1. **State the problem:** Evaluate $\frac{1}{4}xy$ given $x = -\frac{2}{3}$ and $y = \frac{3}{5}$. Write the answer as a fraction in simplest form. 2. **Formula used:** The expression is $\frac{1}{4}xy$, which means multiply $\frac{1}{4}$ by $x$ and $y$. 3. **Substitute the values:** $$\frac{1}{4} \times \left(-\frac{2}{3}\right) \times \frac{3}{5}$$ 4. **Multiply the numerators and denominators:** $$\frac{1 \times (-2) \times 3}{4 \times 3 \times 5} = \frac{-6}{60}$$ 5. **Simplify the fraction:** Divide numerator and denominator by their greatest common divisor, which is 6: $$\frac{-6 \div 6}{60 \div 6} = \frac{-1}{10}$$ 6. **Final answer:** $$\boxed{-\frac{1}{10}}$$ The value of $\frac{1}{4}xy$ when $x = -\frac{2}{3}$ and $y = \frac{3}{5}$ is $-\frac{1}{10}$.