Poll: What is the answer to 48/2(9+3)?

[Theron Julius]

It's nothing more than simple PEMDAS

48/2*(9+3)

You do what's in the parentheses first

48/2*12

No.

You multiply into the paranthesis, as such:
2*(9+3) = (2*9)+(2*3) = 18+6 = 24

Then you do whatever multiplication or division comes first. In this case it was 48/2

24*12

Dude, wat? You'd do that if the question was (42/2)*(9+3). You can't divide by a single number in the denominator and leave out the rest. Everything "above" the division and everything "below" the division.


I hope this is not an indication of American math. Honestly, I suck at math, and this just seems like elementary school stuff to me. Whatever PEMDAS is, this is a clear and easy matter of calculating it using your brain, not a standard formula.

48/2(9+3) = 48/(2*9)+(2*3) = 48/18+6 = 48/24 = 2

Anything else is incorrect.

Yeah, just so you know, google has a built in calculator:
http://lmgtfy.com/?q=48%2F2(9%2B3)

Also, here's a link to the wikipedia page for order of operations:http://en.wikipedia.org/wiki/PEMDAS#Mnemonics. You should see PEMDAS amongst the list of acronyms for it. Pardon my incompetence if you were taught a different form.

 

[Woem]

What if you look at s simple question like 5-3+2? Do you not read this left to right?

Exactly. You can do 5 -3 + 2 or 2 -3 +5 or -3 + 5 + 2 or 2 + 5 -3. Please correct me if I'm wrong. (I'm not.)

Im really lost as to what your arguement is here. These are all equal to one another because you do the addition and subraction in order from left to right. Thus proving my point, that the order of the operations is important. If the order didnt matter, then 5-3+2 could just as easily be 0 if you do the addition first, but you don't, because you read the equation left to right.

I'm not reading it from left to right when I say that 5 -3 +2 is the same as 2 -3 +5. I just read it backwards.

 

[darkstarangel]

People still seem to be using division instead of fraction. Division is linear & in regards to BODMAS works in sequence. Fractions are dual & everything must be done above & below before dividing the two final values.

I wont use algebra to explain this because that actually makes it complicated & is easier just using numbers.

 

[sam42ification]

It saddens me that 2 is at 43.5%

Agreed

According to my 8th grade education, the problem is 288. Add the 9 and 3, divide the 48 and 2, multiply the 24 and 12. Of course, there could be some fancy college learnin' that I have yet to get through, rendering this a trick question.

It's not fancy it's an 8th grade problem, nothing more. Your 8th grade education failed you.

Expand the brakets so 2 times 9 then 2 times 3. so you get 18 and 6 plus them to gether you get 24 then divide 48 by 24 to get 2.

Or you could plus 9 and 3 to get 12 then times by 2 to get 24 then divide 48 by 24. It's order in which you do things that you get the right answer.

I don't see why you would do either of those orders. Sure, you can, but as I said, the accepted answer would be 288, unless using the PEMDAS system. However, as I said, my 8th grade education said my 3rd grade PEMDAS education was incorrect, so I naturally went with the higher level teaching.

What the hell is PEMDAS? Is it somthing they do in america? Any ways the way i was taught was
48/2(9+3)
2 times 9
2 times 3
plus the result
divide.
Because there is a 2 outside of the brakets mean you have to expand them before doing anything else. (Expanding is when you times the number outs side the brakets to everything inside them). if you do this you get 48/24. Do you understand how expanding works? the accepted answer is wrong. the answer is 2 it makes sense. In your comment you said "the problem is 288. Add the 9 and 3, divide the 48 and 2, multiply the 24 and 12." You got the first part right add the 9 and 3 but then you divided 48 by which is a later step before you divide you have to times the 12 (which you got from adding 9 and 3) and the 2 so you get 48 divided by 24. You have to do things in the right order and the dividing step comes last you always expand the brakets.

I understood what expanding was, but that's not what you're supposed to do. You need to add the numbers inside the parentheses before going left-to-right at the beginning of the problem, dividing the 48 by 2 before multiplying it by 12.

And PEMDAS is: parentheses (as in, do whatever is inside the parentheses first), exponents, multiplication, division, addition, subtraction. You're following it, but as I said, my later education explained to me that PEMDAS was incorrect. I can see what you're doing, all I'm saying is that I was taught that it was wrong.

How late in your education because i'm in year ten (10th grade) and thats still how we do it.

 

[Da_Vane]

The answer is 2. When following PEMDAS/BODMAS you need to solve brackets first. This doesn't mean reduce the contents within the brackets to a single number, but removing the brackets completely.

Thus, not only do you need to solve 9+3 to get 12 first, you also need to solve 2(12) because this is still part of solving brackets. This gives you 24.

The fact that this method also backs up the implied format that this is a fraction, where both parts automatically imply brackets, means it is the correct solution. The question is best viewed as (48)/(2(9+3)).

To reach the answer as 288, the question would have to be written as (48/2)(9+3), which is such a deviation from the norm, that it would have to specifically written as such.

Oh, and for the record, 48/2x 24x. The correct answer is 24/x. 48x/2 = 24x. Thus, using substitution, we still arrive at the answer 2 for this equation, given that x=9+3 or 12.

This. Also, does anyone else think that maybe the question is a troll, given how ambiguously it's written?

I read it that the 2(9+3) was its own entity; ie. you have to multiply it out, rather than treating the 2 as the bottom of a bracket and the (9+3) as a separate multiplier. So, doing it this way, you get 2(9+3)=(2x9)+(2x3)=24. You then divide 48 by this, giving you 2

I think the main dispute here comes from the reading of the question. Personally, I'm interested in knowing if this is a cultural thing. I'm English, and I'm curious as to whether the other people who got 2 as their answer are also English, or at least European

I am English, so there may actually be some validation to your assertion that it is a cultural thing. I'd definitely request this to be better written out, because you don't know whether the equation as written is a limitation of posting on these forums, or the actual equation.

It's worth noting that multiplying out brackets are the inverse of factorising, which is of a higher magnitude than indices and mulitiplication, which is why Brackets are come first - this is taught in any higher math book. Thus, you need to do the 2(12) = 24 first... because it's the inverse of 24 = 2(12). This will come in handy when you deal with quadratic equations.

To be safe: Put down both answers and comment that it depends upon how it is written - one is going to be correct.

By the way - you cannot use Excel as proof: The equation is 48/2(9+3) not 48/2*(9+3). Unfortunately, Excel doesn't allow the former, since this is actually used for another purpose rather than mathematics, and suggests the revision of the latter, which is a different equation.

 

[RonHiler]

you know that on the link, the last paragraph was describing weither or not in normal standards xy has priority in calculation over x*y... right?

this has nothing to do with w/x which is quiet clear on the matter that x goes first.

No offense, man, but horsepucky.

CLEARLY, it is not "quite clear" that x goes first. If that was a universally accepted truth, then computers, calculators, and Excel would not have messed it up (these are all items that were SPECIFICALLY designed to do math, you don't mess up a basic math issue like that if there was a clear consensus in place).

I think we have determined that the order of calculating z/x versus z/x* is a cultural difference. To you, they calculate to different values. To me, they are the same. And I think that's exactly what that web site is saying (I've read it over a couple of times now, and that's what I'm taking from it, I don't know where you are getting your argument from, because honestly I can't come up with your interpretation from what is written there).

This is a question of semantics now. There is no right or wrong anymore. The "correct" answer depends entirely on how you were taught to order those operations. I think we can all agree it was a poorly written question (which was probably the point, I suppose, heh).

One thing I can say. I was initially dismissive of anyone that thought the answer was 2, because to me it was obviously 288. I had no idea that to some people, there was a difference in whether or not there was a * in there or not. So I learned something new, which is cool.

 

[DwMrDw]

(48/2)(9+3) is the same as 48/2(9+3)
there is however a difference between 48/(2(9+3)) and 48/2(9+3).
48/(2(9+3)) means 48 divided by (two times ( nine + three)) (= 48/24)
48/2(9+3) means 48 divided by two (=24) times (9+3) (= 24*12)

 

[Quazimofo]

I don't know why you want us to do your homework for you, but I got 288... after you do the parentheses, you're supposed to do them from left to right. I think it's a poorly written problem, though.

lol it's not a homework problem man, I'm not in middle school. This question is blowing up other forums and reddit.

48/2(12) = 2

Yeah, that's how I did it. But the way it's written, it doesn't specify if the only the 2 is being multiplied by 12 or if the entire fraction is. If the first, then it's 2. If the second, then it's 288.

So, as Professor Layton wisely pointed out, the problem is poorly written.

not really. due to the limitations of computers, we cant write fractions on forums quite as well as by hand, so one must assume that since the whole fraction was not in parenthesis to be multiplied, the multiplication by 12 only applies to the denominator of the fraction. and so, by adding (9+3) to get 12, then 12*2 to get 24, 48/24=2. simple

yay high school freshman pre calc class!

Hmmmmm. You should pay a little more attention in your calc class. If the intentionn was for the 9+3 to be applied only to the denominator then that would have to be expressed with parenthesis. When this isn't specified, then we do the operations of division and multiplication in order from left to right. So:

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

When a multiplication and division step takes place in the same equation and the second operation isn't included in parenthesis to indicate that the question requires you to complete that operation first we have to read the question left to right. This is the way calculators would solve this problem. Of course if the question was written (48/2)*(9+3) it would remove all ambiquity.

Yay for 3rd year university mathematics

hmm, i see your point. i guess the first poster really is right in that the way the problem is written allows it to be easily taken either way, and so unless the writer had a specific way in mind, this is a debate that will never have a clear winner or right answer.
and which university? im just curious.

Ya it's silly the way its phrased, I'm sure specifically to get a reaction like this, but when the question doesnt specify with parenthesis which operation takes priority you have to read the question left to right. So the correct step is to divide the 48 by 2 before you multipy the 12 giving you 288. That would be how simple calculator solves this problem. Its funny cause you can program graphing calculators to preform operation using different rules and get different answers then people can use this to agrue points. But the correct algebraic system will never change. Why would it?

I am at the university of alberta in an education degree with a major in mathematics. I'm actually in the middle of a practicum teaching these mundane algebraic rules to grade 8 students. Its funny that almost every middle school students could do this problem with no issues but full grown adults struggle so much.

yeah, well im hardly an adult, but i guess it is because once we get past the basics, everything becomes more confusing, even the stuff we used to know, because we know many ways to approach problems as we go further; there is probably even a philosophical lesson in this, as we learn more, we forget the basics.

 

[Pyro Paul]

you know that on the link, the last paragraph was describing weither or not in normal standards xy has priority in calculation over x*y... right?

this has nothing to do with w/x which is quiet clear on the matter that x goes first.

No offense, man, but horsepucky.

CLEARLY, it is not "quite clear" that x goes first. If that was a universally accepted truth, then computers, calculators, and Excel would not have messed it up (these are all items that were SPECIFICALLY designed to do math, you don't mess up a basic math issue like that if there was a clear consensus in place).

I think we have determined that the order of calculating z/x versus z/x* is a cultural difference. To you, they calculate to different values. To me, they are the same. And I think that's exactly what that web site is saying (I've read it over a couple of times now, and that's what I'm taking from it, I don't know where you are getting your argument from, because honestly I can't come up with your interpretation from what is written there).

This is a question of semantics now. There is no right or wrong anymore. The "correct" answer depends entirely on how you were taught to order those operations. I think we can all agree it was a poorly written question (which was probably the point, I suppose, heh).

One thing I can say. I was initially dismissive of anyone that thought the answer was 2, because to me it was obviously 288. I had no idea that to some people, there was a difference in whether or not there was a * in there or not. So I learned something new, which is cool.

there is a right and wrong though.

n(x+y) is apart of a slightly more complex form of algebra which you should learn after the basic order of operations and should be the first step into functions, coefficents, graphing, and more complex mathmatics. n(x+y) being a single expression is the key stone of all more complex mathmatics from College Algebra to Calc, to Trig, to theoretical quantem mathmatics...

the real point isn't so much so on who is correct, but rather what level of math you apply to.

the biggest example of this is
sqrt of -1.
Roots can not be negative, thus in general mathmatics this is not calculated and no answer can be given.

but in later levels you're taught imaginary numbers, and in turn this equation can become calculated.
sqrt of -1 = i
-so-
i^2 = -1

this expansion allows more complex computations to occur. yet if you are never taught imaginary numbers and ran into the equation 'what is the square root of -1' the only correct answer you can give is 'there is none'.

 

[Drago-Morph]

It saddens me that 2 is at 43.5%

Agreed

According to my 8th grade education, the problem is 288. Add the 9 and 3, divide the 48 and 2, multiply the 24 and 12. Of course, there could be some fancy college learnin' that I have yet to get through, rendering this a trick question.

It's not fancy it's an 8th grade problem, nothing more. Your 8th grade education failed you.

Expand the brakets so 2 times 9 then 2 times 3. so you get 18 and 6 plus them to gether you get 24 then divide 48 by 24 to get 2.

Or you could plus 9 and 3 to get 12 then times by 2 to get 24 then divide 48 by 24. It's order in which you do things that you get the right answer.

I don't see why you would do either of those orders. Sure, you can, but as I said, the accepted answer would be 288, unless using the PEMDAS system. However, as I said, my 8th grade education said my 3rd grade PEMDAS education was incorrect, so I naturally went with the higher level teaching.

What the hell is PEMDAS? Is it somthing they do in america? Any ways the way i was taught was
48/2(9+3)
2 times 9
2 times 3
plus the result
divide.
Because there is a 2 outside of the brakets mean you have to expand them before doing anything else. (Expanding is when you times the number outs side the brakets to everything inside them). if you do this you get 48/24. Do you understand how expanding works? the accepted answer is wrong. the answer is 2 it makes sense. In your comment you said "the problem is 288. Add the 9 and 3, divide the 48 and 2, multiply the 24 and 12." You got the first part right add the 9 and 3 but then you divided 48 by which is a later step before you divide you have to times the 12 (which you got from adding 9 and 3) and the 2 so you get 48 divided by 24. You have to do things in the right order and the dividing step comes last you always expand the brakets.

I understood what expanding was, but that's not what you're supposed to do. You need to add the numbers inside the parentheses before going left-to-right at the beginning of the problem, dividing the 48 by 2 before multiplying it by 12.

And PEMDAS is: parentheses (as in, do whatever is inside the parentheses first), exponents, multiplication, division, addition, subtraction. You're following it, but as I said, my later education explained to me that PEMDAS was incorrect. I can see what you're doing, all I'm saying is that I was taught that it was wrong.

How late in your education because i'm in year ten (10th grade) and thats still how we do it.

Well, I learned it in 8th, but we're still using it in 10th, so make of that what you will.

Captcha'd.

 

[RonHiler]

there is a right and wrong though.

Well, I guess that's where we have to agree to disagree then. Not much more to say than that

I've shown that equation to a couple of different people here (without any explanation so as not to bias the results) and have gotten the same answer both times. 288.

Now, these are Americans, and computer programmers, so there's a built in bias there I suppose. But in our day-to-day work, we have to go with what the computers think, because that's what we work with.

To be fair, though, it's kind of a moot point. No programming language I know would take that equation anyway. It would give you a syntax error. You have to type it in as 48/2*(9+3). So in that respect, I suppose this issue doesn't even really exist for us programmer types, since that is unambiguous (right, we agree the answer to that equation is 288?). Or, if you wanted it to distribute like you want, it would have to go in as 48/(2*(9+3)). The compiler simply wouldn't take 48/2(9+3) at all. I suspect that is entirely on purpose, heh.

Good discussion man.

 

[GodofCider]

Strictly following the rules will lead you to an answer of 288.

except that you're forgetting that once you get to the multiply and/or divide step you tackle the problem from left to right, in this case the division is done first.

I'm a little embarrassed to admit that i also put this into my TI-83, exactly as shown. The calculator will always pick to do the steps in the same order and it will always answer 288 in this case. there is no "toss up" there is nothing ambiguous about mathematics if you know the rules.

I did not forget. My first sentence clearly illustrated that by following the rules you'll only get 288. I simply elaborated later as to how one might end up with 2 for an answer.

Edit:

Just took a glance at the poll...
2: 43.4% (463)
288: 56.6% (604)

...that's quite a bit of fail right there.

 

[Shoqiyqa]

I don't THINK I'm right, I KNOW I'm right.

Tony Blair KNEW he was. That's hardly a good start.

Let's look at the problem (CORRECTLY). 48/2(9+3) What else can we do with this problem? Oh, I know, we can take a 2 out of 48, making the problem 2(24)/2(9+3). That's not all though, we can turn 24 into something else as well! The problem can then become 2(18+6)/2(9+3).

Only if we assume, as you have done from the start, that 48/2(9+3) = 48/(2(9+3)) and not (48/2)(9+3).

As the OP provided neither context nor further description of the question, neither interpretation is infallible.

48/2x = 48/(2x) indeed, but without knowing whether the question originally came in a computer programming class or in another format, whether it was meant that way remains unclear.

--

Ten years, eh? You must have quit school at fifteen, then, right?

Oh, wait. Did you say "ten" or "10"? If it was "10" you really should have specified the base in which you were working, because that could reasonably be interpreted as two, four, eight, ten, twelve or sixteen, depending on context.

 

[mps4li3n]

there is a right and wrong though.

n(x+y) is apart of a slightly more complex form of algebra which you should learn after the basic order of operations and should be the first step into functions, coefficents, graphing, and more complex mathmatics. n(x+y) being a single expression is the key stone of all more complex mathmatics from College Algebra to Calc, to Trig, to theoretical quantem mathmatics...

I think we all believe you, but the thing is that it's just a notation, and mistaking those to be set in stone like math is is just a bad idea... and would lead you to assume that aliens that have technology to break the laws of physics as we know them to get here (assuming no generation ship with slower the light travel, though that would also be advanced enough) don't know math because they have no clue what a (, + or = is...


The only thing whichever side is technically wrong is doing is misreading the symbols used, the actual calculations being done are perfectly fine math... wrong math would be is 2+2 resulted in 5, not if they interpreted the "+" as subtraction (=0) because that's how they've been taught to understand that symbol.

And the saddest thing here is that the only reason anyone is writing it 48/2(9+3) at all is because in the last 50 years computers have become so important.

Before that it would be either:

or

And writing it anyway else would be considered wrong ... and it still wouldn't be wrong math... (well ok, you could also do it like this, but it's still pretty clear what over and under:

, while the one we're using here is basically a "," http://designorati.com/articles/t1/typography/693/typography-words-of-the-day-slashes.php)

 

[flippedthebitch]

What if you look at s simple question like 5-3+2? Do you not read this left to right?

Exactly. You can do 5 -3 + 2 or 2 -3 +5 or -3 + 5 + 2 or 2 + 5 -3. Please correct me if I'm wrong. (I'm not.)

Im really lost as to what your arguement is here. These are all equal to one another because you do the addition and subraction in order from left to right. Thus proving my point, that the order of the operations is important. If the order didnt matter, then 5-3+2 could just as easily be 0 if you do the addition first, but you don't, because you read the equation left to right.

I'm not reading it from left to right when I say that 5 -3 +2 is the same as 2 -3 +5. I just read it backwards.

*sigh*


You rearranged the expression, yes, but to get the correct answer you do the operations left to right. If you do the operations right to left, the answer is different. So, yes, your reading it left to right. You've just switched around the numbers in such a way that the answer remains the same because addition is communative (I think I spelt that wrong).

 

[jomo_25]

********HERE IS YOUR ANSWER*********** (step by step written out the way bodmas/pedmas/bedmas would solve it)

48/2x(9+3) <--- note I'm not arbitrarily adding the multiplication. If you remember anything from math you would remember that a bracket
implies multiplication.

48/2x12
24x12
288

I don't understand how nearly 50% of you can't get this right. The "Brackets" part of bedmas only refers to stuff inside the bracket (parenthesis). If it is not in the bracket it is not part of the bracket . The person that suggested that anything touching the bracket gets worked out first clearly needs math lessons. By his account 5(3-2) could equal 13, it actually equals 5.

Second if you don't go left to right then you straight up fail at math.

(Flippedthebitch the word you wanted was cumulative)

 

[4li3n]

The person that suggested that anything touching the bracket gets worked out first clearly needs math lessons. By his account 5(3-2) could equal 13, it actually equals 5.

Second if you don't go left to right then you straight up fail at math.

Funny how you should say that someone else fails at math, as 5*3-5*2=5 too...




Oh and BTW, we're all on Candid Camera: http://knowyourmeme.com/memes/48293 in case you didn't figure it out yet.

 

[SeaCalMaster]

Since this appears to still be going, let me drop this here:

In a field, the only operations that are actually defined are addition and multiplication. Phrase the problem in terms of those and you can only get 288.

 

[4li3n]

In a field, the only operations that are actually defined are addition and multiplication. Phrase the problem in terms of those and you can only get 288.

That still leaves the problem of the "/"... the original notation, on paper, was more clear, but on most computers you can't use it because they don't have the proper formatting for it...