# stupid maths problem

## 6÷2(1+2)= ?

• ### 9

• Total voters
1

#### palmerq

6÷2(1+2)= ?

is it 1 or 9, I see this argument on many places, did we have it here yet?

anyway in my mind it is 1

#### Bag_O_Wallet

BEDMAS says 9 too.

#### krebs303

Order of Operations (PEMDAS,BEMDAS)says 9

I say it's 1.

#### Hugh Januss

9
Operations in brackets are done first after that it just goes from left to right.
6 divided by 2= 3 X 3 = 9

#### Libertine Seguros

Hugh Januss said:
9
Operations in brackets are done first after that it just goes from left to right.
6 divided by 2= 3 X 3 = 9
But if the operations in brackets are done first that gives us 6 / 2(3), and any way you spin it, 2(3) = 6. You don't just do the operation that is in the brackets - 2(1+2) is the operation, which = 6.

If it was to be 9, you'd need it to be (6/2)(1+2), or 6/2∙(1+2) in order to specify that the 6/2 is its own operation, rather than 6 being a modifier of the 2(1+2) operation.

Excel doesn't let me enter =6/2(1+2) as a formula, and autocorrects it to 6/2*(1+2), i.e. 3*3.

However, 6/2 x (1+2) is a fundamentally different operation to 6 / 2(1+2), which is how I read the equation.

In reality, it's a vague equation that allows two readings which are both correct from accepted mathematical methods. In order to properly parse it we would need more parentheses:

(6/2)(1+2) = 9
6/(2(1+2)) = 1
6/2(1+2) = 1 OR 9 depending on which system you grew up with.

#### The Hitch

I think this could be a country or even continent thing. My mind automatically goes to multiply the brackets by the number next to it. not the whole equation. The British school system has trained me to do this.

If the brackets were to be multiplied by the whole equation it would be (6/2)(1+2)

I heard once it might vary in different countries.

#### Cobblestones

You do the operation in the brackets so you get 6/2(3) at which point the bracket is obsolete (goes away). Then you do the operations from left to right, i.e. 6/2*3=3*3=9.

Actually it would be better to pose the problem either as a fraction or with one additional set of parentheses. Usually chains like 6/2*3 are discouraged precisely because they can be interpreted wrongly.

#### Mambo95

Libertine Seguros said:
But if the operations in brackets are done first that gives us 6 / 2(3), and any way you spin it, 2(3) = 6. You don't just do the operation that is in the brackets - 2(1+2) is the operation, which = 6.
That's not what an operation is. An operation is an exponent or a root.

2(3) is just a different way of writing 2 x 3.

#### Hugh Januss

OK then what is the answer to this equation?
6/2 X 3 = ?
because that is what the other equation becomes the moment you complete the portion in brackets, once that part is done, and operations in brackets are always completed on their own first, then all other operations are simply carried out in the order that they occur from left to right

#### Libertine Seguros

Mambo95 said:
That's not what an operation is. An operation is an exponent or a root.

2(3) is just a different way of writing 2 x 3.

But it isn't.

That's what the whole crux of the problem is. It is ambiguous, and both readings are correct under different systems. One system says it's 9, one system says it's 1. The one I've been taught says it's 1, the one you've been taught says it's 9. Neither are wrong.

As I posted, and Cobblestones pointed out, it's an inherently flawed equation because of the ambiguity and would be better solved by an additional parentheses indicating which format it should use.

To you, the operation is (6/2) (1+2) i.e. 3 x 3 = 9
To me, the operation is 6 / (2(1+2)) as "2(1+2)" is one item. i.e. 6 / 6 = 1.

Neither you nor I are wrong.

#### Libertine Seguros

Hugh Januss said:
OK then what is the answer to this equation?
6/2 X 3 = ?
because that is what the other equation becomes the moment you complete the portion in brackets, once that part is done, and operations in brackets are always completed on their own first, then all other operations are simply carried out in the order that they occur from left to right
6/2x3 = 9.

But as the system I learnt (and evidently Hitch learnt too) indicates that 2(1+2) is a single item, therefore we are arguing between (6/2)x3 and 6/(2x3).

It's like the whole collective noun thing.

Both of us are correct, and have logic and reason on our side.

#### Captain_Cavman

Libertine Seguros said:
But it isn't.

That's what the whole crux of the problem is. It is ambiguous, and both readings are correct under different systems. One system says it's 9, one system says it's 1. The one I've been taught says it's 1, the one you've been taught says it's 9. Neither are wrong.

As I posted, and Cobblestones pointed out, it's an inherently flawed equation because of the ambiguity and would be better solved by an additional parentheses indicating which format it should use.

To you, the operation is (6/2) (1+2) i.e. 3 x 3 = 9
To me, the operation is 6 / (2(1+2)) as "2(1+2)" is one item. i.e. 6 / 6 = 1.

Neither you nor I are wrong.
No, you're right. they're wrong.

6÷2a where a = (1+2) is 1.

As you said, the denominator is 2 whatever comes after it, in this case a bracket which simplifies to 3, so 2 3s which is 6.

#### palmerq

Cobblestones said:
Actually it would be better to pose the problem either as a fraction or with one additional set of parentheses. Usually chains like 6/2*3 are discouraged precisely because they can be interpreted wrongly.
If you do that then the problem has gone away though and there is no fun... well if this is fun :S

#### cyclingrookie

Didn't doubt for a second that it is 1, but I dont know whats being teached in other countries.
Im studying mathematics in Norway and I think we are using the same books as most USA and UK universities do.

2(1+2)=2x1+2x2

#### Sparta

The answers 9. You work from left to right as if you were reading a book.

#### Mambo95

Libertine Seguros said:
But it isn't.

That's what the whole crux of the problem is. It is ambiguous, and both readings are correct under different systems.
The system I use is the BODMAS system.

B = Brackets - simplify what's inside the brackets* - which gives us 6 / 2 x 3
O = Operations - there's nothing here that I understand as an operation, as previously stated
DM = Divide and multiply - these should have equal weight (a common oversight) and done left to right - which gives 9

I dare say there may be other systems - but I don't know them myself.

*(this is probably where any difference comes)

#### Libertine Seguros

Sparta said:
The answers 9. You work from left to right as if you were reading a book.
If you were writing it in a book you'd do it as either

6
_ (1+2) = 9

2

or

6
______ = 1

2 (1+2)

and then save us all the trouble.

If, as Captain Cavman points out, it was expressed algebraically as 6/2a where a is (1+2) (therefore 3), your first reading would be that it is 6 / (2x3) and therefore the answer is 1. This is the system that I learnt. You may have learnt the other system, and the logic behind the answer 9 is persuasive.

Basically, it's a poorly written equation that invites argument by being unclear. And that's the whole point of it.

#### Hugh Januss

Libertine Seguros said:
If you were writing it in a book you'd do it as either

6
_ (1+2) = 9

2

or

6
______ = 1

2 (1+2)

and then save us all the trouble.

If, as Captain Cavman points out, it was expressed algebraically as 6/2a where a is (1+2) (therefore 3), your first reading would be that it is 6 / (2x3) and therefore the answer is 1. This is the system that I learnt. You may have learnt the other system, and the logic behind the answer 9 is persuasive.

Basically, it's a poorly written equation that invites argument by being unclear. And that's the whole point of it.
I think that last may well be the correct answer in which case it's hardly even fun anymore.

#### The Hitch

The more I look at the equation the more I am convinced the answer is 1.

2 points

1 If you wanted to write the other equation (the one to which the answer is 9) using brackets, there are otherways to do it.

You could write 6/2x(1+2) or (6/2)(1+2). Both present the idea that the number in brackets is mutliplied by the whole equation.

But if you want to write the equation to which the answer is 1 in brackets, this is the only way to do it 6/2(1+2).

2 I think it defeats the point of using brackets if it is just meant to be used as a multiplication sign against the whole equation. The whole point is that it can be used to convay the idea that a equation is to be multiplied only by one particular number in the equation?

How else are you going to present the idea that you want the 1+2 only multiplied by the 2.

#### Libertine Seguros

Use the algebraic substitute.

6/2a

In your opinion does 6/2a = 6a/2?

If so, it's 9.

6/2a = (6/2)a
a = 1+2
a = 3
6/2 = 3
(6/2)a = 3x3 = 9

If not, it's 1.

6/2a
a = 1+2
a = 3
2a = 6
6/2a = 6/6 = 1

#### Sparta

na libertine my favourite person to disagree with its definitely 9 no doubt. Just like Gilbert is the best rider in the peleton.

6/2a is 3a that's not debatable really the (2a) needs to be in brackets for it to be any different.

#### Sparta

you would have to write it 6
then it would be like you say -------
2a