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# 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?

Given:

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.

To do:

We have to the find whose bookshelf is more full and by what fraction.

Solution:

Fraction of Asha’s bookshelf full $= \frac{5}{6}$

Fraction of Samuel’s bookshelf full $= \frac{2}{5}$

To find whose bookshelf is more full, we have to convert them into like fractions.

This implies,

LCM of denominators 6 and 5 is 30.

Therefore,

Fraction of Asha’s bookshelf full $= \frac{5}{6}$

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

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

$= \frac{25}{30}$

Fraction of Samuel’s bookshelf full $= \frac{2}{5}$

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

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

$= \frac{12}{30}$

Here,

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

This implies,

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

Therefore,

Asha’s bookshelf is more full than Samuel’s bookshelf

Asha’s bookshelf is more full than Samuel’s bookshelf by,

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

$= \frac{13}{30}$

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