jmc

We first have to find what fraction of students walk to school. Since the total fraction of students is $\frac{120}{120}$ or 1, we must find:$$\frac{120}{120}-\frac{2}{5}-\frac{5}{12}.$$To solve this expression, we have to get common denominators. In this case, the common denominator is 120.

To get this common denominator for the fraction $\frac{2}{5}$, multiply the numerator and denominator by 24 to get $\frac{48}{120}$.

To get the common denominator for $\frac{5}{12}$, multiply the numerator and denominator by 10 to get $\frac{50}{120}$. So now we have: $$\frac{120}{120}-\frac{48}{120}-\frac{50}{120}=\frac{120-48-50}{120}=\frac{22}{120}.$$Notice that $\frac{22}{120}$ can be written as $\frac{2\cdot 11}{2\cdot 60}$, so our final answer is $\boxed{\frac{11}{60}}$.