Comparing Absolute Values

Evaluating and comparing absolute values

Let's do some examples comparing absolute values.

So, let's say we were to ask ourselves

how -9, the absolute value of -9 I should say,

how that compares to the absolute value of

-let me think of a good number--the absolute value of -7.

So, let's think about this a little bit and

let's think about what -9 looks like or

where it is in the number line and

where -7 is on the number line.

Let's see where the absolute values mean and

then we should probably be able to do this comparison.

So there are a couple ways to think about it.

One is you can draw them on the number line.

So, if this is 0 and this is -7

and then this is -9 right over here.

Now when you take the absolute value of a number,

you are really saying how far is that number from 0,

whether it is to the left or the right of 0.

So for example, -9 is 9 to the left of 0.

So the absolute value of -9 is exactly 9.

This evaluates to 9. -7 is exactly 7 to the left of 0.

So the absolute value of -7 is +7.

And so, if you were to compare 9 and 7

then this is a little bit more straight forward.

9 is clearly greater than 7.

And if you ever get confused with the greater than and less than symbols,

just remember that the symbol is larger on the left hand side,

so that is the greater than side.

If I were to write this, and this is actually also a true statement.

If you took this without the absolute value signs,

it is also true that -9 is less than -7.

Notice the smaller side is on the smaller number.

And so that is the interesting thing: -9 is less than -7

but their absolute values, since -9 is further to the left of 0,

it is the absolute value of -9 , which is 9,

is greater than the absolute value of -7.

Another way to think about it is

if you take the absolute value of a number,

it really is just the positive value of that number.

So if you took the absolute value of 9 that equals 9.

Or the absolute value of -9, that is also equal to 9.

When you think of it visually, that is

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 is just going to be that same value.

2 is 2 to the right of 0. So this is just going to evaluate to 2.

And then the absolute value of 3,

that is just going to evaluate to 3.

That is actually pretty straight forward.

So 2 is clearly the smaller number here

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 am trying to find a suitable color-

the absolute value of -8 to the absolute value of 8.

One way to think about it is that they are both 8 away from 0.

This is 8 to the left of 0 and this 8 to the right of 0.

So both of these things evaluate to 8.

Absolute value of negative 8 is 8 and absolute value of 8 is 8.

So clearly 8 is equal to 8.

Let's do a couple more examples.

Let's say that I wanted to compare the absolute value of -1 and

I want to compare that to +2.

So the absolute value of -1 is just positive version of -1 which is just 1.

So 1 is clearly less than 2.

Or, the other way to think about it is

the absolute value of negative 1 is clearly less than 2.