Order of Operations

U01_L5_T2_we1 Order of Operations

We're asked to simplify 8 plus
5 times 4 minus, and then in

parentheses, 6 plus 10
divided by 2 plus 44.

Whenever you see some type of
crazy expression like this

where you have parentheses and
addition and subtraction and

division, you always want
to keep the order of

operations in mind.

Let me write them
down over here.

So when you're doing order of
operations, or really when

you're evaluating any
expression, you should have

this in the front of your brain
that the top priority

goes to parentheses.

And those are these little
brackets over here, or however

you want to call them.

Those are the parentheses
right there.

That gets top priority.

Then after that, you want to
worry about exponents.

There are no exponents in this
expression, but I'll just

write it down just for future
reference: exponents.

One way I like to think about it
is parentheses always takes

top priority, but then after
that, we go in descending

order, or I guess we should
say in-- well, yeah, in

descending order of how fast
that computation is.

When I say fast, how
fast it grows.

When I take something to an
exponent, when I'm taking

something to a power, it grows
really fast. Then it grows a

little bit slower or shrinks
a little bit slower if I

multiply or divide,
so that comes

next: multiply or divide.

Multiplication and division
comes next, and then last of

all comes addition
and subtraction.

So these are kind of the
slowest operations.

This is a little bit faster.

This is the fastest operation.

And then the parentheses,
just no matter

what, always take priority.

So let's apply it over here.

Let me rewrite this
whole expression.

So it's 8 plus 5 times 4 minus,
in parentheses, 6 plus

10 divided by 2 plus 44.

So we're going to want to do the
parentheses first. We have

parentheses there and there.

Now this parentheses is pretty
straightforward.

Well, inside the parentheses
is already evaluated, so we

could really just view
this as 5 times 4.

So let's just evaluate that
right from the get go.

So this is going to result in
8 plus-- and really, when

you're evaluating the
parentheses, if your evaluate

this parentheses, you literally
just get 5, and you

evaluate that parentheses, you
literally just get 4, and then

they're next to each other,
so you multiply them.

So 5 times 4 is 20 minus--
let me stay

consistent with the colors.

Now let me write the next
parenthesis right there, and

then inside of it, we'd evaluate
this first. Let me

close the parenthesis
right there.

And then we have plus 44.

So what is this thing right here
evaluate to, this thing

inside the parentheses?

Well, you might be tempted
to say, well, let me

just go left to right.

6 plus 10 is 16 and then
divide by 2 and

you would get 8.

But remember: order
of operations.

Division takes priority over
addition, so you actually want

to do the division first, and
we could actually write it

here like this.

You could imagine putting
some more parentheses.

Let me do it in that
same purple.

You could imagine putting some
more parentheses right here to

really emphasize the fact that
you're going to do the

division first.

So 10 divided by 2 is 5, so this
will result in 6, plus 10

divided by 2, is 5.

6 plus 5.

Well, we still have to evaluate
this parentheses, so

this results-- what's
6 plus 5?

Well, that's 11.

So we're left with
the 20-- let me

write it all down again.

We're left with 8 plus
20 minus 6 plus 5,

which is 11, plus 44.

And now that we have everything
at this level of

operations, we can just
go left to right.

So 8 plus 20 is 28, so you
can view this as 28

minus 11 plus 44.

28 minus 11-- 28 minus 10
would be 18, so this

is going to be 17.

It's going to be 17 plus 44.

And then 17 plus 44-- I'll
scroll down a little bit.

7 plus 44 would be 51, so
this is going to be 61.

So this is going to
be equal to 61.

And we're done!