Which statement is correct?(1 point)
Responses
Division is commutative but not associative.
Division is commutative but not associative.
Division is associative but not commutative.
Division is associative but not commutative.
Division is neither commutative nor associative.
Division is neither commutative nor associative.
Division is both commutative and associative.
Division is neither commutative nor associative.
The correct statement is:
Division is neither commutative nor associative.
To determine which statement is correct, we need to understand the properties of division: commutativity and associativity.
Commutativity refers to the ability to change the order of the numbers being divided without changing the result. In other words, if a and b are two numbers, then a ÷ b is equal to b ÷ a.
Associativity refers to the ability to regroup the numbers being divided without changing the result. In other words, if a, b, and c are three numbers, then (a ÷ b) ÷ c is equal to a ÷ (b ÷ c).
Let's compare the statements one by one:
1. "Division is commutative but not associative."
This statement contradicts the principles of division. Division is actually not commutative, which means that changing the order of the numbers being divided changes the result. For example, 6 ÷ 3 = 2, but 3 ÷ 6 = 0.5. Therefore, Statement 1 is incorrect.
2. "Division is associative but not commutative."
This statement also contradicts the principles of division. Division is not associative, which means that regrouping the numbers being divided changes the result. For example, (6 ÷ 3) ÷ 2 = 1, but 6 ÷ (3 ÷ 2) = 4. Therefore, Statement 2 is incorrect.
3. "Division is neither commutative nor associative."
This statement accurately describes the properties of division. Division is neither commutative nor associative, as explained in the previous statements. Therefore, Statement 3 is correct.
4. "Division is both commutative and associative."
This statement is incorrect because division is neither commutative nor associative, as stated in Statement 3 above.
So, the correct statement is: "Division is neither commutative nor associative."