By Takashi Kojima
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Additional info for Advanced abacus: Japanese theory and practice
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. For further details see Examples 2 and 3, section 2 of this chapter. 48 Advanced Abacus Japanese Theory and Practice, by Takashi Kojima EXAMPLE 2: Subtract 12 days 17 hours 48 minutes from 25 days 12 hours 43 minutes.
STEP 4: Multiplying the 5 on D by 10, set the product 50 on FG. This makes a total of 580 on FGH. Next, multiplying the same 5 on D by 2, add the product 10 to the 58 on FG, and clear D of the 5. This gives you a total of 680 on FGH (Fig. 134). STEP 5: Multiplying the 2 remaining on C by 10, set the product 20 on EF. This makes a total of 2 680 on EFGH. Finally, multiplying the same 2 on C by 2, add the product 4 to the 6 on F, and clear C of the 2. This gives you a total of 3 080 on EFGH (Fig.
187). Mark off the digits in sets of twos. The largest square less than 6 is 4. 55 Advanced Abacus Japanese Theory and Practice, by Takashi Kojima STEP 2: Set, on A, 2, the root of the 4. Square this 2, and subtract the product 4 from the 6 on C. 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.
Advanced abacus: Japanese theory and practice by Takashi Kojima