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 3/2This becomes:6/6 1 1 8/9 8/9 8/9 _____ = _____ = _____ * _____ = _____ = _____ = 8/9 9/8 9/8 9/8 8/9 72/72 1Notice 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.
If you got to this page without reading Dividing Fractions, you should do that first.