Let's look at a few somewhat more involved order of operations examples.
Here's our first one.
We have seven minus the quantity, ah, three plus, parenthesis two minus one closed parenthesis,
plus one closed brackets.
So we have a lot of stuff going on here.
We have parenthesis, exponents, multiplication, division, addition and subtraction.
Please excuse my dear aunt sally.
So let's do these in the right order, first we'll take care of any parenthesis or brackets.
Now I see two sets of parenthesis and brackets.
I have this one, but if you tried to compute what's inside this one, then we have, on the
inside of the brackets, three plus parenthesis two minus one, plus one.
I can't tell you what that is until I know what this parenthesis is, so I think I have
to start with the innermost parenthesis, and then I'll be able to tell you what's in the
brackets.
So we'll have seven minus bracket.
Okay, uh, two minus one, is one.
So we'll have three plus one, plus one.
Alright now that I've done the innermost parenthesis, now I can do the outer set of parenthesis,
we're writing them as brackets here.
So we'll have seven minus three, plus one is four.
Four plus one, makes five.
Cause I do the operations from left to right.
And so I'll have seven minus five.
And lastly, parenthesis, exponents, multiplication, division, addition, and subtraction is the
last one.
Seven minus five is two.
So two would be my final answer.
So again you be careful with the order of operations, you'll get the right answer.
Okay here's another one.
And if you, oh, by the way if you want to pause the video, you're welcome to try these
before I finish them, and then you can see if you and I get the same answer.
So we get parenthesis, exponents, multiplication, division, addition, and subtraction again.
Please excuse my dear aunt sally, we'll keep our eye on that.
Alright, I don't see any parenthesis here.
Now I do see some exponents, I see a squared here.
But I put this in this example intentionally, because this is a hugely common mistake that
I want you to be careful about.
Here we see negative five squared.
It's tempting to say that's negative five times, negative five and the answer would
be twenty-five.
And that seems like the right thing to do but in fact it's not.
Here's why.
See this negative is not attached to this five inside a parenthesis before it's squared.
I don't see any parenthesis here grouping the negative five.
You can think of this negative and the five as negative one times five that's being squared.
And so since we do exponents before multiplication, I actually need to square the five, because
exponents come first.
And then multiply that times a negative one.
So in fact this will be five squared first, which is twenty-five, and then I'll make that
quantity negative.
So I'll have negative twenty-five.
Minus three times two, minus ten.
Okay, exponents are taken care of.
Next I'll take care of this multiplication, the three times two which is six.
Negative twenty-five minus six, minus ten.
I don't have any division or addition but I do have subtraction.
And negative twenty-five, minus six, minus ten, if you compute that algebra would make
minus forty-one.
So minus forty one would be our final answer for this problem.
Alright last example, we have some parenthesis, some exponents, some division, and multiplication,
we have a little bit of everything here.
So please excuse my dear aunt sally.
Okay, we'll start with parenthesis, so I have to compute what's inside the green parenthesis
before I do anything.
Now I�ve negative nine, plus six, divided by three.
How do we compute what that is?
Well I have to do order of operations on that as well.
And even though it's not written, there's an understood parenthesis grouping the numerator
and the denominator.
So I'll compute the numerator.
Negative nine, plus six, makes negative three.
So we'd have negative parenthesis negative three, over three, quantity squared.
Okay so, parenthesis is almost finished.
I still need to compute negative three, over three.
So negative three divided by three, is negative one.
That's squared, so parenthesis have been finished.
Alright now exponents, negative one squared would actually make positive one, but I still
have this positive on the outside.
Exponents are taken care of.
Next multiplication.
Negative one times one is negative one, there is no division; there is no addition or subtraction
remaining.
So our final answer for this one is negative one.
So this is one of those things you just have to practice a lot.
This is one of those things where you should just do uh, just numbers, and numbers of examples,
until you get good, very good, at order of operations.
Because when you get later in the course and you're doing these massively big problems
you don't want to be having to think about okay, what comes first parenthesis or multiplication
and that sort of thing?
When you get good at order of operations these things should just come naturally and you
should be able to do most of it without even thinking about it.