Advanced abacus: Japanese theory and practice by Takashi Kojima

By Takashi Kojima


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Extra info for Advanced abacus: Japanese theory and practice

Sample text

In this procedure, first multiply the 1 on A by the 2 on H, then set the product 2 on J. This gives you 29 on JK. Next multiply the 8 on B by the same 2 on H; add the product 16 to the 29 on JK, and clear H of its 2. This gives you a total of 45 on JK (Fig. 165). STEP 5: Now divide the 45 on JK by 20, and you get the quotient 2 on H, with 5 left over on K (Fig. 166). STEP 6: Finally you must multiply the 4 on E by 18, and add the product 72 to the 2 on H. In this process, first multiply the 1 on A by the 4 on E, and set the product 4 on G.

Our square root is 67 on BC (Fig. 199). EXAMPLE 3: Find the square root of 119 716. The method of finding the three-digit square root of a number is founded upon the algebraic method of finding the square of an ordinary trinomial (or three-membered) expression, (a + b + c). A number is analyzed as in algebra, into (a2 + 2ab + b2 + 2ac + 2bc + c2) and the square root is found. STEP 1: Set 119 716 on CDEFGH, and mark off the digits in sets of twos. In the first pair 11, the highest square root is 3 (Fig.

METHOD B: Calculating from lower to higher denominations: An alternative is to calculate column by column from lower to higher denominations. I. First do the pence column on HI by means of complementary numbers, yielding 5 d. on Next do the shillings column on EF by means of complementary numbers, and you get minus 2 s. on F. So borrow £1 from L95 to rectify this minus quantity, and you get 18 s. on EF and £94 left on BC. In subtracting 19 s. , you may borrow L1 instead of calculating by means of complementary numbers.

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