Which statement is correct is division, associative, or commutative?
The statement "division is not commutative" is correct.
In division, neither the associative property nor the commutative property applies.
The associative property states that the grouping of numbers being divided does not affect the result. However, in division, changing the grouping of numbers will change the result. For example, (12 ÷ 3) ÷ 2 = 2 ÷ 2 = 1, but 12 ÷ (3 ÷ 2) = 12 ÷ 1.5 = 8.
The commutative property states that the order of numbers being divided does not affect the result. However, in division, changing the order of numbers will generally yield different results. For example, 10 ÷ 5 = 2, but 5 ÷ 10 = 0.5.
Therefore, neither the associative property nor the commutative property holds true for division.
The correct statement in division is the commutative property.
To understand why, let's first define the properties of division:
1. Commutative property: This property states that changing the order of the numbers being divided does not change the result. For example, a ÷ b is equal to b ÷ a.
2. Associative property: This property states that changing the grouping of numbers being divided does not change the result. For example, (a ÷ b) ÷ c is equal to a ÷ (b ÷ c).
Now, let's consider division using an example:
Suppose we have two numbers, a = 12 and b = 4. We want to perform the division a ÷ b.
Using the commutative property of division, we can switch the order of the numbers: b ÷ a. In this case, it would be 4 ÷ 12.
However, changing the order of the numbers in this case does not give us the same result. 12 ÷ 4 is equal to 3, but 4 ÷ 12 is equal to 0.33.
So, the commutative property is not valid for division in general.