I asked the teacher at Kumon and he said the answer was two. He said that the 2(9+3) is actually one term and that it must be done first so yea the answer is 2.

ONLY ONE ANSWER IS CORRECT AND IT IS THIS

afzal to help you understand what i mean by implied brackets

Noone insane enough writes the equation like shown most people would write (48/2)(9+3)=288 or 48/(2*(9+3))=2

To be more precise most people wouldn't write it in one line but more like a proper fraction.

Haha, I knew BEDMAS was bullshit.

Originally Posted by Scarecrow

Haha, I knew BEDMAS was bullshit.

Actually, it's not. It's quite necessary, since it's a gauge on whether the rules of formation for particular mathematical sentences (here, in the 'language of commutative rings', although it applies to many other popular mathematical structures) have been adhered to. In fact, I think this problem precisely illustrates my point - if a string is ambiguous when you try to apply BEDMAS to it, then the string isn't well-formed.

Originally Posted by thedog123123

afzal to help you understand what i mean by implied brackets

Noone insane enough writes the equation like shown most people would write (48/2)(9+3)=288 or 48/(2*(9+3))=2

To be more precise most people wouldn't write it in one line but more like a proper fraction.

I didn't even read your post until after reading this post...

The problem with the statement you quoted is that it's taken off this site:
http://www.purplemath.com/modules/orderops2.htm

That site tells you to use a calculator to verify this problem...ahem...we'v e established that different calculators present different results for this problem.

You're right in this post, but I think that's just because people have to explicitly define exactly what they're asking to get a correct answer. If someone would ask something like that on a test or genuinely (i.e. They also don't know that it's ambiguous), most people would ask about the implied brackets.

2 or 288 = 1
48÷2(9+3) =/= 1

Thread fail.

Originally Posted by Mahratta

What exactly do you mean by "normal"? That seems to be more of an aesthetic question - namely, 'what sort of number system is the canonical one?', and I don't really think it stems from an ambiguity in the same manner as this one does. There is, it seems, an 'incurable' sort of ambiguity to it, though. I always justified it by considering the reals as a sort of 'canonical' numeric form, drawing the analogue between the continuum and time (or something similarly irrational, haha).
This problem, on the other hand, stems from the fact that the string may not be well-formed. I mean, the very fact that people are arguing over its interpretation kind of points out that this is the case.

So I don't quite see how the questions are similar, unless one stretches the idea of well-formedness rather far (I think, absurdly far) back.

Hmm yeah I said the question can be compared, because there is some ambiguity to it. But you're right, there is definitely better examples.

BEDMAS - Brackets, Exponents, Division, Multiplication, Addition, Subtraction

48/2(9+3)

1) You do brackets 48/2(9+3)
2) You then get 48/2(12)
3) So at the moment, we have to do both division and multiplication
4) According to BEDMAS, we would do division first, and get 24(12)
5) Then you do multiplication last abd that leads to 288!

The only way you get 2, is if you did multiplication in step 4, and got 48/24, then did division last. however its BEDMAS and not BEMDAS.

..................... ..................... ..................... ...........

Sorry guys, the distributive property takes the cake here.

a(b+c) = ab + ac

Hence:

48/2(9+3)
= 48/29 + 48/23
=
...
3.7421289355322338830 584707646177?!?!

ZOMG IT EQUALS PI!

Seriously though, it's not a well-formed-formula (WFF). (http://en.wikipedia.org/wiki/Well-formed_formula)

Mathematically it makes about as much sense as (pineapple)$$*cucumbe r*.

Now everyone can look at this bizarre string and infer meaning from it: If you interpret pineapple to be 48/2, and cucumber to be (9+3) and $$ to be *, you get 288. If you interpret the pineapple to be 48, cucumber to be 2(9+3) and $$ to be / then we get 2.

...

IF.
But this is why we have formal arithmetic in the first place.

Originally Posted by Mowicz

Sorry guys, the distributive property takes the cake here.

a(b+c) = ab + ac

Hence:

48/2(9+3)
= 48/29 + 48/23
=
...
3.7421289355322338830 584707646177?!?!

ZOMG IT EQUALS PI!

Seriously though, it's not a well-formed-formula (WFF). (http://en.wikipedia.org/wiki/Well-formed_formula)

Mathematically it makes about as much sense as (pineapple)$$*cucumbe r*.

Now everyone can look at this bizarre string and infer meaning from it: If you interpret pineapple to be 48/2, and cucumber to be (9+3) and $$ to be *, you get 288. If you interpret the pineapple to be 48, cucumber to be 2(9+3) and $$ to be / then we get 2.

...

IF.
But this is why we have formal arithmetic in the first place.

First of all that was not pi, that was some random number. second of all, you're making no sense there is no need to get complicated this is simple bedmas. you can start off:

48 [SIZE=2px]÷ 2(9+3) - brackets, addition
= 48 [/size][SIZE=2px]÷ 2(12) - division
= 24(12) - multiplication
= 288

or you can do it a second way to eliminate the need for bedmas and simple multiply the entire time by converting [/size][SIZE=2px]÷ 2 into * 1/2 because division is simply inverse of multiplication, so:

48 * 1/2(9+3)
= 48 * 1/2(12) - brackets, addition
= 48 * 6 or 24(12) - see in both ways of solving this simple elementary school math equation, you're last step is equivalent in both cases, therefore:
= 288
[/size]
this is so simple, i did not even need to convert everything into multiplication, simple BEDMAS would of worked as i stated in method one. tsk tsk, university students not understanding simple arithmetic. SMH

Btw, the reason why the calculators had different answers is because of the way it interprets the division sign which they use / on those TI calculators the way you enter fractions is by using division sign. similar to how we type fractions on computer

e.g. one-quarter is 1/4, so the calc is reading this as 1 over 4, which in this case would be 1 divided by 4 which the TI calc would give you 0.25.

now back to the equation in order to enter 48 [SIZE=2px]÷ 2(9+3), we would input 48/2(9+3), and im pretty sure the calculator is reading that as 48 all over 2(9+3)

so:

48
2(9+3)

which indeed is equivalent to 2, because that ends up becoming 48/24. that is not bedmas however, that is fractions. the equation we actually want to solve isn't suppose to be read as a fraction, it is simply 48 [/size][SIZE=2px]÷ 2(9+3) which should be done using bedmas. the correct way to enter into the TI calculator to avoid this error is to type (48/2)(9+3) because we want division first, so 48 divided by 2, then multiply it with what 9+3 equals to. so it becomes (24)(12).[/size]

mat9, either you haven't read the entire thread or you're just a troll

Multiplication and Division are interchangeable in BEDMAS, just like Addition and Subtraction. I'm sure you've come across this situation before, even in elementary school.

Edit: Nevermind, you're in commerce.

Originally Posted by Mowicz

Sorry guys, the distributive property takes the cake here.

a(b+c) = ab + ac

Hence:

48/2(9+3)
= 48/29 + 48/23
=
...
3.7421289355322338830 584707646177?!?!

ZOMG IT EQUALS PI!

EGADS! PI IT IS!

First of all that was not pi, that was some random number. second of all, you're making no sense there is no need to get complicated this is simple bedmas. you can start off:

"simple" BEDMAS...yes, the rule may be simple, but it's actually a distillation of quite a bit of structural information. As I said earlier, it's a way of checking that your strings are well-formed. This one clearly isn't, hence the debate over BEDMAS - of course, the only real chance for ambiguity is when the division-multiplication order is considered, and that's precisely what happens here.

As Mowicz said, this string only makes sense if you interpret portions of the string outside of the formal system - thus this string couldn't conceivably have been formed formally (i.e. as a deduction of formal arithmetic), or is not well-formed.

Originally Posted by Silver

I asked the teacher at Kumon and he said the answer was two. He said that the 2(9+3) is actually one term and that it must be done first so yea the answer is 2.

You applied argumentum ad verecundiam there, eh? "My Kumon teacher says <X>, so <X> is true!"
Could you ask him about the Riemann hypothesis, by any chance? We really wanted a machine to churn out truth and falsity (for the interested: http://en.wikipedia.org/wiki/Entscheidungsproblem) , but Turing turned us down. It seems to me like you've got what the mathematical community has been dreaming of!