पाटीगणित (श्रीधराचार्य - प्राचीन संस्कृत टीका एवं प्रो. कृपाशंकर शुक्ल सविस्तार व्याख्या)

22 LOGISTICS
Now applying the rule to the uppermost two fractions of this reduced
chain, we get
333
64
1 +
20
1 +
5
Applying the same rule to this chain, it reduces to
6659
1280
1 +
5
and then to
33294 / 6400 or 16647 / 3200
Hence the required result is
16647 / 3200 or 5 647/3200 purâṇas.
Rule for reducing fractions of the bhâgamâtâ class :
42. That (class of fractions) in which fractions of the
'bhâga and other classes occur in combination (of two or
more) is called bhâgamâtâ. In that (class), the result is obtained
by applying the aforesaid rules separately.¹
Ex. 23. What amount is obtained by adding together
½, ¼ of ¼, 1 ÷ ⅓, ½+½ of ½, and ⅓-½ of ⅙ ?
Ex. 24. If you know the method of calculation, say
what amount will be obtained by the addition of ¼, ½ of ⅓,
1 ÷ ½, and 8+½ ?
(23) Rule of three (trairâśika)
Rule of three :
43. In (solving problems on) the rule of three, the
argument (pramâṇa) and the requisition (icchâ), which are
of the same denomination, should be set down in the first and
last places ; the fruit (phala), which is of a different deno-
mination, should be set down in the middle. (This having
¹ Cf. GSS, iii. 138.