Evaluate \( \frac{1}{4} x y \) if \( x=-\frac{2}{3} \) and \( y=\frac{3}{5} \). Write your answer as a fraction in simplest form.

To evaluate \( \frac{1}{4} x y \) with the given values \( x = -\frac{2}{3} \) and \( y = \frac{3}{5} \), we first substitute the values into the expression: \[ \frac{1}{4} \cdot \left(-\frac{2}{3}\right) \cdot \left(\frac{3}{5}\right) \] Next, we multiply the fractions: 1. Multiply \( -\frac{2}{3} \) by \( \frac{3}{5} \): \[ -\frac{2 \cdot 3}{3 \cdot 5} = -\frac{6}{15} \] 2. Now simplify \( -\frac{6}{15} \): \[ -\frac{6 \div 3}{15 \div 3} = -\frac{2}{5} \] Now, we multiply this result by \( \frac{1}{4} \): \[ \frac{1}{4} \cdot -\frac{2}{5} = -\frac{2}{20} \] Finally, simplify \( -\frac{2}{20} \): \[ -\frac{2 \div 2}{20 \div 2} = -\frac{1}{10} \] Thus, the final answer is \[ \boxed{-\frac{1}{10}} \]