To add the fractions $\frac{1}{3}$ and $\frac{2}{5}$, we need to find a common denominator. Here’s how you do it:

1. Find the Least Common Denominator (LCD):
   The denominators are 3 and 5. The least common multiple (LCM) of 3 and 5 is 15. So, the LCD is 15.

2. Convert each fraction to an equivalent fraction with the LCD:

   • For $\frac{1}{3}$, multiply both the numerator and the denominator by 5 to get $\frac{5}{15}$.
   • For $\frac{2}{5}$, multiply both the numerator and the denominator by 3 to get $\frac{6}{15}$.

3. Add the fractions:
   Now that the fractions have the same denominator, simply add the numerators:

$\frac{5}{15} + \frac{6}{15} = \frac{5 + 6}{15} = \frac{11}{15}$

So, the result of adding $\frac{1}{3} + \frac{2}{5}$ is:

$\frac{11}{15}$

Would you like more details or have any questions?

Here are some related questions you might find interesting:

1. How do you find the least common multiple (LCM) of two numbers?
2. What is the process for adding fractions with different denominators?
3. How do you subtract fractions with different denominators?
4. How can we convert an improper fraction to a mixed number?
5. What are the steps to add mixed numbers?

Tip: When adding fractions, always convert them to have a common denominator before performing the addition.