A Fraction Divided By a Fraction

Date: Wed, 30 Aug 1995 18:52:47 -0700 (MST)
From: Petrescu
Subject: Answer please

Please answer this math problem me and my dad are fighting about.

18/6 divided by 2/3

Sincerely,
Alex P.

Date: 9/1/95 at 16:16:45
From: Doctor Ken
Subject: Re: Answer please

Hello!

The thing to remember here is that multiplication and division are opposites.
Mathematicians call operations like these two "inverse operations."  So if
you have x divided by y, that's the same as x times 1/y.  

So there are a couple of ways to do your problem: you could change it to
18/6 times 3/2, and you multiply and cancel to get 9/2.  Or you could change
the 18/6 at the beginning of the problem to 3, since 18/6 = 3.  

Or you could do it as a great big complex fraction:

         18/6
         ----   and then you can multiply it by 6/6, which is 1.
         2/3

         18/6     6       18       9
         ----  * ---  =  ----  =  ---
         2/3      6       4        2

Any way you slice it, the answer is 9/2.

-Doctor Ken,  The Geometry Forum