6÷2(1+2)=?

Keen2win

This is a pretty big question on facebook at the mo... What's the answer? I say 1.

(The option is 1 or 9)

---

It was asked by this fella
http://www.facebook.com/home.php#!/m...s?sk=questions

Just click "asked" at the top right and you should see it.

mikhail

It's 1. BOMDAS says you do the bit in brackets first (leaving 6/2.3), then the multiplication (6/6) and finally the division gives 1. To get nine, you have to do the division before the multiplication, which is wrong.

Ciano35

It's 1, because of bomdas as said above.

RoundTower

if it is 1, it definitely isn't for that reason

was this moved to this forum?

William Powell

It has to be ONE.

If you were to write it out differently something like this

6

---

= ?
2(1+2)

then it becomes more obvious that the

---

bit is like a brackets in itself so you do everything underneath it first and the division last.

OK not a great explaination but the best I can manage.

muboop1

The answer is 9...

BOMDAS is a rough held rule,

It kinda works in groupings almost.

(B)(O)(MD)(AS)

Multiplication and division are more of a pair. You solve which ever if first.

Actually, found it here: http://en.wikipedia.org/wiki/Order_of_operations

Mnemonics are often used to help students remember the rules, but the rules taught by the use of acronyms can be misleading. In Canada the acronym BEDMAS is common. It stands for Brackets, Exponents, Division, Multiplication, Addition, Subtraction. In other English speaking countries, Brackets may be called Parentheses, 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 BIMDAS, BODMAS, BOMDAS, BERDMAS, PERDMAS, PEMDAS, PEDMAS and BPODMAS.

folan

jblack wrote: »

6/2(3/1) = 18/2 = 9

what you have done is (6/2)(1+2), not 6/2(1+2)

It's 1

Chefburns

No doubt about it, its 1.

jblack

see it now..

Bemdas

Brackets
Exponents
Multiplication
Division
Addition
Subtraction

So it's 1+2 =3

Next is the multiplication of 2(3)= 6

Finally division 6/6=1

Shane732

Is there a link to the question??

I'd like to laugh at people!!

Screaminmidget

muboop1 wrote: »

The answer is 9...

BOMDAS is a rough held rule,

It kinda works in groupings almost.

(B)(O)(MD)(AS)

Multiplication and division are more of a pair. You solve which ever if first. Same with addition and subtraction.

You're wrong. Its 1.

mikhail

muboop1 wrote: »

The answer is 9...

BOMDAS is a rough held rule,

It kinda works in groupings almost.

(B)(O)(MD)(AS)

Multiplication and division are more of a pair. You solve which ever if first. Same with addition and subtraction.

I see what you mean, but I don't agree that you first solve whichever appears first. That works fine for addition and subtraction because the answer is the same any way you like.

In light of what you've said above, I'd like to change my answer to "Kick whoever set the question in the balls."

muboop1

I edited my original answer... please look...proof is there!

Ill accept your apologies after...

muboop1

Guys think about it... We all agree that brackets come first..

So, sum is effectively 6/2*3 yeh??

well...

that could similarily be written (6/2)*3 or

6*3
2 1

seamus

mikhail wrote: »

I see what you mean, but I don't agree that you first solve whichever appears first. That works fine for addition and subtraction because the answer is the same any way you like.

Actually it would appear that this is the case, learn something new every day.

Rule of thumb is to convert everything to the same operator to avoid confusion.

So the above becomes 6 * ½ * (2 + 1)

Which is a whole lot clearer.

Shane732

48÷2(9+3)=

muboop1

Shane732 wrote: »

48÷2(9+3)=

288...

What sort of game is this?? Your calculator can do it for u! :P

28064212

mikhail wrote: »

It's 1. BOMDAS says you do the bit in brackets first (leaving 6/2.3), then the multiplication (6/6) and finally the division gives 1. To get nine, you have to do the division before the multiplication, which is wrong.

Multiplication does not come before division. Multiplication and division have exactly equal precedence.

The problem can be rewritten: 1+2 can be replaced by 3, since that will always be done first, so we have 6 ÷ 2 * 3. Because division and multiplication have the same preference, we have to look at operator associativity. Both are left-associative, meaning they're grouped from the left, so it's (6 ÷ 2) * 3, not 6 ÷ (2 * 3). The answer is most definitely 9.

And to anyone who still thinks the answer is 1 after that: What's 6 - 2 + 3? Should it be 6 - (2 + 3) = 1 or (6 - 2) + 3 = 7?

William Powell

Oh dear someone is missing the point of the brackets :rolleyes:

Shane732

It's poor notation.

The standard is that multiplication and division have same precedence, and are done left to right.

A lack of parentheses.

(6/2)(1+2) =

Shane732

muboop1 wrote: »

288...

What sort of game is this?? Your calculator can do it for u! :P

You'd be amazed at the amount of people who say 2 is the answer to 48÷2(9+3)

stephendevlin

Where's Einstein when ya need him ....

testicle

http://www.google.ie/search?hl=en&source=hp&biw=1280&bih=673&q=6%C3%B72(1%2B2)&aq=f&aqi=g-z1&aql=&oq=&cad=h

28064212

seamus wrote: »

Actually it would appear that this is the case, learn something new every day.

Rule of thumb is to convert everything to the same operator to avoid confusion.

So the above becomes 6 * ½ * (2 + 1)

Which is a whole lot clearer.

Changing it to the same operator doesn't really clear it up. Is it 6 * ½ * (2 + 1) or should it be 6 * 1/(2 * (2 + 1))? You don't know whether you should get the reciprocal of 2 or the reciprocal of 2 * (2 + 1)

William Powell wrote: »

Oh dear someone is missing the point of the brackets :rolleyes:

Is that aimed at me? The rules of precedence and associativity are there so that brackets aren't needed all over the place. Precedence isn't enough to separate the OP's question, so you have to look at the associativity rules

stephendevlin

6/2(1+2)=3(1+2)=9

William Powell

28064212 wrote: »

Changing it to the same operator doesn't really clear it up. Is it 6 * ½ * (2 + 1) or should it be 6 * 1/(2 * (2 + 1))? You don't know whether you should get the reciprocal of 2 or the reciprocal of 2 * (2 + 1)


Is that aimed at me? The rules of precedence and associativity are there so that brackets aren't needed all over the place. Precedence isn't enough to separate the OP's question, so you have to look at the associativity rules

So you are saying 6÷2(1+2)=? is the same as 6÷2x(1+2)=?

thats why :rolleyes:

Chemistry Ftw

Shane732 wrote: »

You'd be amazed at the amount of people who say 2 is the answer to 48÷2(9+3)

The answer IS 2!!! :P

EL_Loco

I whacked this into excel:

=6/2*(1+2)

it says 9.

personally I was thinking 1, because the 2(2+1) parts looks "unresolved" or something, as in, you should get it to it's conclusion first. then do the division.

My world is rocked. I need to lie down.

28064212

William Powell wrote: »

So you are saying 6÷2(1+2)=? is the same as 6÷2x(1+2)=?

thats why :rolleyes:

What? That's not something I've specifically stated, it's something universally understood. What on earth do you think it means? What do you think is the difference between 2(1+2) and 2x(1+2)?

Chemistry Ftw wrote: »

The answer IS 2!!! :P

It's really not. Multiplication and division have the same precedence and are both left-associative, that means you read it from the left

Chemistry Ftw

Type it on a calculator the exact way it is presented, calculators always multiply before division... so I would go with that :P

seamus

28064212 wrote: »

Changing it to the same operator doesn't really clear it up. Is it 6 * ½ * (2 + 1) or should it be 6 * 1/(2 * (2 + 1))? You don't know whether you should get the reciprocal of 2 or the reciprocal of 2 * (2 + 1)

Of course you do. As said, you work from the left. In your second example there, you've added a parentheses to the equation, which fundamentally changes it. I didn't add or remove anything from the equation, it remains unchanged.

EL_Loco

if you use it like a fraction it makes it a bit easier (in my mind anyway)

something like

6/2(2+1)

3(3)

9

I'll jump out here, I'm off to hand back my degree. :S

28064212

Chemistry Ftw wrote: »

Type it on a calculator the exact way it is presented, calculators always multiply before division... so I would go with that :P

They really don't. And if yours does, you should replace it with one that follows the rules of mathematics.
6 ÷ 2 * 3 = 9
6 * 2 ÷ 3 = 4

seamus wrote: »

Of course you do. As said, you work from the left. In your second example there, you've added a parentheses to the equation, which fundamentally changes it. I didn't add or remove anything from the equation, it remains unchanged.

6 ÷ 2 * 3 (I'm replacing 1+2 with 3 for clarity's sake)

Without using the associativity rules, you don't know whether the division is 6 ÷ 2 or 6 ÷ (2 * 3). You can't get the reciprocal until you know what the divisor is. You've just selected 2 by working from the left, which already clears it up: (6 ÷ 2) * 3. Converting it to the same operator doesn't give any more clarity

Screaminmidget

Lookit, do the brackets first:
6/ 2x1 + 2x2
2 + 4
6
Therefore. 6/6 = 1
QED

Chemistry Ftw

28064212 wrote: »

They really don't. And if yours does, you should replace it with one that follows the rules of mathematics.
6 ÷ 2 * 3 = 9
6 * 2 ÷ 3 = 4


6 ÷ 2 * 3 (I'm replacing 1+2 with 3 for clarity's sake)

Without using the associativity rules, you don't know whether the division is 6 ÷ 2 or 6 ÷ (2 * 3). You can't get the reciprocal until you know what the divisor is. You've just selected 2 by working from the left, which already clears it up: (6 ÷ 2) * 3. Converting it to the same operator doesn't give any more clarity

Your changing it now... if you type 6÷2(1+2) you will get one! try it. If you type 6÷2x3 you will get 9.

nickcave

It my work (MSc Applied Maths) I never use the ÷ symbol, nor do i find that anybody does. We also never use BOMDAS or BODMAS or any rule like that.

That said, we all know that the reason there's confusion over whether multiplication come before division or vice versa is that division by a term is simply multiplication by it's inverse. This is always the way division is dealt with in professional maths.

So,

6 ÷ 2(1 + 2) =

6 x 2(1 + 2)^-1 =

6^-1 x 2(1 + 2) =

(1/6) x 2 x (1 + 2)

And what is the answer now? Since multiplication is associative, it doesn't matter what the order is.






(Hint: It's 1)

Chemistry Ftw

nickcave wrote: »

It my work (MSc Applied Maths) I never use the ÷ symbol, nor do i find that anybody does. We also never use BOMDAS or BODMAS or any rule like that.

That said, we all know that the reason there's confusion over whether multiplication come before division or vice versa is that division by a term is simply multiplication by it's inverse. This is always the way division is dealt with in professional maths.

So,

6 ÷ 2(1 + 2) =

6 x 2(1 + 2)^-1 =

6^-1 x 2(1 + 2) =

(1/6) x 2 x (1 + 2)

And what is the answer now? Since multiplication is commutative, it doesn't matter what the order is.






(Hint: It's 1)

What he said...

28064212

Chemistry Ftw wrote: »

Your changing it now... if you type 6÷2(1+2) you will get one! try it. If you type 6÷2x3 you will get 9.

The google calculator already supplied above disagrees with you

nickcave wrote: »

It my work (MSc Applied Maths) I never use the ÷ symbol, nor do i find that anybody does. We also never use BOMDAS or BODMAS or any rule like that.

That said, we all know that the reason there's confusion over whether multiplication come before division or vice versa is that division by a term is simply multiplication by it's inverse. This is always the way division is dealt with in professional maths.

So,

6 ÷ 2(1 + 2) =

6 x 2(1 + 2)^-1 =

6^-1 x 2(1 + 2) =

(1/6) x 2 x (1 + 2)

And what is the answer now? Since multiplication is commutative, it doesn't matter what the order is.[/SIZE]

Oh-oh, argument from authority. Why are you grouping 2(1+2) together to get the inverse? Do you agree that 2(1+2) is shorthand for 2 * (1+2) and they are exactly equivalent?

HeisenbergBB

It's 27.4

Can't believe this is even debatable

JustAddWater

It's pi

Mmmmmm pie ...

Screaminmidget

Chemistry Ftw wrote: »

Your changing it now... if you type 6÷2(1+2) you will get one! try it. If you type 6÷2x3 you will get 9.

they're different equations altogether...

seamus

Deleted User wrote: »

Can't believe this is even debatable

You come up against some curiosities borne out of incorrect, incompetent or misunderstood teachers in the Irish system.

I posed a question before about rounding. As in, round the below number to the nearest two decimal places:

1.564987

In my experience, roughly half of (Irish) people will give the incorrect answer of 1.57. Foreign people don't seem to have this issue.

muboop1

Chemistry Ftw wrote: »

Your changing it now... if you type 6÷2(1+2) you will get one! try it. If you type 6÷2x3 you will get 9.

No you dont...

Guys, please check this link/ quote.... link: http://en.wikipedia.org/wiki/Order_of_operations

Quote state that "Powers or Orders, and since multiplication and division are of equal precedence, M and D are often interchanged, leading to such acronyms as BIMDAS, BODMAS, BOMDAS, BERDMAS, PERDMAS, PEMDAS, PEDMAS and BPODMAS."

You do not differentiate between the two... Guys, this is basic sh1t here... think about it!

Opinicus

Shane732 wrote: »

48÷2(9+3)=

miscers unite!


"PEMDAS"
"Who?"

https://www.youtube.com/watch?v=SB3Ekgt1pHw

Yahew

I see

6÷2(1+2)

as

6÷2 * (1+2)

google sees this as equivalent to

(6 ÷2 ) * (1 + 2)

due to, as the man said, associativity. Thats certainly how I would see it in my head.

9

By removing the * for multiplication the eye is drawn to the parenthesis, but thats to read it wrong.

muboop1

nickcave wrote: »

It my work (MSc Applied Maths) I never use the ÷ symbol, nor do i find that anybody does. We also never use BOMDAS or BODMAS or any rule like that.

That said, we all know that the reason there's confusion over whether multiplication come before division or vice versa is that division by a term is simply multiplication by it's inverse. This is always the way division is dealt with in professional maths.

So,

6 ÷ 2(1 + 2) =

6 x 2(1 + 2)^-1 =

6^-1 x 2(1 + 2) =

(1/6) x 2 x (1 + 2)

And what is the answer now? Since multiplication is associative, it doesn't matter what the order is.






(Hint: It's 1)

No.

nickcave

28064212 wrote: »

Why are you grouping 2(1+2) together to get the inverse? Do you agree that 2(1+2) is shorthand for 2 * (1+2) and they are exactly equivalent?

Are you suggesting I take the inverse of 2 alone and get 6 x (1/2) x (1+2) = 9?

Or that I take the inverse of (1+2) alone and get 6 x 2 x (1/3) = 4?

(*tears up thesis*)

No, trust me, if you write A ÷ BCDEFG, you mean A divided by everything to the right of it unless there is delimitation with brackets e.g. (A ÷ BCD)EFG

There are no brackets delimiting the ÷ operation.

The OP's question is slightly ambiguous, but not really. In my writing and certainly in programming in (MATLAB etc.) we delimit everything to avoid ambiguity and for debugging etc.. Even still, the answer is definitely definitely 1.

Didn't know that Ronnie Drew knew Math