The point of the property is so that you can apply it when you get to more difficult things that don't have any order, but can be grouped in a different way such as you can simplify it or so that you can see a way to simplify it.
eg, you might be sitting down trying to simplify 1 + x^2 - 2x, and because you've only seen things in the form x^2 - 2x + 1, you wouldn't see that you can simplify it to (x + 1)^2 were it not for that property. In fact, Euler's Identity used the commutative property of addition to mix and match the Taylor series for cos(x) and i*sin(x).
That's essentially true of any property. When you first learn it you think, "Well, duh!" But unless you really commit it to memory you probably won't see the various connections between something new and something old.
@Golden: To be honest, I didn't know what I wanted to do for the longest time. Up until 2 years ago I had no clue, and was going to major in music simply because marching band was my life at that point (even though I've always been good at math). Then, while taking a stats course, I realized that I wanted to find a job that used math a lot. Then, this past year I took a computer science course (as required by my school for math majors) and realized I loved the problem solving and the logic, and also the opportunities to build some really cool things (including math-related programs that can do various things).
For me it was taking courses and realizing that I seriously enjoyed whatever topic we were studying. But if you can land whatever job you want, as you say, that's great too (and also a bit better long-term, I'd say).
![[FBC] Papa Mink](/data/avatars/l/166/166410.jpg?1363023093){kind=avatar}
