Writing a Remainder as a Reduced Fraction

Date: 08/29/2001 at 23:56:03
From: Maria Verduzco
Subject: To do division and write the the remainder as a reduced 
fraction 

Dr. Math,

I am having trouble doing division and writing the remainder as a 
reduced fraction. I only have two problems to solve: 1,652 divided by 
12 and 43,144 divided by 45. 

Thanks so much!

Date: 08/30/2001 at 13:03:05
From: Doctor Peterson
Subject: Re: To do division and write the the remainder as a reduced 
fraction 

Hi, Maria.

I'll give you a simple example. Let's divide 23 by 4:

      ___5_
    4 ) 23
        20
        --
         3

This means that if we divide 23 by 4 we get 5, with a remainder of 3. 
How can we treat that remainder as a fraction?

Look at it this way. I want to fill boxes with books. Four books fit 
in a box, and I have 23 books. The division shows me that I can fill 
5 boxes completely, and will have 3 books left over. How full will the 
next box be? It will contain 3 out of 4 books, so it will be 3/4 full.

So our answer is, 23 / 4 = 5 3/4. We use the remainder as the 
numerator of the fraction, and the divisor as the denominator.

This process is actually identical to that of converting an improper 
fraction to a mixed number. You can read more about that by going to 
our Search page

   http://mathforum.org/mathgrepform.html   

and looking for the keywords   improper fraction mixed  .

If you still have trouble, write back and show me your work so I can 
check it and see where, if at all, you have made a mistake.

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