Dissociations within Arithmetic Rules: different neural bases and solution processes in Zero and One Multiplications

Zero and One single-digit multiplications (e.g., N × 0 = 0; N × 1 = N) are often excluded in studies of arithmetic because they are considered to be solved using a separate strategy, namely by referring to a rule. However, there is no clear evidence that these types of multiplications form a homogeneous group. In this study, we compare the behavioral and neural responses that operate when young adults solve Zero, One, and other single-digit multiplications (Facts). Twenty-one healthy participants completed an event-related functional magnetic resonance imaging (fMRI) study while performing an arithmetic verification task with Arabic digits. We use univariate and multivariate approaches (i.e., Representational Similarity Analysis - RSA) of fMRI-BOLD signal to make quantitative comparisons across task-related activation patterns. In terms of performance, participants were generally slower and made more errors in Zero compared to One-multiplications. The fMRI results showed higher activations in the right precuneus when participants solved Zero versus One-multiplications, possibly reflecting greater abstraction and larger shifts of spatial attention in the former compared to the latter operation, a hypothesis that needs to be verified further. RSA results showed the activation pattern for Facts in areas traditionally involved in multiplications (i.e., inferior and middle frontal gyrus, superior parietal lobule). In addition, RSA also revealed discriminative capacity in the right precuneus for distinguishing between Zero and One-multiplication. These dissociable patterns at both behavioral and neural levels support the view that Zero and One multiplications engage distinct solution processes, rather than relying on a single, unified rule-based strategy.