I don't understand this. Can you do some examples?
One student had the following way of dividing fractions. First the student renamed the two fractions with a common denominator. Then the student ignored the denominators and just divided the numerators to obtain the answer. Does this method work? Try it on enough examples to form a conclusion about whether it always, sometimes, or never works.
Please show work
Renaming fractions:
1/2 / 1/4 = 2/4 / 1/4
Divide numerators:
2 / 1 = 2
That seems to be what your question is asking.
Like 4/1=4 its the same thing but on both sides
To determine whether the method of dividing fractions always, sometimes, or never works, let's test it out using a few examples.
Example 1:
Let's divide 1/2 by 1/4 using the method described.
First, we need to find a common denominator for both fractions, which in this case is 4.
1/2 can be rewritten as 2/4.
Now we ignore the denominators and simply divide the numerators: 2 ÷ 1 = 2.
So according to this method, 1/2 ÷ 1/4 = 2.
Example 2:
Let's divide 2/3 by 2/5 using the same method.
Finding a common denominator, we get 3/5 for 2/3.
Ignoring the denominators, we divide the numerators: 3 ÷ 2 = 1.5.
So, 2/3 ÷ 2/5 = 1.5.
Example 3:
Let's divide 3/4 by 1/2.
Renaming the fractions with a common denominator, we get 3/4 and 2/4.
Ignoring the denominators, we have 3 ÷ 2 = 1.5.
Hence, 3/4 ÷ 1/2 = 1.5.
Based on these examples, it seems that the method of renaming the fractions with a common denominator and then dividing the numerators alone does work for dividing fractions. However, to establish a conclusion, we need to test more examples.
Example 4:
Let's divide 2/3 by 3/4.
Finding a common denominator, we get 8/12 for 2/3.
Now, when we ignore the denominators and divide the numerators, we have 8 ÷ 3 ≈ 2.67.
So, 2/3 ÷ 3/4 is approximately equal to 2.67.
In this case, the method still seems to work.
Examining all the examples, we can conclude that the method of renaming the fractions with a common denominator and then dividing the numerators does indeed work for dividing any two fractions. Therefore, the conclusion is that this method always works for dividing fractions.