Is there a commutative property of addition, subtraction, multiplication, or division and does order matter when doing any of them, why or why not?

Addition and Multiplication ARE commutative, while
Subtraction and Division are NOT commutative.

e.g, in
simple addition and multiplication, no matter what the order, the result is still the
same. Whereas, subraction and division need to have a particular order or the result
will change.

When doing more complex expressions and
equations, order IS important or the answer will change
completely.

An easy way to remember order is
BIMDAS

B -
Brackets
I -
Indices
M - Multiplication (from
left of expression to right)
D - Division (from
left of expression to right)
A - Addition(Left of
expression to right)
S- Subtraction (Left of
expression to right)

Hope that
helped.