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 256

CHAPTER III--FRACTIONS,
than one for their numerators, when the sum (of those fractions) has either one or (any number) other than one for its numerator :
87. (Either) numerator mulitiplied by a chosen (number), then combined with the other numerator, then divided by the numerator of the (given) sum of the intended fractions) so as to leave no remainder, and then divided by the above) chosen number and mulitiplied by the denominator of the (above) sum (of the intended fractions), gives rise to a (required) denominator. The denominator of the other (fraction), however, is this (denominator) multiplied by the (above) chosen (quantity).
Examples in illustration thereof. 88. Say what the denominators are of two (intended fractional) quantities which have 1 for each of their numerators, when the sum (of those fractional quantities) is either or }; as also of two (other fractional quantities) which have 7 and 9 (respectively) for (their) numerators.
The second rule (is as follows) :
89. The numerator (of one of the intended fractions as multiplied by the denominator of the sum of the intended fractions), when combined with the other numerator and then divided by the numerator of the sum of the intended fractions), gives rise to the denominator of one of the fractions). This (denominator), when multiplied by the denominator of the sum (of the intended fractions), becomes the denominator of the other (fraction).
87. Algebraically, if "
is the sum of two intended fractions with a and b
n
т
* Хр
a as their namerators, then the fractions are
-----, where p
ap +b
m P is avy number #o chosen that ap + b is divisible by m. The sum of these fractions. it will be found, is : 89. This rule is only a particular case of the rule given in stanza No. 87, as the denominator of the sum of the intended fractions is itself substituted in this role for the quantity to be chosen in the previous rule.