To solve the expression $\frac{3}{4} + 4 \frac{1}{8}$:

1. Convert the mixed number $4 \frac{1}{8}$ to an improper fraction: $4 \frac{1}{8} = \frac{4 \times 8 + 1}{8} = \frac{32 + 1}{8} = \frac{33}{8}$

2. Find a common denominator to add $\frac{3}{4}$ and $\frac{33}{8}$:

   • The denominators are 4 and 8. The least common denominator is 8.
   • Convert $\frac{3}{4}$ to an equivalent fraction with a denominator of 8: $\frac{3}{4} = \frac{3 \times 2}{4 \times 2} = \frac{6}{8}$

3. Add the fractions $\frac{6}{8} + \frac{33}{8}$: $\frac{6}{8} + \frac{33}{8} = \frac{6 + 33}{8} = \frac{39}{8}$

4. Convert the improper fraction $\frac{39}{8}$ back to a mixed number: $\frac{39}{8} = 4 \frac{7}{8}$

So, $\frac{3}{4} + 4 \frac{1}{8} = 4 \frac{7}{8}$.

Would you like more details or have any questions?

Here are five related questions:

1. How do you convert a mixed number to an improper fraction?
2. How do you find the least common denominator for fractions?
3. What steps are involved in adding fractions with different denominators?
4. How do you simplify an improper fraction to a mixed number?
5. How can you subtract a fraction from a mixed number?

Tip: When adding fractions, always check if they have a common denominator. If not, find the least common denominator to make the addition straightforward.