Which statement is correct.
A. Division is neither commutative 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, let's first understand the definitions of commutativity and associativity in mathematics.
Commutativity refers to the order of operations or operands not affecting the result. In other words, the order in which you perform the operation does not change the outcome. For example, in addition, 2 + 3 and 3 + 2 give the same result because addition is commutative: 2 + 3 = 3 + 2.
Associativity, on the other hand, pertains to grouping or combining operations. If an operation is associative, it means that when you have three or more operands, the grouping of the operands does not change the result. For example, in addition, (2 + 3) + 4 and 2 + (3 + 4) yield the same result because addition is associative: (2 + 3) + 4 = 2 + (3 + 4).
Now, let's examine the options:
A. Division is neither commutative nor associative.
If we consider two numbers, a and b, division is not commutative because a ÷ b is generally not equal to b ÷ a. For example, 6 ÷ 3 = 2, but 3 ÷ 6 = 0.5. Therefore, this statement is correct about commutativity. However, the statement also claims division is not associative, which is incorrect.
B. Division is both commutative and associative.
As we just discussed, division is not commutative, so this statement is incorrect.
C. Division is associative but not commutative.
Division is indeed associative. For example, (4 ÷ 2) ÷ 2 is equal to 4 ÷ (2 ÷ 2), both yielding the result 1. However, since division is not commutative, this statement accurately describes the properties of division. Therefore, this statement is correct.
D. Division is commutative but not associative.
As we discussed, division is not commutative. Hence, this statement is incorrect.
In conclusion, the correct statement is:
C. Division is associative but not commutative.