36÷(12÷3) and (36÷12)÷3 Are they equivalent and what property is applied?
36÷(12÷3) = 36/4 = 9
(36÷12)÷3 = 1
To determine if the expressions 36÷(12÷3) and (36÷12)÷3 are equivalent, we need to simplify them and compare the results.
Let's solve the first expression, 36÷(12÷3), step by step:
Step 1: Simplify the inner division 12÷3 = 4.
Step 2: Substitute the result back into the original expression: 36÷4 = 9.
Now, let's solve the second expression, (36÷12)÷3, step by step:
Step 1: Simplify the division 36÷12 = 3.
Step 2: Substitute the result back into the original expression: 3÷3 = 1.
Comparing the results, we see that 9 ≠ 1. Therefore, the expressions 36÷(12÷3) and (36÷12)÷3 are not equivalent.
Now, let's discuss the property that is applied in the simplification. The property used here is the Associative Property of Division. According to this property, when dividing multiple numbers, the grouping of the numbers does not affect the result. However, it is important to note that the order of the numbers being divided does matter.
In the given expressions, when we use the Associative Property of Division, it allows us to group the numbers differently without changing the result. But still, since the numbers being divided are different in each expression, the results are not equivalent.