An electrically variable transmission having a single motor/generator provides electrically variable power flow along dual power paths and provides an electrically variable reverse operating mode. The transmission includes a compound differential gear set having at least four gear elements operatively interconnected with one another. A transmission input member and the single motor/generator selectively provide power to a transmission output member via the differential gear set. The transmission includes a plurality of intermeshing gears, including a reversing gear and gears connected for rotation with the output member, for operatively connecting the differential gear set with the output member. Torque-transmitting mechanisms are selectively engagable to provide power flow between the input member and the output member in multiple operating modes, including a parallel hybrid electrically variable reverse operating mode utilizing the reversing gear. A method of operating a transmission that allows shifting between different gearing portions of the transmission is provided.