In order of operations, do you multiply or divide first?

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That's because division isn't commutative like multiplication.

4-3+2 is 3.
4-(3+2) is -1.

That's why you work left to right, because division and subtraction aren't commutative.

i say they take equal priority if there arent any brackets, so i leave it to whatever order they are in the sum eg, 8/2*3 = 6, not 1.333333

It goes left-to-right.

Not that it matters, of course. 3*6/2, 3/2*6 and 6/2*3 all equal 9. As long as you're doing the correct operation, the order in which you multiply and divide doesn't matter.

In case anyone's wondering, the same goes for addition and subtraction, though you really have to watch your negatives in that case, so it can be a bit tricky.
1+2-3 = -3+2+1 = 2-3+1 = 0

RatherDull:
My friends and I are in an argument about which you should do first. Many sources say many different things.

divide et impera! - divide and conquer!

but not with math. i think multiply comes first. but i am surely wrong.

ooh, math, YAY!

When you do multiply and divide you do them from left to right in the problem.
In the problem 5X2+3%6 you do multiplication first. In 5%2+3X6 you do division first. (percent sign standing in for divide, bite me.)

There is an instance where you do multiply FIRST (as in before parentheses) and that's when you need to distribute

so 1+5(2+3)-2%6 you'd distribute the 5 before (or immediately after) the parentheses. And I can prove it!

1= 6 % 6
1= 6 % (2+4)
1= 6 % 2(1+2)
1= 6 % 2(3)
1= 3(3)
1= 9

So yeah, If you don't distribute before you divide shit gets weird. really weird.

burningdragoon:
Are you still in school of some sort? Ask a math teacher/professor. Multiplication and Division are treated of equal priority so whichever is first in the equation (from left to right).

The second, and more proper way I was tought was BEMA. Or was it PEMA? I dunno.

Anyway, Brackets/parentheses first, then Exponents, then Multiplication/Division from left to right, then Addition/Subtraction from left to right.

Also I'm pretty sure order won't change the answer if it's in the same part of the equation, but don't hold me to that.

pretty much this. Addition and Subtraction are considered the same species of opperation, same with Division and Multiplication. As such you simply go left to right when either pair is concerned.

Reece Borgars:
8/2*3 = 6, not 1.333333

Ummm... 8/2*3 = 12, not 6 or 1.33.

8/2*3
4*3
12

I was taught to use BIDMAS. With division and multiplication, assuming there's no brackets then do the operations in the order they're written. Same goes for addition/subtraction.

Mikeyfell:
In the problem 5X2+3%6 you do multiplication first. In 5%2+3X6 you do division first. (percent sign standing in for divide, bite me.)

Actually, in no shape or form does it matter which goes first in those examples. I'll just fudge your numbers a bit for better looking results but I'll use the same structure:

8?2+12?3 (multiplication and division to go to the ? signs)

Lets try this going from left to right

8X2+12%3=
=16+12%3=
=16+4=
=20

8%2+12X3=
=4+12X3=
=4+36=
=40

Now right to left

8X2+12%3=
=8X2+4=
=16+4=
=20

8%2+12X3=
=8%2+36=
=4+36=
=40

More realistically, you'll actually do them at the same time (8X2+12%3=16+4=20) but you don't actually do any "first" - as long as they are from the same importance tier, they can go in any direction, really.

Kotep:
That's because division isn't commutative like multiplication.

4-3+2 is 3.
4-(3+2) is -1.

That's why you work left to right, because division and subtraction aren't commutative.

Erm...those two equations are not equivalent at all. I mean beyond the obvious different results. You do have two completely different things there. The first one is 4-3+2, which can also be expressed as 4+(-3)+2, while the second is 4-(3+2), which is actually 4-3-2. You don't get to randomly add brackets, as you're not doing it properly - had you done it the right way, you'd have had 4+(-3+2), otherwise you're actively changing the meaning.

Division and multiplication are "equal" in terms of priority. If there are no brackets to inform on which should come first, you should solve it left to right. The same goes for addition and subtraction.

In programming languages you divide first.. and one does not argue with the machines.

It is most clear to always write in fractions where ever possible. That way you see that if there are no difference, deviding is multiplying by the inverse.

O wait I see Darknacht already mentioned that. But, at least for me, putting al your devisions in fraction ussually clears up the math greatly. And the next step is basically putting brackets around everything between 2 consecutive addition and or substraction signs.

Doesn't matter. In a way they're both the same thing.

A divided by 2 = A multiplied by 1/2.

Please, left to right. It doesn't matter either way, so why be unnecessarily convoluted.

Fluffythepoo:
In programming languages you divide first.. and one does not argue with the machines.

I work with some equipment that does some pretty interesting calculations. My all time favorite error to get is when the screen and system lock up completely and it spits out the following message; 'Error: Divide by zero detected." I have no idea why they sometimes called for that to happen, but it freaks me out every time. I have a feeling that one day it will be a machine that just happens upon the right method to do so. Then we will either evolve to a whole new understand of mathematics... or Skynet is born.

Whatever comes first in the sequence.

Multiplication and division are of equal value. So whichever comes first.

Same with addition and subtraction.

Whichever comes first. First you do brackets, then multiplication/division then addition/subtraction. Think of it this way: division is just multiplying by the reciprocal. 2*3/5 is the same as 2*(1/5)*3.

its left to right unless it is like 5 over 6*8 then you do the top and bottom and then divide them. and you get 5/48

DevilWithaHalo:

Fluffythepoo:
In programming languages you divide first.. and one does not argue with the machines.

I work with some equipment that does some pretty interesting calculations. My all time favorite error to get is when the screen and system lock up completely and it spits out the following message; 'Error: Divide by zero detected." I have no idea why they sometimes called for that to happen, but it freaks me out every time. I have a feeling that one day it will be a machine that just happens upon the right method to do so. Then we will either evolve to a whole new understand of mathematics... or Skynet is born.

But... Skynet will divide first, case closed the machine overlords have spoken

They're equal.
Dividing by 2 is the same as multiplying by 0.5.

It doesn't matter. 5/3*4 in that order will give the same as 5*4/3

Darknacht:

TheKasp:
Eh... as long as they are not lined off by brackets or calculations with other priorities you can do them in whatever order you want.

(3*4)/3 = 3*4/3 = 3*(4/3) = 4.

That works with that example but
3/4*3=2.25
(3/4)*3=2.25
3/(4*3)=.25

order does matter.

If your not sure of the order the best thing is to convert every thing to multiplication.
3*(1/4)*3=2.25

Remove the parenthesis completely and it will always come up the same. That's why we carry out multiplications from left to right. Then do the addition/subtraction from left to right. The order does matter, but the order of operations for multiplication is the same as the one for division thus only left to right matters.

RatherDull:
My friends and I are in an argument about which you should do first. Many sources say many different things.

You and your friends are all right. Or all wrong. Equally, anyway, since they are exactly the same. MIND BLOWN YET?

See, dividing is simply multiplying by a fraction. Dividing by two is simply multiplying by one half, and so on, so it doesn't make any difference whatsoever which is done first of the two, because the end result will always be the same. For a simple example, do 15x2/3.

15x2 = 30, /3 becomes 10.
2/3 becomes two thirds, two thirds of 15 is 10.
15/3 = 5, x2 becomes 10.

Same answer every time, no matter the order. So yeah. Also, maths graduate here for the record, BSc Mathematics. Although that shouldn't matter anyway since this is primary school stuff...

EDIT: Reading some of the other thread replies, it makes me wonder just how did the Western world deliver such an astounding number of illiterate people? Seriously, there are people here who are flat out denying or ignoring the things they were (or should have been) taught in their very first year of school, whether they're from the UK, US, Canada, or Europe, or elsewhere. Just saying, it's little wonder the Chinese are catching up fast in economic terms - they actually give a damn about educating their kids, after all...

ooohhh one of these threads, buckle your shoe (that's my captcha) and fasten your seat-belts, it will be a rough ride.

OT: it doesn't really matter as long as there are no brackets, but generally you'd want to do them from left to right.

You multiply or divide on a left to right basis. For example if it was 5x12/3 you would multiply 5 with 12 and then divide the product by 3 which would give you 20.

It doesn't really matter, the order is brackets, exponents, addition, multiplication
Subtraction is the same as the addition of negative numbers, therefore subtraction and addition can be treated as the same operation.
1+4-5= 0
1+4+-5=0

Division is the same as multiplication. It is the result of a multiplying by a less then a number less then 1.
2/4=0.5
or
2/1 * 1/4=0.5
2 * 0.25= 0.5
therefore it does not matter which order multiplication and division are done, or addition and subtraction are done

I still prefer to do my divisions first as it removes the need for a second line of paper to be used when writing equations.

Lizardon:

If BODMAS was the rule

10-3+2

would equal 5 (add 3 and 2 first to get 5,and then subtract it from 10) rather than 9.

No matter which way this is read it will still be = 9
the longer version of the sum is
10 + -3 + 2
which reveals that 10+(-3+2) would just turn into 10-1.
it is not the same as 10-(+3+2), which is 10-3-2 when expanded. That seems to be the error that was made before.

EDIT: Ninja'ed

Addition and subtraction, multiplication and division, and exponents and roots are equal because they're the same thing. So with division and multiplication it's left to right. Although anyone who doesn't use that mathematical equation form (pictured below) or brackets is making things unnecessarily complicated and ambiguous.
image

Trivun:

See, dividing is simply multiplying by a fraction. Dividing by two is simply multiplying by one half, and so on, so it doesn't make any difference whatsoever which is done first of the two, because the end result will always be the same. For a simple example, do 15x2/3.

15x2 = 30, /3 becomes 10.
2/3 becomes two thirds, two thirds of 15 is 10.
15/3 = 5, x2 becomes 10.

Same answer every time, no matter the order. So yeah. Also, maths graduate here for the record, BSc Mathematics. Although that shouldn't matter anyway since this is primary school stuff...

Well yeah, when you put multiplication first, but take 15/2*3:
(15/2)*3 = 22,5 (correct)
15/(2*3) = 2,5 (incorrect)
You would have to write it a bit different (15*0,5*3) for it to work like that.

We do acknowledge here that multiplication and division are exactly the same right...

Smertnik:
It doesn't matter, it's the same operation. Same with addition and subtraction.

Sande45:
addition and subtraction, multiplication and division, and exponents and roots are equal because they're the same thing. So with division and multiplication it's left to right. Although anyone who doesn't use that mathematical equation form (pictured below) or brackets is making things unnecessarily complicated and ambiguous.
image

Kyrinn:
As a biologist, what's the difference? Are they not both the same thing?
Ok I'll leave

Revnak:
As others have already stated, it doesn't matter. Think about it like this, what is the difference between multiplying by one fourth and dividing by four? None. Same deal with any other fraction you can think of. Division and multiplication are essentially the same thing. Do them together. Same deal with addition and subtraction, for reasons already stated.

Auron225:
Doesn't matter. In a way they're both the same thing.

A divided by 2 = A multiplied by 1/2.

No they are absolutely not the same my fellow scientist and dudes with the weird avatars.

In fields ( http://en.wikipedia.org/wiki/Field_(mathematics) ), the mathematical structures that non mathematicians or theoretical physicist normally use they are inverse operations (not the same, still you can get one from the other). However most of modern mathematics and theoretical physics happen in more general stuctures, like Rings ( http://en.wikipedia.org/wiki/Ring_(mathematics) ), which can have multiplication and not division.

Let me put an example: Imagine the king decrees that you can only use integer numbers (..., -3, -2, -1, 0, 1, 2, 3, ...), with just those you can indeed add, subtract and multiply. But can you divide? Sure, you can write 1/2, but that is NOT an integer, so that operation doesn't make sense with the integers, and since you can't define the division for an infinity of combinations like that (such as 1/3, 1/4, 2/5, etc) you don't have the division for the Ring of integers with the usual add an multiply. Since you can multiply and not divide, then they MUST be different things.

To use another example: Take R(2) the field of matix ( http://en.wikipedia.org/wiki/Matrix_(mathematics) ) with 2x2 size over the Real numbers, there you also can add and multiply, but not divide due the non commutative aspect of the field.

To use a methaphor: Imagine that solving a math problem is like climbing a skyscraper. Normal people go to the top when it's the building it's done and just need to push a button on the lift to get to the top enjoying the climate and rugs and whatnot; mathematicians and teo physicist enjoy the danger and exporting, thus thry to climb when the skyscraper has less structure, first Sir Isaac Newton decided to take out the walls and electricity and climb, then Evariste Galois decided to take out the floors and ceilings for the lolz and see what he could do. Why? Because less structure allows you to see more from the top, and even more interesting allows you to comprehend the iron skeleton better and model it into new shapes.

It is through this kind of mathematical shenanigans into "less structured mathematical objects" we get the knowledge to build computers, go to the moon or try to design warp drives ( http://en.wikipedia.org/wiki/Miguel_Alcubierre ). Though the inverse is also true, it's because we wanted to measure the land, understand the universe structure or describe evolution that this math appeared.

OT: Unless you are doing advanced math or physics (mayor in college and past), its the same shit, don't sweat it. But it's good to know they are not the same really.

I was taught BIDMAS.

Brackets
Indices
Division
or
Multiplication
Addition
or
Subtraction

So, it was just which ever came first after doing the previous step.

In Canada, I was tought the acronym "BEDMAS"

It was

Brackets
Exponents
Division/Multiplication
Addition/Subtraction

The questions been answered, but that's how we did it xD

Wayneguard:
We do acknowledge here that multiplication and division are exactly the same right...

No, nobody should aknowledge that because it isn't true.I'm not sure how you could even think they are, they work very differently.

Tanakh:

Smertnik:
It doesn't matter, it's the same operation. Same with addition and subtraction.

Sande45:
addition and subtraction, multiplication and division, and exponents and roots are equal because they're the same thing. So with division and multiplication it's left to right. Although anyone who doesn't use that mathematical equation form (pictured below) or brackets is making things unnecessarily complicated and ambiguous.
image

Kyrinn:
As a biologist, what's the difference? Are they not both the same thing?
Ok I'll leave

Revnak:
As others have already stated, it doesn't matter. Think about it like this, what is the difference between multiplying by one fourth and dividing by four? None. Same deal with any other fraction you can think of. Division and multiplication are essentially the same thing. Do them together. Same deal with addition and subtraction, for reasons already stated.

Auron225:
Doesn't matter. In a way they're both the same thing.

A divided by 2 = A multiplied by 1/2.

No they are absolutely not the same my fellow scientist and dudes with the weird avatars.

In fields ( http://en.wikipedia.org/wiki/Field_(mathematics) ), the mathematical structures that non mathematicians or theoretical physicist normally use they are inverse operations (not the same, still you can get one from the other). However most of modern mathematics and theoretical physics happen in more general stuctures, like Rings ( http://en.wikipedia.org/wiki/Ring_(mathematics) ), which can have multiplication and not division.

Let me put an example: Imagine the king decrees that you can only use integer numbers (..., -3, -2, -1, 0, 1, 2, 3, ...), with just those you can indeed add, subtract and multiply. But can you divide? Sure, you can write 1/2, but that is NOT an integer, so that operation doesn't make sense with the integers, and since you can't define the division for an infinity of combinations like that (such as 1/3, 1/4, 2/5, etc) you don't have the division for the Ring of integers with the usual add an multiply. Since you can multiply and not divide, then they MUST be different things.

To use another example: Take R(2) the field of matix ( http://en.wikipedia.org/wiki/Matrix_(mathematics) ) with 2x2 size over the Real numbers, there you also can add and multiply, but not divide due the non commutative aspect of the field.

To use a methaphor: Imagine that solving a math problem is like climbing a skyscraper. Normal people go to the top when it's the building it's done and just need to push a button on the lift to get to the top enjoying the climate and rugs and whatnot; mathematicians and teo physicist enjoy the danger and exporting, thus thry to climb when the skyscraper has less structure, first Sir Isaac Newton decided to take out the walls and electricity and climb, then Evariste Galois decided to take out the floors and ceilings for the lolz and see what he could do. Why? Because less structure allows you to see more from the top, and even more interesting allows you to comprehend the iron skeleton better and model it into new shapes.

It is through this kind of mathematical shenanigans into "less structured mathematical objects" we get the knowledge to build computers, go to the moon or try to design warp drives ( http://en.wikipedia.org/wiki/Miguel_Alcubierre ). Though the inverse is also true, it's because we wanted to measure the land, understand the universe structure or describe evolution that this math appeared.

OT: Unless you are doing advanced math or physics (mayor in college and past), its the same shit, don't sweat it. But it's good to know they are not the same really.

What is the purpose of it? It seems like it would just be a whole new system of doing things with artificial limits put in, like doing math on a computer that can only recognize intergers. Unless I'm wrong (and I probably am, as the last math class I took was Calculas about two years ago) it is creating a whole new structure that is entirely artificial. I really just want to know what kind of stuff needs this.

Edit- I knew computers only know intergers. I was just making it more clear.

whatever comes first. in reality, it doesnt matter.

Holy crap... I logged in just to reply because there are a lot of misconceptions floating about.

1. For the example of 10-3+2 Mr.BadExample is correct.

Mr.BadExample:

Lizardon:

If BODMAS was the rule

10-3+2

would equal 5 (add 3 and 2 first to get 5,and then subtract it from 10) rather than 9.

It doesn't matter whether you add or subtract first. As has been said, subtraction is simply the addition of a negative number. It is dishonest to restructure the problem as 3+2 when in reality it should be -3 + 2.

It is the same regardless of order.

If you go left to right:
10-3+2
=7+2
=9

If you go right to left:
10-3+2
=10-1
Quick side lesson: -3 is actually -1 times 3 which means you cannot separate it if you deal with the 3 and the 2 first. The correct first step as Mr.BadExample pointed out is actually -3 + 2 since the multiplication of the -1 and 3 rank above the addition of the 3 to the 2.

=9

2. The following is completely incorrect about the reasoning. This is unfortunately due to making some easy to make but hard to spot errors.

Mikeyfell:
ooh, math, YAY!

When you do multiply and divide you do them from left to right in the problem.
In the problem 5X2+3%6 you do multiplication first. In 5%2+3X6 you do division first. (percent sign standing in for divide, bite me.)

There is an instance where you do multiply FIRST (as in before parentheses) and that's when you need to distribute

so 1+5(2+3)-2%6 you'd distribute the 5 before (or immediately after) the parentheses. And I can prove it!

1= 6 % 6
1= 6 % (2+4)
1= 6 % 2(1+2)
1= 6 % 2(3)
1= 3(3)
1= 9

So yeah, If you don't distribute before you divide shit gets weird. really weird.

1 = 6/6
1 = 6/(2+4)
Now the next line is where the error is made...
It should be:
1 = 6/(2(1+2))
The brackets exist. Just because Mikeyfell didn't put the brackets does not mean that they shouldn't be there. You can still write it without brackets when writing it normally on the board, but you have to understand that the 6 is divided by everything underneath it. This is what the brackets indicate.
Let's continue...

1 = 6/(2(3))
1 = 3/3

Now you may be a bit confused here and that is understandable so let's break it down a bit more. You can solve the 6/2 portion to get 3. That part is correct. But that 3 is still divided by the 3 that you left down there in the first place.

1 = 1

The simple truth is that the Order of Operations is correct. If you've found an example that disproves it then you have found an example that is incorrect.

PEMDAS

Parenthesis (complete the functions in parenthesis first, in PEMDAS order if they are multi-part)
Exponents (complete the functions that a variable or number is raised to the power of, again in PEMDAS order)
Multiplication
Division
Addition
Subtraction

In that order.

If the function has a lot of different parts,complete sub problems on the left first.

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