1. Convert mixed numbers to improper fractions:
7 \frac{3}{4} = \frac{31}{4} and
4 \frac{1}{2} = \frac{9}{2}
2. Subtract hours worked on Friday from total hours:
\frac{31}{4} - \frac{9}{2} = \frac{31}{4} - \frac{18}{4} = \frac{13}{4}
3. Simplify the result:
\frac{13}{4} = 3 \frac{1}{4}
4. Final answer: 3 1/4 hours