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Q&A #4130 |
From: annie
To: Teacher2Teacher Public Discussion
Date: 2008072520:36:29
Subject: Re: a German algorithm
Actually, there is more structure to the German style beyond the multiplication approach you specified. First off, the German method follows the conventions of all other calculations where we write down the operation in the order we complete it in. In the US the long division is a very disturbing exception to this rule and so far I did not find a logical (historical?) explanation for this. The "corner" very much resembles a square root for the unsuspecting German eye seeing the US long division algorithm for the first time. 12785 divided by 5 equals? (In lieu of the international division symbol I'll use the backward slash): 12785 / 5 = _______ It will look exactly like the US long division and follows the same lay out of subtracting and bringing down digits! Only the operation itself is written out differently to reflect the flow of thinking in a much more logical way. You'll see the simple beauty of executing the operation German style by following a circular sweeping motion first from left to right doing the simple division and then from right to left completing the reverse operation (multiplication) to figure out any remainders. 1 divided by 5? 5 does not go into 1, skip this and bring down next digit 12 divided by 5? Yes, that would be two and 2 left over: Here is the circular motion in action: from left to right operating above the equation you divide 12 by 5 (cover the other digits to make it obvious) and write down the first result next to the = sign like this: to (left) 12XXX / 5 = 2 (right) Now continue your circular motion right to left below the equation with multiplying (reverse operation) 2 X 5 = 10 like this: (left) 10 = 5 X 2 (right) to and writing the product down underneath the dividend we started with, lining it up nicely, preferably using graph paper 12785 / 5 = 2557 10 do right to left multiplication 10 = 5 x 2 -____ 27 pull down 7 to get next dividend and divide by 5 (left to right)! 25 do right to left multiplication 25 = 5 x 5 -_____ 28 pull down 8 to get next dividend and divide by 5 ! 25 do right to left multiplication 25 = 5 x 5 -______ 35 pull down 5 to get next dividend and divide by 5 35 do right to left multiplication 35 = 5 x 7 -_______ 0
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