Let's solve the sum of the mixed numbers:

We have:
\[
12 \frac{5}{6} + 9 \frac{14}{15} + 8 \frac{4}{5}
\]

### Step 1: Convert the mixed numbers to improper fractions.
- \(12 \frac{5}{6}\): 
  \[
  12 \frac{5}{6} = \frac{12 \times 6 + 5}{6} = \frac{77}{6}
  \]
- \(9 \frac{14}{15}\): 
  \[
  9 \frac{14}{15} = \frac{9 \times 15 + 14}{15} = \frac{149}{15}
  \]
- \(8 \frac{4}{5}\): 
  \[
  8 \frac{4}{5} = \frac{8 \times 5 + 4}{5} = \frac{44}{5}
  \]

### Step 2: Find the least common denominator (LCD) for the fractions.
The denominators are 6, 15, and 5. The least common denominator is 30.

### Step 3: Convert all fractions to have the same denominator.
- \(\frac{77}{6}\): 
  \[
  \frac{77}{6} = \frac{77 \times 5}{30} = \frac{385}{30}
  \]
- \(\frac{149}{15}\): 
  \[
  \frac{149}{15} = \frac{149 \times 2}{30} = \frac{298}{30}
  \]
- \(\frac{44}{5}\): 
  \[
  \frac{44}{5} = \frac{44 \times 6}{30} = \frac{264}{30}
  \]

### Step 4: Add the fractions.
\[
\frac{385}{30} + \frac{298}{30} + \frac{264}{30} = \frac{385 + 298 + 264}{30} = \frac{947}{30}
\]

### Step 5: Simplify the fraction.
\(\frac{947}{30}\) is already in its simplest form.

### Step 6: Convert the improper fraction back to a mixed number.
\[
\frac{947}{30} = 31 \frac{17}{30}
\]

Thus, the sum of \(12 \frac{5}{6} + 9 \frac{14}{15} + 8 \frac{4}{5}\) is:

\[
31 \frac{17}{30}
\]

Would you like more details or have any questions?

### Related Questions:
1. How do you convert improper fractions to mixed numbers?
2. Can you explain how to find the least common denominator (LCD)?
3. What is the process for adding fractions with different denominators?
4. How do you simplify improper fractions after addition?
5. How do you convert mixed numbers to improper fractions?

### Tip:
When adding fractions with different denominators, always look for the least common denominator to simplify the process.

Learn how to add mixed numbers like 12 5/6, 9 14/15, and 8 4/5 with a step-by-step guide. This problem explores key fraction concepts, including conversion between mixed and improper fractions, finding the least common denominator, and simplifying fractions. Ideal for students in Grades 6-8.

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