To multiply the fractions \( \frac{5}{6} \) and \( \frac{3}{10} \), you multiply the numerators together and the denominators together:
\[ \frac{5}{6} \times \frac{3}{10} = \frac{5 \times 3}{6 \times 10} = \frac{15}{60} \]
Next, simplify \( \frac{15}{60} \). Both the numerator and the denominator can be divided by 15:
\[ \frac{15 \div 15}{60 \div 15} = \frac{1}{4} \]
So, \( \frac{5}{6} \times \frac{3}{10} = \frac{1}{4} \).