________________
CHAPTER 11-FRACTIONS.
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 au reduced us to have equal denominators. (Then) removing ono 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 numerator 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) common 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 multiplying those (denominators and numerators by means of the quotients derived from the division of the niruddha by the (respective) denominators, the denominators become equal (in value).
Examples in illustration thereof.
57 and 58. Aravaku purchased, for the worship of Jina, jambu fruits, limes, cranges, cocoanuts, plantains, mangoes and pomegranates for 4, 4, 12, 20, 30, 2, and of the golden coin in order; tell (me, what the result is when these fructions) are added together.
59. Add together 15, 20, 36, 4 and
60. (There are 3 sets 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
GO. The resulting problems are to find the values of
1
)
(i)
+ 1X2
2
(ii) .in ru 2 X 3+ the given h is the numerato,+
2x2+5x1 +
3
2
3 X 4
3
4X5
+
UI
+
2
4 X 5
3 XB
1 8X9 2 79 x 10 3 16
10 3
16 x 18+ iu
1
H
