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## 6th grade

### Unit 4: Lesson 4

Order of operations introduction# Worked example: Order of operations (PEMDAS)

The order of operations is a rule that tells the correct sequence of steps for evaluating a math expression. We can remember the order using PEMDAS: Parentheses, Exponents, Multiplication and Division (from left to right), Addition and Subtraction (from left to right). Created by Sal Khan.

## Want to join the conversation?

- Parenthesies is the same as brackets, right?

and in BODMAS, what does 'O' stand for?(321 votes)- It's Brackets, Orders(ex.- powers and square roots which means exponents), Division, Multiplication, Addition, Subtraction. :)(271 votes)

- Do square roots count as exponents? Or are they in a separate spot, and if so, where is that spot?(103 votes)
- Yes, they do count. In BEDMAS, E (exponents) can count as square roots, exponents, yadda yadda.(2 votes)

- Does Pemdas Equal P: Parentheses E: Exponents M: Multiplication D: Division A: Addition S: Subtraction?(9 votes)
- Yes, PEMDAS means parentheses, exponents, multiplication, division, addition, and subtraction. Multiplication and division go together, so you do whichever one comes first. Same goes to addition and subtraction. A way to remember the order is Please Excuse My Dear Aunt Sally.(14 votes)

- why did Sal say a hairy beastly problem?(10 votes)
- Hi, Alex,

A "hairy beastly problem" refers to a difficult or challenging problem. It sounds weird but it isn't.

-Logical(6 votes)

- 7x2 + (7+3(5-2)) / 4x2

7x2 + (7+3x3) / 4x2

7x2 + 16 / 4x2

14 + 16 / 8

14 + 2

=16 Did I get it that time(10 votes)- what you did wrong was that you did 4*2 before 16/4

In Pemdas it says multiplication then division but their actually the same level. If you would've watched the other videos, he would've explained it to you.

The answer should be 22

7 * 2 + (7+3(5-2)) /4 * 2

first solve 5-2=3 because it's in parenthesis.

7 * 2 + (7+3*3) /4 * 2

then solve 3*3=9 because multiplication and division come before addition and subtraction

7 * 2 + (7+9) / 4 * 2

then solve 7+9=16 because it's in parenthesis

7 * 2 + 16 /4 * 2

then solve 7*2=14 Because Multi comes before + and -

14 + 16 /4 * 2

after, solve 16/4=4 notice I did division before the Multiplication. why because the one that comes first is the one you solve first. Even if M comes before D in Pemdas.

14 + 4 * 2

then solve 4*2=8 because peMdas

14 + 8

last but not least solve 14+8=22 because it's the last expression.

22 is your answer! :)(3 votes)

- When you have parentheses within parentheses, isn't one supposed to use brackets and also parentheses? Or does it not matter?(5 votes)
- I might use brackets instead of curved parentheses for better discernment, but it is not really a rule (as in not really a rule of mathematics). Also, if after using the parentheses, just use brackets for the second group/section, and not both.

Furthermore, "{" and "}" are more used in creating lists of numbers, rather than basic parentheses "(" and ")". However, the best thing to do for any group/pair is to "begin" and "end" with the same type of brackets, regardless of their level/order.

For example, if I happen to have three different levels which I have orders (that do not follow the regular order of operations), I might use something like {[(9+7)*2]-5} The overall expression is read "9 plus 7 (equals 16), times 2 (equals 32), minus 5 (equals 27).(6 votes)

- Parenthesies is the same as brackets, right?

and in BODMAS, what does 'O' stand for?(4 votes)- So Melanie, O in BODMAS stands for operations. Hope this helps! Its a little different from PEMDAS, but the concept is basically the same.(5 votes)

- (5)(4) is apparently 5x4 . Where is the lesson on this website about not needing the "x"

and why you use "." (dot) to mean multiplication as well? Thanks(2 votes)- We do not use x for the multiplication symbol because it may be confused with the variable _x_.
`https://www.khanacademy.org/math/algebra/introduction-to-algebra/alg1-intro-to-variables/v/why-aren-t-we-using-the-multiplication-sign`

(5 votes)

- How would you do problems like this:

12 - 1 * 0 + 4 / 2

I'm confused right now.(2 votes)- ok. First, you would multiply. 1*0 = 0. now the problem is 12-0+4/2. we then divide. 4/2 = 2.

the problem is now 12-0+2. we then do basic addition/subtraction. 12-0 = 12. 12+ 2 = 14.

14 is the correct answer(5 votes)

- Who does the square root go in to the problem,(3 votes)
- the square root of something goes in the exponits place, that is if it can be turned into a whole number. If it doesn't then don't do anything with it.(4 votes)

## Video transcript

Now that we've got the basics
of order of operations out of the way, let's try to tackle a
really hairy and beastly problem. So here, we have all
sorts of parentheses and numbers flying around. But in any of these order of
operations problems, you really just have to take a deep breath
and remember, we're going to do parentheses first. Parentheses. P for parentheses. Then exponents. Don't worry if you don't know
what exponents are, because this has no exponents in them. Then you're going to do
multiplication and division. They're at the same level. Then you do addition
and subtraction. So some people remember PEMDAS. But if you remember PEMDAS,
remember multiplication, division, same level. Addition and subtraction,
also at the same level. So let's figure what the
order of operations say that this should evaluate to. So the first thing we're going
to do is our parentheses. And we have a lot of
parentheses here. We have this expression in
parentheses right there, and then even within that we
have these parentheses. So our order of operations say,
look, do your parentheses first, but in order to evaluate
this outer parentheses-- this orange thing-- we're going to
have to evaluate this thing in yellow right there. So let's evaluate
this whole thing. So how can we simplify it? Well, if we look at just inside
of it, the first thing we want to do is simplify the
parentheses inside the parentheses. So you see this 5
minus 2 right there? We're going to do that
first no matter what. And that's easy to evaluate. 5 minus 2 is 3. And so this simplifies to--
I'll do it step by step. Once you get the hang of
it, you can do multiple steps at once. So this is going to be
7 plus 3 times the 5 minus 2, which is 3. And all of those have
parentheses around it. And of course, you have
all the stuff on either side-- the divide 4-- no. Oops. That's not what I want. I wanted to copy and paste. I want to copy and paste
that right there. So copy, then-- no, that's
giving me the wrong thing. It would've been easier--
let me just rewrite it. That's the easiest thing. I'm having technical
difficulties. So divided by 4 times 2. And on this side, you had that
7 times 2 plus this thing in orange parentheses there. Now, at any step you
just look again. We always want to do
parentheses first. Well, you keep wanting to
do and is there really no parentheses left? So we have to evaluate this
parentheses in orange here. So we have to evaluate
this thing first. But in order to evaluate
this thing, we have to look inside of it. And when you look inside of it,
you have 7 plus 3 times 3. So if you just had 7 plus
3 times 3, how would you evaluate it? Well, look back to your
order of operations. We're inside the parentheses
here, so inside of it there are no longer any parentheses. So the next thing we should do
is-- there are no exponents. There is multiplication. So we do that before we do
any addition or subtraction. So we want to do the 3 times
3 before we add the 7. So this is going to be 7
plus-- and the 3 times 3 we want to do first. We want to do the
multiplication first. 7 plus 9. That's going to be in
the orange parentheses. And then you have the 7
times 2 plus that, on the left hand side. You have the divided by 4 times
2 on the right hand side. And now this-- the thing in
parentheses-- because we still want to do the
parentheses first. Pretty easy to evaluate. What's 7 plus 9? 7 plus 9 is 16. And so everything we have
simplifies to 7 times 2 plus 16 divided by 4 times 2. Now we don't have any
parentheses left, so we don't have to worry
about the P in PEMDAS. We have no E, no
exponents in this. So then we go straight to
multiplication and division. We have a multiplication--
we have some multiplication going on there. We have some division
going on here, and a multiplication there. So we should do these
next, before we do this addition right there. So we could do this
multiplication. We could do that
multiplication. 7 times 2 is 14. We're going to wait
to do that addition. And then here we have a
16 divided by 4 times 2. That gets priority of the
addition, so we're going to do that before we do the addition. But how do we evaluate that? Do we do the division first,
or the multiplication first? And remember, I told you in the
last video, when you have 2-- when you have multiple
operations of the same level-- in this case, division and
multiplication-- they're at the same level. You're safest going
left to right. Or you should go left to right. So you do 16 divided by 4 is 4. So this thing right here--
simplify 16 divided by 4 times 2. It simplifies to 4 times 2. That's this thing in
green right there. And then we're going to want to
do the multiplication next. So this is going to simplify
to-- because multiplication takes priority over addition--
this simplifies to 8. And so you get 14-- this
14 right here-- plus 8. And what's 14 plus 8? That is 22. That is equal to 22. And we are done.