A comparison of ratios and fractions and their roles as tools in proportional reasoning

In an attempt to develop our shared understanding of the relationship between ratios and fractions, we began a phenomenological study to gather evidence from teachers and textbooks and to collect evidence from our own experiences. In this article, we present five possible models for this relationship and a summary of evidence to support each. We also present the model that we developed to represent our shared understanding and provide the results of a study for which we have used our model to help us analyze students' uses of ratios and fractions in their solutions to proportion-related problems.