The ability to detect environmental regularities is a cognitive skill essential for survival. Human beings have a capacity, called numerical reasoning, to identify and extrapolate number serial patterns in such diverse areas as scientific discovery, economics, and the weather. Numerical reasoning and calculation have long been intimately associated, leading to the suggestion that they share a common system of the manipulation of numbers. The question of interest is whether numerical inductive reasoning is fully embedded in number calculation, or operates beyond calculation? To directly address these issues, we run an fMRI experiment to compare the number series completion task with the addition calculation task, and to understand the results in a cognitive architecture. Our results show that the fronto-parietal network was recruited uniquely in the numerical reasoning including the left dorsolateral prefrontal cortex (DLPFC 46/9), left precentral gyrus (BA 6), right superior parietal lobule (BA 7) and left inferior occipital gyrus (BA 18); whereas the bilateral thalamus, caudate, and posterior cingulate cortex (PCC) extending into cuneus were uniquely activated in calculation problems. This study suggested that relative to calculation, numerical reasoning is more related to spatial processing. A cognitive model predicts the behavioral results.