Fraction Division Diagrams

Date: 04/21/99 at 15:31:12
From: Lanette Mitchell
Subject: Dividing fractions/diagrams

How do you diagram the following problem:  1 divided by 1 1/2?

This was asked after explanations and diagramming of division problems 
where there were whole numbers divided by fractions less than 1. Mixed 
number divisors were not part of the diagramming examples but were 
part of the practice on the page.

Date: 04/21/99 at 17:02:02
From: Doctor Peterson
Subject: Re: Dividing fractions/diagrams

Hi, Lanette.

I'm not sure exactly what kind of diagram you are using; if mine is 
too far off, maybe you can write back with an example for whole 
numbers and proper fractions.

The first approach that comes to mind is something like this, for 3 
divided by 1/2:

    +---------------+---------------+---------------+
    |                       3                       |
    +---------------+---------------+---------------+
    +-------+-------+-------+-------+-------+-------+
    |  1/2  |  1/2  |  1/2  |  1/2  |  1/2  |  1/2  |
    +-------+-------+-------+-------+-------+-------+

There are 6 1/2's in 3.

When the result is a fraction, it's a little more awkward; for 3 
divided by 2, the best I can do is:

    +---------------+---------------+---------------+
    |                       3                       |
    +---------------+---------------+---------------+
    +---------------+---------------+---------------+---------------+
    |               2               |               2               |
    +---------------+---------------+---------------+---------------+

There are 1 1/2 2's in 1.

For 1 divided by 1 1/2, it would look like

    +-------------------------------+
    |               1               |
    +-------------------------------+
    +-------------------------------+---------------+
    |                      1 1/2                    |
    +-------------------------------+---------------+

There are 2/3 of a 1 1/2 in 1 (since each 1/2 is 1/3 of 1 1/2).

Is that anything like what you need?

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