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Question:

Find the value of the following expression:

$\frac{4 \frac{1}{3} + 3 \frac{1}{3} \times 1 \frac{4}{5} \div 3 \frac{3}{4} \times (6 \frac{1}{4} o f 1 \frac{1}{15})}{\frac{2}{3} \div \frac{5}{6} \times \frac{2}{3}}$

Explanation:

Given, $\frac{4 \frac{1}{3} + 3 \frac{1}{3} \times 1 \frac{4}{5} \div 3 \frac{3}{4} \times (6 \frac{1}{4} o f 1 \frac{1}{15})}{\frac{2}{3} \div \frac{5}{6} \times \frac{2}{3}}$

= $\frac{\frac{13}{3} + \frac{10}{3} \times \frac{9}{5} \times \frac{4}{15} \times (\frac{25}{4} \times \frac{16}{15})}{\frac{2}{3} \times \frac{6}{5} \times \frac{2}{3}}$

= $\frac{\frac{13}{3} + \frac{8}{5} \times (\frac{20}{3})}{\frac{8}{15}}$

= $\frac{\frac{13}{3} + \frac{32}{3}}{\frac{8}{15}}$

= $15 \times \frac{15}{8}$ = $\frac{225}{8}$

= $28 \frac{1}{8}$

Hence, option (a).

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