30) Evaluate \( -\frac{2}{3} \) mnop if \( m=-1.5, n=-2 \frac{1}{2}, o=\frac{2}{8} \), and \( p=0.9 \). Write your answer as a fraction in simplest form.

To evaluate \( -\frac{2}{3} \) mnop with the given values, we first convert the values of \( m, n, o, \) and \( p \) into consistent forms: - \( m = -1.5 = -\frac{3}{2} \) - \( n = -2\frac{1}{2} = -\frac{5}{2} \) - \( o = \frac{2}{8} = \frac{1}{4} \) - \( p = 0.9 = \frac{9}{10} \) Now, we can calculate \( mnop \): \[ m \cdot n \cdot o \cdot p = \left(-\frac{3}{2}\right) \cdot \left(-\frac{5}{2}\right) \cdot \left(\frac{1}{4}\right) \cdot \left(\frac{9}{10}\right) \] Calculating step-by-step: 1. \( m \cdot n = \left(-\frac{3}{2}\right) \cdot \left(-\frac{5}{2}\right) = \frac{15}{4} \) 2. \( \frac{15}{4} \cdot o = \frac{15}{4} \cdot \frac{1}{4} = \frac{15}{16} \) 3. \( \frac{15}{16} \cdot p = \frac{15}{16} \cdot \frac{9}{10} = \frac{135}{160} \) Now simplifying \( \frac{135}{160} \): The GCD of 135 and 160 is 5. \[ \frac{135 \div 5}{160 \div 5} = \frac{27}{32} \] Now we calculate \( -\frac{2}{3} \) times \( \frac{27}{32} \): \[ -\frac{2}{3} \cdot \frac{27}{32} = -\frac{2 \cdot 27}{3 \cdot 32} = -\frac{54}{96} \] Lastly, we simplify \( -\frac{54}{96} \): The GCD of 54 and 96 is 6. \[ -\frac{54 \div 6}{96 \div 6} = -\frac{9}{16} \] Therefore, the final answer is: \[ \boxed{-\frac{9}{16}} \]