Chris and Nathan order a giant cookie together. If Chris eats $\frac{2}{7}$ of the cookie and Nathan eats $\frac{3}{5}$ of the cookie, what fraction of the original cookie is left?
The total amount eaten is $\frac{2}{7} + \frac{3}{5}$. The denominators have a common multiple of 35, so this is equivalent to $\frac{10}{35} + \frac{21}{35} = \frac{10 + 21}{35} = \frac{31}{35}$. Thus, the amount that Chris and Nathan didn't eat is $1 - \frac{31}{35} = \frac{35}{35} - \frac{31}{35} = \boxed{\frac{4}{35}}.$