I love a 'simple' math problem that gets everyone talking. In my research of this one it turns out it has been on the go for ages but I like it all the same. 

 

The problem is what is the answer to this equation: 6 ÷ 2(1+2) = ?

 

Now the answer I get is 1. I was pretty good at maths in school and college so I'm pretty sure I'm correct and depending who you listen to online they agree. However some people (including Google, Excel etc.) say that the answer is 9. But I just cannot get my head around their logic for that at all. 

 

Discuss 

Its 9. You complete the sum inside the ( ) first = 3 then the sum thats left which also = 3. As there is no instruction to deviate from the rule, +, x etc then the two numbers are multiplied together so answer = 9

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The way I work it out is I express it as a ratio. So I say 6 / 2(1+2) = ? or in other words 6 ÷ (2(1+2)) =? in which case the answer can only be 1.

Also if you turn it into an equation in which you solve for X so...

 

X = 6 ÷ 2(1+2)   - Multiply both sides by 2(1+2)

2(1+2)X = 6       - Do the brackets

2(3)X = 6           - Do the multiplication

6X = 6                - divide by 6 to get X

X = 1

6/2 = 3 x the sum of (2+1) = 9  

I've figured it out and I know why I'm convinced it is 1, let me explain. So everyone agrees we can simply the equation first off to read 6 ÷ 2(3)= X. So lets mix it up a bit and take the solution X=1 then turn the 3 into a Y and solve for Y.

 

So if X=1

 

6 ÷ 2Y = 1

6 = 2Y

3 = Y or Y = 3

 

But then the light bulb moment came....If the equation above is written how the original sum is apparently intended it can be solved for Y with X = 9

 

6 ÷ 2 x Y = 9

6 ÷ 2 = 9 ÷ Y

3 = 9 ÷ Y

3Y = 9

Y =3 

 

So anyway now I've solved that one in my own head, any other interesting math problems driving the internet crazy?

 

There is no first process between multiplying and dividing as you've said, however once at this stage the accepted rule is to work left to right, so in this case divide first and then multiple. 

So the answer to the sum is 9.

the same is true in your solution for X, you must work out the brackets

x=6/2(3)

x=6/2x3

and then work left to right

x=3x3

x=9

This is why I hate 'simple' maths.

So many people struggle with maths because you can work it out, get an answer but may still be wrong due to method or a rule applied incorrectly.

 

This is BODMAS @kwijibo_coupe , a rule that I disagree with like many others.

 

 

After a little more research it is pretty much all down to the rules of this particular equation not being explained. Typing 6÷2(1+2) into a scientific calculator gives you an answer of 1, change it to 6÷2x(1+2) gives you an answer of 9 (deemed the correct answer), depending on which set of rules you follow in regards to notation determines which answer is correct. 

Personally typing 6÷2(1+2) into a scientific calculator is the method I'd use :)

Wrong but its 'scientific' it should know what I mean!