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balamw
Apr 11, 2011, 09:36 AM
I assume any time I see a division symbol that it takes the place of a bar in traditional handwriting.

Would you also make the same assumption if we had a consistent way of entering http://etc.usf.edu/clipart/41700/41704/FC_Dev_41704_sm.gif?

That is how those of us in the 288 camp are interpreting "/" because that is how it has become to be used in all of the tools we use daily.

B

KnightWRX
Apr 11, 2011, 09:37 AM
Wrong. As I posted, the expression as typed here is ambiguous because its interpretation depends on the conventions used. It has nothing to do with understanding or not mathematics. Both 2 and 288 are correct answers, according to the conventions you used.

Any answer could be right if you use the wrong conventions. There's only 1 right convention and only 1 right answer here though.

iStudentUK
Apr 11, 2011, 09:39 AM
Step back a bit. Someone in your group would actually send you an expression that was full of constant numbers rather than reducing that to the answer?

As s a physicist by training I hate it when the meaning is bled out of an expression, by rote plugging in of numbers. Engineers love to do this kind of thing and take a perfectly nice equation, lump a bunch of stuff together and take a few implied logs for good measure and think it has meaning. :p

I'd expect anyone who knows what they are doing to send something like x/y(a+b) rather than 48/2(9+3). Preferably with an extra pair of parens/brackets. Or send you TeX $\frac{x}{y}(a+b)$. This would assist in your sanity checking if, for example, you saw that x was a distance, y was a time and a and b were also times and you knew the expected answer was a distance you'd know that (x/y)*(a+b) was meant. If you were looking for acceleration you might go back to the author and ask, "did you mean (x/[y*(a+b)])?" instead of taking the original expression at its face value.

In the absence of context and any other information the answer is 288.

B

Of course not! I was simply giving an example of how I would have expected this to have been written in an email with two pairs of brackets, not that anyone actually did send anything like that. The equations we used were to do with modelling enzyme kinetics. So they were algebraic, nobody emailed an equation that said 1+1=2! :D

Our fitting programme didn't use TeX, which was really annoying. It had standard models built in, but on one occasion we had to derive a model from scratch and the equation I used needed 47 pairs of brackets to make the stupid machine understand it! :mad:

ender land
Apr 11, 2011, 09:48 AM
Thank you!

Division should be written as a fraction "_" or ( ... )^-1. Nobody with maths skills beyond that of a ten year old should be using "/". This question is using this notation only because MR forums aren't good for writing equations. We must think of this in our heads as being a fraction, and ask how it would be written, and your's makes the most sense.

ugh.

Someone already pointed out that "/" is used as "divide by" in programming. I do not know of a single programming language which would evaluate that expression to 2. Most would either give an error or 288. I use this symbol 100% of the time I use division on the computer.

What about the following expressions. I think part of the reason 2 is such a popular answer is most people without math/programming backgrounds are only used to seeing fractions like 1/2 or 2/3 and never would assume that 48/2 is mathematically evaluated in a similar sense.

1/2(x+y) or 2/3(x+4) should be much more "intuitively" obvious that the "/" sign does not mean fraction, but rather is a basic division sign.

balamw
Apr 11, 2011, 09:52 AM
on one occasion we had to derive a model from scratch and the equation I used needed 47 pairs of brackets to make the stupid machine understand it! :mad:

And I'm sure if you had to share and discuss that with someone else by email, you would have sent the actual version that you were trying to get the machine to understand rather than paraphrasing it into some potentially unclear form.

IMHO this is an academic grade school math problem designed to trip people up who are still unclear about the rules, and to try and encourage the better use of additional parens to improve clarity.

B

iStudentUK
Apr 11, 2011, 09:53 AM
What about the following expressions. I think part of the reason 2 is such a popular answer is most people without math/programming backgrounds are only used to seeing fractions like 1/2 or 2/3 and never would assume that 48/2 is mathematically evaluated in a similar sense.

We've covered this. Someone with a programming background may use a/b. However, a mathematician would not. They would use-

a
b

I am saying this equation is meant to be thought of in terms of the second option, / is being used as a convenient alternative to _ because we are in a forum. I would say this is-

48 (9+3) = 288
2

But that step of converting into _ is important. As I say, we have covered this.

chaoticbear
Apr 11, 2011, 10:13 AM
Would you also make the same assumption if we had a consistent way of entering http://etc.usf.edu/clipart/41700/41704/FC_Dev_41704_sm.gif?

That is how those of us in the 288 camp are interpreting "/" because that is how it has become to be used in all of the tools we use daily.

B

If it were a division symbol there instead of "/", I'd find it even more ambiguous. The lack of an operand between the two arguments in the denominator is the most compelling piece of evidence to me that it all belongs in the denominator.

Rodimus Prime
Apr 11, 2011, 10:57 AM
Nobody uses / when writing down by hand (they do when programming on a computer- fine), or at least they shouldn't. It doesn't matter if / has a strict definition if it is not strictly enforced. I did a chemistry degree, and that obviously involves maths. Yet, if someone had emailed by an equation like this I would have asked for clarification, because I know they are thinking in terms of two lines (using ______).

We have been over this before I know plenty of people myself included who use "/" for division when doing math by hand. Reason being is that is is quicker and easier to write than other methods.
My math skills are well beyond what most of the people here have. In terms of college credit hours I have 21 hours of math from Cal I and above. If you want to count my stuff before calculus I have 30 hours.
On top of those 21 hours of math I have all the classes that use heavy math in my engineering classes so safe to say that is a lot more. that "/" is used for division all the time in hand writing by students and professors. Only time I tend to go to fraction is when I have a fair amount of stuff above and below it.

I would write 48/(2(9+3)) as a big fraction. but the one given nope. More trouble than it is worth.

ncl
Apr 11, 2011, 11:07 AM
There's only 1 right convention and only 1 right answer here though.

Well no. Both conventions are used. That's why you get a 50/50 ratio on the answers, here and on nearly all the boards this question appeared (since this question appeared on quite a lot of boards). And it has nothing to do with math knowledge or skills. You'll have mathematicians, physicists, engineers, etc. in both camp.

Bored at work, I made some research on the subject. Apparently, this "debate" has been going for quite some time (like here (http://mathforum.org/library/drmath/view/57021.html), Feb 2000). It looks like the juxtaposition=grouping rule originated in printing (in order to minimize cost or improve readability of inline expressions, I don't know). Lots of text books used this rule. The AMS had this text (http://replay.waybackmachine.org/20011201061315/http://www.ams.org/authors/guide-reviewers.html) (through the wayback machine):

You can help us to reduce production and printing costs by avoiding excessive or unnecessary quotation of complicated formulas. We linearize simple formulas, using the rule that multiplication indicated by juxtaposition is carried out before division.

So, no. There is not only 1 right convention and 1 right answer here. Or, if you really want one, since the AMS text is the closest thing to an "official" document I could find on the matter, the right answer is 2. If you wanted 288, you'd have to write it: 48(9+3)/2 or explicitely put the multiplication operator.

But, just for the record, I am in the 288 camp :)

balamw
Apr 11, 2011, 11:45 AM
The AMS had this text (http://replay.waybackmachine.org/20011201061315/http://www.ams.org/authors/guide-reviewers.html) (through the wayback machine):

I fail to see how the example really represents that rule or has bearing on the discussion at hand.

Here are the two equations:

http://www.texify.com/img/%5CLARGE%5C%21%7B1%5Cover%7B2%5Cpi%20i%7D%7D%5Cint_%5CGamma%20%7Bf%28t%29%5Cover%20%28t-z%29%7Ddt.gif and http://www.texify.com/img/%5CLARGE%5C%21%281/2%5Cpi%20i%29%5Cint_%5CGamma%20f%28t%29%28t-z%29%5E%7B-1%7Ddt.gif

I interpret the integral and dt as an implied bracket that surrounds the integrand and defines the variable and domain of integration, and I can see why the second form is cheaper to print than a displayed equation that uses \over.

EDIT: Are they saying that the brackets are needed around the (1/2 \pi i) to stop it from being interpreted as http://www.texify.com/img/%5CLARGE%5C%211/%282%5Cpi%20i%5Cint_%5CGamma%20f%28t%29%28t-z%29%5E%7B-1%7Ddt%29.gif

B

benbondu
Apr 11, 2011, 12:00 PM
I fail to see how the example really represents that rule or has bearing on the discussion at hand.

FTA--
We linearize simple formulas, using the rule that multiplication indicated by juxtaposition is carried out before division.

I think that is the relevant sentence.

iStudentUK
Apr 11, 2011, 12:02 PM
We have been over this before I know plenty of people myself included who use "/" for division when doing math by hand. Reason being is that is is quicker and easier to write than other methods.

It isn't quicker to write / compared to ___ . Both are the same.

I can't remember a single textbook, paper or lecturer who systematically uses / when writing when I was an undergrad. The only time I use it is where there is a e^(x/y) or something in the denominator of a fraction as it makes everything fit better. Just do a quick google image search for "maths", "math", "algebra" or "equation". 95% of the time in both writing and in print a fraction is used, not a / .

I'd be willing to bet / is very much in the minority.

Don't panic
Apr 11, 2011, 12:06 PM
it comes down to this:

the expression x/yz is equal to
[a] x/zy
[b] xz/y
[c] xy/z
[d] 42

balamw
Apr 11, 2011, 12:07 PM
I think that is the relevant sentence.

I know it is. How does it relate to the concrete examples they use which I posted above? I still fail to see it. Which multiplication by juxtaposition is given precedence over division?

it comes down to this:

the expression x/yz is equal to
[a] x/zy
[b] xz/y
[c] xy/z
[d] 42

Just to mix memes you could have worked in a ... profit! in there. The underpants gnomes would be proud.

B

benbondu
Apr 11, 2011, 12:13 PM
Bored at work, I made some research on the subject. Apparently, this "debate" has been going for quite some time (like here (http://mathforum.org/library/drmath/view/57021.html), Feb 2000). It looks like the juxtaposition=grouping rule originated in printing (in order to minimize cost or improve readability of inline expressions, I don't know). Lots of text books used this rule. The AMS had this text (http://replay.waybackmachine.org/20011201061315/http://www.ams.org/authors/guide-reviewers.html) (through the wayback machine):

Nice find. I'd never heard of the juxtaposition=grouping rule, but I think it makes sense. I originally answered 288, but I'm leaning more towards 2 now.

The expression is better written 48/2*(9+3) if you want it to evaluate to 288.

dukebound85
Apr 11, 2011, 12:14 PM

Anyone with a decent education is taught B.E.D.M.A.S not PEDMAS.

Uhhh BEDMAS=PEDMAS=PEMDAS=PEDMSA=BEMDSA and so on you know right?

Anyone with a decent education knows that

Thank you!

Division should be written as a fraction "_" or ( ... )^-1. Nobody with maths skills beyond that of a ten year old should be using "/". This question is using this notation only because MR forums aren't good for writing equations. We must think of this in our heads as being a fraction, and ask how it would be written, and your's makes the most sense.

You keep saying this and I disagree. There is nothing wrong with using it

We have been over this before I know plenty of people myself included who use "/" for division when doing math by hand. Reason being is that is is quicker and easier to write than other methods.
My math skills are well beyond what most of the people here have. In terms of college credit hours I have 21 hours of math from Cal I and above. If you want to count my stuff before calculus I have 30 hours.
On top of those 21 hours of math I have all the classes that use heavy math in my engineering classes so safe to say that is a lot more. that "/" is used for division all the time in hand writing by students and professors. Only time I tend to go to fraction is when I have a fair amount of stuff above and below it.

I would write 48/(2(9+3)) as a big fraction. but the one given nope. More trouble than it is worth.

You would be surprised at how many here have as much or more education than what you listed. I hate it when people throw "credentials" around lol

But I agree, anyone that has done a technical background in college has taken a crapload of math in terms of dedicated courses as well as courses like in physics or engineering that is essentially a math class with application

Regarding "/", I use it all the time still as it allows me to write an equation out in one line vs more lines. I do however, notate the equation in a clear form with ()

benbondu
Apr 11, 2011, 12:17 PM
I know it is. How does it relate to the concrete examples they use which I posted above? I still fail to see it. Which multiplication by juxtaposition is given precedence over division?

B

Sorry. It's the (1/2 \pi*i)-- nothing to do with the integral as far as I can tell. The juxtaposition=grouping rule ensures it is not interpreted as (0.5* \pi*i)

Don't panic
Apr 11, 2011, 12:18 PM
I know it is. How does it relate to the concrete examples they use which I posted above? I still fail to see it. Which multiplication by juxtaposition is given precedence over division?

Just to mix memes you could have worked in a ... profit! in there. The underpants gnomes would be proud.

B
hehe, don't want to upset ncl and knightwrx too much.

but, seriously that is the crux:
if you think that x/yz is the same as x/zy, then you should be a "2" guy,
if you think that x/yz is the same as xz/y, then you should be a "288" guy,
if you think that x/yz is the same as xy/z, then you should pass the joint,
if you think that x/yz is the same as 42, then you probably have a tail and white fur

EDIT:

push it even more:
y/2x=7

what is y for x=3?

balamw
Apr 11, 2011, 12:25 PM
Sorry. It's the (1/2 \pi*i)-- nothing to do with the integral as far as I can tell. The juxtaposition=grouping rule ensures it is not interpreted as (0.5* \pi*i)

I guess it shows I'm a physicist at heart, I didn't even interpret the 2 pi i as possibly being separable into bits. It's a single number. :p

I do see that that should not be interpreted as (1/2)*(pi*i) and doesn't need to be typeset as 1/(2*pi*i). However in ASCII text without other context I would still find the (1/2 pi i) to evaluate to the same thing as (pi i)/2.

Weird.

B

-aggie-
Apr 11, 2011, 12:25 PM
Until this guy (http://forums.macrumors.com/member.php?u=73221) comes into this thread, no one knows the answer. :)

Shaun.P
Apr 11, 2011, 12:28 PM
Correct me if I am wrong, but I was taught to do operations in this order:

Brackets
Of
Divide
Multiply
Subtract

i.e. BODMAS

48/2(9+3)

1. Do brackets first. Within the brackets is an add sum, so you do that and you get 48 / 2(12)

2. Now "Of" 2(12) is the same as 2/1 of 12 which is simply 24. So now we have 48 / 24

3. 2

iStudentUK
Apr 11, 2011, 12:32 PM
Correct me if I am wrong, but I was taught to do operations in this order:

Brackets
Of
Divide
Multiply
Subtract

i.e. BODMAS

I was taught BODMAS, and the O stands for "order". As in power or indices. It refers to things like x^2 (x squared). x(y) is just multiplication.

balamw
Apr 11, 2011, 12:35 PM
Of

How is "Of" different from multiplication or division?

Where do your exponents or "orders" go?

How do you interpret this per your prescription?

10 - 3 + 2 = ?

B

dukebound85
Apr 11, 2011, 12:39 PM
Until this guy (http://forums.macrumors.com/member.php?u=73221) comes into this thread, no one knows the answer. :)

Nah, we need the Q in here lol

Correct me if I am wrong, but I was taught to do operations in this order:

Brackets
Of
Divide
Multiply
Subtract

i.e. BODMAS

48/2(9+3)

1. Do brackets first. Within the brackets is an add sum, so you do that and you get 48 / 2(12)

2. Now "Of" 2(12) is the same as 2/1 of 12 which is simply 24. So now we have 48 / 24

3. 2

of? not exponent or order?

Rodimus Prime
Apr 11, 2011, 12:43 PM
You would be surprised at how many here have as much or more education than what you listed. I hate it when people throw "credentials" around lol

But I agree, anyone that has done a technical background in college has taken a crapload of math in terms of dedicated courses as well as courses like in physics or engineering that is essentially a math class with application

Regarding "/", I use it all the time still as it allows me to write an equation out in one line vs more lines. I do however, notate the equation in a clear form with ()

Oh I know people do.
But I am also willing to bet that a vast majority of the people who selected the 2 for the answer have fairly little math comparably.
This is breaking down more to the people who have the degrees based in math/ engineering to those who do not.

Which group do you think is going to understand the rules of math better. The people with heavy math based degrees or those who do not.

dukebound85
Apr 11, 2011, 12:47 PM
Oh I know people do.
But I am also willing to bet that a vast majority of the people who selected the 2 for the answer have fairly little math comparably.
This is breaking down more to the people who have the degrees based in math/ engineering to those who do not.

Which group do you think is going to understand the rules of math better. The people with heavy math based degrees or those who do not.

Oh I agree, hence why I suggested waaaaaaay back in post 129 of this lol as it would be interesting to see

I wish there was a poll option of who is getting 288 and is say in a technical field such as engineering/stats/physics, etc

My guess is that 288 is coming from people who use math extensively and 2 coming from those who may not...

Rodimus Prime
Apr 11, 2011, 12:47 PM
Correct me if I am wrong, but I was taught to do operations in this order:

Brackets
Of
Divide
Multiply
Subtract

i.e. BODMAS

48/2(9+3)

1. Do brackets first. Within the brackets is an add sum, so you do that and you get 48 / 2(12)

2. Now "Of" 2(12) is the same as 2/1 of 12 which is simply 24. So now we have 48 / 24

3. 2

You are wrong.

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

Rodimus Prime
Apr 11, 2011, 12:49 PM
Oh I agree, hence why I suggested waaaaaaay back in post 129 of this lol

Yeah. This break down showing 50% of the people think the answer is 2 is telling me that Math skills all over the world suck. It is use it or lose it.
For me I considered basic Math to be Cal I and down. So basic math for me starts at Cal I.

Shaun.P
Apr 11, 2011, 12:54 PM
I was taught BODMAS, and the O stands for "order". As in power or indices. It refers to things like x^2 (x squared). x(y) is just multiplication.

You're right, Of is the same as Multiply. Yet I can distinctively remember being told that the O stands for Of. You're right. I'm embarrassed - I have a degree in maths!

Can you give me an example of what you mean by order?

How is "Of" different from multiplication or division?

Where do your exponents or "orders" go?

How do you interpret this per your prescription?

10 - 3 + 2 = ?

B

Of is the same as multiplication. It doesn't matter what order you do your above sum.

10 - 3 + 2 = 7 + 2 = 9

or

10 - 3 + 2 = 10 - 1 = 9.

Nah, we need the Q in here lol

of? not exponent or order?

You're right - we do need Doctor Q!

Yes, my mistake.

You are wrong.

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

You are correct!

benbondu
Apr 11, 2011, 12:56 PM
Yeah. This break down showing 50% of the people think the answer is 2 is telling me that Math skills all over the world suck. It is use it or lose it.
For me I considered basic Math to be Cal I and down. So basic math for me starts at Cal I.

I have a degree in math and use it all the time for my job. I think evaluating the expression as 2 has merit. At the very least, it's a poorly formed expression for the very fact it's open to interpretation.

dukebound85
Apr 11, 2011, 12:57 PM
You're right, Of is the same as Multiply. Yet I can distinctively remember being told that the O stands for Of. You're right. I'm embarrassed - I have a degree in maths!

Can you give me an example of what you mean by order?

Order= exponent

as in 2^3 and so on

Rodimus Prime
Apr 11, 2011, 01:00 PM
I have a degree in math and use it all the time for my job. I think evaluating the expression as 2 has merit. At the very least, it's a poorly formed expression for the very fact it's open to interpretation.

and I also willing to bet that even you think 2 is the wrong answer. It merit is very low. Yes I can see how someone can come to that result but does not change the fact that 2 is incorrect and wrong.

Only way it could be 2 is if it was written 48/(2(9+3))

iStudentUK
Apr 11, 2011, 01:02 PM
Yeah. This break down showing 50% of the people think the answer is 2 is telling me that Math skills all over the world suck. It is use it or lose it. For me I considered basic Math to be Cal I and down. So basic math for me starts at Cal I.

That may be harsh, this is one small issue. This one thing isn't a good indication.

What is "proper maths" is quite subjective. I was always reasonably happy with things like calculus, it wasn't easy but I got it. I could merrily go along with it. I learned the basics of matrices/determinants before that but I struggled, because my brain just doesn't work that way. I'd look like a toddler poking at the question with my fingers and crying. Most of my friends were the other way around.

balamw
Apr 11, 2011, 01:02 PM
Of is the same as multiplication. It doesn't matter what order you do your above sum.

Order, exponents or powers could be what you were thingking "of" ;)

3^3 is three to the power of three.

At least you see it as a sum.

Many who take the mnemonic seriously and don't understand it would say 5 because they do the addition first before subtracting.

10 - 3 + 2 = 10 - 5 = 5.

In order to get 2 from the problem at hand you somehow have to prioritize the implied multiplication operation from juxtaposition. The AMS link above does just that. Otherwise, if you do the equal precedence operators left to right. 48/2*12 is 288.

B

Watabou
Apr 11, 2011, 01:04 PM
I asked my Calculus 2 teacher today just to put this to a rest and he agreed with me and said it was 288.

This is how my teacher said he would solve it:

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

He then asked me if this was a problem in the book and I had to laugh and say no.

I cannot believe people think the order doesn't matter, the fact that this thread has so many pages and the fact that ~50% believe the answer is 2. :confused:

-aggie-
Apr 11, 2011, 01:13 PM
Oh I know people do.
But I am also willing to bet that a vast majority of the people who selected the 2 for the answer have fairly little math comparably.
This is breaking down more to the people who have the degrees based in math/ engineering to those who do not.

Which group do you think is going to understand the rules of math better. The people with heavy math based degrees or those who do not.

Does having a math-based degree from Texas Tech count though?:D

Shaun.P
Apr 11, 2011, 01:21 PM
Order, exponents or powers could be what you were thingking "of" ;)

3^3 is three to the power of three.

At least you see it as a sum.

Many who take the mnemonic seriously and don't understand it would say 5 because they do the addition first before subtracting.

10 - 3 + 2 = 10 - 5 = 5.

In order to get 2 from the problem at hand you somehow have to prioritize the implied multiplication operation from juxtaposition. The AMS link above does just that. Otherwise, if you do the equal precedence operators left to right. 48/2*12 is 288.

B

Thanks balamw. Probably what I've been taught is Of as in 2 to the power of 2 etc (like you said), and over the years I've adapted it to make me think it meant the same as three quarters of 100 when in actual fact that is multiply.

For your question when performing the calculation in my head it see it as 10 + (-3) + 2.

Rodimus Prime
Apr 11, 2011, 01:23 PM
Does having a math-based degree from Texas Tech count though?:D

Yes.
Beside it is a hell of a lot better than a math based degree from Aggie Land.:D

killr_b
Apr 11, 2011, 01:29 PM
All the people who chose "2" as the answer clearly never did their college math homework on a computer. When you get to a number next to a number in parentheses it means multiply. ex: 3(10) =30. It's not an exponent as exponents are expressed 3^10 and without a second set of parentheses around the 2(9+3) you start on the left and go right.

The answer is 288. I suggest a college-level math refresher course.

Don't panic
Apr 11, 2011, 01:32 PM
and I also willing to bet that even you think 2 is the wrong answer. It merit is very low. Yes I can see how someone can come to that result but does not change the fact that 2 is incorrect and wrong.

Only way it could be 2 is if it was written 48/(2(9+3))

I asked my Calculus 2 teacher today just to put this to a rest and he agreed with me and said it was 288.

This is how my teacher said he would solve it:

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

He then asked me if this was a problem in the book and I had to laugh and say no.

I cannot believe people think the order doesn't matter, the fact that this thread has so many pages and the fact that ~50% believe the answer is 2. :confused:

y/2x=7
what is y when x=3?

and more in general, would you consider
x/yz = xz/y generally true for z≠1?

All the people who chose "2" as the answer clearly never did their college math homework on a computer. When you get to a number next to a number in parentheses it means multiply. ex: 3(10) =30. It's not an exponent as exponents are expressed 3^10.
The answer is 288. I suggest a college-level math refresher course.
and i suggest an elementary-level reading refresher course, because people in the "2" camp is NOT suggesting that it should be an exponent (i am not sure anyone suggested that at all).

-aggie-
Apr 11, 2011, 01:38 PM

y/2x=7
what is y when x=3?

and more in general, would you consider
x/yz = xz/y generally true for z≠1?

and i suggest an elementary-level reading refresher course, because people in the "2" camp is NOT suggesting that it should be an exponent (i am not sure anyone suggested that at all).

It’s “are” not “is.” :D

killr_b
Apr 11, 2011, 01:38 PM

y/2x=7
what is y when x=3?

and more in general, would you consider
x/yz = xz/y generally true for z≠1?

and i suggest an elementary-level reading refresher course, because people in the "2" camp is NOT suggesting that it should be an exponent (i am not sure anyone suggested that at all).

Also, you can go join that entry-level grammar course: "... because people in the "2" camp ARE not suggesting..." fixed.

Don't panic
Apr 11, 2011, 01:43 PM
It’s “are” not “is.” :D
never said i couldn't use one as well, besides that would be grammar ;)

you can :rolleyes: until they get stuck, but you post still makes no sense, since you are claiming people are say things they never said.

iStudentUK
Apr 11, 2011, 01:46 PM
y/2x=7
what is y when x=3?

That's an excellent point.

I'm happy to express y/2(3) as 3y/2 for example (which is why I voted 288 here, that's what the writer means). But having 2x like that makes it much harder even though it is really the same thing. I just can't imagine why anyone would write that instead of xy/2. I can't help but think that is supposed to be y/(2x) and someone missed out the brackets. This is what I've been saying, it doesn't matter how strict the definition of "/" is if people don't consistently use it in that way.

Shaun.P
Apr 11, 2011, 01:47 PM
y/2x=7
what is y when x=3?

14/3?

killr_b
Apr 11, 2011, 01:48 PM
never said i couldn't use one as well, besides that would be grammar ;)

you can :rolleyes: until they get stuck, but you post still makes no sense, since you are claiming people are say things they never said.

It's two ideas separated with a period. Should I make them separate paragraphs?

TuffLuffJimmy
Apr 11, 2011, 01:49 PM
The answer is 288. I suggest a college-level math refresher course.
I suggest a middle school level refresher course. If it took until college to learn order of operations you did something very wrong in your math studies.

Rodimus Prime
Apr 11, 2011, 01:49 PM

y/2x=7
what is y when x=3?

and more in general, would you consider
x/yz = xz/y generally true for z≠1?
y would = (7/3)*2

Your your 2nd question x/y*z = x*z/y is true even if z =1. Hell no matter what z = it would be true. Remember division is nothing more than multiply something by x^-1.

Hellhammer
Apr 11, 2011, 01:49 PM
y/2x=7
what is y when x=3?

y=14/3

It's 288 and the reason has been posted a million times already.

Don't panic
Apr 11, 2011, 01:53 PM
y would = (7/3)*2

Your your 2nd question x/y*z = x*z/y is true even if z =1. Hell no matter what z = it would be true. Remember division is nothing more than multiply something by x^-1.

y=14/3

It's 288 and the reason has been posted a million times already.

well, i would be willing to bet good money that a vast majority of people, including mathematicians (and the two of you if you had seen it before this thread) would have quickly said 42, without a second thought, because convention makes you read that as "y over 2x" not as "y over 2, times x".

StruckANerve
Apr 11, 2011, 02:06 PM
This equation has been blowing up all the forums I post on. The correct answer is 288.

benbondu
Apr 11, 2011, 02:08 PM
and I also willing to bet that even you think 2 is the wrong answer. It merit is very low. Yes I can see how someone can come to that result but does not change the fact that 2 is incorrect and wrong.

Only way it could be 2 is if it was written 48/(2(9+3))

The question is whether the juxtaposition=grouping rule is valid. It's not something any of us were taught in grade school and almost certainly does not have universal acceptance, but maybe it should.

At first glance, I read 2(9+3) as a group. If this wasn't presented to me as a "puzzle", I might have said the answer was 2. Not necessarily because that was the "correct" answer (if you follow all of the OOO rules), but because that's what it appears the author intended it to be (most of the people I work with do not have math degrees). If the author wanted it to equal 288, they probably would have also known enough to realize the expression was not very clear, and instead written it as 48/2*(9+3) to avoid any confusion (assuming the goal wasn't to trick you).

I'm personally in favor of making some kind of official rule governing the order of operations in the context of multiplication by juxtaposition and teaching it to all the 5th graders. Obviously a lot of people currently think it's a rule, regardless of whether or not it actually is.

benbondu
Apr 11, 2011, 02:15 PM
well, i would be willing to bet good money that a vast majority of people, including mathematicians (and the two of you if you had seen it before this thread) would have quickly said 42, without a second thought, because convention makes you read that as "y over 2x" not as "y over 2, times x".

If both the person asking this question and the person answering it are reasonable people, then the answer is 42 and you move on. You start to have issues if either one of them thinks about it too long.

Nice example.

SidBala
Apr 11, 2011, 03:02 PM
Multiplication and Division are of equal precedence. Hence the expression given is ambiguous.

TuffLuffJimmy
Apr 11, 2011, 03:49 PM
Multiplication and Division are of equal precedence. Hence the expression given is ambiguous.
No it isn't. Multiplication and division you do in order of which comes first when reading left to right. Same with addition and subtraction. Please, read the thread before posting.

fireshot91
Apr 11, 2011, 06:16 PM
The multiplication doesn't take precedence over the division. They are equal in the order of operations.

It would be:

48/2(9+3)
48/2*12

24 * 12.

In cases where there are both division and multiplication, the order goes from left -> Right (As one would read it in a logical English manner).

EDIT: Am I the only one who transformed it, in my head, to be [48(9+3)]/2.
And P.S: It's not like I have a math degree or anything. I'm only in Precalculus. But, I would have gotten this right in 7th-8th grade also. I was always taught that when there is ambiguity, you move left->right, as in this case.

McGiord
Apr 11, 2011, 06:19 PM

Anyone with a decent education is taught B.E.D.M.A.S not PEDMAS.

Before Ending Discussion Must Acknowledge Self-Stupidity

McGiord
Apr 11, 2011, 06:30 PM
i fail to see how the example really represents that rule or has bearing on the discussion at hand.

Here are the two equations:

http://www.texify.com/img/%5clarge%5c%21%7b1%5cover%7b2%5cpi%20i%7d%7d%5cint_%5cgamma%20%7bf%28t%29%5cover%20%28t-z%29%7ddt.gif and http://www.texify.com/img/%5clarge%5c%21%281/2%5cpi%20i%29%5cint_%5cgamma%20f%28t%29%28t-z%29%5e%7b-1%7ddt.gif

i interpret the integral and dt as an implied bracket that surrounds the integrand and defines the variable and domain of integration, and i can see why the second form is cheaper to print than a displayed equation that uses \over.

Edit: Are they saying that the brackets are needed around the (1/2 \pi i) to stop it from being interpreted as http://www.texify.com/img/%5clarge%5c%211/%282%5cpi%20i%5cint_%5cgamma%20f%28t%29%28t-z%29%5e%7b-1%7ddt%29.gif

b
wtf?

Nice find. I'd never heard of the juxtaposition=grouping rule, but I think it makes sense. I originally answered 288, but I'm leaning more towards 2 now.

The expression is better written 48/2*(9+3) if you want it to evaluate to 288.

Finally some common sense.

-aggie-
Apr 11, 2011, 06:33 PM
Finally some common sense.

If you could get to level 148, it would all be clear to you that the answer is 288. :)

McGiord
Apr 11, 2011, 06:38 PM
If you could get to level 148, it would all be clear to you that the answer is 288. :)

The bunnies don't even get to level 2. Not even during Easter Hunt Season.

McGiord
Apr 11, 2011, 06:54 PM
This is what Excel does:

It has been demonstrated that those calling for the 288 result are assuming that first there is fraction 48/2, and then it has to be multiplied with (9+3).

Once again, Mac OS X is the Man here.

Using the expression as it is originally written, gives the result of 2.

But if you assume the use of an *, you get your manipulated result of 288.

Call it Bomdas...whatever you want to call it. You guys are assuming something.

In real life, like someone else pointed out, you go back and ask the right questions to clarify the doubts.

Most of the people out there use tools like Excel or a simple calculator to do real life calculations.

Those in the Academic world are sometimes so focused on their theories that they get away from real life practical application of the theories.

Some people are so focused on getting their point made that they slip in questions like: who said that it is an equation? Actually it was written not said.

Also, it has been proven that those who get a big refund from taxes have poor math skills.

Thanks for a fun discussion.

Loge
Apr 11, 2011, 06:58 PM
In APL the answer to 48/2(9+3) is

2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 12 12 12 12 12 12 12 12 12 12 12 12 12 12 12 12 12 12 12 12 12 12 12 12 12 12 12 12 12 12 12 12 12 12 12 12 12 12 12 12 12 12 12 12 12 12 12 12

or to 48÷2(9+3), the answer is

24 4

But then APL is unusual :p

JoeG4
Apr 11, 2011, 07:08 PM
My G5 is defective:

Don't panic
Apr 11, 2011, 07:24 PM
i am telling you, the answer is always 42!!!!! :eek::eek::eek:

McGiord
Apr 11, 2011, 07:29 PM
i am telling you, the answer is always 42!!!!! :eek::eek::eek:

Only in the US.

GimmeSlack12
Apr 11, 2011, 07:32 PM
If you presented me with the expression "a/b(c+d)" in any form, I'd parse it the same way every time.

If you are intending for the problem to read in such a way to get 288, I'd expect to see "(a/b)(c+d)".

The answer is 2. Because that is how it is written out in the Thread title. There is really no excuse for answering the problem 288, because that is simply wrong. There is no debate here.

48 / 24 = 2

Clear and simple. 11 pages? really?

iJohnHenry
Apr 11, 2011, 07:35 PM
Clear and simple. 11 pages? really?

No, 16, but that depends on your post per page choice. :p

McGiord
Apr 11, 2011, 07:41 PM
No, 16, but that depends on your post per page choice. :p
Not even on this can we agree?

pianojoe
Apr 11, 2011, 07:49 PM
There can't be no correct answer because the question is crooked. You can't write a mathematical term like the OP did. The spelling is wrong.

Writing up math requires lots of special symbols and formatting. If you choose to write your equation in ASCII, it's good practice to use "standard BASIC" notation. This means that you can't leave out the multiplication sign after the "2".

This being said, you'll need to construe the meaning of the formula. I think that the daisy-chain version is slightly more probable

48 / 2 * 12 = 48 * 12 / 2 = 288

but there's room for interpretation. If all of the "2(9+3)" should be the divisor, you'd need to indicate this in some way, like

48/(2*(9+3))

Hint: There is no rule that "everything after the / must be the divisor".

chaoticbear
Apr 11, 2011, 07:53 PM
well, i would be willing to bet good money that a vast majority of people, including mathematicians (and the two of you if you had seen it before this thread) would have quickly said 42, without a second thought, because convention makes you read that as "y over 2x" not as "y over 2, times x".

What a good example. You know, it'd totally clear up any ambiguity to just take the suggestion upthread and express it as 48(9+3)/2

balamw
Apr 11, 2011, 08:00 PM
wtf?

Read the AMS link and then the discussion with benbondu later http://forums.macrumors.com/showpost.php?p=12371018&postcount=267.

Only in the US.

B

Tomorrow
Apr 11, 2011, 08:09 PM
...convention makes you read that as "y over 2x" not as "y over 2, times x".

Unless you read it as "y divided by two times x."

Don't panic
Apr 11, 2011, 08:20 PM
Unless you read it as "y divided by two times x."

which still means two different things depending whether you pause before or after the "two".

which brings it back to the original concept that, no matter how much either side is "absolutely certain" they are correct, the expression is ambiguous.

for example, the people at purplemath (http://www.purplemath.com/modules/orderops2.htm) seem to think that the lack of the 'times' operator (multiplication by juxtaposition) implies a stronger connection that supersedes the left-to-right order, so in my example it would be "y divided by _ two times x" and not "y divided by two _ times x" and, in the original example, the answer would be 2 and not 288.

darkcurse
Apr 11, 2011, 08:35 PM
If both the person asking this question and the person answering it are reasonable people, then the answer is 42 and you move on. You start to have issues if either one of them thinks about it too long.

Nice example.

The question and the answer are mutually exclusive though. If both are found together, the universe might reorient itself in a more bizarre and unexplainable way!

Tomorrow
Apr 12, 2011, 10:40 AM
which still means two different things depending whether you pause before or after the "two".

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

2. Why would you pause in that equation?

for example, the people at purplemath (http://www.purplemath.com/modules/orderops2.htm) seem to think that the lack of the 'times' operator (multiplication by juxtaposition) implies a stronger connection that supersedes the left-to-right order

Implied parentheses? That's a new one on me.

balamw
Apr 12, 2011, 11:04 AM
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:

http://www.texify.com/img/%5CLARGE%5C%21%281/2%20%5Cpi%20i%29%20%3D%20%281/%282%20%5Cpi%20i%29%29%20%5Cneq%20%28%281/2%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: http://www.texify.com/img/%5CLARGE%5C%21%28x/y%28a%2Bb%29%29.gif wish I knew.

B

Don't panic
Apr 12, 2011, 11:09 AM
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.

MarkCollette
Apr 12, 2011, 11:43 AM
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.

iMJustAGuy
Apr 12, 2011, 12:36 PM
If you follow the OOO there is no way it can't be 2... right?

TuffLuffJimmy
Apr 12, 2011, 12:37 PM
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.
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.

ender land
Apr 12, 2011, 12:37 PM
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.

iMJustAGuy
Apr 12, 2011, 12:39 PM
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.

Hellhammer
Apr 12, 2011, 12:43 PM
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.

Don't panic
Apr 12, 2011, 12:59 PM
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".

balamw
Apr 12, 2011, 01:01 PM
Math has rules. Following them gives you 288.

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

reynavictor
Apr 12, 2011, 01:09 PM
It's 288

Don't panic
Apr 12, 2011, 01:09 PM

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.

LeahM
Apr 12, 2011, 04:23 PM
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.

Mac'nCheese
Apr 12, 2011, 04:23 PM
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.

LeahM
Apr 12, 2011, 04:32 PM
Pst @Mac'nCheese... read 1 post above yours.. Now read your last post.. Now, you are a liar..
:p

bern1812
Apr 12, 2011, 04:38 PM
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.

Mac'nCheese
Apr 12, 2011, 04:44 PM
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

-aggie-
Apr 12, 2011, 04:44 PM
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.:)

LeahM
Apr 12, 2011, 05:24 PM
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.

TuffLuffJimmy
Apr 12, 2011, 05:26 PM
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.

Mac'nCheese
Apr 12, 2011, 05:47 PM
The force is weak with this one...

Ok, so maybe I didn't notice that. My bad. Now here is your stick back.

Stick?

iJohnHenry
Apr 12, 2011, 05:56 PM
Stick?

Previous residence in your butt, I believe. http://i55.photobucket.com/albums/g158/MouseMeat/Smilies/Combolaugh.gif

Don't panic
Apr 12, 2011, 06:01 PM
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://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? :)

Don't panic
Apr 12, 2011, 06:07 PM
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.

TuffLuffJimmy
Apr 12, 2011, 06:17 PM
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.

ncl
Apr 12, 2011, 06:23 PM
There is little room for opinions in mathematics.
In maths, sure. But mathematical notations are *full* of ambiguities (just read gnasher's examples). This is one of them. And it has nothing to do with "one's understanding of order of operations."

As I wrote, the American Mathematical Society tells you "multiplication indicated by juxtaposition is carried out before division". The American Institute of Physics tells you "don't write 1/3x unless you mean 1/(3x)". The best I could find not leaning in this way was that the notation is ambiguous and should not be used (from a statistics institute, don't remember the country though).
Of course, you could still argue that the people in the AMS or AIP are just a bunch of morons who don't know their basic maths.

Lastly, it is quite poor math discussion skills to suggest that the right answer is merely an opinion.
Not in this case. It's a misunderstanding based on the fact that this expression can be interpreted in two different ways because of two different widespread conventions.
That's the reason I searched more on this issue. When I first read it, my first thought was "Who could be stupid enough to get 2 ?". Then it hit me: in a lot of books or papers I've read (I would even say, the majority of them), this expression would be evaluated as 2, because they used the juxtaposition=grouping rule. The other books avoided inline divisions entirely or used enough parenthesis to avoid any confusion.
And in the end, nobody cares. Based on context, you automatically get the convention used by the person who wrote the expression, without even thinking about it. Except, in this case, there isn't any context. Hence ambiguity.

People should realise that this problem, this misunderstanding, has very little to do with actual maths and more with typography.

And I will finish with this (I've wasted too much time on this :D). You can argue all you want about who is right and who is wrong, it is pointless: this debate has been going for (at least) 40 years !

Now, skimming through this thread and others, I'm starting to think that the 50/50 split is more likely due to half the people learning PEMDAS and the other half learning PEDMAS, which is quite saddening :(

iJohnHenry
Apr 12, 2011, 06:26 PM
Now, skimming through this thread and others, I'm starting to think that the 50/50 split is more likely due to half the people learning PEMDAS and the other half learning PEDMAS, which is quite saddening :(

The vagaries of scientific notation make you sad?

You need to get out more. Oh, and turn on your TV.

Mac'nCheese
Apr 12, 2011, 06:35 PM
Previous residence in your butt, I believe. http://i55.photobucket.com/albums/g158/MouseMeat/Smilies/Combolaugh.gif

Pointing out that I'm not a liar makes me stuck up? Ok.

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'.

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.

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? :)

I would have no problem admitting either if proved. I looked at some of the links you showed and didn't see anything that would do either. You can feel free to cut and paste and show me what I missed. From what I see, everyone's proof of the answer 2 or that this is ambiguous always uses some sort of "when a problem is discussed in this way..." or "sometimes you could do this, IF the problem was this...." I see no proof that this very simple math problem, when taken exactly as written, has one very clear answer, 288. This is a simple test of a child's knowledge of the order of operation, plain and simple.

ncl
Apr 12, 2011, 06:36 PM
The vagaries of scientific notation make you sad?
No. That is actually fun (and can even be interesting). It's the fact that people will remember a stupid acronym but not its meaning.
You need to get out more.
A lot of people tell me that, but I never understand why :D
Oh, and turn on your TV.
I would, if only there was something interesting to watch...

TuffLuffJimmy
Apr 12, 2011, 06:41 PM
I would have no problem admitting either if proved. I looked at some of the links you showed and didn't see anything that would do either. You can feel free to cut and paste and show me what I missed. From what I see, everyone's proof of the answer 2 or that this is ambiguous always uses some sort of "when a problem is discussed in this way..." or "sometimes you could do this, IF the problem was this...." I see no proof that this very simple math problem, when taken exactly as written, has one very clear answer, 288. This is a simple test of a child's knowledge of the order of operation, plain and simple.

Here here.

I will admit, however, multiplication by juxtaposition does take precedence over other operations in some cases, usually in formulaic situations and that's only because the juxtaposition is short hand and should be understood as a single value. In this case it obviously has no precedence.

MarkCollette
Apr 12, 2011, 06:46 PM
purplemath, example 5: http://www.purplemath.com/modules/orderops2.htm
bctf, page 4 (2 in the page numbering in the pdf) example 3

I've read this thread, and the only website anyone's given, for their bizarre broken order of operations has been the purple math site. Well, they're wrong. And given the bazillion of other site that disagree with that one site, I think it's clear they made the mistake.

But let me spell out why I consider them wrong

16 ÷ 2[8 – 3(4 – 2)] + 1

Given the use of brackets () and [], I would assume that whoever made this equation is not relying on arcane order of operations rules, but is in fact being explicit. So, when it comes down to:

16 ÷ 2[2] + 1

I'm going to assume that since they used brackets everywhere else, and did not use a bracket to contain 2[2] as [2[2]], that they full well know that the division happens before the multiplication.

Put another way, if this magical "like terms" operator somehow has more precedence than multiplication and division, then which precedence does it have? If I have:

2x^2

If 2x is a like term, and has higher precedence than multiplication and division, does it also have higher precedence than exponents? Does it mean:

(2x)^2 gives 4xx

No, obviously not. So now we're saying that it somehow lies in-between exponents and /* on the precedence scale, but that none of the literature explains it as a special step, except for one practice example on one website.

Phew, that's pretty cool that one website can define how math works.

balamw
Apr 12, 2011, 07:15 PM
I've read this thread, and the only website anyone's given, for their bizarre broken order of operations has been the purple math site. Well, they're wrong. And given the bazillion of other site that disagree with that one site, I think it's clear they made the mistake.

The AMS link from the wayback machine provided earlier in the thread is a "hard math" link that supports this view. (http://waybackmachine.org/jsp/Interstitial.jsp?seconds=5&date=1007187195000&url=http%3A%2F%2Fwww.ams.org%2Fauthors%2Fguide-reviewers.html&target=http%3A%2F%2Freplay.waybackmachine.org%2F20011201061315%2Fhttp%3A%2F%2Fwww.ams.org%2Fauthors% 2Fguide-reviewers.html)

My problem with it is that I see it as an artificial typesetting convention.

1/2n or 1/2pi are one thing, but it breaks for me when the parentheses are added. (Bold p is supposed to be pi)

1/2(n+1) however ...

B

McGiord
Apr 12, 2011, 08:08 PM

MarkCollette
Apr 12, 2011, 08:09 PM
The AMS link from the wayback machine provided earlier in the thread is a "hard math" link that supports this view.

So you mean something that's not actually on the Internet anymore? The AMS site is still there, so did they remove that resource themselves? Possibly since it's wrong?

Oh wow, you guys are using a resource that's not an actual math resource, but is something about how to write TEX formulas to save on printing costs.

Formulas. You can help us to reduce production and printing costs by avoiding excessive or unnecessary quotation of complicated formulas. We linearize simple formulas, using the rule that multiplication indicated by juxtaposition is carried out before division. For example, your TeX-coded display

$${1\over{2\pi i}}\int_\Gamma {f(t)\over (t-z)}dt$$

is likely to be converted to

$(1/2\pi i)\int_\Gamma f(t)(t-z)^{-1}dt$

in our production process.

balamw
Apr 12, 2011, 08:27 PM
Oh wow, you guys are using a resource that's not an actual math resource, but is something about how to write TEX formulas to save on printing costs.

As I said, an artificial typesetting convention.

As you point out it isn't in the current version of the same document. Why?

I'm a 288 guy, but I do read the (1/2 pi i) stuff as it is intended. I don't know if it's the typesetting or the parentheses around it.

B

Mac'nCheese
Apr 12, 2011, 08:37 PM

I think we've found our new hitler in the bunker video. thanks for the laugh!

RITZFit
Apr 12, 2011, 08:57 PM
288 because that's what my TI-89 told me...

iMJustAGuy
Apr 13, 2011, 03:58 AM
288 because that's what my TI-89 told me...

I love those! They factor for you and everything. Best calculator ever.

ncl
Apr 13, 2011, 07:26 AM
Possibly since it's wrong?
FFS, it's _not_ wrong ! They removed it simply because at some point, they stopped reformatting the formulas.

If you want a resource still online: http://www.aip.org/pubservs/style/4thed/AIP_Style_4thed.pdf
I couldn't find a more recent version and it still is on the AIP servers. Page 23: "never write 1/3x unless you mean 1/(3x)" And it has nothing to do with printing cost but much more to do with readability and avoiding ambiguity. For years, tons of books and papers have been written (and are still written) with the convention that a/bc == a/(bc). People have been drilled with that convention, others not. That's the reason behind this argument.

Also, what AhmedFaisal said. At school (also in Europe but not Germany, but it was nearly a decade ago), "/" stood for the horizontal fraction bar and everything after was considered as part of the denominator. At the uni, as far as I can remember they never used "/" and always used the horizontal fraction bar (except when even that was ambiguous).

Again you can argue all you want that the people interpreting in one way or the other are wrong, but the fact is both are right and that this question has been debated for more than 40 years and there still isn't an agreement on the matter. And for more references: http://www.ntg.nl/maps/26/16.pdf Fifth page (numbered 124).

I'm a 288 guy, but I do read the (1/2 pi i) stuff as it is intended. I don't know if it's the typesetting or the parentheses around it.
And how would read this: |⟨X1,X2⟩|/∥X1∥∥X2∥ (one of the example in the above document) ?

In the end, gnasher729 said it best (post 103 at page 5 [25 posts per page]):
"The premise is incorrect from the start - this is not a mathematical problem, it is a problem of noting a very simple formula using ASCII characters only, and deciding how that sequence of ASCII characters should be interpreted."

Apr 13, 2011, 10:04 AM
Same brand scientific calculator, two different answers. :rolleyes:

You're holding it wrong.

balamw
Apr 13, 2011, 12:36 PM
And how would read this: |⟨X1,X2⟩|/∥X1∥∥X2∥ (one of the example in the above document) ?

If typeset in TeX I would read it as the 2 camp intends. However, not in straight ASCII in an e-mail.

Again for me there are two major issues with this:

ASCII, unformatted e-mail vs. typesetting using TeX
A "formula" that includes only numbers

All the references are about properly formatted, typeset math using TeX, which is a very different beast than straight ASCII.

If the formula was presented with variable names x1/x2(a1+a2) and gave values for the variables and the context was clearer you might be able to suss it out better as in the case of http://www.texify.com/img/%5CLARGE%5C%21%5Cleft%7C%5Clangle%20X_1%2CX_2%20%5Crangle%5Cright%7C/%5C%7C%7C%20X_1%20%5C%7C%7C%20%5C%2C%20%20%5C%7C%7CX_2%5C%7C%7C.gif which I see as rather different from: |⟨X1,X2⟩|/∥X1∥∥X2∥

For one thing, without context, if I am supposed to read juxtaposition as multiplication then should I read X2 as X*2? Or 22 as "2*2=4", where does it end?

B

blow45
Apr 16, 2011, 09:27 AM
I was taken aback to read that the physics guys suggest that this could be interpreted as 2. I 've never seen this before except when writing informally. I still think though that it's a gross error and misunderstanding on the part of those voting for 2.

McGiord
Apr 16, 2011, 10:09 AM
I was taken aback to read that the physics guys suggest that this could be interpreted as 2. I 've never seen this before except when writing informally. I still think though that it's a gross error and misunderstanding on the part of those voting for 2.

The assumption of using an asterisk in between the 2 and the parenthesis makes the result to be 288.
If no assumption is made the result is 2.
The different software that give the result of 288 are also assuming that there is an asterisk.

If we re-read the OP post it is clear that there is nothing missing in the expression.

blow45
Apr 16, 2011, 10:17 AM
you are confusing me....you mean the assumption between 2 and the parentheses right? :confused: If nothing is assumed there, and in formal math nothing IS assumed there, then the answer is 288. I didn't say there was anything missing, just that I am not accustomed to this kind of notation implying a * there.

McGiord
Apr 16, 2011, 12:54 PM
you are confusing me....you mean the assumption between 2 and the parentheses right? :confused: If nothing is assumed there, and in formal math nothing IS assumed there, then the answer is 288. I didn't say there was anything missing, just that I am not accustomed to this kind of notation implying a * there.

Yes I mean the 2...my mistake

TuffLuffJimmy
Apr 16, 2011, 01:08 PM
The assumption of using an asterisk in between the 2 and the parenthesis makes the result to be 288.
If no assumption is made the result is 2.
The different software that give the result of 288 are also assuming that there is an asterisk.

If we re-read the OP post it is clear that there is nothing missing in the expression.

This isn't true at all. There's no reason that an asterisk would change the order of operations.

-aggie-
Apr 16, 2011, 01:47 PM
This isn't true at all. There's no reason that an asterisk would change the order of operations.

I was thinking the same thing.

chris200x9
Apr 16, 2011, 01:56 PM
holy crap 15 pages:eek: I can't believe ADULTS are this bad at math...I'd flunk an eighth grader for getting 2...congratulations half of macrumors you went full retard.

blow45
Apr 16, 2011, 01:58 PM
I wouldn't think everyone who's voted is an adult, still it's a bit disconcerting that half got it wrong.

McGiord
Apr 16, 2011, 04:50 PM
This isn't true at all. There's no reason that an asterisk would change the order of operations.

The asterisk do change the result, in any computer program the asterisk will make this expression provide a different result.
Try defining a variable with this expression in BASIC, PASCAL, FORTRAN.

I showed several examples of commonly used spreadsheet programs: excel, OpenOffice, Numbers, Google Docs, etc.

holy crap 15 pages:eek: I can't believe ADULTS are this bad at math...I'd flunk an eighth grader for getting 2...congratulations half of macrumors you went full retard.

What do you mean by full retard?

I wouldn't think everyone who's voted is an adult, still it's a bit disconcerting that half got it wrong.

Age and maturity are two different things, that there is a correlation between them doesn't explain why some people see things differently.

Why do you say that half are wrong?
The poll is showing otherwise.

blow45
Apr 16, 2011, 05:20 PM
Age and maturity are two different things, that there is a correlation between them doesn't explain why some people see things differently.

Why do you say that half are wrong?
The poll is showing otherwise.

Ι am not sure what you mean, half have one result and the other half the other result, if we accept there's only one right notation (formalism) for this, half of the people are wrong that's what I am saying.

Gonzo3333
Apr 16, 2011, 05:44 PM
Excuse - exponent
My - multiplication
Dear - division
Sally - subtraction

48/2(9+3)=2

9+3=12

12x2=24

48/24=2

How on Earth or any other planet, galaxy could you get 288? That is like 5th grade math. My guess is that most people forgot the order of operations.

iJohnHenry
Apr 16, 2011, 05:45 PM
half of the people are wrong that's what I am saying.

Who the Hell cares? This is not exactly celestial mechanics.

-aggie-
Apr 16, 2011, 05:47 PM
Excuse - exponent
My - multiplication
Dear - division
Sally - subtraction

48/2(9+3)=2

9+3=12

12x2=24

48/24=2

How on Earth or any other planet, galaxy could you get 288? That is like 5th grade math. My guess is that I forgot the order of operations.

Fixed for you

ender land
Apr 16, 2011, 06:51 PM
How on Earth or any other planet, galaxy could you get 288? That is like 5th grade math. My guess is that most people forgot the order of operations.

You realize that multiplication and division (as well as addition and subtraction) are evaluated from left to right when using order of operation as they are the same "order," right?

What does this expression equal?
100/10/10/10/10*100

The ONLY way to get 2 (even if this is what the writer of the equation meant) is to assume things about the expression which are not explicitly stated.

Using only "48/2(9+3)" the answer is always 288. If you start making assumptions you can make several which cause the answer to become 2. But as written, with the expression as stated, the answer is 288.

Mac'nCheese
Apr 16, 2011, 07:52 PM
Excuse - exponent
My - multiplication
Dear - division
Sally - subtraction

48/2(9+3)=2

9+3=12

12x2=24

48/24=2

How on Earth or any other planet, galaxy could you get 288? That is like 5th grade math. My guess is that most people forgot the order of operations.

It is fifth grade math and you did it wrong.

McGiord
Apr 16, 2011, 10:09 PM
More evidence that you need the asterisk to obtain 288.

-aggie-
Apr 16, 2011, 10:21 PM
More evidence that you need the asterisk to obtain 288.

You are fail.

Mexbearpig
Apr 16, 2011, 10:34 PM
I see it as 288. I'm pretty anal about parentheses as I'm in ap chem. So I'm paranoid and use a lot of parentheses. And the lack of parentheses disturbs me.

InsanelyApple
Apr 16, 2011, 11:14 PM
Hmm interesting. If you treat it like a fraction.

48
__________
2(9+3)

You will get 2.

But if you don't treat it like a fraction and just say 48 divided by 2 times (9+3) you get 228.

Very interesting. Nice brain teaser.

InsanelyApple
Apr 16, 2011, 11:19 PM
I'm pretty anal about parentheses as I'm in ap chem. So I'm paranoid and use a lot of parentheses. And the lack of parentheses disturbs me.

Amen to that brother.

SidBala
Apr 16, 2011, 11:20 PM
Excuse - exponent
My - multiplication
Dear - division
Sally - subtraction

48/2(9+3)=2

9+3=12

12x2=24

48/24=2

How on Earth or any other planet, galaxy could you get 288? That is like 5th grade math. My guess is that most people forgot the order of operations.

My guess is that you had no idea about the fact that multiplication and division have the same precedence. And so do addition and subtraction for that matter.

People are not stupid. This single point is what has spawned so many replies to this thread.

TuffLuffJimmy
Apr 17, 2011, 12:50 AM
More evidence that you need the asterisk to obtain 288.

Dude, take a math class. Just because a programming language requires you to use an asterisk (of course because it needs to know when to multiply, not all languages can deal with implicit multiplication) doesn't make it true.

Please, ask C++ or Java to explain the meaning of life. Then we can have that argument settled too.

web_god61
Apr 17, 2011, 01:39 AM
The answer is 2 because of the distributive property of multiplication.

I'm sure we all agree that 2 ÷ 6x != 2 ÷ 6 * x. Same idea applies, 6x = 6(x).

People falsely assume that a(b + c) = a * (b + c), this is not true altho it does work out most of the time. Imagine a(b + c) expanded to (a * b) + (a * c) and not a * (b + c).

You can rewrite the equation 48 / (9x + 3x) as:
48 / x(9 + 3) => 48 / x(12) => 48 / 12x => 4 * (1 / x) => 4 / x.

and not like:
48 / x * (9 + 3) => 48 / x * 12 => 576 / x <--Wrong!

Arguing over order of operations is a moot point, everyone agrees that BEDMAS (or PEDMAS, etc) applies. The error is that you have to simplify the equation before you you apply BEDMAS.

So 48 / 2(9+3) simplifies to 48 / (18+6), then solve.

Mac'nCheese
Apr 17, 2011, 10:38 AM
The answer is 2 because of the distributive property of multiplication.

I'm sure we all agree that 2 ÷ 6x != 2 ÷ 6 * x. Same idea applies, 6x = 6(x).

People falsely assume that a(b + c) = a * (b + c), this is not true altho it does work out most of the time. Imagine a(b + c) expanded to (a * b) + (a * c) and not a * (b + c).

You can rewrite the equation 48 / (9x + 3x) as:
48 / x(9 + 3) => 48 / x(12) => 48 / 12x => 4 * (1 / x) => 4 / x.

and not like:
48 / x * (9 + 3) => 48 / x * 12 => 576 / x <--Wrong!

Arguing over order of operations is a moot point, everyone agrees that BEDMAS (or PEDMAS, etc) applies. The error is that you have to simplify the equation before you you apply BEDMAS.

So 48 / 2(9+3) simplifies to 48 / (18+6), then solve.

Nope, you are wrong in saying that the order of operations is a moot point. Its is exactly the point. You can't simply ignore it and use the distributive property of multiplication to get the answer you want to. The whole point of the O.o.O. is so people all do simple math problems like this in the correct order.
Another way to see your mistake is in your wording of the post. "You can rewrite the equation" and "The error is that you have to simplify the equation before you you apply BEDMAS." Wrong. Once you rewrite the equation, you are dealing with a new math problem. The problem is to be solved as given. Its a test of BEDMAS or PEMDAS or whatever you call OoO. Changing the equation is changing the question. And why do you think we have to simplify the equation first? I see no proof that we have to do so....

(marc)
Apr 17, 2011, 11:07 AM
Wow, who knew MacRumors was this bad at math. I wonder what the percentage would be on a Linux forum :D

Dr Kevorkian94
Apr 17, 2011, 11:44 AM
Wow, who knew MacRumors was this bad at math. I wonder what the percentage would be on a Linux forum :D

ha but i bet if i ask any math oriented teacher or my fifth grade brother they will get 288

Mac'nCheese
Apr 17, 2011, 12:00 PM
ha but i bet if i ask any math oriented teacher or my fifth grade brother they will get 288

People are over thinking it and trying to feel smart. It's really a simple problem.

McGiord
Apr 17, 2011, 12:14 PM
Dude, take a math class. Just because a programming language requires you to use an asterisk (of course because it needs to know when to multiply, not all languages can deal with implicit multiplication) doesn't make it true.

Please, ask C++ or Java to explain the meaning of life. Then we can have that argument settled too.

I will gladly take a new math class if the topic of interest will actually teach me something.

Explaining the meaning of life with Java or C++:
The program will need a database or reference library to obtain the answer.
Therefore, to answer your question they could prompt the result by opening the web browser to a result like:
http://en.wikipedia.org/wiki/The_meaning_of_life

The meaning of life has nothing to do with this thread, even some people seem to be trying to give their life a meaning by posting on this thread/forum.

Nope, you are wrong in saying that the order of operations is a moot point. Its is exactly the point. You can't simply ignore it and use the distributive property of multiplication to get the answer you want to. The whole point of the O.o.O. is so people all do simple math problems like this in the correct order.
Another way to see your mistake is in your wording of the post. "You can rewrite the equation" and "The error is that you have to simplify the equation before you you apply BEDMAS." Wrong. Once you rewrite the equation, you are dealing with a new math problem. The problem is to be solved as given. Its a test of BEDMAS or PEMDAS or whatever you call OoO. Changing the equation is changing the question. And why do you think we have to simplify the equation first? I see no proof that we have to do so....

For much that I want to believe you, I can't.

TuffLuffJimmy
Apr 17, 2011, 12:39 PM
I will gladly take a new math class if the topic of interest will actually teach me something.

Okay, well then take a sixth grade math class and learn about order of operations, since you don't know anything about it now.

bergmont
Apr 17, 2011, 12:54 PM
Who writes equations like that????

If the answer matters, then it should be written unambiguously 48/(2(9+3)) or (48/2)(9+3).

I read 2(9+3) as a single term. Order of operations don't account for the jacked up way that we type out equations...they assume proper formatting of the equation.

Mac'nCheese
Apr 17, 2011, 01:07 PM
For much that I want to believe you, I can't.

So you are going to take the word of your rabbi who clearly stated that pemdas is not"a well known theory". The only thing he proved is my statement that people are over thinking a simple math problem.

TuffLuffJimmy
Apr 17, 2011, 02:05 PM
Who writes equations like that????

If the answer matters, then it should be written unambiguously 48/(2(9+3)) or (48/2)(9+3).

I read 2(9+3) as a single term. Order of operations don't account for the jacked up way that we type out equations...they assume proper formatting of the equation.

True that it does make it harder to read, but it does not make it ambiguous.

McGiord
Apr 17, 2011, 04:05 PM
Ι am not sure what you mean, half have one result and the other half the other result, if we accept there's only one right notation (formalism) for this, half of the people are wrong that's what I am saying.

Actually it is showing 51% for one side and 49% for the other.
If there is no statistical difference between them, you could say that one half is in favor of one of them vs the other half.

The sample size and the error are key to define this.

But as the poll has not been closed yet, and the sample size and error have not been established we cannot make statistical conclusions.

you realize that multiplication and division (as well as addition and subtraction) are evaluated from left to right when using order of operation as they are the same "order," right?

What does this expression equal?
100/10/10/10/10*100

the only way to get 2 (even if this is what the writer of the equation meant) is to assume things about the expression which are not explicitly stated.

Using only "48/2(9+3)" the answer is always 288. If you start making assumptions you can make several which cause the answer to become 2. But as written, with the expression as stated, the answer is 288.

1

EricNau
Apr 17, 2011, 05:42 PM
MODERATOR NOTE

I've had to remove the last 12 posts in this thread for being far too unfriendly and unnecessarily personal. Please try to keep this thread on-topic and cordial.

Thanks. :)

McGiord
Apr 17, 2011, 05:45 PM
Who writes equations like that????

If the answer matters, then it should be written unambiguously 48/(2(9+3)) or (48/2)(9+3).

I read 2(9+3) as a single term. Order of operations don't account for the jacked up way that we type out equations...they assume proper formatting of the equation.

Agree.

Love
Apr 17, 2011, 07:46 PM
I read it as 48/24 = 2.

blow45
Apr 17, 2011, 08:19 PM
Dude, take a math class. Just because a programming language requires you to use an asterisk (of course because it needs to know when to multiply, not all languages can deal with implicit multiplication) doesn't make it true.

Please, ask C++ or Java to explain the meaning of life. Then we can have that argument settled too.

good post.

bobertoq
Apr 17, 2011, 10:19 PM
Who writes equations like that????

If the answer matters, then it should be written unambiguously 48/(2(9+3)) or (48/2)(9+3).I agree with this.

Doing the equation left to right I get 288.

JoeG4
Apr 17, 2011, 10:25 PM
Still going?!

MacFan782040
Apr 18, 2011, 12:25 AM
Please Excuse My Dear Aunt Sally

Eclipse278
Apr 19, 2011, 11:41 AM
Please Excuse My Dear Aunt Sally

Wow we could have saved 17 pages? :rolleyes:

InsanelyApple
May 1, 2011, 09:37 PM
Sorry for thread bumping, but I need to mention something. It's called juxtaposition, and it says that anything multiplied goes together, which makes sense. Would you say 1/2X is:

1
_
2X

or

1
_X
2

Most math teachers, professors, and students would say the first one, not the second. So here would not be an exception to that. Plus I vote that we get rid of the ÷ and the / permanently in math and only use fractions, that way we don't get confused like this.

iApples
May 1, 2011, 10:48 PM
This thread needs to be closed. Not everyone is going to agree and it should be left at that.

dominickator
May 1, 2011, 11:43 PM
It's really funny how 50% of ADULTS get this extremely simple math problem wrong.

I'm in 7th grade and we've leaned PEMDAS recently.

PEMDAS means Parenthesis Expontent Multiplication Divison Addition Subtraction, and that's the order you do the problem in.

So doing 48/2(9+3), follow PEMDAS. So the first step is doing what's inside the parenthesis so it'll be 48/2(12). So then, still following PEMDAS, you multiply 2 by 12 and get 24. So now you have 48/24. And the answer is obviously 2.

Seriously guys, getting proved wrong by a 13 year old??

ender land
May 2, 2011, 12:00 AM
It's really funny how 50% of ADULTS get this extremely simple math problem wrong.

I'm in 7th grade and we've leaned PEMDAS recently.

PEMDAS means Parenthesis Expontent Multiplication Divison Addition Subtraction, and that's the order you do the problem in.

So doing 48/2(9+3), follow PEMDAS. So the first step is doing what's inside the parenthesis so it'll be 48/2(12). So then, still following PEMDAS, you multiply 2 by 12 and get 24. So now you have 48/24. And the answer is obviously 2.

Seriously guys, getting proved wrong by a 13 year old??

...

I weep for our future.

There are arguments for this being equal to 2 which are somewhat valid or convincing. This is not even close to being one of them. Do people in school really not learn that multiplication/division and addition/subtraction are of equal precedence? Are teachers really teaching so poorly on this note?

iApples
May 2, 2011, 12:01 AM
It's really funny how 50% of ADULTS get this extremely simple math problem wrong.

I'm in 7th grade and we've leaned PEMDAS recently.

PEMDAS means Parenthesis Expontent Multiplication Divison Addition Subtraction, and that's the order you do the problem in.

So doing 48/2(9+3), follow PEMDAS. So the first step is doing what's inside the parenthesis so it'll be 48/2(12). So then, still following PEMDAS, you multiply 2 by 12 and get 24. So now you have 48/24. And the answer is obviously 2.

Seriously guys, getting proved wrong by a 13 year old??

TuffLuffJimmy
May 2, 2011, 02:27 AM
It's amazing that no matter how many pages this thread goes on for there are still people who butt in and completely ignore order of operations and complain about the ambiguity of the problem. It's not ambiguous, and it's an extremely easy math problem.

brayhite
May 2, 2011, 07:18 PM
I got 13?????

iJohnHenry
May 2, 2011, 07:22 PM
I got 13?????

Thinking outside the box is good. :cool:

Thinking outside the Solar System is less so. :(

McGiord
May 2, 2011, 07:28 PM
What this thread proofs is that we have a big communication gap between the different people in this forum.

And for those who say is 288:
:rolleyes:

JoeG4
May 2, 2011, 07:50 PM
Ya'll remind me of this for some funny reason:

http://articles.cnn.com/1999-09-30/tech/9909_30_mars.metric_1_mars-orbiter-climate-orbiter-spacecraft-team?_s=PM:TECH

iJohnHenry
May 2, 2011, 07:51 PM
What this thread proofs is that we have a big communication gap between the different people in this forum.

And for those who say is 288:
:rolleyes:

Us "2"s are just one vote behind the dullards. ;)

I fail to see a closing date, but regardless, there will be a ground-swell for a judicial recount. :mad:

Unless we win.

McGiord
May 2, 2011, 08:12 PM
Ya'll remind me of this for some funny reason:

http://articles.cnn.com/1999-09-30/tech/9909_30_mars.metric_1_mars-orbiter-climate-orbiter-spacecraft-team?_s=PM:TECH

Definitely a communication issue.:)

Huntn
May 3, 2011, 10:47 AM
It's been too long since I've done this kind of math. As all ready been stated, the answer is 2 or 288. The correct answer has to be based on what takes priority the division or the parenthesis? My initial impression was 288 because I was thinking the parenthesis took priority. Therefore 48/2=24*(9+3); 24*12=288. Now I'm thinking the division takes priority so the answer would be 2. 48/2(12)= 48/24= 2. :)

Which one is it?

iStudentUK
May 3, 2011, 10:57 AM
It's been too long since I've done this kind of math. As all ready been stated, the answer is 2 or 288. The correct answer has to be based on what takes priority the division or the parenthesis? My initial impression was 288 because I was thinking the parenthesis took priority. Therefore 48/2=24*(9+3); 24*12=288. Now I'm thinking the division takes priority so the answer would be 2. 48/2(12)= 48/24= 2. :)

Which one is it?

That's what the last 400 posts have been about!

I think everyone agrees the brackets take priority, it is the next step that causes tension! Is is 48/2 first or 2*12?

Using the BODMAS (or PEDMAS as many know it as) approach 288 is probably accurate; however, BODMAS is not a law. Other conventions exist. There is no maths government that says it must be used!

My personal view is that the "/" symbol isn't meant to be read as a "/" symbol but a "___" symbol. Mathematicians tend not to use "/"; however, it is used when coding on a computer.

In reality, the 288 and 2 have been at roughly 50% for ages. So the actual true answer (if there is one!) doesn't really matter in my opinion. The equation should be written in a way that nobody could argue about.

-aggie-
May 3, 2011, 11:00 AM
What this thread proofs is that we have a big communication gap between the different people in this forum.

And for those who say is 288:
:rolleyes:

One of the more ironic posts of this thread.

Huntn
May 3, 2011, 11:23 AM
In reality, the 288 and 2 have been at roughly 50% for ages. So the actual true answer (if there is one!) doesn't really matter in my opinion. The equation should be written in a way that nobody could argue about.

Agreed. Priorities have to be established somewhere.

If it was written like:
48
2(9+3)

I'm thinking this would be better. :)

fermi44
May 7, 2011, 05:00 PM
This stupid thing has been going around for months now.

Dagless
May 7, 2011, 06:05 PM
This stupid thing has been going around for months now.

You had to revive a 4 day old thread for that too :rolleyes:.

oakscastle
Jun 23, 2011, 03:57 AM
People seam to be forgetting distributive properties when dealing with this equation. Consider the following:
48/(9x+3x) = 48/x(9+3) The X is part of the Parenthesis.

48/(18+6), with this everyone would get 2

now, pull a 2 out and you have:

48/2(9+3) = 2

Seams pretty simple if you understand distributive properties.

iStudentUK
Jun 23, 2011, 04:00 AM
Hooray, this thread is back again! :eek:

-aggie-
Jun 23, 2011, 08:51 AM
Hooray, this thread is back again! :eek:

Seems so. This thread seemingly has a life of its own.

(marc)
Jun 23, 2011, 10:08 AM
People seam to be forgetting distributive properties when dealing with this equation. Consider the following:
48/(9x+3x) = 48/x(9+3) The X is part of the Parenthesis.

48/(18+6), with this everyone would get 2

now, pull a 2 out and you have:

48/2(9+3) = 2

Seams pretty simple if you understand distributive properties.

You got your first equation wrong. Quite an achievement, I dare say!

Littleodie914
Jun 23, 2011, 10:43 AM
I've seen problems like this before. :)

The issue is always that some people read PEMDAS incorrectly, assuming that multiplication is performed prior to division, as it appears first in the acronym.

In fact, (multiplication and division) along with (addition and subtraction) have the same level of precedence, and are simply performed left-to-right.

48 / 2 (9 + 3)
parentheses first
48 / 2 x 12
left-to-right, NOT 'multiplication then division'
24 x 12

= 288

:)

(There is of course, the obvious confusion as to whether the divisor acts like a 'bar', separating the 'top and bottom' sections of the equation. I think it's safest to assume that it does not. Don't lose any sleep, that aspect of the problem is totally up to an individual's interpretation.)

oakscastle
Jun 23, 2011, 02:16 PM

There is one fundamental issue that the 288 folks do not understand, or do not know, or whatever.

2(9+3) is NOT the same as 2*(9+3)

As standalone expressions, they will yield the same result. However, when used as part of another expression they are NOT the same. The lack of the operand is the key, this denotes that the 2 is part of the parenthesis and must be resolved before moving to the 'E', we are using PEMDAS.

[EDIT:]
I just realized the 288 folks are changing the equation, which is why you get 288. Follow the rules!

48/2(9+3) = 48/2(12) [Note, you still have parenthesis], so 48/2(12) = 48/24 = 2

NOT, 48/2*12 This is NOT the equation as written, so follow your own rules and you will get 2.

Mac'nCheese
Jun 23, 2011, 03:04 PM
[EDIT:]
I just realized the 288 folks are changing the equation, which is why you get 288. Follow the rules!

48/2(9+3) = 48/2(12) [Note, you still have parenthesis], so 48/2(12) = 48/24 = 2

NOT, 48/2*12 This is NOT the equation as written, so follow your own rules and you will get 2.

If you do the equation as you wrote and follow the rules, you have to divide 48 by 2 first then multiply by 12. The rules of PEMDAS clearly state that when you do multiplication and division, you go left to right; you don't do multiplication first. Same thing when you get down to Addition and Subtraction. Its left to right not Adding first, subtracting second.

oakscastle
Jun 23, 2011, 04:52 PM
If you do the equation as you wrote and follow the rules, you have to divide 48 by 2 first then multiply by 12. The rules of PEMDAS clearly state that when you do multiplication and division, you go left to right; you don't do multiplication first. Same thing when you get down to Addition and Subtraction. Its left to right not Adding first, subtracting second.

I agree with PEMDAS and L-R, but 2(12) is not the same as 2*12. You need to finish P before you move on. Therefore, 2(12) must still be resolved to 24.

Mac'nCheese
Jun 23, 2011, 05:00 PM
I agree with PEMDAS and L-R, but 2(12) is not the same as 2*12. You need to finish P before you move on. Therefore, 2(12) must still be resolved to 24.

You did finish P first. Its is down to one number and no more work needs to be done with it. When a number is next to another number that is in (), multiplication is just as implied as if you had a * or X in between the two.

oakscastle
Jun 23, 2011, 05:33 PM
You did finish P first. Its is down to one number and no more work needs to be done with it. When a number is next to another number that is in (), multiplication is just as implied as if you had a * or X in between the two.

Well, I see where our differances are and I must respectfully disagree. If a number is next to the (), then you must use distributive Properties to fully resolve the () - you cant just treat it as multiplication. All my math from grade school to Calc taught this, which is why I must disagree. :)

Mac'nCheese
Jun 23, 2011, 05:37 PM
Well, I see where our differances are and I must respectfully disagree. If a number is next to the (), then you must use distributive Properties to fully resolve the () - you cant just treat it as multiplication. All my math from grade school to Calc taught this, which is why I must disagree. :)

Ok fair enough to agree to disagree. Good day to you, sir. :)

-aggie-
Jun 23, 2011, 06:04 PM
Well, I see where our differances are and I must respectfully disagree. If a number is next to the (), then you must use distributive Properties to fully resolve the () - you cant just treat it as multiplication. All my math from grade school to Calc taught this, which is why I must disagree. :)

rhett7660
Jun 23, 2011, 07:02 PM
What does wolframalpha say!

http://www.wolframalpha.com/input/?i=48%2F2%289%2B3%29%3D

ender land
Jun 23, 2011, 07:10 PM
Well, I see where our differances are and I must respectfully disagree. If a number is next to the (), then you must use distributive Properties to fully resolve the () - you cant just treat it as multiplication. All my math from grade school to Calc taught this, which is why I must disagree. :)

You know, I was going to post something more involved about how depressing it is you made it through that much math and do not realize this equation is equal to 288, though misleading, but I'm just going to tell you to read the thread instead, since plenty of people have already made the logical arguments which unequivocally support that expression having a value of 288.

The only time it doesn't is if you make assumptions. And you know what they say about assumptions... ;)

oakscastle
Jun 23, 2011, 07:44 PM
First off, I'd like to thank Mac'NCheese for a civil disagreement. As for the rest of you who can't find anything better to do than to be sarcastic and degrading - shove it!!
ender land: I could say the same about you. From where I am standing, I can not understand how anyone can miss, or not understand simple distributive properties - which is depressing. As for this thread "proving" 288, there are plenty of posts proving it's 2.

ender land
Jun 23, 2011, 07:50 PM
What does the "/" sign mean?

oakscastle
Jun 23, 2011, 07:58 PM
What does the "/" sign mean?

The "/" is division.

ender land
Jun 23, 2011, 08:02 PM
So 48/2(9+3)

becomes

48 divided by two times twelve

(since we all agree - hopefully :confused: - this reduces to at least 48/2(12)

Do order of operations on the sentence above and you'll find your answer, and it's not 2 ;)

Unless of course you for some reason read the equation to be - 48 / 2(9+3) - which is an assumption outside what is actually written.

oakscastle
Jun 23, 2011, 08:09 PM
It's not that we disagree on the order of operations, we disagree on the meaning of 2(12). You state this = 2*12, I disagree and believe you still have to use distributive properties to completely resolve the (). It has nothing to do with performing the M and D calculations L-R, I do that after I have resolved the ().

Gregg2
Jun 23, 2011, 08:33 PM
Has anyone made the point that if written out instead of typed, the problem would logically look like this:

48
_____

2(9+3)

??

At least it would have been when I was in school, before computers took over the world. It just doesn't seem like it would be

48/2
_____

(9+3)

But that would give you the same answer.

Turning it into 24*12 just seems wrong intuitively. To me, getting there would require it to be written as (48/2)*(9+3)

I dunno. Just a layman's perspective.

Mac'nCheese
Jun 23, 2011, 09:51 PM
First off, I'd like to thank Mac'NCheese for a civil disagreement. .

Back atcha. Besides, I need the karma to work off the warning I just got for not being civil in another thread. :D

na1577
Jun 23, 2011, 11:59 PM
I stupidly voted 288 when this thread was new. Now I can't figure out why.

oakscastle
Jun 24, 2011, 01:48 AM
I stupidly voted 288 when this thread was new. Now I can't figure out why.

Thats ok, remember, the first step to recovery is admitting you have a problem... :D

yg17
Jun 24, 2011, 11:54 AM
Has anyone made the point that if written out instead of typed, the problem would logically look like this:

48
_____

2(9+3)

??

At least it would have been when I was in school, before computers took over the world. It just doesn't seem like it would be

48/2
_____

(9+3)

But that would give you the same answer.

Turning it into 24*12 just seems wrong intuitively. To me, getting there would require it to be written as (48/2)*(9+3)

I dunno. Just a layman's perspective.

Yes, in the real world, this might be written differently to make it clearer, but the point of the exercise is that you can write a problem on one like that and even though it looks ambiguous, with order of operations, it's not ambiguous at all. Following OOO correctly, the answer is 288.

skinuca
Jul 7, 2011, 03:31 PM

Amazing that it was tied before i voted. Had no idea it was. After reading though all the pages, still not clear why so many get to 2 as the answer, but it is fun reading though all the explanations.

Don't panic
Jul 7, 2011, 04:11 PM

Amazing that it was tied before i voted. Had no idea it was. After reading though all the pages, still not clear why so many get to 2 as the answer, but it is fun reading though all the explanations.

because most people read 1/2x as "1 divided by 2x" and not as "x divided by 2"

CaptMurdock
Jul 9, 2011, 03:34 AM
I think it's helpful, in going by Order of Operations, to treat division as multiplication-by-inverse:

48/2(9 + 3)
48/2*12
48*1/2*12
24*12
288

Allellujah
Jan 18, 2012, 05:46 PM
Lol I don't understand how people can't get 2 as an answer. While following order of operations, you obviously do the parenthesis first, but that doesn't really matter since no matter which way you do it, you will do (9+3), first. So the real question is, do we divide 48 by 24, or do multiply 24 by 12? The Acronym PEMDAS suggest that we Multiply before we Divide, but that isn't the case, however. You do them in order from left to right, normally, so whichever comes first, you do that first, normally. I've read some post of people asking whether its a fraction sign or a regular division sign, but from what I understand, there is no difference between the two. If you simplify the fraction 48/24, is 48 not being divided by 24, ultimately giving you 2 as an answer? So after we solve the equation in the parenthesis, we end up with 48/2(12). That said, if we do simple Order of Operations, going left to right, we will end up with 288 as an answer. Going back to what I said about fractions and division being the same. When you look at fractions, and get something like 12(3x+5) OVER 6(3x+5), you would first solve the equation in the numerator, then the denominator, and then divide/simplify. That being said, if we have 48 OVER 24, the answer will ultimately be 2, which is why some people get 2 as an answer.

People have been taught correctly about Order of Operations, there is no fault in the way either of the Answer's Representatives are doing their math. It is all a matter of how you look at the problem, because both are correct, and with that being said, we know that is wrong. We cannot have math equations to be equal with more than one answer, unless you are using variables, < & > signs, or etc. However, both of the answers, 288 & 2, seem to be true. I can understand how each answer would be obtainable, but personally I believe 2 is the correct answer.;)

iStudentUK
Jan 18, 2012, 05:57 PM
We cannot have math equations to be equal with more than one answer, unless you are using variables, < & > signs, or etc.

X^2 = 4
Solve for X...

sin(Y) = 1
Solve for Y...

wordoflife
Jan 18, 2012, 06:21 PM
Oh dear did I really pick 288? :eek:
It should be 2.

jeremyshaw
Jan 18, 2012, 06:26 PM
o.0

Allellujah
Jan 18, 2012, 08:53 PM
X^2 = 4
Solve for X...

sin(Y) = 1
Solve for Y...

X and Y are variables lol.

balamw
Jan 18, 2012, 08:58 PM
X and Y are variables lol.

X=48/2(9+3)

solve for X. Seem familiar?

EDIT: or arctan(1)?

B

Suno
Jan 18, 2012, 09:06 PM
It's 288.

48/2*12

So do the equation from left to right and you'll get 24 * 12 which equals 288.

wordoflife
Jan 18, 2012, 09:31 PM
So do the equation from left to right and you'll get 24 * 12 which equals 288.

Interesting.
I was looking at it as a fraction.

48
___ = 2

(2)(12)

which is
48
___ = 2
24

lewis82
Jan 18, 2012, 09:37 PM
There isn't any definite answer. Since it is ambiguous one must use parenthesis.

But as it is written right now, I'd say it is 2. Since there is an implicit multiplication, I think it must be made before the division, even though the order of operations says otherwise. When you're used to calculus and higher algebra, x(y+z) usually ends up being treated as a single entity in your head (at least that's how I see it), since it can be developped and become (xy+xz).

TL;DR: use LaTeX and produce .png files. No more problems. I started learning it today, so I was struggling with the document headers and such, but otherwise I would have used this to illustrate my point of view.

<snip>

Turning it into 24*12 just seems wrong intuitively. To me, getting there would require it to be written as (48/2)*(9+3)

I dunno. Just a layman's perspective.

Totally agree.

Skyrim
Jan 18, 2012, 10:15 PM
2. I can see how two answers come out. But i think it should be 2.

iStudentUK
Jan 19, 2012, 03:10 AM
X and Y are variables lol.

Fair enough, missed where you said that. Just seems more elegant with them in, but it's easy to rephrase to remove X. (Just like the equation above could be written 48/2(9+3)=X)

What about simple 'sqrt4'? Or 'arcsin(1)'? More than one answer to those.

---

I still maintain my original opinion using a '/' is forgivable on a forum like this, but when hand writing or using decent software use '_' instead like actual maths-y people do. If you have to use '/' have the courtesy to use lots of brackets!

http://withfriendship.com/images/d/18041/Equation-image.png

CalBoy
Jan 19, 2012, 01:30 PM
2. I can see how two answers come out. But i think it should be 2.

Not if you follow the order of operations.
Parentheses
Exponents
Multiplication/Division

48/2(9+3)=48/2(12)

48/2(12)=24(12)

24(12)=288

To get 2, it should read: 48/(2(9+3))

The "/" mark is exclusively division. It can only operate as a fraction bar when both the numerator and denominator are either single values or bound by parentheses.

lewis82
Jan 19, 2012, 04:42 PM
The "/" mark is exclusively division. It can only operate as a fraction bar when both the numerator and denominator are either single values or bound by parentheses.

To you what is a division? To me it is the same exact thing as a fraction, except that the result of a division is usually expressed as a real number while a fraction stays in fractional form because it's simpler to work with.

Firestar
Jan 19, 2012, 04:53 PM

You do (9+3) first, so you get 48/2(12). Then you divide 48 by 2 to get 24 making the equation 24(12). When you multiply, you get 288. How are people getting 2? I read their posts and I still don't understand.

eric/
Jan 19, 2012, 05:07 PM

You do (9+3) first, so you get 48/2(12). Then you divide 48 by 2 to get 24 making the equation 24(12). When you multiply, you get 288. How are people getting 2? I read their posts and I still don't understand.

Because it's all in the way you look at the problem. For those who normally do calculus level math their minds may tend to see it as

48
_____
2*(9+3)

not as 48÷2*(9+3)

Both are correct ways of looking at the problem. It's just a matter of mathematical semantics.

CalBoy
Jan 19, 2012, 05:10 PM
To you what is a division? To me it is the same exact thing as a fraction, except that the result of a division is usually expressed as a real number while a fraction stays in fractional form because it's simpler to work with.

I'm referring strictly in the operational sense. The "/" mandates an operation, even if it is being used to denote an unsimplified fraction. Because of the way the problem in the OP is written, the fraction is properly viewed as: 48/2*12 because the 2 and (9+3) are not bound by additional parentheses, making 48 the numerator and 2 the entire denominator.

eric/
Jan 19, 2012, 05:12 PM
I'm referring strictly in the operational sense. The "/" mandates an operation, even if it is being used to denote an unsimplified fraction. Because of the way the problem in the OP is written, the fraction is properly viewed as: 48/2*12 because the 2 and (9+3) are not bound by additional parentheses, making 48 the numerator and 2 the entire denominator.

÷ is a division sign
/ is a fraction

CalBoy
Jan 19, 2012, 05:16 PM
÷ is a division sign
/ is a fraction

Same thing.

Most people don't use ÷ after 5th grade though because algebra encourages us to view things in fraction and decimal form.

balamw
Jan 19, 2012, 05:18 PM
How are people getting 2?

They reduce 48/2(12) to 48/24 by saying that the implied multiplication takes precedence over the division.

i.e. 48/(2*(12)) vs (48/2)*12.

B

eric/
Jan 19, 2012, 05:19 PM
Same thing.

Most people don't use ÷ after 5th grade though because algebra encourages us to view things in fraction and decimal form.

And now we have resulting confusion because of math semantics. So it's easy to see how you can get both answers, depending on how you approach the problem.

dukebound85
Jan 19, 2012, 05:22 PM
Because it's all in the way you look at the problem. For those who normally do calculus level math their minds may tend to see it as

48
_____
2*(9+3)

not as 48÷2*(9+3)

Both are correct ways of looking at the problem. It's just a matter of mathematical semantics.
Not for me. I read it the way it should be written, which is fairly obvious if you know the OOO

eric/
Jan 19, 2012, 05:34 PM
Not for me. I read it the way it should be written, which is fairly obvious if you know the OOO

False. If it was written correctly for you to do order of operations (basic math level) than it should have been written:

48÷2*(9+3)

not 48/2(9+3) which is:

48
_____

2(9+3)

In calculus you don't write equations like 48/x+6(9+45) or anything like that, you write it as

48
_____

x+6(9+45)

I've already pointed out that it is very easy to interpret this either way, and it's just semantics. But the problem was written as I've shown in the second and third example, not the first. What's obvious to you is unfortunately incorrect.

ender land
Jan 19, 2012, 05:43 PM
False. If it was written correctly for you to do order of operations (basic math level) than it should have been written:

48÷2*(9+3)

Huh, in all my programming I've never seen a time when I am supposed to use ÷ to represent divide. It's always / instead. I guess my math background (4 semesters of calculus) is making me confused ;)

I guess I must be missing something obvious :confused::confused::confused:

My official position on this is the answer is that it is, strictly speaking, 288. However it is perfectly understandable for people to see it as 2 given how poorly written the problem is.

CalBoy
Jan 19, 2012, 06:03 PM
And now we have resulting confusion because of math semantics. So it's easy to see how you can get both answers, depending on how you approach the problem.

Math is not a field where approaches, opinions or flights of fancy count for anything.

http://www.wolframalpha.com/input/?i=48%2F2%289%2B3%29

320633

dukebound85
Jan 19, 2012, 06:11 PM
False. If it was written correctly for you to do order of operations (basic math level) than it should have been written:

48÷2*(9+3)

not 48/2(9+3) which is:

48
_____

2(9+3)

In calculus you don't write equations like 48/x+6(9+45) or anything like that, you write it as

48
_____

x+6(9+45)

I've already pointed out that it is very easy to interpret this either way, and it's just semantics. But the problem was written as I've shown in the second and third example, not the first. What's obvious to you is unfortunately incorrect.

False. It is written correctly as is.

I have never used a % sign since elementary school. / is the same as %. In fact, I never see the % symbol past elementary math teachings or applications.

What's next, are you going to say that "x" is not the same as *?

For one being in calculus, I thought this was obvious

If you want 2, you need those extra (). Otherwise, one is incorrectly applying the OOO

Intended fractions need to be explicitly written with ()'s when writing single line expressions. That is the purpose of ()'s... to give clarity to the expression. If one ever writes code, this is ingrained behavior. Also, if you wanted to evaluate that expression as you suggest (to get 2) in a calculator, how do you type it? With the (). If you type it in verbatim, you get 288.

From Wiki also (if Wolfram, schooling, experience haven't convinced one yet..)

A second way to show division is to use the obelus (or division sign), common in arithmetic, in this manner:

This form is infrequent except in elementary arithmetic.
http://en.wikipedia.org/wiki/Division_(mathematics)

balamw
Jan 19, 2012, 06:16 PM
http://www.wolframalpha.com/input/?i=48%2F2%289%2B3%29

Math is not a field where approaches, opinions or flights of fancy count for anything.

http://www.wolframalpha.com/input/?i=48%2F2%289%2B3%29

Wow. I would have thought for sure that "Camp 2" would have managed to convince Wolfram otherwise in the 8 months since I last posted that link. :p

B

Heynonny
Jan 19, 2012, 06:31 PM
It isn't an equation. It isn't a mathematical expression. There is no "answer."

EDITED TO ADD: An "implied" multiplication between the 2 and the open parenthesis? Who would do that? But if you insist that is to be taken as a given then you could claim 288 with some tiny bit of validity. There is no argument at any level of validity that an additional set of parenthesis is implied, i.e. that the answer is 2.

CalBoy
Jan 19, 2012, 06:38 PM
Wow. I would have thought for sure that "Camp 2" would have managed to convince Wolfram otherwise in the 8 months since I last posted that link. :p

B

Isn't it amazing?

On the other hand, I have heard that if the expression is entered as 48/2(9+3)-246, Wolfram reduces to "everything."

eric/
Jan 19, 2012, 07:46 PM
I don't want to quote each individual response and state the same thing over so I'll just reiterate what I've said previously.

When typing it in, in this example, actually using the dividing signs would have been appropriate. Others may see it different, and that's fine, however you're incorrect from an order of operations standpoint as " / " denotes a fraction whereas ÷denotes division.

You can disagree all you want, but you're wrong. And citing Microsoft Excel doesn't really refute what I've said because it's programmed to use / as a dividing symbol. So what?

This is all I have to say. It's a semantics argument, and it should have been written using ÷ in order to not create confusion, but then if it had been this thread wouldn't have been created.

Also, internet credentials count for nothing. IE "I took 4 semesters of calc" etc...

I lol at each one of you trying to justify your answer of 288, when at any time had somebody said that you would have written the equation as follows:

48
__

2(whatever it was)

you don't write down equations as 48/x+2(39+8) and then solve. You're being dishonest.

dukebound85
Jan 19, 2012, 07:54 PM

You would think that how productivity programs are coded would enlighten the proper use, as would be other science based sources provided.

But....I guess not

eric/
Jan 19, 2012, 07:57 PM

Is going to give you a headache.

I understand ÷ isn't used outside of elementary school, but that's irrelevant.

Again I have to reinforce that if somebody verbally presented this equation to you you would have written it as a fraction, not as an OOO problems, unless you're an elementary math student.

wordoflife
Jan 19, 2012, 08:02 PM
48
____ or 48 ÷ 2(9+3) -> 48 ÷ 2 * 12 :confused:

2(12)

Question is too ambiguous. We'd never see that in a standardized test due to how poorly it is written. Whenever I see a "/" I think of a fraction though.

dukebound85
Jan 19, 2012, 08:03 PM
Is going to give you a headache.

I understand ÷ isn't used outside of elementary school, but that's irrelevant.

Again I have to reinforce that if somebody verbally presented this equation to you you would have written it as a fraction, not as an OOO problems, unless you're an elementary math student.

I wouldn't. Those who aren't quite proficient at math would. There really is no debate as there is no ambiguity. The expression is clear and only yields one possible answer.

To get 2, you violate the basic fundamentals of math. Not quite sure how you don't understand this...

/ is the inverse of multiple. That is the definition. Thus an equivalent expression is 48*2^-1*(9+3)

wordoflife
Jan 19, 2012, 08:07 PM
To get 2, it should read: 48/(2(9+3))

Actually, this true. You can't get 288 by doing 48/(2(9+3))

dukebound85
Jan 19, 2012, 08:09 PM
Actually, this true. You can't get 288 by doing 48/(2(9+3))

OOO is why. When applied to the original expression, using the same OOO, you get, and can only get, 288

When written with the extra(), you get, and can only get, 2

I have yet to see any application, proof or correct reason why it would ever be 2
http://thecorridortheory.blogspot.com/2011/05/ending-48293-debate.html

Matlab gives 288 as does every other piece of mathematical software

eric/
Jan 19, 2012, 08:11 PM
I wouldn't. Those who aren't quite proficient at math would. There really is no debate as there is no ambiguity. The expression is clear and only yields one possible answer.

To get 2, you violate the basic fundamentals of math. Not quite sure how you don't understand this...

/ is the inverse of multiple. That is the definition. Thus an equivalent expression is 48*2^-1*(9+3)

Except you're wrong. / is not the inverse of multiple. / denotes a fraction

÷ is the inverse of a multiple

When somebody states the problem verbally, you will always write it as:

48
___

2(9+3)

unless you're an elementary student in which case you will follow the OOO

and you will get 48(where you will actually be using ÷) 2(9+3)

dukebound85
Jan 19, 2012, 08:20 PM
Except you're wrong. / is not the inverse of multiple. / denotes a fraction

÷ is the inverse of a multiple

When somebody states the problem verbally, you will always write it as:

48
___

2(9+3)

unless you're an elementary student in which case you will follow the OOO

and you will get 48(where you will actually be using ÷) 2(9+3)

That is the point

The OOO is not there to use sometimes,and not other times

If you were correct, then every programmer,mathematical software, and mathematician is wrong. That should be telling

I mean c, matlab, excel, calculator, python, wolfram, google, IDL all give 288
Must be a conspiracy on a worldwide scale. Lol

eric/
Jan 19, 2012, 08:28 PM
That is the point

The OOO is not there to use sometimes,and not other times

If you were correct, then every programmer,mathematical software, and mathematician is wrong. That should be telling

I don't know any other way to explain it to you. You're wrong and I know that's hard to admit on the Internet, but it's simply the case. Had the problem been written with the division sign, it would have been a simple OOO. Since it was written as a fraction, you treat it as such. Bottom line. You can refute that, and that's fine as you automatically interpret / as a division sign, which is something typical of somebody that isn't accustomed to calculus or higher level math, but when spoken, or written, it's:

48
___

2(9+3) or whatever it was

if you would like to agree to disagree, as you interpret the problem differently, fine. But otherwise as far as I'm concerned you're simple incorrect.

mobilehaathi
Jan 19, 2012, 08:29 PM
Except you're wrong. / is not the inverse of multiple. / denotes a fraction

÷ is the inverse of a multiple

÷ and / are exactly the same. To get an answer of 2 you need an extra set of parentheses.

I can't believe I'm actually engaging in this thread. :rolleyes:

eric/
Jan 19, 2012, 08:31 PM
÷ and / are exactly the same. To get an answer of 2 you need an extra set of parentheses.

I can't believe I'm actually engaging in this thread. :rolleyes:

No they are not.

÷ denotes division

/ can denote division but usually denotes a fraction

TEG
Jan 19, 2012, 08:33 PM
÷ and / are exactly the same. To get an answer of 2 you need an extra set of parentheses.

I can't believe I'm actually engaging in this thread. :rolleyes:

Exactly. In college we were taught that ÷ and / are the same. If you want it to read as 48 over 2 times 9 plus 3, you either need the extra parens, write it out like I did, or show it as an actual fraction.

TEG

balamw
Jan 19, 2012, 08:35 PM
I believe that the approach taken at Physics Forums is the only sane way to put an end to this

An issue of mathematical grammar circulating the internet lately has been how to read a mathematical expression like
48÷2(9+3)
that involves a combination of division and implied multiplication.

The standard way to read arithmetic expression (i.e. order of operations) involves dealing with parentheses first, then you do all division and multiplication operations from left to right, then all addition and subtraction operations from left to right.

So, this expression is computed as
48÷2(12)

24(12)

288

It doesn't matter whether or not the multiplication is made explicit, as in
48÷2×(9+3)=288
or if division is represented by a slash, as in
48/2(9+3)=288
all of these variations mean the same thing.

One thing to keep in mind is that not everybody follows the standard. Some people prefer to do implied multiplication before other multiplication and division operations. Some people prefer to do all multiplications before division with /. Some people even prefer to do addition before division with /.

So, when you are reading math from an unfamiliar source, make sure you know what convention they are adopting. And no matter what convention you prefer, you really ought to write things in an unambiguous fashion -- e.g. you should avoid
48/2(9+3)
and instead use the crystal clear
(48/2)(9+3)