A students was asked to find the value of $$9\frac{4}{9} \div 11\frac{1}{3}{\text{ of }}\frac{1}{6} + \left( {1\frac{1}{3} \times 1\frac{4}{5} \div \frac{3}{5}} \right) \times 2\frac{1}{6}{\text{ of }}\frac{2}{3} \div \frac{4}{3}{\text{ of }}\frac{2}{3}.$$           His answer was $$19\frac{1}{4}.$$  What is the difference between his answer and the correct answer?

$$\eqalign{ & 9\frac{4}{9} \div 11\frac{1}{3}{\text{ of }}\frac{1}{6} + \left( {1\frac{1}{3} \times 1\frac{4}{5} \div \frac{3}{5}} \right) \times 2\frac{1}{6}{\text{ of }}\frac{2}{3} \div \frac{4}{3}{\text{ of }}\frac{2}{3} \cr & = \frac{{85}}{9} \div \frac{{34}}{3}{\text{ of }}\frac{1}{6} + \left( {\frac{4}{3} \times \frac{9}{5} \div \frac{3}{5}} \right) \times \frac{{13}}{6}{\text{ of }}\frac{2}{3} \div \frac{4}{3}{\text{ of }}\frac{2}{3} \cr & = \frac{{85}}{9} \times \frac{{18}}{{34}} + \left( 4 \right) \times \frac{{13}}{9} \times \frac{9}{8} \cr & = 5 + \frac{{13}}{2} \cr & = \frac{{23}}{2} \cr & {\text{Difference of answer}} = \frac{{77}}{4} - \frac{{46}}{4} \cr & = \frac{{31}}{4} \cr & = 7\frac{3}{4} \cr} $$