The answer has nothing to do with multiplicative inverses / reciprocals.
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2 Answers
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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.
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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.)
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3$\begingroup$ This is very similar to Phylyp's answer from a few hours ago, no? $\endgroup$ Commented Mar 31, 2018 at 17:59
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2$\begingroup$ @Wizard, try not to repost answers that have already been posted. $\endgroup$ Commented Mar 31, 2018 at 18:22