To find the product of \( \frac{2}{3} \times \frac{5}{9} \), you multiply the numerators together and the denominators together:
\[ \frac{2 \times 5}{3 \times 9} = \frac{10}{27} \]
So, the product of \( \frac{2}{3} \times \frac{5}{9} \) is \( \frac{10}{27} \).