Division as Repeated Subtraction

Date: 03/06/98 at 10:34:25
From: Maren Lewis
Subject: division using only addition and subtraction

I get straight A's in math, but my stepfather has me stumped. He says 
that you can do division using only addition and subtraction. He says 
you can take two integers (A and B) and divide A by B using only 
addition and subtraction.

We have a bet and I want to win. My stepfather works on computers and 
he is very good at math, and I know he just wants to see if I can 
figure this out. 

Can you help me solve this problem?

Date: 03/06/98 at 16:22:02
From: Doctor Sam
Subject: Re: division using only addition and subtraction

Maren,

Your stepfather is correct. After all, multiplication is repeated 
addition: you can find 256 * 781 by adding up two hundred fifty-six 
781s.

Likewise, division is repeated subtraction. You've probably forgotten 
how you first learned division, but it probably included a problem 
like this:

"I have 15 candy bars and want to share them with 4 other friends.  
How many candy bars will each get?"

The method is to give everybody candy bars one-at-a-time until none is 
left. This is like dealing cards where everybody gets one card at a 
time. Since there are five friends, you can give everybody one candy 
bar (that's 5 all together, so you have 15 - 5 = 10 left). Now give 
everybody a second candy bar. Now each person has 2 and you have 
10 - 5 = 5 left...and so on.

So you can divide 23 into 781 by repeatedly subtracting 23 and keeping 
track of how many 23s you have subtracted. It's nothing that you or I 
would want to do . . . long division is MUCH easier and faster. But 
computers are fast and patient. They don't mind doing several million 
subtractions in order to find a result!

Does that help?

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