The Tabula Alimentaria of Veleia records the details of two second-century a.d. imperial alimentary schemes at the northern Italian town of Veleia, providing a rare insight into the workings of these schemes. Imperial loans are made to local landowners in exchange for pledges of specified property. Interest paid by landowners is used to fund cash subsidies for the upbringing of selected local children. In the early twentieth century, the French scholar Félix de Pachtere came close to demonstrating a consistent arithmetical relationship between a landowner's declared property value and the loan received. However, anomalies remained. This article proposes a revised formula which establishes a precise and consistent linkage between loan amounts and property declarations. Based on this arithmetical dataset, the paper proposes some hypotheses about how these fractional computations might have been performed in second-century Rome.