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 \( m = -1.5 \), \( n = -2 \frac{1}{2} \), \( o = \frac{2}{8} \), and \( p = 0.9 \), we first convert all numbers to fractions. 1. Convert \( m = -1.5 \) to a fraction: \[ m = -\frac{3}{2} \] 2. Convert \( n = -2 \frac{1}{2} \) to an improper fraction: \[ n = -\frac{5}{2} \] 3. Simplify \( o = \frac{2}{8} \): \[ o = \frac{1}{4} \] 4. Convert \( p = 0.9 \) to a fraction: \[ p = \frac{9}{10} \] Now substituting these values into the expression: \[ -\frac{2}{3} mnop = -\frac{2}{3} \left(-\frac{3}{2}\right) \left(-\frac{5}{2}\right) \left(\frac{1}{4}\right) \left(\frac{9}{10}\right) \] Calculating step by step: - First, let's calculate the product of \( m, n, o, p \): \[ -\frac{3}{2} \times -\frac{5}{2} \times \frac{1}{4} \times \frac{9}{10} \] Calculating two at a time: \[ -\frac{3}{2} \times -\frac{5}{2} = \frac{15}{4} \] Now multiplying with \( \frac{1}{4} \): \[ \frac{15}{4} \times \frac{1}{4} = \frac{15}{16} \] Now multiplying with \( \frac{9}{10} \): \[ \frac{15}{16} \times \frac{9}{10} = \frac{135}{160} \] Now simplifying \( \frac{135}{160} \): Both 135 and 160 are divisible by 5: \[ \frac{135 \div 5}{160 \div 5} = \frac{27}{32} \] Now substituting back into the expression: \[ -\frac{2}{3} \times \frac{27}{32} = -\frac{2 \times 27}{3 \times 32} = -\frac{54}{96} \] Now we simplify \( -\frac{54}{96} \): Both 54 and 96 are divisible by 6: \[ -\frac{54 \div 6}{96 \div 6} = -\frac{9}{16} \] Thus, the final answer is: \[ \boxed{-\frac{9}{16}} \]