George is building a fence. He builds his fence at a constant rate of

To find the fraction that represents the section of fence George can build per hour, we need to consider the given rate.

George builds \( \frac{1}{3} \) of a section of fence every \( \frac{1}{2} \) hour.

To find out how much he builds in 1 hour, we can set up a calculation based on his rate.

Since there are 2 halves in 1 hour, we can multiply the amount he builds in half an hour by 2:

\[ \text{Amount built in 1 hour} = \left( \frac{1}{3} \text{ sections} \right) \times 2 = \frac{2}{3} \text{ sections} \]

Thus, the fraction that represents the section of fence George can build per hour is \( \frac{2}{3} \).

So, the final answer is:

\[ \frac{2}{3} \]