Dividing Fractions

Date: 8/4/96 at 16:1:48
From: Jeffrey Paul Goins
Subject: Dividing fractions

Dear Dr. Math,

Why do you flip the second fraction when dividing fractions (who 
figured that out anyway)?  

Thank you!

Levi Goins

Date: 8/5/96 at 11:29:51
From: Doctor Anthony
Subject: Re: Dividing fractions

Why when dividing fractions do you turn the second one upside down and 
multiply?
 
Example 5/(1/2) = 5*2 = 10

By keeping the rules consistent this rule is easy to derive.

A fraction is unchanged if you multiply top and bottom by the same 
number. In this case if we multiply top and bottom by 2 (which is 1/2 
turned upside down) we get:

   (5*2)/{(1/2)*2} = 10/1 = 10

You will notice that by multiplying top and bottom by the bottom 
fraction turned upside down we are ensuring that the denominator of 
the original fraction becomes equal to 1.  In practice this is 
achieved by applying the rule you quoted.

-Doctor Anthony,  The Math Forum
 Check out our web site!  http://mathforum.org/dr.math/