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

OPERATIONS FOR FRACTIONS 15
(9-16) Operations for fractions
Rule for the addition of fractions :
32(i). Reduce the fractions to a common denominator
and then add the numerators. The denominator of a whole
number is unity.¹
Ex. 6. Say the sum of ½, ⅓, ⅙ and ¹/₁₂, and of 2 plus ½,
3 minus ¼, and 6.
Ex. 7. Friend, if you know the method of calculation
(gaṇita-vidhi), quickly say the sum of 1½ terms, ½ term, and of
⅓ term of the series whose first term (ādi) and common
difference (caya) are each unity.
Rule for the subtraction of fractions :
32(ii). Take the difference of the numerators of the
positive and negative fractions reduced to a common denomi-
nator.²
Ex. 8. Subtract ¼, ⅓ and ⅙ from 1 and say what remains.
Also, subtract 3 — ½ and 2+⅓ from 5 (and say the remainder).
Ex. 9. Say what remains as the remainder when the
sum of 2 plus ½ terms is subtracted from the sum of 5 plus ½
terms of the series whose first term and common difference are
(each) unity.
It may be remarked here that, according to the author of the
present work, rule 14(i) applies also to series of natural numbers
having a fractional number of terms. Series in A. P. having frac-
tional number of terms have generally no meaning but they may be
interpreted geometrically by means of figures called series-figures. See
infra, ‘Determinations pertaining to series’ (śreḍhī-vyavahāra).
¹ Cf. MSi, xv. 14(i) ; GT, p. 15, lines 20-21 ; SiŚe, xiii. 8 ; L
(ASS), p. 35, vs. 37 ; GK, I, p. 11, lines 6-7. Also see BrSpSi, xii. 2.
² Cf. BrSpSi, xii. 2(ii); MSi, xv. 14(ii) ; GT, p. 18, lines 3-4 ;
SiŚe, xiii. 8 ; L (ASS), p. 35, vs. 37; GK, I, p. 11, lines 6-7.