1
00:00:00,000 --> 00:00:00,540


2
00:00:00,540 --> 00:00:04,790
We're told to list in order from smallest to largest. So

3
00:00:04,790 --> 00:00:07,290
each of these quantities, it looks like we have expressions

4
00:00:07,290 --> 00:00:09,419
inside of absolute value signs.

5
00:00:09,419 --> 00:00:12,320
And just as a bit of review, absolute value just means your

6
00:00:12,320 --> 00:00:13,880
distance from 0.

7
00:00:13,880 --> 00:00:17,039
Or another way to think about it is, if it's a negative

8
00:00:17,039 --> 00:00:18,289
number inside of the absolute value

9
00:00:18,289 --> 00:00:19,469
sign, it becomes positive.

10
00:00:19,469 --> 00:00:21,799
If it's already positive, it stays positive.

11
00:00:21,800 --> 00:00:23,589
So let's think about these numbers.

12
00:00:23,589 --> 00:00:29,019
So the first one is the absolute value of 5.

13
00:00:29,019 --> 00:00:30,890
How far is 5 away from 0?

14
00:00:30,890 --> 00:00:33,439
Well, it's 5 away from 0.

15
00:00:33,439 --> 00:00:35,899
So it's equal to 5.

16
00:00:35,899 --> 00:00:37,159
So I were to actually draw a number line,

17
00:00:37,159 --> 00:00:38,609
you would see that.

18
00:00:38,609 --> 00:00:42,240
0 is here, 5 is over here, this distance

19
00:00:42,240 --> 00:00:43,440
right there is 5.

20
00:00:43,439 --> 00:00:46,229
So the absolute value of 5 is 5.

21
00:00:46,229 --> 00:00:50,619
Now, the next quantity they want us to figure out is the

22
00:00:50,619 --> 00:00:55,589
absolute value of 9 minus 7.

23
00:00:55,590 --> 00:00:58,540
Well, this is the same thing as the absolute value of 2.

24
00:00:58,539 --> 00:01:00,189
9 minus 7 is 2.

25
00:01:00,189 --> 00:01:04,099
And once again, 2 is just 2 units away from 0,

26
00:01:04,099 --> 00:01:05,239
so it's just 2.

27
00:01:05,239 --> 00:01:07,719
If you have a positive value in the absolute value sign, it

28
00:01:07,719 --> 00:01:08,980
just is itself.

29
00:01:08,980 --> 00:01:11,760
The absolute value of 2 is 2.

30
00:01:11,760 --> 00:01:21,500
Then we have the absolute value of 5 minus 15.

31
00:01:21,500 --> 00:01:22,810
Well, that's going to be the same thing as

32
00:01:22,810 --> 00:01:23,609
the absolute value.

33
00:01:23,609 --> 00:01:26,659
5 minus 15 is negative 10, so it's the same thing as the

34
00:01:26,659 --> 00:01:28,929
absolute value of negative 10.

35
00:01:28,930 --> 00:01:31,130
Now, there's two ways you can think about it.

36
00:01:31,129 --> 00:01:33,209
If it's a negative number inside of the absolute value

37
00:01:33,209 --> 00:01:35,559
sign, it just becomes the positive version of it, so it

38
00:01:35,560 --> 00:01:37,010
just becomes 10.

39
00:01:37,010 --> 00:01:39,480
Another way to think about it is, if you had negative 10,

40
00:01:39,480 --> 00:01:41,310
you would plot it-- it would be out here someplace,

41
00:01:41,310 --> 00:01:44,159
negative 10, we'd have to extend the number line-- it is

42
00:01:44,159 --> 00:01:46,119
10 to the left of 0.

43
00:01:46,120 --> 00:01:48,840
That's what the absolute value is telling us.

44
00:01:48,840 --> 00:01:52,270
Then we have the absolute value of 0.

45
00:01:52,269 --> 00:01:55,209


46
00:01:55,209 --> 00:01:57,329
Well, 0 is just 0 away from the number line.

47
00:01:57,329 --> 00:02:00,219
Absolute value of 0 is just 0.

48
00:02:00,219 --> 00:02:01,269
That is just 0.

49
00:02:01,269 --> 00:02:02,799
That's just right there.

50
00:02:02,799 --> 00:02:05,489
It has no distance from the origin.

51
00:02:05,489 --> 00:02:09,340
And then finally, we have the absolute value of negative 3.

52
00:02:09,340 --> 00:02:12,640


53
00:02:12,639 --> 00:02:15,869
That's 3 to the left of 0, or you can just think of it as

54
00:02:15,870 --> 00:02:19,629
getting rid of this negative sign, so it is equal to 3.

55
00:02:19,629 --> 00:02:22,819
So, now that we've expressed them all as just simple

56
00:02:22,819 --> 00:02:26,120
integers, let's list them in order from smallest to

57
00:02:26,120 --> 00:02:26,719
largest.

58
00:02:26,719 --> 00:02:29,669
So of all of these values, which is the smallest?

59
00:02:29,669 --> 00:02:32,679
This one is the smallest, the absolute value of 0.

60
00:02:32,680 --> 00:02:36,050
So let me write that down, absolute value of 0.

61
00:02:36,050 --> 00:02:38,160
What's the next smallest?

62
00:02:38,159 --> 00:02:38,859
What's the next one?

63
00:02:38,860 --> 00:02:41,570
Since we have a 2 there, this is the next

64
00:02:41,569 --> 00:02:43,299
smallest, right there.

65
00:02:43,300 --> 00:02:45,870
And that original expression was the absolute value of 9

66
00:02:45,870 --> 00:02:50,810
minus 7, so the absolute value of 9 minus 7.

67
00:02:50,810 --> 00:02:52,039
And then what's the next smallest?

68
00:02:52,039 --> 00:02:54,359
We have this 3, and then we have a 5 and a 10.

69
00:02:54,360 --> 00:02:58,230
So the next smallest is this 3, right here.

70
00:02:58,229 --> 00:03:01,139
That 3, and that original expression was the absolute

71
00:03:01,139 --> 00:03:02,389
value of negative 3.

72
00:03:02,389 --> 00:03:05,189


73
00:03:05,189 --> 00:03:08,460
Then we have this 5 over here, which is just the absolute

74
00:03:08,460 --> 00:03:10,629
value of 5.

75
00:03:10,629 --> 00:03:13,599
And then finally, we have this 10 over here, which was the

76
00:03:13,599 --> 00:03:19,199
absolute value of 5 minus 15.

77
00:03:19,199 --> 00:03:21,530
And we are done.

78
00:03:21,530 --> 00:03:21,866