Here is a bit more information than you asked for:
The commutative property is stated as: a+b=b+a, or ab = ba. Notice that the numbers (a and b) move back and forth. Think of a commuter, who travels back and forth to work each day.
The associative property is stated as: (a+b)+c=a+(b+c) or (ab)c = a(bc). In this case the parentheses move back and forth, so you might want to call it the commutative property too! But there's something else going on here. Parentheses are grouping symbols, and a you group is the people you hang out with or associate with.
So remember: If the grouping symbols move, it's the associative property. If it's the other one where things move, it's the commutative property.
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The commutative property of addition.
This is called the Commutative property of addition.
That's called the commutative property.That's called the commutative property.That's called the commutative property.That's called the commutative property.
The commutative property of addition states that x + y = y + x for any two elements x and y.
The property you described, where x + y = y + x, is called commutativity. In the case of addition, it is called the commutative property of addition.