P2006T CFI reported a gear up landing while performing single engine training with a student. CFI reported gear had been selected down but had not extended.

Narrative

On a training flight for a private Multi-Add on I had vectored the student onto the ILS XX into ZZZ from the northeast. upon catching the Localizer he turned inbound at 3000 ft and began his decent to 1900 to catch the glide slope. at two miles before the final approach fix I gave him a simulated single engine situation to practice single engine instrument approach. He executed the proper actions for having an engine failure and maintained directional control and pitched for blue line Vyse. Upon reaching the final approach fix we had adequate altitude and airspeed so the gear leaver was put into the down position. continuing the approach we still had adequate airspeed and the flaps were set to takeoff. the student was maintaining Vyse and was on the Localizer continuing descent managing well. There was another aircraft on a practice RNAV in front of us and 2 aircraft in the traffic pattern for Runway XX. all planes were communicating well and spacing was being maintained and given for every aircraft to make their approaches and ladings with adequate distance between. The aircraft in front of us landed and exited the runway at the first taxiway and there was an aircraft on extended left downwind for Runway XX so we continued our approach. at 1.5 miles out I double checked that gear switch was down; flaps were down and fuel pumps were on. upon crossing the threshold I was coaching the student on maintaining coordination as the thrust of the operating engine was brought to idle to land. we were on center stripe and when the plane touched down it was on the belly of the plane and the gear had not extended.