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

REDUCTION OF FRACTIONS 19
this is the process (of reduction) for the bhāga-bhāga class.¹
That is,
a ÷ b/c = ac / b .
Ex. 16. Friend, if you know (the method), say after
thinking, what sum will be obtained by adding together (the
fractions) :
1 ÷ 1/6 , 1 ÷ 1/10 , 1 ÷ 1/3 , 1 ÷ 1/9 , and 1 ÷ 1/2 .
Ex. 17. 1 has been severally divided by fractions
having (the integers) 3 to 6 for their denominators and (the
integers) 2 etc., for their respective numerators. Say what
sum will be obtained when they are added together.
Rule for reducing a fraction of the bhāgānubandha class (i.e., a
whole number increased by a fraction, or a fraction increa-
sed by a fraction of itself) :
39. In the bhāgānubandha class, the whole number
(rūpagaṇa) as multiplied by the denominator (of the fraction)
should be increased by the numerator (of the fraction) ; or,
the upper denominator having been multiplied by the lower
denominator, the initial numerator (i.e., the upper numerator)
should be multiplied by the sum of the lower numerator and
denominator.²
That is,
(i) a + b/c = (ac + b) / c ,
(ii) a/b + c/d of a/b ( which was written in the Hindu
way as³ [ (a/b) / (c/d) ] ) = a (d + c) / bd .
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¹ Cf. BrSpSi, xii. 9(i) ; GSS, iii. 99(ii) ; MSi, xv. 19(i).
² Cf. BrSpSi, xii 9(ii) ; GSS, iii. 113 ; MSi, xv. 11(ii)-12 ; GT,
p. 34, lines 15-16 ; L (ASS), p. 32, vs. 34 ; GK, I, p. 9, vs. 27.
³ Actually it was written as a
b
c
d