The double form (a and an) of the English indefinite article, encourages this misdivision.
late 14c., from Old French division, from Latin divisionem (nominative divisio), from divid-, stem of dividere (see divide). Military sense is first recorded 1590s. Mathematical sense is from early 15c. The mathematical division sign supposedly was invented by British mathematician John Pell (1611-1685) who taught at Cambridge and Amsterdam.
division di·vi·sion (dĭ-vĭzh'ən)
The act or process of dividing.
The operation of determining how many times one quantity is contained in another; the inverse of multiplication.