Which statement is correct?(1 point)

Responses

Division is both commutative and associative.
Division is both commutative and associative.

Division is associative but not commutative.
Division is associative but not commutative.

Division is neither commutative nor associative.
Division is neither commutative nor associative.

Division is commutative but not associative.

1 answer

The correct statement is: Division is neither commutative nor associative.

In more detail:

  • Commutative property means that changing the order of the numbers does not change the result (e.g., \( a + b = b + a \) for addition). For division, \( a \div b \neq b \div a \) in general.
  • Associative property means that the grouping of the numbers does not change the result (e.g., \( (a + b) + c = a + (b + c) \) for addition). For division, \( (a \div b) \div c \neq a \div (b \div c) \) in general.

Thus, division fails to satisfy both properties.