Which statement is correct?
A. Division is neither commutative or nor associative
B. Division is both commutative and associative
C. Division is associative but not Commutative
D. Division is Commutative but not associative
C. Division is associative but not Commutative
The correct statement is C. Division is associative but not commutative.
To determine which statement is correct, we need to understand the properties of division.
Commutativity refers to the ability to interchange the order of the numbers or elements in an operation without changing the result.
Associativity refers to the ability to group numbers or elements in an operation without changing the result.
Now let's analyze each option:
A. Division is neither commutative nor associative: This statement suggests that division does not possess either commutativity or associativity.
B. Division is both commutative and associative: This statement suggests that division possesses both commutativity and associativity.
C. Division is associative but not commutative: This statement suggests that division is associative but lacks commutativity.
D. Division is commutative but not associative: This statement suggests that division is commutative but lacks associativity.
To find the correct statement, let's consider the properties of division.
Commutativity: Division is not commutative. Swapping the dividend and divisor generally results in a different result. For example, 8 ÷ 4 is not equal to 4 ÷ 8.
Associativity: Division is associative. When dividing multiple numbers, it doesn't matter how we group them. For example, (8 ÷ 4) ÷ 2 is equal to 8 ÷ (4 ÷ 2).
Based on our analysis, the correct statement is:
C. Division is associative but not commutative.