That doesn't explain why they would need a different precedence. `a + b - c` is not the same as `a - b + c` even through the precedence's of + and - are the same (in most syntaxes).
Granted, the intersection of precedence and associativity is a great source of confusion (and any number of annoying Facebook memes)
I'm not a formally trained mathematician, but one way to rationalize + and - having the same precedence, is to consider them as inverses of each other, so your two examples can be written as
a + -b + c
And
a + b + -c
At which point precedence and associativity no longer matter. The same can be done with multiplication and division
I'm not a formally trained mathematician, but one way to rationalize + and - having the same precedence, is to consider them as inverses of each other, so your two examples can be written as
a + -b + c
And
a + b + -c
At which point precedence and associativity no longer matter. The same can be done with multiplication and division