Advanced abacus: Japanese theory and practice by Takashi Kojima

By Takashi Kojima

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0032 = 98. The reason this might seem strange is that when an Occidental sets up any of these three problems on paper for long division, he immediately reduces them all to the same problem, namely 3 136 / 32 = 98. These are treated as distinct problems in Japan because of the abacus tradition of avoiding any mental effort and following the une of least resistance. The Western reader may not be satisfied with this solution and may want to work out his own compromise with the Japanese method. I think, however, that after a beginner has practiced this method enough so that it becomes mechanical, he will consider it better than any system which requires a non-mechanical, mental effort— better than the Western method of recognizing the essential simplicity of some problems.

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 3: Now the 256 on CDE must be multiplied by 12 and added to the 8 on H. First multiply the 6 on E by 10, and set the product 60 on GH. This makes a total of 68 on GH. Next multiplying the same 6 on E by 2, add the product 12 to the 68 on GH, and clear E of the 6. This gives you a total of 80 on GH (Fig. 133). NOTE: Be sure to dispose of the 6 of 256 first, next the 5, and finally the 2. 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.

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Advanced abacus: Japanese theory and practice by Takashi Kojima
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