Practice changes how the brain does the problem
Early on, a less familiar sum leans on working memory and step-by-step calculation, with heavy use of frontal and parietal regions. With practice, many problems shift toward direct retrieval of the answer. Imaging studies of multiplication and subtraction training show that shift: the brain does less slow computing and more fact retrieval for the operations you actually trained. The gain is specific. Getting faster at 7 × 8 does not, by itself, make you faster at unrelated thinking.
Ischebeck, A., Zamarian, L., Siedentopf, C., et al. (2006). How specifically do we learn? Imaging the learning of multiplication and subtraction. NeuroImage, 30(4), 1365–1375. Zamarian, L., Ischebeck, A., & Delazer, M. (2009). Neuroscience of learning arithmetic — Evidence from brain imaging studies. Neuroscience & Biobehavioral Reviews, 33(6), 909–925.