To multiply the fractions \( \frac{3}{5} \) and \( \frac{1}{9} \), you multiply the numerators together and the denominators together:
\[ \frac{3}{5} \times \frac{1}{9} = \frac{3 \times 1}{5 \times 9} = \frac{3}{45} \]
Now, you can simplify \( \frac{3}{45} \) by dividing both the numerator and the denominator by their greatest common divisor, which is 3:
\[ \frac{3 \div 3}{45 \div 3} = \frac{1}{15} \]
Therefore, \( \frac{3}{5} \times \frac{1}{9} = \frac{1}{15} \).
