The　ability　to　draw　numerical　inductive　reasoning　requires　two　key　cognitive　processes,　identification　and　extrapolation.　This　study　aimed　to　identify　the　neural　correlates　of　both　component　processes　of　numerical　inductive　reasoning　using　event-related　fMRI.　Three　kinds　of　tasks:　rule　induction　(RI),　rule　induction　and　application　(RIA),　and　perceptual　judgment　(Jud)　were　solved　by　twenty　right-handed　adults.　Our　results　found　that　the　left　superior　parietal　lobule　(SPL)　extending　into　the　precuneus　and　left　dorsolateral　prefrontal　cortex　(DLPFC)　were　commonly　recruited　in　the　two　components.　It　was　also　observed　that　the　fronto-parietal　network　was　more　specific　to　identification,　whereas　the　striatal-thalamic　network　was　more　specific　to　extrapolation.　The　findings　suggest　that　numerical　inductive　reasoning　is　mediated　by　the　coordination　of　multiple　brain　areas　including　the　prefrontal,　parietal,　and　subcortical　regions,　of　which　some　are　more　specific　to　demands　on　only　one　of　these　two　component　processes,　whereas　others　are　sensitive　to　both.　(C)　2011　Elsevier　Inc.　All　rights　reserved.