Question: User: 2 5/6 + 7/4
1. **State the problem:** We need to add the mixed number $2 \frac{5}{6}$ and the fraction $\frac{7}{4}$.
2. **Convert the mixed number to an improper fraction:**
$$2 \frac{5}{6} = \frac{2 \times 6 + 5}{6} = \frac{12 + 5}{6} = \frac{17}{6}$$
3. **Find a common denominator:**
The denominators are $6$ and $4$. The least common denominator (LCD) is $12$.
4. **Convert both fractions to have denominator $12$:**
$$\frac{17}{6} = \frac{17 \times 2}{6 \times 2} = \frac{34}{12}$$
$$\frac{7}{4} = \frac{7 \times 3}{4 \times 3} = \frac{21}{12}$$
5. **Add the fractions:**
$$\frac{34}{12} + \frac{21}{12} = \frac{34 + 21}{12} = \frac{55}{12}$$
6. **Convert the improper fraction back to a mixed number:**
$$\frac{55}{12} = 4 \frac{7}{12}$$
Because $12 \times 4 = 48$ and $55 - 48 = 7$.
**Final answer:** $4 \frac{7}{12}$