Short Division

Date: 01/11/2002 at 20:57:33
From: Alexis Rushing
Subject: Short division

I know how to do long division, but I have math problems that say 
solve by using "short division." Can you explain what this means, how 
it is different from long division (if it is), and how I would do a 
problem such as 205 divided by 4 using "short" division?

Thank you very much, 
Alexis Rushing

Date: 01/11/2002 at 22:26:26
From: Doctor Peterson
Subject: Re: Short division

Hi, Alexis.

I checked the Web to make sure that what I call short division is 
still called that; here's one explanation:

   Short Division - Garden Schools, Missouri
   http://www.gardenschools.com/Class/MA/MAIN0010.htm   

This method can be used to save paper when you are dividing by a one-
digit number. You do all the same work as in long division, but do 
most of it in your head. I would have expected your text to tell you 
what it is before asking you to use it. I'll demonstrate on a problem 
like yours, first as long division:

      ____5_8_
    3 ) 1 7 5
        1 5
        ---
          2 5
          2 4
          ---
            1

and then as short division:

      ____5_8_rem_1
           2
    3 ) 1 7 5

The extra 2 is meant to be a small raised 2 just to the left of the 5. 
What I did here was to divide 17 by 3, giving 5, and subtract 17-15 in 
my head, leaving a remainder of 2. Then, where in long division I 
would "bring down" the 5, I instead "put up" the 2 next to the 5, 
making the new dividend 25. Now I divide 25 by 3 and get 8; when I 
subtract 25-24 in my head I just write the remainder in the answer.

Your specific problem is even easier than this one; I didn't do yours 
because I couldn't have demonstrated putting up the remainder.

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