What are the Commutative Properties of Addition and Multiplication?

'a' and 'b' are variables that stand for any number or expression
The order in which you add numbers doesn't matter! You can first add 'b' to 'a', or first add 'a' to 'b', and you'll get the same answer!
The order in which you multiply numbers doesn't matter! You can first multiply 'b' by 'a', or first multiply 'a' by 'b', and you'll get the same answer!

1. 'a' and 'b' are variables that stand for any number or expression
1. Order doesn't matter when you're just adding up numbers!
1. See how flipping the 2 and 3 around the + sign doesn't change anything!
1. 'a' and 'b' are variables that stand for any number or expression
1. See how flipping the 2 and 3 around the • sign doesn't change anything!
1. a-b only equals b-a if a=b! Like 3-3=3-3! But 2-3 does not equal 3-2. That's why the commutative property does not work for subtractions!
1. a÷b=b÷a only if a=±b, and otherwise a÷b does not equal b÷a!
2. For example, 2÷2=2÷2, and 2÷(-2)=(-2)÷2. But 2÷3 does not equal 3÷2!

Definition: Commutative Property