# पृष्ठम्:गणितसारसङ्ग्रहः॒रङ्गाचार्येणानूदितः॒१९१२.djvu/२५६

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60
GAŅIITASĀRASAŃGRAHA.

Examples in illustration thereof.

90. O friend, tell me what the denominators are of two (fractional) quantities which have 1 for each of their numerators, when the sum (of those intended fractions) is ${\displaystyle {\tfrac {2}{7}}}$; as also of (two other intended fractions) which have 6 and 8 (respectively) for (their) numerators.

91. The sum of ${\displaystyle {\tfrac {1}{2}},{\tfrac {1}{10}},{\tfrac {1}{10}}}$ and ${\displaystyle {\tfrac {1}{20}}}$ is 1. When ${\displaystyle {\tfrac {1}{15}}}$ is left out here, what two (fractions) having 1 (for each of their numerators) have to be added (instead so as to give the same total)?

92. ${\displaystyle {\tfrac {1}{2}},{\tfrac {1}{4}},{\tfrac {1}{5}}}$ and ${\displaystyle {\tfrac {1}{20}}}$ is 1. If ${\displaystyle {\tfrac {1}{2}},{\tfrac {1}{10}},{\tfrac {1}{10}}}$ and ${\displaystyle {\tfrac {1}{20}}}$ is 1. If ${\displaystyle {\tfrac {1}{20}}}$is left out here, what two (fractions) having 7 and 11 for their numerators should be added (instead so as to give the same total) ?

The rule for arriving at the denominators (of a number of intended fractions) by taking (them) in pairs:--

98. After splitting up the sum (of all the intended fractions) into as many parts having one for each of their numerators as here are (numbers of) pairs (among the given numerators), these (parts) are taken (severally) as the sums of the pairs ; (and from them) the (required) denominators are to be found out in accordance with the rule relating to two (such component fractional quantities).

Examples in illustration thereof.

94. What are the denominators of (those intended) fractions whose numerators are 3, 5, 13, 7, 9 and 11, when tho sum of (those fractional) quantities is 1 or ${\displaystyle {\tfrac {4}{3}}}$ ?

The rule for arriving at (a number of) denominators, with the help of the denominators that have one as (their corresponding) numerators and are arrived at according to one of the (already given) rules (for finding out the denominators), as also with the help of the denominators that have one as (their corresponding) numerators and are arrived at according to any other of those

98. The rules relating to two fractional qantities have been given in stanza 85, 87 and 89.