Which statement is correct division is associative, but not commutative. Division is commutative, but not associative. Division is neither commutative. Aurness associative division is both communicative and associative.
The statement "Division is neither commutative" is correct.
The correct statement is: Division is neither commutative nor associative.
The correct statement is:
"Division is neither commutative."
To understand why, let's break down the concepts of commutativity and associativity in relation to division.
Commutativity refers to the ability to change the order of the operands without changing the result. In other words, if division is commutative, swapping the numerator and denominator should not affect the outcome.
For example, consider the division problem:
10 ÷ 5 = 2
If we swap the numerator and denominator, we get:
5 ÷ 10 = 0.5
As you can see, the result changes when we swap the order. This demonstrates that division is not commutative.
Associativity, on the other hand, refers to the ability to change the grouping of the operands without changing the result. In other words, if division is associative, it should not matter how you group the numbers before dividing.
For example, consider the division problem:
(10 ÷ 5) ÷ 2 = 1
If we group the numbers differently, we get:
10 ÷ (5 ÷ 2) = 4
As you can see, changing the grouping leads to different results. This shows that division is not associative either.
In summary, division is neither commutative nor associative. It is important to understand these properties in mathematics as they help us manipulate numbers and operations in a consistent manner.