The given problem is asking us to add two mixed fractions:

$1 \frac{3}{10} + 2 \frac{2}{5}$

To solve this, let's follow these steps:

1. Convert the mixed numbers to improper fractions:

   • For $1 \frac{3}{10}$: $1 \frac{3}{10} = \frac{1 \times 10 + 3}{10} = \frac{13}{10}$

   • For $2 \frac{2}{5}$: $2 \frac{2}{5} = \frac{2 \times 5 + 2}{5} = \frac{12}{5}$

2. Find a common denominator: The least common denominator (LCD) of 10 and 5 is 10.

3. Convert the fractions:

   • $\frac{12}{5} = \frac{12 \times 2}{5 \times 2} = \frac{24}{10}$

4. Add the two fractions: $\frac{13}{10} + \frac{24}{10} = \frac{37}{10}$

5. Convert the improper fraction back to a mixed number: $\frac{37}{10} = 3 \frac{7}{10}$

Thus, the final answer is: $3 \frac{7}{10}$

Would you like a more detailed explanation or have any further questions on this topic?

Here are some related questions you might find helpful:

1. How do you convert improper fractions to mixed numbers?
2. What is the process for adding fractions with different denominators?
3. How do you subtract mixed numbers?
4. What is the difference between a proper fraction and an improper fraction?
5. Can you explain how to simplify mixed numbers?

Tip: When adding or subtracting mixed numbers, always first convert them to improper fractions before performing the operation.