Dividing by zero can be confusing for students at all levels. If teachers are to provide clear and understandable explanations of this topic, they must possess a strong conceptual understanding of it themselves. In this article, the authors present qualitative data on fourth- through eighth-grade teachers' perceptions of division by zero. They discuss three categories: teachers who did not know that division by zero is undefined; teachers who knew that division by zero is undefined but could not provide an explanation; and, teachers who displayed correct conceptual understanding of division by zero. The authors conclude with several explanations of dividing by zero that should help teachers understand this topic by making appropriate connections to multiplication and division of positive integers. (Contains 1 table.)