Åk 6–9
 
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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.