Why the Fraction Division Technique Works

Date: 11/27/2004 at 15:46:38
From: Julia
Subject: (no subject)

Why do we need to flip the second fraction when we divide fractions?

For example:

  (1/2) / (2/3) = 1/2 x 3/2 = 3/4

I am not confused about dividing fractions, but all these years I have 
wondered why we need to flip the second fraction when we are dividing.

Date: 11/29/2004 at 12:22:28
From: Doctor Roy
Subject: Re: (no subject)

Hi Julia,

Thanks for writing to Dr. Math.

We aren't _really_ flipping the second fraction, but it is a useful
mnemonic device.  We are really multiplying by 1:

     (1/2) / (2/3)

  = [(1/2) / (2/3)]   * 1
  = [(1/2) / (2/3)] * [(3/2) / (3/2)]
  = [(1/2) * (3/2)] / [(2/3)*(3/2)]
  = [(1/2) * (3/2)] / 1
  = [(1/2) * (3/2)]
  = (1/2) * (3/2)

The end result is the same as if we flipped the second fraction, but
the full process (entirely written out) shows that it is really
multiplying by 1 (in a different way).

Does this help?  Please feel free to write back with any questions you
may have.

- Doctor Roy, The Math Forum
  http://mathforum.org/dr.math/ 

Date: 11/29/2004 at 22:05:37
From: Julia
Subject: Thank you ((no subject))

Thank you very much for your help and time to answer this question.
Now I fully understand the concept of why we need to flip the second
fraction when we are dividing.