6.2
Peter’s Method with Fractions
When you are dividing two fractions with each other, it gets a little more difficult. One of our students, Peter, has come up with a smart way to solve the problem. He does the following:

÷ 


Earlier, you have learned that you can multiply with the same number in the numerator and denominator without changing the size of the number. It is called multiplying by a factor.
We should clarify what the numerator and the denominator is because we are dividing with fractions:
Numerator:


Denominator:


We should multiply this fraction by 4/3. We then see this:
You may wonder why we multiply by the factor 4/3. We had in the denominator 3/4, and 4/3 is just an upsidedown version of the fraction 3/4. This is called inverting a fraction. What will happen with the denominator when we multiply by the factor? Look here:
If we multiply by the denominator’s inverted fraction, we get the number 1 in the denominator.
We continue with the numerator and look at what we get after having multiplied with the denominators inverted fraction.
We then get: 
Numerator: 


Denominator: 1 


÷ 
1 
= 







The conclusion becomes that you can simply do division of fractions by multiplying by the denominator’s inverted fraction. 
