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

REDUCTION OF FRACTIONS 17
Ex. 13. Say, if you know, the cube of 7 plus ½ ,
of 17 plus ¼ , of ¼ , and of ⅕ .
Rule for extracting the cube root of a fraction :
35(ii). The cube root of the numerator divided by the
cube root of the denominator gives the cube root (of the
fraction).¹
(17-22) Reduction of fractions (kalâ-savarṇa)
Rule for reducing fractions of the bhâga class (i.e., fractions
connected by + and – signs):
36. In the bhâga class, in order to reduce the (two given)
fractions to a common denominator, remove the common
factor, if any, from the denominators, and then by each of
them (i.e., the reduced denominators) multiply the denomina-
tor and numerator of the other fraction.²
Ex. 14. What sum is obtained by adding together the
fractions having (the integers) 2 to 6 for their denominators,
and 1 for their numerators, and by adding together the frac-
tions having (the integers) 3 to 9 for their denominators and
(the integers) 2 etc. for their respective numerators.
Alternative rule for reducing fractions of the bhâga class :
37. By the lower denominator multiply the upper
numerator, (then) by the upper denominator multiply the
lower denominator, and (then) add the product of the
numerator and the denominator in the middle to the upper
numerator.³
Suppose, for example, that we want to reduce the fraction
2/3 + 4/5
───────────────────────────────────────────────────────────
¹ Cf. GSS, iii. 13 ; MSi, xv. 17(ii) ; GT, p. 26, line 27 ; L (ASS),
p. 38, lines 2-3 ; GK, I, p. 12, lines 17-18.
² Cf. BrSpSi, xii. 2(i) ; MSi, xv. 13(ii) ; GT, p. 30, line 16 ;
SiŚe. xiii. 11(i) ; L (ASS), p. 28, line 9 ; GK, I, p. 9, vs. 26(i). Also see
GSS, iii. 55 (i);
³ Cf. SiŚe, xiii. 12.