Let’s solve these fraction problems step by step.

1. $2 \frac{3}{4} + 1 \frac{3}{4}$

1. Convert the mixed numbers to improper fractions: $2 \frac{3}{4} = \frac{11}{4}, \quad 1 \frac{3}{4} = \frac{7}{4}$
2. Add the fractions: $\frac{11}{4} + \frac{7}{4} = \frac{11 + 7}{4} = \frac{18}{4}$
3. Simplify the result: $\frac{18}{4} = 4 \frac{1}{2}$

So, the result is: $4 \frac{1}{2}$

---

2. $4 \frac{5}{8} + 3 \frac{7}{8}$

1. Convert the mixed numbers to improper fractions: $4 \frac{5}{8} = \frac{37}{8}, \quad 3 \frac{7}{8} = \frac{31}{8}$
2. Add the fractions: $\frac{37}{8} + \frac{31}{8} = \frac{37 + 31}{8} = \frac{68}{8}$
3. Simplify the result: $\frac{68}{8} = 8 \frac{1}{2}$

So, the result is: $8 \frac{1}{2}$

---

Final Answers:

1. $2 \frac{3}{4} + 1 \frac{3}{4} = 4 \frac{1}{2}$
2. $4 \frac{5}{8} + 3 \frac{7}{8} = 8 \frac{1}{2}$

Would you like further details or assistance with similar problems?

---

Here are 5 related problems for practice:

1. $3 \frac{2}{5} + 2 \frac{4}{5}$
2. $1 \frac{7}{10} + 2 \frac{3}{10}$
3. $5 \frac{3}{4} - 2 \frac{1}{4}$
4. $3 \frac{6}{7} + 4 \frac{5}{7}$
5. $6 \frac{3}{8} - 2 \frac{7}{8}$

Tip: When adding or subtracting mixed numbers, always convert them to improper fractions first—it simplifies the process!