Topic: Simple math problem, or not !

[Spanner 1]

So a raging math problem has been involving many on Facebook.... lots of smart folks here, so what is the solution to this;
                                                                            6-:- 2(1+2).              ( couldn't find proper division sign, '6 divided by' ).
Thanks for answers.

[kmb69]

"PEMDAS"
Parentheses,
Exponents,
Multiplication/Division (left to right)
Addition/Subtraction (left to right)
6/2*3
3*3
9

[Spanner 1]

More!

[Spanner 1]

I should have parsed the problem... "There is a hostile missile directed at the U.S....... the anti missile system needs to be adjusted these many degrees to knock it out '
                                                                    6  -:- 2(1+2 )                  ?   ( again -:- thing = 'divided by' )

[eigenvector]

I interpret it as 6/6 = 1
6/(2*(1+2))
6/(2*3)

I'd like to add that as soon as you add (no pun intended) a divisor to a written equation it becomes ambiguous.  As an engineer I would have thrown this back to the person who wrote it for clarification.
It would just as easily be
(6/2)*(1+2) as KMB wrote because we have no way of knowing what was supposed to be on the denominator.

This is how I would have written my equation
6/(2*(1+2))
(6/2)*(1+2) is how KMB would have written his.

[Bailgang]

As an engineer I would have thrown this back to the person who wrote it for clarification.

BINGO!!!
That is precisely why I stay away from these PEMDA riddles because being multiplication and division have equal priorities that means 9 or 1 are potentially correct  but without that clarification it's impossible to determine which order of operations to choose to get the correct answer. The people who originally post these equations know that and intentionally DON'T clarify their question and instead set back and watch everyone argue, sometimes very vigorously, insisting 9 is the only correct answer while another group insists the answer is 1 without realizing they're being duped into a pointless debate because without that clarification they are both potentially correct. Mathematicians can't even come to a full agreement on this.

[Spanner 1]

                                6 -:- 2x(1+2)   = 9     but,

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

The 2 is 'welded' to the problem and cannot be separated and divided into the 6. The problem has to be resolved before you know what to divide the 6 by.
The problem is 2(1+2),not (1+2). No ambiguity at all !

Another way to say the same thing ;            6
                                                         __________           
                                                          2(1+2)

[MikeSimon]

I showed this to a math teacher and he agreed with me on: 6 divided by 2 then times 3 . Equals 9.
He says if it should have been 6 divided by 6, it should have been written 6/(2 (2+1))
But he also agrees, that it is debatable.

[Spanner 1]

Nope !....

O.K..... go ahead and divide the 6 by the 2

 Now we go from 6 -:- 2( 1+2) to   3 -:- (1+2) . You don't lose the -:- and turn it into an 'x' !! you took the only multiplier ,2, out of the problem, you still divide the 3 by the result of (1+2 ). 

[BomberMann650]

A math equation with two possible solutions?  No wonder kids these days hate school.

But I got a story problem for ya.

Doug has 35 candy bars, he eats 32 of them.  What does doug have now?
Wait for it....


Diabetes

Wah wah waaaahhhhhh

[kmb69]

.....
But he also agrees, that it is debatable.

Not debatable IMHO.    Your teacher was being too PC!    

Nope !....

O.K..... go ahead and divide the 6 by the 2

 Now we go from 6 -:- 2( 1+2) to   3 -:- (1+2) . You don't lose the -:- and turn it into an 'x' !! you took the only multiplier ,2, out of the problem, you still divide the 3 by the result of (1+2 ). 

Disagree.   
I personally do not think this equation is ambiguous if following the "PEMDAS" rules. Neither multiplication or division has precedence other than left-to-right.
2n = 2*n  and it does not matter what is in front of it, so.... 2(1+2) = 2*(1+2)

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

This equation as written in your original post, has to be entered in a calculator as 6/2*(1+2) and the result is 9.

[MikeSimon]

Nope !....

O.K..... go ahead and divide the 6 by the 2

 Now we go from 6 -:- 2( 1+2) to   3 -:- (1+2) . You don't lose the -:- and turn it into an 'x' !! you took the only multiplier ,2, out of the problem, you still divide the 3 by the result of (1+2 ). 

I can't really follow this logic. If we divide the 6 by the 2, ( 6 -:- 2) we are done with the first part of the equation. All that is left now is the (2+1) and that must be multiplied with the first part. Ergo 3x3 =9

[Spanner 1]

I still disagree  ... the 2 before the bracket applies to the problem only. If you insist on dividing it into the LH side of the equation, then you must also divide it into the RH side too without the RH side being solved or the equation is lost !Or solve the problem first !!! the problem being 2(1+2), then proceed as you like 

Consider this; I have 6 apples and I decide to give 1 to John and 2 to Jane, then here's the problem    6 - (1+2) = 3 apples left
Now if I decide to do the exact same thing again, give 1 more apple to John and 2 more apples to Jane then the problem becomes 6 - 2(1+2 ). The 2 before the bracket only describes the fact that the action happened 2 times.
By any other logic, I would have 12 apples left after I clearly gave all 6 away 

Same as this         6 - (1+2 ) - (1+2) = 0

 Or even better, just to say the RH side is not a number must be solved first before dividing into the LH side which is a number ( original problem ).

[kmb69]

So a raging math problem has been involving many on Facebook.... lots of smart folks here, so what is the solution to this;
                                                                            6-:- 2(1+2).              ( couldn't find proper division sign, '6 divided by' ).
Thanks for answers.

I still disagree  ... the 2 before the bracket applies to the problem only. If you insist on dividing it into the LH side of the equation, then you must also divide it into the RH side too without the RH side being solved or the equation is lost !Or solve the problem first !!! the problem being 2(1+2), then proceed as you like 
.....

There is NO EQUATION in your problem. An EQUATION is an expression on both sides of the = sign. Your problem is a MATHEMATICAL EXPRESSION - NOT an equation.

[MikeSimon]

Really, I cannot follow the train of thoughts of some. In math there is clearly a rule that divisions and multiplications have to be executed before additions and subtractions. That's why, in the problem at hand, the 2+1 was put in parenthesis, making sure the two numbers were added.
In the left part of the equation, the 6 is being divided by 2. This will make 3. Then the 3 is being multiplied by the content of the parenthesis. 3x3 = 9.

The only issue here would be if the 2 in front of the parenthesis would be multiplied by the content of the parenthesis, like 2 x 3 =6 before.
Then you would have 6 divided by 6 = 1. These are the only two possible solutions. With the latter being eliminated by the rule that you execute a calculation from left to right.

[Spanner 1]

Yes, it is a problem, not an equation , oops.   6 is a number and is divisible, 2(1+2) is not a number.  You must solve the problem first to know what to divide the 6 by. The problem always comes first, in this case 2(1+2), turn that into an actual number, then proceed. Basic rule of math IMO. It is not 6 divided by 2 and then x ( 1+2). It is 6 divided by the solution of 2(1+2) , proven by how it is written...... 2(    not 2x   ,  left right rule does not uber 'problem first' to make the problem real numbers, 6 -:- 6 =1.

[kmb69]

Yes, it is a problem, not an equation , oops.   6 is a number and is divisible, 2(1+2) is not a number.  You must solve the problem first to know what to divide the 6 by. The problem always comes first, in this case 2(1+2), turn that into an actual number, then proceed. Basic rule of math IMO. It is not 6 divided by 2 and then x ( 1+2). It is 6 divided by the solution of 2(1+2) , proven by how it is written...... 2(    not 2x   ,  left right rule does not uber 'problem first' to make the problem real numbers, 6 -:- 6 =1.

That is incorrect. The 2(1+2) is not a "problem" in itself without another set of parentheses, i.e. 6 / ( 2 ( 1 + 2 ) ). The 2(1+2) means 2*(1+2).
You can Google this very expression:
https://socratic.org/questions/how-do-you-simplify-6-2-1-2-using-pemdas
https://www.mathway.com/popular-problems/Algebra/201404
Your expression means 6 / 2 * (1 + 2).
Do the parentheses FIRST 6 / 2 * 3.
Then the multiplication/division - left to right 3 * 3 = 9.

[jgger]

Well OK, now that you guys got that one sorted out...........


Does anyone know what the white stuff in chicken poop is?
MORE CHICKEN POOP!

Dang you would think this was something more useful to argue about.........like OIL!

[kmb69]

Well OK, now that you guys got that one sorted out...........
.....
Dang you would think this was something more useful to argue about.........like OIL!

Yeah, no kidding. This one is a 4th Grade level problem according to the experts on the internet.

Got OIL?     

[Rookster]

   6-:- 2(1+2) 

There is only 1 solution.  PEMDAS is the rule.

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

There is no ambiguity.  The parentheses are done first.  The division and multiplication are next from left to right.  6 / 2 = 3. Then the multiplication 3 x 3 = 9. To do the problem in any other order is incorrect.

Scott

[kmb69]

   6-:- 2(1+2) 

There is only 1 solution.  PEMDAS is the rule.

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

There is no ambiguity.  The parentheses are done first.  The division and multiplication are next from left to right.  6 / 2 = 3. Then the multiplication 3 x 3 = 9. To do the problem in any other order is incorrect.

Scott

Ditto. Been saying that all day.

[Spanner 1]

                              6                     6                       6                   3                  3           =real number
                     ----------------  =   -------------  =    --------- OR --------------- = --------
                        2(1+2)                 2(3)                    6                 1(3)                3               = real number
You must work the problem all the way to a real number to have a real number top and bottom . Answer is 1.  Good evening, gentlemen
 

[Rookster]

Spanner you are rewriting the problem wrong.  It is not 6 over 2(1+2).  It is 6 over 2 times (1+2) or 6/2 x (1+2) =
6/2 x (3) =
3 x (3) =
9

The number in front of parenthesis is multiplied by whatever is in the parenthesis.  The parenthesis do not get multiplied by 2, they get multiplied by the quotient of 6/2 because that operation happens before the multiplication.  PEMDAS is the rule left to right.  This is not a difficult problem and to do it any other way is to ignore PEMDAS.  Either way I'm out on this one.  It feels a little like an argument for arguments sake if you ignore the order of operations.

Scott

[MikeSimon]

Spanner you are rewriting the problem wrong.  It is not 6 over 2(1+2).  It is 6 over 2 times (1+2) or 6/2 x (1+2) =
6/2 x (3) =
3 x (3) =
9

 .  Either way I'm out on this one.   

Scott

+1 here

[Spanner 1]

I'll leave y'all alone now and come back when I think you have had enough time to see that I am right  It's all about 2x vs 2( problem). That 2 by the bracket is not free to divide into anything is only dedicated to multiplying the result of the problem in the brackets ( ) it's attached to . Must be resolved before any PEMDAS. 2x , free to do what ya want !

Oh, and Rookster       6
                            -------------- does NOT = 6/2 x (1+2)     it equals     6/2  x 1/ (1+2).  =1. 
                              2(1+2)

The (1+2) does not magically become a multiplier .. lol.. it's still below the line = divider .