By Takashi Kojima
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Additional info for Advanced abacus: Japanese theory and practice
This leaves 225 on CDE (Fig. 188). NOTE: The 225 on CDE corresponds to the (2ab +b2) of the algebraic expression. 5 on CDEF (Fig. 189). 5 on FGHI and later set it on CDEF. 5 on CDEF corresponds to (ab + b2/ 2) of the algebraic expression. STEP 4: The 2 on A divides into the 11 on CD five times. Set the second trial quotient figure 5 on B (Fig. 190). NOTE: The 5 on B corresponds with the b of the expression. STEP 5: Multiply the 2 on A by the 5 on B, and subtract the product 10 from the 11 on CD.
However, it should be noted that its utility is limited to problems in which the multipliers are numbers a little smaller than 100, 1 000, etc. 96, etc. 92 = 3 312 Advanced Abacus Japanese Theory and Practice, by Takashi Kojima IV - OTHER METHODS OF DIVISION There is an older method of division which is as fast as the standard method of division that I explained in my first book. But this method is no faster and it requires the memorization of a complicated division table. Although this method is still used by the older generation, it is generally becoming obsolete.
EXAMPLE 2: Find the square root of 4 489 (Method B). 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.