1. **State the problem:** Subtract the mixed numbers $3 \frac{1}{4}$ and $2 \frac{1}{3}$. 2. **Convert mixed numbers to improper fractions:** $3 \frac{1}{4} = \frac{3 \times 4 + 1}{4} = \frac{13}{4}$ $2 \frac{1}{3} = \frac{2 \times 3 + 1}{3} = \frac{7}{3}$ 3. **Find a common denominator:** The denominators are 4 and 3. The least common denominator (LCD) is 12. 4. **Convert fractions to have the LCD:** $\frac{13}{4} = \frac{13 \times 3}{4 \times 3} = \frac{39}{12}$ $\frac{7}{3} = \frac{7 \times 4}{3 \times 4} = \frac{28}{12}$ 5. **Subtract the fractions:** $$\frac{39}{12} - \frac{28}{12} = \frac{39 - 28}{12} = \frac{11}{12}$$ 6. **Final answer:** $3 \frac{1}{4} - 2 \frac{1}{3} = \frac{11}{12}$