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

18 LOGISTICS
Writing these fractions one below the other without the lines of
separation as the Hindus used to do, we get
2
3
4
5
[In this scheme, 2 is the upper numerator and 3 the upper denomi-
nator ; similarly 4 is the lower numerator and 5 the lower denominator.]
Now according to the rule, multiplying the upper numerator by the
lower denominator, and multiplying the lower denominator by the upper
denominator, we get
2 × 5      10
  3        3
     i.e.,
  4        4
5 × 3      15
Next, adding the product of the numerator and the denominator in
the middle (viz. 3 and 4) to the upper numerator, we get
(10 + 12) / 15   i.e.,   22 / 15   or   22 / 15
rubbing out the figures in the middle, which are not required.
Rule for reducing fractions of the prabhāga class (i.e., fractions
connected by 'of') :
38(i). In the prabhāga class, one should multiply the
numerators together, and the denominators together.¹
That is,
(a / b) of (c / d) of (e / f) = ace / bdf .
Ex. 15. Tell (me) the sum of
1/4 of 1/2 of 1/2 , 1/10 of 1/6 of 1/5 of 1/3 , and 1/7 of 1/6 of ( 2 + 1/2 ).
Rule for reducing a fraction of the bhāga-bhāga class (i.e., a
whole number divided by a fraction) :
38(ii). Having multiplied the whole number (rūpa) by
the denominator of the fraction, remove the denominator :
¹ Cf. BrSpSi, xii. 8(ii) ; GSS, iii. 99 ; MSi, xv. 13(i) ; SiŚe, xiii.
11(i) ; L (ASS), p. 31, vs. 32 ; GK, I, p. 9, vs. 26(ii).
Indological Truths