The answer has nothing to do with multiplicative inverses / reciprocals.
When you're referring to
Cellular reproduction - This can occur through mitosis or meiosis in eukaryotes and binary fission in prokaryotes.
A cell divides into two, the effect of which is that the cell/ organism has multiplied in a reproductive sense.
When you are talking about something which does not lose its nature, but rather creates a clone of itself when divided, then the number or quantity of that thing increases when divided, causing it to multiply in number. (Example - cell division of one cell may create two identical cells.)