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### Course: 6th grade > Unit 4

Lesson 4: Order of operations introduction# Order of operations introduction

The order of operations is a crucial math concept that ensures consistent results when solving problems with multiple operations. By following PEMDAS (Parentheses, Exponents, Multiplication and Division, and Addition and Subtraction), students can accurately evaluate expressions and avoid common mistakes. Mastering this skill is essential for success in mathematics. Created by Sal Khan.

## Want to join the conversation?

- When Sal said "armed by the order of operations" my brother yelled "oh no, its another D-Day, and I died laughing at that(27 votes)
- D-DAY is war, like the world war 1, 2 , or 3(2 votes)

- Wouldn't it be addition before subtraction to make the last answer 17?(14 votes)
- If you want to do addition first, you would have 20-2+1, but -2+1=-1, so 20-1=19.(7 votes)

- the answer is 13.

first, 5 x 2 = 10.

Then, 10 + 3 = 13(11 votes) - I dont get it can someone explain?(8 votes)
- Hi! Don't worry, once you read this comment you might be able to understand.

So, most people when doing a problem with multiple operations, they tend to do the wrong operations first, and they get the wrong answer.

Order of operations is used to find the correct Order the operations you do first so that when you do them, you get the correct answer. Let me show you an example:

4 x 5 + 8 - 3

Order of operations says

Parenthesis

Expontents

Multiplication

Division

Addition

Subtraction.

We don't see parenthesis or exponents, but we do see multiplication. So, 4 x 5 =20. No division, but there is addition and subtraction. So,

20 + 8 = 28, 28 - 3 = 25.

You got this and don't give up! 😊(2 votes)

- I learned Pemdas in like, 5th grade(7 votes)
- I learned it in fourth what state/county are you in, only so I know what district taught fifth(3 votes)

- my teacher calls it pemdas(10 votes)
- pemdas is easy(3 votes)
- I have all the questions.(6 votes)
- So is 10/5*2 = 1 or 4 (ie. does left to right rule mentioned for +/- apply?) and what about square root etc? (assuming it to be the opposite function of an exponent). This topic has always seemes incomplete and confusing to me.

BODMAS = 'O' is for operations (could assume operations to be exponents and roots only but again, assume left to right or exponents then roots?)and division comes before multiplication in this one.

PEMDAS = specifies exponents but not roots and multiplication comes before division.(4 votes)- Those acronyms do not suggest a specific order for multiplication, division, addition and subtraction! Their order is that way just so it rolls off the tongue well and is easier to remember.

Since multiplication and division are inverse operations, same with addition and subtraction, each can be done left-to-right in a "same-operation chain", so long as you always do M or D before A or S.

SO, 10/5*2 = 2*2 = 4(3 votes)

## Video transcript

- Every few months, you'll see an expression like
this go viral on social media because it looks simple but depending on how people
interpret this expression, they often get different answers. So first, why don't you pause this video and think about what you think
three plus two times five is equal to. All right, now let's work
through this together. Now some of you might
have interpreted this as we should just go from left to right. So you might've said, all right, let me first add three plus two. So I can do that part first, which is of course equal to five. And then I could multiply that times five. And that is going to get me to 25. Now others of you would have said no, that makes no sense at all. We know that we should do
some operations before others. For example, multiplication
should come before addition. And so if you follow that, you would do the two times
five first to get 10. And so this would become three plus 10, which is of course,
going to be equal to 13. Who do you think would be right? Well, it turns out that
the second way of doing it is the correct way and that's because we have something known as order of operations. And the order of operations
is the convention that mathematicians have decided to use in order for us to have one
way to interpret an expression like this and the order of operations are to do parentheses first. So, for example, if you really wanted to add
the three and the two first, you should put parentheses around it to say, hey, that's what
you've got to do first. But then after parentheses, do exponents, which is really, you could view
as repeated multiplication, then do multiplication and division. Then do addition and subtraction. Now, some people might just
memorize this as PEMDAS, or PEDMAS or something like that. And you can do that, but there's a rationale to this. Parentheses are just, the person who writing
the expression saying do this for sure first. But then if you think about it, exponents are repeated multiplication and multiplication is repeated addition. So you're doing the most
repeated things first, then next repeated things
like multiplication. And then you go straight to the addition. The reason why multiplication and division are on the same line and addition and
subtraction on the same line is the convention there
is just go left to right. So now that we are armed
with our order of operations, let's tackle another
slightly hairier expression. And I use the term hairy for
a little bit more complex. So two times 10, minus eight, divided by four, plus one. Pause the video and see
how you could evaluate this now that you know about
order of operations. All right, now let's do this together. We don't see any parentheses here. We don't see any exponents here but we do see some
multiplication and division here. So we could see it over here. This two times 10. And we also have this
eight divided by four. So that's what we're
going to want to do first. So that two times 10, that
is going to be equal to 20. The eight divided by four,
is of course, equal to two. And then we have 20 minus two plus one. And this is now going to get
us, if we go left to right, which we should do when we're
just adding and subtracting, is we get 20 minus two is 18, plus one, which is going to be equal to 19. And we're done. Now, you might say, well, what if we wanted someone to
add the four and the one first? Well, one way to do that is you could have added a
parentheses there to force it or you could have even written
your division differently. For example, you could use a fraction sign to make things clearer. If we wanted to add the
four plus one first, instead of writing eight divided
by four plus one like that, you could write eight over four plus one. Now of course, this is
fundamentally different than this right over here. 'Cause here we would do the
eight divided by four first, then add the plus one, while here, you would
add the four plus one and then divide eight by that.