# Basic Math Problem - Need Help



## mevans154 (Mar 22, 2013)

OK, all you engineers. I have a basic math problem here.

The older engineers in the office get one answer and the younger engineers get a different answer

6/2(1+2)=??

What is the correct answer?


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## snickerd3 (Mar 22, 2013)

1


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## mevans154 (Mar 22, 2013)

snickerd3 said:


> 1


That's what I said, but the older engineers get a different answer.

Anyone else??


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## Capt Worley PE (Mar 22, 2013)

1 is correct.


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## snickerd3 (Mar 22, 2013)

THey get 9 don't they.


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## mevans154 (Mar 22, 2013)

snickerd3 said:


> THey get 9 don't they.


Yes, the older engineers say the answer is 9, and the younger engineers say the answer is 1

The older engineers say once you do the math in the brackets (2+1), you then work left to right.

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

6/2=3

3*3=9

So what is the right answer??


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## mevans154 (Mar 22, 2013)

If you type "6/2*(1+2)" in Excel you get the answer 9


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## Judowolf PE (Mar 22, 2013)

The question is does 6/2(1+2) equal 6/2*(1+2) or is 2(1+2) a whole expression


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## snickerd3 (Mar 22, 2013)

and if you use some calculators you get 1. The math experts out there still argue about this.

Using the () to act as * tends to mess people up.


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## Master slacker (Mar 22, 2013)

Perform action within parentheses --&gt; 2 + 1 = 3

Perform math left to right --&gt; 6/2(3) = 3(3) = 9


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## snickerd3 (Mar 22, 2013)

mevans154 said:


> If you type "6/2*(1+2)" in Excel you get the answer 9




That is not the same equation int he orginal question


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## Capt Worley PE (Mar 22, 2013)

Master slacker said:


> Perform math left to right --&gt; 6/2(3) = 3(3) = 9




Or, do numerator and denominator math first ---&gt; 6/2(3) = 6/6=1


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## EM_PS (Mar 22, 2013)

^ please my dear aunt sally

apparently some of you better find an older engineer to cling to


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## snickerd3 (Mar 22, 2013)

bottom line it is a badly written question that replies on the writers intent.


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## Master slacker (Mar 22, 2013)

Capt Worley PE said:


> Master slacker said:
> 
> 
> > Perform math left to right --&gt; 6/2(3) = 3(3) = 9
> ...




If it's numerator / denominator, the numerator is 6 and the denominator is 2. Answer is 9. If the 2 AND 3 were the denominator in this linear layout, there would be additional parentheses around the 2 AND 3.

6/2(3) = 9

6/(2(3)) = 1


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## Judowolf PE (Mar 22, 2013)

hey, it's 9 or 1, just slap a big safety factor on it and call it good...


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## solomonb (Mar 24, 2013)

The answer is 9. In the Hierarchy of order of operations, multiplication/division comes before addition and subtraction. In the same vein, exponentiation comes before multiplication/subtraction. As I recall the order of operations, it is exponentiation------- multiplication/division-------addition/subtraction.

So, divide 6/2=3. THEN work the problem INSIDE the brackets (2+1=3). Restate the problem, 3*3=9

That is the way that I remember it. It has nothing to do with what direction, i.e., left to right you solve the problem-- it is the hierarchy of operations that is accomplished first. I am not an algebra teacher, however, this is how I recall it being done.

Yes, I would be in the more seasoned engineer group!


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## IlPadrino (Mar 24, 2013)

There is no *right* answer... this one has been around the interwebs for quite a while. It doesn't matter what a calculator, Excel, or Wolframalpha gives for the result because each one is based on its own interpretation of the "rules".

There's always confusion about the difference between unary and binary operations and the difference between "/" and "÷". As snickerd3 writes, clear up any ambiguity with parentheses!


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## Master slacker (Mar 24, 2013)

IlPadrino said:


> As snickerd3 writes, clear up any ambiguity with parentheses!


The answer is ( 9 ) !


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## IlPadrino (Mar 24, 2013)

9 factorial?


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## benbo (Mar 24, 2013)

sin(X + Y) = sinx + y ?

sin(0+0) = sin0 + 0 = 0 + 0 = 0 = sin(0).

That proves it, right?



I may have located a technical explanation -

http://www.schooltube.com/video/efb63be016b142e4a64c/


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## MA_PE (Mar 24, 2013)

I say 9. I'm old


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## benbo (Mar 24, 2013)

Let's hold a poll. THat's the best way to solve math problems.


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## ptatohed (Mar 25, 2013)

I think the answer is 9. Parenthesis and then left to right. This assumes the "/" means division and we also have to assume implied multiplication using the parenthesis. These are fair assumptions.

If the "/" is a fraction bar, then the answer is still 9 if we assume the 6 is the numerator and the 2 is the denominator.

If the "/" is a fraction bar, the answer can only be 1 if we assume the 6 is the numerator and the 2(1+2) is the denominator but I don't think that's the fairest assumption.

I say 9.


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## csb (Mar 25, 2013)

Sap-i learned PEMDAS...you don't have the parentheses.

That's how I got nine.

Now where's the SOH CAH TOA problem so I can use all my math chants?


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## Ble_PE (Mar 25, 2013)

csb said:


> Sap-i learned PEMDAS...you don't have the parentheses.
> 
> That's how I got nine.
> 
> Now where's the SOH CAH TOA problem so I can use all my math chants?


Same here.


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## Capt Worley PE (Mar 25, 2013)

Never mind the reason why, just invert and multiply!


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## Master slacker (Mar 25, 2013)

^^^ This ain't sex ed.


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## Capt Worley PE (Mar 25, 2013)

I had a vector calc professor that would be halfway through a proof and write, "BAOG," then the final equation. When asked about it, he said, "By act of God. I know you people don't really care how we got there."


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## mizzoueng (Mar 27, 2013)

What if you were using a calculator, on a plane, on a treadmill, to solve this equation, would that affect the answer?

Side question, when is it appropriate to use affect over effect?


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## civengPE (Mar 28, 2013)

I am of the opinion that it can be both, because it is just a poorly written equation. It can be interpreted two different ways:

6

---------------

2(1+2)

Or

6

----- (1+2)

2

I would ASSUME that if the intention was for case 1 then the equation should have been 6/(2(1+2)). But the argument could be made that case 2 should be written as (6/2)(1+2).

So my answer is &lt;10. ;-)

Edit: Why does the board remove the spaces in my post?


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## mudpuppy (Mar 28, 2013)

civengPE said:


> Edit: Why does the board remove the spaces in my post?






That's normal HTML behavior. HTML don't allow extra spaces. Use a Code Box to preserve them:


6

---------------

2(1+2)

Or

6

----- (1+2)

2


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## ptatohed (Mar 28, 2013)

civengPE said:


> I am of the opinion that it can be both, because it is just a poorly written equation. *It can be interpreted two different ways*:
> 
> 6
> 
> ...



Actually, not so. As written, it can only be interpreted one way. The answer has to be 9, as written.


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## Supe (Mar 28, 2013)

Unsurprisingly, I agree with 9, my coworker who grew up with a TI-34234091 platinum edition says its 1.

I think most people are just so used to hearing PEMDAS, they forget that this is how it works:

http://www.factmonster.com/ipka/A0933340.html

When I rewrote the problem for him as 6*(1/2)(1+2) it blew his mind...


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## Capt Worley PE (Mar 29, 2013)

Supe said:


> When I rewrote the problem for him as 6*(1/2)(1+2) it blew his mind...


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## mudpuppy (Mar 29, 2013)

I know it is hard for engineers to accept, especially considering math is the foundation of science, a subject we've been taught always give a concrete, factual answer, but there is no correct answer to this. But it does teach the lesson that you should always communicate your thoughts clearly.


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## Capt Worley PE (Mar 29, 2013)

> But it does teach the lesson that you should always communicate your thoughts clearly.




True dat.


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## MA_PE (Mar 29, 2013)

Made me think of this.

Three Stooges "Dizzy Pilots"

(Moe sees Curly sawing the plane's wings instead of the hanger doors. He quickly stope him.)

Moe: Hey, you nitwit! Don't saw the wings, you saw the garage!

Curly: I see the garage, but I don't saw the garage. You are speaking incorrectly. You are murdering the King's English! Et cetera.


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## ptatohed (Mar 30, 2013)

mudpuppy said:


> I know it is hard for engineers to accept, especially considering math is the foundation of science, a subject we've been taught always give a concrete, factual answer, *but there is no correct answer to this*. But it does teach the lesson that you should always communicate your thoughts clearly.




mp, I respectfully disagree. If the rules of operations are applied correctly, there is only one answer to the original equation (answer = 9). There are several videos on youtube about this (even videos "proving" the answer is 1) but this video is pretty good (in favor of 9).

 .

Yes, I agree, all math problems should be written so as to avoid any ambiguity (although, this thread would have been a lot more boring if the equation had been written as "(6/2)(1+2)"  ).


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## mudpuppy (Mar 30, 2013)

Order of operations is not a mathematical theory that can be proven, it is a mutually agreed-upon set of rules that create a method of communication. Just like any other language there are times it can be interpreted in different ways. Sometimes, like in poetry, this is encouraged. In the language of math, it's very much discouraged. What we have here is people taking advantage in a weakness of the clarity of our current system of order of operations in order to create arguments. I think this is a good thing when it gets people thinking about the problem and how to avoid it. But to try to prove they're right is futile.


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## benbo (Mar 30, 2013)

> Order of operations is not a mathematical theory that can be proven, it is a mutually agreed-upon set of rules that create a method of communication.





> Yes, I agree, all math problems should be written so as to avoid any ambiguity (although, this thread would have been a lot more boring if the equation had been written as "(6/2)(1+2)"


If we accept MP's statement this wouldn't help. There is no way to write this problem clearly. Or to commuinicate at all. Everything is based on mutually agreed upon symbology and open to interpretation. 2+2 can equal anything if I don't accept the "mutually agreed upon" meaning of the symbol "2" or the symbol "+". At what point does it become ridiculous?
The only thing that matters is what the boss thinks.


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## mudpuppy (Mar 30, 2013)

It depends on what your definition of "is" is.


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## IlPadrino (Mar 30, 2013)

Reminds me of a t-shirt I want to buy... "There are 10 kinds of people in the world - those that understand binary and those that don't."


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## Master slacker (Mar 30, 2013)

I'd fork that shirt's repo.


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