The present study extended previous research by clarifying the hierarchy and unique shared cognitive architectures among arithmetic operations. We examined how addition and subtraction fluency at the second grade fall relate to multiplication fluency at the third grade spring, and whether they have a shared cognitive architecture. This study was part of a longitudinal study comprising five assessment points of arithmetic, reading, and cognitive factors from the first to third grades (207 children; Mage = 7 years 8 months). Using structural equation modeling, the foundational numerical and nonnumerical cognitive precursors were included in a hierarchical development framework to explore the cognitive architecture of arithmetic skill development. By contrasting the findings concerning addition and subtraction fluency with those of reading fluency, we learned about the results’ domain specificity. Both numerical abilities and serial retrieval fluency predicted multiplication skill in the baseline analysis. In the hierarchical models, their shared variance with prior arithmetic (addition and subtraction fluency) skills or reading fluency was partialled out to examine the shared unique cognitive architecture between operations. Addition fluency explained most of the variance in multiplication fluency, but numerical abilities, retrieval fluency, and working memory also had small predictive associations in the addition fluency model. The subtraction fluency model remained on par with the addition fluency model. In the reading fluency model, numerical abilities were the strongest predictor following by reading fluency and serial retrieval fluency, and reading fluency predicted multiplication fluency, but working memory did not. These findings indicate domain specificity and partially distinct cognitive underpinnings for different arithmetic operations. (PsycInfo Database Record (c) 2026 APA, all rights reserved)