Can you do this simple maths problem?
- Thread starter Rathaus
- Start date
Well I could have a better rebuttal I'd forgotten about but thanks, sure. I think this has got to be about done here.
A couple of things I'd like to say in all politeness though, especially if someone like Paradigm wants to read this thread again. Yes, the question as posed in the OP here - and elsewhere on the Internet, is a bit ambiguous and trollicious. That's recognized. . Making people "choose sides" certainly leads to fun social results, but it is a good answer to recognize that really no one would formally write or code something much like in the OP as a numeric calculation(code that can't be interpreted most often, after all). The points I would still insist on making though is that, firstly implicit multiplication is a valid convention applied at the professional and university level. An actual convention, it's really common enough, and furthermore the opposite is not just a different convention, it's not even used and it's wrong. PV/RT =/= PVT/R, E/kt =/= Et/k and so on. The second is that it's not actually true to say everyone was taught "BODMAS" or whatever one way when they were 8 years old, especially in favor of the 288 answer. This in my view led to lots of the trolliciousness on the Internet but anyway, it's definitely not a universal acronym or something in any way guys, Americans clearly use PEMDAS for instance. But I've posted several links on that and Americans or whomever could give firsthand experience. I particularly do like that I found that Canadian teacher's link and a link to a British children's algebra book with equations like 5a ÷ 2b, which were read and solved as (5a) ÷ (2b). I'd still tease about BODMAS or whatever but really...
If someone thinks they have something valid to contribute I would just personally like to see something along the following lines: first, if you do find an example of something like wx / yz = wxz / y in an actual university physics or math book, printed or online source both, post it out of sheer curiousity. If you have another non professional source but it's in print (not just a website) also at least worth seeing out of curiousity.
The second is the slightly unrelated debate but it's reasonable enough to talk about for human interest if people are being honest. "An 8 year old child in x school in y country would learn it this way" could probably go either way. But please post some sort of evidence, a scan of a book or something. For the record I would point out again that if Truronian did want to argue this about British youngsters using the obelus, he didn't actually post a source indicating this. If you do find an example though, nothing against you posting it.
Above all, please try to find print sources though guys if you have anything left to add. Not a computer or calculator tool or another Internet site, that's beaten to death and not useful. (printed documentation on the design of something could be curious though, that sounds like something nobody would really have but just in case can't hurt)
A couple of things I'd like to say in all politeness though, especially if someone like Paradigm wants to read this thread again. Yes, the question as posed in the OP here - and elsewhere on the Internet, is a bit ambiguous and trollicious. That's recognized. . Making people "choose sides" certainly leads to fun social results, but it is a good answer to recognize that really no one would formally write or code something much like in the OP as a numeric calculation(code that can't be interpreted most often, after all). The points I would still insist on making though is that, firstly implicit multiplication is a valid convention applied at the professional and university level. An actual convention, it's really common enough, and furthermore the opposite is not just a different convention, it's not even used and it's wrong. PV/RT =/= PVT/R, E/kt =/= Et/k and so on. The second is that it's not actually true to say everyone was taught "BODMAS" or whatever one way when they were 8 years old, especially in favor of the 288 answer. This in my view led to lots of the trolliciousness on the Internet but anyway, it's definitely not a universal acronym or something in any way guys, Americans clearly use PEMDAS for instance. But I've posted several links on that and Americans or whomever could give firsthand experience. I particularly do like that I found that Canadian teacher's link and a link to a British children's algebra book with equations like 5a ÷ 2b, which were read and solved as (5a) ÷ (2b). I'd still tease about BODMAS or whatever but really...
If someone thinks they have something valid to contribute I would just personally like to see something along the following lines: first, if you do find an example of something like wx / yz = wxz / y in an actual university physics or math book, printed or online source both, post it out of sheer curiousity. If you have another non professional source but it's in print (not just a website) also at least worth seeing out of curiousity.
The second is the slightly unrelated debate but it's reasonable enough to talk about for human interest if people are being honest. "An 8 year old child in x school in y country would learn it this way" could probably go either way. But please post some sort of evidence, a scan of a book or something. For the record I would point out again that if Truronian did want to argue this about British youngsters using the obelus, he didn't actually post a source indicating this. If you do find an example though, nothing against you posting it.
Above all, please try to find print sources though guys if you have anything left to add. Not a computer or calculator tool or another Internet site, that's beaten to death and not useful. (printed documentation on the design of something could be curious though, that sounds like something nobody would really have but just in case can't hurt)
Defiant's point about implicit multiplication is a fair one. At secondary school level it does not have the increased priority that it does at university, probably because such rules would just confuse.
In British schools students are taught to perform operations in BIDMAS/BODMAS order and as such, would be expected to get the answer 288 (I posted the government's 'suggestions' on order of operations up the thread if anyone is interested). I accept that by applying university level convention you would arrive at an answer of 2. Neither answer is more intrinsically correct than the other, they merely follow different conventions.
I would still answer 288 is someone asked me this question, simply because it looks a lot more like a question you'd get in secondary school (what with the presence of an obelus) than one you'd get at university. Indeed the only scenario I'm likely to ever see a question like this (outside of wholly pointless CFC threads) is one in which I am teaching BIDMAS.
In British schools students are taught to perform operations in BIDMAS/BODMAS order and as such, would be expected to get the answer 288 (I posted the government's 'suggestions' on order of operations up the thread if anyone is interested). I accept that by applying university level convention you would arrive at an answer of 2. Neither answer is more intrinsically correct than the other, they merely follow different conventions.
I would still answer 288 is someone asked me this question, simply because it looks a lot more like a question you'd get in secondary school (what with the presence of an obelus) than one you'd get at university. Indeed the only scenario I'm likely to ever see a question like this (outside of wholly pointless CFC threads) is one in which I am teaching BIDMAS.
ParadigmShifter
Random Nonsense Generator
It's because WolframAlpha uses whitespace to try and guess what you mean when your input could be interpreted as ambiguous.
Look see:
http://www.wolframalpha.com/input/?i=48/2+x,+x=2
Look see:
http://www.wolframalpha.com/input/?i=48/2+x,+x=2
What this question basically comes down to is whether implicit multiplication is given a higher priority than explicit multiplication. This is what I found when googling:
I also found TI's take on the matter, as they have to interpret equations like this somehow:
So in short there is no rule that implicit multiplication is given a higher priority than explicit multiplication, but nevertheless both are used. Also, I checked, none of my university level books have this problem as equations are written unambiguously as
numerator
-----------
denominator
Therefore eliminating any chance of confusion. For the record, most computer programs and calculators will interpret the equation in the OP as 48÷2*(9+3)
TL;DR There's no rule that implicit multiplication is given higher priority, but that convention is nevertheless sometimes used, as a result, the equation in the OP can be interpreted both ways.
http://mathforum.org/library/drmath/view/54341.html
I also found TI's take on the matter, as they have to interpret equations like this somehow:
http://epsstore.ti.com/OA_HTML/csksxvm.jsp?nSetId=103994
So in short there is no rule that implicit multiplication is given a higher priority than explicit multiplication, but nevertheless both are used. Also, I checked, none of my university level books have this problem as equations are written unambiguously as
numerator
-----------
denominator
Therefore eliminating any chance of confusion. For the record, most computer programs and calculators will interpret the equation in the OP as 48÷2*(9+3)
TL;DR There's no rule that implicit multiplication is given higher priority, but that convention is nevertheless sometimes used, as a result, the equation in the OP can be interpreted both ways.
I was at school when they first allowed calculators in maths class (not in exams, just during lessons) and we had to have lessons in using them because of this kind of ambiguity.
We were taught to work out everything to the right of division sign first and store that in memory then work out everything to the left and then divide that by the number in the memory. Which in the op's example would give the answer 2, so it just seems like students are being taught how to use calculators differently (or complicators as one of my maths teachers called them!) in the UK at least.
I'm glad I have found this out, as it may explain some of the shocking numbers that turn up in my bills and credit card statements
.
We were taught to work out everything to the right of division sign first and store that in memory then work out everything to the left and then divide that by the number in the memory. Which in the op's example would give the answer 2, so it just seems like students are being taught how to use calculators differently (or complicators as one of my maths teachers called them!) in the UK at least.
I'm glad I have found this out, as it may explain some of the shocking numbers that turn up in my bills and credit card statements
.
NickyJ
Retired Narrator
I'll try to break this down as best I can:
1. Solve the parentheses, which means the problem is changed to 48/2(12).
2. Solve in order of multiplication and division, so basically, since multiplying and dividing is all that is left, you start at the beginning again, so you divide 48 by 2. The full problem is now 24(12).
3. Multiply 24 by 12, answer is 288.
This whole thread stems from the problem that ÷ and / are both shorthands for the true notation, which is much harder to express with keyboards.
we don't know if the problem is supposed to be
48
-- * (9+3)
2
or
48
-----
2 * (9+3)
We lack faith in the person who transcribed the long form into the short, so we're faced with a dilemma in interpretation. A (well-trained) scientist writing the long form on a board and then transcribing it for a computer program would not assume the program implements the desired precedence correctly, so would disambiguate the expression with enough parenthesis (aka brackets) to make it clear.
People do not interpret this as strictly as a computer, which is why debates of this type show up periodically. When I see a question of this type I ask where the missing brackets should be. (well, much more complicated questions following this pattern ). But the underlying cause of the problem is that we've become lazy as a society about writing out the problem correctly in the first place. 
we don't know if the problem is supposed to be
48
-- * (9+3)
2
or
48
-----
2 * (9+3)
We lack faith in the person who transcribed the long form into the short, so we're faced with a dilemma in interpretation. A (well-trained) scientist writing the long form on a board and then transcribing it for a computer program would not assume the program implements the desired precedence correctly, so would disambiguate the expression with enough parenthesis (aka brackets) to make it clear.
People do not interpret this as strictly as a computer, which is why debates of this type show up periodically. When I see a question of this type I ask where the missing brackets should be. (well, much more complicated questions following this pattern
). But the underlying cause of the problem is that we've become lazy as a society about writing out the problem correctly in the first place. Similar threads
