1. **State the problem:** Subtract the mixed numbers $2 \frac{1}{4}$ and $1 \frac{1}{2}$. 2. **Convert mixed numbers to improper fractions:** $$2 \frac{1}{4} = \frac{2 \times 4 + 1}{4} = \frac{9}{4}$$ $$1 \frac{1}{2} = \frac{1 \times 2 + 1}{2} = \frac{3}{2}$$ 3. **Find a common denominator:** The denominators are 4 and 2. The least common denominator is 4. 4. **Convert fractions to have the same denominator:** $$\frac{9}{4} - \frac{3}{2} = \frac{9}{4} - \frac{3 \times 2}{2 \times 2} = \frac{9}{4} - \frac{6}{4}$$ 5. **Subtract the numerators:** $$\frac{9}{4} - \frac{6}{4} = \frac{9 - 6}{4} = \frac{3}{4}$$ 6. **Final answer:** $$2 \frac{1}{4} - 1 \frac{1}{2} = \frac{3}{4}$$