To solve the expression \( \frac{13}{17} \times 4 \frac{7}{11} \times 3 \frac{4}{39} \), follow these steps:

1. **Convert the mixed numbers to improper fractions**:
   - Convert \( 4 \frac{7}{11} \):
     \[
     4 \frac{7}{11} = \frac{4 \times 11 + 7}{11} = \frac{44 + 7}{11} = \frac{51}{11}
     \]
   - Convert \( 3 \frac{4}{39} \):
     \[
     3 \frac{4}{39} = \frac{3 \times 39 + 4}{39} = \frac{117 + 4}{39} = \frac{121}{39}
     \]

   The expression now becomes:
   \[
   \frac{13}{17} \times \frac{51}{11} \times \frac{121}{39}
   \]

2. **Multiply the fractions**:
   - Multiply the numerators together:
     \[
     13 \times 51 \times 121 = 80283
     \]
   - Multiply the denominators together:
     \[
     17 \times 11 \times 39 = 7293
     \]
   So, the expression becomes:
   \[
   \frac{80283}{7293}
   \]

3. **Simplify the fraction**:
   - Find the greatest common divisor (GCD) of 80283 and 7293, which is 3.
   - Divide both the numerator and the denominator by 3:
     \[
     \frac{80283 \div 3}{7293 \div 3} = \frac{26761}{2431}
     \]

The final simplified fraction is \( \frac{26761}{2431} \).

Would you like more details or have any questions?

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Here are some related questions for practice:

1. How do you determine the GCD of large numbers efficiently?
2. What are the steps for converting improper fractions back to mixed numbers?
3. How can you simplify fractions before multiplying them?
4. What is the LCM, and how does it differ from the GCD?
5. How do you approach multiplying multiple fractions involving different denominators?

**Tip:** Always simplify the fractions as early as possible in the multiplication process to make calculations easier.

Learn how to solve the expression involving fractions: 13/17 x 4 7/11 x 3 4/39 with a step-by-step solution. This problem covers converting mixed numbers to improper fractions, multiplying fractions, and simplifying fractions using the GCD. Suitable for Grades 6-8.

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