Even though in mathematics education the discussion and description of competences is more advanced than in other fields of knowledge, many of these descriptions do not provide enough detail for guiding the analysis and design of (computer-based) learning tasks. Therefore, the purposes of the present study are to (a) develop a two-dimensional conceptualization of fraction competences, and (b) evaluate the developed competence-framework through an empirical task analysis of a set of computer-based fraction tasks. The results of this task analysis revealed that for 76.3% of the 173 tasks, a clear competence assignment was possible. Furthermore, we found that in this set of tasks, the cognitive processes associated with mere algorithmic calculation and formula manipulation are much more frequently addressed than complex cognitive processes (i.e., communicate model). Future research and practice in designing computer-based fraction tasks should thus focus on developing and investigating tasks addressing these complex processes.