This study investigated three pre-service elementary teachers' understanding of fractions and fraction multiplication and division. The motivation for this study was lack of conceptual understanding of fractions and fraction multiplication and division. Pre-service elementary teachers were chosen because teachers are the conduit of information for their students. The subjects were followed through the fractions unit in a mathematics methods course for pre-service elementary teachers at Brigham Young University. Each subject volunteered to participate and were interviewed and videotaped throughout the study, and they also provided copies of all work done in the fractions unit in the course. The data is presented as three case studies, each beginning with a discussion of the subject's math history and prior understanding of fractions. Then the case studies discuss the subject's change in understanding of fractions, fraction multiplication, and fraction division. Finally, at the end of each case study, a discussion of the subject's conceptual understanding is discussed. Each participant showed a deepened conceptual understanding of fractions, fraction multiplication, and fraction division. The subjects' prior knowledge of fractions and fraction multiplication and division did affect their growth of understanding. Each participant had unique levels of growth and inhibitors to growth of understanding. At the times of most growth of understanding, the subjects' inhibitors of growth were also the most evident.