1. **State the problem:** Subtract the mixed numbers $7 \frac{2}{3} - 3 \frac{5}{12}$. 2. **Convert mixed numbers to improper fractions:** $7 \frac{2}{3} = \frac{7 \times 3 + 2}{3} = \frac{21 + 2}{3} = \frac{23}{3}$ $3 \frac{5}{12} = \frac{3 \times 12 + 5}{12} = \frac{36 + 5}{12} = \frac{41}{12}$ 3. **Find a common denominator:** The denominators are 3 and 12. The least common denominator (LCD) is 12. 4. **Convert fractions to have the LCD:** $\frac{23}{3} = \frac{23 \times 4}{3 \times 4} = \frac{92}{12}$ $\frac{41}{12}$ stays the same. 5. **Subtract the fractions:** $$\frac{92}{12} - \frac{41}{12} = \frac{92 - 41}{12} = \frac{51}{12}$$ 6. **Simplify the fraction:** Divide numerator and denominator by their greatest common divisor (GCD) which is 3: $$\frac{\cancel{51}^{17}}{\cancel{12}^{4}} = \frac{17}{4}$$ 7. **Convert back to mixed number:** $\frac{17}{4} = 4 \frac{1}{4}$ because $17 \div 4 = 4$ remainder $1$. **Final answer:** $$7 \frac{2}{3} - 3 \frac{5}{12} = 4 \frac{1}{4}$$