (b \div c)\) (e.g., \((8 \div 4) \div 2 \neq 8 \div (4 \div 2)\)).
Thus, division is neither commutative nor associative.
To clarify:
- **Commutative** means that the order of the operation does not change the result. For example, addition and multiplication are commutative (e.g., \(a + b = b + a\)). However, division is not commutative because \(a \div b\) does not equal \(b \div a\) (e.g., \(6 \div 2 \neq 2 \div 6\)).
- **Associative** means that the way in which numbers are grouped does not change the result. For example, addition and multiplication are associative (e.g., \((a + b) + c = a + (b + c)\)). However, division is not associative because \((a \div b) \div c\) does not equal \(a \div (b \div c)\) (e.g., \((8 \div 4) \div 2 \neq 8 \div (4 \div 2)\)).
Thus, division is neither commutative nor associative.
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