CHAPTER III-FRACTIONS. 67 to 71. The denominators of certain given fractions) are stated to be 19, 23, 62, 29, 123, 35, 188, 37, 98, 47, 140, 141, 115. 31, 92, 57, 73, 55, 110, 49, 74, 219, (in order); and the numerators begin with 1 and rise successively in value by 1 (in order). Add (all) these (fractions) and give the result, O you who have reached the other shore of the ocean of simple fracttous. 0 53 Here, the rule for arriving at the numerators, when the deno- minators and the sum of a number of fractions are given, is as follows) :- 72. Make one the numerator in relation to all the given deno- minators); then, multiply by means of such numbers as are optionally chosen, those numerators which are derived from these fractions so as to have a common denominator. (Here, those (numbers) turn out to be the required numerators, the sum of the products whereof, obtained by multiplying them with the numera- tors (derived as above), is equal to the numerator of the given sum (of the fractions concerned). The rule for arriving at the numerators, (the denominators and the sum being given as before), in relation to such (fractional) quantities as have their numerators (successively) rising in value by one, when, in the (given) sum (of these fractions), the deno- minator is higher in value than the numerator:- 73. The quotient obtained by dividing the (given) sum (of the fractions concerned) by the sum of those (tentative fractions) 72. This rule will become clear from the working of the example in stanza No. 74, wherein we assume 1 to be the provisional numerator in relation to each of the given denominators; thus we get , and h, which, being reduced so as to have a common denominator, become 33%, and When the numerators are multiplied by 2, 3 and 4 in order, the sum of the products thus obtained becomes equal to the numerator of the given suni, namely, 877. Hence, 2, 3, and 4 are the required numérators. Here it may be pointed out that this given sum also must be anderstood to have the same denominator as the common denominator of the fractions. 73. To work out the sum given under 74 below, according to this rule :--- Reducing to the same denominator the fractions formed by assuming 1 to be the numerator in relation to each of the given denominators, we get 33%, and . Dividing the given sum 5 by the sum of these fractions , we get the quotient 2, which is the numerator in relation to the first denozeinator. The remainder 279 990
