Let the area of square be $y$ And the area of the circle be $x$ As per the instructions we have $\frac{x}{2}=\frac{y}{4}...(1)$ Area of square outside the circle $= y - \frac{y}{4} = \frac{3y}{4}$ Total area of the figures $y+\frac{x}{2}=\frac{5y}{4}$ Thus, the ratio of areas is $\frac{3}{5}$

Let the circle's area be $2x$. Then the area of the circle portion inside the square is $x$, so the area of the square is $4x$ and hence the portion of the square that's not a circle has area $3x$. The whole figure has area $3x+2x=5x$, so the answer is $\boxed{\frac{3}{5}}$.