To solve the expression \( \frac{3}{5} \times \frac{7}{9} \times 1 \frac{2}{7} \), follow these steps:

1. **Convert the mixed number to an improper fraction**:
   - \( 1 \frac{2}{7} \) can be converted as follows:
   \[
   1 \frac{2}{7} = \frac{7 \times 1 + 2}{7} = \frac{9}{7}
   \]
   So, the expression becomes:
   \[
   \frac{3}{5} \times \frac{7}{9} \times \frac{9}{7}
   \]

2. **Multiply the fractions**:
   - Multiply the numerators together:
     \[
     3 \times 7 \times 9 = 189
     \]
   - Multiply the denominators together:
     \[
     5 \times 9 \times 7 = 315
     \]
   So, the expression becomes:
   \[
   \frac{189}{315}
   \]

3. **Simplify the fraction**:
   - Find the greatest common divisor (GCD) of 189 and 315, which is 63.
   - Divide both the numerator and the denominator by 63:
     \[
     \frac{189 \div 63}{315 \div 63} = \frac{3}{5}
     \]

The final answer is \( \frac{3}{5} \).

Would you like more details or have any questions?

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Here are some related questions for practice:

1. How would you multiply three mixed numbers together?
2. How do you convert a mixed number to an improper fraction?
3. What is the GCD, and how is it used in simplifying fractions?
4. How do you multiply fractions involving negative numbers?
5. How do you simplify a complex fraction with multiple steps?

**Tip:** When multiplying fractions, always simplify the product if possible by finding the GCD of the numerator and the denominator.

Learn how to solve the expression 3/5 x 7/9 x 1 2/7 with a detailed step-by-step solution. This problem covers key concepts in fractions, including multiplication of fractions and simplification. Suitable for students in Grades 5-7.

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