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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 Limoncello)
This 48/2(9+3) could be either

1) (48)/(2(12)) = 48/24 = 2

.

2) (48/2)(9+3) = 24(12) = 288
Sorry, I'll rephrase it:
I always thought brackets had to be worked out first

48/2(9+3)
=48/2(12) = 48/24 = 2
or it can also be
= 48/ (18+6) = 48/24 = 2

I still don't understand.

2. Oh, my calculator says 2
fx-991ES plus
3. The reason it "could" be equal to either depends on whether the (9+3) is on the numerator or denominator. If this problem were to be interpreted by a computer [EDIT: most computers, depending on whether the programmers have made concessions precisely for this issue], then because computers follow BIDMAS pretty much accurately, what they'll see is:

48÷2×(9+3)

And because of the lack of bracket around 2×(9+3), the computer will interpret this as "take 48, divide it by 2, and then multiply what you get by 9+3", giving the answer 288. This is because, as far as a computer is concerned, "÷2" is the same as "×(1/2)" and then all the multiplications are done sequentially, so you get 48×(1/2)×(9+3).

However, because we're humans, we might think that the (9+3) lies on the denominator of the fraction, in which case what we do is "take 48, work out 2×(9+3) and then divide 48 by that", giving the answer 2. Alternatively, we might think in the same way as the computer, which is how this whole silly debate started.

Personally I think the notation is ambiguous. It's unclear whether the 9+3 should be on the numerator or denominator, and whatever the implicit prescribed rules for this sort of thing are, you could forgive anyone for making a notational error.

However these threads do illustrate why LaTeX is a good idea; far too often people don't make it clear what's on a numerator or denominator, e.g. when people write, say, 1+x/3+x, they might have meant or or a number of other things, and whether they got the notation right or wrong makes no difference to what they meant. So I think future reference to this thread for such people is probably the only good thing to come out of all this.

Sigh. The maths forum is usually so nice.

EDIT: This post might also be useful for:
Quotes
(Original post by Miss Anonymous)
.
(Original post by StephenP91)
Don't know why anyone would think anything bar 2.
(Original post by tripleeagle)
My calculations and my calculator (http://www.wolframalpha.com/input/?i...B72%289%2B3%29) agree that it's 288
(Original post by King-Panther)
Using the rules of BODMAS, the answer is 288 and also according to my calculator (I typed in 48/2(9+3)) the answer is 288.
(Original post by street.lovin')
Why are so many people thinking its 288.

Stupid.
4. (Original post by Jallenbah)
No. There is an unambiguous order of preference. Brackets, Indices, then Multiplication and Division, then Addition and Subtraction.
If the precedence is equal, i.e. Multiplication and Division, then you go left to right.

Always.
There is no debate.
I don't know what you call 17 pages of, well, debate then.
5. (Original post by Fallen)
I don't know what you call 17 pages of, well, debate then.
That's poorly educated people trying to disagree with the basic laws of operator precedence.
It's not a matter of opinion, there is only one correct answer.
6. There are strong arguments for both answers. I would argue that there is a slightly better argument for 2 just because I haven't seen the ÷ sign being used for an amazingly long time in any question I've come across for the past 3 years. It's bad notation. Perhaps this is just because using ÷ is ambiguous whereas have 48 ALL OVER 2(9+3) has only one answer, which is 2.

However, as the question is written I think the answer is 288. How confusing.
7. (Original post by Edwin Okli)
Personally, I would say 2 since:
48/2(9+3)
= 48/(2*12)
= 48/24
= 2
Where does the second pair of brackets come from? The one in second line? After dealing with (9+3), you're left with 48/2(12), which is the same as 48/2x12 = 24x12 = 288.
8. (Original post by wanderlust.xx)
Knowing the more complicated stuff in maths doesn't mean you know the easier stuff.

One of my lecturers knows a hell of a lot about real variable theory but that doesn't mean he can answer any of my quantum questions.
It would give anything he does say a damn lot more weight. You don't just learn the complicated stuff at more advanced levels, you learn how to derive it from the simple stuff so that you actually understand it.
9. (Original post by nuodai)
Yes, because using a big font isn't needlessly irritating or anything.

The reason it &quot;could&quot; be equal to either depends on whether the (9+3) is on the numerator or denominator. If this problem were to be interpreted by a computer, then because computers follow BIDMAS pretty much accurately, what they'll see is:

48÷2×(9+3)

And because of the lack of bracket around 2×(9+3), the computer will interpret this as &quot;take 48, divide it by 2, and then multiply what you get by 9+3&quot;, giving the answer 288. This is because, as far as a computer is concerned, &quot;÷2&quot; is the same as &quot;×(1/2)&quot; and then all the multiplications are done sequentially, so you get 48×(1/2)×(9+3).

However, because we're humans, we might think that the (9+3) lies on the denominator of the fraction, in which case what we do is &quot;take 48, work out 2×(9+3) and then divide 48 by that&quot;, giving the answer 2. Alternatively, we might think in the same way as the computer, which is how this whole silly debate started.

Personally I think the notation is ambiguous. It's unclear whether the 9+3 should be on the numerator or denominator, and whatever the implicit prescribed rules for this sort of thing are, you could forgive anyone for making a notational error.

However these threads do illustrate why LaTeX is a good idea; far too often people don't make it clear what's on a numerator or denominator, e.g. when people write, say, 1+x/3+x, they might have meant or or a number of other things, and whether they got the notation right or wrong makes no difference to what they meant. So I think future reference to this thread for such people is probably the only good thing to come out of all this.

Sigh. The maths forum is usually so nice.

My calculator says 2 though other people say they get 288 though
10. its effin 2.......close the effin thread!!!
11. (Original post by Miss Anonymous)
My calculator says 2 though other people say they get 288 though
Ultimately calculators are programmed by people, and if people have programmed it so that a sequence of multiplications after a ÷ sign should be calculated first and then divided by, then it'll say 2. [And alternatively, if it's programmed as per my post, then it'll say 288.]
12. (Original post by Crazydavy)
There are strong arguments for both answers. I would argue that there is a slightly better argument for 2 just because I haven't seen the ÷ sign being used for an amazingly long time in any question I've come across for the past 3 years. It's bad notation. Perhaps this is just because using ÷ is ambiguous whereas have 48 ALL OVER 2(9+3) has only one answer, which is 2.

However, as the question is written I think the answer is 288. How confusing.
Surely the lack of multiplication sign between 2 and (9+3) means 2(9+3) should be treated as 1 number, for they are coefficients, so the answer must be 2.
13. (Original post by DFranklin)
There are people with Maths degrees supporting both answers.
Which supports my stance that it's too ambiguous to warrant an answer!
14. (Original post by nuodai)
Ultimately calculators are programmed by people, and if people have programmed it so that a sequence of multiplications after a ÷ sign should be calculated first and then divided by, then it'll say 2. [And alternatively, if it's programmed as per my post, then it'll say 288.]
okay, thanks
15. 2 x (9+3) does not represent a number yet, it only represents instructions. 2(9+3) represents a number.
16. (Original post by Miss Anonymous)
Oh, my calculator says 2
fx-991ES plus
BODMAS B=Brackets O=Order D=Division M=Multiply A=Add S=Subtract, that is the order of BODMAS. Bracket first (9+3) = 12. Now we have 48/2(12), when there are two things (can't remember the correct term) together and no symbol, its automatically multiply. So that will be 48/2x(12). So what is next according to Bodmas? D comes before M, so we do the division next, 48/2=24. Now we have 24(12) or 24x(12) which equals 288.
Surely the lack of multiplication sign between 2 and (9+3) means 2(9+3) should be treated as 1 number, for they are coefficients, so the answer must be 2.
The lack of a multiplication sign merely leaves an implied one. It still has to be resolved according to operator precedence and it is outside the parentheses so comes in order left to right.
18. (Original post by Miss Anonymous)
I don't understand how it can be 288.
I still think its 2.

thanks

(Original post by StephenP91)
Don't know why anyone would think anything bar 2.
I thought that using BODMAS, you go:

First, look at the brackets, 9+3 is 12
So we've got 48/2*12

Then, look at the divisions and multiplications. Since there are only divisions and multiplications, we go from left to right. 48/2 is 24
So we've got 24*12

All that's left is the multiplication. 24*12 is 288

---

Of course, I might be wrong But that's what I thought it was!

Although I see why, if the calculations was written as a fraction, you would calculate bottom and top separately. But in that case the question would be: 48/(2(9+3))
19. (Original post by Crazydavy)
I would argue that there is a slightly better argument for 2 just because I haven't seen the ÷ sign being used for an amazingly long time in any question I've come across for the past 3 years. It's bad notation.
What the ****?
20. The way I see it is this:

People are seeing it like this 48(9+3)/2 and some I seeing it like this 48/2(9+3).

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