Multiply and reduce. \[ \frac{4}{15} \times \frac{25}{16} \]

Step 1 ：Multiply the numerators together to get the numerator of the product, and multiply the denominators together to get the denominator of the product. So, \(\frac{4}{15} \times \frac{25}{16} = \frac{100}{240}\).

Step 2 ：Reduce the fraction to its simplest form. So, \(\frac{100}{240} = \frac{5}{12}\).

Step 3 ：The product of the two fractions is \(\frac{5}{12}\). This is the simplest form of the fraction, so no further reduction is necessary.

Step 4 ：Final Answer: \(\boxed{\frac{5}{12}}\)