which statement is correct?

Question

Both division is both commutive and associative
division is commutive neither nor associative
division is commutive but not associative
division is associative but not commutive

Answer 1

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

To elaborate:

1. Commutative Property: This states that changing the order of the numbers does not change the result. For example, \( a \div b \) is not equal to \( b \div a \) (e.g., \( 6 \div 3 \neq 3 \div 6 \)). Therefore, division is not commutative.

2. Associative Property: This states that the way in which numbers are grouped in an operation does not change the result. For example, \( (a \div b) \div c \) is not equal to \( a \div (b \div c) \). Thus, division is not associative either.

So, division is neither commutative nor associative.