## Task 3 - 100733

Of the students in an 8th grade class, exactly 35 belong to the school choir and exactly 710 belong to the school sports club (SSG). Exactly 25 of the total number of students in this class are members of both the choir and the SSG.

Calculate what fraction of the total number of students in this class are neither in the choir nor in the SSG!
According to the task, $\frac{3}{5}-\frac{2}{5}=\frac{1}{5}$ of the total number of students in the class are members of the choir but not members of the SSG; and $\frac{7}{10}-\frac{2}{5}=\frac{3}{10}$ of the number of students are members of the SSG but not members of the choir.

Considering the $\frac{2}{5}$ of the total number of students in this class who belong to both, this leaves $\frac{1}{5}+\frac{3}{10}+\frac{2}{5}=\frac{9}{10}$, so exactly $\frac{1}{10}$ of the total number of students in this class remain, and this is exactly the proportion that is neither in the choir nor in the SSG.