The explanation that makes most sense to me is that it's mostly to avoid having to explicitly write out parentheses a lot of the time. Especially for things like polynomials, which are a bunch of multiplied terms added together, eg 3x+2y and not (3*x)+(2*y). And in polynomials you can even drop the explicit multiplication symbol, so it's much neater. And once you've done this for algebra now you have to do it for plain arithmetic as well to make it all match up, and 3*5+2*7 gives the same answer as evaluating the polynomial at 5,7