Poll: 6÷2(1+2)

[Pinkribbonscars]

My point is and always has been that the "solutions" arriving at 1 are wrong, because they are not following the standard order of operations.

If you want to throw that out of the window and ignore the fact that it is how expressions should be processed, then fine - you're right, it is ambiguous.

But if you do follow the standard order of operations, the solution isn't ambiguous.

It's not ambiguous if you use a rule designed to teach 15 year olds still using the division symbol, but it is ambiguous to anyone with greater education than that, who would write out the equation properly.

 

[Castiel]

Someone wake up BetaNumeric.......

If he doesn't know then no-one does.

 

[Tokenbrit]

My point is and always has been that the "solutions" arriving at 1 are wrong, because they are not following the standard order of operations.

If you want to throw that out of the window and ignore the fact that it is how expressions should be processed, then fine - you're right, it is ambiguous.

But if you aren't ignorant about the standard order of operations, the solution isn't ambiguous.

I feel your pain.

 

[[FnG]magnolia]

Here's a nice picture to calm everyone down.

OH COME ON!

 

[Jokester]

My point is and always has been that the "solutions" arriving at 1 are wrong, because they are not following the standard order of operations.

If you want to throw that out of the window and ignore the fact that it is how expressions should be processed, then fine - you're right, it is ambiguous.

But if you aren't ignorant about the standard order of operations, the solution isn't ambiguous.

Mathematically the correct answer is 1, but many calculators and programming languages will give an answer of 9 because they don't understand that the correct processing order is out of order, they just run through it sequentially.

 

[Hatter The Mad]

It's not ambiguous if you use a rule designed to teach 15 year olds still using the division symbol, but it is ambiguous to anyone with greater education than that, who would write out the equation properly.

The rule taught to 15 year olds is wrong, but 99.9% of the time it didn't matter then. But there is a right way and it has been properly defined.

http://en.wikipedia.org/wiki/Order_of_operations#The_standard_order_of_operations

 

[guyfawkes5]

Here's a nice picture to calm everyone down.

http://img.photobucket.com/albums/v303/looperark/imagesqtbnANd9GcS65r-eeM2grFLbnhRLAw8ULWzT13jcTG7OLvM-M2mOWjXD7ugt.jpg[IMG]

OH COME ON![/QUOTE]
"It ain't easy bein' white..."

:D

 

[Hatter The Mad]

Mathematically the correct answer is 1, but many calculators and programming languages will give an answer of 9 because they don't understand that the correct processing order is out of order, they just run through it sequentially.

You have it backwards. Mathematically the correct answer is 9, but many low-end calculators do not follow the standard order of operations and thus arrive at the wrong answer (you need to be explicit with brackets in these calculators).

For example:

A low-end calculator that doesn't follow the standard order of operations: http://forums.overclockers.co.uk/newreply.php?do=newreply&p=19013406

A calculator that does follow the standard order of operations: http://grab.by/grabs/17d63b16251a10fb970ff3574a776a8454747fe0f9.jpg

or

Or are you saying that the TI doesn't follow the standard order of operations?

 

[Scrutinize]

I would have leant towards the answer being 1 and on first glance that is what I said when Lucero and I were debating this last night.

He said 9 and I said 1 and much arguing ensued. How you read the equation depends on the sort of work you do / background because it is ambiguous.

 

[dowie]

I just want to post that the answer is 9, if only by convention.

Try asking anybody who does any scientific programming what 6/2*3 evaluates to and they will tell you 9.

If there was any freedom in things like this vast amounts of software would simply cease to function.

This

The question is really over the definition of '/' to represent division

There wouldn't be an issue with the question if written down on paper as the divisor is clear - however when written on a single line you need to know what '/' means. With '/' just applying to '2' the answer is of course 9.

 

[Hatter The Mad]

This

The question is really over the definition of '/' to represent division

There wouldn't be an issue with the question if written down on paper as the divisor is clear - however when written on a single line you need to know what '/' means. With '/' just applying to '2' the answer is of course 9.

Even with this division symbol, the answer is the same when you follow the standard order of operations.

Here is another explanation of why the standard order of operations renders it unambiguous:

http://en.wikibooks.org/wiki/Algebra/Order_of_Operations#The_Standard_Order_of_Operations

Solve equations in this order.
Parentheses (evaluate what's inside them)
Exponents
Multiplication and/or division from left to right
Addition and/or subtraction from left to right

6/2(1+2)

6/2(3)

(remember, left to right)

3(3)

= 9

 

[D.P.]

Mnemonics

Mnemonics are often used to help students remember the rules, but the rules taught by the use of acronyms can be misleading. In the United States the acronym PEMDAS is common. It stands for Parentheses, Exponents, Multiplication, Division, Addition, Subtraction. If PEMDAS is followed without remembering to do multiplication and division at the same time and done instead with multplication then division students will get wrong answers. For example: 6÷2(1+2)=1 not 9. In other English speaking countries, Parentheses may be called Brackets, or symbols of inclusion and Exponentiation may be called either Indices, Powers or Orders, and since multiplication and division are of equal precedence, M and D are often interchanged, leading to such acronyms as BEDMAS, BIMDAS, BODMAS, BOMDAS, BERDMAS, PERDMAS, PEMDAS, and BPODMAS.

These mnemonics may be misleading, especially if the user is not aware that multiplication and division are of equal precedence, as are addition and subtraction. Using any of the above rules in the order "addition first, subtraction afterward" would also give the wrong answer.

10 - 3 + 2

The correct answer is 9, which is best understood by thinking of the problem as the sum of positive ten, negative three, and positive two.

10 + (-3) + 2

 

[Hatter The Mad]

At least the majority of people have voted for the right answer

 

[Jokester]

You have it backwards. Mathematically the correct answer is 9, but many low-end calculators do not follow the standard order of operations and thus arrive at the wrong answer (you need to be explicit with brackets in these calculators).

For example:

A low-end calculator that doesn't follow the standard order of operations: http://forums.overclockers.co.uk/newreply.php?do=newreply&p=19013406

A calculator that does follow the standard order of operations: http://grab.by/grabs/17d63b16251a10fb970ff3574a776a8454747fe0f9.jpg

or



Or are you saying that the TI doesn't follow the standard order of operations?

Hmmm, you're right, because divide and multiply are treated with equal importance it just does the first term it comes to which is divide in this case. To get one it would have to be written:-

6/(2(1+2))

Angus would be proud.

*rips up degree*

 

[FNGsam]

Worst 6/(2*3) or (6*3)/2 thread ever.

hey, you have to choose a side, 9 is teh answer or 1 is teh answer. I choose 9 don't let the uneducated know that there are 2 answers depending on how you view parent's-esusses

 

[FoxEye]

Sorry skipped a few pages, but:

6/2 (1+2) =
6/2 + 12/2 =
18/2 =
9

Which is not how I did it in my head, but I just wanted to be different Got 9 either way tho!

 

[[FnG]magnolia]

e : guyfawkes5, hey brother

 

[Hatter The Mad]

Hmmm, you're right, because divide and multiply are treated with equal importance it just does the first term it comes to which is divide in this case. To get one it would have to be written:-

6/(2(1+2))

Angus would be proud.

*rips up degree*

Which degree do you have? I read Computer Science and spent an (unfortunate) lot of time dealing with expression parsing, which is the only reason why I have such a standard order of operations boner.

Had I not done this, I don't think I'd have been this certain.

The only argument for it is ambiguous is because some calculators (whether computer or people) are arriving at a wrong answer... which isn't ambiguity at all, it is just misunderstanding.

 

[dowie]

Even with this division symbol, the answer is the same when you follow the standard order of operations.

Here is another explanation of why the standard order of operations renders it unambiguous:

http://en.wikibooks.org/wiki/Algebra/Order_of_Operations#The_Standard_Order_of_Operations

Well yes - you're essentially arguing about the same thing - the standard order of operations in itself defines how those symbols work.

i.e. 2/6x means (2/6)x and not 2/(6x)

 

[guyfawkes5]

I think if a person leads a bad and selfish life, and still have sins on their conscience when they take their final breath, they are taken to a place between the two great divides of the afterlife where it is not quite heaven nor is it quite the other. It is nothing but waiting and confusion, and memory clouds into infinity.

Your only companion stares at you blankly, and thus begins the process of purgatory or cleansing of your evil deeds in a past life:

"I have a degree in maths, the answer can be '1' or '9'."

"I learned in school that PODMAS says it is definitely '9' and no other."

"PODMAS is not infallible my friend, it is just a useful crutch to beginners and nothing more. I think if you look at it ag..."

"I learned PODMAS in school. It says that it is '9'. You are wrong."

"Consider for a moment that PODMAS doesn't cover every mathematically situation perfectly..."

"...PODMAS said you'd say that. I will explain to you again. If you read the equation left to right..."

"Er, if I say I don't think PODMAS applies here that doesn't mean I don't know what PODMAS is, isn't that a bit arro..."

"I learned in school that PODMAS says it is definitely '9' and no other."

Continued on into forever.