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Comparing Absolute Values

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    Let's do some examples comparing absolute values.
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    So, let's say we were to ask ourselves
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    how -9, the absolute value of -9 I should say,
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    how that compares to the absolute value of
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    -let me think of a good number--the absolute value of -7.
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    So, let's think about this a little bit and
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    let's think about what -9 looks like or
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    where it is in the number line and
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    where -7 is on the number line.
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    Let's see where the absolute values mean and
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    then we should probably be able to do this comparison.
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    So there are a couple ways to think about it.
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    One is you can draw them on the number line.
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    So, if this is 0 and this is -7
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    and then this is -9 right over here.
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    Now when you take the absolute value of a number,
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    you are really saying how far is that number from 0,
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    whether it is to the left or the right of 0.
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    So for example, -9 is 9 to the left of 0.
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    So the absolute value of -9 is exactly 9.
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    This evaluates to 9. -7 is exactly 7 to the left of 0.
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    So the absolute value of -7 is +7.
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    And so, if you were to compare 9 and 7
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    then this is a little bit more straight forward.
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    9 is clearly greater than 7.
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    And if you ever get confused with the greater than and less than symbols,
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    just remember that the symbol is larger on the left hand side,
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    so that is the greater than side.
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    If I were to write this, and this is actually also a true statement.
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    If you took this without the absolute value signs,
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    it is also true that -9 is less than -7.
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    Notice the smaller side is on the smaller number.
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    And so that is the interesting thing: -9 is less than -7
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    but their absolute values, since -9 is further to the left of 0,
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    it is the absolute value of -9 , which is 9,
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    is greater than the absolute value of -7.
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    Another way to think about it is
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    if you take the absolute value of a number,
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    it really is just the positive value of that number.
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    So if you took the absolute value of 9 that equals 9.
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    Or the absolute value of -9, that is also equal to 9.
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    When you think of it visually, that is
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    because both of these numbers are exactly 9 away from 0.
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    This is 9 to the right of 0 and this is 9 to the left of 0.
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    Let's do a few more of these.
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    So let's say that we wanted to compare
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    the absolute value of 2 to the absolute value of 3.
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    Well the absolute value of a positive is just going to be that same value.
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    2 is 2 to the right of 0. So this is just going to evaluate to 2.
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    And then the absolute value of 3,
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    that is just going to evaluate to 3.
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    That is actually pretty straight forward.
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    So 2 is clearly the smaller number here
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    so we clearly get 2 is less than 3.
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    Or the absolute value of 2 is less than 3.
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    So we have a less than right over here.
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    Let's say you wanted to compare
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    -I am trying to find a suitable color-
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    the absolute value of -8 to the absolute value of 8.
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    One way to think about it is that they are both 8 away from 0.
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    This is 8 to the left of 0 and this 8 to the right of 0.
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    So both of these things evaluate to 8.
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    Absolute value of negative 8 is 8 and absolute value of 8 is 8.
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    So clearly 8 is equal to 8.
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    Let's do a couple more examples.
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    Let's say that I wanted to compare the absolute value of -1 and
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    I want to compare that to +2.
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    So the absolute value of -1 is just positive version of -1 which is just 1.
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    So 1 is clearly less than 2.
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    Or, the other way to think about it is
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    the absolute value of negative 1 is clearly less than 2.
Title:
Comparing Absolute Values
Description:

Evaluating and comparing absolute values

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Video Language:
English
Duration:
04:07

English subtitles

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