6÷2(1+2)=?

[EWU2012]

Okay so this equation has been going around facebook for a couple weeks now and it has brought up a lof of debates with my friends and coworkers. The two possible answers are 1 and 9. I'm just curious as to what everyone on here thinks the answer is. On facebook almost 2.2 million people say one answer and 1.6 million say the other answer. I understand how someone can get one or the other but the way I worked it out is how I have always done the equation. So I figured I would bring the debate to EC and see what members on here answer. I figured I would wait for other to post before I say what my thought was.

[GoinStag]

Lmfao I got 6. I need to go back to school.

[malachite]

well, if I recall my math correctly when two numbers are next to each other in () it is assumed they are multiplied.
So 9 would be my guess

[GoinStag]

Wait, no. I see now. I got 9. Haha

[Victor]

Oh god. I remember seeing that a week or so ago. The debates people have are so hilarious. The answer is 9, btw. Anyone who uses PEMDAS as justification for saying it is 1 do not understand the difference between parentheses and multiplication written using parentheses and/or they don't know that M and D have equal priority. And then there are those who wrongly assume that 6/2(1+2) is the same as 6/[2(1+2)].

Using the order of operations properly will get you 9.

[Meropspusillus]

Originally Posted by Victor

Oh god. I remember seeing that a week or so ago. The debates people have are so hilarious. The answer is 9, btw. Anyone who uses PEMDAS as justification for saying it is 1 do not understand the difference between parentheses and multiplication written using parentheses and/or they don't know that M and D have equal priority. And then there are those who wrongly assume that 6/2(1+2) is the same as 6/[2(1+2)].

Using the order of operations properly will get you 9.

I was going to say the same thing, but I wasn't going to be as sassy. My hat is off to you sir.

Also: why isn't there a "Sassy" mood available. This is a site for GLBTQ people, there NEEDS to be a sassy.

[EWU2012]

My answer to the question was 1. I said that because I was always taught that when you have something like 2(1+2) you have to add the 1+2 so it is 2(3) then multiply that out to get rid of the parantheses. I also looked at it that the 6 is the numerator and the 2(1+2) is the denominator. So you figure out what the denominator is then divide them into each other which would be 6/6=1. I understand the whole order of operations and that M and D are looked at being equal but I wass still always taught that just adding the 1+2 doesn't get rid of the patantheses. Some of my friends and coworkers who are math majors say 9 while some others say 1. I even asked accountants in different offices around my University and most said 1 while a few said 9. No matter what the answer is I think it is crazy how so many people get each one. So again my answer was 1.

[Makaio1]

I got 9. You do the brackets first I believe so:
(1+2) = 3
therefore (6/2)x3 = 3x3 = 9

I might be wrong though...

[Z3ni]

I got 0?

1 + 2 = 3

3 x 2 = 6

6 / 6 = 0?

BODMAS?

---------- Post added 5th May 2011 at 06:02 PM ----------

Nvm its 9

[Hexagon]

Originally Posted by Z3ni

I got 0?

1 + 2 = 3

3 x 2 = 6

6 / 6 = 0?

BODMAS?

---------- Post added 5th May 2011 at 06:02 PM ----------

Nvm its 9

Nope. It is bodmas. 2+1 is 3. 2x3 is 6. 6/6 is 1, not zero. trust me.

[Steve]

i got 1

6:2(1+2)

6:2(3)

6:6=1

[Adam]

I say its 1

[lostinthought9]

It's totally 9.

[NickT]

Oh my God. I've seen so many people screw this up, I'm tired of being nice. If you think it's 1, go back to elementary school, because you obviously didn't learn order of operations.
1. PARENTHESIS
2. EXPONENTS
3. MULTIPLICATION/DIVISION*
4. ADDITION/SUBTRACTION*

Nick! What does the * mean? Well it's quite SIMPLE. It means that once you reach a point in an equation where there's both multiplication AND division, you go LEFT TO EFFING RIGHT.

THEREFORE

6 / 2 ( 1 + 2 ) = ?

PARENTHESIS: (1 + 2) = 3

6 / 2 (3) = ?

Now you go left to right!

6 / 2 = 3
3 * 3 = 9

It's 9! 9 9 9 9 9 9 9 9 9!

[Edit]HELL! I put this into a C++ program just for the hell of it! Guess what came out? NINE![/Edit]

[Lexington]

I first saw it as "6 / 2(1+2)". And the actual answer is "the answer cannot be determined from the information given". It isn't clear whether the division sign encompasses the amount in the parenthesis. The spacing seems to indicate that the "2(1+2)" is the denominator of the 6. In which case, the answer would be 1. But that's not entirely clear.

If the question is actually "6 ÷ 2 (1 + 2)", then the answer is clearly 9.

Lex

[Bryan90]

Originally Posted by NickT

Oh my God. I've seen so many people screw this up, I'm tired of being nice. If you think it's 1, go back to elementary school, because you obviously didn't learn order of operations.

Whoever thinks that those with the answer 1 is dumb, you need to go to college. (JOKING!)

I'm sure if you guys bother reading the debate, you would have known this already. The problem stems from the use of 'shorthand' for multiplication.

For example, the variable 5y = 5*y. Similarly, when one writes 2(1+2) = 2*(1+2). As far as my knowledge is concerned, parentheses in NO WAY implies multiplication. (Uses of Parenthesis by Wolfram Alpha: Parenthesis -- from Wolfram MathWorld). The only reason why 2(1+2) = 2*(1+2) is due to the shorthand of having 2 numbers written side by side denoting multiplication.

Now, it is sometimes commonly accepted that when the shorthand is used to denote multiplication, there is an implicit bracket surrounding it.

If you type in 3/5x on Wolfram Alpha, you get 3/(5x) instead of 3/5*X: 3/5x - Wolfram|Alpha

Which means 6/2(1+2) if written in proper form might be interpreted as: 6/(2*(1+2)) = 1

Note: MIGHT! Again, I stress that different mathematicians will have a different say on whether the implicit brackets are there when the shorthand is used.


Those who assume that all others (huge percentage on this debate) who disagree with them to be wrong and stupid without considering their reasons diligently tend to be furthest from the truth. *cough* politics *cough*

[EM68]

I got 1.

6÷2(3)

6÷6

1

[NickT]

No! No No No No No No! Left. To. Right. God Damnit!

From http://math.about.com/library/weekly/aa040502a.htm :
1. Calculations must be done from left to right.

2. Calculations in brackets (parenthesis) are done first. When you have more than one set of brackets, do the inner brackets first.

3. Exponents (or radicals) must be done next.

4. Multiply and divide in the order the operations occur.

5. Add and subtract in the order the operations occur.

It is MATH. There are RULES. And. You. Follow. Them. I've always been taught that () mean multiplication, and I'll bet that if you go to any math teacher they will tell you the same.

The reason you do not assume it's 6 / (2(1+2)) is because, gasp, now there are parenthesis in there! Why would there be parenthesis in there? Because otherwise it would be, naturally, read left-right and come out to 9. The addition of parenthesis makes it an ENTIRELY DIFFERENT problem.

Note: Yes, I treat math as seriously as I treat grammar. Grammar I sometimes let slide, but damnit you DO NOT MESS WITH MATH.

[Bryan90]

Originally Posted by NickT

The reason you do not assume it's 6 / (2(1+2)) is because, gasp, now there are parenthesis in there! Why would there be parenthesis in there? Because otherwise it would be, naturally, read left-right and come out to 9. The addition of parenthesis makes it an ENTIRELY DIFFERENT problem.

Note: Yes, I treat math as seriously as I treat grammar. Grammar I sometimes let slide, but damnit you DO NOT MESS WITH MATH.

Nick, if you treat math as seriously as you say, READ MY POST....

There is an entire debate out there on multiplication by juxtaposition, and mathematicians have been saying that there really is no universal rule on that.

I am right now doing a little more research on whether or not parentheses is commonly interpreted as multiplication by juxtaposition or if an entirely distinct role has been set out for it.

You can see the confusion even in applications like Wolfram Alpha where:
6/5x = 6/(5x)
BUT
6/5(x) = 6/5 * X

it is 9 if there was a problem like 2-1+(3+1)
it would go: 2-1+4=5 not =2-5=-3
it goes left to right.