We examined, on a trial-by-trial basis, fraction magnitude comparison strategies of adults with more and less mathematical knowledge. College students with high mathematical proficiency used a large variety of strategies that were well tailored to the characteristics of the problems and that were guaranteed to yield correct performance if executed correctly. Students with less mathematical proficiency sometimes used strategies similar to those of the mathematically proficient students, but often used flawed strategies that yielded inaccurate performance. As predicted by overlapping waves theory, increases in accuracy and speed were related to differences in strategy use, strategy choice, and strategy execution. When asked to choose the best strategy from among 3 possibilities--the strategy the student originally used, a correct alternative, and an incorrect alternative--students with lower fraction knowledge rarely switched from an original incorrect strategy to a correct alternative. This finding suggests that use of poor fraction magnitude comparison strategies stems in large part from lack of conceptual understanding of the requirements of effective strategies, rather than difficulty recalling or generating such strategies.