We derive conditions on the functions $\varphi$, $\rho$, $v$ and $w$ such that the 0-1 fractional programming problem$\max\limits_{x\in \{0;1\}^n}$ $\frac{\varphi \circ v(x)}{\rho \circ w(x)}$ can be solved in polynomial time by enumerating the breakpoints of the piecewise linear function $\Phi(\lambda) = \max\limits_{x\in \{0;1\}^n} v(s)-\lambda w(x)$ on $[0; +\infty)$. In particular we show that when $\varphi$ is convex and increasing, $\rho$ is concave, increasing and strictly positive, $v$ and $-w$ are supermodular and either $v$ or $w$ has a monotonicity property, then the 0-1 fractional programming problem can be solved in polynomial time in essentially the same time complexity than to solve the fractional programming problem $\max\limits_{x\in \{0;1\}^n}$ $\frac{v(x)}{w(x)}$, and this even if $\varphi$ and $\rho$ are nonrational functions provided that it is possible to compare efficiently the value of the objective function at two given points of $\{0;1\}^n$. We apply this result to show that a 0-1 fractional programming problem arising in additive clustering can be solved in polynomial time.