# पृष्ठम्:गणितसारसङ्ग्रहः॒रङ्गाचार्येणानूदितः॒१९१२.djvu/२६३

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CHAPTER III--FRACTIONS.

128. Tell me friend, quickly the amount of the money remaining after subtracting from 6 x 4 of it, (the quantities) 9, 7 and 9 as diminished in order by ${\tfrac {3}{4}},{\tfrac {1}{2}}$ and ${\tfrac {3}{8}}$ Examples on Bhāgāpavāha containing dissociated fractions

129. Add ${\tfrac {2}{5}},{\tfrac {1}{9}},{\tfrac {1}{3}},{\tfrac {1}{8}}$ and ${\tfrac {2}{7}}$ which are (respectively) diminished by ${\tfrac {1}{6}},{\tfrac {1}{4}},{\tfrac {1}{4}},{\tfrac {1}{3}}$ and ${\tfrac {1}{8}}$ of themselves in order; and (then) give out (the result)

130. (Given) ${\tfrac {6}{7}}$ of a paņa diminished by ${\tfrac {1}{6}},{\tfrac {1}{8}},{\tfrac {1}{9}}$ and ${\tfrac {1}{10}}$ of itself (in consecution); ${\tfrac {5}{12}}$ (similarly) diminished by ${\tfrac {1}{4}},{\tfrac {1}{3}}$ and ${\tfrac {1}{5}}$ of itself; ${\tfrac {5}{6}}$ (similarly) diminished by ${\tfrac {2}{3}},{\tfrac {2}{5}}$ and ${\tfrac {1}{2}}$ of itself: and another (quantity). viz., ${\tfrac {2}{3}}$ diminished by ${\tfrac {5}{8}}$ of itself--when these are (all) added, what is the result ?

131. If you have taken pains, O friend, in relation to Bhāvāpavāha fractions, give out the remainder after subtracting from $1{\tfrac {1}{2}}$ (the following quantities): ${\tfrac {1}{2}}$ diminished (in consecution) by ${\tfrac {3}{8}},{\tfrac {1}{4}}$ and ${\tfrac {1}{9}}$ of itself; also ${\tfrac {1}{3}}$ (similarly) diminished by ${\tfrac {1}{8}},{\tfrac {1}{7}}$ and ${\tfrac {1}{4}}$ of itself; and (also)${\tfrac {1}{7}}$ (similarly) diminished by ${\tfrac {1}{8}}$ and ${\tfrac {1}{6}}$ of itself.

Here, the rule for finding out the (one) unknown element at the beginning (in each of a number of dissociated fractions, their sum being given):--

132. The optionally split up parts of the (given) sum which are equal (in number) to the (intended) component elements (thereof), when divided in order by the resulting quantities arrived at by taking one to be the dissociated quantity (in relation to these component elements), give rise to the value of the (required) unknown (quantities in dissociation) .

Examples in illustration thereof.

188. A certain fraction is diminished (in consecution) by ${\tfrac {1}{4}},{\tfrac {1}{5}}$ and ${\tfrac {1}{6}}$ of itself; another fraction is (similarly) diminished by ${\tfrac {1}{2}},{\tfrac {1}{6}}$ and ${\tfrac {1}{5}}$ of itself; and (yet) another is (similarly) diminished by ${\tfrac {2}{5}}$ ,

132. The working is similar to what has been explained under stanza No. 122. 