2\ \frac{1}{4}\div\frac{1}{2\ }=

2\ \frac{1}{4}\div\frac{1}{2} = 2\frac{1}{4} \times 2 = 2\frac{1}{4} \times \frac{2}{1} = 2\frac{1}{4} \times \frac{8}{4} = 2\frac{1}{4} \times 2 = 2\frac{1}{2} = 4.