Improving the mathematical skills of the next generation of students will require that elementary and middle school teachers are competent and confident in their abilities to perform fraction operations and to solve algebra equations The present study was conducted to (a) quantify relationships between prospective teachers' abilities to perform fraction operations and their abilities to solve algebra equations, and (b) explore prospective teachers' levels of confidence and bias with respect to their abilities to perform fraction operations and to solve linear algebra equations containing fractions. Data were collected from prospective teachers (n = 573) who had completed a mathematics course required of education majors. The multivariate effect size for the analysis used to address the first research questions was quite large (R[subscript c][superscript 2] = 40.6%). With respect to the second research question, we determined that the prospective teachers varied in the accuracy and bias of their confidence levels according to problem type, but tended overall to be overconfident, and had more dispersed levels of bias when they obtained incorrect answers.