The role of language in performing numerical computations has been a topic of special interest in cognition. The “Triple Code Model” proposes the existence of a language-dependent verbal code involved in retrieving arithmetic facts related to addition and multiplication, and a language-independent analog magnitude code subserving tasks such as number comparison and estimation. Neuroimaging studies have shown dissociation between dependence of arithmetic computations involving exact and approximate processing on language-related circuits. However, a direct manipulation of language using different arithmetic tasks is necessary to assess the role of language in forming arithmetic representations and in solving problems in different languages. In the present study, 20 English-Chinese bilinguals were trained in two unfamiliar arithmetic tasks in one language and scanned using fMRI on the same problems in both languages (English and Chinese). For the exact “base-7 addition” task, language switching effects were found in the left inferior frontal gyrus (LIFG) and left inferior parietal lobule extending to the angular gyrus. In the approximate “percentage estimation” task, language switching effects were found predominantly in the bilateral posterior intraparietal sulcus and LIFG, slightly dorsal to the LIFG activation seen for the base-7 addition task. These results considerably strengthen the notion that exact processing relies on verbal and language-related networks, whereas approximate processing engages parietal circuits typically involved in magnitude-related processing.