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?

Asha's shelf = $\dfrac{5}{6}$ full.

Samuel's shelf = $\dfrac{3}{5}$ full.

Compare $\dfrac{5}{6}$ and $\dfrac{3}{5}$ by cross multiplication:

5 × 5 = 25 and 6 × 3 = 18.

Since 25 > 18, therefore, $\dfrac{5}{6} \gt \dfrac{3}{5}$.

So, Asha's bookshelf is more full.

Difference = $\dfrac{5}{6} - \dfrac{3}{5}$

LCM of 6 and 5 = 30.

$\Rightarrow \dfrac{5 \times 5}{6 \times 5} - \dfrac{3 \times 6}{5 \times 6}\\[1em] \Rightarrow \dfrac{25}{30} - \dfrac{18}{30}\\[1em] \Rightarrow \dfrac{25 - 18}{30}\\[1em] \Rightarrow \dfrac{7}{30}$

Hence, Asha's bookshelf is more full by $\dfrac{7}{30}$.