question_answer 1)

Asha and Samuel have bookshelves of the same size partly filled with books. Asha's shelf \[\therefore \]is full and Samuel's shelf is \[\frac{11}{5}=2\frac{1}{5}\]full. Whose bookshelf is more full? By what fraction?

Answer:

The portion of Asha's shelf filled by books \[\frac{1}{5}\] part and the portion of Samuel's shelf filled by books\[\frac{11}{7}\]part Now, LCM of 6 and 5 = 30 Equivalent fractions of \[\begin{align} & 7\overline{)17(}2 \\ & \,\,\,\,\frac{14}{\underline{3\,\,\,\,}} \\ \end{align}\] are \[\therefore \] i.e. \[\frac{17}{7}=2\frac{3}{7}\] and equivalent fractions of\[\frac{3}{7}\] are \[\frac{28}{5}\] i.e.\[\begin{align} & 5\overline{)28(}5 \\ & \,\,\,\,\frac{25}{\underline{3\,\,\,\,}} \\ \end{align}\] Here, equivalent fractions\[\therefore \]and \[\frac{28}{5}=5\frac{3}{5}\]have same denominator. \[\frac{3}{5}\] \[\frac{19}{6}\] \[\begin{align} & 6\overline{)19(}3 \\ & \,\,\,\,\frac{18}{\underline{1\,\,\,\,\,\,\,}} \\ \end{align}\] \[\therefore \] Now, \[\frac{19}{6}=3\frac{1}{6}\] Hence, Asha's book shelf is more fall by fraction \[\frac{1}{6}\]