Why the order of operations?

Hi,



I am wondering why the order of operations where made? Is it the case that mathematics is just a tool of solving physical problems, and hence the order is physically defined? For example, if I say: I took 3 apples from 9 apples and divided the rest to two persons equally, I won't write this mathematically as: 9-3/2 but rather (9-3)/2. Right? In other words, the vague order of operations doesn't appear when solving physical problems using mathematical tools.



Thanks