Evaluate \( \frac{1}{5} r s t \) if \( r=0.8, s=3 \frac{1}{4} \), and \( t=-8.5 \)

To evaluate \( \frac{1}{5} r s t \) with the given values \( r = 0.8 \), \( s = 3 \frac{1}{4} \), and \( t = -8.5 \), we first need to convert \( s \) into an improper fraction or a decimal. The mixed number \( 3 \frac{1}{4} \) can be converted as follows: \[ 3 \frac{1}{4} = 3 + \frac{1}{4} = \frac{12}{4} + \frac{1}{4} = \frac{13}{4} \] Now substituting the values into the expression: \[ \frac{1}{5} r s t = \frac{1}{5} (0.8) \left(\frac{13}{4}\right)(-8.5) \] Calculating the product \( 0.8 \times \frac{13}{4} \): \[ 0.8 = \frac{8}{10} = \frac{4}{5} \] Thus, \[ \frac{4}{5} \times \frac{13}{4} = \frac{4 \times 13}{5 \times 4} = \frac{13}{5} \] Now combining this with \( t = -8.5 \): \[ \frac{13}{5} \times (-8.5) = \frac{13}{5} \times \left(-\frac{85}{10}\right) = \frac{13 \times -85}{5 \times 10} = \frac{-1105}{50} \] Finally, we multiply by \( \frac{1}{5} \): \[ \frac{1}{5} \times \frac{-1105}{50} = \frac{-1105}{250} \] This can be simplified: \[ \frac{-1105 \div 5}{250 \div 5} = \frac{-221}{50} \] or \( -4.42 \) in decimal form. Thus, the final answer is: \[ \frac{1}{5} r s t = -\frac{221}{50} \] or \(-4.42\) when rounded.