Two microwave photonic signal processing structures, which are capable to realise microwave frequency division with a tunable integer or non-integer division ratio, are presented. They are based on applying an RF signal into a Mach Zehnder modulator, which is biased to generate a carrier-suppressed double sideband (DSB) or single sideband (SSB) optical signal. The carrier-suppressed DSB optical signal consists of the upper and lower 1 st order sidebands with a separation of two times the input RF signal frequency. The carrier of the SSB optical signal is suppressed by a fibre Bragg grating (FBG) connected to the modulator output. Hence the FBG output consists of the upper 1 st order and lower 2 nd order sidebands with a separation of three times the input RF signal frequency. The carrier-suppressed DSB or SSB optical signal is injected into a semiconductor laser. The semiconductor laser is oscillated in the period-one state that generates a number of equally spaced frequency components, which are frequency locked by the injection light wave. Beating of these optical frequency components at the photodetector produces an RF signal with a frequency of 2/N or 3/N times the input RF signal frequency where N can be between 3 and 6. Hence the 2/N frequency divider can realise 2/3, 1/2, 2/5 and 1/3 frequency division operation, and the 3/N frequency divider can realise 3/4, 3/5 and 1/2 frequency division operation. The proposed 2/N and 3/N frequency dividers have a very simple structure compared to the reported photonics-based microwave frequency divider that can realise both integer and non-integer frequency divisions. The frequency division ratio can be tuned by simply adjusting the forward bias current of the semiconductor laser subject to optical injection. Experimental results demonstrate the two proposed structures can realise microwave frequency division with a tunable integer and non-integer division ratio for different input RF signal frequencies of 10 to 18 GHz, and over 60 dB output signal-to-noise ratio performance. More than 27 dB suppression in the unwanted frequency components around the frequency divided signal is also demonstrated.