ब्राह्मस्फुटसिद्धान्त (ब्रह्मगुप्त - शून्य, कुट्टक, बीजगणित एवं सम्पूर्ण २१ अध्याय सान्वय सटीक)

176 BRAHMAGUPTA AND ARITHMETIC
In the bhāgānubandha class, the whole number (rūpa-
gaṇa) is multiplied by the denominator (of the frac-
tion) 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 multi-
plied by the sum of the lower numerator and denomi-
nator.¹
(Pātīgaṇita, 39 cf. BrSpSi. XII. 9 (ii); GSS. (iii) 113
This means that
(i) a + b/c = (ac + b)/c
(ii) a/b + c/d of a/b (which was written by Indians in
the style
┌───┐
│ a │
│ b │
│ c │
│ d │
└───┘
is equal to a(d + c)/bd
Addition and Subtraction of Fractions
In the Brāhmasphuṭa-siddhānta, Brahmagupta gives the
rule for the addition and subtraction of fractions :
If the denominators (cheda) of fractions are different
then reduce these fractions to a common denomina-
tor. Now for the additions, unite the numerators and
take their difference in case of subtraction.²
Brahmagupta and Mahāvīra give the method under Bhāga-
jāti.
Multiplication
Brahmagupta says :
The product of the numerators divided by the pro-

1. भागानुबन्धजातौ रूपगणश्छेद सङ्गुणः सांशः ।
   अवरहरन्धोर्ध्वं हरेऽथोंशाद्युतहरघ्न आद्यंशः ॥ —Patīganita 39.
2. विपरीतच्छेदगुणाः राश्योश्छेदांशकाः समच्छेदाः ।
   संकलितेंऽशा योज्या व्यवकलितेऽशान्तरं कार्यम् ॥ —BrSpSi. XII. 2