\(\rm \frac{5\frac{1}{2}-\frac{2}{3}\ of\ \frac{4}{5}}{2\div \frac{1}{6}-\left(\frac{3}{5}+2\right)}=?\)

Given:

\(\dfrac{5\frac{1}{2} - \dfrac{2}{3} \times \dfrac{4}{5}}{2 \div \dfrac{1}{6} - \left(\dfrac{3}{5} + 2\right)}\) = ?

Formula used:

Basic arithmetic operations and BODMAS rule

Calculation:

\(\dfrac{5\frac{1}{2} - \dfrac{2}{3} \times \dfrac{4}{5}}{2 \div \dfrac{1}{6} - \left(\dfrac{3}{5} + 2\right)}\) = ?

⇒ \(\dfrac{\dfrac{11}{2} - \dfrac{2}{3} \times \dfrac{4}{5}}{2 \div \dfrac{1}{6} - \left(\dfrac{3}{5} + 2\right)}\)

⇒ \(\dfrac{\dfrac{11}{2} - \dfrac{8}{15}}{2 \div \dfrac{1}{6} - \left(\dfrac{13}{5}\right)}\)

⇒ \(\dfrac{\dfrac{165}{30} - \dfrac{16}{30}}{2 \div \dfrac{1}{6} - \dfrac{13}{5}}\)

⇒ \(\dfrac{\dfrac{149}{30}}{2 \div \dfrac{1}{6} - \dfrac{13}{5}}\)

⇒ \(\dfrac{\dfrac{149}{30}}{2 \times 6 - \dfrac{13}{5}}\)

⇒ \(\dfrac{\dfrac{149}{30}}{\dfrac{60 - 13}{5}}\)

⇒ \(\dfrac{149}{6 \times 47}\)

⇒ \(\frac{149}{282}\)

∴ The correct answer is option 1: \(\dfrac{149}{282}\).