Findings and Conclusions: This study found that the secondary mathematics preservice teachers exhibited a high level of procedural knowledge of operations with rational numbers as well as common representations of rational numbers. The preservice teachers exhibited a moderate to high level of conceptual knowledge on the Rational Numbers and Their Representations survey as they related fractional pieces to wholes. However, the secondary mathematics preservice teachers who participated in the interview process exhibited a moderate level of conceptual knowledge of rational numbers. The three preservice teachers who completed an interview were dependent on a standard algorithm and based many of their explanations on that algorithm. The three preservice teachers included in the interview process exhibited a low level of pedagogical content knowledge. They could list no misconceptions their future students may have. Their main approach to correcting mistakes students would make was to refer the students back to the standard algorithm.