The arithmetic mean of two numbers is the sum of the two numbers divided by 2.
So, the arithmetic mean of $\frac{2}{5}$ and $\frac{4}{7}$ is \[\frac{\frac{2}{5} + \frac{4}{7}}{2} = \frac{\frac{14}{35} + \frac{20}{35}}{2} = \frac{\frac{34}{35}}{2} = \boxed{\frac{17}{35}}.\]
The answer is: \frac{17}{35}
Below is a math problem. Provide a detailed, step-by-step solution.

### Problem:
What is the arithmetic mean of $\frac{2}{5}$ and $\frac{4}{7}$ ? Express your answer as a common fraction.

### Answer:
