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Marjanovic, M.M. (2015) Division—A Systematic Search for True Digits, II. The Teaching of Mathematics, XVIII, 84-92.
http://www.elib.mi.sanu.ac.rs/journals/tm

has been cited by the following article:

  • TITLE: Elaboration of Division—A Systematic Search for True Digits

    AUTHORS: Milosav M. Marjanović

    KEYWORDS: Canonical Division, Long Division, Rounding up Divisor, Rounding down Dividend, Algorithm to Find True Digits

    JOURNAL NAME: Open Access Library Journal, Vol.4 No.2, February 21, 2017

    ABSTRACT: In this paper, a new procedure of division is proposed and the corresponding didactical elaboration is sketched. A division task A:B is called canonical when A is less than tenfold B. As it is well known, each procedure of division splits into a number of canonical ones. The proposed elaboration is carried out in two main steps: the cases of canonical division by a two-digit divisor and the cases of long division. In order to make division easier, in the first step, a divisor is rounded up, increasing its first digit by 1 and replacing the second one by 0. In the same time, the dividend is rounded down replacing its last digit by 0. In this way the calculation is reduced to divisions by a one-digit divisor. This step is technically important and should precede the case of long divisions. Let A:B be a case of canonical long division. The divisor B is rounded up, increasing its second digit by 1 and replacing all those that follow by 0’s. In the same time, the dividend A is rounded down, replacing by 0’s the same number of its final digits as in the case of B. Thus, this division task is reduced to a “short” canonical division whose divisor is a two-digit number. According to a fact proved by this author in his paper Division—A Systematic Search for True Digits, II, The Teaching of Mathematics, XVIII, 2, (2015), 84-92, the quotient of the “short” division is equal or just 1 less than the number representing the true digit. This fact is the basis for the algorithm of producing true digits that we propose which is a contrast to the traditional “trial and error” method.