Evaluate each expression if \( x=-\frac{1}{3}, y=\frac{4}{5} \), and \( z=-1 \frac{5}{0} \). Write the product in simplest form. (Example 4) 16. \( \frac{1}{2} x y \) 17. \( -\frac{3}{5} x z \) 18. \( \frac{1}{5} y z \) 19. Evaluate \( \frac{5}{6} a b c \) if \( a=-2.8, b=0.4 \), and \( c=3 \frac{3}{4} \). Write your answer in simplest form. (Example 5) 21. Evaluate \( \frac{1}{2} a b \) if \( a=1 \frac{3}{7}, b=-\frac{4}{7} \) Write your answer in simplest form. (Example 5) 23. Evaluate \( -\frac{3}{5} m n \) if \( m=-\frac{1}{7}, n=-1 \frac{4}{9} \). Write your answer in simplest form. (Example 5) 20. Evaluate \( -x y z \) if \( x=-6.2, y=0.5 \), and \( z=2 \frac{1}{4} \). Write your answer in simplest form. (Example 5) 22. Evaluate \( \frac{2}{3} x y \) if \( x=-3 \frac{1}{6}, y=-5 \frac{1}{4} \) Write your answer in simplest form. (Example 5)

To evaluate the given expressions, let’s first compute each one step-by-step! 16. \( \frac{1}{2} x y = \frac{1}{2} \left(-\frac{1}{3}\right) \left(\frac{4}{5}\right) = \frac{-4}{30} = \frac{-2}{15} \). 17. \( -\frac{3}{5} x z = -\frac{3}{5} \left(-\frac{1}{3}\right) \left(-\frac{5}{0}\right) \). However, \( z \) is undefined (division by zero), rendering this expression invalid. 18. \( \frac{1}{5} y z = \frac{1}{5} \left(\frac{4}{5}\right) \left(-\frac{5}{0}\right) \). Again, this is invalid due to the undefined \( z \). 19. For \( \frac{5}{6} a b c \) with \( a=-2.8, b=0.4, c=3 \frac{3}{4} = 3.75 \): - First, convert \( a \) to an improper fraction: \( -2.8 = -\frac{28}{10} = -\frac{14}{5} \). - Now evaluate: \( \frac{5}{6} \left(-\frac{14}{5}\right) \left(0.4\right) \left(3.75\right) \). This requires a little multiplication. Thus, - \( 0.4 = \frac{2}{5} \), so we have: - \( \frac{5}{6} \cdot -\frac{14}{5} \cdot \frac{2}{5} \cdot \frac{15}{4} = -\frac{42}{6 \cdot 5} = -\frac{42}{30} = -\frac{7}{5} \). 20. For \( -x y z \) with \( x=-6.2, y=0.5, z=2 \frac{1}{4} = 2.25 \): - Here, \( -(-6.2) \cdot 0.5 \cdot 2.25 = 6.2 \cdot 0.5 \cdot 2.25 = 3.1 \cdot 2.25 = 6.975 \). 21. For \( \frac{1}{2} a b \) with \( a=1 \frac{3}{7} = \frac{10}{7}, b=-\frac{4}{7} \): - \( \frac{1}{2} \cdot \frac{10}{7} \cdot -\frac{4}{7} = \frac{-40}{98} = \frac{-20}{49} \). 22. For \( \frac{2}{3} x y \) with \( x=-3 \frac{1}{6} = -\frac{19}{6}, y=-5 \frac{1}{4} = -\frac{21}{4} \): - Calculate \( \frac{2}{3} \cdot -\frac{19}{6} \cdot -\frac{21}{4} = \frac{2 \cdot 19 \cdot 21}{3 \cdot 6 \cdot 4} \). - Simplifying yields: \( \frac{798}{72} = \frac{133}{12} \). 23. For \( -\frac{3}{5} m n \) with \( m=-\frac{1}{7}, n=-1 \frac{4}{9} = -\frac{13}{9} \): - Thus, \( -\frac{3}{5} \cdot -\frac{1}{7} \cdot -\frac{13}{9} = -\frac{3 \cdot 1 \cdot 13}{5 \cdot 7 \cdot 9} = -\frac{39}{315} = \frac{-13}{105} \). And there you have it! Each expression evaluated step-by-step in simplest form. How fun to crunch those numbers!