jmc

The area of the circle inscribed inside the semicircle is $\pi r^2\Rightarrow \pi (2^2)=4\pi .$ The area of the larger circle (semicircle's area x 2) is $\pi r^2\Rightarrow \pi (4^2)=16\pi$ (the diameter of the inscribed circle, $4$, is the same as the radius of the semicircle). Thus, the area of the semicircle is $\frac{1}{2}(16\pi )\Rightarrow 8\pi .$ The fraction of the semicircle that is unshaded is $\frac{4\pi }{8\pi }=\frac{1}{2}$. Therefore, the fraction of the semicircle that is shaded is $1-\frac{1}{2}=\boxed{\frac{1}{2}}$.