By Takashi Kojima

Abacus--Advanced

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**Sample text**

96 with respect to 1 (Fig. 94). 04). , a decimal with its first significant digit in the tenths place. 04. You should note that when the multiplier is a decimal with its first significant digit in the tenths place, the unit rod of the product remains that of the multiplicand. STEP 2: Multiplying the 4 on A by the 5 on F, subtract the product 20, which is to be set on GH, from the 5 on F. This leaves 7 248 on DEFG (Fig. 95). NOTE: As the 5 on F is in the tens place of the dividend, the product 20 must be set on GH.

NOTE: The 68 which was on AB corresponded to the 2ab of the algebraic expression. 58 Advanced Abacus Japanese Theory and Practice, by Takashi Kojima VIII – MORE EXERCISES The exercises for the first, second, and third grades were actually used in recent national abacus license examinations and are here reprinted through the courtesy of the Japan Chamber of Commerce and Industry. 1. ) (1) (2) (3) (4) (5) (6) (7) (8) (9) (10) (11) (12) (13) (14) (15) (16) (17) (18) (19) (20) 45 x 8 = 360 73 x 4 = 292 52 x 2 = 104 38 x 7 = 266 94 x 3 = 282 15 x 6 = 90 86 x 9 = 774 67 x 5 = 335 21 x 8 = 168 79 x 6 = 474 134 x 3 = 402 509 x 2 = 1 018 876 x 8 = 7 008 623 x 4 = 2 492 258 x 9 = 2 322 480 x 6 = 2 880 942 x 5 = 4 710 715 x 7 = 5 005 301 x 4 = 1 204 697 x 3 = 2 091 (1) (2) (3) (4) (5) (6) (7) (8) (9) (10) (11) (12) (13) (14) (15) (16) (17) (18) (19) (20) 59 72 / 2 = 36 135 / 5 = 27 246 / 3 = 82 126 / 9 = 14 413 / 7 = 59 300 / 4 = 75 744 / 8 = 93 288 / 6 = 48 183 / 3 = 61 435 / 5 = 87 8 829 / 9 = 981 420 / 4 = 105 2 634 / 6 = 439 752 / 2 = 376 4 336 / 8 = 542 4 050 / 5 = 810 1 906 / 2 = 953 2 124 / 3 = 708 1 068 / 4 = 267 4 368 / 7 = 624 (10) 49 80 21 68 32 14 95 70 53 76 558 Advanced Abacus Japanese Theory and Practice, by Takashi Kojima 2.

The product, 4, is written below the 6. The 4 is subtracted from 6 and the next pair of numbers is brought down—making 225. The number which is above the square root sign, 2, is doubled and brought down to the side—here the 4 of the 45 at the side. Then a number is selected, 5, such that when placed with 4 to make a two-digit number, 45, and that number is multiplied by the original number selected, 45 x 5, the result is the largest number less than or equal to the “quotient,” which at this point is 225.

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

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