________________
56
THE INDIAN ANTIQUARY.
(FEBRUARY, 1891.
The subtracting process is & curious reversal of the scoepted European method. Thus, take 78 from 95 : - 70 out of 90 leaves 20 in my hand :10 8 out of 5 I cannot take, so I take 10 out of the 20 in my hand : 8 out of the 10 I have taken leaves 2 in my hand, I add the 2 to the 5 which makes 7, so I bave 17 in my hand. - Q. E. D.
Multiplication is to the average Burman a science requiring much exertion of the brain. In its simplest form the principle adopted may be said to be the multiplication of each cipher of the multiplicand separately, from the large figures to the units, and adding up the results. Here we see the play of mental arithmetic again. Thus in multiplying 391 by 65 he multiplies 300 by 60 which gives him 18,000, then 3C0 by 5 which gives 1,500, adding the results he gets 19,500. Next he multiplies 90 by 60 = 5,400, and 90 by 5 = 450, total 5,850 : this added to 19,500 = 25,350. Then 1 x 60 = 60 and 1 x 5 = 5 which added together 65, and this added to 25,350 = 25,415.11 A multiplication of the two sums in European fashion will shew this result to be correct : thus
391 65
1955 2346
25415
The above explains the mental process only. The Burman in practice keeps the untouched ciphers of the multiplicand constantly before him, which obliges him to adopt the roles of thumb shewn on pages 60 ff. infrd.
In applying the principle of working from the large figures to the units for division, the Burmese arrive at a complicated process, but it has the advantage over all the rest of checking the caloulation as it proceeds,
Suppose you are given 589 to divide by 27. In this problem to find the first cipher of the product, which must needs be a multiple of 10, you can take 2 tens of the 20 of the divisor out of the 500 of the dividend ; and then as the full dividend is 589 and the full divisor 27 yon can find your true remainder by multiplying 27 by 20 (the quotient just reached) and subtracting the product of this multiplication from the dividend ; thus 589 — 540 = 49. This is the remainder after the first division. You have now to divide 49 by 20 to find the second cipher of the final quotient, and as this must needs be a unit you can take 2 units of the 20 of the divisor out of the 40 of the dividend; and then as the full dividend is 49 and the full divisor is 27, you can find your true remainder by maltiplying 27 by 2 = 54. But 54 cannot be substracted from 49 and this shews you that you cannot take 2 units of 27 out of 49 : you can, however, take 1 unit, leaving a remainder of 22. Your two quotients then are 20 and 1 with 22 over, which gives 21 with 22 over as the final quotient of the division. This result is correct, as division by the European method will show; thus
27589 21
49
27
22 The above again shews the process of reasoning only. The practice is given below at pages 63 ff. infri.
10 As the Burman nons. 11 Of course, all the additions are done by the Barman in Burmese fashion. 11 The Burman, of course, goes through every addition, mbtrnotion and multiplication, in his own fashion.
