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# Identify and order absolute values

Video transcript

We're told to list in order from
smallest to largest. So each of these quantities, it
looks like we have expressions inside of absolute
value signs. And just as a bit of review,
absolute value just means your distance from 0. Or another way to think about
it is, if it's a negative number inside of the
absolute value sign, it becomes positive. If it's already positive,
it stays positive. So let's think about
these numbers. So the first one is the
absolute value of 5. How far is 5 away from 0? Well, it's 5 away from 0. So it's equal to 5. So I were to actually
draw a number line, you would see that. 0 is here, 5 is over
here, this distance right there is 5. So the absolute value
of 5 is 5. Now, the next quantity they want
us to figure out is the absolute value of 9 minus 7. Well, this is the same thing
as the absolute value of 2. 9 minus 7 is 2. And once again, 2 is just
2 units away from 0, so it's just 2. If you have a positive value in
the absolute value sign, it just is itself. The absolute value of 2 is 2. Then we have the absolute
value of 5 minus 15. Well, that's going to
be the same thing as the absolute value. 5 minus 15 is negative 10, so
it's the same thing as the absolute value of negative 10. Now, there's two ways you
can think about it. If it's a negative number inside
of the absolute value sign, it just becomes the
positive version of it, so it just becomes 10. Another way to think about it
is, if you had negative 10, you would plot it-- it would
be out here someplace, negative 10, we'd have to extend
the number line-- it is 10 to the left of 0. That's what the absolute
value is telling us. Then we have the absolute
value of 0. Well, 0 is just 0 away
from the number line. Absolute value of 0 is just 0. That is just 0. That's just right there. It has no distance
from the origin. And then finally, we have the
absolute value of negative 3. That's 3 to the left of 0, or
you can just think of it as getting rid of this negative
sign, so it is equal to 3. So, now that we've expressed
them all as just simple integers, let's list them in
order from smallest to largest. So of all of these values,
which is the smallest? This one is the smallest,
the absolute value of 0. So let me write that down,
absolute value of 0. What's the next smallest? What's the next one? Since we have a 2 there,
this is the next smallest, right there. And that original expression
was the absolute value of 9 minus 7, so the absolute
value of 9 minus 7. And then what's the
next smallest? We have this 3, and then
we have a 5 and a 10. So the next smallest is
this 3, right here. That 3, and that original
expression was the absolute value of negative 3. Then we have this 5 over here,
which is just the absolute value of 5. And then finally, we have this
10 over here, which was the absolute value of 5 minus 15. And we are done.