# 48÷2(9+3) = ??

• ### 288

• Total voters
510

#### BreakPoint

##### Bionic Poster
i highly doubt that. did you go to standford too? :roll:
Stanford (or "standford") is not an Ivy League school. If you had gone to a halfway decent school, you'd know that.

#### NinjaKiwi

##### Banned
The format used to program a computer to solve equations is not the same as writing out the equation in a format to be solved by hand.

BTW, if the 12 was supposed to be in the numerator, the equation would have been written:

48(9+3)÷2 or 48(9+3)/2

The fact that the equation was written:

48÷2(9+3) which is the same as 48/2(9+3) means that the (9+3) or (12) is in the denominator.

Numbers or variables to the left of the / are in the numerator and numbers or variables to the right of the / are in the denominator. Why? Because using the forward slash / symbol is how people type out the divide by line using a keyboard because they can't easily type out a horizontal line and put numbers and variables above the line for the numerator and numbers and variables below the line for the denominator. Thus, the / sign is used for convenience, with the numerator to the left of the / and the denominator to the right of the /.
That's right. You've got it!

#### NinjaKiwi

##### Banned
Stanford (or "standford") is not an Ivy League school. If you had gone to a halfway decent school, you'd know that.
Just ignored it. Does not mean all posters go to a IVY League School like us.

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#### aceX

##### Hall of Fame

This should help people pick the right answer.
Hi there,

Thanks for your question. I hope this helps:

Cheers,
aceX

#### BreakPoint

##### Bionic Poster
What, you don't appreciate a free math lesson?

If the (9+3) is supposed to be in the numerator, please explain why the equation wasn't written as:

48(9+3)÷2

Putting the (9+3) to the right of the ÷ sign means it's in the denominator. Didn't you learn that in 2nd grade?

#### NinjaKiwi

##### Banned
What, you don't appreciate a free math lesson?

If the (9+3) is supposed to be in the numerator, please explain why the equation wasn't written as:

48(9+3)÷2

Putting the (9+3) to the right of the ÷ sign means it's in the denominator. Didn't you learn that in 2nd grade?
I like the argument. Yes, we did learn it in 1st grade. Good luck with your arguments with those posters here.

#### BreakPoint

##### Bionic Poster
Good to see some people stop and think rather than blindly following rules they learned in school.

Yes, that's exactly it!

Using the / symbol is the same as using the horizontal line in a division problem. It's just that everything is typed out on a computer keyboard these days and not hand written. So what's to the left of the / is the same as what's above the horizontal line which, of course, is the numerator. And everything to the right of the / is the same as what's below the horizontal line which is the denominator.

If you put the (9+3) to the right of the / symbol but still want it to be in the numerator, you need to include another arithmetic operative sign, such as x or *. This is caused by the limitations of typing out mathematical equations on a computer keyboard rather than written by hand.

So, with 48÷2(9+3) or 48/2(9+3), the (9+3) is in the denominator.

With 48÷2 x (9+3) or 48÷2*(9+3) or 48/2 x (9+3) or 48/2*(9+3), the (9+3) CAN be in the numerator.

Again, this is caused by the limitations of typing out equations on a computer keyboard, which makes the inclusion of the additional arithmetic operative sign x or * necessary. This additional operative sign offsets the ÷ sign and separates the equation into two parts and two operations. With only the ÷, it is a one part division equation with everything to the left of the ÷ in the numerator and everything to the right of the ÷ in the denominator.

#### dr325i

##### G.O.A.T.
What, you don't appreciate a free math lesson?

If the (9+3) is supposed to be in the numerator, please explain why the equation wasn't written as:

48(9+3)÷2

Putting the (9+3) to the right of the ÷ sign means it's in the denominator. Didn't you learn that in 2nd grade?
WOW, and you really think that way?!
Does not matter how equation is written!

Tell us if:
5-3+2 = 5+2-3 = 4
same is with 48/2*12 = 48*12/2 = 288

The ORDER of multiplication/division DOES NOT matter!!!

For those (sadly) educated in the USA:
"PEMDAS" = "Parentheses, Exponents, Multiplication and Division, and Addition and Subtraction"

B-A-S-I-C-S!!!

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#### jester911

##### Rookie
If you want to see something amazing search the equation on yahoo.
Forums from body building to physics all over the world are arguing over this thing. Much like here there seems to be about a 50/50 split on the correct answer.

#### Netzroller

##### Semi-Pro
Regarding PEDMAS:

WIKIPEDIA:
The standard order of operations, or precedence, is expressed in the following chart.

terms inside brackets
exponents and roots
multiplication and division

In other English speaking countries, Brackets may be called Parentheses, or symbols of inclusion and Exponentiation may be called either Indices, Powers or Orders, and since multiplication and division are of equal precedence, M and D are often interchanged, leading to such acronyms as BIMDAS, BODMAS, BOMDAS, BERDMAS, PERDMAS, PEMDAS, and BPODMAS.
->288

#### dr325i

##### G.O.A.T.
Stanford (or "standford") is not an Ivy League school. If you had gone to a halfway decent school, you'd know that.
WHY???
Why would ANYONE need to know what Ivy League schools are???
Do they teach that in "a halfway decent school"???

I would stay away from here and stop wasting 30k posts on some forum and get to some BASIC education.

One day attitude like this may cost you a lot...

#### aceX

##### Hall of Fame
Is that a conclusion?
That is generally what is meant by "/thread"

#### HellBunni

##### Rookie
The format used to program a computer to solve equations is not the same as writing out the equation in a format to be solved by hand.

BTW, if the 12 was supposed to be in the numerator, the equation would have been written:

48(9+3)÷2 or 48(9+3)/2

The fact that the equation was written:

48÷2(9+3) which is the same as 48/2(9+3) means that the (9+3) or (12) is in the denominator.

Numbers or variables to the left of the / are in the numerator and numbers or variables to the right of the / are in the denominator. Why? Because using the forward slash / symbol is how people type out the divide by line using a keyboard because they can't easily type out a horizontal line and put numbers and variables above the line for the numerator and numbers and variables below the line for the denominator. Thus, the / sign is used for convenience, with the numerator to the left of the / and the denominator to the right of the /.
that is generally the case, but those are not the rules.
in absence of any other text associated with the expression, you can't assume the meaning of the expression with your personal preference.

because that creates confusion, since ppl are taught differently, that is why the argument is here (although some of the other arguments for 2 are plain wrong)

that is why in absence of any more text, we can't assume anything and simply follow the established rules.

true, the expression is very poorly written and semi-ambiguous looking, but I think it was done on purpose to show what can happen (different interpretations of the expression) and why at points like this you should follow the established rules.

#### MegacedU

##### Professional
The only thing you asked me was a rhetorical question on how someone as strikingly dumb as me could ever get through the logic games portion of the LSAT. Then you volunteered your (probably made up) score. No one's interested guy. I don't feel the need to get into a d--- measuring contest with you.

Clearly, the teachers of America have failed here, since I so stupidly follow the ORDER of OPERATIONS, God forbid. I don't know how I ever got through my third calculus class in college without it.

Cool your jets, there's arguments to be made for each way of doing the math.

#### jonnythan

##### Professional
Here's the bottom line:

The rules of mathematics demand that the answer is 288.

However, the expression writer's intent is slightly ambiguous. You may think that the expression writer meant 48/(2(9+3)) and perform the calculation thusly, but you are eschewing the rules and taking a leap of faith by guessing at the writer's intent.

If this question were on a math test, the professor may have meant the answer to be 2 and accept 2. If you wrote 288 and he marked you wrong, you would be able to defend yourself with the actual rules of math and probably convince him you were right.

However, if the professor meant the answer to be 288, and that is indeed the answer as it is written, you would have no argument for writing 2. "I thought you meant..." is not an excuse on a math test. "That's the thing about math," I'd say. "You don't have to assume anything. The rules strictly, concisely, and clearly cover this exact situation,"

#### Bartelby

##### Bionic Poster
If you punch the sum into google it gives you 288.

#### jonnythan

##### Professional
My TI-89 gives 288.

Matlab, Maple, TI-89, Wolfram Alpha, desk calculators, Mathematica, Google, mathematics PhD candidates, and certified licensed engineers all agree: the answer is 288.
The only dissidents appear to be BreakPoint and

##### Legend
My TI-89 gives 288.

Matlab, Maple, TI-89, Wolfram Alpha, desk calculators, Mathematica, Google, mathematics PhD candidates, and certified licensed engineers all agree: the answer is 288.
The only dissidents appear to be BreakPoint and
Yeah, that's the kind of person I'd never want as a co-worker, someone who is stubborn and can't admit a mistake.

The mistake is totally understandable. Refusing to change one's mind and going with a "but you see, this is how it seems to me!" attitude, says alot about a person, IMO.

#### Jaewonnie

##### Professional

This should help people pick the right answer.
----edit----
nvm

10char

#### diredesire

The format used to program a computer to solve equations is not the same as writing out the equation in a format to be solved by hand.

BTW, if the 12 was supposed to be in the numerator, the equation would have been written:

48(9+3)÷2 or 48(9+3)/2

The fact that the equation was written:

48÷2(9+3) which is the same as 48/2(9+3) means that the (9+3) or (12) is in the denominator.

Numbers or variables to the left of the / are in the numerator and numbers or variables to the right of the / are in the denominator. Why? Because using the forward slash / symbol is how people type out the divide by line using a keyboard because they can't easily type out a horizontal line and put numbers and variables above the line for the numerator and numbers and variables below the line for the denominator. Thus, the / sign is used for convenience, with the numerator to the left of the / and the denominator to the right of the /.
Everything to the right of the first / is in the denominator? It's not a convention of mathematics, it's a convention of what you choose to read it as. What you state above isn't "factual." It's your interpretation. ANY time you change it into a statement as above (where it isn't written on paper) you follow these rules. You remove ambiguity (and give implied parenthesis, etc, etc) when you are writing it out by hand. The divide sign and the / are equivalent and exactly the same. Whether or not you decide to remove ambiguity (BY the order of operations, aka encapsulating EVERYTHING you want in the denominator inside parens) is your choice. I'm not seeing the ambiguity.

What, you don't appreciate a free math lesson?

If the (9+3) is supposed to be in the numerator, please explain why the equation wasn't written as:

48(9+3)÷2

Putting the (9+3) to the right of the ÷ sign means it's in the denominator. Didn't you learn that in 2nd grade?
The equation was written as such to make a point. It's not like the equation has malicious intent. The point is PEMDAS is apparently completely misunderstood...

Clearly, the teachers of America have failed here, since I so stupidly follow the ORDER of OPERATIONS, God forbid. I don't know how I ever got through my third calculus class in college without it.

Cool your jets, there's arguments to be made for each way of doing the math.
Unfortunately, you're following a blind interpretation of PEMDAS. As stated, it does not explicitly going in the order of P, E, M, D, A, S. It's P > E > M=D > A=S
When equal, go left to right. Also, P is anything INSIDE parenthesis.

#### BreakPoint

##### Bionic Poster
WOW, and you really think that way?!
Does not matter how equation is written!

Tell us if:
5-3+2 = 5+2-3 = 4
same is with 48/2*12 = 48*12/2 = 288

The ORDER of multiplication/division DOES NOT matter!!!

For those (sadly) educated in the USA:
"PEMDAS" = "Parentheses, Exponents, Multiplication and Division, and Addition and Subtraction"

B-A-S-I-C-S!!!
But what's in the numerator and what's in the denominator DOES MATTER!!!!!

The original equation of 48÷2(9+3) does not have a * arithmetic operative to make it clearer that the (9+3) is a separate calculation and not part of the denominator. Therefore, given the lack of the * sign when using a computer keyboard to type out the equation, whatever is to the right of the ÷ sign or the / sign is part of the denominator. The / sign is the same as a horizontal division line!

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#### BreakPoint

##### Bionic Poster
WHY???
Why would ANYONE need to know what Ivy League schools are???
Do they teach that in "a halfway decent school"???

I would stay away from here and stop wasting 30k posts on some forum and get to some BASIC education.

One day attitude like this may cost you a lot...
If you went to Harvard, wouldn't you know that Yale is also in the Ivy League? :roll:

#### BreakPoint

##### Bionic Poster
Here's the bottom line:

The rules of mathematics demand that the answer is 288.
The rules of mathematics do not say that the (9+3) must be in the numerator. That was YOUR assumption.

My assumption is that it's in the denominator because it is to the right of the / sign, which is exactly the same as being below the division horizontal line, the convention for the denominator.

#### BreakPoint

##### Bionic Poster
Everything to the right of the first / is in the denominator?
What about it? What's to the right of the first / and to the left of the second / is in the denominator, and what's to the right of the second / is in the numerator.

That is, in an equation where you have a division operative in the denominator, such as a/b/c, it is the same as (a*c)/b. This is not the case in the equation being discussed.

#### Faceb**k

##### Banned
The Question should be
8+12/3(9+3)/15{(12+3)*16}

NOT
8+12/3(9+3)/15((12+3)*16)

#### Claudius

##### Professional
But what's in the numerator and what's in the denominator DOES MATTER!!!!!

The original equation of 48÷2(9+3) does not have a * arithmetic operative to make it clearer that the (9+3) is a separate calculation and not part of the denominator. Therefore, given the lack of the * sign when using a computer keyboard to type out the equation, whatever is to the right of the ÷ sign or the / sign is part of the denominator. The / sign is the same as a horizontal division line!
Using your logic, what stops the (9+3) from being in the denominator even if there was a *?

#### BreakPoint

##### Bionic Poster
Using your logic, what stops the (9+3) from being in the denominator even if there was a *?
A * sign makes it clearer that the (9+3) is a separate operation and not tied to the 2. But, yes, one can still make an argument that it's still in the denominator. But given the limitations of computer keyboards and the mathematical equation typing conventions that have resulted from those limitations, if you don't use the * sign to separate the two parts of the equation, it is the accepted convention that the (9+3) is in the denominator because it is to the right of the /, which is the same as being below the division horizontal line.

#### Netzroller

##### Semi-Pro
The original equation of 48÷2(9+3) does not have a * arithmetic operative to make it clearer that the (9+3) is a separate calculation and not part of the denominator. Therefore, given the lack of the * sign when using a computer keyboard to type out the equation, whatever is to the right of the ÷ sign or the / sign is part of the denominator. The / sign is the same as a horizontal division line!
Just repeating what you already said doesn't make it correct.

Show us a notable authority that agrees with your thesis. Right now we have all state of the art math software, scientific calculators and various books disagreeing with you. Shouldn't be so hard for you to provide some evidence, considering your great academic achievements you tell everyone about...

-You're right about one thing though, a * sign would make it clearer, but it'll still be the same...

#### sureshs

##### Bionic Poster
The only FAIL here is you, because you're so damn upset over an internet forum. I didn't go to college, so fail x 10.
But you attended college, like James Blake, right?

I thought you played college tennis and also graduated?

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#### Claudius

##### Professional
A * sign makes it clearer that the (9+3) is a separate operation and not tied to the 2. But, yes, one can still make an argument that it's still in the denominator. But given the limitations of computer keyboards and the mathematical equation typing conventions that have resulted from those limitations, if you don't use the * sign to separate the two parts of the equation, it is the accepted convention that the (9+3) is in the denominator because it is to the right of the /, which is the same as being below the division horizontal line.
What argument? By your definition, everything after / has to be in the denominator. That * does jack.

#### sureshs

##### Bionic Poster
BTW, I just realized PEDMAS is not wrong because it puts D ahead of M.

Consider: a/b*c

Answer is ac/b per PEDMAS or otherwise

Consider a*b/c

Modern method and PEDMAS both give ab/c

So it doesn't matter that PEDMAS puts D over M

I am more concerned with putting A over S:

a+b-c is not affected

But:

a-b+c is (a-b)+c but putting A first will give a-(b+c) = a-b-c

I think PEDMAS should retire.

#### sureshs

##### Bionic Poster
What argument? By your definition, everything after / has to be in the denominator. That * does jack.
That is usually how people understood it in college level science and engineering, once they were past the trick questions of high school. As I said before, many professors will informally write x/x+y to mean that x + y is entirely in the denominator. Specially professors above a certain age. If you tell them it means 1+y, they will laugh and say you didn't understand the context of the physics.

The next generation trained in computers will not do it.

#### tennisnoob3

##### Professional
Stanford (or "standford") is not an Ivy League school. If you had gone to a halfway decent school, you'd know that.
did you get the joke? i was referring to fedace's standford, something you should know about with 30k posts. halfway decent school doesnt even make sense(halfway to where?). you probably went a lower ivy anyway or donated a building, big whoop.

#### MegacedU

##### Professional
But you attended college, like James Blake, right?

I thought you played college tennis and also graduated?
I was just kidding. Of course I went to college...and graduated...with honors....and played tennis too. I was just being a pip.

#### cucio

##### Legend
I cannot believe what I am reading... Do teachers in USA/UK really teach that PEDMAS/PEMDAS acronym? Seriously? That's one of the most anti-pedagogical acronyms ever created, as this thread nicely shows, since it implies precedence between M and D, and between A and S.

And Breakpoint is a friggin legend, but I don't want to be near anything he has engineered, so please publish a list, for public safety.

#### tennisnoob3

##### Professional
I cannot believe what I am reading... Do teachers in USA/UK really teach that PEDMAS/PEMDAS acronym? Seriously? That's one of the most anti-pedagogical acronyms ever created, as this thread nicely shows, since it implies precedence between M and D, and between A and S.

And Breakpoint is a friggin legend, but I don't want to be near anything he has engineered, so please publish a list, for public safety.
uhh pemdas is taught that m/d and a/s are interchangeable and you do whichever comes first, thats not the issue. its the random insertion of parenthesis that some are imagining.

#### tennisnoob3

##### Professional
I was just kidding. Of course I went to college...and graduated...with honors....and played tennis too. I was just being a pip.
....you're an accountant with that math?? :shock:

or do we blame the alcohol?

#### FlamEnemY

##### Hall of Fame
Wow. Guys, this thread is 20 pages long.

#### Dedans Penthouse

##### Legend
1. The message you have entered is less than 10 characters . Please eat me.....whatever...

#### cucio

##### Legend
uhh pemdas is taught that m/d and a/s are interchangeable and you do whichever comes first
A lot of people here are saying: hey, D comes before M, so let's do the D first. or viceversa. It is all too easy to remember the acronym and not remember the caveats. My point is that a good acronym should not need any caveat, otherwise it hinders more than it helps. I find this particular one appalling, and some of the posts in this thread are living proof.

#### cucio

##### Legend
Ouch! Big F for you. You are actually breaking up implicit parenthesis.

If you rewrite 48/2(9+3) using the commonly accepted implicit precedence rules to make them explicit, the result is: (48/2)(9+3)

By breaking up the expression as you did, you happily brought along to your expression the end of the first parenthesis and then simply dropped it.

#### sureshs

##### Bionic Poster
I cannot believe what I am reading... Do teachers in USA/UK really teach that PEDMAS/PEMDAS acronym? Seriously? That's one of the most anti-pedagogical acronyms ever created, as this thread nicely shows, since it implies precedence between M and D, and between A and S.

And Breakpoint is a friggin legend, but I don't want to be near anything he has engineered, so please publish a list, for public safety.
My son learnt PEDMAS in elementary school (maybe without the E), and then the modern method in middle school.

Precedence between M and D is harmless as I showed before.

#### cucio

##### Legend
Precedence between M and D is harmless as I showed before.
Oh, really? What's the result of 6 / 2 * 5 ?

6 / (2 * 5) = 0.6
(6 / 2) * 5 = 15

#### sureshs

##### Bionic Poster
Oh, really? What's the result of 6 / 2 * 5 ?

6 / (2 * 5) = 0.6
(6 / 2) * 5 = 15
That was not my point. My point was that:

6/2*5 = 15 by modern method

and also 15 if you put D ahead of M.

I was NOT saying DM is same as MD. I am saying DM is consistent with modern method.

As I said in the previous post,

a/b*c = ac/b, whether you go left to right, or give D higher precedence over M.

What you are saying is that MD is wrong because a/b*c will become a/bc instead of ac/b

That is why the variant PEMDAS of PEDMAS is wrong, and a previous poster already made that mistake.

#### dr325i

##### G.O.A.T.
If you went to Harvard, wouldn't you know that Yale is also in the Ivy League? :roll:
Ah, I forgot that Harvard is the only "a halfway decent school"...
Your logic, just like "with *" and "without" is just...disturbing...

Give up, becoming too embarrassing...

Again, this is a 3rd (in the US) and 2nd (in Europe) grade level math... Most of us should not even discuss it...

#### dr325i

##### G.O.A.T.
The only thing you asked me was a rhetorical question on how someone as strikingly dumb as me could ever get through the logic games portion of the LSAT. Then you volunteered your (probably made up) score. No one's interested guy. I don't feel the need to get into a d--- measuring contest with you.

Clearly, the teachers of America have failed here, since I so stupidly follow the ORDER of OPERATIONS, God forbid. I don't know how I ever got through my third calculus class in college without it.

Cool your jets, there's arguments to be made for each way of doing the math.
WOW, out of everything, my score really got the most of the attention.
Again, I ask you HOW did you do it?!

I truly do not understand how you got through the Calc 3 not understanding the basics?! How did you go through the difeq or complex integrals? No way you can solve those without understanding a simple division and multiplication.

Again, I NEVER called you a "strikingly dumb" as you claim (to enforse your argument), I am just wondering how you write a book without knowing the alphabet?

#### sureshs

##### Bionic Poster
I think GOAT of this thread is the OP for faking the Matlab screen