1. **State the problem:** Evaluate $\frac{1}{2} yz$ given $y = \frac{3}{5}$ and $z = -1 \frac{7}{8}$. Write the answer as a fraction in simplest form. 2. **Convert mixed number to improper fraction:** $z = -1 \frac{7}{8} = -\left(1 + \frac{7}{8}\right) = -\frac{8}{8} - \frac{7}{8} = -\frac{15}{8}$ 3. **Write the expression:** $\frac{1}{2} yz = \frac{1}{2} \times \frac{3}{5} \times \left(-\frac{15}{8}\right)$ 4. **Multiply the fractions:** First multiply numerators: $1 \times 3 \times (-15) = -45$ Multiply denominators: $2 \times 5 \times 8 = 80$ So, $\frac{1}{2} yz = \frac{-45}{80}$ 5. **Simplify the fraction:** Find the greatest common divisor (GCD) of 45 and 80. Prime factors of 45: $3^2 \times 5$ Prime factors of 80: $2^4 \times 5$ Common factor: $5$ Divide numerator and denominator by 5: $\frac{-45 \div 5}{80 \div 5} = \frac{-9}{16}$ 6. **Final answer:** $\boxed{\frac{-9}{16}}$ This is the simplest form of the fraction.