Which statement is correct
Division is commutative but not associative
Division is both commutative and associative
Division is neither commutative nor associative
Division is associative but not commutative
Division is neither commutative nor associative.
The correct statement is:
Division is neither commutative nor associative.
The correct statement is "Division is associative but not commutative."
To understand why this is the correct statement, let's break down the properties of division:
1. Commutative: A binary operation (like division) is commutative if the order of the operands does not affect the result. For example, if we have two numbers a and b, then a ÷ b = b ÷ a. However, division does not follow this property. For example, 4 ÷ 2 is not equal to 2 ÷ 4.
2. Associative: A binary operation is associative if the grouping of the operands does not affect the result. In other words, (a ÷ b) ÷ c = a ÷ (b ÷ c). Division does follow this property. For example, (10 ÷ 5) ÷ 2 is equal to 10 ÷ (5 ÷ 2), both resulting in 1.
Therefore, division is not commutative but it is associative.