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# Comparing absolute values

Video transcript

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