6/2(1+2)= SOLVED. WITH PROOF!! (Watch until end)

How to solve for 6/2(1+2)= with explanation.
I am Asian.

[Spuffiy]

"It's 1!"
"No, it's 9!"

Me who got 1.5: _confused confusion_

[ryburnsjr]

Its 42. The ultimate answer to everything..

[PaulJosephdeWerk]

PEMDAS works great for 5th graders. Higher learning adds more rules. Following PEMDAS, 3^3^3 should be evaluated as (3^3)^3 => 19683 [left to right], while the usual rule is 3^(3^3) => 7.6255975*10^12 [right to left]. Same goes for unary minus: -3^2, it should evaluate as -(3^2) => -9, while some systems have the unary minus as a higher priority to exponent, giving (-3)^2 => 9. College level courses tend to put implied multiplication at a higher precedence to explicit multiplication, giving 6/2(1+2) => 1 and 6/2*(1+2) => 9

[scottwipf]

finally, somebody that does this problem right, in a way too complicated way, but at least he got it right.

[Ghiaccio.]

You see, this question is a big problem because of how ambiguous it is. No mathematician would write this because of how messy it is, two different problems can come from 6/2(1+2). It could be 6/(2(1+2) or (6/2)(1+2) depending on who looks at it. Do to poor structure, this question has two answers. I hope this makes sense, no one is wrong.

[winterknight]

This problem comes about because people are lazy and also they want to fit it in one line of text and use the / rather than the ÷ which is not available directly on the keyboard. (to get ÷ it is ALT plus 0247) Confusion can also be included when same people use · instead of * for multiplication. They also don't consider juxtaposition. The dot (·) is for use in Π = 3·14159...

So if the problem is to be calculated using PEMDAS (or BODMAS or any other suitable acronym) it should be be written as 6 ÷ 2 * (1 + 2) to equal 9, until then I will take the engineers way and say the answer is 1.

[the-dave-house-project]

Kinda wish everyone could agree on this. It concerns me that everyone is so wrapped up in PEMDAS (or whatever version you prefer), that they forget the Law of Distribution, which IS the only way to remove the parenthesis. Adding (1+2) gives (3)... it does NOT remove the parenthesis. To do that in this equation you MUST multiply by the associated factor (the 2, in this case). Simply put... the equation is 6/2(3), NOT 6/2x3... and, because of that, it is 100% mandatory to multiply the 2(3) before dividing. I expect someone is going to tell me that the 'x' is implied when you use parenthesis like this. That's correct, but it doesn't change the fact that they still exist and must be dealt with first. That's the ONLY reason they exist. The answer IS 1. Most modern calculators (and modern mathematicians) ARE wrong. Consequently, this is junior-high level math at best. It shouldn't be an argument.

[LokiScarletWasHere]

To those of you getting 9, I'd hate to see how you handle sin(), cos(), and tan().
Oh and don't get me started on adjacent variables or constants.
Y'all are gonna get soooo lost.

[GanonTEK]

It's just ambiguous notation.
Academically, multiplication by juxtaposition implies grouping but the programming interpretation does not.

Wolfram Alpha's Solidus article mentions the a/bc ambiguity and modern international standards like ISO-80000-1 mention about division on one line with multiplication or division directly after and that brackets are required to remove ambiguity.

Even over in America where the programming interpretation is more popular, the American Mathematical Society stated it was ambiguous notation too.

Multiple professors and mathematicians have said so also like:

Dr. Trevor Bazett, Dr. Jared Antrobus, Prof. Keith Devlin, Prof. Anita O'Mellan (an award winning mathematics professor no less), Prof. Jordan Ellenberg, David Darling, Matt Parker, David Linkletter etc.

Even scientific calculators don't agree on one interpretation or the other.

Calculator manufacturers like CASIO have said they took expertise from the educational community in choosing how to implement multiplication by juxtaposition and mostly use the academic interpretation. Just like Sharp does. TI who said implicit multiplication has higher priority to allow users to enter expressions in the same manner as they would be written (TI knowledge base 11773) so also used the academic interpretation. TI later changed to the programming interpretation but when I asked them were unable to find the reason why.

It's just a really poorly written expression written like that on purpose to be misleading and go viral. It's a trick.

[franksnyder]

Your approach is consistent with fundamental Field Axioms which are the basis of Algebra. Two thumbs up for explaining it using Field Axiom #9 (Identity Axiom) and #7 (Distributive Axiom).

[knightd]

I think the confusion is some people view it as 6 over 2 times (1+2) resulting in 9 and others view it as 6 over 2(1+2) resulting in 1

[sienius]

By mathematics, no matter what approach you are using, you should have always the same answer. So lets try that. Lets say instead of 2(1+2) we rewrite it as sum of two brackets so we have equation as :
6÷((1+2)+(1+2))
6÷(3+3)
6÷6=1
Oh i know. You will say that i shouldn't use brackets with the sum of brackets. Lets assume i shouldn't
Then we will get this equation :
6÷(1+2)+(1+2)
And by your order of operation rules we get
6÷(3)+(3) and as you say that division comes first then we get
2+3=5 completely different answer, how ?
you could use it other way
you could rewrite 2(1+2) as in the video : 2*1 + 2*2
then:
6÷(2*1+2*2)
6÷(2+4)
6÷6=1
and you will still say again that HEY you shouldn't use brackets even when multiplying it . Well ok, what we have there then
6÷2*1+2*2
6÷2+4
and by order of operation
3+4=7
again completely different answer. How so! What kind of sorcery is this right ?
Don't always depend on one rule. Always look deeper and you will find right answer through logic. That's why i like mathematics. Even when sometimes it can get confusing like in this poorly written equation, you can still find logical one answer.
Other argument i can give is
when you see the equation
6/2y, you think about (6/2)×y or
6/(2*y). In math, it is always used as the 6/(2×y) as then you can simplify it as 3y. I think the ones who don't know the answer to these similar equations, are just not experienced with math enough, and just try to solve it with basic rules, when more experienced people tend to see different solutions to the same problem and then find the correct answer. If you always will use just that simple logic as order of operators, you will usually answer those online poorly written equations wrong. I have seen a lot of similar equations like these, and people always tend to answer wrong and are 100% certain they are right when in fact they are very very wrong. Always try to rewrite your equation different ways and test if you have the same answer by your rules. If not, then you are probably doing something wrong.

Btw i say the answer is 1. Its just explanation for those who don't get it and can only use what they have learned in primary school. You always use logic. You can a lot of times rewrite your equation into more basic equation. You can rewrite power to multiplication, multiplication to addition and so on if you are confused.

[gbhxu]

Finally found someone that gives the correct answer as being 1 (one) rather than the BS answer of 9 (nine)

[abubaker]

6=2×3=9 according to yours point of view.But
as we know that in multiplication commutative property holds.
Then:
6÷2×3=6÷3×2=4
So, I am not satisfy on PAMDAS
Hence, according to BODMAS 1 is the correct answer.

[RealMesaMike]

PEMDAS is not "order of operations." It is precedence of operations.
You don't necessarily have to do what's in parentheses first. Do what you want to do first, just don't break precedence. There is no "left-to-right" rule. You can go right to left, start in the middle and work outwards, or however you want, as long as you understand that a subtraction is actually an addition of a negative, and that a division is a multiplication by a reciprocal.

PEMDAS is for 5th grade math. Once you get past 5th grade, there are more things about math expressions you need to pay attention to, such as how implied multiplications are actually treated in the real world.

Further, the example expression is crap. You would never encounter such a thing in the real world, and if you did, you'd better ask for clarification before you do something important with it.

[POlNTBLANK]

It's 9. you are not a math asian, you are a karate asian.

[howellwong]

If we all agree to follow PEMDAS, the answer is 9. If you want 1, rewrite the problem as 6/[2(1+2)].

[tkjyxrb]

You didn't elaborate on why you used the distributive property on 2 instead of 6÷2 (which is the essence of the argument)

[sharif]

Hey, I'm Asian. I'm also Asian, and I got 1 as well.

[edwardprice]

The real question is what is the power of (parentheses) in the rules of order.
I believe the 2 is bound to the ( ) and it is not up to you to change the first ( to *times after you add 1+2 So the answer is 1. Those who say it is 9 are doing this : (6÷2)(1+2) Wrong ! You are editing the problem, by inserting what you believe the writer intended.
If 1+2 is "contained" in parentheses, then the other 2 is excluded by the parentheses, until the 1+2 is solved, then the other 2 which is barred/bound by the open ( is allowed in.
Giving credit to the writer of the problem for using one set of ( ), who am I to add a second set of ( ) which the "9 people" assume they can do.