Reduction to lowest terms.-A non-mathematical work, Tattvarthadhigama-Sutra-Bhasya by Umasvati (c.150A.D.) casua- lly mentions as follows in the context of a philosophic discourse: Or, as when the expert mathematician, for the purpose of simplifying operations, removes common factors. from the numerator and denominator of a fraction. there is no change in the value of the fraction, so.... ¹ Reduction to common denominator. Whenever we have to add or subtract fractions, we follow this reduction operation to a common denominator. Brahmagupta gives the reduction along with the similar processes : By the multiplication of the numerator and denomi- nator of each of the (fractional) quantities by other denominators, the quantities are reduced to a common denominator. In addition, the numerators are united, In subtraction their difference is taken. Fractions in combination Since there was no proper symbolism available to these early Indian mathematicians, they divided combination of fractions into four classes : Bhaga, prabhaga, bhagapavāha and bhaga-bhaga. (i) Bhaga has been mentioned by Brahmagupta (BrSpSi. XII, 8) thus: ..) usually written as F FRACTIONS C a d a c B + a .e lor 2 where the dots denote subtraction. (ii) Prabhaga: The form of of This is written as (iii) Bhaganubandha The form A 173 1. II, 52, 2. विपरीतच्छेदगुणा: राश्योश्छेदांशकाः समच्छेदाः । संकलितेंऽशा योज्या व्यवकलितेऽशान्तरं कार्यम् || =...) (a+b) is is written as -BrSpSi. XII. 2.
