The least fraction to be subtracted from the expression $\frac{3 \frac{1}{4} - \frac{4}{5} of \frac{5}{6}}{4 \frac{1}{3} \div \frac{1}{5} - (\frac{3}{10} + 21 \frac{1}{5})}$ $\frac{{3\frac{1}{4} - \frac{4}{5}{\text{ of }}\frac{5}{6}}}{{4\frac{1}{3} \div \frac{1}{5} - \left( {\frac{3}{{10}} + 21\frac{1}{5}} \right)}}$ to make it an integer?

1 $\frac{1}{2}$ $\frac{1}{2}$
2 $\frac{5}{6}$ $\frac{5}{6}$
3 $\frac{1}{4}$ $\frac{1}{4}$
4 $\frac{3}{10}$ $\frac{3}{{10}}$

Answer:- 1

Explanation:-

Solution:

\begin{aligned} According to question \\ \frac{3 \frac{1}{4} - \frac{4}{5} of \frac{5}{6}}{4 \frac{1}{3} \div \frac{1}{5} - (\frac{3}{10} + 21 \frac{1}{5})} \\ \Rightarrow \frac{\frac{13}{4} - \frac{4}{5} \times \frac{5}{6}}{\frac{13}{3} \times 5 - (\frac{3}{10} + \frac{106}{5})} \\ \Rightarrow \frac{\frac{13}{4} - \frac{2}{3}}{\frac{65}{3} - \frac{3}{10} - \frac{106}{5}} \\ \Rightarrow \frac{\frac{39 - 8}{12}}{\frac{650 - 9 - 636}{30}} \\ \Rightarrow \frac{31}{12} \times \frac{30}{5} \\ \Rightarrow \frac{31}{2} \\ \Rightarrow 15 \frac{1}{2} \end{aligned}

$\eqalign{ & {\text{According to question}} \cr & \frac{{3\frac{1}{4} - \frac{4}{5}{\text{ of }}\frac{5}{6}}}{{4\frac{1}{3} \div \frac{1}{5} - \left( {\frac{3}{{10}} + 21\frac{1}{5}} \right)}}{\text{ }} \cr & \Rightarrow \frac{{\frac{{13}}{4} - \frac{4}{5} \times \frac{5}{6}}}{{\frac{{13}}{3} \times 5 - \left( {\frac{3}{{10}} + \frac{{106}}{5}} \right)}}{\text{ }} \cr & \Rightarrow \frac{{\frac{{13}}{4} - \frac{2}{3}}}{{\frac{{65}}{3} - \frac{3}{{10}} - \frac{{106}}{5}}} \cr & \Rightarrow \frac{{\frac{{39 - 8}}{{12}}}}{{\frac{{650 - 9 - 636}}{{30}}}} \cr & \Rightarrow \frac{{31}}{{12}} \times \frac{{30}}{5} \cr & \Rightarrow \frac{{31}}{2} \cr & \Rightarrow 15\frac{1}{2} \cr}$
∴ Least fraction number should be subtracted is