1. **State the problem:** Multiply the mixed number $9 \frac{1}{2}$ by 4. 2. **Convert the mixed number to an improper fraction:** $$9 \frac{1}{2} = \frac{(9 \times 2) + 1}{2} = \frac{18 + 1}{2} = \frac{19}{2}$$ 3. **Multiply the improper fraction by 4:** $$\frac{19}{2} \times 4 = \frac{19}{2} \times \frac{4}{1} = \frac{19 \times 4}{2 \times 1} = \frac{76}{2}$$ 4. **Simplify the fraction:** $$\frac{76}{2} = 38$$ 5. **Final answer:** $$9 \frac{1}{2} \times 4 = 38$$ This means when you multiply $9 \frac{1}{2}$ by 4, the result is 38.