1 00:00:00,570 --> 00:00:04,590 Use the commutative law of addition-- let me underline 2 00:00:04,590 --> 00:00:07,970 that-- the commutative law of addition to write the 3 00:00:07,970 --> 00:00:12,510 expression 5 plus 8 plus 5 in a different way and 4 00:00:12,510 --> 00:00:13,470 then find the sum. 5 00:00:13,470 --> 00:00:16,550 Now, this commutative law of addition sounds like a very 6 00:00:16,550 --> 00:00:19,790 fancy thing, but all it means is if you're just adding a 7 00:00:19,790 --> 00:00:23,680 bunch of numbers, it doesn't matter what order you add the 8 00:00:23,680 --> 00:00:24,500 numbers in. 9 00:00:24,500 --> 00:00:29,090 So we could add it as 5 plus 8 plus 5. 10 00:00:29,090 --> 00:00:33,990 We could order it as 5 plus 5 plus 8. 11 00:00:33,990 --> 00:00:38,140 We could order it 8 plus 5 plus 5. 12 00:00:38,140 --> 00:00:40,750 These are all going to add up to the same things, and it 13 00:00:40,750 --> 00:00:41,235 makes sense. 14 00:00:41,235 --> 00:00:43,750 If I have 5 of something and then I add 8 more and then I 15 00:00:43,750 --> 00:00:46,250 add 5 more, I'm going to get the same thing as if I had 16 00:00:46,250 --> 00:00:49,280 took 5 of something, then added the 5, then added the 8. 17 00:00:49,280 --> 00:00:50,270 You could try all of these out. 18 00:00:50,270 --> 00:00:51,770 You'll get the same thing. 19 00:00:51,770 --> 00:00:54,420 Now, they say in a different way, and then find the sum. 20 00:00:54,420 --> 00:00:56,480 The easiest one to find the sum of-- actually, let's do 21 00:00:56,480 --> 00:00:56,950 all of them. 22 00:00:56,950 --> 00:00:59,110 But the easiest one, just because a lot of people 23 00:00:59,110 --> 00:01:02,660 immediately know that 5 plus 5 is 10, is to maybe start with 24 00:01:02,660 --> 00:01:04,150 the 5 plus 5. 25 00:01:04,150 --> 00:01:06,980 So if you have 5 plus 5, that's 10, plus 26 00:01:06,980 --> 00:01:09,690 8 is equal to 18. 27 00:01:09,690 --> 00:01:13,370 Now, let's verify that these two are the same exact thing. 28 00:01:13,370 --> 00:01:17,040 Up here, 5 plus 8 is 13. 29 00:01:17,040 --> 00:01:20,840 13 plus 5 is also 18. 30 00:01:20,840 --> 00:01:22,520 That is also 18. 31 00:01:22,520 --> 00:01:25,550 If we go down here, 8 plus 5 is 13. 32 00:01:25,550 --> 00:01:28,720 13 plus 5 is also equal to 18. 33 00:01:28,720 --> 00:01:30,900 So no matter how you do it and no matter what order you do it 34 00:01:30,900 --> 00:01:33,420 in-- and that's the commutative law of addition. 35 00:01:33,420 --> 00:01:35,790 It sounds very fancy, but it just means that order doesn't 36 00:01:35,790 --> 00:01:39,370 matter if you're adding a bunch of things.