11. (6 points) The number of girls in Class 6A is $\frac{10}{9}$ times the number of boys. During the New Year's party, $\frac{2}{5}$ of the girls and $\frac{1}{3}$ of the boys participated in the performance, so the number of participants accounts for $\qquad$ of the total class.
【Solution】Solve: $\left(\frac{10}{9} \times \frac{2}{5}+1 \times \frac{1}{3}\right) \div\left(1+\frac{10}{9}\right)$
$$
\begin{array}{l}
=\left(\frac{4}{9}+\frac{1}{3}\right) \div \frac{19}{9} \\
=\frac{7}{9} \times \frac{9}{19} \\
=\frac{7}{19}
\end{array}
$$

Answer: The number of people participating in the performance accounts for $\frac{7}{19}$ of the total class. Therefore, the answer is: $\frac{7}{19}$.