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### Course: Get ready for 8th grade > Unit 1

Lesson 4: Order of operations# Order of operations example

The order of operations tells us the order to solve steps in expressions with more than one operation. First, we solve any operations inside of parentheses or brackets. Second, we solve any exponents. Third, we solve all multiplication and division from left to right. Fourth, we solve all addition and subtraction from left to right. Created by Sal Khan and Monterey Institute for Technology and Education.

## Want to join the conversation?

- Hello, I had two questions in regards to order of operations. 1. I was wondering where does the order of operations come from? In my limited google research :), I have found that no one really knows this, but we see it being used in history back in the 1500s or so.

2. Is there a mathematical reason why this works? Or, does this just seem to be the historical standard or traditional way to perform equations based on history or precedence?

Thanks!(230 votes)- i dont know. i'm guessing mathmaticians were finding several different ways to do the same problem and argued over which way is right so they came up with the traditional, modern, Order of Operations.(19 votes)

- Should there be a multiplication sign between the 5 and 4?(56 votes)
- If there is no sign in the question let’s say (6)(5) it be multiplication so the answer is 30(8 votes)

- How come you didn't distribute the negative sign within the parenthesis?(34 votes)
- You have to take care of everything in the parentheses first: 6+10/2

There weren't any variables inside the parentheses, so it could be simplified right to 11, and the negative sign just tells us to subtract that 11. If there were variables involved, then we would need to distribute a negative sign. However, in this case it was just straight subtraction.

Does that help?(38 votes)

- At the end, when there was 28-11+44, wouldn't you add 11 and 44 first because adding comes before subtracting?(10 votes)
- Nope. You do the addition and subtraction in the same step, always moving from
*left to right*and doing the addition/subtraction in the order that you see them.

Here we have: 28 - 11 + 44*See how the subtraction comes first?*

You want to work through the all the addition/subtraction in left to right order.

28 - 11 + 44

17 + 44

61

(*You might notice that for this problem you get the same answer either way you do it. This doesn't always happen, though, especially when you have more complicated problems.*)

Hope this helps!(7 votes)

- When dividing, for example, 8^2bc-b^2? b=4 c=16 how would u do it?(4 votes)
- You can use
**PEMDAS**to solve this expression:**P**= parentheses**E**= exponents**MD**= multiplication / division**AS**= addition / subtraction*First, plug in the given values for b and c*

8²bc - b²

b=4, c=16

= 8²⋅4⋅16 - 4²**P**= parentheses*There aren't any parentheses, so we can go on to the next step.***E**= exponents*Next, calculate the exponents from left to right:*

8²⋅4⋅16 - 4²

= 64⋅4⋅16 - 4²

= 64⋅4⋅16 - 16**MD**= multiplication / division*Now, going from left to right, work out any multiplication or division:*

64⋅4⋅16 - 16

= 256⋅16 - 16

= 4096 - 16**AS**= addition / subtraction*Finally, do any remaining addition or subtraction in left to right order:*

4096 - 16

= 4080

So (given the values b=4 and c=16):

8²bc - b² = 4080

Hope this helps!(6 votes)

- hi ,I'm having a doubt that why we we can't follow the order of operations,why can't it be correct when we do it in some other way(5 votes)
- So im stuck in a problem 5(2-4+1)+2/3(6)= and i know im going to end up with -5+2/3(6)= put from there i dont know how to work it out can i get some help??...(4 votes)
- Hello! I have two questions with the order of operations. What if a problem has parentheses, brackets, and exponents? What is the order then?

Thanks!(3 votes)- If there is both brackets and parentheses, it indicates to do them first in PEMDAS, they just added brackets so they don't have two sets of parentheses. Using the example Kim gave, [15-(3+6)^2] You would add 3+6 first which would add up to 9. Then you would do the exponent next with 9^2 then with that answer you subtract it from 15(3 votes)

- don't listen to Joe, think PEMDAS(1 vote)
- or Please Excuse My Dear Aunt Sally which is the same thing(4 votes)

- Why does the order have to be the way it is? Why couldn't we just read it left to right? It would make more sense.(3 votes)
- But it wouldn't be the wrong answer if everyone did it that way. It would be right because that would be the rule. PEMDAS is much more confusing.(2 votes)

## Video transcript

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!