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

To evaluate \( \frac{1}{2} x y \) given \( x = -\frac{1}{3} \) and \( y = \frac{4}{5} \), we start by substituting the values of \( x \) and \( y \) into the expression. \[ \frac{1}{2} x y = \frac{1}{2} \left(-\frac{1}{3}\right) \left(\frac{4}{5}\right) \] Now, let's calculate the multiplication first: \[ -\frac{1}{3} \cdot \frac{4}{5} = -\frac{1 \cdot 4}{3 \cdot 5} = -\frac{4}{15} \] Next, we multiply this result by \( \frac{1}{2} \): \[ \frac{1}{2} \cdot -\frac{4}{15} = -\frac{4}{30} \] Now, to simplify \( -\frac{4}{30} \): \[ -\frac{4}{30} = -\frac{2}{15} \] Thus, the final answer is: \[ \boxed{-\frac{2}{15}} \]