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# 48÷2(9+3) = ? watch

• View Poll Results: 48/2(9+3)
2
117
52.47%
288
106
47.53%

1. (Original post by Glutamic Acid)
What the ****?
In maths past key stage 3 the division sign ÷ as you see it here is never used. Equations involving a division are written differently so avoid the confusion being displayed here. Although it is technically correct notation I would argue that it is bad because it can start to get confusing. The correct answer is 288 but the more obvious (and in my opinion incorrect answer would be 2). I just don't agree with equations being written like this. I didn't really want to come across as supporting 2 because I don't like the equation I just worded my argument wrong.
2. It's 288... this is like first year of high school stuff.
3. (Original post by little_wizard123)
The thing with maths is that it shouldn't be 'ambiguous', though. Just because people interpret things differently, it doesn't mean that both are correct.

You could argue however that if somebody was to write this, nobody would write it in a one line style that the OP has. I think DFranklin wrote a few pages back that if two different people wrote it (a Uni lecturer/a GCSE student), then the interpretation would be different. Whilst this is true, I don't think it's the point. It can't be correct to interpret in both ways, otherwise there'd be no point in a common mathematical notation, principles and axioms.

I'd say that the 'correct' answer is 288; and I'd say any other answer such as 2 could be 'assumed' because of how it's written, but it's not correct.
That's the point though, its not accepted mathematical notation to write
4/3(2+1) because it doesn't make it clear which operation takes precedence. Its like asking what does this formula equal:

3*6{^5&23(8!0].4)

obviously, the answer is "who the **** knows?"
4. Having looked at various posts and articles, I'm tending towards saying there's enough consensus that 288 should be regarded as the "correct" answer here.

On the other hand, the people screaming BIDMAS as if it overrides everything are oversimplifying.

For one thing, many (albeit a minority) of academics do consider that "implicit multiplication" has a higher priority than explicit. But it's actually more complicated than that. Most will agree that "2x" should be treated as one entity (nearly everyone is happy with writing the quadratic formula as ). But it's less clear that's true for 2xy and even less clear for 2(x+y) or 2(3+4). Most will draw the line somewhere before the last case.

There's also a question about "correctness" versus "what everyone understands". That's not an argument for sloppiness - it's an argument that rules don't keep up with usage.

By BODMAS rules, e^it is unambiguously (e^i)t. It's not even an argument about left-to-right; exponentiation has higher priority than multiplication. But I'd guess 99.9%+ of mathematicians will interpret it as e^(it), whatever the "rules" might say.

Incidentally: Wolfram Alpha treats 2x as a single entity but not 2(x+y). Strangely, it doesn't treat 2pi as a single entity either. Looking around forums, 2pi is pretty well accepted.
5. (Original post by py0alb)
That's the point though, its not accepted mathematical notation to write
4/3(2+1) because it doesn't make it clear which operation takes precedence. Its like asking what does this formula equal:

3*6{^5&23(8!0].4)

obviously, the answer is "who the **** knows?"
Yep, so I'd argue that the fault is in the question, although you can't really argue that 48/2(9+3) is 'incorrect'. It makes sense to anybody with Year 7 knowledge. Therefore I'd argue that it 'should' have a single correct answer. It may 'look' ambiguous, but surely it can't be.
6. Right let's look at this question in detail.
Let us first remind ourselve sof the definition of BODMAS:

B - Brackets first
O - Orders (ie Powers and Square Roots, etc.)
DM - Division and Multiplication (left-to-right)
AS - Addition and Subtraction (left-to-right)

Now with this we should eb able to work this expression out very simply.

So BODMAS tells us to do everything inside the bracket first and so 48÷2(9+3) = 48÷2(12) = 48÷2x12.
Now we are told to do divison and multiplication from left-to-right and so 48÷2(9+3) = 48÷2(12) = 48÷2x12 = 24x12 = 288.

7. (Original post by Planto)
Of course it is ambiguous. It is a rather bold claim that something as vague, ill-defined and flimsy as "work left-to-right" is an absolute, unambiguous axiom. This is why you simply don't write out expressions in such a stupid, in-line format. The only time this is appropriate is when it is being used as a computational expression, at which point you require far more disambiguation in the form of brackets because the behaviour of the computation in this situation is not universally defined and is language-dependent, since the direction of associativity will vary dependent on language, as will whether or not 2(9+3) is treated as an implicit multiplication or, as smiffhead points out, a term with coefficient.
I have never seen a language do anything other than
Brackets > Indicies (rare for a language to have this however) > Multiplication, Division and Modulus > Addition and Subtraction

If it was ambiguous and language dependent, then moving to a new language would be a nightmare in which you have to flood your code with brackets. The order of precedence IS universally accepted and where precedence is equal, it is also universally accepted that you go left to right.
8. 11 pages? Lawl

EDIT: 19 pages
9. (Original post by RamsFanNo1)
Right let's look at this question in detail.
Let us first remind ourselve sof the definition of BODMAS:

B - Brackets first
O - Orders (ie Powers and Square Roots, etc.)
DM - Division and Multiplication (left-to-right)
AS - Addition and Subtraction (left-to-right)

Now with this we should eb able to work this expression out very simply.

So BODMAS tells us to do everything inside the bracket first and so 48÷2(9+3) = 48÷2(12) = 48÷2x12.
Now we are told to do divison and multiplication from left-to-right and so 48÷2(9+3) = 48÷2(12) = 48÷2x12 = 24x12 = 288.

http://www.purplemath.com/modules/orderops2.htm = 2

http://mathforum.org/library/drmath/view/57222.html = 288

BODMAS doesn't tell us in what order you solve values in the format x/y(z) unless you change it to x/y*z yourself.
10. (Original post by RamsFanNo1)
Right let's look at this question in detail.
Let us first remind ourselve sof the definition of BODMAS:

B - Brackets first
O - Orders (ie Powers and Square Roots, etc.)
DM - Division and Multiplication (left-to-right)
AS - Addition and Subtraction (left-to-right)

Now with this we should eb able to work this expression out very simply.

So BODMAS tells us to do everything inside the bracket first and so 48÷2(9+3) = 48÷2(12) = 48÷2x12.
Now we are told to do divison and multiplication from left-to-right and so 48÷2(9+3) = 48÷2(12) = 48÷2x12 = 24x12 = 288.

In BODMAS division & multiplication and addition & subtraction have no authority over each other. Look at my algebra example above (or or a previous page maybe by now), to see why the answer is 2.
11. (Original post by little_wizard123)
The thing with maths is that it shouldn't be 'ambiguous', though. Just because people interpret things differently, it doesn't mean that both are correct.

You could argue however that if somebody was to write this, nobody would write it in a one line style that the OP has. I think DFranklin wrote a few pages back that if two different people wrote it (a Uni lecturer/a GCSE student), then the interpretation would be different. Whilst this is true, I don't think it's the point. It can't be correct to interpret in both ways, otherwise there'd be no point in a common mathematical notation, principles and axioms.
Notation evolves to suit people's needs, not the other way around.

What's the point of BODMAS? Why not just work from left-to-right, no precedence rules? Because once you start doing more complicated maths you find it's much more convenient for 2*x + 3*y not to mean (2*x+3)*y.

Once you're doing "real mathematics", particularly on forums (where layout is restricted), it becomes more convenient to ignore (or refine) some of the rules.

As I've said a few times, no-one has a problem with (-b +/- sqrt(b^2-4ac))/2a, even though it's not correct under BODMAS.

Similarly, mathematicians will understand that

e^it = e^(it), while x^2y = (x^2)y,

even though the first expression is *really* wrong according to BODMAS.
12. (Original post by little_wizard123)
Yep, so I'd argue that the fault is in the question, although you can't really argue that 48/2(9+3) is 'incorrect'. It makes sense to anybody with Year 7 knowledge. Therefore I'd argue that it 'should' have a single correct answer. It may 'look' ambiguous, but surely it can't be.
Well its a question of interpreting what someone means by that notation. The alleged "rule" that kids are taught in school is of left to right precedence, but seeing as hardly anyone actually uses it, how valid can the rule really be said to be? After all, if a colleague of mine had left me with that formula, I would assume he had just meant 48 / (2(*(9+3)) because thats what most maths people would mean. I think DFranklin already said this.

This isn't a maths question, its a notation question, and therefore there doesn't necessarily have to be a right answer.
13. I have to admit I love these threads; I've seen a massive discussion on another board already (where people were a lot more angry and abusive ) and the poll was 50-50 in that as well.
14. Whatever the calculator says.

It has to be said though, the maths forum has never been so popular.
15. (Original post by DFranklin)

Similarly, mathematicians will understand that

e^it = e^(it), while x^2y = (x^2)y,

even though the first expression is *really* wrong according to BODMAS.

Thats to do with expectations of what formulas normally look like, and understanding that its hard to express them correctly online. I would go further and say

e^kx-it would be interpreted as e^(kx-it) which according to bodmas would be really, really wrong.
16. Wow two threads over a simple calculation.

Only on TSR
17. it's 2.
18. (Original post by py0alb)
Thats to do with expectations of what formulas normally look like, and understanding that its hard to express them correctly online. I would go further and say

e^kx-it would be interpreted as e^(kx-it) which according to bodmas would be really, really wrong.
I agree, thoughit would depend a bit on context whether people would interpret e^kx-it correctly. But for sure, no mathematician is going to think e^it = (e^i)t.

The point being "BODMAS says e^it = (e^i)t, but no mathematician will interpret it that way. It's a bit silly to say BODMAS has to take precedence over all actual usage here".
19. http://www.wolframalpha.com/input/?i...%29%289%2B3%29

Just posting this link that I do not believe has been posted before. As you can see in my search term I entered brackets however wolfram took the first set away as they were not needed leaving the answer in the format given by the question. Therefore people can assume that we are working with (48/2)(9+3).

For further reference here is what it would be like if we had 48/(2(9+3))

http://www.wolframalpha.com/input/?i...%289%2B3%29%29

As you can see the question has been set out differently.

288 is given in the top correct link
2 is given in the bottom incorrect link.

That is all.
20. 2.

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