Geodesic
Division - a systematic search for true digits
The Teaching of Mathematics, VIII (2005) no. 2, p. 89 .

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For the sake of an easier understanding of the procedure of division, first this operation is conceived as continual subtraction. Taking into account place values of groups of digits of dividend, while proceeding with successive subtraction of divisor from such groups a slow, and in the real time feasible method of division is established. Based on this method, it is shown how a long division (quotients having two or more digits) is reduced to the short divisions (quotients are one-digit). In the case of short division, the first (second) guide number of divisor is defined which rounds down the corresponding dividend. Increasing by one the first (second) digit of divisor, it becomes rounded up and by dividing these guide numbers by the numbers that are increased by one, two methods of division are obtained, both having their advantages and disadvantages. In Section 6, a combined method is presented that should be at the top of practice in division. All three of these methods are clearly defined algorithms which are neat (free from trial and error correcting and erasing) and they successively produce true digits. This paper is intended for teachers, and it has a form containing all necessary details and examples that are within their reach.
Classification : 00A35 F32
Keywords: long division, short division, "Increase-by-one" methods 
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     title = {Division - a systematic search for true digits},
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Milosav M. Marjanović. Division - a systematic search for true digits. The Teaching of Mathematics, VIII (2005) no. 2, p. 89 . http://geodesic.mathdoc.fr/item/TM2_2005_VIII_2_a4/