A crucial skill underlying all facets of arithmetic knowledge is the ability to distinguish correct solutions from incorrect ones. For this reason, arithmetic verification tasks have been widely used to study numerical cognition. The experimental manipulation of problems and solutions using this experimental paradigm allows to probe the mechanisms participants use to solve these arithmetic problems. Results have reliably shown that verification of correct arithmetic solutions engages different cognitive processes than verification of incorrect solutions. Given how fundamental distinguishing between correct and incorrect arithmetic solutions is for mathematical development, understanding the neurocognitive processes involved in arithmetic verification can also help better understand why fractions are notoriously difficult to learn. Using behavioral, electrophysiological, and neuroimaging techniques, this dissertation aims to extend the current understanding of arithmetic and fraction processing by (a) showing how fraction processing shares similar neurocognitive mechanisms as arithmetic processing, (b) illustrating how fraction components can facilitate or interfere with magnitude verification, and (c) describing the neural correlates of arithmetic verification. The findings from three studies using the arithmetic verification paradigm are integrated under a predictive processing framework which grounds arithmetic verification in a neurobiological plausible functioning of the nervous system and provides a foundation for future work.