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## Math: 6÷2(1+2) = ? | |

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Anonymous Coward User ID: 944253 United States 01/21/2013 11:49 PM Report Abusive Post Report Copyright Violation | I am your college professor that you requested, with a doctorate in Mathematics. I will break this down as simply as possible and end this debate as approx. 10 students have already asked me this today. The problem as it is written is 6÷2(1+2) , the ÷ cannot be substituted with a fraction bar because they have different ranks on the order of operations. It is an illegal math move to do this. The bar ranks with parentheses, ÷ is interchangeable with *. therefore the problem must be solved as 6÷2(1+2) NOT 6 (over) 2(1+2) we do the parentheses first, so 6÷2(3), the parentheses are now no longer relevant, because the number inside is in it's simplest form. Every single number has implied parentheses around it. 6÷2(3) (6) ÷(2)(3) 6÷2*3, or even converting the division to multiplication by a reciprocal (a legal math move) (6)(1 (over) 2)(3) are all correct ways to write this problem and mean exactly the same thing. Using pemdas, where md and as are interchangeable, we work from left to right, so (3)(3) or 3*3= 9 Just because something is implied rather than written does not give it any special rank in the order of operations. The problem in it's simplest form, with nothing implied would look like this: (1+1+1+1+1+1 (over) 1) ÷ (1+1 (over) 1) * ((1(over) 1) + (1+1 (over) 1)) From here, nothing is implied, This again, works out to 9. If the symbol '/' was used this whole debate would be ambiguous since that symbol can mean "to divide by" or it could mean a fraction bar. HOWEVER, because the ÷ symbol is used, it can not be changed to mean a fraction bar because that would change the order of operations and thus the whole problem, you can't change a symbol to mean something because you want to, in doing so you are changing the problem. Once and for all, the answer is 9. Hopefully some of my students see this so I can stop answering this question. End of debate... hopefully. |

CitizenperthFUKUSHIMA, GLPTARD 24/7/365 User ID: 32253509 Australia 01/22/2013 01:59 AM Report Abusive Post Report Copyright Violation | I am your college professor that you requested, with a doctorate in Mathematics. I will break this down as simply as possible and end this debate as approx. 10 students have already asked me this today. Quoting: The problem as it is written is 6÷2(1+2) , the ÷ cannot be substituted with a fraction bar because they have different ranks on the order of operations. It is an illegal math move to do this. The bar ranks with parentheses, ÷ is interchangeable with *. therefore the problem must be solved as 6÷2(1+2) NOT 6 (over) 2(1+2) we do the parentheses first, so 6÷2(3), the parentheses are now no longer relevant, because the number inside is in it's simplest form. Every single number has implied parentheses around it. 6÷2(3) (6) ÷(2)(3) 6÷2*3, or even converting the division to multiplication by a reciprocal (a legal math move) (6)(1 (over) 2)(3) are all correct ways to write this problem and mean exactly the same thing. Using pemdas, where md and as are interchangeable, we work from left to right, so (3)(3) or 3*3= 9 Just because something is implied rather than written does not give it any special rank in the order of operations. The problem in it's simplest form, with nothing implied would look like this: (1+1+1+1+1+1 (over) 1) ÷ (1+1 (over) 1) * ((1(over) 1) + (1+1 (over) 1)) From here, nothing is implied, This again, works out to 9. If the symbol '/' was used this whole debate would be ambiguous since that symbol can mean "to divide by" or it could mean a fraction bar. HOWEVER, because the ÷ symbol is used, it can not be changed to mean a fraction bar because that would change the order of operations and thus the whole problem, you can't change a symbol to mean something because you want to, in doing so you are changing the problem. Once and for all, the answer is 9. Hopefully some of my students see this so I can stop answering this question. End of debate... hopefully. Anonymous Coward 944253 simply.. there is no divided-by key on the keyboard so it is substituted for the divide symbol... not a replacement mathematically... YAY 9! It's life as we know it, but only just. My Fukushima Site: [link to citizenperth.wordpress.com] sic ut vos es vos should exsisto , denego alius vicis facio vos change , exsisto youself , proprie GLP's best Fuku thread: Thread: *** Fukushima *** and other nuclear-----updates and links twitter: #citizenperth “If I had an hour to solve a problem and my life depended on it, I would use the first 55 minutes determining the proper question to ask, for once I knew the proper question, I could solve the problem in less than five minutes.” - Albert Einstein |

Anonymous Coward User ID: 31557420 United States 01/22/2013 02:12 AM Report Abusive Post Report Copyright Violation | I am your college professor that you requested, with a doctorate in Mathematics. I will break this down as simply as possible and end this debate as approx. 10 students have already asked me this today. Quoting: The problem as it is written is 6÷2(1+2) , the ÷ cannot be substituted with a fraction bar because they have different ranks on the order of operations. It is an illegal math move to do this. The bar ranks with parentheses, ÷ is interchangeable with *. therefore the problem must be solved as 6÷2(1+2) NOT 6 (over) 2(1+2) we do the parentheses first, so 6÷2(3), the parentheses are now no longer relevant, because the number inside is in it's simplest form. Every single number has implied parentheses around it. 6÷2(3) (6) ÷(2)(3) 6÷2*3, or even converting the division to multiplication by a reciprocal (a legal math move) (6)(1 (over) 2)(3) are all correct ways to write this problem and mean exactly the same thing. Using pemdas, where md and as are interchangeable, we work from left to right, so (3)(3) or 3*3= 9 Just because something is implied rather than written does not give it any special rank in the order of operations. The problem in it's simplest form, with nothing implied would look like this: (1+1+1+1+1+1 (over) 1) ÷ (1+1 (over) 1) * ((1(over) 1) + (1+1 (over) 1)) From here, nothing is implied, This again, works out to 9. If the symbol '/' was used this whole debate would be ambiguous since that symbol can mean "to divide by" or it could mean a fraction bar. HOWEVER, because the ÷ symbol is used, it can not be changed to mean a fraction bar because that would change the order of operations and thus the whole problem, you can't change a symbol to mean something because you want to, in doing so you are changing the problem. Once and for all, the answer is 9. Hopefully some of my students see this so I can stop answering this question. End of debate... hopefully. Anonymous Coward 944253 You posted this crap a long time ago and you made me even more adamant about my beliefs. What is your name? Where do you teach? Clearly, you are full of it. 1) you don't know that symbol is called an obelus. 2) that does NOT mean "divide by next number". It is a grouping symbol. The answer is 1. Even if the slash was used, this debate would still NOT be ambiguous. Only if a solidus was used, would the answer equal 9. |

Anonymous Coward User ID: 31557420 United States 01/22/2013 02:13 AM Report Abusive Post Report Copyright Violation | The problem as it is written is 6÷2(1+2) , the ÷ cannot be substituted with a fraction bar because they have different ranks on the order of operations. It is an illegal math move to do this. The bar ranks with parentheses, ÷ is interchangeable with *. therefore the problem must be solved as 6÷2(1+2) NOT 6 (over) 2(1+2) we do the parentheses first, so 6÷2(3), the parentheses are now no longer relevant, because the number inside is in it's simplest form. Every single number has implied parentheses around it. 6÷2(3) (6) ÷(2)(3) 6÷2*3, or even converting the division to multiplication by a reciprocal (a legal math move) (6)(1 (over) 2)(3) are all correct ways to write this problem and mean exactly the same thing. Using pemdas, where md and as are interchangeable, we work from left to right, so (3)(3) or 3*3= 9 Just because something is implied rather than written does not give it any special rank in the order of operations. The problem in it's simplest form, with nothing implied would look like this: (1+1+1+1+1+1 (over) 1) ÷ (1+1 (over) 1) * ((1(over) 1) + (1+1 (over) 1)) From here, nothing is implied, This again, works out to 9. If the symbol '/' was used this whole debate would be ambiguous since that symbol can mean "to divide by" or it could mean a fraction bar. HOWEVER, because the ÷ symbol is used, it can not be changed to mean a fraction bar because that would change the order of operations and thus the whole problem, you can't change a symbol to mean something because you want to, in doing so you are changing the problem. Once and for all, the answer is 9. Hopefully some of my students see this so I can stop answering this question. End of debate... hopefully. Anonymous Coward 944253 You posted this crap a long time ago and you made me even more adamant about my beliefs. What is your name? Where do you teach? Clearly, you are full of it. 1) you don't know that symbol is called an obelus. 2) that does NOT mean "divide by next number". It is a grouping symbol. The answer is 1. Even if the slash was used, this debate would still NOT be ambiguous. Only if a solidus was used, would the answer equal 9. Anonymous Coward 31557420 "You posted this crap a long time ago and you made me even more adamant about my beliefs." Which were completely wrong at the time. Luckily Caper26 put up with me and helped me learn some things about mathematics. The answer is 1. |

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Anonymous Coward User ID: 13766129 Canada 01/22/2013 04:22 AM Report Abusive Post Report Copyright Violation | When it's 6 Quoting: Divided By 2(1+2).SyriusThis notation more clearly represents such a problem... 6÷(2(1+2)) [link to www.wolframalpha.com] Anonymous Coward 1194370Hilarious. Parenthesis inside of parenthesis? If you want to be technical, it would like something like this: 6÷(2[1+2]) SyriusSure. That works too. No ambiguity. Have fun. Anonymous Coward 1194370 You dumb yankees are adding brackets to justify incorrect answers and order of operations. Brackets first, then left to right any division or multiplication. 9 is correct, 1 is for dummies or republicans, but that is also equivalent. If you use a dictionary you may understand what I said, but all others will instantly. |

Anonymous Coward User ID: 13766129 Canada 01/22/2013 04:28 AM Report Abusive Post Report Copyright Violation | When it's 6 Quoting: Divided By 2(1+2).SyriusThis notation more clearly represents such a problem... 6÷(2(1+2)) [link to www.wolframalpha.com] Anonymous Coward 1194370Hilarious. Parenthesis inside of parenthesis? If you want to be technical, it would look like this: 6÷(2[1+2]) SyriusYou cannot mess with the order of operations! There is only one outcome: 1. If you have compelling proof that it is something else without breaking the rules of order of operation just show it. Anonymous Coward 1362610 Don't embarrass your country, brackets first, then exponents,division,mulitiplication,addition,subtraction, or bedmas.You added brackets mistakenly, if they were there in the original equation, they would apply, but they weren't, so don't change the equation to justify your chosen answer. |

MustangTerryUser ID: 13766129 Canada 01/22/2013 04:34 AM Report Abusive Post Report Copyright Violation | The problem as it is written is 6÷2(1+2) , the ÷ cannot be substituted with a fraction bar because they have different ranks on the order of operations. It is an illegal math move to do this. The bar ranks with parentheses, ÷ is interchangeable with *. therefore the problem must be solved as 6÷2(1+2) NOT 6 (over) 2(1+2) we do the parentheses first, so 6÷2(3), the parentheses are now no longer relevant, because the number inside is in it's simplest form. Every single number has implied parentheses around it. 6÷2(3) (6) ÷(2)(3) 6÷2*3, or even converting the division to multiplication by a reciprocal (a legal math move) (6)(1 (over) 2)(3) are all correct ways to write this problem and mean exactly the same thing. Using pemdas, where md and as are interchangeable, we work from left to right, so (3)(3) or 3*3= 9 Just because something is implied rather than written does not give it any special rank in the order of operations. The problem in it's simplest form, with nothing implied would look like this: (1+1+1+1+1+1 (over) 1) ÷ (1+1 (over) 1) * ((1(over) 1) + (1+1 (over) 1)) From here, nothing is implied, This again, works out to 9. If the symbol '/' was used this whole debate would be ambiguous since that symbol can mean "to divide by" or it could mean a fraction bar. HOWEVER, because the ÷ symbol is used, it can not be changed to mean a fraction bar because that would change the order of operations and thus the whole problem, you can't change a symbol to mean something because you want to, in doing so you are changing the problem. Once and for all, the answer is 9. Hopefully some of my students see this so I can stop answering this question. End of debate... hopefully. Anonymous Coward 944253 Thanks for explaining to the morans the correct procedure, I was shocked by so many wrong answers.Very many from the USA, but not all....Most Canadians are correct, of course, eh? |

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MustangTerryUser ID: 13766129 Canada 01/22/2013 05:02 AM Report Abusive Post Report Copyright Violation | ...Read all my previous statements. I did not use /, did I? However, like I stated 3 times before this the brackets are juxtaposed next to the 2 to signify it being part of the denominator. Like your link stated, "to clarify." Syrius1. It does not matter what symbol you choose to represent division, the precedence rules always stay the same. The '/' is just a more common choice, perhaps because its more easily typed on a computer. 2. Are you an idiot? Parentheses raise the precedence order for operations found INSIDE the parentheses, not OUTSIDE them! If you truly cannot read and understand the wikipedia quote I gave you properly, then there's just no point discussing with you further. You don't have the necessary brainpower. If you can't bring your Ego to listen to your intellectual superiors here on GLP, bring this question to any professional involved with math, or feed it into calculating programs such as Matlab, Excel, or Mathematica. Perhaps it will sink in then. Anonymous Coward 300884Intellectual superiors don't resort to name calling. That describes people who have ran out of ideas to argue and need justification in its lowest form. You can twist my words; but, at the end of the day the equation I presented and the material that was provided proves beyond a doubt that it can be interpreted in the way I postulated. Run back to your technology and assume the position, sir. Your ego is done. SyriusIntellectual superiors do resort to name calling when fools don't have the good sense of shutting up about things beyond their understanding. Smart people are just human too you know... At the end of the day, you've been kindly corrected over and over in this thread by a lot of knowledgeable people, but you refuse to listen to any of them, because you believe you know best. That's a case of Ego gone horribly wrong. But I will leave this thread now and leave you to your delusions. Anonymous Coward 300884 Typical arrogant yankee know-it-all that knows little. |

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CitizenperthFUKUSHIMA, GLPTARD 24/7/365 User ID: 32253509 Australia 01/22/2013 06:28 AM Report Abusive Post Report Copyright Violation | yeeeeeeeeeeeeeeeeahhhhhhhhhhhhhhhhhh............. 9 It's life as we know it, but only just. My Fukushima Site: [link to citizenperth.wordpress.com] sic ut vos es vos should exsisto , denego alius vicis facio vos change , exsisto youself , proprie GLP's best Fuku thread: Thread: *** Fukushima *** and other nuclear-----updates and links twitter: #citizenperth “If I had an hour to solve a problem and my life depended on it, I would use the first 55 minutes determining the proper question to ask, for once I knew the proper question, I could solve the problem in less than five minutes.” - Albert Einstein |

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ForgottenUser ID: 1448291 United States 01/22/2013 09:39 AM Report Abusive Post Report Copyright Violation | I have shown scientific calculator doing the problem and many other websites and programs doing the problem. All getting 9. Have you shown anything showing an answer of 1? [link to imageshack.us] [link to img255.imageshack.us] [link to vimeo.com (secure)] [link to img339.imageshack.us] Everyone of these websites I typed the equation EXACTLY as the OP had it. Using ÷ not /,x or adding anything after the first 2. Forgotten: Reach me at admin@TheGoldenRuleNow.org |

ForgottenUser ID: 1448291 United States 01/22/2013 09:40 AM Report Abusive Post Report Copyright Violation | |

ForgottenUser ID: 1448291 United States 01/22/2013 09:49 AM Report Abusive Post Report Copyright Violation | i went through it again and i actually now come up with 1. Quoting: Order of operations: Brackets Exponents Division Multiplication Addition Subtraction 6÷2(1+2) = = 6÷2(3) = 3(3) = 1 i respectfully retract my previous answer of 9 i was doing M before D :s Anubis [link to simple.wikipedia.org] Quoting: Solve any multiplication and division in the problem. Quoting: Note that multiplication does not precede division, this is a common mistake while the fact is that they are solved from left to right as they occur.Example: 5 * 4 - 9 / 3 5 * 4 - 9 / 3 20 - 9 / 3 20 - 9 / 3 20 - 3 Article[link to www.purplemath.com] This tells you the ranks of the operations: Parentheses outrank exponents, which outrank multiplication and division (but multiplication and division are at the same rank), and these two outrank addition and subtraction (which are together on the bottom rank). Quoting: When you have a bunch of operations of the same rank, you just operate from left to right. For instance, 15 ÷ 3 × 4 is not 15 ÷ 12, but is rather 5 × 4, because, going from left to right, you get to the division first.Article[link to www.eduplace.com] When children initially learn addition, subtraction, multiplication, and division, they begin by performing operations on two numbers. But what happens when an expression requires multiple operations? Over time, mathematicians have developed a set of rules called the order of operations to determine which operation to do first. The rules are: Quoting: Multiply and divide from left to right. Add and subtract from left to right. ArticleI can show about 50+ more sites that all show this same thing. But I am sure it is all a conspiracy. (We all agree we do parenthesis first... that much I am sure of) Work from left to right when things are equal. Forgotten Forgotten: Reach me at admin@TheGoldenRuleNow.org |

ForgottenUser ID: 1448291 United States 01/22/2013 09:53 AM Report Abusive Post Report Copyright Violation | [link to img255.imageshack.us] Video here show me inputting exactly as OP put it. [link to vimeo.com (secure)] [link to img339.imageshack.us] MULTIPLICATION BEFORE DIVISION Quoting: X=1 MULTIPLICATION BEFORE DIVISION X=1 MULTIPLICATION BEFORE DIVISION X=1 MULTIPLICATION BEFORE DIVISION X=1 MULTIPLICATION BEFORE DIVISION X=1 MULTIPLICATION BEFORE DIVISION X=1 MULTIPLICATION BEFORE DIVISION X=1 MULTIPLICATION BEFORE DIVISION X=1 MULTIPLICATION BEFORE DIVISION X=1 MULTIPLICATION BEFORE DIVISION X=1 MULTIPLICATION BEFORE DIVISION X=1 MULTIPLICATION BEFORE DIVISION X=1 MULTIPLICATION BEFORE DIVISION X=1 MULTIPLICATION BEFORE DIVISION X=1 MULTIPLICATION BEFORE DIVISION X=1 MULTIPLICATION BEFORE DIVISION X=1 Anonymous Coward 9839140 Solve any multiplication and division in the problem. Quoting: Note that multiplication does not precede division, this is a common mistake while the fact is that they are solved from left to right as they occur.Example: 5 * 4 - 9 / 3 5 * 4 - 9 / 3 20 - 9 / 3 20 - 9 / 3 20 - 3 Article[link to www.purplemath.com] This tells you the ranks of the operations: Parentheses outrank exponents, which outrank multiplication and division (but multiplication and division are at the same rank), and these two outrank addition and subtraction (which are together on the bottom rank). Quoting: When you have a bunch of operations of the same rank, you just operate from left to right. For instance, 15 ÷ 3 × 4 is not 15 ÷ 12, but is rather 5 × 4, because, going from left to right, you get to the division first.Article[link to www.eduplace.com] When children initially learn addition, subtraction, multiplication, and division, they begin by performing operations on two numbers. But what happens when an expression requires multiple operations? Over time, mathematicians have developed a set of rules called the order of operations to determine which operation to do first. The rules are: Quoting: Multiply and divide from left to right. Add and subtract from left to right. ArticleI can show about 50+ more sites that all show this same thing. Last Edited by Forgotten on 01/22/2013 09:54 AM Forgotten: Reach me at admin@TheGoldenRuleNow.org |

Anonymous Coward User ID: 24364944 United States 01/22/2013 09:56 AM Report Abusive Post Report Copyright Violation | Still 9. Multiplication DOES NOT come before Division. [link to www.factmonster.com] |

ForgottenUser ID: 1448291 United States 01/22/2013 09:59 AM Report Abusive Post Report Copyright Violation | the input in wolfram alpha is wrong. Quoting: the input I saw used a solidus. However, I used a high powered calculator on an electrical engineering website and that also calculated it wrong. Anonymous Coward 31557420 Check my wolfram image. Input exactly as OP. Cant believe you let Casper's double talk change your mind. Especially after all the proof against 1. Including your own variable work. Every image I put in I used 6÷2(1+2)... exactly. I substituted nothing. [link to imageshack.us] [link to img255.imageshack.us] Video of me doing on scientific calculator. And image to prove it was "scientific". [link to vimeo.com (secure)] [link to img339.imageshack.us] :this^^^: Funny because Syrius, the original poster is actually aruging there is a difference between... 6÷2(1+2) and 6÷2*(1+2)... Which is the weakest argument for 1 in this whole thread. Saying he was showing the 2 up against the parenthesis as indication it was the "denominator". WTF!! Even though it would still be wrong, he would of at least put... 6/2(2+1).... I might of bought his story then. The answer would still be 9, but this thread is getting better and better. OP didnt even know the answer. Last Edited by Forgotten on 01/22/2013 10:04 AM Forgotten: Reach me at admin@TheGoldenRuleNow.org |

ForgottenUser ID: 1448291 United States 01/22/2013 10:13 AM Report Abusive Post Report Copyright Violation | The left to right rule really only applies to division and Quoting: subtraction. This is because they don't satisfy the associative property of equality. To be really precise, it is because we are really "loose" about the definition of subtraction and division. If we define subtraction properly, it is adding by an inverse. For example, (3 - 5) + 7, is really 3 + (-5) + 7. By writing it this way, we can rewrite to get 3 + ((-5)+ 7), since addition is associative. We get the same result as before. The same applies to division. By dividing, we are really multiplying For example 5/3 is really 5 * (1/3). by a multiplicative inverse. Written this way, we can use the associative property. article[link to mathforum.org] Division is the inverse of multiplication. This is why the "left to right" rule is in place. To help people who cant see the inverse. We can get rid of "left to right" by making everything multiplication. See below Which would make this equation. 6 * .5 * (2+1)... this should be really easy for anyone. 6*.5*3=9 Can re-arragne in any order. .5*6*3=9 Can even distribute.6 * .5 * (2+1) 6 (1+.5) 6*1.5 9 Anyone want to argue with this? and multiplicative identity Quoting: (multiplying by 1/3 instead of dividing by 3). articleSo instead of dividing by 2 multiple by .5!!!!! 6/1 ÷ 2/1*(2+1) = 6*.5*(2+1) Last Edited by Forgotten on 01/22/2013 10:19 AM Forgotten: Reach me at admin@TheGoldenRuleNow.org |

caper_26User ID: 32057798 Canada 01/22/2013 12:37 PM Report Abusive Post Report Copyright Violation | I am your college professor that you requested, with a doctorate in Mathematics. I will break this down as simply as possible and end this debate as approx. 10 students have already asked me this today. Quoting: End of debate... hopefully. Anonymous Coward 944253 It would be nice if they looked at all aspects of math before solving. Nice COPY & PASTE from yahoo... On yahoo, I am a space physicist, didn't you know? "I'm trying to free your mind, Neo. But I can only show you the door. You're the one that has to walk through it." |

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