# 48÷2(9+3)=?

#### bliebblob

##### Plushy wrangler, die-curious
Keava said:
Your way i guess you would do:
48:2(x+3) = 2
48:2x+6 = 2 | -6
48:2x = 2 - 6
48:2x = -4
and.. it would be that x has to be negative number.
The only way it would work is if 2(x+3) was written as [2(x+3)] since then you would have
48 2x+6) = 2 so 48 = 2(2x+6) so 48 = 4x + 12 so 4x = 36
When you drop brackets you can't suddenly create another set out of nowhere. It's not how mathematics work.

the third line is wrong
This would be clear if you wrote above and below lines instead of everything in one line so I'll try to do so as best as I can in this texthingy:

48:2(x+3)=2 is the same as
48
-------- = 2 because 2(x+3) is a single term, just as 3x
2(x+3)

48
-------- = 2
2x+6

Hopefully now you see you cannot move the 6 to the other side as -6. You have to move the entire lower part to the other side as *(2x+6)

#### InfiniteSingularity

##### New member
Keava said:
InfiniteSingularity said:
2(9+3) is part of "Brackets" in BODMAS. Yes, even the 2 is part of it. So by definition, it is one term. Because the brackets are evaluated before anything else. And 2(9+3) = 24. You do not half-expand the brackets, by saying it equals 2 times 12, then moving the 2 to the other side of the division.

Remember that 2 is the coefficient of (9+3), so it is ALWAYS bound to (9+3). When you take it out in your fraction, you are separating it from it's coefficient. Or with the distributive law of multiplication, you are moving the 12 to the other side of the division sign, which doesn't work. So either way you are doing it wrong.
I have no damn idea what BODMAS is because in my times, in my country they didn't teach using mnemonics. Want to know why? Because mnemonics are not rules. They taught me, however, how to solve math problems.

2 is not part of any brackets. 2 is 2. Noting more, nothing less. Solve the x in my post and you will see.

Your way i guess you would do:
48:2(x+3) = 2
48:2x+6 = 2 | -6
48:2x = 2 - 6
48:2x = -4
and.. it would be that x has to be negative number.
The only way it would work is if 2(x+3) was written as [2(x+3)] since then you would have
48 2x+6) = 2 so 48 = 2(2x+6) so 48 = 4x + 12 so 4x = 36
When you drop brackets you can't suddenly create another set out of nowhere. It's not how mathematics work.

Now 48:2(x+3) = 288
24(x+3)=288
24x+72=288 | -72
24x=216 | :24
x = 9

Magick.
No, I would go

48:2(x+3) = 2
48:2x+6 = 2
2x+6:48 = 1:2 (note that when in an equation, taking the reciprocal of BOTH sides retains the equality. And i did use 2x+6 as one whole term)
2x+6 = 48:2
2x = 24 - 6
x = 18/2 = 9

The "extra set of brackets" you refer to is implied in the brackets - as 2 is multiplied by (x+3) by definition it is part of the bracket. So 2(x+3) is the denominator underneath 48.

And BODMAS is a fundamental rule for solving linear equations. So you solve the brackets first. Which means OP's question should be resolved to 48/24 which equals 2.

#### ACman

##### New member
Gentlemen we have been trolled.

http://knowyourmeme.com/memes/48293

#### Keava

##### New member
InfiniteSingularity said:
No, I would go

48:2(x+3) = 2
48:2x+6 = 2
2x+6:48 = 1:2 (note that when in an equation, taking the reciprocal of BOTH sides retains the equality. And i did use 2x+6 as one whole term)
2x+6 = 48:2
2x = 24 - 6
x = 18/2 = 9
But it's not a whole term. That's the point. It's not 48 2x+6) it's 48:2x+6. There is a huge difference between the two, difference that the brackets are used for. You pretty much added those brackets despite them not existing in original calculation.

What you did was taking 2*2+1 and turning it into 2(2+1). See the difference?

#### bliebblob

##### Plushy wrangler, die-curious
ACman said:
Gentlemen we have been trolled.

http://knowyourmeme.com/memes/48293

I knew it was a troll question from the start but like I told the other guy who said so:
I'm pretty sure it IS correct form. Just really easily confused. A few extra brackets would have been nice to avoid confusion though.
It's like in chemistry where you can (for example) leave out the number that indicates where the Cl atom is located on a molecule because it can't be in any other spot anyway. ( because of certain properties of the molecule etc.)
It is correct form but you have to be pretty good at chemisty to just instantly see the H atom can only be in that spot. So not leaving the number out is just best to avoid confusion.
It's the same story here (I think): they left out some brackets in a way that is legit, because it can still only be interpreted in one way, but it makes confusion much more likely.

#### ACman

##### New member
I still think that the multiplication is implied.

So 2.

#### Morti

##### New member
ACman said:
I still think that the multiplication is implied.

So 2.
But not everyone subscribes to the principal of implied multiplication because it is not part of the standard order of operations:
terms inside parentheses or brackets
exponents and roots
multiplication and division

alot of people do though (which is why this verbal tug-o-war is happening), meaning that the correct answer is to tell the OP to "STFU, only noobs use "÷", pro's use brackets!".

#### bliebblob

##### Plushy wrangler, die-curious
Going over the knowyourmeme page again I think I found the heart of the problem:

It IS ambigious because it can be interpreted as

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

or as

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

Neither is truly wrong because this:

x(a+b)

IMPLIES it is a single term but apparently it's not an actual rule. So now we know why our teachers at some point started to insist we use big divisionlines instead of "÷"

So yeah, that'll show me for getting into a forum argument. But hey, everyone won And it actually was a pretty fun brainexercise.

Now, anyone got a good idea for revenge on OP?

#### dday4you

##### New member
bliebblob said:
Going over the knowyourmeme page again I think I found the heart of the problem:

It IS ambigious because it can be interpreted as

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

or as

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

Neither is truly wrong because this:

x(a+b)

IMPLIES it is a single term but apparently it's not an actual rule. So now we know why our teachers at some point started to insist we use big divisionlines instead of "÷"

So yeah, that'll show me for getting into a forum argument. But hey, everyone won And it actually was a pretty fun brainexercise.

why revenge?

Now, anyone got a good idea for revenge on OP?

It's 2, easy.

#### Axolotl

##### New member
theklng said:
Cogwheel said:
Well, you'd handle the division first.

Which would mean it's 24x12, so yes, 288.

Edit: Apparently I'm a complete idiot.
Axolotl said:
There is no correct answer. The whole BEDMAS or Order of Operations thing is primarily based on custom and is taught differently in different parts of the world. The question uses that to be ambiguous, it is not a "real" mathematical question so much as hook to try and start semantical arguements based on pointless mathematical principles that nobody above the age of 12 should be bothering with.

TL R It's a troll thread.
you know a computer actually uses these operations in a uniform fashion right? and without that uniformity, you wouldn't be able to write that message.
A computer will yes. Two seperate computers may calculate them differently however. For example I personally have two calculators of different models (for refrence a CASIO fx-83GT PLUS and a CASIO fx-83ES) they give me different answers, one says 2 the other 288. This is because they've been made by different people who were taught different methods of order of operations because there are no uniformly agreed set of rules for order of operations. This is because it is not real mathematics, it is a crutch for people who do not understand how the write mathematical questions.

#### theklng

##### New member
Axolotl said:
theklng said:
Cogwheel said:
Well, you'd handle the division first.

Which would mean it's 24x12, so yes, 288.

Edit: Apparently I'm a complete idiot.
Axolotl said:
There is no correct answer. The whole BEDMAS or Order of Operations thing is primarily based on custom and is taught differently in different parts of the world. The question uses that to be ambiguous, it is not a "real" mathematical question so much as hook to try and start semantical arguements based on pointless mathematical principles that nobody above the age of 12 should be bothering with.

TL R It's a troll thread.
you know a computer actually uses these operations in a uniform fashion right? and without that uniformity, you wouldn't be able to write that message.
A computer will yes. Two seperate computers may calculate them differently however. For example I personally have two calculators of different models (for refrence a CASIO fx-83GT PLUS and a CASIO fx-83ES) they give me different answers, one says 2 the other 288. This is because they've been made by different people who were taught different methods of order of operations because there are no uniformly agreed set of rules for order of operations. This is because it is not real mathematics, it is a crutch for people who do not understand how the write mathematical questions.
http://en.wikipedia.org/wiki/Reverse_Polish_notation

we're talking computers here son, not some cheapskate calculators. reverse polish notation is used in every stack based machine, which includes pretty much every cpu over the past 20 years. this ensures uniformity.

#### TiefBlau

##### New member
theklng said:
TiefBlau said:
theklng said:
you're wrong. you release brackets first, so it would be 48/(18+6)
Oh dear. I don't think "release brackets" means what you think it means.

You operate on the brackets, meaning, whatever's inside the brackets is calculated first.

Hence, you first calculate (9+3) to be 12. Then it's multiplication/division, so you go left to right.

You don't distribute the 2. That's not even what the "brackets" operation is. Distribution is multiplication, which is interchangeable with division, so even if you wanted to do it that way, it'd be like this:

48 / 2 * (9+3)
24 * (9+3)
216 + 72
288
theklng said:
your other example is faulty logic, 48 - 2 + 12 = 48 + 10 = 58 (incidentally, (48 - 2) + 12 = 46 + 12 = 58).
You still don't get it...
you're talking to a programmer here, i've been doing math for longer than you've lived. i do these equations pretty much every day, why else would i link the goddamn system that makes everything uniform?
Holy shit, I didn't know I was talking to a programmer. Allow me to alter the foundations of basic arithmetic to accommodate someone of your incredible stature.

You're also going to need to contact Sun Microsystems on their serious error in judgment, because in Java, 48 / 2 * (9+3) still equals 288. I'd hate to think of the catastrophic failures that might have stemmed from this oversight.

And while I'd hate to think of the kind of math you've been doing, I'm actually kind of curious to see the kind of person (assuming you have done mathematics for longer than I've lived) that can breeze by differential equations and discrete mathematics without a basic grasp of arithmetic and the order of operations. I can't imagine you could possibly acquire a firm understanding of the chain rule if you didn't know what goes inside or outside brackets, so please, enlighten a scrub like myself.

#### theklng

##### New member
TiefBlau said:
theklng said:
TiefBlau said:
theklng said:
you're wrong. you release brackets first, so it would be 48/(18+6)
Oh dear. I don't think "release brackets" means what you think it means.

You operate on the brackets, meaning, whatever's inside the brackets is calculated first.

Hence, you first calculate (9+3) to be 12. Then it's multiplication/division, so you go left to right.

You don't distribute the 2. That's not even what the "brackets" operation is. Distribution is multiplication, which is interchangeable with division, so even if you wanted to do it that way, it'd be like this:

48 / 2 * (9+3)
24 * (9+3)
216 + 72
288
theklng said:
your other example is faulty logic, 48 - 2 + 12 = 48 + 10 = 58 (incidentally, (48 - 2) + 12 = 46 + 12 = 58).
You still don't get it...
you're talking to a programmer here, i've been doing math for longer than you've lived. i do these equations pretty much every day, why else would i link the goddamn system that makes everything uniform?
Holy shit, I didn't know I was talking to a programmer. Allow me to alter the foundations of basic arithmetic to accommodate someone of your incredible stature.

You're also going to need to contact Sun Microsystems on their serious error in judgment, because in Java, 48 / 2 * (9+3) still equals 288. I'd hate to think of the catastrophic failures that might have stemmed from this oversight.

And while I'd hate to think of the kind of math you've been doing, I'm actually kind of curious to see the kind of person (assuming you have done mathematics for longer than I've lived) that can breeze by differential equations and discrete mathematics without a basic grasp of arithmetic and the order of operations. I can't imagine you could possibly acquire a firm understanding of the chain rule if you didn't know what goes inside or outside brackets, so please, enlighten a scrub like myself.
this equation has already been resolved as ambiguous. i took the liberty of finding the a source related to this, explaining why it has been deemed as ambiguous:

I?m a math professor, and my view is that although the standard convention, if applied precisely and rigorously, does give an unambiguous procedure to follow, nobody, and that includes professional mathematicians, would ever write a formula like this. This is mostly because, after about 3rd grade, none of us ever use the division symbol ever again.

or in the case you don't believe that, here's a comparison between the two:

and

http://www.wolframalpha.com/input/?i=48%C3%B72%289%2B3%29

oh and: obviously even if i did do arithmetic errors in my code, it'd be fixed way before any sort of release due to this thing called testing. and even if an arithmetic fault would slip through that,given that i'm not in the medicinal or third party medicinal business, what i do isn't exactly living up to your hyperbole.

#### luke10123

##### New member
TheKwertyeweyoppe said:
luke10123 said:
BODMAS
brackets of divide multiply add subtract.
that's maths for a ten year old I'm kinda sick of the people who come into this thread thinking it's simple maths and boasting about dumb we are while completely missing the point of the thread because I can only assume they didn't bother to read it.
1) It really IS simple maths.
2) missing the point of the thread am I? "is it 2 or 288?" I really don't see how...
3) I believe you meant to say 'about HOW dumb we are'. Believe that shows it didn't need saying...

#### cookyy2k

##### New member
MercurySteam said:
Titan Buttons said:
must not be a scientific Calculator, normal ones are not programed to prioritise brackets
cookyy2k said:
Most calculators also say sqrt(-1) is syntax error and that ain't right. those things need to be used as a tool not trusted completly. Also different calculators say different results for this since it's ambiquous.
My calculator is a Casio fx-82AU and it clearly says "Scientific Calculator" on the front. They're given out by our school for use from years 8-12 and are approved by the Board of Studies to use in all exams. Trust me when I say that this calculator is the correct one to work an equation out with.

Besides, I showed you how I did it on paper with the working so the calculator is irrelevant.
Doesn't really matter what type your calculator is. Different calculators give different results for the problem... Also type root(-1) in, syntax error is not the answer, calculators are wrong in certain instances, hell take a calculator as advanced as you want and you have a computer and even they can give wrong answers in certain instances. A calculator is a nice tool to help with such things but really you should never rely on one completly.

edit: my scientific, every day use calc gives 288. My graphical, bust out for trickier stuff gives 2.

#### DaMullet

##### New member
Cerdog said:
No. You are completely missing the point of what everyone is saying. Even if you ignore the different rules for variables and constants, your maths is incorrect. Let's look at the first line:

48/2(9+x)=2

What you have done is distributed the 2 into the brackets. THIS IS INCORRECT. As this is multiplication, and not "part of the brackets", you have to do division and multiplication from left to right, as they have equal precedence. So rather than:

48/(18+2x)=2

you should have:

24(9+x)=2
216+24x = 2
24x = -214
x = -8.917

Which is not 3, obviously.

Despite your algebraic method, you are still falling for the trap that so many others are falling for, which is to assume that the 2 is part of the brackets, which is WRONG. Algebra does not make your answer more valid, especially when the core idea of the method, which happens to be what people have been trying to tell you is wrong, is completely overlooked.
So... let's do it your way then

48/2(9+x)=288
24(9+x)=288
216+24x=288
24x=72
x=3

........... UH...............

Interesting. No wonder this is a debate.

Alright, so what's the difference between 2(1+1) and 2*(1+1)?

and if they're not, why write it like that? Cause now I'm curious

#### cookyy2k

##### New member
DaMullet said:
Interesting. No wonder this is a debate.

Alright, so what's the difference between 2(1+1) and 2*(1+1)?

and if they're not, why write it like that? Cause now I'm curious
2(1+1)=2*(1+1)... when missed out the multiplication is implied. It all depends on if you really feel the need to explicitly state multiplication or not.

EDIT:

The answer is either.... it's implicit. it depends how you interpret the question when it's condenced to one line.

24
------
2(9+3)​

24
---- (9+3)
2​

And you know what... it's ambiguous which you interpret that one line of text to be. It's an implied relation which people can read 2 ways. This would have to be made explicit which before one answer could be chosen. As it stand it can be EITHER.

#### DaMullet

##### New member
cookyy2k said:
DaMullet said:
Interesting. No wonder this is a debate.

Alright, so what's the difference between 2(1+1) and 2*(1+1)?

and if they're not, why write it like that? Cause now I'm curious
2(1+1)=2*(1+1)... when missed out the multiplication is implied. It all depends on if you really feel the need to explicitly state multiplication or not.

EDIT:

The answer is either.... it's implicit. it depends how you interpret the question when it's condenced to one line.

------
2(9+3)

---- (9+3)
2

And you know what... it's ambiguous which you interpret that one line of text to be. It's an implied relation which people can read 2 ways. This would have to be made explicit which before one answer could be chosen. As it stand it can be EITHER.
Hmm... okay.

So, how do you work out x/2(9+3)=288 and 48/x(9+3)=288?

#### cookyy2k

##### New member
DaMullet said:
So, how do you work out x/2(9+3)=288 and 48/x(9+3)=288?
Again these are implicit statements due to one line condencement.

Is it x/(2(9+3)) or (x/2)(9+3)? the brackets are required to make these explicit statements.