Commutative property

The commutative property says that the order of the numbers when adding or multiplying can be changed without changing the answer. For example, both formula_1 and formula_2 are equal to 10, and both formula_3 and formula_4 are equal to 35. This can be done with any numbers, or with more than two numbers.
Definition.
The definition of commutative property of addition is formula_5. "a" and "b" are variables and can be any number.
Some operations like dividing are not commutative. For instance, formula_6 is 2, but formula_7 is formula_8. Subtraction is not commutative either: formula_9 is 4, but formula_10 is negative 4.
Higher mathematics.
In higher mathematics like calculus, there are other commutative operations besides adding and multiplying. Commutative property must hold for each two elements of an Abelian group.