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The problem asks you to add two mixed numbers:

\[
3 \frac{4}{5} + 2 \frac{5}{6}
\]

### Step-by-step solution:

1. **Convert the mixed numbers to improper fractions**:
   - \( 3 \frac{4}{5} = \frac{3 \times 5 + 4}{5} = \frac{15 + 4}{5} = \frac{19}{5} \)
   - \( 2 \frac{5}{6} = \frac{2 \times 6 + 5}{6} = \frac{12 + 5}{6} = \frac{17}{6} \)

2. **Find the least common denominator (LCD)** of 5 and 6:
   - The LCD of 5 and 6 is 30.

3. **Rewrite both fractions with the common denominator**:
   - \(\frac{19}{5} = \frac{19 \times 6}{5 \times 6} = \frac{114}{30} \)
   - \(\frac{17}{6} = \frac{17 \times 5}{6 \times 5} = \frac{85}{30} \)

4. **Add the fractions**:
   \[
   \frac{114}{30} + \frac{85}{30} = \frac{114 + 85}{30} = \frac{199}{30}
   \]

5. **Convert the improper fraction back to a mixed number**:
   - \( \frac{199}{30} \) can be written as:
   \[
   199 \div 30 = 6 \text{ remainder } 19
   \]
   So, \( \frac{199}{30} = 6 \frac{19}{30} \).

### Final Answer:
\[
3 \frac{4}{5} + 2 \frac{5}{6} = 6 \frac{19}{30}
\]

Would you like more details or have any questions about this solution?

Here are 5 questions to expand on this:

1. How do you find the least common denominator (LCD) of two fractions?
2. What are the steps to convert an improper fraction back into a mixed number?
3. Can you explain why we convert mixed numbers to improper fractions when adding?
4. How do you simplify fractions after adding or subtracting?
5. What are some tips for handling fractions with large denominators?

**Tip:** Always ensure both fractions have the same denominator before adding or subtracting them.

Learn how to add mixed numbers such as 3 4/5 and 2 5/6 by converting to improper fractions, finding the least common denominator, and simplifying. This step-by-step solution is suitable for students in Grades 5-7.

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