A transmission includes a continuously variable unit and a fixed-gear-ratio unit. The continuously variable unit includes a variator input, and a variator output that is continuously connected to the transmission output member. A first torque transmitting mechanism interconnects the variator input and a transmission input member. The fixed-gear-ratio unit includes a single planetary gear set having a ring gear, planet gears supported by a carrier, and a sun gear. The fixed-gear-ratio unit includes a fixed input and a fixed output. The fixed input is continuously connected to the transmission input member, and one node of the planetary gear set. The fixed output is continuously connected to the transmission output member, and is selectively connected to another node of the planetary gear set. The fixed-gear-ratio unit includes second, third, fourth, and fifth torque transmitting mechanisms that are selectively engageable and/or disengageable for changing between fixed gear ratios.