Absolute Value 1

Absolute Value 1

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 zero.

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 zero?

5 away from zero. So it's equal to five.

So if I were to actually draw a number line,

you would see that.

0 is here, 5 is over here.

This distance right there is five.

So the absolute value of 5 is 5.

Now, the next quantity they want us to figure out is

the absolute value of... absolute value of 9 minus 7.

Well, this is the same thing as the absolute 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.

Absolute value of 5 minus 15.

Well that's going to be the same thing as 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 out here some place, negative 10.

We would 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 zero.

Well zero is just zero away from the number line.

The absolute value of zero is just zero.

That is just zero, that is 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 the 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 zero.

So, let me write that down, the absolute value of zero.

What's the next smallest?

We have a 2 there. This is the next smallest.

Right there.

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 a 5 and a 10.

So the next smallest is this 3 right here.

and that original expression was the absolute value of negative 3.

And 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.