Properties of numbers and order of operations
Commutative law of addition
Use the commutative law of addition-- let me underline that-- the commutative law of addition to write the expression 5 plus 8 plus 5 in a different way and then find the sum. Now, this commutative law of addition sounds like a very fancy thing, but all it means is if you're just adding a bunch of numbers, it doesn't matter what order you add the numbers in. So we could add it as 5 plus 8 plus 5. We could order it as 5 plus 5 plus 8. We could order it 8 plus 5 plus 5. These are all going to add up to the same things, and it makes sense. If I have 5 of something and then I add 8 more and then I add 5 more, I'm going to get the same thing as if I had took 5 of something, then added the 5, then added the 8. You could try all of these out. You'll get the same thing. Now, they say in a different way, and then find the sum. The easiest one to find the sum of-- actually, let's do all of them. But the easiest one, just because a lot of people immediately know that 5 plus 5 is 10, is to maybe start with the 5 plus 5. So if you have 5 plus 5, that's 10, plus 8 is equal to 18. Now, let's verify that these two are the same exact thing. Up here, 5 plus 8 is 13. 13 plus 5 is also 18. That is also 18. If we go down here, 8 plus 5 is 13. 13 plus 5 is also equal to 18. So no matter how you do it and no matter what order you do it in-- and that's the commutative law of addition. It sounds very fancy, but it just means that order doesn't matter if you're adding a bunch of things.