Question

Shikha and priya have bookshelves of the same size Shikha's shelf is $\frac{5}{6}$ full of book and Priya's shelf is $\frac{2}{5}$ full. Whose bookshelf is more full? By what fraction?

Answer 1

Fraction of Shikha's filled bookshelf = $\frac{5}{6}$

Fraction of Priya's filled bookshelf = $\frac{2}{5}$
Comparing $\frac{5}{6}\&\frac{2}{5}$, we get:
LCM of 5 & 6 is 30, so we will convert each fraction into an equivalent fraction with denominator 30.

$$\begin{gathered} =\frac{5\times 5}{6\times 5},\frac{2\times 6}{5\times 6} \\ \frac{25}{30}>\frac{12}{30} \end{gathered}$$

Shikha's shelf is more full.

∴​ $\frac{25}{30}-\frac{12}{30}=\frac{25-12}{30}=\frac{13}{30}$