Simple Math?

[Commo_Soldier]

Many have probably seen this in the past few weeks as it has been quite popular on the internet, but I have not seen a thread on this here and am curious what this board thinks.

48÷2(9+3) = ???

http://i56.tinypic.com/16h6ja8.jpg

[Pumpy Tudors]

Seems pretty obvious to me.

[Commo_Soldier]

My understanding is the 2 should not be done with the bracket as you solve what is in the bracket first. Once you add the 9 and 3 together the bracket can disappear and a multiplication sign now exists. Then following the order of operations you get 288.

[RomaGoth]

Pie?

[Pumpy Tudors]

My understanding is the 2 should not be done with the bracket as you solve what is in the bracket first. Once you add the 9 and 3 together the bracket can disappear and a multiplication sign now exists. Then following the order of operations you get 288.
Yeah, that's what I would think. Just because there's no multiplication sign visible doesn't mean that you evaluate the 2*12 before you divide 48 by it.

[Pumpy Tudors]

Now I see the images, and I guess both Texas Instruments and Casio have some 'splaining to do.

[Commo_Soldier]

Seems pretty obvious to me.


That is what I'd think, but I've seen threads on other boards that are almost 3000 posts on such a seemingly obvious problem.

[Comey]

FOFC is behind the times. This has been breaking the internet for the last month. ; )

[RomaGoth]

My understanding is the 2 should not be done with the bracket as you solve what is in the bracket first. Once you add the 9 and 3 together the bracket can disappear and a multiplication sign now exists. Then following the order of operations you get 288.

See, I would think that the parentheses remain, even after you add the 9+3, so you would multiply first, then divide by 48. My calculator's answer is 2 (which is the same as when I did it in my head).

*shurg*

[Tigercat]

I always took 2(9+3) to basically represent one number on that level of the problem, a number that needed to be addressed and placed before you work out anything else on the same level of the problem.

[Pumpy Tudors]

See, I would think that the parentheses remain, even after you add the 9+3, so you would multiply first, then divide by 48. My calculator's answer is 2 (which is the same as when I did it in my head).

*shurg*
Although parentheses come first in order of operations, my understand is that's just for evaluating what's inside the parentheses. Once you have a 12 in the parentheses, it's just an element of the multiplication, and since division and multiplication are equal in the order, you just go from left to right.

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

Although from what folks are saying here, there's some faction on the internet and some calculators that disagree.

[Pumpy Tudors]

Dola

To get the number to be 2, I would think it'd have to be written as 48/(2(9+3)).

[CU Tiger]

4th grade.
Please Excuse My Dear Aunt Sally
Parenthesis, Exponents, Multiply, Divide, Add, Subtract

48 /2(9+3)

Parenthesis, check
48/2(12)
Exponents, nope
Multiply, check
48/ 24
Divide, check
2
done.

[Pumpy Tudors]

4th grade.
Please Excuse My Dear Aunt Sally
Parenthesis, Exponents, Multiply, Divide, Add, Subtract

48 /2(9+3)

Parenthesis, check
48/2(12)
Exponents, nope
Multiply, check
48/ 24
Divide, check
2
done.
Multiplication does not necessarily come before division, though. If you're evaluating something that has only multiplication and division in it, you just work left to right. Same with addition and subtraction.

5-4+3 == 4
5-4+3 != -2

[jbergey22]

4th grade.
Please Excuse My Dear Aunt Sally
Parenthesis, Exponents, Multiply, Divide, Add, Subtract

48 /2(9+3)

Parenthesis, check
48/2(12)
Exponents, nope
Multiply, check
48/ 24
Divide, check
2
done.

+1

[sabotai]

Although parentheses come first in order of operations, my understand is that's just for evaluating what's inside the parentheses. Once you have a 12 in the parentheses, it's just an element of the multiplication, and since division and multiplication are equal in the order, you just go from left to right.

That's the issue with this. There is no standardized order of operations when it comes to "bracket multiplication". Some people say it makes it go ahead of normal division and multiplication in the order of operations (Otherwise it would be written as 48 ÷ 2 * (9+3) ), others say it's just short hand for normal multiplication. But there's no formal rule about it.

[jbergey22]

IT should be written like this instead.

The reason why some people are getting 288 is that they're forgetting that there's an invisible multiply sign in the expression.


http://www.physicsforums.com/latex_images/32/3235069-0.png (javascript:;)

[Pumpy Tudors]

IT should be written like this instead.

The reason why some people are getting 288 is that they're forgetting that there's an invisible multiply sign in the expression.


http://www.physicsforums.com/latex_images/32/3235069-0.png (javascript:;)
No, I am absolutely aware that there's an invisible multiplication sign. In fact, that sign is precisely why I'm saying it's 288.

To sabotai's point, if there's no formal rule for the "bracket multiplication", then we'll never get everybody to come to agreement. The points both sides make are pretty obvious. It's just a matter of which you agree with. Given that this makes the discussion rather futile, I guess I'm done here.

[sabotai]

That's a separate problem. Written that way, you'd do the multiplication first regardless of the debate over the way the multiplication is written since you always fully work out the numerator and denominator first before dividing.

48 ÷ 2(9+3) is not the same thing as that.

For instance: 40 * 2 / 10 * 10

If that division sign is shorthand for a fraction, then the answer is 0.8, since you do both multiplications first. If it's simply division, than the answer is 80, since you work left to right.

[Schmidty]

Math sucks.

[jbergey22]

Well shit. I have we even come to a time when we cant even agree on math answers.

I always assumed the order was like CU Tigers post but now the more I am reading up on this it appears around 50 percent of the nation use the same method as I believe Pumpy is using where

P
E
MD
AS

[sabotai]

To sabotai's point, if there's no formal rule for the "bracket multiplication", then we'll never get everybody to come to agreement. The points both sides make are pretty obvious. It's just a matter of which you agree with. Given that this makes the discussion rather futile, I guess I'm done here.

Yes, it's just like every other debate on the internet. :)

It's just what I read when it looked it up a week or two ago. There may be a formal ruling somewhere, but Google is keeping it secret from me.

[Commo_Soldier]

IT should be written like this instead.

The reason why some people are getting 288 is that they're forgetting that there's an invisible multiply sign in the expression.


http://www.physicsforums.com/latex_images/32/3235069-0.png (http://javascript%3Cb%3E%3C/b%3E:;)

There are actually two ways for it to be written. So I believe it is safer to stick with the order of operations rather than pick which way it should be written out on paper.
http://i804.photobucket.com/albums/yy322/mrtonyali13/IMG00018-20110408-1647-1.jpg

That's the issue with this. There is no standardized order of operations when it comes to "bracket multiplication". Some people say it makes it go ahead of normal division and multiplication in the order of operations (Otherwise it would be written as 48 ÷ 2 * (9+3) ), others say it's just short hand for normal multiplication. But there's no formal rule about it.

I'd argue if there is no formal rule one should go with a formal rule. Order of operations states you complete what is only inside the parentheses first. When the 2 appears next to them all it really is saying is multiply in shorthand as you stated. Which to me means it should be treated as such in the order of operations.

[Commo_Soldier]

Yes, it's just like every other debate on the internet. :)

It's just what I read when it looked it up a week or two ago. There may be a formal ruling somewhere, but Google is keeping it secret from me.


If we are going off of Google (http://www.google.com/#hl=en&sugexp=gsqvhc&xhr=t&q=48%C3%B72%289%2B3%29&cp=9&qe=NDj3Mig5KzMp&qesig=VfHPozfSXJZ1GEnG-Ar59Q&pkc=AFgZ2tnZDQ--jrP5dagxTj9LN9-GQPyFAQ9Eq2WjER_W_6hhhPsUDOk-cWk_WlmHEuf2fuRN8SBE-6ZEsGLBRo4V5_3qOPRWRg&pf=p&sclient=psy&site=&source=hp&aq=f&aqi=&aql=&oq=48%C3%B72%289%2B3%29&pbx=1&fp=6e51f3b7bd5a4d48)...

[fantom1979]

I believe the answer is 288

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

[sabotai]

I'd argue if there is no formal rule one should go with a formal rule. Order of operations states you complete what is only inside the parentheses first. When the 2 appears next to them all it really is saying is multiply in shorthand as you stated. Which to me means it should be treated as such in the order of operations.

There's also the rule that a(b + c) = (ab + ac)

So that 48 ÷ 2(9 + 3) = 48 ÷ ((2 * 9) + (2 * 3)) = 48 ÷ (18 + 6) = 48 ÷ 24 = 2

[jbergey22]

48/2(9+3).............................? - Yahoo! Answers (http://answers.yahoo.com/question/index?qid=20110408131705AAGkueR)

I think this best sums it up.

[stevew]

You guys probably stand up to wipe your asses after you take a shit too, i bet. 288?gtfo---->

[sabotai]

There's a very easy way to find out which is the correct answer, though. Replace one of the values with "x" and try to solve for both answers. I'll replace the 2 outside of the brackets with an x and which ever answer solves "x = 2" (to get us back to the original equation) is the correct answer.

48 ÷ x(9+3) = 288
48 ÷ (9x + 3x) = 288
48 ÷ 12x = 288
48 ÷ 12x * 12x = 288 * 12x (The two 12x on the left cancel each other out)
48 = 288 * 12x (divide both sides by 288)
48 ÷ 288 = 288 * 12x ÷ 288 (the two 288s on the right cancel out)
48 ÷ 288 = 12x (now divide both sides by 12)
48 ÷ 288 ÷ 12 = 12x ÷ 12
48 ÷ 288 ÷ 12 = x
0.013888888888888888888888888888889 = x

Well that didn't work out. Let's try 2

48 ÷ x(9 + 3) = 2
48 ÷ (9x + 3x) = 2
48 ÷ 12x = 2
48 ÷ 12x * 12x = 2 * 12x (The two 12x on the left cancel each other out)
48 = 2 * 12x (divide both sides by 2)
48 ÷ 2 = 2 * 12x ÷ 2 (the two 2s on the right cancel out)
48 ÷ 2 = 12x (now divide both sides by 12)
48 ÷ 2 ÷ 12 = 12x ÷ 12
48 ÷ 2 ÷ 12 = x
2 = x


The answer is 2.

:D

[Pumpy Tudors]

There's a very easy way to find out which is the correct answer, though. Replace one of the values with "x" and try to solve for both answers. I'll replace the 2 outside of the brackets with an x and which ever answer solves "x = 2" (to get us back to the original equation) is the correct answer.

48 ÷ x(9+3) = 288
48 ÷ (9x + 3x) = 288
48 ÷ 12x = 288
48 ÷ 12x * 12x = 288 * 12x (The two 12x on the left cancel each other out)
48 = 288 * 12x (divide both sides by 288)
48 ÷ 288 = 288 * 12x ÷ 288 (the two 288s on the right cancel out)
48 ÷ 288 = 12x (now divide both sides by 12)
48 ÷ 288 ÷ 12 = 12x ÷ 12
48 ÷ 288 ÷ 12 = x
0.013888888888888888888888888888889 = x

Well that didn't work out. Let's try 2

48 ÷ x(9 + 3) = 2
48 ÷ (9x + 3x) = 2
48 ÷ 12x = 2
48 ÷ 12x * 12x = 2 * 12x (The two 12x on the left cancel each other out)
48 = 2 * 12x (divide both sides by 2)
48 ÷ 2 = 2 * 12x ÷ 2 (the two 2s on the right cancel out)
48 ÷ 2 = 12x (now divide both sides by 12)
48 ÷ 2 ÷ 12 = 12x ÷ 12
48 ÷ 2 ÷ 12 = x
2 = x


The answer is 2.

:D
I guess I'm not done here. I can't resist.

You're taking a hell of a leap here on the bolded parts. The distributive property doesn't tell you to put those pieces in parentheses. a(b + c) = ab + ac, necessarily. a(b + c) does not imply (ab + ac) when put into an equation as above.

[sabotai]

I guess I'm not done here. I can't resist.

You're taking a hell of a leap here on the bolded parts. The distributive property doesn't tell you to put those pieces in parentheses. a(b + c) = ab + ac, necessarily. a(b + c) does not imply (ab + ac) when put into an equation as above.

Yes, yes, I know the debate is if you can do that or not. I'm just being difficult. And bored. And wide awake at 2 am.

I'm just happy I got Serious Pumpy to make a special appearance on FOFC. :D

[BishopMVP]

2/3

[Pumpy Tudors]

Yes, yes, I know the debate is if you can do that or not. I'm just being difficult. And bored. And wide awake at 2 am.

I'm just happy I got Serious Pumpy to make a special appearance on FOFC. :D
Well, I'm not even sure if people who are asserting one or the other even think about it that way. Your post just seemed so definitive that I was trying to squelch others' cheers of "SEE, IT'S CLEARLY 2!!! THERE'S THE PROOF!!!" because I'm being difficult, too.

I'll acknowledge that a case could be made either way, so I'll concede this as somewhat ambiguous. With that said, I still can't parse the logic that shows the answer as 2, but that could be my fault.

And I'm only serious because I used up all my fun at bowling a few hours ago. So you did catch me at the right time.

[Groundhog]

I haven't heard of this till just now, but using what I was taught in high school, I got 288.

[stevew]

403 Forbidden (http://knowyourmeme.com/memes/48293)

[britrock88]

...I'm just confusing myself.

[jbergey22]

48÷2(9+3) = ???

That part screws me up ÷


48/2(9+3)=288

Either learned or assumed the fact that the 2 was linked to the parentheses made me think I needed to multiply that part first.
In order for this equation to equal 2 it should look like 48/(2(9+3))

Id like to change my vote:)

[QuikSand]

The answer I get is too gross to share.

[Mustang]

Well shit. I have we even come to a time when we cant even agree on math answers.

I always assumed the order was like CU Tigers post but now the more I am reading up on this it appears around 50 percent of the nation use the same method as I believe Pumpy is using where

P
E
MD
AS

That is the method I was taught so I got 288.

[mckerney]

If we are going off of Google (http://www.google.com/#hl=en&sugexp=gsqvhc&xhr=t&q=48%C3%B72%289%2B3%29&cp=9&qe=NDj3Mig5KzMp&qesig=VfHPozfSXJZ1GEnG-Ar59Q&pkc=AFgZ2tnZDQ--jrP5dagxTj9LN9-GQPyFAQ9Eq2WjER_W_6hhhPsUDOk-cWk_WlmHEuf2fuRN8SBE-6ZEsGLBRo4V5_3qOPRWRg&pf=p&sclient=psy&site=&source=hp&aq=f&aqi=&aql=&oq=48%C3%B72%289%2B3%29&pbx=1&fp=6e51f3b7bd5a4d48)...

And if we're going off of Wolfram (http://www.wolframalpha.com/input/?i=48%2F2%289%2B3%29).

[TargetPractice6]

Anyone that says 2 is wrong. There is no ambiguity. If you want to use the distributive property, then 24 (not 2) must be distributed over the additive clause so it becomes (9*24) + (3*24).

[JWAH]

obviously the correct answer is simply 42

[mckerney]

<iframe width="480" height="390" src="http://www.youtube.com/embed/8wHDn8LDks8" frameborder="0" allowfullscreen></iframe>

[SteveMax58]

It's been a while since I've contemplated this type of ruleset with any conscious effort.

Going on what I recall being taught (which may not be the correct recollection)...my answer would have been 2. After checking with Excel, I see I am incorrect (btw...excel forces the * between the 2 and the (9+3) ). :)

But thinking about it further...I see I would be wrong on many occasions.

5+3/1+3 = 11

11 doesn't feel natural to me as I would tend to solve the sides of the fraction (in my mind) and come up with 2.

Hmm...not much of a point to my post other than to point out how evil & tricky the number 2 can be.

[21C]

I saw this problem on another site. I teach Math and have a Math degree and it is funny to me that all of the mathematicians agree that the answer is 288. :)

[Ronnie Dobbs2]

<iframe width="425" height="349" src="http://www.youtube.com/embed/bwpWw-iVKHc" frameborder="0" allowfullscreen></iframe>

[Passacaglia]

Well, it's a good bit of comeuppance for anyone who's ever said, "why do we need to learn this stuff? Let the calculator do it."

[Suburban Rhythm]

I'm just happy I got Serious Pumpy to make a special appearance on FOFC. :D

This is the most incomprehensible part of this whole thread.

[tyketime]

288 looks right to me. Evaluate the parenthesis first, then work left to right since division and multiplication are both the same level of "importance".

[gstelmack]

This is why when I write code, I put all the parentheses in to make sure the compiler evaluates it in the order I intended. I'd hate for the PS3 compiler to evaluate it one way and the 360 compiler to evaluate it another.

I agree, the original formula is a stupid way of writing out what you want, just like 4 * 2 / 10 * 3 is stupid. Put the parentheses in to be clear.

That said, I'm on the side of "you solve math problems via simplification". So when you write 48 / 2 ( 9 + 3 ) you get:

48 / 2 (12) = 48 / 2 * 12 = 24 * 12 = 288

Anyone else is just getting tricky with the formula. They're not WRONG per se, they're just going about math the hard way...

[Butter]

Anybody doing any kind of serious math would not write it in such a sloppy format, so the whole debate is kind of pointless.

But I personally got "2". In any math problem, I consider anything after the division sign to ALL be the divisor, so it would be 48 over (2*(9+3)). Obviously, so do about half the people on here and around the internets.

OR I would say quit writing your problems in such a douchey way to allow different interpretations and be clear.

[Drake]

Anybody doing any kind of serious math would not write it in such a sloppy format, so the whole debate is kind of pointless.

But I personally got "2". In any math problem, I consider anything after the division sign to ALL be the divisor, so it would be 48 over (2*(9+3)). Obviously, so do about half the people on here and around the internets.

OR I would say quit writing your problems in such a douchey way to allow different interpretations and be clear.

This.

And what Greg said.

I see this as the language equivalent of substituting homophones for the word you actually mean. Sure, I can make sense of it, but you may not be conveying the information you intended with the correct level of precision.

Or you're just being a douche.

[Pumpy Tudors]

Anybody doing any kind of serious math would not write it in such a sloppy format, so the whole debate is kind of pointless.

But I personally got "2". In any math problem, I consider anything after the division sign to ALL be the divisor, so it would be 48 over (2*(9+3)). Obviously, so do about half the people on here and around the internets.

OR I would say quit writing your problems in such a douchey way to allow different interpretations and be clear.
Doesn't this risk violating order of operations, then?

3/2*2 is obviously very different from 3/(2*2). In the first case, since multiplication and division hold the same precedence, evaluate from left to right. In the second case, the parentheses are clearly evaluated first.

Going back to the original problem, it seems like a bad idea to write 48/2*(9+3) when you mean to write 48/(2*(9+3)). Then again, it also seems like we all agree that the problem is badly written in the first place, although it's apparently done that way on purpose to polarize us and make us think somebody out there is stupid. So, yeah, internet in a nutshell, I guess.

[DanGarion]

According to Wolfram Alpha

288

48/2(9+3) - Wolfram|Alpha (http://www.wolframalpha.com/input/?i=48%2F2%289%2B3%29)

[Rizon]

Many have probably seen this in the past few weeks as it has been quite popular on the internet, but I have not seen a thread on this here and am curious what this board thinks.

48÷2(9+3) = ???

http://i56.tinypic.com/16h6ja8.jpg

I said 2, but now that I think about it doesn't the Order of Operations for multiplication and division state you multiply and/or divide from left to right? If so, then it's 288.

[Rizon]

Dola

The correct answer in accounting to this question is "whatever the hell I want it to be". So being an accountant, I'm going with that one.

[terpkristin]

42

/tk

[Marc Vaughan]

48÷2(9+3) = ??

BODMAS = Binary, Operator, Divide, Multiply, Addition, Subtraction

Hence write it long hand:
48 / 2 x ( 9 + 3 )
Brackets first =
48 / 2 x 12
Divide Next
24 x 12
Multiply Next
288

At least thats how a computer would undertake it; personally I'd say any coder who wrote an equation like that needs shooting - as its not instantly clear what it'll do and bracketing takes 2 minutes to do and makes reading equations FAR simpler.

[Rizon]

48÷2(9+3) = ??

BODMAS = Binary, Operator, Divice, Multiply, Addition, Subtraction



I think where a lot of people were hung up was that the correct way to say this is Binary, Operator, Divide and/or Multiply left to right, Addition and/or Subtraction left to right. So it's really BODAOML2RAAOSL2R

[Rizon]

personally I'd say any coder who wrote an equation like that needs shooting - as its not instantly clear what it'll do and bracketing takes 2 minutes to do and makes reading equations FAR simpler.

I think this is my final answer, too. It's unsolvable because of the lack of brackets. 2(9+3) doesn't necessarily mean 2*(9+3), so it's left to the interpretation of the reader. I can see an argument for both 2 and 288 because of that.

[Pumpy Tudors]

I think this is my final answer, too. It's unsolvable because of the lack of brackets. 2(9+3) doesn't necessarily mean 2*(9+3), so it's left to the interpretation of the reader. I can see an argument for both 2 and 288 because of that.
If 2(9+3) doesn't necessarily mean 2*(9+3), what else could it mean?

[jbergey22]

If 2(9+3) doesn't necessarily mean 2*(9+3), what else could it mean?

(2*(9+3)) is how I initially thought of it as.

[Rizon]

It's a trick question that can't be answered unless you assume something. Basically a troll math question to divert nerds attentions away from the Death Star long enough to set up a trap.

[BillJasper]

I came up with 288. :lol:

[heardie]

Really, 2 pages? Come on...

There is obivously no correct, cannonical, answer to this. The question, as stated is ambigious.

Getting google,yahoo or whatever to calculate is useless, as it just depends on the algorithm they use to intepert your input.

Edit: Aggh, see this has been dormant for a few days. Hope I don't awaken the beast...

[Pumpy Tudors]

Really, 2 pages? Come on...

There is obivously no correct, cannonical, answer to this. The question, as stated is ambigious.

Getting google,yahoo or whatever to calculate is useless, as it just depends on the algorithm they use to intepert your input.

Edit: Aggh, see this has been dormant for a few days. Hope I don't awaken the beast...
Buzzkill. Would you mind stepping into some other threads and telling us how many pages the topic warrants? Thanks in advance.

[Passacaglia]

So is 2 pages too many or too few? Are you saying that since it's ambiguous, we should be arguing about it more, or that since it's ambiguous, we should all check the 'no answer' box and move on?

That said, personally, I hope you *do* awaken the beast.

[albionmoonlight]

I voted 2 b/c that was my gut instinct.

But, having read this thread, I think that I would change to either "trout" or "288."

[Raiders Army]

Between this and Beyonce's Run the World which has a line that says "Who run the world?" numerous times, I weep for the United States. We can't do simple math and we can't speak correctly.

[Johninja]

I just don't see how this type of mathematics would be relevant in a real life situation. Trout.