0:00:00.570,0:00:04.590
Use the commutative law of[br]addition-- let me underline

0:00:04.590,0:00:07.970
that-- the commutative law[br]of addition to write the

0:00:07.970,0:00:12.510
expression 5 plus 8 plus 5[br]in a different way and

0:00:12.510,0:00:13.470
then find the sum.

0:00:13.470,0:00:16.550
Now, this commutative law of[br]addition sounds like a very

0:00:16.550,0:00:19.790
fancy thing, but all it means[br]is if you're just adding a

0:00:19.790,0:00:23.680
bunch of numbers, it doesn't[br]matter what order you add the

0:00:23.680,0:00:24.500
numbers in.

0:00:24.500,0:00:29.090
So we could add it as[br]5 plus 8 plus 5.

0:00:29.090,0:00:33.990
We could order it as[br]5 plus 5 plus 8.

0:00:33.990,0:00:38.140
We could order it[br]8 plus 5 plus 5.

0:00:38.140,0:00:40.750
These are all going to add up[br]to the same things, and it

0:00:40.750,0:00:41.235
makes sense.

0:00:41.235,0:00:43.750
If I have 5 of something and[br]then I add 8 more and then I

0:00:43.750,0:00:46.250
add 5 more, I'm going to get[br]the same thing as if I had

0:00:46.250,0:00:49.280
took 5 of something, then added[br]the 5, then added the 8.

0:00:49.280,0:00:50.270
You could try all[br]of these out.

0:00:50.270,0:00:51.770
You'll get the same thing.

0:00:51.770,0:00:54.420
Now, they say in a different[br]way, and then find the sum.

0:00:54.420,0:00:56.480
The easiest one to find the sum[br]of-- actually, let's do

0:00:56.480,0:00:56.950
all of them.

0:00:56.950,0:00:59.110
But the easiest one, just[br]because a lot of people

0:00:59.110,0:01:02.660
immediately know that 5 plus 5[br]is 10, is to maybe start with

0:01:02.660,0:01:04.150
the 5 plus 5.

0:01:04.150,0:01:06.980
So if you have 5 plus[br]5, that's 10, plus

0:01:06.980,0:01:09.690
8 is equal to 18.

0:01:09.690,0:01:13.370
Now, let's verify that these two[br]are the same exact thing.

0:01:13.370,0:01:17.040
Up here, 5 plus 8 is 13.

0:01:17.040,0:01:20.840
13 plus 5 is also 18.

0:01:20.840,0:01:22.520
That is also 18.

0:01:22.520,0:01:25.550
If we go down here,[br]8 plus 5 is 13.

0:01:25.550,0:01:28.720
13 plus 5 is also equal to 18.

0:01:28.720,0:01:30.900
So no matter how you do it and[br]no matter what order you do it

0:01:30.900,0:01:33.420
in-- and that's the commutative[br]law of addition.

0:01:33.420,0:01:35.790
It sounds very fancy, but it[br]just means that order doesn't

0:01:35.790,0:01:39.370
matter if you're adding[br]a bunch of things.