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 piano compared to playing soccer, we first convert the mixed numbers to improper fractions. For piano practice: \[ 4 \frac{1}{2} = \frac{9}{2} \text{ hours} \] For soccer: \[ 1 \frac{3}{4} = \frac{7}{4} \text{ hours} \] Now, we need a common denominator to subtract the two times. The least common multiple of 2 and 4 is 4. We convert \( \frac{9}{2} \) to have a denominator of 4: \[ \frac{9}{2} = \frac{18}{4} \] Now we can subtract the two fractions: \[ \frac{18}{4} - \frac{7}{4} = \frac{11}{4} \] Converting \( \frac{11}{4} \) back to a mixed number gives: \[ 11 \div 4 = 2 \text{ remainder } 3 \] So, \( \frac{11}{4} = 2 \frac{3}{4} \). Therefore, Franco practices piano \( 2 \frac{3}{4} \) hours longer than he plays soccer.