Find the product of `3 1/7 xx1 5/6 xx 1 2/5 xx 1 1/11`

Answer

To find the product of the mixed fractions \(3 \frac{1}{7} \times 1 \frac{5}{6} \times 1 \frac{2}{5} \times 1 \frac{1}{11}\), we will convert each mixed fraction to an improper fraction and then multiply them together.

### Step 1: Convert mixed fractions to improper fractions
1. **Convert \(3 \frac{1}{7}\)**:
\[ 3 \frac{1}{7} = \frac{3 \times 7 + 1}{7} = \frac{21 + 1}{7} = \frac{22}{7} \]

2. **Convert \(1 \frac{5}{6}\)**:
\[ 1 \frac{5}{6} = \frac{1 \times 6 + 5}{6} = \frac{6 + 5}{6} = \frac{11}{6} \]

3. **Convert \(1 \frac{2}{5}\)**:
\[ 1 \frac{2}{5} = \frac{1 \times 5 + 2}{5} = \frac{5 + 2}{5} = \frac{7}{5} \]

4. **Convert \(1 \frac{1}{11}\)**:
\[ 1 \frac{1}{11} = \frac{1 \times 11 + 1}{11} = \frac{11 + 1}{11} = \frac{12}{11} \]

### Step 2: Multiply the improper fractions
Now we can multiply the improper fractions together:
\[ \frac{22}{7} \times \frac{11}{6} \times \frac{7}{5} \times \frac{12}{11} \]

### Step 3: Simplify the multiplication
We can simplify before multiplying:
- The \(7\) in the numerator of \(\frac{7}{5}\) cancels with the \(7\) in the denominator of \(\frac{22}{7}\).
- The \(11\) in the numerator of \(\frac{11}{6}\) cancels with the \(11\) in the denominator of \(\frac{12}{11}\).

After cancellation, we have:
\[ \frac{22 \times 12}{6 \times 5} \]

### Step 4: Calculate the remaining product
Now we calculate:
1. **Numerator**: \(22 \times 12 = 264\)
2. **Denominator**: \(6 \times 5 = 30\)

So we have:
\[ \frac{264}{30} \]

### Step 5: Simplify the fraction
We can simplify \(\frac{264}{30}\):
- Both numbers can be divided by 6:
\[ \frac{264 \div 6}{30 \div 6} = \frac{44}{5} \]

### Step 6: Convert to mixed number
Now convert \(\frac{44}{5}\) to a mixed number:
- \(44 \div 5 = 8\) remainder \(4\), so:
\[ \frac{44}{5} = 8 \frac{4}{5} \]

### Final Answer
Thus, the product of \(3 \frac{1}{7} \times 1 \frac{5}{6} \times 1 \frac{2}{5} \times 1 \frac{1}{11}\) is:
\[ \boxed{8 \frac{4}{5}} \]