CHAPTER III-FRACTIONS than one for their numerators, when the sum (of those fractious) 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) closen number and mulitiplied by the denominator of the (above) sum (of the intended fractions), gives rise to a (required) denominator. The denomi- nator 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 aud 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 fumerator 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). 59 87 Algebraically, if is the sum of two intended fractions with and b n as their numerators, then the fractions are it will be found, is ap+b n x- 7₁
-, where p
+xxp 22 IN P The sum of these fractions. and- 212 2 is ary number so chosen that ap + his divisible by an m 12 89. This rule is only a particular case of the iuie given in stauza No. 87, as the denommator of the sum of the intended fractions is itself sulstituted in this rule for the quantity to be chosen in the previous rule.
