Franco sprinted \( 81 / 2 \) laps and then took a break by jogging \( 1 / 4 \) of a lap. How much farther did Franco sprint than jog? Write your answer as a fraction or as a whole or mixed number.

Franco sprinted \( 81/2 \) laps, which can also be expressed as \( 8 \) whole laps and \( 1/2 \) lap. He jogged \( 1/4 \) of a lap. To find out how much farther he sprinted than jogged, we need to subtract the distance he jogged from the distance he sprinted: \[ \frac{81}{2} - \frac{1}{4} \] To do this subtraction, we need a common denominator. The least common denominator of \( 2 \) and \( 4 \) is \( 4 \). So we convert \( \frac{81}{2} \) into \( \frac{162}{4} \): \[ \frac{162}{4} - \frac{1}{4} = \frac{161}{4} \] This means Franco sprinted \( \frac{161}{4} \) laps farther than he jogged. Converting this into a mixed number, we find that \( \frac{161}{4} = 40 \frac{1}{4} \) laps. So, the answer is \( \frac{161}{4} \) laps or \( 40 \frac{1}{4} \) laps.