48÷2(9+3)

[danclough]

For f*** sake people. This is the most ridiculous thing ever. It's math...there is a RIGHT answer, there's no agree to disagree.

[BossHogg]

I say 2. PEMDAS!

[LeafLover]

I am willing to wager my Gurkha Black Dragon that the answer is 2

[mykeuva]

this is making me dizzy... i guess that the answer is both, depending on what sequence you use... my original thought was 2

It really comes down to the question of whether or not implicit multiplication trumps explicit rules. Here's a little discussion on the topic:

"There is still some development in this area, as we frequently hear

from students and teachers confused by texts that either teach or

imply that implicit multiplication (2x) takes precedence over

explicit multiplication and division (2*x, 2/x) in expressions

such as a/2b, which they would take as a/(2b), contrary to the

generally accepted rules. The idea of adding new rules like this

implies that the conventions are not yet completely stable; the

situation is not all that different from the 1600s."

http://mathforum.org/library/drmath/view/52582.html

Actually, I think this is a pretty good example not of math, but of how people perceive things.

If the equation were written

48/2x

I think most of the people saying 288 would say instead that you divide 48 by 2x.

If the equation were written

48 ÷ 2 * 12, then those saying 2 would say 288.

It's intentionally vague. Hopefully the author intended for it to be that way. If not, it's just a poorly written expression.

[mazolaman]

I am willing to wager my Gurkha Black Dragon that the answer is 2

Aren't they the best and rarest cigars in the world....?wow.

Can we get back to religion and politics now?

[Trevor2118]

Can we get back to religion and politics now?

:rotfl: :rotfl:

[Trevor2118]

Statistically the answer is...................................145.

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.The average of 2 & 288. :rotfl:

PS: thats it for me

[mykeuva]

Statistically the answer is...................................145.

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.The average of 2 & 288. :rotfl:

PS: thats it for me

It's 15....The 4 is silent!!!!

[dochowl]

I'm offf for a week and this is what FoH turns into? Sad... truly sad.

[davidl]

Guys - this is NOT cool...i am studying for the GMAT now, and seriously don't need someone messing with my head now!!!

[Colt45]

I'm offf for a week and this is what FoH turns into? Sad... truly sad.

On one hand I disagree - for the most part, members have been courteous with one another. Some of us (myself included) have had some good natured

fun with it, and a large number of members have simply stayed out of it (kudos).

On the other hand I do, in some ways, agree. A few members have mentioned this has been going around the internet - to me, a kind of internet spam.

Knowing it contentious, it was brought here just the same. So as much as I like to think otherwise, perhaps we are just another internet forum......

[perfectform]

This is not a matter of opinion. The answer is 288. Plain and simple.

[FireDigger]

Before, I would agree with perfectform and TradedDavid, that this equation is not open to interpretations. However, after reading up on juxtaposition, this equation CAN be open to interpretation. Read this:

http://mathforum.org/library/drmath/view/57021.html I'm not about to argue with an EE professor.

Therefore, 2 and 288 are both correct depending on how you read the equation.

[Trevor2118]

On one hand I disagree - for the most part, members have been courteous with one another. Some of us (myself included) have had some good natured

fun with it, and a large number of members have simply stayed out of it (kudos).

On the other hand I do, in some ways, agree. A few members have mentioned this has been going around the internet - to me, a kind of internet spam.

Knowing it contentious, it was brought here just the same. So as much as I like to think otherwise, perhaps we are just another internet forum......

As a moderator, I suppose I am doing a "Ken" on this thread, but as Ross points out "for the most part, members have been courteous with one another".

I think that because we can be courteous and have a bit of fun with it, we are not "just other internet forum".

If the thread becomes offensive, I'll be the first to pull the plug on it.

Perhaps if it drags on too long it should be closed (but I want one more say first )

[Trevor2118]

Perhaps if it drags on too long it should be closed (but I want one more say first )

Can I take you all on a journey.....

.....back to before there was the internet,

.....back before Personal Computers,

.....back before hand-held calculators,

.....back to when I learned mathematics while completing a university degree in Civil and Structural Engineering,

.....back to when a slide rule, logarithms, and trigonometry tables were all there was available.

So let’s consider we are back at that time.

.....So, no Google searching,

.....No “plugging” in values to a calculator,

.....No need to remember computers golden rule..... "“rubbish in, rubbish out"”.

We are going to solve an equation (find x).

2a + 2b = x .....(1)

Equation (1) can be rewritten as:

2( a + b ) = x .....(2)

Equation (1) and (2) are identical..... (I trust no one disagrees at this point)

So, say if a = 9 and b = 3, the result is 24 both times..... (so far, so good)

Let’s make equation (1) a bit more complex by adding a value:

48 + 2a + 2b = x .....(3)

As shown above, equation (3) can be rewritten as:

48 + 2( a + b ) = x .....(4)

Solving (3) and (4) with the same variables for a & b above, we get:

Equation (3)..... 48 + 2x9 + 2x3 = 48 + 18 + 6 = 72

And as equation (3) is equal to equation (4), the result must also be 72.

Equation (4)...... 48 + 2(9 + 3) = 48 + 2(12) = 48 + 24 = 72.

If you add 48 + 2 before multiplying by (9 + 3) you get the wrong answer (600)...

i.e. 48 + 2(9 + 3) = 50(9 + 3) = 50(12) = 600.

This result must be wrong as equations (3) and (4) are identical.

So, let’s make equation (4) a bit more complex by changing the first + to ÷

Equation (4) becomes:

48 ÷ 2(9 + 3) = x .....(5)

Equation (5) must be solved in the same way as equations (1) to (4) or the logic makes no sense.

Therefor 48 ÷ 2(9 + 3) = 48 ÷ 2(12) = 48 ÷ 24 = 2

Back then, there was no way I would have ever come up with 288......but that was back then....lucky I have a computer now

Now it’s back to the future..............................................................

[Colt45]

As a moderator, I suppose I am doing a "Ken" on this thread, but as Ross points out "for the most part, members have been courteous with one another".

I think that because we can be courteous and have a bit of fun with it, we are not "just other internet forum".

If the thread becomes offensive, I'll be the first to pull the plug on it.

Perhaps if it drags on too long it should be closed (but I want one more say first )

Trev (et al),

I've found the topic educational, and I'm actually curious to see if there is ever agreement on a final answer - I tryd ta figger it owt, but I dun runned

owt a fingers tryin ta carry tha naughts.

I've been having fun with it along with some others, but I understand the slight "frustration" of some members as well. After it had gone on a bit, I took

a look around the 'net, and we're all doing much better with it than most if not all.

But I also understand Doc's perspective - and I hope everyone understands I'm not trying to knock anybody or the topic, even though perhaps personally

I'd rather not see everything splashed across the 'net posted here - I don't know.

I guess if we were all together at the FOH lounge and the topic came up, I might quietly slip away and attempt to chat up our waitress

P.S. I smoked a great Upmann Sir Winston (2000) today.

[mykeuva]

Can I take you all on a journey.....

48 ÷ 2(9 + 3) = x .....(5)

Equation (5) must be solved in the same way as equations (1) to (4) or the logic makes no sense.

Therefor 48 ÷ 2(9 + 3) = 48 ÷ 2(12) = 48 ÷ 24 = 2

Back then, there was no way I would have ever come up with 288......but that was back then....lucky I have a computer now

Now it’s back to the future..............................................................

You are correct, up until you hit equation 5. At that point is where the question comes in.

There is no issue up to and including equation 4, because according to the standard order of operations, multiplication is done before addition (PEMDAS or BODMAS, or any other acronym people learned to remember the order).

The problem comes in when you switch that + to a ÷

Now that we have the ÷ sign, according to the standard order of operations, multiplication does not take priority over division, and division does not take priority over multiplication. So we go from left to right, and get an answer of 288.

There are 2 problems that are out there, however, that the math community apparently has run into.

The first issue is that some people are taught to multiply first. The problem here is that there are conflicting sources. Some are taught this, while others aren't. Technically, according to the order of operations, there doesn't seem to be a rule to multiply first.

The second issue is whether the juxtaposition of the 2 and the parentheses means that we do this multiplication first, before the division. Again, the problem with this is that juxtaposition priority isn't taught in the standard order of operations.

I originally voted 2, but I think that if we go strictly by the rules, we cannot come to a conclusion of 2. The answer has to be 288. Neither juxtaposition nor multiplication priority are part of the standard order of operations. As that is the case, as you stated previously, the equation is simply

48 ÷ 2 * (9+3).

The first step is to do what is in the parentheses. So we get

48 ÷ 2 * (12).

Now, we have an expression that simply has division and multiplication. They are equal in the order of operations (again, PEMDAS or BODMAS), so we go from left to right.

24 * 12 = 288.

If we want to come to an answer of 2, we would essentially be saying that

48 ÷ 2(9 +3) is the equivalent of

48 ÷ [2(9+3)]

Ultimately, it's up to the math community, whoever decides these things, to come up with rules discussing both the priority of multiplication over division, and whether or not juxtaposition of terms gets priority over explicit symbols.

[traded]

Before, I would agree with perfectform and TradedDavid, that this equation is not open to interpretations. However, after reading up on juxtaposition, this equation CAN be open to interpretation. Read this:

http://mathforum.org/library/drmath/view/57021.html I'm not about to argue with an EE professor.

Therefore, 2 and 288 are both correct depending on how you read the equation.

I first want to say sorry if I ever became rude (i don't think I did, but as one of the more active peeps on this thread, I just want to make sure).

I still think that the people getting 2 are automatically correcting a poorly written question. AS WRITTEN (which is poorly) I still firmly believe the answer is 288. As it should be written, it would be 2.

[Trevor2118]

You are correct, up until you hit equation 5. At that point is where the question comes in.

48 ÷ 2 * (9+3).

The first step is to do what is in the parentheses. So we get

48 ÷ 2 * (12).

Now, we have an expression that simply has division and multiplication. They are equal in the order of operations (again, PEMDAS or BODMAS), so we go from left to right.

24 * 12 = 288.

Two things, I was tought BODMAS, the O was for "of"........ ie 2(12) is actually 2 lots of (12), just like 2(9+3) is 2 lots of 9's and 3's.

So the * in your formular 2 * (12) is not simple multiplication, but the higher order "of", and that is why the * is not written...it is just 2(12).

The left to right concept (to my knowledge and use) was only needed when non-RPG calculators were introduced.

[mykeuva]

Two things, I was tought BODMAS, the O was for "of"........ ie 2(12) is actually 2 lots of (12), just like 2(9+3) is 2 lots of 9's and 3's.

So the * in your formular 2 * (12) is not simple multiplication, but the higher order "of", and that is why the * is not written...it is just 2(12).

The left to right concept (to my knowledge and use) was only needed when non-RPG calculators were introduced.

I was taught PEMDAS, but BODMAS, to my understanding, is

B Brackets

O Orders (exponents and roots)

DM Division/Multiplication

AS Addition/Subtraction

http://www.mathsisfun.com/operation-order-bodmas.html

2(9+3) is merely multiplying (9+3) by 2. As it's multiplication, it doesn't come first in the order of operations (again, unless it gets cleared up that implicit operations are done before explicit ones, or that multiplication is a higher priority).

And as TradedDavid posted, and probably what we all agree on, is that it's definitely poorly written.

[danclough]

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

Division is just the inverse operation of multiplication, thus X / 2 = X * (1/2) = X * .5. This is analogous to how addition and subtraction are related where 20 - 10 = 20 + (-10) = 10. Just convert all your divisions to multiplications and everything has the same precedence and multiply left to right. This is one of the first things you cover when you start writing proofs as an undergrad math major.

[khomeinist]

Comedy.

May all ye seekers of 'objective truth' be referred to a discipline called....

Philosophy of Mathematics

clearly this equation is open to multiple interpretations

lighten up folks....

I got 2. I have taken plenty of post-graduate mathematics courses. Step away from the keyboard. Pick up a pencil.

[Trevor2118]

Comedy.

I got 2. I have taken plenty of post-graduate mathematics courses. Step away from the keyboard. Pick up a pencil.

Lets all pick up cigars......I'm going for a Punch Punch.

[warren516]

I happen to be in a math class this semeter, albeit a refresher class, since I didn't do well on the placement test. To many years have passed since I was in school.

My $120 calculator says the answer is 288. I have one of those graphing/scientific ones and it's never wrong.

[khomeinist]

I am smoking a Tampa custom and drinking some Tokaji. Recommended combination.

I stand by my pencil comment. We are not machines.