Question: Divide. Simplify your answer.
4 1/2 \div 2 1/4
1. **State the problem:** We need to divide the mixed number $4 \frac{1}{2}$ by the mixed number $2 \frac{1}{4}$ and simplify the answer.
2. **Convert mixed numbers to improper fractions:**
$$4 \frac{1}{2} = \frac{(4 \times 2) + 1}{2} = \frac{9}{2}$$
$$2 \frac{1}{4} = \frac{(2 \times 4) + 1}{4} = \frac{9}{4}$$
3. **Division of fractions rule:** To divide by a fraction, multiply by its reciprocal.
$$\frac{9}{2} \div \frac{9}{4} = \frac{9}{2} \times \frac{4}{9}$$
4. **Multiply the fractions:**
$$\frac{9}{2} \times \frac{4}{9} = \frac{9 \times 4}{2 \times 9}$$
5. **Cancel common factors:**
$$\frac{\cancel{9} \times 4}{2 \times \cancel{9}} = \frac{4}{2}$$
6. **Simplify the fraction:**
$$\frac{4}{2} = 2$$
7. **Final answer:**
The simplified result of $4 \frac{1}{2} \div 2 \frac{1}{4}$ is $2$.