[Script Info]
Title: 
[Events]
Format: Layer, Start, End, Style, Name, MarginL, MarginR, MarginV, Effect, Text
Dialogue: 0,0:00:00.00,0:00:04.39,Default,,0000,0000,0000,,Let's do some examples comparing absolute values.
Dialogue: 0,0:00:04.39,0:00:06.48,Default,,0000,0000,0000,,So, let's say we were to ask ourselves
Dialogue: 0,0:00:06.48,0:00:12.23,Default,,0000,0000,0000,,how -9, the absolute value of -9 I should say,
Dialogue: 0,0:00:12.23,0:00:19.04,Default,,0000,0000,0000,,how that compares to the absolute value of
Dialogue: 0,0:00:19.04,0:00:24.06,Default,,0000,0000,0000,,-let me think of a good number--the absolute value of -7.
Dialogue: 0,0:00:24.06,0:00:25.85,Default,,0000,0000,0000,,So, let's think about this a little bit and
Dialogue: 0,0:00:25.85,0:00:27.91,Default,,0000,0000,0000,,let's think about what -9 looks like or
Dialogue: 0,0:00:27.91,0:00:29.07,Default,,0000,0000,0000,,where it is in the number line and
Dialogue: 0,0:00:29.07,0:00:30.93,Default,,0000,0000,0000,,where -7 is on the number line.
Dialogue: 0,0:00:30.93,0:00:33.67,Default,,0000,0000,0000,,Let's see where the absolute values mean and
Dialogue: 0,0:00:33.67,0:00:36.41,Default,,0000,0000,0000,,then we should probably be able to do this comparison.
Dialogue: 0,0:00:36.41,0:00:38.32,Default,,0000,0000,0000,,So there are a couple ways to think about it.
Dialogue: 0,0:00:38.32,0:00:41.22,Default,,0000,0000,0000,,One is you can draw them on the number line.
Dialogue: 0,0:00:41.22,0:00:45.91,Default,,0000,0000,0000,,So, if this is 0 and this is -7
Dialogue: 0,0:00:45.91,0:00:49.67,Default,,0000,0000,0000,,and then this is -9 right over here.
Dialogue: 0,0:00:49.67,0:00:52.18,Default,,0000,0000,0000,,Now when you take the absolute value of a number,
Dialogue: 0,0:00:52.18,0:00:55.74,Default,,0000,0000,0000,,you are really saying how far is that number from 0,
Dialogue: 0,0:00:55.74,0:00:58.49,Default,,0000,0000,0000,,whether it is to the left or the right of 0.
Dialogue: 0,0:00:58.49,0:01:02.100,Default,,0000,0000,0000,,So for example, -9 is 9 to the left of 0.
Dialogue: 0,0:01:02.100,0:01:07.08,Default,,0000,0000,0000,,So the absolute value of -9 is exactly 9.
Dialogue: 0,0:01:07.08,0:01:16.28,Default,,0000,0000,0000,,This evaluates to 9. -7 is exactly 7 to the left of 0.
Dialogue: 0,0:01:16.28,0:01:20.23,Default,,0000,0000,0000,,So the absolute value of -7 is +7.
Dialogue: 0,0:01:20.23,0:01:22.41,Default,,0000,0000,0000,,And so, if you were to compare 9 and 7
Dialogue: 0,0:01:22.41,0:01:24.08,Default,,0000,0000,0000,,then this is a little bit more straight forward.
Dialogue: 0,0:01:24.08,0:01:29.17,Default,,0000,0000,0000,,9 is clearly greater than 7.
Dialogue: 0,0:01:29.17,0:01:32.28,Default,,0000,0000,0000,,And if you ever get confused with the greater than and less than symbols,
Dialogue: 0,0:01:32.28,0:01:35.64,Default,,0000,0000,0000,,just remember that the symbol is larger on the left hand side,
Dialogue: 0,0:01:35.64,0:01:37.74,Default,,0000,0000,0000,,so that is the greater than side.
Dialogue: 0,0:01:37.74,0:01:41.91,Default,,0000,0000,0000,,If I were to write this, and this is actually also a true statement.
Dialogue: 0,0:01:41.91,0:01:44.19,Default,,0000,0000,0000,,If you took this without the absolute value signs,
Dialogue: 0,0:01:44.19,0:01:49.57,Default,,0000,0000,0000,,it is also true that -9 is less than -7.
Dialogue: 0,0:01:49.57,0:01:53.03,Default,,0000,0000,0000,,Notice the smaller side is on the smaller number.
Dialogue: 0,0:01:53.03,0:01:56.70,Default,,0000,0000,0000,,And so that is the interesting thing: -9 is less than -7
Dialogue: 0,0:01:56.70,0:02:01.02,Default,,0000,0000,0000,,but their absolute values, since -9 is further to the left of 0,
Dialogue: 0,0:02:01.02,0:02:04.51,Default,,0000,0000,0000,,it is the absolute value of -9 , which is 9,
Dialogue: 0,0:02:04.51,0:02:07.90,Default,,0000,0000,0000,,is greater than the absolute value of -7.
Dialogue: 0,0:02:07.90,0:02:09.55,Default,,0000,0000,0000,,Another way to think about it is
Dialogue: 0,0:02:09.55,0:02:11.97,Default,,0000,0000,0000,,if you take the absolute value of a number,
Dialogue: 0,0:02:11.97,0:02:14.77,Default,,0000,0000,0000,,it really is just the positive value of that number.
Dialogue: 0,0:02:14.77,0:02:19.51,Default,,0000,0000,0000,,So if you took the absolute value of 9 that equals 9.
Dialogue: 0,0:02:19.51,0:02:22.97,Default,,0000,0000,0000,,Or the absolute value of -9, that is also equal to 9.
Dialogue: 0,0:02:22.97,0:02:24.20,Default,,0000,0000,0000,,When you think of it visually, that is
Dialogue: 0,0:02:24.20,0:02:27.63,Default,,0000,0000,0000,,because both of these numbers are exactly 9 away from 0.
Dialogue: 0,0:02:27.63,0:02:32.05,Default,,0000,0000,0000,,This is 9 to the right of 0 and this is 9 to the left of 0.
Dialogue: 0,0:02:32.05,0:02:33.86,Default,,0000,0000,0000,,Let's do a few more of these.
Dialogue: 0,0:02:33.86,0:02:37.45,Default,,0000,0000,0000,,So let's say that we wanted to compare
Dialogue: 0,0:02:37.45,0:02:43.75,Default,,0000,0000,0000,,the absolute value of 2 to the absolute value of 3.
Dialogue: 0,0:02:43.75,0:02:47.84,Default,,0000,0000,0000,,Well the absolute value of a positive is just going to be that same value.
Dialogue: 0,0:02:47.84,0:02:52.02,Default,,0000,0000,0000,,2 is 2 to the right of 0. So this is just going to evaluate to 2.
Dialogue: 0,0:02:52.02,0:02:53.90,Default,,0000,0000,0000,,And then the absolute value of 3,
Dialogue: 0,0:02:53.90,0:02:55.57,Default,,0000,0000,0000,,that is just going to evaluate to 3.
Dialogue: 0,0:02:55.57,0:02:57.26,Default,,0000,0000,0000,,That is actually pretty straight forward.
Dialogue: 0,0:02:57.26,0:03:00.83,Default,,0000,0000,0000,,So 2 is clearly the smaller number here
Dialogue: 0,0:03:00.83,0:03:03.17,Default,,0000,0000,0000,,so we clearly get 2 is less than 3.
Dialogue: 0,0:03:03.17,0:03:05.70,Default,,0000,0000,0000,,Or the absolute value of 2 is less than 3.
Dialogue: 0,0:03:05.70,0:03:07.90,Default,,0000,0000,0000,,So we have a less than right over here.
Dialogue: 0,0:03:07.90,0:03:12.63,Default,,0000,0000,0000,,Let's say you wanted to compare
Dialogue: 0,0:03:12.63,0:03:15.93,Default,,0000,0000,0000,,-I am trying to find a suitable color-
Dialogue: 0,0:03:15.93,0:03:19.23,Default,,0000,0000,0000,,the absolute value of -8 to the absolute value of 8.
Dialogue: 0,0:03:19.23,0:03:23.12,Default,,0000,0000,0000,,One way to think about it is that they are both 8 away from 0.
Dialogue: 0,0:03:23.12,0:03:25.92,Default,,0000,0000,0000,,This is 8 to the left of 0 and this 8 to the right of 0.
Dialogue: 0,0:03:25.92,0:03:28.75,Default,,0000,0000,0000,,So both of these things evaluate to 8.
Dialogue: 0,0:03:28.75,0:03:34.18,Default,,0000,0000,0000,,Absolute value of negative 8 is 8 and absolute value of 8 is 8.
Dialogue: 0,0:03:34.18,0:03:38.08,Default,,0000,0000,0000,,So clearly 8 is equal to 8.
Dialogue: 0,0:03:38.08,0:03:39.98,Default,,0000,0000,0000,,Let's do a couple more examples.
Dialogue: 0,0:03:39.98,0:03:46.82,Default,,0000,0000,0000,,Let's say that I wanted to compare the absolute value of -1 and
Dialogue: 0,0:03:46.82,0:03:48.90,Default,,0000,0000,0000,,I want to compare that to +2.
Dialogue: 0,0:03:48.90,0:03:57.97,Default,,0000,0000,0000,,So the absolute value of -1 is just positive version of -1 which is just 1.
Dialogue: 0,0:03:57.97,0:04:00.19,Default,,0000,0000,0000,,So 1 is clearly less than 2.
Dialogue: 0,0:04:00.19,0:04:01.35,Default,,0000,0000,0000,,Or, the other way to think about it is
Dialogue: 0,0:04:01.35,0:04:07.04,Default,,0000,0000,0000,,the absolute value of negative 1 is clearly less than 2.