Commutative, Associative Property Question

[Gina]

I hate being unsure about these things but I don't want to get in a habit of doing it wrong.

Here's an example:

9 + 2y + x - 25 + 3 + x

In using the commutative property, when I move stuff around, is there a rule as to which order it should be in? If I arbitrarily move things around I'll end up with different solutions, obviously.

So, if a constant comes first, a 'y' monomial second, and an 'x' variable third, should I move all the constants up, then the 'y' monomials, followed by the 'x' variables?

9 - 25 + 3 + 2y + x + x


According to PEMDAS, I should do addition before subtraction. So, the associative step would look like this:

9 - (25 + 3) + 2y + (x + x)


Or should I just go in order: (9 - 25) + 3 + 2y + (x + x)

[stapel_eliz]

9 + 2y + x - 25 + 3 + x

In using the commutative property, when I move stuff around, is there a rule as to which order it should be in?

Unless they've given you a rule, no, there are only conventions. In general, it is expected that the variable terms go first, and in alphabetical order. So "the" answer would be:

. . . . .x + x + 2y + 9 + 3 - 25 = 2x + 2y - 13

According to PEMDAS, I should do addition before subtraction.

Actually, addition and subtraction are at the same "level" or order of importance. Once you're down to just adding and subtracting, then you "should" work from left to right but, in practical terms, you would group in whatever manner you found most helpful.

[Gina]

Thank you very much!