0:00:00.000,0:00:04.390
Let's do some examples comparing absolute values.

0:00:04.390,0:00:06.480
So, let's say we were to ask ourselves

0:00:06.480,0:00:12.234
how -9, the absolute value of -9 I should say,

0:00:12.234,0:00:19.042
how that compares to the absolute value of

0:00:19.042,0:00:24.058
-let me think of a good number--the absolute value of -7.

0:00:24.058,0:00:25.846
So, let's think about this a little bit and

0:00:25.846,0:00:27.912
let's think about what -9 looks like or

0:00:27.912,0:00:29.073
where it is in the number line and

0:00:29.073,0:00:30.931
where -7 is on the number line.

0:00:30.931,0:00:33.671
Let's see where the absolute values mean and

0:00:33.671,0:00:36.411
then we should probably be able to do this comparison.

0:00:36.411,0:00:38.315
So there are a couple ways to think about it.

0:00:38.315,0:00:41.220
One is you can draw them on the number line.

0:00:41.220,0:00:45.908
So, if this is 0 and this is -7

0:00:45.908,0:00:49.669
and then this is -9 right over here.

0:00:49.669,0:00:52.177
Now when you take the absolute value of a number,

0:00:52.177,0:00:55.742
you are really saying how far is that number from 0,

0:00:55.742,0:00:58.493
whether it is to the left or the right of 0.

0:00:58.493,0:01:02.998
So for example, -9 is 9 to the left of 0.

0:01:02.998,0:01:07.084
So the absolute value of -9 is exactly 9.

0:01:07.084,0:01:16.279
This evaluates to 9. -7 is exactly 7 to the left of 0.

0:01:16.279,0:01:20.227
So the absolute value of -7 is +7.

0:01:20.227,0:01:22.409
And so, if you were to compare 9 and 7

0:01:22.409,0:01:24.081
then this is a little bit more straight forward.

0:01:24.081,0:01:29.167
9 is clearly greater than 7.

0:01:29.167,0:01:32.278
And if you ever get confused with the greater than and less than symbols,

0:01:32.278,0:01:35.645
just remember that the symbol is larger on the left hand side,

0:01:35.645,0:01:37.735
so that is the greater than side.

0:01:37.735,0:01:41.914
If I were to write this, and this is actually also a true statement.

0:01:41.914,0:01:44.190
If you took this without the absolute value signs,

0:01:44.190,0:01:49.567
it is also true that -9 is less than -7.

0:01:49.567,0:01:53.033
Notice the smaller side is on the smaller number.

0:01:53.033,0:01:56.700
And so that is the interesting thing: -9 is less than -7

0:01:56.700,0:02:01.024
but their absolute values, since -9 is further to the left of 0,

0:02:01.024,0:02:04.507
it is the absolute value of -9 , which is 9,

0:02:04.507,0:02:07.900
is greater than the absolute value of -7.

0:02:07.900,0:02:09.546
Another way to think about it is

0:02:09.546,0:02:11.967
if you take the absolute value of a number,

0:02:11.967,0:02:14.770
it really is just the positive value of that number.

0:02:14.770,0:02:19.507
So if you took the absolute value of 9 that equals 9.

0:02:19.507,0:02:22.967
Or the absolute value of -9, that is also equal to 9.

0:02:22.967,0:02:24.198
When you think of it visually, that is

0:02:24.198,0:02:27.634
because both of these numbers are exactly 9 away from 0.

0:02:27.634,0:02:32.046
This is 9 to the right of 0 and this is 9 to the left of 0.

0:02:32.046,0:02:33.857
Let's do a few more of these.

0:02:33.857,0:02:37.453
So let's say that we wanted to compare

0:02:37.453,0:02:43.749
the absolute value of 2 to the absolute value of 3.

0:02:43.749,0:02:47.836
Well the absolute value of a positive is just going to be that same value.

0:02:47.836,0:02:52.018
2 is 2 to the right of 0. So this is just going to evaluate to 2.

0:02:52.018,0:02:53.900
And then the absolute value of 3,

0:02:53.900,0:02:55.567
that is just going to evaluate to 3.

0:02:55.567,0:02:57.263
That is actually pretty straight forward.

0:02:57.263,0:03:00.833
So 2 is clearly the smaller number here

0:03:00.833,0:03:03.167
so we clearly get 2 is less than 3.

0:03:03.167,0:03:05.700
Or the absolute value of 2 is less than 3.

0:03:05.700,0:03:07.900
So we have a less than right over here.

0:03:07.900,0:03:12.633
Let's say you wanted to compare

0:03:12.633,0:03:15.933
-I am trying to find a suitable color-

0:03:15.933,0:03:19.233
the absolute value of -8 to the absolute value of 8.

0:03:19.233,0:03:23.116
One way to think about it is that they are both 8 away from 0.

0:03:23.116,0:03:25.916
This is 8 to the left of 0 and this 8 to the right of 0.

0:03:25.916,0:03:28.749
So both of these things evaluate to 8.

0:03:28.749,0:03:34.183
Absolute value of negative 8 is 8 and absolute value of 8 is 8.

0:03:34.183,0:03:38.084
So clearly 8 is equal to 8.

0:03:38.084,0:03:39.980
Let's do a couple more examples.

0:03:39.980,0:03:46.815
Let's say that I wanted to compare the absolute value of -1 and

0:03:46.815,0:03:48.900
I want to compare that to +2.

0:03:48.900,0:03:57.967
So the absolute value of -1 is just positive version of -1 which is just 1.

0:03:57.967,0:04:00.189
So 1 is clearly less than 2.

0:04:00.189,0:04:01.350
Or, the other way to think about it is

0:04:01.350,0:04:07.037
the absolute value of negative 1 is clearly less than 2.