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Q.8 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 :

Fraction of Asha’s bookshelf = \(\frac{5}{6} \)
Fraction of Samuel’s bookshelf = \(\frac{2}{5} \)
\(\frac{5}{6} \) and \(\frac{2}{5} \)
By cross multiplication
5×5 and 6×2
25 > 12
\(\frac{5}{6} \) > \(\frac{2}{5} \)
\(\therefore \) Asha’s bookshelf is more full than Samuel’s bookshelf
Difference = \(\frac{5}{6} \) - \(\frac{2}{5} \)
= \(\frac{5×5}{6×5} \) - \(\frac{2×6}{5×6} \)
= \(\frac{25}{30} \) - \(\frac{12}{30} \)
= \(\frac{13}{30} \)

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