Its an interesting question. I think the way it could have been discovered is rooted in how we learn about it in elementary.
You got a pizza. The pizza is considered 1 whole thing. You got 3 friends. So you need to split the pizza among (ඞ) 4 people. So you devide 1/4 every one gets 1/4 of the pizza. If you got 2 whole pizzas for the 4 people everyone gets 2/4 so half a pizza.
Multiplication can be though of as repeatedly adding something. Like we got seven guys everyone should get 2 slices of bread so 2×7=14.
Mathematically you start with defining the numbers and two operations between them addition and multiplication. You start treating them as functions define their inverses and expand into the whole numbers and rationals. So the multipication wasn’t really discovered it was defined like addition. And the inverse of multiplication is division.
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