To solve the addition of the mixed numbers $2 \frac{3}{4} + 1 \frac{2}{5}$:

1. Convert the mixed numbers to improper fractions: $2 \frac{3}{4} = \frac{2 \times 4 + 3}{4} = \frac{8 + 3}{4} = \frac{11}{4}$ $1 \frac{2}{5} = \frac{1 \times 5 + 2}{5} = \frac{5 + 2}{5} = \frac{7}{5}$

2. Find a common denominator: The least common denominator (LCD) for 4 and 5 is 20. $\frac{11}{4} = \frac{11 \times 5}{4 \times 5} = \frac{55}{20}$ $\frac{7}{5} = \frac{7 \times 4}{5 \times 4} = \frac{28}{20}$

3. Add the fractions: $\frac{55}{20} + \frac{28}{20} = \frac{55 + 28}{20} = \frac{83}{20}$

4. Convert back to a mixed number: $\frac{83}{20} = 4 \frac{3}{20}$

So, the sum of $2 \frac{3}{4} + 1 \frac{2}{5}$ is $4 \frac{3}{20}$.

Would you like more details on any part of this calculation, or do you have any other questions?

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Here are 5 related questions:

1. How do you subtract mixed numbers with different denominators?
2. What is the process for multiplying mixed numbers?
3. How do you divide mixed numbers?
4. Can you add mixed numbers with like denominators directly?
5. How do you convert a decimal to a mixed number?

Tip: When adding or subtracting fractions, always make sure to find the least common denominator for easier calculation.