To add the fractions $\frac{1}{2}$ and $\frac{2}{5}$, we need to find a common denominator.

1. Identify the common denominator: The denominators are 2 and 5. The least common denominator (LCD) is 10.

2. Convert each fraction to an equivalent fraction with the common denominator of 10:

   • $\frac{1}{2} = \frac{5}{10}$ (because $1 \times 5 = 5$ and $2 \times 5 = 10$)
   • $\frac{2}{5} = \frac{4}{10}$ (because $2 \times 2 = 4$ and $5 \times 2 = 10$)

3. Add the fractions: $\frac{5}{10} + \frac{4}{10} = \frac{5 + 4}{10} = \frac{9}{10}$

So, $\frac{1}{2} + \frac{2}{5} = \frac{9}{10}$.

Would you like more details on this solution or have any other questions?

Here are some related questions you might find interesting:

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

Tip: When adding or subtracting fractions, always make sure to find a common denominator before performing the operation.