I got 2 and was sure of my working now I'm wondering even though I did engineering at Uni. I always used the method I used to get 2 when doing calcs on my course.
That is a valid translation of what I entered. 2(9+3) is just a shorthand of 2*(9+3)
So presumably, 48 / 2(9 + 3) is the same as 48 / 24. Excel doesn't do a(x + y) so proposes a * (x + y) ... Surely that would distort the following equation 49 / 2(9 + 3) by doing the following (49 / 2) x (9 + 3).
But at the end of the day, whoever writes such an equation should be aware of the possibility of ambiguity in some people's minds and clarify it accordingly, by the use of additional brackets if necessary. It's a badly written equation both as originally presented and as above.
The last example applies directly to this discussion.
Again it explains that 16 ÷ 2(2) is ambiguous.
And then goes on to say:
"The general consensus among math people is that "multiplication by juxtaposition" (that is, multiplying by just putting things next to each other, rather than using the "×" sign) indicates that the juxtaposed values must be multiplied together before processing other operations. But not all software is programmed this way, and sometimes teachers view things differently. If in doubt, ask!"
Given the debate this has created on two forums I visit (one frequently, one not so), I thought I'd bring this little debate over here.
48÷2(9+3) = ?
Simply, what's the answer? It'll become pretty clear after a few posts that some will get one answer and one will get another.
I think it's two myself:
48÷2(9+3)
48÷2(12)
48÷24
= 2
However, a lot are saying it is 288, by following this method (although I believe the above is technically more 'correct'):
48÷2(9+3)
24*(9+3)
24*12
= 288
Which is right?
Returning to this, because it's bugging me.
Surely it has to be 2.
If it meant 48/2*(9+3) it would have said so.
If you divide 48 by 2, all you are left with is 9+3 in a set of decorative brackets, with no clue what to do with their sum.
If the (9+3) is meant to be ruled by the 2 before it, then it has to be that the 48 is divided by the total sum.
Mind you, I was in C division for maths.
On the other hand, that was because I couldn't see the point of geometry and calculus, not because I couldn't do mental arithemtic.
Only because of the ambiguity of how the original sum was written, the only way to clarify the answer is to write the sum in either of the long forms.
This is the answer to the question! ^
48÷2(9+3) could also be seen as 48/2*12. If we followed BIDMAS we would do division first. 48/2=24. Then 24*12=288
Or
48
2*12 = 2
Maybe there isn't a certain right or wrong answer to this question. There is a possibility of two answers which can be extracted so there's only one way to find out.....FIGHT!
In this case, the "divided by" implies a bracket around the terms following it. Strictly speaking, the "2(9+3)" is a single term, which needs to be simplified into 24.
If the problem had been 42 / 3 + 4, you'd have no idea whether the answer was 18 or 6.
The last example applies directly to this discussion.
Again it explains that 16 ÷ 2(2) is ambiguous.
And then goes on to say:
"The general consensus among math people is that "multiplication by juxtaposition" (that is, multiplying by just putting things next to each other, rather than using the "×" sign) indicates that the juxtaposed values must be multiplied together before processing other operations. But not all software is programmed this way, and sometimes teachers view things differently. If in doubt, ask!"
Comments
Well, I'm not. Even my calculator comes up with 288.
I got 2 and was sure of my working now I'm wondering even though I did engineering at Uni. I always used the method I used to get 2 when doing calcs on my course.
A Doubter !!!
Quick ! I'm claiming you for the Church of Two !
People already have
http://www.computerworld.com/s/article/9068599/Just_patched_Excel_makes_calculation_mistakes
We were taught mental arithmetic in school; I don't see why people need to use computerised means.
So it prompts you to confirm you entered what you wanted to.
The do occasionally introduce bugs. But certainly not ones in simple maths
So presumably, 48 / 2(9 + 3) is the same as 48 / 24. Excel doesn't do a(x + y) so proposes a * (x + y) ... Surely that would distort the following equation 49 / 2(9 + 3) by doing the following (49 / 2) x (9 + 3).
its not ambiguous. Excel is just clarifying that you didn't make a mistake.
And that's the problem - this is simple calculus but people are using algebraic logic.
Corrected - my error!
^^ This
Unless it's written:
48
---- x (9+3)
2
Which is 288.
http://mathforum.org/library/drmath/view/57021.html
Particularly the response by the Dr of Maths where he says
6/2(3)
is too ambiguous for any reasonable mathematician ever to write.
48
--- (9+3)
2
Oops, already asked. But I too think 288.
But at the end of the day, whoever writes such an equation should be aware of the possibility of ambiguity in some people's minds and clarify it accordingly, by the use of additional brackets if necessary. It's a badly written equation both as originally presented and as above.
The 2 crowd should get 1 and the 288 crowd should get 9
http://www.purplemath.com/modules/orderops2.htm
The last example applies directly to this discussion.
Again it explains that 16 ÷ 2(2) is ambiguous.
And then goes on to say:
"The general consensus among math people is that "multiplication by juxtaposition" (that is, multiplying by just putting things next to each other, rather than using the "×" sign) indicates that the juxtaposed values must be multiplied together before processing other operations. But not all software is programmed this way, and sometimes teachers view things differently. If in doubt, ask!"
Isn't shorthand for (2x9)+(2x3) ?
As the number outside the bracket affects everything inside the bracket?
I may, however, have made an error.
Only because of the ambiguity of how the original sum was written, the only way to clarify the answer is to write the sum in either of the long forms.
It completely depends on the interpretation of the priority of juxtaposed values.
The original sum requires clarification before answering completely.
FINISH
DONE
Hopefully we can all agree
Returning to this, because it's bugging me.
Surely it has to be 2.
If it meant 48/2*(9+3) it would have said so.
If you divide 48 by 2, all you are left with is 9+3 in a set of decorative brackets, with no clue what to do with their sum.
If the (9+3) is meant to be ruled by the 2 before it, then it has to be that the 48 is divided by the total sum.
Mind you, I was in C division for maths.
On the other hand, that was because I couldn't see the point of geometry and calculus, not because I couldn't do mental arithemtic.
This is the answer to the question! ^
48÷2(9+3) could also be seen as 48/2*12. If we followed BIDMAS we would do division first. 48/2=24. Then 24*12=288
Or
48
2*12 = 2
Maybe there isn't a certain right or wrong answer to this question. There is a possibility of two answers which can be extracted so there's only one way to find out.....FIGHT!
In this case, the "divided by" implies a bracket around the terms following it. Strictly speaking, the "2(9+3)" is a single term, which needs to be simplified into 24.
If the problem had been 42 / 3 + 4, you'd have no idea whether the answer was 18 or 6.
It's got a '2' in it, so I think it's a small error.
I would never have found this ambiguous until this discussion.
I consider the 2(2) to be bracketed therefore would be worked out first rather than 16/2 x 2.
Worrying that professional maths guys are talking about ambiguity as maths is supposed to be an exact science.
Hawking and Penrose at Cambridge, oops forget all that Blackhole and space/time business, we had a bracket in the wrong place