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## Arithmetic properties

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# Commutative law of addition

## Video transcript

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.