A solid foundation in mathematics is beneficial not only for individuals' concurrent and later academic achievement, but also for future career success and financial stability. Rational number knowledge plays a pivotal role in mathematical success, yet it is often regarded as a challenging area to grasp comprehensively. The dissertation aims to enhance our understanding of how individuals process rational numbers; to deepen our comprehension of the relation between rational number processing and overall mathematics achievement; to highlight the role of math anxiety in mathematical performance; and to contribute to the broader field of learning. Two studies within this dissertation contributed to each of these aims. This work offers valuable insights into numerical development and learning in general. The first study investigated how children conceptualize non-symbolic fractions and its relation to overall math achievement. The findings showed that children in grades 3 to 5 predominantly conceptualize non-symbolic fractions either by surface features or by quantity, with quantitative conceptualization increasing with higher grade levels. While quantitative conceptualization was linked to higher math achievement, this relation no longer held after controlling for math anxiety. These findings support the idea of a foundational cognitive framework that processes quantitative information across non-symbolic and symbolic conceptualizations of fractional magnitudes. Additionally, our research suggests the need for further investigations into the role of math anxiety in the relation between fractional knowledge and math achievement. The second study examined college students' adaptive strategy use in fraction comparison tasks and its relation to their algebra performance using eye-tracking methods. Eye patterns provided evidence of adaptive strategy use according based on the type of fraction comparison problems. However, the use of these strategies itself was not significantly related to algebra performance or fraction comparison performance. These findings underscore the robustness of the findings regarding adaptive strategy use across different methods of measurement. Furthermore, the study calls for further research to examine the relation with varied stimuli and diverse samples. Together, the current dissertation delves into individuals' rational number processing across development, supporting the key idea of the integrated theory of numerical development, which explains how individuals expand their numerical understanding in continuous ways. Both studies highlight the importance of fraction knowledge and advocate for further research on the impact of math anxiety in specific domains of mathematics. The findings also have broader implications for learning, highlighting how surface features and contexts can impact the learning process and how individuals employ various strategies when solving problems. In conclusion, this dissertation makes a significant contribution to advancing our scientific knowledge in the areas of rational number processing, mathematics, and broader cognitive processing. [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://bibliotheek.ehb.be:2222/en-US/products/dissertations/individuals.shtml.]