Two and one half, divided by six

$$2\frac{1}{2}/6$$

The general method 

Turn the mixed numerals into an improper fraction using this formula (can you see why it's true):

$$a\frac{b}{c}=\frac{ac+b}{c}$$

We get:

$$2\frac{1}{2}=\frac{2*2+1}{2}=\frac{5}{2}$$

Thus the whole expression gets:

$$\frac{5}{2}/6=\frac{5}{2*6}=\frac{5}{12}$$

The efficient method

Realise that 2 1/2 =2.5

We get: 2.5/6 = 5/12