Division as Repeated SubtractionDate: 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/ |
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