Solve 48

By webeagle12
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Grand Master

Syanide

Posted
Posted

@primexx: They're the same, the only confusion starts when people use / for fractions ie on the internet, if I wrote 1/2*3, it should be seen as (1/2)x3 (by some logic I guess, at least what I learned in school), but some people use it in a way to describe this fraction:

1

--

2*3

And the only correct way of writing this fraction in one line is: 1/(2*3).

So, to clarify it once and for all, the formula in the post title reads:

48

-- * (9+3)

2

And the only correct solution is 288.

Anyway, I read both / and ? as DIVISION, and as such, it applies only to the digit right of it, unless specified differently by brackets.

Grand Master

Ambroos

Posted
Posted

@primexx: They're the same, the only confusion starts when people use / for fractions ie on the internet, if I wrote 1/2*3, it should be seen as (1/2)x3 (by some logic I guess, at least what I learned in school), but some people use it in a way to describe this fraction:

1

--

2*3

And the only correct way of writing this fraction in one line is: 1/(2*3).

Well yeah, but here you don't have the problem of the juxtaposition.

1/2*3 should be solved by writing each factor between brackets like this:

(1)*(1/2)*(3).

It's just the juxtaposition that has multiple interpretations depending on what convetions you learned that is causing the problems.

Rising Star

Nayos

Posted
Posted

@primexx: They're the same, the only confusion starts when people use / for fractions ie on the internet, if I wrote 1/2*3, it should be seen as (1/2)x3 (by some logic I guess, at least what I learned in school), but some people use it in a way to describe this fraction:

1

--

2*3

And the only correct way of writing this fraction in one line is: 1/(2*3).

So, to clarify it once and for all, the formula in the post title reads:

48

-- * (9+3)

2

And the only correct solution is 288.

Anyway, I read both / and ? as DIVISION, and as such, it applies only to the digit right of it, unless specified differently by brackets.

Good points, indeed.

Now I'm unsure again.

Grand Master

Ambroos

Posted
Posted

PEMDAS. Order of operations.

Parenthesis/Exponents/Multiplication/Division/Addition/Subtraction

Zzz... Read last two pages. Multiplication does not have priority over Division (and the other way around). Same goes for addition and substraction.

Grand Master

primexx

Posted
Posted

Good points, indeed.

Now I'm unsure again.

he's right, but it doesn't address the original point of the juxtaposition convention, which Ambroos correctly identifies as the point of difference.

I still maintain that multiplying any arbitrary term by 1 should not result in a different answer, and if a rule of precedence results in a discrepancy, then the rule is demonstrably flawed.

edit: at least we can all agree that the people citing mnemonics in the exact order need to RTFT :p

Grand Master

Syanide

Posted
Posted

he's right, but it doesn't address the original point of the juxtaposition convention, which Ambroos correctly identifies as the point of difference.

I still maintain that multiplying any arbitrary term by 1 should not result in a different answer, and if a rule of precedence results in a discrepancy, then the rule is demonstrably flawed.

edit: at least we can all agree that the people citing mnemonics in the exact order need to RTFT :p

His beginning premise was wrong, if you look at the formula the way I've written it (and the correct way), he can't possibly multiply (9 +3) with 2, therefore multiplying anything by 1 doesn't change the end result in no way whatsoever -- which is one of the basic things we learn in math.

Grand Master

Ambroos

Posted
Posted

I still maintain that multiplying any arbitrary term by 1 should not result in a different answer, and if a rule of precedence results in a discrepancy, then the rule is demonstrably flawed.

I agree with you that it shouldn't, but that's the exact problem of conventions. Not everyone follows them, they're not mathematically correct and they only apply to strict situations that would otherwise not be possible to be solved... Conventions are basically just incorrect rules that exist to solve the unsolvable...

Grand Master

primexx

Posted
Posted

His beginning premise was wrong, if you look at the formula the way I've written it (and the correct way), he can't possibly multiply (9 +3) with 2, therefore multiplying anything by 1 doesn't change the end result in no way whatsoever -- which is one of the basic things we learn in math.

i don't think he began with the premise that the division symbol encapsulated everything following it. he was arguing that some little known rule of precedence (which I've demonstrated to be stupid by now) requires you do the number beside the bracket first, which of course is ridiculous especially with the way you wrote the formula.

I agree with you that it shouldn't, but that's the exact problem of conventions. Not everyone follows them, they're not mathematically correct and they only apply to strict situations that would otherwise not be possible to be solved... Conventions are basically just incorrect rules that exist to solve the unsolvable...

that's a rather strict definition of what it is to be "correct", but of course conventions are not laws.

Rising Star

ArKeYa

Posted
Posted

We have this convention in high school that for ambiguous terms, if you mean to have a parenthesis in it then put it. Otherwise no parenthesis means there shouldn't be one there. So in this case if you mean to divide 48 by 2 should put (48?2)(9+3)=288. But since there's no parenthesis so the answer is 2.

Veteran

Stetson

Posted
Posted

We have this convention in high school that for ambiguous terms, if you mean to have a parenthesis in it then put it. Otherwise no parenthesis means there shouldn't be one there. So in this case if you mean to divide 48 by 2 should put (48?2)(9+3)=288. But since there's no parenthesis so the answer is 2.

Actually I think that's backwards. If you don't assume parentheses* around the 2(9+3) then what you actually have is 48 / 2 * 12, which evaluates to 288. In order to get 2 you have to assume parentheses*, so 48/(2(9+3)) which is 48/24, or 2.

* And by assume parentheses I mean treating a distribution as higher presidence than normal multiplication, which is the main argument in this thread.

Rising Star

ArKeYa

Posted
Posted

Actually I think that's backwards. If you don't assume parentheses* around the 2(9+3) then what you actually have is 48 / 2 * 12, which evaluates to 288. In order to get 2 you have to assume parentheses*, so 48/(2(9+3)) which is 48/24, or 2.

* And by assume parentheses I mean treating a distribution as higher presidence than normal multiplication, which is the main argument in this thread.

I'm talking about parenthesis around 48/2. The convention in parentheses is on top of juxtaposition precedence. If it seems ambiguous this is how we resolve it. The need to put parentheses in the denominator comes when the denominator is composed of addition elements. e.g. 48/[2(9+3) + 18 + 6] = 1 whereas 48/2(9+3) + 18 + 6 = 26.

If you didn't put parentheses then it's not meant to be there, on top of other conventions/rules. If I meant (48/2)(9+3) I would have written 48(9+3)/2.

Veteran

rfirth

Posted
Posted

48?2(9+3)

48/2*(9+3)

48/2*(12)

48/2*12 because (12) evaluates to 12

24*12

288

Very tricky question. It doesn't help that ? looks like +. Anyway, it's pretty obvious if you do some manipulations. For instance:

X = (9 + 12);

Y = 48/2*X;

Obviously the value of Y would be 288 because the order of operations are more clear.

Or if you represent it as a fraction as you would on paper:

48

--- x (9 + 3) = 48(9+3)/2 = 288

2

Veteran

rfirth

Posted
Posted

Look, this isn't a difficult problem. If you don't believe that the answer is 288, try typing it into a calculator. Write a program in any programming language. Try WolframAlpha.

http://www.wolframalpha.com/input/?i=48%2F2%289%2B3%29

You are making this WAY more difficult than it really is.

If you can't solve this problem, you also will have trouble with problems like this: 1/2((3/4)5)/6 = 5/16

Veteran

leedogg

Posted
Posted

Actually I think that's backwards. If you don't assume parentheses* around the 2(9+3) then what you actually have is 48 / 2 * 12, which evaluates to 288. In order to get 2 you have to assume parentheses*, so 48/(2(9+3)) which is 48/24, or 2.

* And by assume parentheses I mean treating a distribution as higher presidence than normal multiplication, which is the main argument in this thread.

Do you need to distribute in order to solve the expression in parentheses?

If so then the very first expression that is calculated by priority of Parentheses is 2(9+3) or (2 x 9 + 2 x3). The fundamental question is can the 9 and 3 be added together without factoring in the 2?

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