Which statement is correct?(1 point)

Responses

A. Division is neither commutative nor associative.
B. Division is commutative but not associative.
C. Division is associative but not commutative.
D. Division is both commutative and associative.

1 answer

The correct statement is:

A. Division is neither commutative nor associative.

In detail:

  • Commutative property: For division, \( a \div b \) is not necessarily equal to \( b \div a \). For example, \( 10 \div 5 = 2 \) and \( 5 \div 10 = 0.5 \).

  • Associative property: For division, \( (a \div b) \div c \) is not necessarily equal to \( a \div (b \div c) \). For example, \( (8 \div 4) \div 2 = 2 \div 2 = 1 \), but \( 8 \div (4 \div 2) = 8 \div 2 = 4 \).

Therefore, division fails both the commutative and associative properties.