Question

Asha and Samuel have bookshelves of the same size partly filled with books. Asha's shelf is $$\dfrac{5}{6}$$ full and Samuel's shelf is $$\dfrac{3}{5}$$ full. Whose bookshelf is more full and by what fraction?

Answer 1

Asha's shelf is $$\dfrac{5}{6}$$th fukk of book Samuel's shelf is $$\dfrac{3}{5}$$th full of book. $$\left[LCM \left(6,5\right) = 30\right]$$
Like fractions of $$\dfrac{5}{6} \, and\,\dfrac{3}{5}$$ is :
$$\Rightarrow \dfrac{5}{6} \times \dfrac{5}{5} = \dfrac{25}{30}$$
$$\Rightarrow \dfrac{3}{5} \times \dfrac{6}{6} = \dfrac{18}{30}$$
$$\therefore \dfrac{25}{30} > \dfrac{18}{30}$$
$$\therefore$$ Asha's bookshelf is more full by fraction
$$\dfrac{25}{30} - \dfrac{18}{30}$$.
i.e. by fraction $$\dfrac{25 - 18}{30} = \dfrac{7}{30}$$