Fractions are highly important. Therefore, it is crucial to understand the developmental trajectory of fraction knowledge and its main predictors and consequences. Our research team has proposed that we have a neurocognitive architecture dedicated to processing nonsymbolic ratios, which serves as a startup tool for fractions: the Ratio Processing System (RPS). The RPS model (Lewis et al., 2016) predicts that this system directly and indirectly contributes to fraction and algebra knowledge. This model has been corroborated by cross-sectional studies with older children and studies with adults. However, it is still unclear how early RPS acuity longitudinally predicts fraction and algebra skills. In this dissertation, we started addressing this gap. In a series of studies, we investigated questions about the associations between the RPS and fraction and algebra skills: Is symbolic fraction processing associated with the RPS at the neural level? How is the RPS associated with the developmental trajectory of symbolic fraction magnitude understanding? How are the RPS and symbolic fraction magnitude processing associated with fraction and algebra knowledge? We followed younger children (2nd graders), who had no formal experience with fractions, and older children (5th graders), who had few years of fraction education, for three years to address these questions. Overall, our results corroborate and expand the RPS model. Our results indicate that symbolic fraction magnitude understanding builds upon the RPS. Furthermore, our results show that the RPS and symbolic fraction magnitude understanding are associated with fraction and algebra knowledge early in development (2nd-4th grades). However, our results suggest a stronger role of symbolic fraction skills and a weaker role of the RPS in predicting advanced mathematics later in development (5th-7th grades). Finally, our results show that general cognitive factors are also significant predictors of fraction and algebra knowledge. Integrating these results, we propose modifications for the RPS model. This dissertation contributes to our understanding of the development of fraction and algebra knowledge and has implications for educational practices. In particular, promoting stronger symbolic fraction magnitude understanding at earlier grades, by linking symbolic fractions to the RPS, may contribute to future fraction and algebra knowledge. [The dissertation citations contained here are published with the permission of ProQuest LLC. Further reproduction is prohibited without permission. Copies of dissertations may be obtained by Telephone (800) 1-800-521-0600. Web page: http://www.proquest.com.bibliotheek.ehb.be/en-US/products/dissertations/individuals.shtml.]