Question

Asha and Samuel have bookshelves of the same size partly filled with books. Asha's shelf is $\frac{5}{6}$th full and Samuel's shelf is $\frac{2}{5}$th full. Whose bookshelf is more full? By what fraction?

Answer 1

A fraction of books in Asha’s shelf $=\frac{5}{6}$

A fraction of books in Samuel’s shelf $=\frac{2}{5}$

We compare the fractions to find whose shelf is more full.

LCM of $5$ & $6$ is $30$

$\frac{5}{6}=\frac{5\times 5}{5\times 6}=\frac{25}{30}$

$\frac{2}{5}=\frac{2\times 6}{5\times 6}=\frac{12}{30}$

$\frac{25}{30}>\frac{12}{30}$

$\frac{5}{6}>\frac{2}{5}$

So, Asha’s shelf has more books and is more full.

$\frac{5}{6}-\frac{2}{5}$

$=\frac{25}{30}-\frac{12}{30}$

$=\frac{25-12}{30}$

$=\frac{13}{30}$

Asha’s shelf is more full and by $\frac{13}{30}$