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# Takashi Kojima's Advanced abacus: Japanese theory and practice PDF

By Takashi Kojima

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Sample text

STEP 1: Set 4 489 on DEFG, with G as the unit rod (Fig. 193). Mark off the digits in sets of twos. In the first pair 44, the highest square root is 6. STEP 2: Set, on B, 6, which is the root of the 44 on DE. Square this 6, and subtract the product 36 from the 44 on DE. This leaves 889 on EFG (Fig. 194). STEP 3: Double the 6 on B into 12 on AB (Fig. 195). STEP 4: The 12 on AB divides into the 88 On EF seven times. Set the second trial divisor figure 7 on C (Fig. 196). NOTE: The 7 on C corresponds with the b of the expression.

151). STEP 5: Finally add 21, 15, and 29 successively to the 2 on B. This makes a total of 67 on AB. The answer is 67 yd. 1 ft. 2 in. on AB, D, and G respectively (Fig. 152). NOTE: Why are the yards, feet, and inches figures set as they are in this example? The great advantage of this arrangement of these figures is that the standard methods of multiplication and division can be used. Notice the use of the standard method of division in steps 4 and 5 of Method A, and in steps 2 and 4 of Method B in this example.

Clear CD of its 12, and set the divisor 20 on AB, leaving four vacant rods between it and the 515 on GHI (Fig. 140). STEP 6: Now comparing the 2 on A and the 5 on G, set the quotient 2 on E. Multiplying the 2 on A by this 2 on E, subtract the product 4 from the 5 on G. This leaves 115 on GHI (Fig. 141). 46 Advanced Abacus Japanese Theory and Practice, by Takashi Kojima STEP 7: Next compare the 2 on A and the 11 on GH and set the quotient figure 5 on F. Multiplying the 2 on A by this 5 on F, subtract the product 10 from the 11 on GH.

### Advanced abacus: Japanese theory and practice by Takashi Kojima

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