Can you do this simple maths problem?

[Truronian]

I wouldn't believe one could find a university level text using the "÷" sign either, and neither did I ever claim that, to be clear.

So then what does this question have to do with university level maths?

If you have a solid reference that describes how precedence orders should change regarding "÷" versus "/" it would be great to hear about. It's maybe possible some programming language or random thing on the web has problems with said symbols but that could go either way and doesn't really count, I'm sure we could agree.

I have plenty of sources that use the obelus in accordance with the BIDMAS principle.

Here's one from the UK government: http://nationalstrategies.standards.dcsf.gov.uk/node/64533

Here's an education book (can find more at the library):
Becoming a Successful teacher of Mathematics, Tanner and Jones, 2000

Here are some secondary school textbooks:
http://goo.gl/Cv3qS
http://goo.gl/IpAEs

If we then combine our sources together we find that a solidus is typically used one way and that an obelus is typically used in a different way; or to rephrase that, the conventions are different.

 

[Hehehe]

As for sources, like I've said, most scientific calculators will tell you that the answer is 288. I cannot find a printed source from the top of my head, since this stuff is elementary level and those books are long gone. My university level books do not teach the order of operations, as it is assumed that people attending university are familiar with it.

I assume that the people who say the answer is 2 will calculate it like this (correct me if I assume wrong, since Earthling did not provide a step by step solution I'm going to write one for him). Also in my examples I will use / to represent ÷.

Step 1: 48/2(9+3)
Step 2: = 48/2(12)
Step 3: = 48/24
Step 4: = 2

When calculated like this, step 3 is wrong. Multiplying 2(12) before dividing 48/2 is wrong because it is ignoring the order of operations. 2(12) is not inside brackets and thus it is subject to the order of operations. Another way to misunderstand it is to assume that it is

48
-----
2(9+3)

But in order for it to be interpreted like this, brackets would required. For example

ab+c
-----=(ab+c)/(de+f)
de+f

Writing above equation in linear mode requires brackets to maintain the order of operations. The same thing works in reverse too. If you assume that one term is the denominator and the other is the numerator, then they might have be in brackets so that the order of operations is maintained. In other words assuming that it is

48
-----
2(9+3)

messes up the ooo. This, written in linear mode, would be 48/(2(9+3)).

 

[Quackers]

Guys I just put the operation into my calculator. It is a decent one and I got 2.


image uploader

..is the calculator.

 

[Truronian]

The answer depends upon how you input it.

42/2(3+9) should give a different answer to 42÷2(3+9)

 

[Quackers]

I entered the exact order in the OP.

 

[Hehehe]

Guys I just put the operation into my calculator. It is a decent one and I got 2.

Yes. I have a casio too (casio fx-9860G). The problem is that casio uses incorrect order of operations. Now I can't use this example in the op against casio (it would be circular reasoning, wouldn't it?) but for example, casio interprets 2^3^4 as (2^3)^4=2^12=4096, which is the wrong answer. It should be interpreted as 2^(3^4) >> 4096. Casio is a good calculator but you're going to need extra brackets. Texas insruments will give you the correct answer.

The answer depends upon how you input it.

42/2(3+9) should give a different answer to 42÷2(3+9)

There is no "/" in my or Quackers' casio, only "÷"

 

[Truronian]

I entered the exact order in the OP.

Then that is very strange. My calculator gives me 288... maybe you have it an odd setting. I can say with some certainty that most Casio's give 288, I was teaching this topic to a class with a large variety of calcs and they all got the BIDMAS answer.

There is no "/" in my or Quackers' casio, only "÷"

/ is the fraction key, below Abs.

EDIT:

Apparently this was a bug in older Casios

http://www.imperial.edu/~rick.castrapel/files/impliedgroupings.html

 

[Quackers]

Double checked it am still getting 2.

 

[Truronian]

Yeah, see my edit above.

 

[dutchfire]

Anyone trying to seriously discuss this "problem" in an academic (that is, not high school) environment would (and should) get punched in the face.

 

[MobBoss]

When you type the equation into google, google changes it to read: (48/2)*(3+9)=288

 

[Earthling]

I have ]plenty of sources that use the obelus in accordance with the BIDMAS principle.

None of the sources you listed actually provide evidence for the point that 288 is the right answer or that the convention is common. None of them involve implicit multiplication.

So then what does this question have to do with university level maths?

You could say that the specific expression from the OP should only be examined in context for childern, but you still haven't really given evidence on why there is an explicit difference between the obelus and solidus. The OP never stated this as part of the question anyway. To the point though, ParadigmShifter and others have extended their claim to say that even when using the "/" symbol, which is used in professional and academic work, that the convention they believe is more common.

Apparently this was a bug in older Casios

No, it's not a bug. A random guy's website might call it a bug but Casio probably calls it a feature or a version difference. Texas Instruments has explicitly stated some of their calculators do the same (and they do, getting the answer 2) to conform to professional convention.

edit - wanted to throw in a source for Truronian though, that came up on the obelus issue which it still seems he's not getting
http://www.amazon.com/GCE--LEVEL-PA...=sr_1_1?s=books&ie=UTF8&qid=1302891031&sr=1-1
Which is actually a British book, for a British exam, states problems like the below actually using the obelus sign

5a² ÷ 3b = (5a²) ÷ (3b)

So again, I'm not asking you to find any old random book that uses an obelus sign. If you're convinced it is convention or at least convention in Britain, find a source where wx/yz and wx ÷ yz are spelled out to mean different things. Otherwise, I'm saying that part is a non-issue from my point of view.

 

[KMRblue1027]

With the exact formatting my calculator gets 288.

 

[Truronian]

None of the sources you listed actually provide evidence for the point that 288 is the right answer or that the convention is common.

How many do I need to cite to cross the 'common' threshold? There are certainly plenty; after all every teenager in the country learns this stuff. Doesn't really get more common than that.

I'll repost this one: http://nationalstrategies.standards.dcsf.gov.uk/node/64533

The National Strategies set out the topics that every school in the UK much cover in it's curriculum. One of these topics is order of operations in accordance with BIDMAS. Given that everyone child in the country studies Math at school, I'd say that the convention is pretty common; even more common than the university level use of solidi.

You could say that the specific expression from the OP should only be examined in context for childern, but you still haven't really given evidence on why there is an explicit difference between the obelus and solidus. The OP never stated this as part of the question anyway.

Why does the difference exist? I don't know.

To the point though, ParadigmShifter and others have extended their claim to say that even when using the "/" symbol, which is used in professional and academic work, that the convention they believe is more common.

I on the other hand, have not.

No, it's not a bug. A random guy's website might call it a bug but Casio probably calls it a feature or a version difference. Texas Instruments has explicitly stated some of their calculators do the same (and they do, getting the answer 2) to conform to professional convention.

If it's a feature, then it's one Casio removed from it's post-2007 calculators. Why might that be?

edit - wanted to throw in a source for Truronian though, that came up on the obelus issue which it still seems he's not getting
http://www.amazon.com/GCE--LEVEL-PA...=sr_1_1?s=books&ie=UTF8&qid=1302891031&sr=1-1
Which is actually a British book, for a British exam, states problems like the below actually using the obelus sign

5a² ÷ 3b = (5a²) ÷ (3b)

Interesting. You don't get this nowadays, because it goes against the National Strategies.

So again, I'm not asking you to find any old random book that uses an obelus sign. If you're convinced it is convention or at least convention in Britain, find a source where wx/yz and wx ÷ yz are spelled out to mean different things. Otherwise, I'm saying that part is a non-issue from my point of view.

Round in circles we go. I've given you different sources in which order of operations works differently for obeluses and soliduses; there exist more than enough such sources to verify my claim that the conventions are different.

 

[Earthling]

I'll repost this one: http://nationalstrategies.standards.dcsf.gov.uk/node/64533

Yes, and I looked at that earlier and pointed out it didn't say what you said it said. It still doesn't. Could you try to post a source that actually says what you're claiming?

 

[nato2101]

(After looking at my iGCSE and IB text books)
The "brackets" rule, I've always seen "brackets" never "inside brackets" and technically in the OP's question the 2 is an operation with the bracket, because you are multiplying the contents of the bracket, and should come before the division which is a separate function outside the brackets.

So at the very least it is poorly explained.

 

[Truronian]

Earthling: Yes it does...

 

[Earthling]

There are a grand total of zero soliduses in that image. It doesn't say what you're claiming it says.

 

[Truronian]

There are a grand total of zero soliduses in that image. It doesn't say what you're claiming it says.

I'm claiming it says exactly what is in that image, which clearly it does. It's the convention you seek.

 

[Earthling]

What you posted in that image is completely irrelevant to anything in this thread. It does not suggest anything relevant to the OP's question or anything I or anyone else besides you on this thread have said. (Can't speak for you if you meant to say something else and didn't) And for your own personal crusade of trying to prove different uses of the obelus or solidus, it also has nothing to do with that.