Uploaded by opencourselib on 17.08.2011

Transcript:

(male narrator) In this video,

we're going to take a look

at how absolute value works into the order of operations.

Absolute value in a problem works just like parentheses...

which means we will work inside the absolute value first

and finally make positive at the end.

Or after...the inside...

is simplified.

Once that's complete, we can finish the problem

like any other order of operations problem.

Let's look at some examples

where we treat the absolute value like a parentheses

and then look at the distance from 0

or make it positive at the end.

Here, we see the absolute value.

Inside the absolute value, then,

we will work just like any other problem--

as if it were a parentheses-- which means we will start

by doing the innermost parentheses first.

We now have -3; absolute value of 2 to the 4th;

minus 9 squared.

Continuing to work inside the absolute value,

we can evaluate the exponents next.

We now have -3;

absolute value of 2 to the 4th, which is 16;

minus 9 squared, which is 81.

Continuing to work inside the absolute value,

we can subtract.

We now have -3, absolute value of -65.

Finally, the absolute value

has been completely simplified on the inside.

Now, we can evaluate the absolute value operation,

making the 65 positive.

We now have -3 times 65.

Finish the problem by simply multiplying -3 by 65.

This gives us -195.

And that completes our problem.

Let's try another example

where we simplify inside the absolute value first;

then make it positive, so we can finish the problem.

Here, we again have an absolute value.

Inside the absolute value,

we will do the innermost parentheses first--

doing the exponents before the subtraction.

We now have 2 minus 4; absolute value of 3 squared;

plus 5 squared, which is 25; minus 6 squared, which is 36.

We then can finish

inside those innermost parentheses by subtracting.

We now have 2 minus 4; absolute value of 3 squared;

plus 25; minus 36, which is -11.

Now that the innermost parentheses has been simplified,

we continue to simplify inside the absolute value,

doing the exponents first.

We now have 2 minus 4;

absolute value of 3 squared, which is 9; plus -11.

We can now finish the absolute value by doing the addition:

2 minus 4; absolute value of -2.

Finally, the absolute value on the inside

is completely simplified.

Now, we are allowed to take the absolute value of the -2,

making it positive.

We now have 2 minus 4, times +2.

Now, we can continue to simplify the rest of the expression.

Order of operations has us multiply first.

We end up with 2 minus 8,

and finally, we can finish

by doing our subtraction: 2 minus 8 is -6.

And that completes our problem.

Again, we treat absolute value just like parentheses:

Simplify inside the absolute value first

and make the result positive at the end.