To simplify the expression \(\frac{5}{6} \times \frac{9}{10}\), you can multiply the numerators together and the denominators together:
\[ \frac{5 \times 9}{6 \times 10} = \frac{45}{60} \]
Next, we simplify \(\frac{45}{60}\) by finding the greatest common divisor (GCD) of 45 and 60. The GCD is 15.
Now, divide both the numerator and the denominator by 15:
\[ \frac{45 \div 15}{60 \div 15} = \frac{3}{4} \]
Thus, the simplified form of \(\frac{5}{6} \times \frac{9}{10}\) is \(\frac{3}{4}\).