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Dividing Fractions - Inverting the Denominator Fraction

When dividing fractions, why does it matter which fraction we invert? If you simply invert the numerator fraction and multiply it by the denominator, then you get the wrong answer; it comes out upside-down.

Read on if you want to understand why it's a little more complicated to invert the numerator fraction and why it doesn't result in a nice shortcut.

Let's work out our problem using the reciprocal of the numerator fraction.

     2/3       3/2
    _____  *  _____

     3/4       3/2
     
This becomes:
     6/6        1         1        8/9       8/9       8/9
    _____  =  _____  =  _____  *  _____  =  _____  =  _____  =  8/9

     9/8       9/8       9/8       8/9      72/72       1
    
Notice that at one point, we had:
     1
    ___

    9/8
...but we had to go through extra steps to simplify it. Dividing a number by 1 is not the same as dividing 1 by another number.

So it's much easier to invert the denominator fraction.

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