Which statement is correct?(1 point)

Question

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.

Answer 1

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.