# 48÷2(9+3) = ??

• ### 288

• Total voters
510

#### pushing_wins

##### Hall of Fame
brackets means inside the brackets

#### BreakPoint

##### Bionic Poster
please scan the page of the (engineering) book where 1/3x means 1/(3x) rather than x/3.
Are you sure you have a MSEE and a BSEE?

The very first thing I searched for under electrical engineering came up with this website: http://www.bowest.com.au/library/formulae.html#17

Look under the Energy section.

This is one of the equations:

The energy W stored in a capacitance C holding voltage V with charge Q is: W = CV2 / 2 = QV / 2 = Q2 / 2C

Solve for V in the first two equations and you get W = Q^2/2C with 2C in the denominator and no parentheses around the 2C.

##### Professional
Because somehow it doesn't seem to sink into the heads of you 288ers. Ok, with your logic, what is a/b/c or a/b/c/d/e? or even a/b/c/d/e/f/g/h/i/j/k/l/m/n...?

The way we do it can give a clear and single answer to all above questions, your way CANNOT.

#### dr325i

##### G.O.A.T.
Are you sure you have a MSEE and a BSEE?

The very first thing I searched for under electrical engineering came up with this website: http://www.bowest.com.au/library/formulae.html#17

Look under the Energy section.

This is one of the equations:

The energy W stored in a capacitance C holding voltage V with charge Q is: W = CV2 / 2 = QV / 2 = Q2 / 2C

Solve for V in the first two equations and you get W = Q^2/2C with 2C in the denominator and no parentheses around the 2C.
First of all -- you embarrasse yourself again.
This is NOT an official book, but a web page.

Second, notice the way the equations are written -- with spaces, ASSUMING something, which is the wrong assumption (not following the strict rules).

Lastly, I will actually give you a credit for the "engineering" example as some things, just like omitting the "*" are "allowed" in engineering, and those are NOT strict to the rules.

Do not question someone with the math experience longer than Your existance about simple things like this...

#### BreakPoint

##### Bionic Poster
First of all -- you embarrasse yourself again.
This is NOT an official book, but a web page.

Second, notice the way the equations are written -- with spaces, ASSUMING something, which is the wrong assumption (not following the strict rules).

Lastly, I will actually give you a credit for the "engineering" example as some things, just like omitting the "*" are "allowed" in engineering, and those are NOT strict to the rules.

Do not question someone with the math experience longer than Your existance about simple things like this...
Um...I thought we were talking about the limitations of typing out equations with a computer keyboard? "Official textbooks" can show actual equations with the horizontal divide line and a numerator above and a denominator below that horizontal line. Not so easy to do with a computer keyboard, which is why the / sign is often used to substitute for the horizontal divide line. Do a search on the Internet. You'll find tons of examples of engineering equations using the / sign in which everything to the right of the / sign is in the denominator and with no parentheses around the denominator.

Oh, and your "math experience" can't possibly be that long if you've never seen denominators with more than one variable with no parentheses around them.

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#### krz

##### Professional
It makes me laugh people taking pictures of calculators and software like they don't have a brain. Work it out yourself. Was that taking pictures of calculators comment directed at me? Because last time I checked I have some credentials and you...?

No one is questioning how to solve the 2 different equations. They are questioning how to interpret a 1 line written equation and if multiplication by juxtaposition outranks regular multiplication, which given what is posted on purple math there is no final verdict.

We are well aware of how the equations are written when one gets 2 or 288. So, please stop making yourself look like you "don't have a brain" and posting the same thing over and over.

This is how I would interpret this equation into a non-1-line keyboard typed equation. In a math book you would never see a multiplication sign between the parentheses and the fraction. The (9+3) is still to the "right" of the division like in the original equation. Last edited:

#### jonnythan

##### Professional
What I know is that there is no basis for believing that the (9+3) in the equation 48÷2(9+3) MUST be in the numerator and CANNOT be in the denominator. So far, no one has been able to explain this.
There is no numerator and denominator. There are three actions: a division, a multiplication, and an addition.

Order of operations explicitly states in what order they must be performed. Explicitly.

You feel like you must do the 2*12 before 48÷2 because you feel like the notation implies a fraction where 9+3 is in the denominator.

That is simply not the case.

#### TripleB

##### Hall of Fame

( ) first, so you do the 9+3 first.

That leaves 48 divide by 2 (12).

Since there are no operations left inside the ( ) then all the ( ) mean is that whatever is inside ( ) is multiplied by what's outside.

Therefore all you have left is 48 divided by 2 times 12.

Now you work left to right.

48 divided by 2 is 24 and then 24 times 12 is 288.

I don't care how you word it, how you think it should be, the way it is written 288 is the correct answer.

In order for the answer to be 2 then the 2(9+3) would have to be in another set of parentheses such as [2(9+3)]; then the answer would come out to be 2.

TripleB

#### 0d1n

##### Hall of Fame
But what's inside the parentheses is in the denominator, not the numerator.

48/2(12) = 2

(48/2)(12) or (48/2)12 = 288

Thus, the way it's written, the answer is 2.

(Note: I have scored in the Top 1% or 2% in the country in every standardized math test I have ever taken, and have engineering and MBA degrees from Ivy universities.)
And this is why a MAJOR percentage of your programmers, engineers, and scientists of any kind are from Asia (India, China...etc) and Eastern Europe (Russia and Romania included).
Because you (who CLAIM to have superior education) can't even properly assess the requirements of a problem (project) and start making assumptions regarding what "the guy giving you the problem that needs solving" (a.k.a. the "customer") actually meant instead of assuming that what he gives you is what he actually wants...and he does know what he wants.

Yes...the problem is formulated ambiguosly (probably on purpose) and any proper math book will make sure to state things properly, but you quoting blogs or informal online sites to somehow support your so called arguments on why you are making ASSUMPTIONS is not going to help.

Your kind will probably start asking if (or even worse...start assuming) you have an additional tool (like a marker pen) available for making some signs on the recipients if asked the question "[FONT=&quot]If you had an infinite supply of water and a 5 liter and 3 liter jar, how would you measure exactly 4 liter?"[/FONT] instead of putting your little gray cells to work with the tools available...and clearly stated in the problem.

Numerator? Denominator? This is all on one line. Simply replace "÷2" with (1/2), (that's what the "÷" sign tells you to do, use the reciprocal of the number immediately after it.) Now it's all about multiplying! (Because dividing is simply multiplying by reciprocals.) We have (48 )(1/2)(12) which = 288.

Now order doesn't make a difference.

(48 )(12)(1/2) = (576)(1/2) = 288
(1/2)(48 )(12) = (24)(12) = 288
(1/2)(12)(48 ) = (6)(48 ) = 288
(12)(48 )(1/2) (576)(1/2) = 288
(12)(1/2)(48 ) = (6)(48 ) = 288

The "÷" is a bad symbol IMO. When you see one, use it to convert the number in question into a factor. Now, order won't matter, and you can hardly go wrong! That's all great...but you see...logic doesn't work with Breakpoint once he has made up his mind about something.
He will just argue his "point" until you get bored and admit "defeat" due to being drowned in an ocean of posts from said user. How do you think he got to those post numbers ???

Ah...one more thing. I think quoting "University Education" in this context is completely irrelevant because we are dealing with pretty basic math and not the kind you would learn about in university. As a result even if one studied geography in university they still would have been exposed to this kind of math much earlier in their life.
Still...I'll just do it for the sake of earlier posters who did it already. I finished a Technical University ... Faculty of Automation and Computer Science...and currently work as a Software Engineer.
I don't think this problem is clearly formulated...but given the choice I will take the path that doesn't require any "assumptions" from me, which is why I wouldn't take "the Breakpoint path".

#### movdqa

##### Talk Tennis Guru
> Ah...one more thing. I think quoting "University Education" in
> this context is completely irrelevant because we are dealing
> with pretty basic math and not the kind you would learn about
> in university.

> I finished a Technical University ... Faculty of Automation and
> Computer Science...and currently work as a Software Engineer.

Did you cover this sort of thing in Computer Language Theory and Compilers?

#### maleyoyo

##### Professional
It's great to see!!!

It's great to see many Americans still CARE about math because learning math is so important for (developing) the minds. You are all WINNERS in my book.

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#### soyizgood

##### G.O.A.T.
If 2(9+3) had () around the whole line like (2(9+3)) this would have been so straight forward.

I initially thought it was 2, but I think it's 288 now.

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#### BreakPoint

##### Bionic Poster
There is no numerator and denominator. There are three actions: a division, a multiplication, and an addition.

Order of operations explicitly states in what order they must be performed. Explicitly.

You feel like you must do the 2*12 before 48÷2 because you feel like the notation implies a fraction where 9+3 is in the denominator.

That is simply not the case.
Oh really? And what if the equation was written as: 48÷(9+3)2 ?

Doesn't ab = ba? So 2(9+3) and (9+3)2 should be the same, right?

#### jonnythan

##### Professional
Oh really? And what if the equation was written as: 48÷(9+3)2 ?

Doesn't ab = ba? So 2(9+3) and (9+3)2 should be the same, right?
Then it would be different. ab = ba but a÷b*c != a÷(b*c).

I'd expect someone who graduated from an Ivy League college would know that.

#### Polaris

##### Hall of Fame
Breakpoint, you've got to accept that, in this case, you're wrong. Especially after touting your Ivy League education, your counter-arguments to dr325i and jonnythan are somewhat depressing. This isn't about what you think should be the correct answer. By mathematical convention, there is only one correct answer, which is 288.

Take this one, for instance, :neutral:

Breakpoint said:
Doesn't ab = ba? So 2(9+3) and (9+3)2 should be the same, right?
It would be true if the monomial consisted of "a" and "b" alone. With the addition of a third variable with a division operation, as in "c÷a*b", the variables "a" and "b" do NOT commute under multiplication.

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#### BreakPoint

##### Bionic Poster
And this is why a MAJOR percentage of your programmers, engineers, and scientists of any kind are from Asia (India, China...etc) and Eastern Europe (Russia and Romania included).
Because you (who CLAIM to have superior education) can't even properly assess the requirements of a problem (project) and start making assumptions regarding what "the guy giving you the problem that needs solving" (a.k.a. the "customer") actually meant instead of assuming that what he gives you is what he actually wants...and he does know what he wants.

Yes...the problem is formulated ambiguosly (probably on purpose) and any proper math book will make sure to state things properly, but you quoting blogs or informal online sites to somehow support your so called arguments on why you are making ASSUMPTIONS is not going to help.

Your kind will probably start asking if (or even worse...start assuming) you have an additional tool (like a marker pen) available for making some signs on the recipients if asked the question "[FONT=&quot]If you had an infinite supply of water and a 5 liter and 3 liter jar, how would you measure exactly 4 liter?"[/FONT] instead of putting your little gray cells to work with the tools available...and clearly stated in the problem.
That's because the programmers and engineers in those countries are willing to work for 10%-30% of the salary that American engineers demand. THAT'S why companies hire them! It's all about profits for the tech companies. If the programmers and engineers in those countries demanded \$200,000 salaries, believe me, companies wouldn't hire so many of them.

I cited a website because people use computer keyboards to type out equations on websites. So much so that using the / symbol as a substitute for a horizontal divide line is now the accepted convention.

Oh, and do you really want me to answer that water question? It's quite simple if you want me to explain it. And, no, a marker is not required.

BTW, I assumed what the intention of the originator of the equation was because he or she specifically wrote it as 48÷2(9+3) and NOT 48(9+3)÷2. There's a reason for that. Those two equations are not the same.

#### BreakPoint

##### Bionic Poster
Then it would be different. ab = ba but a÷b*c != a÷(b*c).

I'd expect someone who graduated from an Ivy League college would know that.
But what makes you think that both b and c are not both in the denominator? There's no requirement that denominators (what's below the horizontal divide line) must have parentheses around it. I've seen millions of fractions in my lifetime in which denominators with more than one variable did not have parentheses around it.

Again, we're not talking about programming a computer nor a calculator. We're talking about interpreting and solving this equation by hand.

Yes, they taught us what's below the horizontal divide line is called the denominator. :???:

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#### BreakPoint

##### Bionic Poster
It would be true if the monomial consisted of "a" and "b" alone. With the addition of a third variable with a division operation, as in "c÷a*b", the variables "a" and "b" do NOT commute under multiplication.
But what makes you so sure that in the equation c÷ab that ab is not the denominator?

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#### jonnythan

##### Professional
Division is an operation. There is a dividend and a divisor. The divisor is 2 because the rules of math say so. For the divisior to be 2(9+3) you would need to put the entire expression in parentheses or write it as an explicit fraction with 2(9+3) in the denominator.

This expression is not in fractional notation. It's an explicit series of arithmetic operations, and they must be done in the proper order.

#### BreakPoint

##### Bionic Poster
Division is an operation. There is a dividend and a divisor. The divisor is 2 because the rules of math say so. For the divisior to be 2(9+3) you would need to put the entire expression in parentheses or write it as an explicit fraction with 2(9+3) in the denominator.

This expression is not in fractional notation. It's an explicit series of arithmetic operations, and they must be done in the proper order.
Isn't the / symbol in the equation 48/2(9+3) a substitute for and the same as a horizontal divide line? That's makes the denominator 2(9+3). I've never seen a rule that states you must put everything that's below the horizontal divide line in parentheses. Again, we're not talking about programming a computer nor a calculator. We're talking about interpreting and solving this equation by hand.

I guess kids today have no idea how to interpret nor solve math problems without the aid of a calculator or computer (or Google). #### jonnythan

##### Professional
It's an expression.

It's not an equation.

One more piece of elementary math your Ivy League education missed.

#### BreakPoint

##### Bionic Poster
It's an expression.

It's not an equation.

One more piece of elementary math your Ivy League education missed.
How is 48÷2(9+3)=X not an equation? I guess you must have missed the semester on elementary math?

BTW, do kids today even know how to do long division with pen and paper?

Do you even know how to solve a division problem that looks like this by hand without the use of a calculator or computer? #### dr325i

##### G.O.A.T.
Oh really? And what if the equation was written as: 48÷(9+3)2 ?

Doesn't ab = ba? So 2(9+3) and (9+3)2 should be the same, right?
Wooohoooo...this just killed the mood totally...
Even those expensive schools are not what they used to be...

I am so glad I got my basics from the Russian books FOR FREE rather than paying big bucks to get embarrassed with the elementary math at a tennis forum...

#### sureshs

##### Bionic Poster
How many of you know how to do square roots by hand? It is not taught any more.

#### tenis1

##### Banned
Plain and simple BreakPoint is incorrect. The rule is to go left to right if everything else is equal. So you have to divide 48/2 first and than multiply by (9+3).

#### BreakPoint

##### Bionic Poster
Plain and simple BreakPoint is incorrect. The rule is to go left to right if everything else is equal. So you have to divide 48/2 first and than multiply by (9+3).

Even when the denominator is 2(9+3)? #### BreakPoint

##### Bionic Poster
Wooohoooo...this just killed the mood totally...
Even those expensive schools are not what they used to be...

I am so glad I got my basics from the Russian books FOR FREE rather than paying big bucks to get embarrassed with the elementary math at a tennis forum...
That explains EVERYTHING!! No need for you to post in this thread any more. You've just lost all credibility.

Oh, and those nuclear engineers that worked at Chernobyl and the automotive engineers that designed the Lada probably also learned their basics from Russian books for free. #### sureshs

##### Bionic Poster
We need to put a break point and debug the problem.

#### BobFL

##### Hall of Fame
That explains EVERYTHING!! No need for you to post in this thread any more. You've just lost all credibility.

Oh, and those nuclear engineers that worked at Chernobyl and the automotive engineers that designed the Lada probably also learned their basics from Russian books for free. Why?

........

#### Polaris

##### Hall of Fame
We need to put a break point and debug the problem.
LOL, good one!

Breakpoint said:
But what makes you so sure that in the equation c÷ab that ab is not the denominator?
What makes me absolutely sure that ab is NOT in the denominator, is that there are no parentheses around them. In c÷(ab), you can say that ab is in the denominator. In c÷ab, you cannot say that.

That is just how it is. There is no harm in saying that you have labored under a wrong assumption all these years. It is a fairly common error among people who don't use math on a daily basis. You're apparently doing well in your professional life, so nothing bad came out of it. Perhaps, your error can be attributed to the fact that you don't have too much experience with scientific programming. I don't know.

But, at some point, even if you don't agree with it, you have to acknowledge that this is how the mathematical rules were written down, that they are consistent and unambiguous.

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#### sureshs

##### Bionic Poster
Wooohoooo...this just killed the mood totally...
Even those expensive schools are not what they used to be...

I am so glad I got my basics from the Russian books FOR FREE rather than paying big bucks to get embarrassed with the elementary math at a tennis forum...

I remember they would distribute them for free or at ridiculously low prices. I had many of their math and physics books.

But frankly, compared to American or British textbooks (which of course were not free), they were not good. Maybe it was a translation issue, I don't know.

#### HellBunni

##### Rookie
BTW, I assumed what the intention of the originator of the equation was because he or she specifically wrote it as 48÷2(9+3) and NOT 48(9+3)÷2. There's a reason for that. Those two equations are not the same.
that's the whole point.
you are assuming the intention, that is your whole argument.

what most of us on the 288 camp is arguing is that:

- when there are no other context (defined parameters, additional text, etc...), you can't just assume the intention.

because different ppl with different backgrounds can come to different "obvious" assumptions.

- in cases like this, you must use the defined set of rules (order of operations without assumptions). Not what you are used it, or the "general" practice of a specific community.

I think the intent of the originator is to make the equation ambiguous on purpose, to demonstrate that you need to use parenthesis, and that in case of an ambiguous equation you should follow the order of operations without assuming anything.

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#### Rippy

##### Hall of Fame
Even when the denominator is 2(9+3)? We don't know if the denominator is 2(9+3) or not! You're just assuming it is, which is wrong.

#### BreakPoint

##### Bionic Poster
Plain and simple BreakPoint is incorrect. The rule is to go left to right if everything else is equal. So you have to divide 48/2 first and than multiply by (9+3).

Does the fraction a/b have a left to right? No? Then why does the fraction a/bc have a left to right? #### BreakPoint

##### Bionic Poster
We don't know if the denominator is 2(9+3) or not! You're just assuming it is, which is wrong.
And most of you are assuming that (9+3) is NOT in the denominator, which is wrong.

#### Talker

##### Hall of Fame
The problem is if this were an SAT/ACT type question they would expect you to know the order of operations and rules without the parentheses to clarify. It's tricky no doubt.
Not too tricky, just go from left to right as the rules say, what comes in parenthesis doesn't have to be done first, when you come to that term you'll have 24(9 + 3) and then you can add the 9 and three, both ways are right but both give 288. This is really taught before high school but can be forgotten if not used.

Left to right says take the first 2 terms 48/2 and calculate giving 24.
take 24 and calculate the next term... 24(9 + 3) and calculate. Since it ends here that is the result. Some are doing the second and third term first giving
48/24 but this is illegal and will lower your percentiles in aptitude tests if you run into it.

#### BreakPoint

##### Bionic Poster
What makes me absolutely sure that ab is NOT in the denominator, is that there are no parentheses around them. In c÷(ab), you can say that ab is in the denominator. In c÷ab, you cannot say that.
Why not? There's no rule that says you have to put the denominator in parentheses, is there? When you see fractions in textbooks, where they use the standard horizontal divide line, how often do you see the entire denominator in parentheses?

Again, we're not talking about typing an equation into a calculator nor programming a computer. We're talking about doing math by hand, which judging by this thread very few people know how to do anymore. #### FlamEnemY

##### Hall of Fame
Guys, this thread is 30 pages long.

PS: I hope for the sake of mankind that it doesn't reach 40.

#### LameTennisPlayer

##### Professional
originator of the equation was because he or she specifically wrote it as 48÷2(9+3) and NOT 48(9+3)÷2. There's a reason for that. Those two equations are not the same.
This is like arguing that 48 x.5(9+3) is different to 48(9+3) x .5

well using Bedmas again, the result is the same

48÷2(9+3) = 48÷2x12
= 24x12
=288

48(9+3)÷2 =48x12÷2
=576÷2
=288

As already mentioned it's because dividing by two is the same as multiplying by .5 and it doesn't matter which side of the brackets the .5 or ÷2 is located, the result is still the same.

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#### BreakPoint

##### Bionic Poster
well using Bedmas again, the result is the same

48÷2(9+3) = 48÷2x12
= 24x12
=288

48(9+3)÷2 =48x12÷2
=576÷2
=288
Nope.

48÷2(9+3) has the (9+3) in the denominator, while 48(9+3)÷2 has the (9+3) in the numerator. It makes a difference being on the left or the right of the ÷ sign. The left side is the dividend (numerator) while the right side is the divisor (denominator).

#### olliess

##### Semi-Pro
that's the whole point.
you are assuming the intention, that is your whole argument.

what most of us on the 288 camp is arguing is that:

- when there are no other context (defined parameters, additional text, etc...), you can't just assume the intention.

because different ppl with different backgrounds can come to different "obvious" assumptions.
Given the vehemence of the arguments in this thread, this definitely seems like a good idea.

- in cases like this, you must use the defined set of rules (order of operations without assumptions). Not what you are used it, or the "general" practice of a specific community.
Except for lots of people repeating that the "defined" or "standard" or "obvious" rules for the notation are such-and-such, I have seen NO definitive source establishing what those standards are. However, given that advanced publications in mathematics and engineering do sometimes use one notation or the other, you probably do need to figure out what the text or paper actually meant, and how others in the community take the expression probably does matter.

What are you gonna do, say "The idiot who passed me these equations obviously didn't write the proper notation AS ALL NON IDIOTS WHO GRADUATED FROM CALTECH INSTEAD OF AN IVY SHOULD KNOW so I wrote -3 pts in the margin and went ahead and slammed the lander into the planetary surface"?

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#### Claudius

##### Professional
Nope.

48÷2(9+3) has the (9+3) in the denominator, while 48(9+3)÷2 has the (9+3) in the numerator. It makes a difference being on the left or the right of the ÷ sign. The left side is the dividend (numerator) while the right side is the divisor (denominator).
So is 48÷2(9+3) not equal to 48÷2*(9+3) ?

You would surely agree that the second expression is 288, yet somehow the first one is 2, even though that star makes absolutely no difference?

#### diredesire

And none of you 288ers have been able to explain why, if the (9+3) is in the numerator, the original equation wasn't 48(9+3)÷2.

And you guys also haven't explained why the (9+3) CAN ONLY be in the numerator and CANNOT possibly be in the denominator.

If the originator of this equation had wanted the (9+3) to be in the numerator, he or she would have written it: 48(9+3)÷2.

The fact that he or she specifically DID NOT write it 48(9+3)÷2, but specifically chose to write it 48÷2(9+3), is proof enough that he or she wanted the (9+3) in the denominator!
If we are talking about intention, the formula posed was written with intention to be less than clear. You are putting your personal bias onto a math equation. You are also injecting your assumptions/prejudice into the thread, when was it established that we are discussing EITHER limitations of computer formula entry OR solving equations by hand? That was a creation all your own. If you are going to insist on debating this, at least make it clear you are having your own discussion off to the side. Don't assume we are all on the same page with frames of reference, otherwise we wouldn't be having this discussion at all.

What I know is that there is no basis for believing that the (9+3) in the equation 48÷2(9+3) MUST be in the numerator and CANNOT be in the denominator. So far, no one has been able to explain this.
*to your satisfaction. It can be in the denominator, if you're following an assumed set of rules that according to you are common knowledge and widely accepted. If they are so widely accepted, can you justify the mat lab/maple/google calculator business? If you decide to ignore this argument, that's fine by me. I think if it was ever accepted, it has long since fallen out of favor.

Um...I thought we were talking about the limitations of typing out equations with a computer keyboard? "Official textbooks" can show actual equations with the horizontal divide line and a numerator above and a denominator below that horizontal line. Not so easy to do with a computer keyboard, which is why the / sign is often used to substitute for the horizontal divide line. Do a search on the Internet. You'll find tons of examples of engineering equations using the / sign in which everything to the right of the / sign is in the denominator and with no parentheses around the denominator.

Oh, and your "math experience" can't possibly be that long if you've never seen denominators with more than one variable with no parentheses around them.
Finding examples of engineering equations online from a web 1.0 site that doesn't insert images for equations or use embedded markup such as LaTeX isn't the most solid evidence. People make mistakes, and if they DO operate under the assumptions that you do, fine by me. It is more ambiguous and it doesn't follow established conventions that a computer (read as: non biased, strict operation following machines) can read. If you can't see why this is a problem, then I don't really care to continue posting in the thread, I'm not losing sleep over it at night (although i am fascinated by this thread).

I cited a website because people use computer keyboards to type out equations on websites. So much so that using the / symbol as a substitute for a horizontal divide line is now the accepted convention.

BTW, I assumed what the intention of the originator of the equation was because he or she specifically wrote it as 48÷2(9+3) and NOT 48(9+3)÷2. There's a reason for that. Those two equations are not the same.
If you want to use the isolated sources argument, I think you are going to find it also a moot point. Counter examples can be shown, and it wil just end up in the situation that no one will end up being swayed. Implying that / is a substitute for a horizontal divide is FINE, and CORRECT, but the argument is over what it is going to divide over, and assuming (as you mention in the second paragraph quoted) anything in a mathematical equation is a mistake.

But what makes you think that both b and c are not both in the denominator? There's no requirement that denominators (what's below the horizontal divide line) must have parentheses around it. I've seen millions of fractions in my lifetime in which denominators with more than one variable did not have parentheses around it.

Again, we're not talking about programming a computer nor a calculator. We're talking about interpreting and solving this equation by hand.

Yes, they taught us what's below the horizontal divide line is called the denominator. :???:
I have also seen a lot of equations in the fashion you mentioned. The difference to the ones you mentioned was that they were more clearly defined.

Isn't the / symbol in the equation 48/2(9+3) a substitute for and the same as a horizontal divide line? That's makes the denominator 2(9+3). I've never seen a rule that states you must put everything that's below the horizontal divide line in parentheses. Again, we're not talking about programming a computer nor a calculator. We're talking about interpreting and solving this equation by hand.

I guess kids today have no idea how to interpret nor solve math problems without the aid of a calculator or computer (or Google). You are injecting your interpretation here again. Why AREN'T we talking about programming computers? Math is a set of established, defined conventions that should be able to be systematically followed by a non-human object. There isn't a need for so-called "interpretations". What's the difference? If we were solving this by hand, it would be in a situation whewre this isn't a problem, IMHO. THe problem is contrived for a reason.

that's the whole point.
you are assuming the intention, that is your whole argument.

what most of us on the 288 camp is arguing is that:

- when there are no other context (defined parameters, additional text, etc...), you can't just assume the intention.

because different ppl with different backgrounds can come to different "obvious" assumptions.

- in cases like this, you must use the defined set of rules (order of operations without assumptions). Not what you are used it, or the "general" practice of a specific community.

I think the intent of the originator is to make the equation ambiguous on purpose, to demonstrate that you need to use parenthesis, and that in case of an ambiguous equation you should follow the order of operations without assuming anything.
Fully agreed. Breakpoint, if you were in charge of a billion dollar project, and you came across this equation and needed to give an answer, do you follow your assumption, or go with the established, machine readable rules?

And most of you are assuming that (9+3) is NOT in the denominator, which is wrong.
...

Isn't tis what you are doing, and isn't it wrong for the same reason (being on the flip side of the coin?)

#### sureshs

##### Bionic Poster
When writing an expression in a single line, if a double line fraction is intended, it is best to put explicit parantheses around the denominator.

Over time, I have developed the habit of writing zero as phi on handwritten notes. It started with programming, but now I find it useful even for such things as license plate numbers, to distinguish between Oh and zero.

Family members see it as weird.

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#### LameTennisPlayer

##### Professional
Nope.

48÷2(9+3) has the (9+3) in the denominator, while 48(9+3)÷2 has the (9+3) in the numerator. It makes a difference being on the left or the right of the ÷ sign. The left side is the dividend (numerator) while the right side is the divisor (denominator).

Nope.
You read it as 48(numerator) ÷ 2(9+3) (denominator)

Since when does division take precedence over brackets/parenthesis?

#### FlamEnemY

##### Hall of Fame
You need to change your nickname to /b/reakpoint.

Oh sh... rule 1 \$@%! #### BreakPoint

##### Bionic Poster
Here's the output from WolframAlpha, scientists use this the world over, you can trust it.

http://www.wolframalpha.com/input/?i=48÷2(9+3)
WolframAlpha is a computer. I think the point to writing this equation this way is to prove that using a computer to solve equations is not always going to give you the same answer as solving the equation by hand. Computers have limitations. They interpret notations (or lack thereof) differently. Apparently, most computers can't tell what's in the denominator unless you put parentheses around the entire denominator. Real people don't have that problem. People are smarter than computers. Computers can only output exactly what you put in. That's why if you mis-type just one letter or symbol in a long URL, the computer can't find that web page, even though it's obvious what web page you were looking for.