A PA44 INSTRUCTOR PILOT REPORTED SHUTTING DOWN THE RIGHT ENGINE ON FINAL APPROACH BECAUSE OF LOW FUEL QUANTITY.

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WHILE ON FINAL APCH TO ZZZ ON THE PRACTICE ILS XX APCH; WE MADE THE DECISION TO SHUT DOWN OUR R ENG DUE TO LOW FUEL. THE WIND WAS CALM AND THERE WAS ONLY 1 AIRPLANE IN THE PATTERN THAT I WAS AWARE OF. I ASKED THE TWR; AS WE MADE THIS DECISION; IF WE COULD LAND ON RWY XX INSTEAD OF THE ACTIVE RWY YY. NO EMER WAS DECLARED AND I TOLD THEM THAT NO ASSISTANCE WAS NEEDED. PRIORITY WAS GRANTED AND WE LANDED STRAIGHT-IN TO RWY XX WITH NO PROB. AFTER LNDG; WE EXITED ON TXWY X AND THEN TRIED TO TURN L ONTO TXWY Y. BECAUSE THE L ENG WAS THE ONLY ONE RUNNING; WE COULD NOT MAKE THE TURN; SO WE SHUT THE ENG DOWN; MANUALLY TOWED IT TO AN OPEN AREA; REFUELED AND TAXIED BACK TO THE FLT SCHOOL. THERE WAS NO DAMAGE TO THE ACFT; NO ONE WAS HURT AND NO REGS WERE BROKEN. AS I REVIEW THIS SITUATION; I KNOW THAT MORE ATTN TO DETAIL IS NEEDED AS IT PERTAINS TO FUEL LEVELS AND SITUATIONAL AWARENESS. WE LEFT THE ARPT WITH TANKS 1/2 FULL AND BELIEVED THAT WOULD BE ENOUGH TO COMPLETE THE TRAINING THAT WAS PLANNED. IN THE FUTURE; MUCH BETTER PLANNING WILL TAKE PLACE IN THESE SITUATIONS. IN CASES LIKE THIS; WE WILL ALWAYS LEAVE WITH FULL TANKS TO AVOID THIS SITUATION FROM EVER TAKING PLACE AGAIN.