To solve the mixed fraction addition $2 \frac{1}{2} + 3 \frac{3}{4}$, follow these steps:

1. Convert the mixed numbers to improper fractions:

   • $2 \frac{1}{2}$ becomes $\frac{5}{2}$
   • $3 \frac{3}{4}$ becomes $\frac{15}{4}$

2. Find a common denominator:

   • The least common denominator (LCD) of 2 and 4 is 4.
   • Convert $\frac{5}{2}$ to $\frac{10}{4}$ by multiplying both numerator and denominator by 2.

3. Add the fractions:

   $\frac{10}{4} + \frac{15}{4} = \frac{25}{4}$

4. Convert the improper fraction back to a mixed number:

   • $\frac{25}{4} = 6 \frac{1}{4}$

So, $2 \frac{1}{2} + 3 \frac{3}{4} = 6 \frac{1}{4}$.

Would you like more details or have any questions?

Here are some related questions:

1. How do you subtract mixed fractions?
2. What is the process for multiplying mixed fractions?
3. How can you convert an improper fraction to a decimal?
4. How do you simplify a mixed fraction?
5. How do you find the least common denominator of two fractions?

Tip: Always convert mixed numbers to improper fractions for easier calculations in addition and subtraction.