Advanced abacus: Japanese theory and practice by Takashi Kojima

By Takashi Kojima


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Additional resources for Advanced abacus: Japanese theory and practice

Sample text

But they can also move down each column—completing each column before moving to the higlier denomination. METHOD A: Calculating from higher to lower denominations: STEP 1: Set £95 on BC, with C as the unit rod, set 7 s. on unit rod F, and set 3 d. on unit rod I (Fig. 157). STEP 2: Add 12 to the 95 on BC, producing 107 on ABC. Add 8 to the 7 on F, yielding 15 on EF. Add 5 to the 3 on I producing 8 on I (Fig. 158). STEP 3: Subtract 7 from the 107 on ABC, leaving 100 on ABC. As you cannot subtract 49 Advanced Abacus Japanese Theory and Practice, by Takashi Kojima 19 from the 15 on EF, borrow 1 from rod C.

This gives you 900 on DEF. Since the divisor 98 is a two-whole-digit number, the unit rod of the quotient is formed on D. The answer is 9 on D (Fig. 113). EXAMPLE 2: 8 160 / 96 = 85 STEP 1: Set the dividend 8 160 on DEFG, and set on A, 4, which is the complement of 96 with respect to 100 (Fig. 114). Since the dividend is a two-digit number, 100 is used as the divisor. STEP 2: Divide the 816 on DEF by 100, with the 8 on D as the first trial quotient figure. 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.

110). STEP 5: Finally multiplying the 2 on B by the 8 on F, subtract the product 16 from the 16 on GH. This clears the board of the subtrahend and leaves 48 as the quotient on EF (Fig. 111). The answer is $4 800. 12 is a mixed decimal whose whole figure one is in the unit place, the unit rod of the dividend remains that of the quotient. Rules for Finding the Unit Rod of the Quotient RULE 1: When the divisor is a mixed decimal whose whole digit one is in the unit place, the unit rod of the quotient forms on that of the dividend.

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