There is no ambiguity if you follow the rules laid down. This kind of scenario must have been first encountered centuries ago. From what your saying, no one has thought about laying down some rules...which if you think about it is absurd.
Agreed. We just have to all use the same convention, at the moment we appear to be using at least two.
There is no ambiguity if you follow the rules laid down. This kind of scenario must have been first encountered centuries ago. From what your saying, no one has thought about laying down some rules...which if you think about it is absurd.
Ah, splendid. A maths lawyer.
<Sits back and awaits the wheeling out of the Mighty Tome of Precedence Precedents, wherein all such disputes are resolved to everyone's complete satisfaction>
we need to end this noncence right here. There are OBVIOUSLY two conventions at work here, and simply repeating your convention is not going to make the other go away.
How the hell we got into the mess of having two commonly held contradictory conventions at play when only one was needed I don't know.
It evolved over time. Any maths textbook at the appropriate level will explain it.
Also it would appear it is not universal as we would not be having the debate.
It is universal within maths, science and engineering. Obviously there are some people who have not yet been taught the standard, or have been taught it wrongly, or who don't fully understand how to use it, or have forgotten it, or who refuse to accept it, or for some other reason don't adhere to it. Likewise there are plenty of people who for one reason or another would evaluate 1+2x3 from left to right and make it 9. In both cases they differ from professional mathematicians, scientists, engineers and teachers, and they would get the relevant questions wrong in an exam.
It evolved over time. Any maths textbook at the appropriate level will explain it.
It is universal within maths, science and engineering. Obviously there are some people who have not yet been taught the standard, or have been taught it wrongly, or who don't fully understand how to use it, or have forgotten it, or who refuse to accept it, or for some other reason don't adhere to it. Likewise there are plenty of people who for one reason or another would evaluate 1+2x3 from left to right and make it 9. In both cases they differ from professional mathematicians, scientists, engineers and teachers, and they would get the relevant questions wrong in an exam.
If it evolved perhaps it is still evolving. evolution implies change and if things change they are not set in stone. Why do you act as if they are?
CLEARLY (its the only thing that is) it is NOT universal. You may want it to be, you may have thought it was, but it isn't.
48÷2(9+3) = ? (Do the brackets 1st)
48÷2x12 = ? (Multiply & Divide next, starting at the left and heading right)
24x12 = ? (Still multiplication & divides to do, continue with these)
288 = ?
Also worth pointing out that 2(12) ≡ 2 x (12) ≡ 2 x 12, so having the 12 in the brackets doesn't mean it gets priority multiplication with the 2, before the 48 on the left gets divided by the 2. The B in BODMAS refers to doing the operations inside the brackets, not on the outside adjacent.
48
2(9+3)
would be written on a single line as 48÷(2(9+3)) {48 over everything on the bottom}, not as the original post was.
To avoid ambiguity, the original could be written as (48÷2)(9+3), but the original still is 288 and not 2.
I can understand this - from the point of view that it's an unusual symbol to use on-screen since it doesn't naturally appear from a keyboard stroke and typographically speaking it creates a significant gap, affecting the presentation in a way that can be seen as suggesting a particular interpretation.
Not one said it was ambiguous!
I am surprised at this - not one of them suggested the possibility that it might be interpreted differently?
Perhaps what we are really finding out in this thread is 'if for some reason whilst in a drunken stupor you wrote this, what was it that you probably meant?'.
It evolved over time. Any maths textbook at the appropriate level will explain it.
I've put in some effort to post examples at your request, one of which was was from a book aimed at O'Level students that contradicts this statement - it's very clear in fact.
Please could you supply some excerpts from a text book that backs up your belief that implied multiplication does not take precedence over explicit multiplication/division.
It is universal within maths, science and engineering.
I qualified in science so of course I'll need some evidence before I can accept this statement at face value ;-) The evidence I've posted so far contradicts this statement.
What and you just did an improptu poll of these statisticians who happened to be hanging around, gathered the results and posted them within minutes?!
No. I asked for it to be left in the common room. (sometime on Monday).
I got the results just now.
I do not regard Phd as authoritative and wanted a senior lecturer/ professor to offer an opinion on the debate (rather than simply saying "2" or "288"), but apparently they were not keen to give an answer (odd,but perhaps they felt in a waste of their time)
No wonder this country is in such a mess if the eggheads can't even work out a simple sum like this......it's what you get for leaving out common sense brackets and multiplication signs just to make a simple thing seem clever
Comments
Also it would appear it is not universal as we would not be having the debate.
Like it or not, some use 1/2x as being 1/(2x). No amount of shouting BODMAS is going to change that.
http://community.tes.co.uk/forums/p/481254/6668920.aspx
63 posts? Lightweights!!
<Sits back and awaits the wheeling out of the Mighty Tome of Precedence Precedents, wherein all such disputes are resolved to everyone's complete satisfaction>
1/2x
comes out as 1/(2x)
http://www3.wolframalpha.com/input/?i=1%2F2x
1/2*x
comes out as
x/2
http://www3.wolframalpha.com/input/?i=1%2F2*x
we need to end this noncence right here. There are OBVIOUSLY two conventions at work here, and simply repeating your convention is not going to make the other go away.
How the hell we got into the mess of having two commonly held contradictory conventions at play when only one was needed I don't know.
CLEARLY (its the only thing that is) it is NOT universal. You may want it to be, you may have thought it was, but it isn't.
I think it should be a sticky.
Maths post grads.
12 say 288
9 say 2.
1 blames the "÷" symbol
Not one said it was ambiguous!
The two lecturers did not offer an opinion! (probably becuase they didn't want to embarrasses themselves -)
Where did you get these results from? Not that I'm going to argue with them.
48÷2(9+3) = ? (Do the brackets 1st)
48÷2x12 = ? (Multiply & Divide next, starting at the left and heading right)
24x12 = ? (Still multiplication & divides to do, continue with these)
288 = ?
Also worth pointing out that 2(12) ≡ 2 x (12) ≡ 2 x 12, so having the 12 in the brackets doesn't mean it gets priority multiplication with the 2, before the 48 on the left gets divided by the 2. The B in BODMAS refers to doing the operations inside the brackets, not on the outside adjacent.
48
2(9+3)
would be written on a single line as 48÷(2(9+3)) {48 over everything on the bottom}, not as the original post was.
To avoid ambiguity, the original could be written as (48÷2)(9+3), but the original still is 288 and not 2.
However, it is an unambiguous accepted convention for everyone involved with the use or teaching of maths, science or engineering.
I am surprised at this - not one of them suggested the possibility that it might be interpreted differently?
Perhaps what we are really finding out in this thread is 'if for some reason whilst in a drunken stupor you wrote this, what was it that you probably meant?'.
What and you just did an improptu poll of these statisticians who happened to be hanging around, gathered the results and posted them within minutes?!
Go with 288, SK. It's the right answer (with or without Keio's statisticians).
Please could you supply some excerpts from a text book that backs up your belief that implied multiplication does not take precedence over explicit multiplication/division. I qualified in science so of course I'll need some evidence before I can accept this statement at face value ;-) The evidence I've posted so far contradicts this statement.
I got the results just now.
I do not regard Phd as authoritative and wanted a senior lecturer/ professor to offer an opinion on the debate (rather than simply saying "2" or "288"), but apparently they were not keen to give an answer (odd,but perhaps they felt in a waste of their time)