On the basis of results from molecular dynamics and using Weeks-Chandler-Andersen theory, a simple and exact analytical expression for the Helmholtz free energy of a system of particles interacting through the Lennard-Jones potential is obtained for a wide range of densities and temperatures. The values obtained from this expression and its derivative, the potential energy, are compared with existing published values, and are in reasonable agreement. The combination of accuracy with simplicity-only five parameters are used-could be very useful in theoretical and chemical engineering applications, where straightforward mathematical handling of thermodynamic properties is an important requirement. The high temperature approximation for the radial distribution function and for the Helmholtz free energy are compared with results from exact calculation. The results show this approximation to work well for the radial distribution function at high densities only, but to be good even at low densities for the Helmholtz free energy.