1. **State the problem:** Calculate $3 \frac{1}{2} - \frac{4}{3}$. 2. **Convert mixed number to improper fraction:** $$3 \frac{1}{2} = \frac{3 \times 2 + 1}{2} = \frac{7}{2}$$ 3. **Find common denominator:** Denominators are 2 and 3, least common denominator (LCD) is 6. 4. **Rewrite fractions with LCD:** $$\frac{7}{2} = \frac{7 \times 3}{2 \times 3} = \frac{21}{6}$$ $$\frac{4}{3} = \frac{4 \times 2}{3 \times 2} = \frac{8}{6}$$ 5. **Subtract fractions:** $$\frac{21}{6} - \frac{8}{6} = \frac{21 - 8}{6} = \frac{13}{6}$$ 6. **Convert improper fraction to mixed number:** $$\frac{13}{6} = 2 \frac{1}{6}$$ **Final answer:** $2 \frac{1}{6}$