Solve 48÷2(9+3)

[spoonitnow]

Solve 48÷2(9+3)

Apparently this is a really popular thing making the rounds and tends to see about a 50/50 split about what the right answer is. I'll post the right answer and why later or tomorrow or something.

[bikes]

2 obv

PLEASE EXCUSE MAH DEAR AUNT SALLY

[Stacks]

PLEASE EXCUSE MAH DEAR AUNT SALLY

^^^

[fat-b]

looks like i won the flip

[wufwugy]

I worked harder on sophomore geometry/pre-trig than any other class, yet didn't understand anything, to this day have no clue what sine cosine and tangent are, and how the fuck I was able to barely pass with a D+. I can't even do my niece's third grade long division anymore. I'm a math neanderthal

Yet I knew this was 2

[spoonitnow]

I worked harder on sophomore geometry/pre-trig than any other class, yet didn't understand anything, and to this day have no clue what sine cosine and tangent are, and how the fuck I was able to barely pass with a D+. I can't even do my niece's third grade long division anymore. I'm a math neanderthal

Yet I knew this was 2

You forgot Overeem.

[eugmac]

I wonder if writing it as 48/2(9+3) changes how people see it.

[wufwugy]

You forgot Overeem.

[Keith]

2 obv

PLEASE EXCUSE MAH DEAR AUNT SALLY

288

Bollocks, obviously my dear aunt sally works left to right in England.

[a500lbgorilla]

This is a good one.

It's 288.

[a500lbgorilla]

I wonder if writing it as 48/2(9+3) changes how people see it.

I'd bet it would because it becomes second nature to treat the elementary school division sign like a plus sign in order of ops after so many years of never seeing it.

[BennyLaRue]

BEDMAS, MF-ERs.

[kevster]

It's 288 where I come from.

I can see how you get to 2 obv but not in any textbook that I was ever taught from.

[eugmac]

I'd bet it would because it becomes second nature to treat the elementary school division sign like a plus sign in order of ops after so many years of never seeing it.

Really? For me, I end up seeing it as a fraction:

48
____
2(9+3)

[eugmac]

Anyway my answer is that there's a bracket missing and so the problem is ambiguous.

[profnabeshin]

I used to be a math major... and I get 2 following parenthesis first rule {PMDAS}

[BooG690]

LEFT TO RIGHT GAIZ, LEFT TO RIGHT.

288

[jyms]

288

[spoonitnow]

Okay so the answer is.....

Start with 48÷2(9+3)
Do brackets first to get 48÷2(12)
Do multiplication and division at the same time, left to right, to get (24)(12) and then 288

What usually screws people up is they think that multiplication comes before division in the order of operations, though they are really done at the same time, left to right.

[profnabeshin]

It's not that I think multiplication comes before division. Brackets come first. You do the inside of the brackets and then the multiplication of brackets with the 2.

Answer is 2

[spoonitnow]

It's not that I think multiplication comes before division. Brackets come first. You do the inside of the brackets and then the multiplication of brackets with the 2.

Answer is 2

The multiplication of 2 is not inside of the brackets, so it doesn't come before the division by 2.

[profnabeshin]

I agree with you if you restate the equation as such:

48 ÷ 2 x (9+3)

Otherwise the bracket's guts should be multiplied with the 2 first as written.

[d0zer]

the division symbol is gay. slashes are a man's notation

[profnabeshin]

@spoon- please provide a reputable source that backs up your claim

[jyms]

It's always been brackets first and then the rest is done left to right. The multiplication is just assumed after solving the bracket while going left to right. You always go left to right with division and multiplication then again for addition subtraction.


Order of Operations - BODMAS

Order Of Operations Tutorial: BODMAS

Order of operations - Wikipedia, the free encyclopedia

[profnabeshin]

[a500lbgorilla]

Cool thread.

On the whole, I suppose I agree with you
that it would be easier and perhaps more consistent to give
multiplication precedence over division everywhere; but of course
there is no authority to decree this, so the more prudent approach is
probably just to recognize that there really isn't any universal rule.
I ran across the same AMS reference that you found while trying to see
if any societies had made official statements on the rules of
operations in general; the fact that they took note of this one rule
alone demonstrates only that this is the one rule on which there is
not universal agreement at the present time, but it probably is
growing in acceptance.

Math Forum - Ask Dr. Math

Some googles suggest that there is no authority to decide. It's allowed to whichever rule you wish.

Making this the correct answer.

Anyway my answer is that there's a bracket missing and so the problem is ambiguous.

Wolfram Alpha says 288 but that's because it rewrites it as I rewrote it (48/2)(9+3)

[a500lbgorilla]

The Order of Operations: More Examples

Here is that source.

Cut from the picture:

(And please do not send me an e-mail either asking for or else proffering a definitive verdict on this issue. As far as I know, there is no such final verdict. And telling me to do this your way will not solve the issue!)

[a500lbgorilla]

At the other end, I think that computers have influenced the subject,
so that it is taught more rigidly now than it used to be, since
programming languages have had to define how every expression is to be
interpreted. Before then, it was more acceptable to simply recognize
some forms, like x/yz, as ambiguous and ignore them - something I
think we should do more often today, considering some of the questions
we get on such issues.

I spent some time researching this question, because it is asked
frequently, but I have not found a definitive answer yet. We can't say
any one person invented the rules, and in some respects they have
grown gradually over several centuries and are still evolving.

...

5. There is still some development in this area, as we frequently hear
from students and teachers confused by texts that either teach or
imply that implicit multiplication (2x) takes precedence over
explicit multiplication and division (2*x, 2/x) in expressions
such as a/2b, which they would take as a/(2b), contrary to the
generally accepted rules. The idea of adding new rules like this
implies that the conventions are not yet completely stable; the
situation is not all that different from the 1600s.

In summary, I would say that the rules actually fall into two
categories: the natural rules (such as precedence of exponential over
multiplicative over additive operations, and the meaning of
parentheses), and the artificial rules (left-to-right evaluation,
equal precedence for multiplication and division, and so on). The
former were present from the beginning of the notation, and probably
existed already, though in a somewhat different form, in the geometric
and verbal modes of expression that preceded algebraic symbolism. The
latter, not having any absolute reason for their acceptance, have had
to be gradually agreed upon through usage, and continue to evolve.

Math Forum - Ask Dr. Math

[EasyPoker]

I got 2

[Donachello]

24*12 = 288

[bode]

saw this on 2+2 yesterday. My initial reaction was 288, but i convinced myself it should be 2 when i voted.

[kevster]

Brackets come first

I agree with this. But not with this...

You do the inside of the brackets and then the multiplication of brackets with the 2.

But also think that the person that wrote the equation is a big gay bear by not making it clearer.

(48/2)(9+3) = 288

48/(2(9+3)) = 2


Or better still.......

(48/2)*(9+3) = 288

48/(2*(9+3)) = 2


Or better still.......

(48 / 2) * (9 + 3) = 288

48 / (2 * (9 + 3)) = 2


Are you bored yet, huh? Are you fucking bored yet??

No? Whaddya mean no.....? Ok, then......


(
48 / 2
)
*
(
9 + 3
)
= 288


48 /
(
2 *
(
9 + 3
)
)
= 2

[Icanhastreebet]

coinflip imo

[kiwiMark]

obv 145

[bigred]

[rong]

I think everyone who says 288 is wrong, for 2 reasons.

1. This essentially the same as 48/2x (where x=12), in which case we would always multiply x and 2 first.

And

2. We always have the option of expanding the brackets, which would always be done as follows:

48÷2(9+3) =

48
2(9+3) =

48
2*9 +2*3 =

48 / 24 = 2

[jyms]

I was always taught that you solve the bracket first and when you do you no longer treat it as such. It's just left to right multiply and divide and then left to right add and subtract.

[rong]

Ignoring half of what I wrote, but focusing on the first bit, how would you solve:

48/2x when x = 9+3

Would you ever end up with 288 if given that question? From my experience I don't beleive many people would.

It's basically a question of whether you consider x to be below the line or at the end of the line.

[a500lbgorilla]

I think everyone who says 288 is wrong, for 2 reasons.

1. This essentially the same as 48/2x (where x=12), in which case we would always multiply x and 2 first.

And

2. We always have the option of expanding the brackets, which would always be done as follows:

48÷2(9+3) =

48
2(9+3) =

48
2*9 +2*3 =

48 / 24 = 2

This word makes you incorrect.

The answer is that the question is ambiguous. Thusly, we would not always do anything to solve it.

48÷2(9+3) - Wolfram|Alpha

Wolfram Alpha suggests expanding it as

[swiggidy]

Anyway my answer is that there's a bracket missing and so the problem is ambiguous.

This.

By math it's 288 and it's not even close. If you plug it into some calculator you might get different answers but that's because it's ambiguous and the actual calculation is dependent on their implementation.

[a500lbgorilla]

Ignoring half of what I wrote, but focusing on the first bit, how would you solve:

48/2x when x = 9+3

Would you ever end up with 288 if given that question? From my experience I don't beleive many people would.

It's basically a question of whether you consider x to be below the line or at the end of the line.

There's no reason to follow up, but yes. You would ever end up with 288 if you treat it correctly as (48/2)*x or no you wouldn't ever end up with 288 if you treat it correctly as 48/(2x).

You'd be best off just ignoring it because it's ambiguous and that's reason enough to just say no.

[Penneywize]

Anyway my answer is that there's a bracket missing and so the problem is ambiguous.

pretty much this, I voted 2, but for the answer to be correctly 2 it should be written as follows:

48/[2(9+3)]

as it stands, the answer is 288, since the correct interpretation of the problem is:

(48/2)*(9+3)

I'm not sure why this is a big deal though, really. The problem is intentionally written to be confounding, which accomplishes what, hrm?

[a500lbgorilla]

pretty much this, I voted 2, but for the answer to be correctly 2 it should be written as follows:

48/[2(9+3)]

as it stands, the answer is 288, since the correct interpretation of the problem is:

(48/2)*(9+3)

I'm not sure why this is a big deal though, really. The problem is intentionally written to be confounding, which accomplishes what, hrm?

Argument. Which spreads like wildfire on the internet.

[spoonitnow]

Argument. Which spreads like wildfire on the internet.

I know right, it's so awesome

[ensign_lee]

I'm changing my vote. I vote for 288 now instead of 2.

It's the same as 48 / 2 * (12)

[Sasquach991]

Pi are round, cornbread are square

[Lukie]

Parentheses are solved first.. and that does not get extended to the multiplied number outside..

48÷2(9+3) = 48/2*(9+3) = 48/2*(12) = 24*12 = 288....

more interesting to me is how non-calculator tards get to 288. I see 2 reasonable approaches.

A. 12x12=144 via basic multiplication table memorization; double this since 24 is double 12, voila 288

B. Slightly more challenging (i.e. still very easy) but more generally applicable, do 24*10 in head (240), add that to 24*2 done in head (48), voila 288.

C. Regardless, the answer is 288.

D. I find it extremely worrying that the ultimate brotarded body building site currently has a higher percentage of correct votes than our very own poker forum.

[Rage2100]

48/2(9+3)

I would do the brackets first to get:-

48/2(12)

Next, I would do the division to get:-

24(12)

Then, multiply together to get:-

288

That's the way I was taught to do it anyway!

[Penneywize]

iblah blah blah 5th grade math lesson blah blah blah pretentious bullshit blah blah blah I visit weightlifting forums

A) Wow thanks for the math lesson, cuz like, totally, no one mentioned how this maffs is sposed' to be done in this thread already!

B) Cool trick, are you part asian or something?!

C) Wao thanks

D) There are any number of reasons why your meathead internet buddies score higher on a "math test" than the ppl in this forum. Maybe they're less confident in their math and decide to read the thread for the correct answer before voting? but nah I guess just carry your shame for FTR and make sure we all know about it etc

[Lukie]

A) Wow thanks for the math lesson, cuz like, totally, no one mentioned how this maffs is sposed' to be done in this thread already!

B) Cool trick, are you part asian or something?!

C) Wao thanks

D) There are any number of reasons why your meathead internet buddies score higher on a "math test" than the ppl in this forum. Maybe they're less confident in their math and decide to read the thread for the correct answer before voting? but nah I guess just carry your shame for FTR and make sure we all know about it etc

A. No problem. I think it is helpful at times to explain some math 'tricks' and 'shortcuts' so to speak. It's one of the reasons that I think Sklansky's non-poker posts on 2p2 tend to be pretty good. While it's likely there are many mathematicians out there that understand complex maths better than DS, he has a way of simplifying things so that the layperson can understand it better. I'm glad you were able to get something of value from my post.

B) You're thinking of trikflow

C) Sure thing

D) Let it be very clear that I stopped reading BB.com 6-7 years ago due to the nonsensical discussion, and that I love FTR and have met many good friends from this site. It was intended to be a light-hearted joke with the implication that those on a poker site (a game, in my opinion, heavily based on math) would be more likely to get the problem right.

[wufwugy]

D) Let it be very clear that I stopped reading BB.com 6-7 years ago due to the nonsensical discussion, and that I love FTR and have met many good friends from this site. It was intended to be a light-hearted joke with the implication that those on a poker site (a game, in my opinion, heavily based on math) would be more likely to get the problem right.

Poker forums are full of degens who think wearing sunglasses at dinner is cool, bodybuilding forums are full of nerds who wanna get swole

[jyms]

A. No problem. I think it is helpful at times to explain some math 'tricks' and 'shortcuts' so to speak. It's one of the reasons that I think Sklansky's non-poker posts on 2p2 tend to be pretty good. While it's likely there are many mathematicians out there that understand complex maths better than DS, he has a way of simplifying things so that the layperson can understand it better. I'm glad you were able to get something of value from my post.

B) You're thinking of trikflow

C) Sure thing

D) Let it be very clear that I stopped reading BB.com 6-7 years ago due to the nonsensical discussion, and that I love FTR and have met many good friends from this site. It was intended to be a light-hearted joke with the implication that those on a poker site (a game, in my opinion, heavily based on math) would be more likely to get the problem right.

Lukie, teach me how you did that. Respect for the responses.

[eugmac]

2(5)^2
is it 50? or is it 100?
FIGHT.

[mbiz]

1+1= :

2?
window?

[eugmac]

1+1= :

2?
window?

11

[bikes]

in so fucking glad i finished math a long time ago so i wont ever get punished again for this shit

[Vinland]

I got it right....i am so smart....smrt.....smrart...

The brackets imply multiplication so once you add the 2 numbers, you work left to right.
I wonder how many people get done over when they win prizes but F up the math question

[EasyPoker]

who gives a f*** anyway

jeez

[swiggidy]

2(5)^2
is it 50? or is it 100?
FIGHT.

50 and not even close to OP. This is std textbook example when learning powers.

That said I challenge you with my nunchucks in the library.

[Galapogos]

Lukie, teach me how you did that. Respect for the responses.

Totally, I'd give him reps if it wasn't fun to keep him at zero. Don't understand why some people feel the need to bring the hate.

[griffey24]

Pretty funny that this thread is two pages long!

I agree with the whatever the first post was that said a bracket is missing.

There isn't a right answer to this question without another bracket.

It has to either be written as:

48÷[2*(9+3)]

or

[48÷2]*(9+3)

It's like phrasing a sentence with a comma missing, such that it can be interpreted in two ways, then asking which is the correct way. There is no correct way until proper punctuation is used

[Vinland]

^ Dont think so....
5(2) means multiply, so 5(2+3) means the same thing except you have to do the calculation in the brackets first, then multiply.

x(2+3) = x5

[griffey24]

Yah you're missing my point though.

I know that the bracket comes first. All I'm saying is that extra brackets are missing elsewhere in the equation. ie: it has to be written like one of the following:

48÷[2*(9+3)]

or

[48÷2]*(9+3)

or after the original bracket is solved for, as the following:

48÷[2*(12)]

or

[48÷2]*(12)

[oskar]

I voted two cos there is almost no doubt in my mind that that is how we learned it in school. But it's been too long and I did not keep the books. If I were to put it in the calculater I would always put extra brackets tho.

[!Luck]

Calculate.

A(Graham's number,Graham's number)

Go!

[Lukie]

my TI-83 plus, TI-89, windows vista calculator (in scientific mode), and google calculator all give 288.

it appears that multiplication via juxtaposition having precedence over explicit multiplication and division has a pretty wide following, but nobody seems to know where it came from. I still feel that the order of operations are pretty clear on this, i.e. the original problem (obelus and all) is mathematically unambiguous.

[a500lbgorilla]

my TI-83 plus, TI-89, windows vista calculator (in scientific mode), and google calculator all give 288.

it appears that multiplication via juxtaposition having precedence over explicit multiplication and division has a pretty wide following, but nobody seems to know where it came from. I still feel that the order of operations are pretty clear on this, i.e. the original problem (obelus and all) is mathematically unambiguous.

You are incorrect. The original problem is mathematically ambiguous. The reasons why are contained within this thread.

[celtic123]

288 gee

[Lukie]

TI-85 - Wikipedia, the free encyclopedia

The TI-85 was a graphing calculator made by Texas Instruments based around the Zilog Z80 microprocessor. Designed in 1992 as TI's second graphing calculator (the first was the TI-81), it has since been replaced by the TI-86, which has also been discontinued.
The TI-85 was significantly more powerful than the TI-81, as it was designed as a calculator primarily for use in engineering and calculus courses. Texas Instruments had included a version of BASIC on the device to allow programming. Each calculator came with a cable to connect calculators (simply a three-conductor cable with 2.5 mm jack plugs on each end). Another cable known as the TI-Graph Link was also sold, along with appropriate software, to connect the calculator to a personal computer. These cables made it possible to save programs and make backups.

From what I understand, the TI-85 was programmed with slightly different rules governing the order of operations. It's very telling that they corrected this with the second/newer version (i.e. the TI-86)

[a500lbgorilla]

TI-85 - Wikipedia, the free encyclopedia



From what I understand, the TI-85 was programmed with slightly different rules governing the order of operations. It's very telling that they corrected this with the second/newer version (i.e. the TI-86)

Exactly though nothing is necessarily 'telling' and nothing was necessarily 'corrected'. As there is no authority to decide which of the two orders of operations are correct, the problem is truly mathematically ambiguous.

I agree with you on your assessment of which order of operations is proper, but others taught other rules would disagree.

[CBAT]

You are incorrect. The original problem is mathematically ambiguous. The reasons why are contained within this thread.

epic

[Lukie]

meh.. the TI-85 is almost 20 years old and was replaced by the TI-86.. the 86 returns 288 as does the TI-83+ and TI-89 that I own.

Windows vista calculator, google calculator, and bing calculator all also give the answer 288.

Google

48/2(9+3) - Bing

we'll just have to agree to disagree. It wouldn't make much sense to have an order of operations if it were necessary to add brackets to everything to make it unambiguous... in that case the order of operations might as well read 'B', then do everything else left to right. Another point is that the field of mathematics is such that there is usually exactly one correct answer and it would blow my mind if something as relatively simple as this could be (correctly) interpreted in more than one way.

[a500lbgorilla]

meh.. the TI-85 is almost 20 years old and was replaced by the TI-86.. the 86 returns 288 as does the TI-83+ and TI-89 that I own.

Windows vista calculator, google calculator, and bing calculator all also give the answer 288.

Google

48/2(9+3) - Bing

we'll just have to agree to disagree. It wouldn't make much sense to have an order of operations if it were necessary to add brackets to everything to make it unambiguous... in that case the order of operations might as well read 'B', then do everything else left to right. Another point is that the field of mathematics is such that there is usually exactly one correct answer and it would blow my mind if something as relatively simple as this could be (correctly) interpreted in more than one way.

No you can agree that we just have to agree to disagree, but the original problem is ambiguous and that has been made very clear in this thread.

If you think the authority of your calculators is the final authority on this issue, then you really don't understand this issue.

I'll say this clearly. Because there is no authority to decide, and because both the order of operations you know and are comfortable with and the order of operations you don't agree with have been taught as true, the original problem is mathematically ambiguous.

It's like saying: Which is correct: The colors of the birds are red, white and blue. OR The color of the birds are red, white, and blue.

There is no deep truth to which order of operations is correct, so yours is no better than theirs. You can not like this for the rest of your days but if you say the original problem is unambiguous you need to qualify it with, "to me." Because it is ambiguous.

edit: also, something like this can be correctly interpreted in more than one way. Three ways. And one way is more correct than the other two.

The answer is 2.

The answer is 288.

The question should be ignored because it is ambiguous.

[Lukie]

No you can agree that we just have to agree to disagree, but the original problem is ambiguous and that has been made very clear in this thread.

If you think the authority of your calculators is the final authority on this issue, then you really don't understand this issue.

The point is that the collective brainpower of google, bing, texas instruments and all current scientific calculators that I'm aware of all come to a consensus.. so your position then is that they are all wrong or that they all came to the same conclusion by coincidence.

I'll say this clearly. Because there is no authority to decide, and because both the order of operations you know and are comfortable with and the order of operations you don't agree with have been taught as true, the original problem is mathematically ambiguous.

Yet every single one of us agree that the order of operations is BEMDAS, or brackets (inside), exponents, multiplication and division left-to-right, addition and subtraction left to right.

What you are saying then is that 24(12) is not the same as 24*(12), and that somehow multiplication via the juxtaposition against brackets takes precedence over regular multiplication and division. But if you are going to take the position that there is no authority to decide this, how is it justifiable to add such an arbitrary wrinkle such that a simple problem can be interpreted in more than one way? That doesn't make any sense. *

It's like saying: Which is correct: The colors of the birds are red, white and blue. OR The color of the birds are red, white, and blue.

The rules of english and maths are quite different I presume.. in this example I believe they actually *are* both correct.. but don't quote me on that; I'm not particularly sure.

There is no deep truth to which order of operations is correct, so yours is no better than theirs. You can not like this for the rest of your days but if you say the original problem is unambiguous you need to qualify it with, "to me." Because it is ambiguous.

I can assure you that I want to spend less time thinking about this in the future, not more


*This begs another interesting question. Where specifically are you arguing that multiplication via juxtaposition should be in the order of operations?

Example that I am coming up with right here:

3(2*2.5)^2

Do you do the 3* as in left to right (same as parenthesis), before the exponent, after the exponent but before other multiplication, or simply left to right?