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### 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
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/
```
Associated Topics:
Elementary Division

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