Evaluate \( \frac{1}{2} y z \) if \( y=\frac{3}{5} \) and \( z=-1 \frac{7}{8} \). Write your answer as a fraction in simplest form.

To evaluate \( \frac{1}{2} y z \) given \( y=\frac{3}{5} \) and \( z=-1 \frac{7}{8} \), we first need to convert \( z \) into an improper fraction. \( z = -1 \frac{7}{8} = -\left( 1 + \frac{7}{8} \right) = -\left( \frac{8}{8} + \frac{7}{8} \right) = -\frac{15}{8}. \) Now we substitute \( y \) and \( z \) into the equation: \[ \frac{1}{2} y z = \frac{1}{2} \cdot \frac{3}{5} \cdot -\frac{15}{8}. \] Calculating the product of the fractions, we have: \[ \frac{3}{5} \cdot -\frac{15}{8} = \frac{3 \cdot (-15)}{5 \cdot 8} = \frac{-45}{40}. \] Now, multiplying by \( \frac{1}{2} \): \[ \frac{1}{2} \cdot \frac{-45}{40} = \frac{-45}{80}. \] Next, we simplify \( \frac{-45}{80} \). The greatest common divisor (GCD) of 45 and 80 is 5, so we divide both the numerator and the denominator by 5: \[ \frac{-45 \div 5}{80 \div 5} = \frac{-9}{16}. \] Thus, the final answer is \[ \boxed{\frac{-9}{16}}. \]