To get this word fixed in your mind :

Think of commuting from one place to another. That is what the numbers are doing when you use this property of Addition or Multiplication. They just move from one place to another in the equation. In the simplest case, they just swap places.

The Commutative Property states that a + b = b + a : (for Addition)
and that a * b = b * a : (for Multiplication).
The multiplication can also be written : ab = ba

This can be extended to three numbers, so that a + b + c = b + c + a, and a * b * c = b * c * a (or abc = bca).

Reworded, this Property says : You can change the order of the numbers without changing the sum or product of the numbers.

Note : This Property does NOT work for subtraction or division, nor with powers or roots.

or commutative?

a + b = b + a
ab = ba

There is the addition commutative property and the multiplication commutative property.