Teacher2Teacher Q&A #4130

Teachers' Lounge Discussion: European long division

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From: poopy gal]

To: Teacher2Teacher Public Discussion
Date: 2018012417:13:50
Subject: Re: Re: a German algorithm

On 2008072520:36:29, annie wrote: >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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