To solve $\frac{1}{7} + \frac{2}{5}$ and express the answer as a fraction in its simplest form, we can follow these steps:

1. Find the common denominator: The denominators here are 7 and 5. The least common multiple of 7 and 5 is 35.

2. Convert each fraction: Rewrite each fraction with 35 as the denominator:

   • $\frac{1}{7} = \frac{5}{35}$
   • $\frac{2}{5} = \frac{14}{35}$

3. Add the fractions: Now, add the two fractions: $\frac{5}{35} + \frac{14}{35} = \frac{5 + 14}{35} = \frac{19}{35}$

4. Simplify if necessary: $\frac{19}{35}$ is already in its simplest form since 19 and 35 have no common factors other than 1.

Thus, the answer is: $\frac{19}{35}$

Would you like more details or have any questions?

Here are 5 related questions to expand on this topic:

1. How do you find the least common multiple of two numbers?
2. What are the steps for converting fractions to have a common denominator?
3. How do you know if a fraction is in its simplest form?
4. Can you add fractions with different denominators directly without finding a common denominator?
5. What are some tips for simplifying fractions effectively?

Tip: Always check if your final fraction answer can be simplified by finding the greatest common divisor of the numerator and denominator!