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288 or 2 ?

  • 288

    Votes: 154 48.4%
  • 2

    Votes: 164 51.6%

  • Total voters
    318
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Implied parentheses? That's a new one on me.

That's basically the gist of the AMS link earlier in the thread. According to that:

2%29%28%5Cpi%20i%29%29.gif


EDIT: What's strange for me is that I do interpret the above in the way that could lead me to interpret the original equation as 2 instead of 288, but only when typeset, and the extra parentheses around it also help provide the hint.

Why is x/y(a+b) different for me than:
y%28a%2Bb%29%29.gif
wish I knew.

B
 
Last edited:
1. How do you figure that? What does a "pause" mean in mathematics? :confused:

if you 'read' a mathematical expression using 'words' than you have to convey order or operations, grouping or parenthesis in some way, like commas or pauses, to avoid ambiguities.

usually "2x" within an equation is considered a 'group', so y/2x is "y divided by (or over) two-x".
If you want to expand the "two x" into the implied "two times x", you still have to maintain the idea that it is a group and as such takes precedence, so your sentence should be "y divided by __pause__ two times x", or with a comma "y divided by, two times x".
On the other hand, if you want to convey (y/2)*x you should write "y divided by two __pause__ times x" or "y divided by two, times x" to avoid confusion.

in the same way, if you see 1/2π it is normally read as "1 over 2 Pi", not "half Pi". Obviously it would be clearer if it was 1/(2π), but most people would still get it right. If you wanted to convey "half Pi" you should write π/2 or (1/2)π or as a minimum 1/2 π (with the space, still ambiguous but better).

In any case, this and the ton of similar threads on the web should clearly indicate that obviously there is no consensus on how to read the original expression, because it is ambiguous.
 
All these implied groupings are sloppy nomenclature. If you're not going to follow order of operations, then add brackets so that you are.

When I code, I add redundant brackets, and don't rely on order of operations. People can't help but understand my code.

And to all the PEMDAS people, multiplcation and division have equal weighting, just like addition and subtraction have equal weighting, they're evaluated left to right.
 
It's 2. Google must be auto-interpreting your format into something different than intended for some reason and causing an error in the OOO.

The entire point of formatting is to not require interpretations.

Which means, of course, the answer is actually 288 and not 2. The author probably means for the answer to be 2, but as written, it is not 2.
 
You have an error in the order of operations. It's 288. Please read the thread before posting. It's been proven over and over and over.

Sure I'll read 300+ posts in each thread I decide to post in... Further, I edited my post into a more rational, less "this IS the answer" one before you even finished replying.

The entire point of formatting is to not require interpretations.

Which means, of course, the answer is actually 288 and not 2. The author probably means for the answer to be 2, but as written, it is not 2.

I still don't comprehend why it's not 2.
 
Sure I'll read 300+ posts in each thread I decide to post in... Further, I edited my post into a more rational, less "this IS the answer" one before you even finished replying.



I still don't comprehend why it's not 2.

Order is
1. Brackets
2. Exponentiate
3. Divide or multiple (which ever comes first left to right)
4. Add or Subtract (which ever comes first left to right.)
So
48/2(9+3)
Brackets 9+3=12 so now you have 48/2(12) or other wise 48/2*12.
Now we work left to right. 48/2 = 24 so now you have 24*12
24*12=288

Math has rules. Following them gives you 288.
 
You have an error in the order of operations. It's 288. Please read the thread before posting. It's been proven over and over and over.

the only thing that has been "proven" is that people have different opinions about it, or, if anything, that the original expression is ambiguous.
Being rude to people over and over and over doesn't make your own opinion more "right".
 
Math has rules. Following them gives you 288.

There are two paths that lead you to the answer 2.

  • Multiplication is always carried out before division (a literal reading of certain mnemonics)
  • Juxtaposition implies precedence (a non-universal typsetting rule designed to save ink and paper)

The first is flat out wrong. The second may have some merit.

As usual in mathematics you need to show your work.

B
 
There are two paths that lead you to the answer 2.

  • Multiplication is always carried out before division (a literal reading of certain mnemonics)
  • Juxtaposition implies precedence (a non-universal typsetting rule designed to save ink and paper)

The first is flat out wrong. The second may have some merit.

As usual in mathematics you need to show your work.

B

agree on both counts

to be unequivocal, it should have been written
(48/2)(9+3)=288
or
48/[2(9+3)]=2

as someone was saying above, just add brackets and the problem is solved.
 
I picked B because thats how I do math in my head, and I've been doing accounting math, and you have to figure out this part of the equation and then multiply it by the first part.. BUT ANYWAY...
I asked a family friend who is a chemistry/math teacher in high school and he said it is 288. And that basically its math grammar, or something along those lines.
 
the only thing that has been "proven" is that people have different opinions about it, or, if anything, that the original expression is ambiguous.
Being rude to people over and over and over doesn't make your own opinion more "right".

He's probably getting a little peeved about the fact that no matter what we 288ers post, the 2ers refuse to admit that they are wrong. This may be due to some weird pride, we are never wrong type thing. They may be effing with us. It could go either way.
To sum up our viewpoint, not only has the problem been solved and proved to be correct but this whole ambiguous thing is silly, as well. A while back (and no, I don't expect new people to this thread to read the entire thing), I posted exactly why the equation was written like it is. Having taught SAT math for a decade and being married to a math teacher (a wacky bunch!), its easy for us to see that you have to make equations harder and harder as kids grow up, to make sure that they remember how to do things like the order of operations of correctly. If every math equation was written with a bunch of () to clear up the order of operations or even included a * every time you needed to multiply, how would that test kid's knowledge of the basic math steps. In other words, you can say the problem is hard, but you can't say its ambiguous. It has only one answer the way it is written; its not an opinion thing. I gave the analogy of why teachers use harder and harder words in vocabulary classes when they can simply make the passages kids are reading so much clearer by using simple words. To test them and have them learn new words, of course. The same teaching principal applies in math. Start simple. 1 step math problems. Slowly add to that. Take away symbols and make sure kids remember stuff like implied multiplication, etc. etc.
To sum up, those of us on the 288 side have posted (and proven with links) why our answer is correct, why 2 is wrong, why some calculators still get the wrong the answer and why its ok to write the equation the way it is written. The other side just lists their incorrect math process over and over again (something we show them is wrong, with links to back it up), post some lame joke about taxes (you'll have to read the posts to understand that part) and then take cheap shots about our education (nothing funnier to me then a poster ragging on other people's education when they can't admit to a simple math error). Like I said, those who can't simply say ooops, I guess I learned something today are either very, very stubborn or just effing around.
 
Pst @Mac'nCheese... read 1 post above yours.. Now read your last post.. Now, you are a liar..
:p
 
I had this argument with my roommate today. He got 2 and I got 288. He believes it was implied that 2(9+3) is under the division bar, while I believed that only the 2 was, given how it was written.

I sent the problem to my mother who is an Algebra teacher and she got 288 as well which we decided would end our argument.

It is a poorly written math problem, that is for sure.
 
Pst @Mac'nCheese... read 1 post above yours.. Now read your last post.. Now, you are a liar..
:p

Huh? We wrote a post at the same exact time and I'm a liar because u actually admitted to being wrong? I Was writing about the three hundred posts before my latest one not the one being typed out at the same exact moment. C
 
He's probably getting a little peeved about the fact that no matter what we 288ers post, the 2ers refuse to admit that they are wrong. This may be due to some weird pride, we are never wrong type thing. They may be effing with us. It could go either way.
To sum up our viewpoint, not only has the problem been solved and proved to be correct but this whole ambiguous thing is silly, as well. A while back (and no, I don't expect new people to this thread to read the entire thing), I posted exactly why the equation was written like it is. Having taught SAT math for a decade and being married to a math teacher (a wacky bunch!), its easy for us to see that you have to make equations harder and harder as kids grow up, to make sure that they remember how to do things like the order of operations of correctly. If every math equation was written with a bunch of () to clear up the order of operations or even included a * every time you needed to multiply, how would that test kid's knowledge of the basic math steps. In other words, you can say the problem is hard, but you can't say its ambiguous. It has only one answer the way it is written; its not an opinion thing. I gave the analogy of why teachers use harder and harder words in vocabulary classes when they can simply make the passages kids are reading so much clearer by using simple words. To test them and have them learn new words, of course. The same teaching principal applies in math. Start simple. 1 step math problems. Slowly add to that. Take away symbols and make sure kids remember stuff like implied multiplication, etc. etc.
To sum up, those of us on the 288 side have posted (and proven with links) why our answer is correct, why 2 is wrong, why some calculators still get the wrong the answer and why its ok to write the equation the way it is written. The other side just lists their incorrect math process over and over again (something we show them is wrong, with links to back it up), post some lame joke about taxes (you'll have to read the posts to understand that part) and then take cheap shots about our education (nothing funnier to me then a poster ragging on other people's education when they can't admit to a simple math error). Like I said, those who can't simply say ooops, I guess I learned something today are either very, very stubborn or just effing around.

The "2" proponents are probably the same ones saying the iPhone has antenna problems over and over on here.:)
 
Huh? We wrote a post at the same exact time and I'm a liar because u actually admitted to being wrong? I Was writing about the three hundred posts before my latest one not the one being typed out at the same exact moment. C

The force is weak with this one...

Ok, so maybe I didn't notice that. My bad. Now here is your stick back.
 
the only thing that has been "proven" is that people have different opinions about it, or, if anything, that the original expression is ambiguous.
Being rude to people over and over and over doesn't make your own opinion more "right".

This argument is getting rather annoying and childish. There is little room for opinions in mathematics. There is a right answer and an infinite number of wrong answers. The right answer here is 288. It's a simple case that is easily solved if you're careful with the order of operations.

True, there would be less room for error had this problem been formatted in a more logical way. However, practice problems like this are often made simply to test one's understanding of order of operations.

Lastly, it is quite poor math discussion skills to suggest that the right answer is merely an opinion.
 
He's probably getting a little peeved about the fact that no matter what we 288ers post, the 2ers refuse to admit that they are wrong. This may be due to some weird pride, we are never wrong type thing. They may be effing with us. It could go either way.
To sum up our viewpoint, not only has the problem been solved and proved to be correct but this whole ambiguous thing is silly, as well. A while back (and no, I don't expect new people to this thread to read the entire thing), I posted exactly why the equation was written like it is. Having taught SAT math for a decade and being married to a math teacher (a wacky bunch!), its easy for us to see that you have to make equations harder and harder as kids grow up, to make sure that they remember how to do things like the order of operations of correctly. If every math equation was written with a bunch of () to clear up the order of operations or even included a * every time you needed to multiply, how would that test kid's knowledge of the basic math steps. In other words, you can say the problem is hard, but you can't say its ambiguous. It has only one answer the way it is written; its not an opinion thing. I gave the analogy of why teachers use harder and harder words in vocabulary classes when they can simply make the passages kids are reading so much clearer by using simple words. To test them and have them learn new words, of course. The same teaching principal applies in math. Start simple. 1 step math problems. Slowly add to that. Take away symbols and make sure kids remember stuff like implied multiplication, etc. etc.
To sum up, those of us on the 288 side have posted (and proven with links) why our answer is correct, why 2 is wrong, why some calculators still get the wrong the answer and why its ok to write the equation the way it is written. The other side just lists their incorrect math process over and over again (something we show them is wrong, with links to back it up), post some lame joke about taxes (you'll have to read the posts to understand that part) and then take cheap shots about our education (nothing funnier to me then a poster ragging on other people's education when they can't admit to a simple math error). Like I said, those who can't simply say ooops, I guess I learned something today are either very, very stubborn or just effing around.

at least you are being nice. :)

however you also are (more politely) making the same mistake that since many posters provide a 'demonstration' that agree with your position, than you conclude that your position is correct and all the 'demonstrations' that agree with the opposite views are incorrect and their proponent just 'refuse to admit that they are wrong'.

to be clear, i think that both answer are correct (or incorrect) because the problem IS ambiguous. and it is ambiguous exactly because there are valid arguments, and conventions, that support both cases.
My first inclination was to say the answer was 288, but after thinking about, reading about it looking at the 'demonstrations' (so to speak) i think there isn't one and actually, if really hard pressed for one answer, i would have to conclude that the answer more in line with the accepted conventions is 2, because of the "multiplication by juxtaposition" argument.
It's a valid one, which is certainly true with expression like y/2x or 1/2π

for example the angular momentum L=n(h/2π)=nħ, where h/2π means h/(2π), not hπ/2!

you also mention links and such, but that is far from convincing too,
for example the poster below provides several links:

Yep. As long as we're throwing credentials around let me get out my two electrical engineering degrees.
It's 288.
If my degrees don't convince you, maybe this will:
http://en.wikipedia.org/wiki/Order_of_operations
http://mathcentral.uregina.ca/QQ/database/QQ.09.07/h/brit1.html
http://www.onlinemathlearning.com/bedmas.html
http://www.mathsisfun.com/operation-order-pemdas.html
http://www.mathsisfun.com/operation-order-bodmas.html
http://math.about.com/library/weekly/aa040502a.htm
http://bctf.ca/diversity/ResourceInventory/LessonsTopics/Davies/BEDMAS.pdf
http://www.purplemath.com/modules/orderops.htm
... and plenty more where those came from.

Notice that "multiplication and division" always appear together as a step, as in one does NOT take precedence over another, but they are expressed left to right. They do NOT say to do the multiplication part (2x12) before the division (48/2)!
however, if you actually look at the links, they either only have the simple bedmas cases (which nobody contests) or, when they do have examples that resemble the problem mention here (with implied multiplication following a division sign) they actually conclude very clearly, that the implied multiplication is performed before the division, hnece the correct answer would be 2 not 288.

http://bctf.ca/diversity/ResourceInventory/LessonsTopics/Davies/BEDMAS.pdf
purplemath, example 5: http://www.purplemath.com/modules/orderops2.htm
bctf, page 4 (2 in the page numbering in the pdf) example 3

so basically this guy is linking 'proof' that directly contradicts his thesis.

so, now that i have 'demonstrated' that 288 is not correct, are you going to come here and admit that you are wrong? or at least that it is ambiguous? :)
 
This argument is getting rather annoying and childish. There is little room for opinions in mathematics. There is a right answer and an infinite number of wrong answers. The right answer here is 288. It's a simple case that is easily solved if you're careful with the order of operations.

True, there would be less room for error had this problem been formatted in a more logical way. However, practice problems like this are often made simply to test one's understanding of order of operations.

Lastly, it is quite poor math discussion skills to suggest that the right answer is merely an opinion.

clearly, a large part of the mathematical community disagrees with you.
 
clearly, a large part of the mathematical community disagrees with you.

Random people on an Internet for hardly constitutes the mathematical community. Please, find me a single reputable source that says you can choose which order to do mathematic operations.
however you also are (more politely) making the same mistake that since many posters provide a 'demonstration' that agree with your position, than you conclude that your position is correct and all the 'demonstrations' that agree with the opposite views are incorrect and their proponent just 'refuse to admit that they are wrong'.

to be clear, i think that both answer are correct (or incorrect) because the problem IS ambiguous. and it is ambiguous exactly because there are valid arguments, and conventions, that support both cases.
This is a very poor assumption to approach any math problem with.

Please read the thread and realize that multiplication by juxtaposition does not take any precedence over multiplication or division denoted in other ways.

There is no ambiguity to this math problem. 2 is simply a wrong answer. Hell there's rarely any ambiguity in math at all! Other than in special cases like ambiguous triangles.
 
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