In this video, we are evaluating a complicated expression. We could go from left to right, but there is a simpler way. We are adding 13, subtracting 13, adding a negative 5, and adding a positive 5. We cannot use the commutative property to change the order because we are subtracting numbers, not just adding.
However, we can rewrite the expression so that it only involves addition. Subtracting a number is the same as adding its opposite. Therefore, we can rewrite the expression as negative 5 plus 13, plus negative 21, plus negative 13, and plus 11.
Now, we can use the commutative and associative properties to simplify the expression. We can pair up the opposites, which will cancel out, and we are left with a positive 11. Hopefully you can see that by rewriting subtraction as adding the opposite, we can use the commutative and associative properties to simplify things, which is really useful for the rest of your mathematical career. I encourage you to try it out yourself and go from left to right with the original expression; you should get the same result, though it may take more time.