By Takashi Kojima


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Extra resources for Advanced abacus: Japanese theory and practice

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The Japanese technical term for this division may be translated as the initial-digit-one elimination division. , such as 103, 1 014, etc. It is a counterpart of the multiplication method in which the initial digit one of the multiplier is left out of calculation. Let us take a very simple example. If you divide 306 by 102, you get the quotient 3. In this case, since the first digit of the divisor 102 is 1, the first digit 3 of the dividend 306 may be used as the quotient. This principie is applied to this method of division on the abacus, On the abacus board, in each step of the division, the first digit of the dividend is used as the trial quotient, and thus the necessity of setting the quotient and that of removing the first digit of the dividend is eliminated, and calculation is considerably simplified and accelerated.

On the board, the procedures of setting the first quotient figure 3 and of subtracting the first digit 3 of the dividend are saved or eliminated. EXAMPLE 2: 2 575 / 103 = 25 STEP 1: Set the dividend 2 575 on DEFG and the 3 of 103 on A (Fig. 100). NOTE: There is no objection to setting the whole divisor 103 on the board. However, experts do not, be-cause this digit is not actually used in calculation, and so long as they remember that the 3 on A stands for 103 it is not important to set the whole divisor on the board.

STEP 4: Since you cannot subtract 48 from the 43 on GH, borrow 1 from the 9 on E, and subtracting 48 from 60, add the result 12 to the 43 on GH. This makes 55 on GH. Now you have 12 on AB, 18 on DE, and 55 On GH. The answer is 12 days 18 hours 55 minutes (Fig. 156). EXAMPLE 3: In the above example, the second and fourth compound numbers are to be added, and the third to be subtracted. When both additions and subtractions are to be performed, calculations generally move from higher to lower denominations on each row.

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