Converting Between Mixed Numbers and Improper Fractions

Date: 04/08/99 at 18:31:46
From: Linday Stahl
Subject: Undoing improper fractions

I get mixed up doing and undoing improper and mixed numbers.

Date: 04/08/99 at 23:16:02
From: Doctor Peterson
Subject: Re: Undoing improper fractions

Hi, Linday.

Let's take a simple example:

What is 1 1/2 as an improper fraction? We can picture it as a box and 
half a box:

    +-------+ +-------+
    |       | |       |
    |       | +-------+
    |       |
    +-------+

If we turn the whole into halves, there are two halves there, plus the 
extra half makes 3:

    +-------+ +-------+
    |       | |       |
    +-------+ +-------+
    |       |
    +-------+

What we've just done is to rewrite 1 as 2/2, then add 2/2 + 1/2 to get 
3/2.

In general, you multiply the whole part by the denominator, then add 
the numerator of the fraction part. One way to think of this is that 
you start at the "bottom" and move clockwise around the mixed number, 
multiplying by the whole, then adding the numerator:

    +--------+
    |        |
    | +  1   +-> 2 x 1 + 1 = 3
    | 1 ---                 ---
    | x  2 ----------------> 2
    |    
    |    |
    +----+

To go the other way, let's start with the 3/2. How many wholes can we 
make out of 3 halves? Just divide the 3 by 2, because it takes 2 
halves to make each whole; we get 1 with a remainder of 1. That means 
there is one whole, and 1 half left over:

    +--------------+
    |              |
    | __1_rem 1    |
    2 ) 3    ---   |
       -2     2 <--+

So you just use the denominator (divisor) as the denominator with the 
remainder as the numerator.

If you have any specific problems you need help with, feel free to 
write back.

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