Solve 48÷2(9+3)

[spoonitnow]

You old farts can say its 288 all you want but ask high school or college level classroom and they'll say it's 2. That notation (the two being right outside the parenthesis with no multiplication sign) is acknowledged in academia as a grouping of the two factors.

This problem NEVER comes up though because nobody uses slashes OR division signs anymore instead a long bar (like a fraction) is used to separate the two top to bottom.

lol wow

[Lukie]

48/2(12)

Expressing this in a more aesthetically pleasing way gives us

48
-------
2(12)

A / indicating division and a horizontal line separating numerator from denominator (vinculum) are not the same thing and are in no way interchangeable. I'm reasonably sure nobody is going to seriously dispute this.

[Lukie]

Also, something else not really relevant to the debate that Rilla and I were having:

I think most of us learned the order of operations as something like PEMDAS or something equivalent (B instead of P and/or O instead of E) but I wonder why that specific acronyn is taught with M before D, and here's why (not 100% sure on this theory but as I was throwing some numbers around it appears to be true):

As the multiplication/division level, I'd argue that putting division first is a superior way to teach it. If the left-to-right rule is observed, it doesn't matter, but if it's forgotten then I *THINK* doing division before multiplication will always yield the correct answer, but doing multiplication before division may not (again, this is a moot point if done left-to-right, but that is an added and perhaps unneeded specific instruction to teach students)

10*5/2

left-to-right method = 25
division first method = 25
multiplication first method = 25

15/5*3

left-to-right method = 9
division first method = 9
multiplication first method = 1

[PlayToWin]

People who do math for a living see the "÷" symbol as "/". Hence, the equation becomes

48/2(12)

Expressing this in a more aesthetically pleasing way gives us

48
-------
2(12)

By making the problem more aesthetically pleasing, you've succeeded in changing the problem. Is that common in academia?

It is standard in academia for brackets to signify a grouping of this sort.

Brackets or parenthesis are optional. You can use them to make the problem more clear, but they are not required. Without them, the "standard in academia" is to go by the "order of operations". That's it. It's not hard and it's not ambiguous. Math is not ambigous.

If I was grading a quiz where the question was "solve 48÷2(9+3)", I would realize my mistake ....

Please tell me you're not a math teacher.

[Lukie]

in fairness, it is somewhat bizarre to see the obelus used in an equation that includes parentheses, but I thought it was sort of understood that ÷ is identical in funtion to /

[spoonitnow]

Also, something else not really relevant to the debate that Rilla and I were having:

I think most of us learned the order of operations as something like PEMDAS or something equivalent (B instead of P and/or O instead of E) but I wonder why that specific acronyn is taught with M before D, and here's why (not 100% sure on this theory but as I was throwing some numbers around it appears to be true):

As the multiplication/division level, I'd argue that putting division first is a superior way to teach it. If the left-to-right rule is observed, it doesn't matter, but if it's forgotten then I *THINK* doing division before multiplication will always yield the correct answer, but doing multiplication before division may not (again, this is a moot point if done left-to-right, but that is an added and perhaps unneeded specific instruction to teach students)

10*5/2

left-to-right method = 25
division first method = 25
multiplication first method = 25

15/5*3

left-to-right method = 9
division first method = 9
multiplication first method = 1

Unless you're multiplying or dividing by 0.5, then you're fucked.

[PlayToWin]

I went to a beer intro tonight at the local tavern with four of my friends. I heard a couple of them talking about the mathematics of fractals (variance), so I decided to give them this test. This is a simple description of the four: Accountant, Air Traffic Controller, Mechanical Engineer, 9th Grade Dropout w/superior memory.

Of the four, the only one that got it right was the high school dropout. The accountant is going to do more research because she didn't believe it. Funny as hell.

[a500lbgorilla]

By making the problem more aesthetically pleasing, you've succeeded in changing the problem. Is that common in academia?

Brackets or parenthesis are optional. You can use them to make the problem more clear, but they are not required. Without them, the "standard in academia" is to go by the "order of operations". That's it. It's not hard and it's not ambiguous. Math is not ambigous.

Google and Wolfram Alpha both change the problem. They both take an ambiguous problem and make it a well-defined problem by rendering it via the order of operations we all know and love. You don't think they're changing the meaning because they're changing it in the only way you think is valid.

Just read all of this.

Math Forum - Ask Dr. Math

It's starts with an engineering professor explaining this exact problem (not these exact numbers). Here's a clip:

I'm a professor in the field of electrical engineering. Occasionally I
remind my students of the precedence order regarding the four
arithmetic operations: addition, subtraction, multiplication, and
division. Apparently though, based upon viewing numerous Web sites and
the messages of various on-line discussion groups, there seems to be
some controversy regarding these simple rules!

Some controversy? I couldn't imagine what sort.

that "multiplication indicated by juxtaposition is carried out before
division." Thus, in general, for any variables a, b and c, we would
have a/bc = a/(bc) (assuming, of course, that b and c are nonzero).
Indeed, this convention is consistent with what I have seen in many
mathematical books at various levels; for example, on p. 84 of
Allendoerfer and Oakley, _Principles of Mathematics_, 1969 (my
pre-college math book), we find:

(a / b) x (c / d) = a c / b d

which is generally true only if the right side is interpreted as:

(a c) / (b d)

Notably, the above equality would *not* be generally true were we to
interpret the right side as:

[(a c) / b] d

Haha, what? Order of operations, people! What is this implicit multiplication crap? Go back to 5th grade math and learn it better.

He goes on to recommend a way to clear up confusion by purposing his own order of ops.

Then some guy calling himself Dr. Math responds:

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.

No universal rule, my ass. It's called order of operations, bub. There is one and it is fine. And it says implicit multiplication is just like any other sort.

As a result, I'm not entirely surprised that you learned a different
rule than I think I did. (I'm not sure I didn't first learn the
equal-precedence rule in a programming class, however.)

Some people may have learned different rules? And these rules are themselves equally valid?
Why under such an understanding wouldn't it be possible to describe simple math problems in an ambiguous manner as two people could approach the same expression and yield different and valid results?

I've heard from too many students whose texts do "give
an example that really puts this rule to the test," but do so by
having them evaluate an expression like:

6/2(3)

that is too ambiguous for any reasonable mathematician ever to write.

This problem is ambiguous until you can prove that implicit multiplication taking precedence over other multiplication is invalid. And as far as I know, you can not. There is no debate, it all balances upon this one point.

[spoonitnow]

This problem is ambiguous until you can prove that implicit multiplication taking precedence over other multiplication is valid. And as far as I know, you can not. There is no debate, it all balances upon this one point.

fyp

[a500lbgorilla]

Nice try, spoon.

The point is that you can't prove either way with regards to this point so you're left to only one conclusion. And it's not the conclusion which says the problem is well-defined.

Had I been arguing that 2 was the only correct answer, you would have had me. But as I am arguing that it could be an answer because this specific bit of order of operations simply comes down to convention, you're allowed to any choices you wish.

It's well-defined if we're applying a standard to it. Be that standard order of operations, or a programming language processing order of precedence (C Precedence Table), or the standard of implicit multiplication, but as no standard is expressed with the problem, we are left to freely choose between all valid options.

It's like saying: Which is correct: The bird is red, white, and blue. OR The bird is red, white and blue.

It's a convention of notation, you're allowed to either. If you want to write your expression intending for one specific result, I suggest you take that into consideration.

Thusly, the problem as stated is ambiguous.

[a500lbgorilla]

I think a better sentence would be: We bought equally bananas, pears and apples.

Did I mean that we bought 4 of each or that we bought 4 bananas and 2 pears and 2 apples? Or do I not care if ambiguity arises?

I think we all agree that it should be read as 4 of each, but because it could be read the other way, a little bit of ambiguity creeps in.

Oxford comma - English Grammar and Usage

Certainly, we can all agree on which standard is most robust (PEDMAS) and that it should become assumed that unless otherwise stated, PEDMAS is the way to go*. But as no authority has decided to agree with us on that stance, we're left to adding parens or rebejiggering our expressions to remove accidental ambiguity.

edit * especially as this is the way computerized math authorities seem to be headed (Google, Wolfram, Later Generation TI calculators)

[a500lbgorilla]

I think I understand now what Lukie was saying about how math has a way of just being true and any error lies with the reader. I'm saying that math notation is paralleled to language and that if the readers can be confused, you need to take special care to keep them from being confused.

In this case, the readers were confused because some readers learned one rule and other readers learned another rule. We all think that one rule is superior, but because the Math Gods have not passed down the commandment - Thou Shalt Follow Order of Operations Always, nor has anyone derived the perfect operator precedence for our convention of notation, we're left to recognize that the problem as stated has a bit of ambiguousness to it.

[StillDeadMoney]

you've succeeded in changing the problem.

For that particular problem, it doesn't, if the brackets indeed work the way I claim them to.

Brackets or parenthesis are optional. You can use them to make the problem more clear, but they are not required. Without them, the "standard in academia" is to go by the "order of operations". That's it.

The "standard in academia" was not an appeal to some hard-and-fast mathematical rule. It was meant by what people do in academia: journal articles, books, conferences, and presentations. The order of operations comes into play only once you're ready to tackle the problem, i.e. there is no ambiguity in the equation you're trying to solve.

The problem itself is silly, because you would never start at a point where the problem is "Solve 48÷2(9+3)" in any situation where the correct answer actually means something.

It's not hard and it's not ambiguous. Math is not ambigous.

Mathematics is plenty ambiguous, and at times downright stupid. I can show you that 0.999~ = 1 and 0.999~ != 1. I can show you sets that are both open and closed. I can argue that there are as many points on the real interval between [0,1] and [0,2].

[d0zer]

The amount of controversy generated by this basic arithmetic suggests that the notation is shitty/ambiguous, that the public education system really sucks balls, or some combination of the two.

[Lukie]

rilla, you keep linking to an 11 year old post on a math forum and comparing 'math language' to the 'english language', yet I'm not sure either is really doing what you're thinking it is doing.

The former shows that there has been confusion on the subject for a long time; the latter is completely irrelevant.

[a500lbgorilla]

rilla, you keep linking to an 11 year old post on a math forum and comparing 'math language' to the 'english language', yet I'm not sure either is really doing what you're thinking it is doing.

The former shows that there has been confusion on the subject for a long time; the latter is completely irrelevant.

Well help me understand what they are doing or why they are irrelevant. I'm not going to attempt to rehash the same lines of reasoning.

So please help me understand why the answer is only 288 and the expression is well defined.

[oskar]

I would like to take this moment to congratulate spoon on sucessfully inciting a math flamewar.
Obama got in the white house with a fake id, nuclear power turning japan into a nation of supermen, but ORDER OF OPERATIONS YOU FUCKING MORONS!

[d0zer]

I would like to take this moment to congratulate spoon on sucessfully inciting a math flamewar.
Obama got in the white house with a fake id, nuclear power turning japan into a nation of supermen, but ORDER OF OPERATIONS YOU FUCKING MORONS!

everytime I see another reply to this thread I facepalm.

*self facepalms at posting in this thread yet again*

[spoonitnow]

I would like to take this moment to congratulate spoon on sucessfully inciting a math flamewar.
Obama got in the white house with a fake id, nuclear power turning japan into a nation of supermen, but ORDER OF OPERATIONS YOU FUCKING MORONS!

tyty

[Lukie]

Edit, woops. I accidentally edited your post instead of quoting your post. That's my bad. If you'd edit it back in, that'd be cool. - a500lbgorilla

[a500lbgorilla]

I'll edit mine out too. No reason responding to a post that's not there.

In any case, I concede the argument for reasons I don't even care to appear like I'm right on.

Sometimes, I hate being a nerd.

[Lukie]

i'm a nerd too

it's all good

[JoeHaw]

Agree with everything stilldeadmoney says. and the post where spoon said if you get 2 its because you should be smart enough to infer somebody wrote one thing where they really meant to say something else. yeah it's "technically" 288 by order of operations but you'd be an imbecile to write it like and mean 288

yadayadayada just because the majority of people do it doesnt mean its right /whatever but it doesn't even matter because like somebody said you'd only ever encounter that notation in fifth grade.

[Fielmann]

It's fun stuff.

In the real number system, we define multiplication as repeated addition as sort of a short-hand, just like we define exponents to be a repeated multiplication (which is then a repeated addition as well), and that's where the order of operations for those things comes from. So when we take a different order of operations, we get screwed up stuff like the following.

3*4+4 = 3*8 = 24 (I changed it from 3*4+2 to make sense)
2*1+11 = 2*12 = 24

Set them equal to each other and we have:

3*4+4 = 2*1+11

Subtract 2 from each side and we get:

3*4+4-2 = 2*1+11-2
3*6 = 2*10
18 = 20

The part in bold doesn't seem to be done right.

In the usual order of operations (where multiplication comes before adding) if we want to add/subtract a number to/from both sides we can simply do so:

2*2+1 = 1*3+2
2*2+1-7 = 1*3+2-7

If however, we want to multiply/divide both sides with a number, we need to put the sides in brackets:

2*2+1 = 1*3+2
(2*2+1)*7 = (1*3+2)*7

Otherwise the equation won't stand:

2*2+1*7 = 1*3+2*7

is wrong.

If we change the order of operations (i.e. agree to do adding before multiplication) then this gets reversed. We would have to use brackets when adding/subtracting and we wouldn't have to use them when multiplying/dividing. The original equation thus becomes:

(3*4+4)-2 = (2*1+11)-2

which doesn't lead to any inconsistency.

[spoonitnow]

The part in bold doesn't seem to be done right.

In the usual order of operations (where multiplication comes before adding) if we want to add/subtract a number to/from both sides we can simply do so:

2*2+1 = 1*3+2
2*2+1-7 = 1*3+2-7

If however, we want to multiply/divide both sides with a number, we need to put the sides in brackets:

2*2+1 = 1*3+2
(2*2+1)*7 = (1*3+2)*7

Otherwise the equation won't stand:

2*2+1*7 = 1*3+2*7

is wrong.

If we change the order of operations (i.e. agree to do adding before multiplication) then this gets reversed. We would have to use brackets when adding/subtracting and we wouldn't have to use them when multiplying/dividing. The original equation thus becomes:

(3*4+4)-2 = (2*1+11)-2

which doesn't lead to any inconsistency.

Yeah that's the entire point. If you put addition ahead of multiplication, things get fucked up because addition isn't subject to distribution across multiplication. If instead you put addition ahead of multiplication and add distribution of addition across multiplication, then it's a different story.

However, by adding either rule (or both rules), we're no longer operating in the real number system by definition.

[kiwiMark]

let's all just downrep jowhaw and lock this thread!

[scott_owen]

i can obviously how one can arrive at either 2 or 288. I was taught multiplication before division so i voted 2. not about to argue with a math major though.

[ZwiFT]

To lazy to read through entire thread, someone has probably come to a conclusion but discussion seems to be ongoing. But spent about 30 mins painting the correct answer

[Nekrogovner]

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

Trolololol.

First of all, the question is a obvious troll.

If you have written:


(1)

48
2(9+3)

or

(2)

48
--- (9+3)
2

there would be absolutely no confusion.

And second...since both multiplication and division have the same precedence they should be done in order...from left to right.

Ofc for those here who actually know math they should also know that (1) is correctly written like 48/(2(9+3)).


Same applies for that ridiculous 48/2x example. The correct way to write what you have done is 48/(2x).



And once more: TROLOLOLOLOLOLOLOLOL!!!!

[Nekrogovner]

LOL I didn't even notice there is actually 4 pages of this insanity.

[OngBonga]

How is 2 winning this poll? Trolls or stupids?

[BankItDrew]

I voted 2 but want to change my vote to 288 after reading the thread.

[BankItDrew]

I'd like to change my vote back to 2, because I think everything under the denominator should be done after the brackets.

[BankItDrew]

I might take that back.

[bjsaust]

Fascinating.

I get 288, however its interesting that it basically comes down to interpretation of the rule (solve parenthesis first). So for me, I see:

20/5(2 +2)

Everyone agrees that 2+2 is solved first, but some people interpret "solve parenthesis first" to mean that 5(4) is solved next as it involves parentheses, however I (and I guess the rest of the people that get 288 in the original) consider the implied 5x(4) to be external to the parenthesis so that rule doesn't apply.

[edit] Yeah, I skipped almost the entire thread.

[Sasquach991]

Poker Math
6+5=J
7+7=K
4-3=A
A-13=A
A+A=2 and A+A=28 and A+A=15 and A-A=0,13,-13

2A=2 and 2A=28 then
2(4-3)=2 and 2(A-13)=28 then 2A-26=28 so 2A=54 so A can be 27
2A=15 so A is 7.5

So A can be 1,7.5,14,27,...

[spoonitnow]

This thread was probably one of my more successful trolls.

[Nekrogovner]

Its brilliant. The funniest thing is that 2 increases its lead in a poll.

[ZwiFT]

looks like the answer was 42

[a500lbgorilla]

Boom, son.

YouTube - ‪Re: Visual Multiplication and 48/2(9+3)‬‏

Explained better than I could while giving it the 45 seconds it deserves.

[d0zer]

Boom, son.

YouTube - ‪Re: Visual Multiplication and 48/2(9+3)‬‏

Explained better than I could while giving it the 45 seconds it deserves.

*like*

I like this video of her's also:

YouTube - ‪How To Snakes‬‏