This letter provides a study on the end-to-end performance of multi-hop wireless communication systems equipped with re-generative (decode-and-forward) relays over Rayleigh fading channels. More specifically, the probability density function (pdf) of the tightly approximated end-to-end signal-to-noise ratio (SNR) of the systems is derived. Using this approximation allows us to avoid considering all possible combinations of correct and erroneous decisions at the relays for which the end-to-end transmission is error-free. The proposed analysis offers a simple and unifying approach as well as reduces computation burden in evaluating important multi-hop system's performance metrics. Simulations are performed to verify the accuracy and to show the tightness of the theoretical analysis.