The aim of this study is to investigate Danish pre-service teachers' (PSTs) mathematical and didactical knowledge of operations with rational numbers. This knowledge is studied through their collaborative activities to certain tasks related to the teaching of operations with rational numbers. An explicit model of the teachers' mathematical and didactical knowledge is designed based on the anthropological theory of the didactic (ATD) and used to analyse five-groups of PSTs' collaborative work. The findings show that the Danish PSTs prefer to use contextual or real-life situations in their teaching, but they encounter various challenges to realise general ideas in the context at hand.