6÷2(1+2)=?

The answer is one because my scientific calculator tells me so

BTW, my calculator also tells me that

6÷2(3) = 1

and

6÷2*3 = 9.

Therefore 2(3) != 2*3.

Calculators which are computer programs treat the brackets the same as multiplication which is wrong and is forgetting a rule.

As already mentioned, it must be treated as

6÷((2*1)+(2*2))

and not treated as

6÷2*(1+2)

The distributive rule which applies here is and which most people are forgetting (including computer programs) is

A(B+C)=AB+AC




.

I think we can all agree 6/2(1+2) and 6/(2+4) are the same.

How can they get different answers then?

Its 1. Maths is not done left to right, thats just plain ridiculous.

I'm really surprised to see 13 pages of this. This is really a simple equation.

PEMDAS this is the order of operations in all math equations. Its the rulebook so to speak.

Parenthesis then exponents then multiplication then division then addition then subtraction. IN THAT ORDER.



6÷2(1+2) First Parenthesis

(1+2)=3

6÷2(3) Next; there are no exponents so skip to multiplication

2(3)=6

6÷6 Lastly in this particular equation is division.

6÷6 =1


PEMDAS

reply to post by ScRuFFy63


I am in a world -class engineering University. And this is pissing me off because I can see where the different answers are coming from. But the rules seem to be based on the form the equation is presented.

example.
6
-----
2(2+1)

or
6/2(2+1)

I will ask a professor tomorrow but I see the issue. I believe the answer is 1 because as I have been schooled the rules in math seem to change as the subject gets more advanced.

This thread should be kept forever as an example of why there is no point listening to experts

We have qualified mathematicians and engineers saying the answer is 1, sometimes rudely and adamantly
We have qualified mathematicians and engineers saying the answer is 9, sometimes rudely and adamantly

...and we're not talking about philosophy or cooking, we're talking about numbers (I'm sure somebody told me once that mathematics is absolute truth, although I disagreed)

Is this problem coming from some difference between the ÷ symbol and the / symbol perhaps? For me as a programmer, I saw the answer as being 9, but I instantly swapped the ÷ for a /, because it's all I know.

For everybody who is so sure it is 1, you may be right and I would not argue with you because I'm not arrogant enough regarding my mathematical knowledge...but you should know that in saying so you are saying that all the computer programming languages are incorrect (or at least PHP, JavaScript, C++, Actionscript are as they will all give you a 9). I'm not being facetious here, computers can't even do fractions properly so you may be right

Originally posted by IamBoon
reply to post by ScRuFFy63

 

I am in a world -class engineering University. And this is pissing me off because I can see where the different answers are coming from. But the rules seem to be based on the form the equation is presented.

example.
6
-----
2(2+1)

or
6/2(2+1)

I will ask a professor tomorrow but I see the issue. I believe the answer is 1 because as I have been schooled the rules in math seem to change as the subject gets more advanced.

edit on 2-5-2011 by IamBoon because: (no reason given)

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


6
---- =
2(3)


6
--- = 1
6



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


I don't know. I'm just not seeing how people are getting other answers. If I follow the rules I keep getting the same answer.

Consider, what is one third times three? How would you write it?

1
-- * 3 = ?
3

1 / 3 * 3 = ?

you would not group 3 * 3 without a parenthesis as this would be the same as one third divided by three.

1 / 3 / 3 = ?

1 / (3 * 3) = ?

Consider then,

6
-- * (1 + 2) = 9
2

6 / 2 (1 + 2) = 9

the 6 is not also being divided by (1+2) but rather multiplied by it.

6 / 2 * (1 + 2) = ?

6
-- (1 + 2) = ? which is 3 * 3 or if you distribute 3 + 6
2

The answer is clearly nine, 9.

edit: to those who wish to distribute the factor through the parenthesis you must distribute the fraction 6/2 or 3.

Originally posted by MegaMind

6 / 2 * (1 + 2) = ?

It is incorrect to write it like you did.

Due to the distribution rule

A(B+C) = AB+AC

it should be written like

6 / ((2*1)+(2*2))

The answer is clearly 1.

reply to post by GobbledokTChipeater


Incorrect you must distribute 6/2 not 2.

A = 6/2 = 3

A(B + C) = AB + AC

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

You can't pick and choose what part of the fraction you are going to distribute.

Edit: you could but A = 1/2 or A = 6 or A = 6/2

6(1/2 + 1) = 9 , (6 + 12)/2 = 9, 3 + 6 = 9

Originally posted by solargeddon

Originally posted by Red_xi
The answer is 1

Not 9......... 1

It shamed me to hear an engineer student ranting that it is 9. I'm an engineering graduate and I'm telling you its 1

Type it in to ANY DECENT calculator (not Google) and you will get 1






If you don't get it that's fine, but please stop slamming people for trying to correct you.


But I just google the answer, and the answer is still 9.

6/2(1+2)=....

First you deal with the brackets

1+2=3 hold onto the 3 cos you need it later....

Then you divide 6 by 2=3.....

The 3 from (1+2) and the 3 from 6/2, now sit side by side like this .... 33, which is the same as 3x3

3x3= 9

The answer is 9. I may have a poor mathematical background, but seriously, this is the answer, unless of course the whole of GCSE Maths is now wrong, in which case, I don't feel so bad for having such a poor outcome in my exam

The correct procedure has been explained over and over, being met with deaf ears

Just put it into THREE more than DECENT calculators, one a casio very similar to the one in the picture (fx-115ES), a TI-89, and a Ti-30XIIS. All gave the answer to be 9.

Still though, calculators are NOT to be trusted. Even though they are right.

The OP has written a linear equation, this is where the trouble comes up. Because the 2 is adjacent to the parentheses, you are interpreting it to be:

6
-----
2(2+1)

This I will agree will solve to be 1. However it its the wrong interpretation of the linear equation.

6÷2(1+2) >> 6÷2(3)

It is being assumed that the 2 and the 3 go to the denominator of the fraction. This is not the case when written linearly like this. It should be interpreted as 6÷2x3 at this point. The parentheses have been addressed and thus PEMDAS or BODMAS or whatever acronym you were taught states that Multiplication and division take the same priority, Left to Right.

6/2=3

3*3=9

If the problem had been written as 6÷(2(2+1)) the answer would in fact be 1.

Another way of looking at it, divison is simply a form of multiplication. 6/2 is the same as 6*0.5

6*0.5(1+2) = 9

The problem here is that it is written as a LINEAR equation. Putting the 2(2+1) all under the 6 is the wrong interpretation. The 2(2+1) or 2(3) is an implied multiplication. Same priority as division when PEMDAS is applied.


Also. Distribution in a property and not a law, and therefore it can be used if you want or not. a(b+c) = ab + ac. whether you distribute or not the answer will not change

In this case distribution applied would be 6/2(2+1) >>> 3(2+1) >>> (6+3)

It all comes down to how the problem is interpreted at the beginning though.

My spin on this:
6÷2(1+2) is the same as 6÷2*(1+2)
2(1+2) is no different than 2*(1+2), just like 2X = 2*X

so 6÷2*(3) = 9

BUT:
6
--------- = 1
2(1+2)

This is because a fraction symbol is slightly different than a division symbol.

1+1
----- = 1
2

1+1÷2 = 1.5

a fraction symbol entails hidden parenthesis around both sides.
(1+1) ÷ (2) = 1

Back to the original problem:

6
--------- = (6) ÷ [2(1+2)] = 1
2(1+2)

(6) ÷ [2(1+2)] does not equal 6÷2*(1+2)

Order of operations isn't
Multiplication
Division
Addition
Subtraction

It's
Multiplication and Division
Addition and Subtraction

-
The answer is 9, but it's a simple oversight to cause it to look like one.

reply to post by MegaMind


The answer would be 9 if it were written as;

(6/2)(1+2)

which as you stated is the same as

6
---- (1+2)
2

But it is written

6/2(1+2)

Which is the same as

6
------
2(1+2)

You have to solve the denominator first before you can touch the numerator

...... How is there 13 pages of this. One of the funniest threads I've read in a while.

Second line.

Here is your problem:

6 ÷ 2 ( 1 + 2 ) =

Do any math in ( ? ) first.

1 + 2 = 3

So you're left with:

6 ÷ 2 x 3 =

so,

6 ÷ 2 = 3

3 x 3 = 9

Found you a website to help you out if you're still a skeptic.
Algebra

reply to post by Mactire


I have a $200 calculator that says 9 is wrong. My cheap one says the answer is 9 though.

reply to post by Red_xi


Disagree - matter of notation and interpretation. Mine is consistent with algebraic notation and distribution and is the most widely accepted notation and interpretation. I am a programer with some education in very advanced math such as differential equations.

I ask again what is one third multiplied by three? How do you write it?

(1+2) is not part of the denominator.

reply to post by MegaMind


That is not the question... if you cannot see the reasons why this is 14 pages long then sorry. I am not that dumb and I can see how the confusion persists. Seems reasonable because I was as adamant about it as you 2 pages back before I did some actual research.

I believe the scientific notation of my $200 calculator more than a website and a dude with a cool name and avatar.

reply to post by Itop1


Please Excuse my dear aunt sally ... working left to right

6÷2x(1+2)
6÷2x(3)
3x3
= 9

Originally posted by MegaMind
reply to post by Red_xi

 

(1+2) is not part of the denominator.

edit on 2-5-2011 by MegaMind because: (no reason given)

Yes exactly! This appears to be the sticking point for everyone as well. In a linear equation as written by the OP, the (1+2) is a multiplication implied by the parentheses and should NOT be put in the denominator with the 2.

I fired up Microsoft Visual Studio 2010 and ran this in C#

//6÷2(1+2)=?
int a = 6;
int b = 2;
int c = 1;
int d = 2;

int answer = a / b * (c + d);
Label1.Text = answer.ToString();

Answer again is 9.

Now I just seen this on Wikipedia. Not sure if it's right or not. But take it for what it's worth.

If PEMDAS is followed without remembering that multiplication and division have the same weight, and addition and subtraction have the same weight. Doing multiplication before division, can give the wrong answer. So can doing addition before subtraction. Some grade school books teach this incorrectly. For example: 6÷2×3 = 9, not 1. 6-2+3 = 7, not 1.

According to Wikipedia. The answer of 1 is wrong. 9 is the correct answer.