Franco practices the piano for \( 4 \frac{1}{2} \) hours each week. He plays soccer for \( 1 \frac{3}{4} \) hours. How much longer does Franco practice piano than play soccer?

To find out how much longer Franco practices the piano than he plays soccer, we first need to convert the mixed numbers into improper fractions. Franco practices the piano for \( 4 \frac{1}{2} \) hours, which can be converted as follows: \[ 4 \frac{1}{2} = \frac{4 \times 2 + 1}{2} = \frac{8 + 1}{2} = \frac{9}{2} \text{ hours} \] He plays soccer for \( 1 \frac{3}{4} \) hours, which can be converted similarly: \[ 1 \frac{3}{4} = \frac{1 \times 4 + 3}{4} = \frac{4 + 3}{4} = \frac{7}{4} \text{ hours} \] Now, we want to find out how much longer he practices piano than plays soccer, which requires us to subtract the hours spent playing soccer from the hours spent practicing piano: \[ \frac{9}{2} - \frac{7}{4} \] To perform the subtraction, we need a common denominator. The least common denominator of 2 and 4 is 4: \[ \frac{9}{2} = \frac{9 \times 2}{2 \times 2} = \frac{18}{4} \] Now, we subtract: \[ \frac{18}{4} - \frac{7}{4} = \frac{18 - 7}{4} = \frac{11}{4} \text{ hours} \] To express this as a mixed number: \[ \frac{11}{4} = 2 \frac{3}{4} \] Therefore, Franco practices the piano for \( 2 \frac{3}{4} \) hours longer than he plays soccer.