Teacher2Teacher |
Q&A #4130 |
From: Pat Ballew
(for Teacher2Teacher Service)
Date: Jun 16, 2000 at 18:30:50
Subject: Re: European long division
Here are two additional responses I got to my search for your answer.. The first is from Fernado Gouvea of Colby College and is similar to the letter from Flo I sent a few days ago. The second is from Martin Flashman who provides comments and a link to a page about Stevin, who perhaps can be called the father of decimal arithmetic.. : ------------------------------------------------------------------------ I grew up in Brazil, but attended an American school there, so one of the more interesting mathematical experiences I had as a young boy was to sort out why the long division algorithm I learned in school looked so different from the way my mother did it... In the end, the differences are merely in the layout of the numbers, I think. Let's take a specific computation: 133 divided by 12 is 11 with remainder 5. To see this right, you'll need to be using a monospaced font. The Americans taught me to do it like this: 11 ------ 12 ) 137 12 --- 17 12 --- 5 In Brazil, you'd typically write this: 137 |12 17 ---- 5 11 In both cases I've approximated the actual symbol used. In the Brazilian division, the divisor is inside an L-shaped symbol. In the American setup, the dividend is inside the symbol that looks like a denatured square root symbol. (In fact, when Brazilian friends saw me write that, they often assumed I was computing a square root!) One curious effect of these arrangements is linguistic. In Portuguese, you always read it as "137 divided by 12". In English, that's allowed, but "dividing 12 into 137", or simply "12 into 137" or "12 goes into 137" are more common. Some people have even suggested that the name of the symbol used for division is "guzinta" (read to sound like "goes into"). Apart from the change in position of dividend and divisor, the main difference is that the subtractions are typically done mentally rather than written out in full (though I've seen people do it that way too). The algorithm is really exactly the same. -- Fernando Q. Gouvea Department of Mathematics Editor, FOCUS and MAA Online Colby College http://www.maa.org Waterville, ME 04901 ---------------------------------------------------------------------------- This recent discussion reminded me of the organization of the work for division by Stevin in his brief treatise on the use of decimal notation for fractions. You can see this (in part) on the web at http://home.wxs.nl/~hopfam/Dime.html . I think you may find this of interest on the issue of how the organization of the work has changed. BTW, IMHO Stevin's development of decimal arithmetic was one of the most important developments in mathematics and western science and culture. from sunny Humboldt County, California martin ---------------------------------------------------------------------------- Hope these help. -Pat Ballew, for the Teacher2Teacher service
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