पृष्ठम्:Ganita Sara Sangraha - Sanskrit.djvu/२४८

50 GANITASARASANGRAHA. Example in illustration of vyutkalita in relation to a series in geometrical progression. 53 The first term is 73, the common ratio is, and the number of terms is 8; and the chosen-off number of terms is 3, 4 or 5. What are the first term, the sum and the number of terms in relation to the (respective) remainder-series? Thus ends the oyulkalata of fractions. The six varieties of fractions. Hereafter we shall expound the six varieties of fractions. 54. Bhaya (or simple fractions), Prabhaga (or fractions of fractions), then Bhayabhāga (or complex fractions), then Bhāgānu- bandha (or fractions in association), Bhagapaváha (or fractions in dissociation), together with Bhagamatr (or fractions consisting of two or more of the above-mentioned fractions)-these are here said to be the six varieties of fractions. Simple fractions: (addition and subtraction). The rule of operation in connection with simple fractions therein - 55. If, in the operations relating to simple fractious, the numerator and the denominator (of each of two given simple fractions) are multiplied in alternation by the quotients obtained 55 The method of reducing fractions to common denominators desenbed m tlus rale apples only to paus of fractions The ule will be clear from the following worked out example - b. a at if 42 To simplify + flere, a and an are to be multiplied by which is the quotient obtained by dividing ys, the denominator of the other fraction, by y which is the common factor of the denominators. Thus we get az xyz Similarly in the second fraction, by multiplying band yz by a which is the quotient obtained by dividing the first denominator ry by y the common factor, bx weget az + br +- = Now a bu xyz Xys 2117