Ganitasara Sangraha

SR No.: 020800
Original Sutra Author: N/A
Author: Mahaviracharya, M Rangacharya
Publisher: Government of Madras
Publication Year: 1912
Total Pages: 523
Language: Hindi, Sanskrit
Classification: Book_Devnagari
File Size: 22 MB

Page 248

CHAPTER 11-FRACTIONS.
51
by dividing the denominators by means of a common factor thereof, (the quotient derived from the denominator of either of the fractions being used in the multiplication of the numerator and the denominator of the other fraction), those (fractions) become so reduced as to have equal denominators. (Then) removing one of these (equal) denominators, the numerators are to be added (to one another) or to be subtracted from one another, so that the result may be the namerator in relation to the other equal denominator).
Another rule for arriving at the common denominator in another manner :
56. The niruddha (or the least common multiple) is obtained by means of the continued multiplication of (all) the (possible) comioon factors of the denominators and (all) their (ultimate) quotients. In the case of (all) such multiples of the denominators and the numerators of the given fractions), as are obtained by inultiplying those (denominators and numerators) by means of the quotients derived from the division of the niruddha by the (rospective) denominators, the denominators become equal (in value).
Examples in illustration thereof. 57 and 58. A rävaka purchased, for the worship of Jina, jambu fruits, limes, oranges, cocoanuts, plantains, mangoes and pomegranates for ì, , 's, zo zo zlo, and of the golden coin in order : tell me what the result is when these (fractions) are added together.
59. Add together 8 do 16 dj and ot.
60. (There are 3 scts of fractions), the denominators whereof begin with 1, 2 and 3, (respectively) and go on increasing gradually by one till the last (of such denominators) becomes 9, 10 and
00. The resulting problems are to find the values of - (i) x2+2x3+3 34+ ..: +8$+
+ ikot ikot :::::+9x10+ä
(ii) Šá + X6+ oxot.....+16 % 18 + in