To multiply the fractions \( \frac{7}{9} \) and \( \frac{3}{7} \), you multiply the numerators together and the denominators together:
\[ \frac{7 \times 3}{9 \times 7} = \frac{21}{63} \]
Next, simplify \( \frac{21}{63} \). Both the numerator and the denominator can be divided by 21:
\[ \frac{21 \div 21}{63 \div 21} = \frac{1}{3} \]
So, \( \frac{7}{9} \times \frac{3}{7} = \frac{1}{3} \).