Over the past decades open clusters have been the subject of many studies. Such studies are crucial considering that the universality of the initial mass function is still a subject of current investigations. Praesepe is an interesting open cluster for the study of the stellar and substellar mass function (MF), considering its intermediate age and its nearby distance. Here we present the results of a wide-field, near-infrared study of Praesepe using the Data Release 9 of the United Kingdom Infrared Telescope Infrared Deep Sky Survey Galactic Clusters Survey. We obtained cluster candidates of Praesepe based on a 3σ astrometric and five-band photometric selection. We derived a binary frequency for Praesepe of 25.6 ± 3.0 per cent in the 0.2-0.45 M&sun; mass range, 19.6 ± 3.0 per cent for 0.1-0.2 M&sun; and 23.2 ± 5.6 per cent for 0.07-0.1 M&sun;. We also studied the variability of the cluster candidates of Praesepe, and we conclude that seven objects could be variable. We inferred the luminosity function of Praesepe in the Z and J bands and derived its MF. We observe that our determination of the MF of Praesepe differs from previous studies: while previous MFs present an increase from 0.6 to 0.1 M&sun;, our MF shows a decrease. We looked at the MF of Praesepe in two different regions of the cluster, i.e. within and beyond 1°.25, and we observed that both regions present an MF which decrease to lower masses. We compared our results with the Hyades, the Pleiades and α Per MF in the mass range 0.072-0.6 M&sun; and showed that the Praesepe MF is more similar to α Per although they are, respectively, of ages ˜85 and ˜600 Myr. Even though of similar age, the Praesepe remains different than the Hyades, with a decrease in the MF of only ˜0.2 dex from 0.6 down to 0.1 M&sun;, compared to ˜1 dex for the Hyades. Based on observations made with the United Kingdom Infrared Telescope, operated by the Joint Astronomy Centre on behalf of the UK Particle Physics and Astronomy Research Council.