Subject: Re: [HM] European or South American Long division?
From: Fernando Q. Gouvea (fqgouvea@colby.edu)
Date: Thu Jun 15 2000 - 09:32:05 EDT
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 fqgouvea@colby.edu http://www.colby.edu/math ==========================================================
Van Roy's Law: An unbreakable toy is useful for breaking other toys.
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