Rational harmonic active and passive modelocking is demonstrated in a figure-of-eight fibre laser for the first time. Optical pulses at repetition rates up to the 19th harmonic of the RF modulation frequency were generated by rationally detuning the modulation frequency. An output pulse train with a repetition rate of 11.08GHz and a pulse duration of 7.1ps has been achieved. The output pulse was nearly transform-limited.