48÷2 (9+3) argument

Ekstasis said:
Some of you must really have some screwed up monthly budgets.....

288
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Sure, we all bow to your mathematical superiority, despite your inability to comprehend the reasoning generally accepted by mathematicians :/
 
milomak said:
48
Hence why the Casio is not wrong. Can't actually believe people were willing to think that one of the world's top calculatir makers made a mistake when it comes to this.
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ALso remember, there are many different input formats on calculators, Direct Algebraic Logic and Sequential algebraic logic being two of the more popular ones (for 'normal, non-scientist' peeps)
So the same equation can be interpreted differently on different calculators, even if entered in the same order.
 
Mike Hoxbig said:
Sure, we all bow to your mathematical superiority, despite your inability to comprehend the reasoning generally accepted by mathematicians :/
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Taken from http://ubuntuforums.org/showpost.php?p=10657195&postcount=273
Here's what I can offer you.
1. "/" is the accepted symbol for division
2. Multiplication and division have equal precedence.
3. Parentheses have a higher precedence than any arithmetic operator, so expressions in parentheses are always evaluated first.
4. SOME TEXTS (and some calculators) adopt their own rule that binds ab together more tightly than a*b, in effect treating ab as being equivalent to (a*b).

5. By CONVENTION (not by "law") the associativity of multiplication, division, addition and subtraction is left to right. Therefore, in the absence of parentheses, BY CONVENTION, these operations are simply evaluated sequentially from left to right. There is no "mathematical law" that requires this; it is simply a convention that is (nearly?) universally accepted. Without this convention, expressions like 105 / 3 * 5 would simply be ambiguous. There would be no way for people to agree as to how to evaluate such expressions in the absence of parentheses.
6. There is NO SUCH CONVENTION concerning "implied multiplication". SOME PEOPLE choose to say ab => (a*b). Most people would say ab => a*b.

IN MY OPINION, those who take it upon themselves to adopt a "new convention" (which is not a convention because it is not generally agreed upon) do us all a disservice by introducing ambiguity where there was none before. Perhaps a better convention is this: don't use implied multiplication because it is ambiguous.
But unfortunately, that's not a convention either. It's just my opinion.

So (again, in my opinion) "105 DS ab where a=3 and b=5"
=> 105/3*5 = (105/3)*5 = 35*5 = 175

And, "12 DS 2(6-3)+3^2"
=> ((12/2)*(6-3)) + 3^2
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If you read the source, you come across
Original Q states:
I need references, not just opinions. We already have lots of those.
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Answer:
Here, we offer help based on our accumulated knowledge. This is not a free research service. You want references, find them yourself.
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Find me a reputable Maths journal or paper discussing this, where they proove a similar equation should be done the 288 way. I will then accept that method, but I still think 2 is the answer..
 
Lets try something a little different

Example 1:
48 / 2(9+3)
I now assign: x=(9+3)
= 48 / 2x
Lets factor out 2
= (2/2) * (24 / x)
resubstitute x = (9+3)
= 1 * (24/(9+3))
= (24/12)
= 2

Example 2:
Gunna really switch this up now....
lets say x = 2

I wanna work out 48 / (x^2+2x+4)
now I know the answer is 4... But lets work it out :)

48 / (x^2+2x+4)
We can contract this to
= 48 / (x+2)(x+2)
Now if we follow the 288 way (notice I'm not grouping anything beyond what I should) we get:
= 48 / (x+2) * (x+2)
lets put x = 2
= 48 / 4 * 4
= 48
Which is wrong?

Now the 2(correct) way
= 48 / (x+2)(x+2)
lets put x = 2
= 48 / (4)(4)
= 48 /12
= 4
 
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ponder said:
Taken from http://ubuntuforums.org/showpost.php?p=10657195&postcount=273
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Yeah but that's one guys view on a Linux forum, where the source he quoted isn't even sure.

Here's an alternate view from a mathematics site and forum:
The confusing part in the above calculation is how "16 divided by 2[2] + 1" (in the line marked with the double-star) becomes "16 divided by 4 + 1", instead of "8 times by 2 + 1". That's because, even though multiplication and division are at the same level (so the left-to-right rule should apply), parentheses outrank division, so the first 2 goes with the [2], rather than with the "16 divided by". That is, multiplication that is indicated by placement against parentheses (or brackets, etc) is "stronger" than "regular" multiplication. Typesetting the entire problem in a graphing calculator verifies this hierarchy.

Note that different software will process this differently; even different models of Texas Instruments graphing calculators will process this differently. In cases of ambiguity, be very careful of your parentheses, and make your meaning clear. 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.
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http://www.purplemath.com/modules/orderops2.htm

As I said previously, the general consensus among mathematicians is that the real number preceding the brackets is part of the brackets expression, and therefore takes precedence since the '*' operator is not explicitly defined.

In any event, let's just agree that the notation is sh*t, and is one of the reasons I despise it when division is written in a single line. It is not clear which of the following is true:
29egprp.jpg


I'm inclined towards the first one, simply because I (and most other mathematicians in general), see the 2 as part of the brackets.
 
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nakedpeanut said:
48 / 2(9+3)
I now assign: x=(9+3)
= 48 / 2x
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You are assuming 48/(2x), why?

48/2x is 48/2*x

Multiplication & division have the same precedence so solve the equation from left to right which gives you 48/2=24 24*x=288 where x=12.

If you follow the rules which state that multiplication & division have the same precedence and you apply the formula from left to right you get 28/2*x. You can't just go and add brackets as you please.
 
ponder said:
You are assuming 48/(2x), why?

48/2x is 48/2*x

Multiplication & division have the same precedence so solve the equation from left to right which gives you 48/2=24 24*x=288 where x=12.

If you follow the rules which state that multiplication & division have the same precedence and you apply the formula from left to right you get 28/2*x. You can't just go and add brackets as you please.
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All I did was replace (9+3) with x.. I did not add an additional * to the equation like you did. Hence it is still in it's current state. I can freely substitite x for (9+3) and vise-versa and it does not change the end result of the equation, unlike your addition of a *.

Edit: if you want to include a * you have to remeber that when you calculate brackets you have to incorporate any value that is 'attached' to the brackets (i.e. it is not seperated by an operand) when working out their value. By adding the * you are changing the equation as '2' is now seperated from the brackets and this results in the erroneous answer of 288..
 
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nakedpeanut said:
All I did was replace (9+3) with x.. I did not add an additional * to the equation like you did. Hence it is still in it's current state. I can freely substitite x for (9+3) and vise-versa and it does not change the end result of the equation, unlike your addition of a *
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So you are saying 2x does not equal 2*x?
 
ponder said:
So you are saying 2x does not equal 2*x?
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This... Sorry I wanted to clarify
nakedpeanut said:
All I did was replace (9+3) with x.. I did not add an additional * to the equation like you did. Hence it is still in it's current state. I can freely substitite x for (9+3) and vise-versa and it does not change the end result of the equation, unlike your addition of a *.

Edit: if you want to include a * you have to remeber that when you calculate brackets you have to incorporate any value that is 'attached' to the brackets (i.e. it is not seperated by an operand) when working out their value. By adding the * you are changing the equation as '2' is now seperated from the brackets and this results in the erroneous answer of 288..
Click to expand...
 
nakedpeanut said:
This... Sorry I wanted to clarify

Edit: if you want to include a * you have to remeber that when you calculate brackets you have to incorporate any value that is 'attached' to the brackets (i.e. it is not seperated by an operand) when working out their value. By adding the * you are changing the equation as '2' is now seperated from the brackets and this results in the erroneous answer of 288..
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No, precedence only applies to what's inside of the brackets, not the outside. 48/2(9+3) will thus be seen as 48/2(12) but there is still a * between the 2*(12) so we can rewrite it as 48/2*12 which is not the same as 48/(2(12)).
 
lol I'm getting bored of this now... I'm gunna email the Mathematics department at tuks on monday and ask them :)
 
Everybody has missed the point of this exercise:
https://encrypted.google.com/search?hl=en&safe=off&biw=1153&bih=668&q=+48/2(9+3)&nocalc=1

The science behind it says that a bunch of meatheads debated this through 85 pages and failed to reach consensus. What we learn then is that the stereotypical bodybuilder - or meathead - presented as a slow, egomaniacal bully may in fact be wrong. Surely a group that manages to debate this very issue over that many pages is not void of intellect.

Until we realise that is was 85 pages. Are we headed the same way?
 
Erm, following Prof Farnsworth, surely the issue is how the problem is represented visually. Is it [49] over [2(9+3)], or [49 over 2][9+3]? It's not a paradox of arithmetic at all.
 
How about (cue shock and horror) you just write the dam equation properly?! Or are mathematicians like women who deliberately say ambiguous things so that you get into trouble no matter what?
 
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