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Even multiplication it's nothing but a shortcut for addition. I can calculate 3x76556 with additions, but it would take me a year to write it down...So I suppose that, in the past, the origin of multiplication was the need to create a shortcut for long tedious additions, and the origin of division was to create a shortcut for long tedious subtractions.

 

 

I agree that this is most likely the origin of multiplication and division. Though I would say that the notion of multiplying mathematical objects can be much more general than this.

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