Diagram Showing Division of Fractions

Date: 01/13/2002 at 19:48:27
From: Donna Mann
Subject: Diagram showing 2/3 / 3/4

I understand how to divide fractions, but would like to be able to 
draw this problem in a diagram.  

   2/3 / 3/4 =  8/9

Please explain what the 8/9 represents. (What part of what?)

Thanks so much.
Donna

Date: 01/14/2002 at 09:26:32
From: Doctor Peterson
Subject: Re: Diagram showing 2/3 / 3/4

Hi, Donna.

Here is an earlier answer to a similar question:

   Picturing Dividing Fractions
   http://mathforum.org/dr.math/problems/katherine.04.02.01.html   

I'll apply the same approach to your problem. The idea is that 
division amounts to measuring the dividend using the divisor as a 
unit. That is, when we divide, we are asking how many 3/4's there are 
in 2/3. Suppose we try to measure a 2/3-foot bar using a 3/4-foot 
stick:

    0                              2/3 3/4          1 foot
    +---+---+---+---+---+---+---+---+---+---+---+---+
                   2/3
    =================================      <--- the bar being measured
    |                                   |  <--- the measuring stick
    +---+---+---+---+---+---+---+---+---+
    0  1/9 2/9 3/9 4/9 5/9 6/9 7/9 8/9  1

You see that if I mark my measuring stick in ninths, each ninth 
corresponds to 1/12 of a foot (1/9 * 3/4), and the 2/3-foot bar 
measures 8/9 of the measuring stick. That is, 2/3 = 8/9 times 3/4, and 
2/3 / 3/4 = 8/9.

In summary, the answer represents 8/9 OF THE 3/4-FOOT MEASURING STICK. 
Does that help?

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