Åk 6–9

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 upside-down 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: · = = = 1

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.