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.

Learn how to add fractions with different denominators, like 1/2 and 2/5, by finding the least common denominator (LCD). This detailed solution is suitable for students in Grades 4-6 and explains each step, including the use of the LCD to simplify the process.

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