By Takashi Kojima
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Extra resources for Advanced abacus: Japanese theory and practice
107). 34 Advanced Abacus Japanese Theory and Practice, by Takashi Kojima NOTE: When a divisor is a mixed decimal, it is advisable for the beginner to set its unit digit on a unit rod. STEP 2: As the divisor is a three-digit number, sup-pose that you have divided the 537 on EFG by 100, with the 5 on E as the first quotient figure, and found that 5 is too large. It is because if you multiply the 1 on A by the 5 on E, the product 5 which is to be set on F is larger than the 3 on F. So try 4 as the first trial quotient figure in your mind.
In this step, apply Rule 2. Now, multiplying the 4 on A by the 8 on D, add the product 32 to the 16 on EF. This gives you 480 on EFG (Fig. 115). 37 Advanced Abacus Japanese Theory and Practice, by Takashi Kojima STEP 3: In this final step, apply Rule 1 and try 5, which is larger than the 4 on E by 1, as the next trial quotient figure. Multiplying the 4 on A by this 5, add the product 20 to the 80 on FG, and you get 500 on FGH. This number is equal to the 500 obtained by multiplying the divisor 100 by the trial quotient 5.
Advantages and Disadvantages The advantages and disadvantages of this method of division are nearly identical with those of the method of multiplication which leaves the initial digit one of the multiplier out of calculation (see chapter 3, section 6). 08, etc. , often this method simplifies calculation, although the sort of difficulties illustrated in Example 4 may arise. (2) As shown in Examples 3 and 4, when the divisor is a mixed decimal whose whole digit one is in the units place, the unit rod of the quotient is identical with that of the dividend.
Advanced abacus: Japanese theory and practice by Takashi Kojima