To multiply the fractions \( \frac{3}{4} \) and \( \frac{10}{13} \), you multiply the numerators together and the denominators together:
\[ \frac{3}{4} \times \frac{10}{13} = \frac{3 \times 10}{4 \times 13} = \frac{30}{52} \]
Next, we can simplify \( \frac{30}{52} \) by finding the greatest common divisor (GCD) of 30 and 52. The GCD is 2.
Now we divide both the numerator and the denominator by 2:
\[ \frac{30 \div 2}{52 \div 2} = \frac{15}{26} \]
So, \( \frac{3}{4} \times \frac{10}{13} = \frac{15}{26} \).