## Math: 6÷2(1+2) = ? | |

Anonymous Coward User ID: 32057798 Canada 01/17/2013 10:15 PM Report Abusive Post Report Copyright Violation | Look at any book. All fractions used as coefficients use 6n2 or (6/2)n therefore, to distribute 6/2, you would NEED parentheses around it. Otherwise, you distribute the 2 into the parentheses, which is called "Eliminating parentheses by distribution". It is not performing multiplication operator, since it is a "property" of math, ie, equality, and you are REPLACING, not multiplying. This is where other people are confused. They think "distributive property" is bound to the order of operations as part of multiplication. It is not. So, What do we have? 2(2+1) is 2 quantities, or groups, of 2+1. In English, "I have 2 bags, with 2 apples and 1 orange in each bag." ie, 6 pieces of fruit. Therefore 2(2+1) = [(2+1) + (2+1)] 6 ÷ [(2+1) + (2+1)] = 1 Ans: 1 Back to 6 ÷ 2n = 3/n. n = 2+1. Ans: 1 again. Distribute: 6 ÷ 2(2+1) = 6 ÷ [2(2) + 2(1)] 6 ÷ 6 = 1 If I add the 2+1 first, i STILL have to distribute, using the Identity Law of a+0 = a 6 ÷ 2(2+1) = 6 ÷ 2(3) = Here, I still have parentheses with a coefficient, so I can still distribute like this: 6 ÷ 2(3 + 0) Here I used the identity law to make it clear 6 ÷ [2(3) + 2(0)] 6 ÷ 6 = 1 No matter what math laws, rules, axioms, or properties are used, you always get ONE if you apply the rules correctly, which is the great thing about math, there is only ONE correct answer for simple equations like this one. |

Anonymous Coward User ID: 31557420 United States 01/17/2013 10:16 PM Report Abusive Post Report Copyright Violation | Number 3 is very easy. I am just dumb and over thought it. I will redo #2 completely instead of just correcting my old work. Quoting: x=1/4y^2-5y Anonymous Coward 31557420 yeah, that's it. Now solve: 6 ÷ 2n = ? Anonymous Coward 32057798 6/2n=? 6=?(2n) [Multiply both sides of equation by 2n] 1=?(2n)/6 [divide both sides of equation by 6] 1=?(2X3)/6 [here is where the raw logic comes it] 1=?(6/6) 1=? n=3 Now, verifying we re enter the numbers into the original equation 6/2n =? 6/(2X3)=1 6/6=1 Have a nice day and suck my balls, asshole. There is NO other correct answer to this question and the fact that it has unknowns on both sides of the equation DOES NOT preclude it's being solved using simple logic. Anonymous Astrophysicist 1492235 n= 1/3 Is the correct way to solve for n... |

Anonymous Coward User ID: 32057798 Canada 01/17/2013 10:18 PM Report Abusive Post Report Copyright Violation | The reason I am doing it differently than I solved the algebra problems, is because I am solving this correctly. Quoting: you cannot treat everything that comes after a ÷ as a denominator of a fraction....Luckily for me, in my schooling, my teachers never used a ÷ but just wrote out the fractions. I didn't become aware that teachers were writing out a ÷ expecting their students to treat it as a fraction... The answer is 9, always will be. I am sorry you cannot learn new things and are so deadset in your ways. Anonymous Coward 31557420 Well, let me refresh your memory on that one: [link to cstl.syr.edu] This is how you do algebra without calculators. |

Anonymous Coward User ID: 31557420 United States 01/17/2013 10:22 PM Report Abusive Post Report Copyright Violation | Look at any book. All fractions used as coefficients use Quoting: 6n2 or (6/2)n therefore, to distribute 6/2, you would NEED parentheses around it. Otherwise, you distribute the 2 into the parentheses, which is called "Eliminating parentheses by distribution". It is not performing multiplication operator, since it is a "property" of math, ie, equality, and you are REPLACING, not multiplying. This is where other people are confused. They think "distributive property" is bound to the order of operations as part of multiplication. It is not. So, What do we have? 2(2+1) is 2 quantities, or groups, of 2+1. In English, "I have 2 bags, with 2 apples and 1 orange in each bag." ie, 6 pieces of fruit. Therefore 2(2+1) = [(2+1) + (2+1)] 6 ÷ [(2+1) + (2+1)] = 1 Ans: 1 Back to 6 ÷ 2n = 3/n. n = 2+1. Ans: 1 again. Distribute: 6 ÷ 2(2+1) = 6 ÷ [2(2) + 2(1)] 6 ÷ 6 = 1 If I add the 2+1 first, i STILL have to distribute, using the Identity Law of a+0 = a 6 ÷ 2(2+1) = 6 ÷ 2(3) = Here, I still have parentheses with a coefficient, so I can still distribute like this: 6 ÷ 2(3 + 0) Here I used the identity law to make it clear 6 ÷ [2(3) + 2(0)] 6 ÷ 6 = 1 No matter what math laws, rules, axioms, or properties are used, you always get ONE if you apply the rules correctly, which is the great thing about math, there is only ONE correct answer for simple equations like this one.Anonymous Coward 32057798 6÷2(1+n) When you want to eliminate the parentheses by distribution, are you first going to distribute the 2 or divide 6 by 2? obviously divide 6 by 2. Now why would you put the (1+n) in the denominator? If it is supposed to be there it should be written there in a fraction or be power to ^-1 |

Anonymous Coward User ID: 32057798 Canada 01/17/2013 10:22 PM Report Abusive Post Report Copyright Violation | That, in a properly normalized and fully expanded form is: Quoting: 6÷2*(1+2)=y Anonymous Coward 18119934 I noticed how you changed the equation so that it equals 9. I am not arguing that 6 ÷ 2 TIMES (1+2) = 9, because it does. 6 ÷ 2 * n = 3n6 ÷ 2n = 3/n a ÷ 1 * a = a^2 a ÷ 1a = 1 If anyone here thinks a ÷ 1a = a^2, you fail not only at math, but in life, because not only does the math work, so does common sense. |

Anonymous Coward User ID: 32057798 Canada 01/17/2013 10:26 PM Report Abusive Post Report Copyright Violation | 6/2n=? Quoting: 6=?(2n) [Multiply both sides of equation by 2n] 1=?(2n)/6 [divide both sides of equation by 6] 1=?(2X3)/6 [here is where the raw logic comes it] 1=?(6/6) 1=? n=3 Now, verifying we re enter the numbers into the original equation 6/2n =? 6/(2X3)=1 6/6=1 Have a nice day and suck my balls, asshole. There is NO other correct answer to this question and the fact that it has unknowns on both sides of the equation DOES NOT preclude it's being solved using simple logic. Anonymous Astrophysicist 1492235 I am confused. You proved me correct. n = 3 = 2 + 1 Answer = 1, also correct Why did you tell me to suck your nutsac ? |

Anonymous Coward User ID: 32057798 Canada 01/17/2013 10:29 PM Report Abusive Post Report Copyright Violation | |

Anonymous Coward User ID: 31557420 United States 01/17/2013 10:29 PM Report Abusive Post Report Copyright Violation | The reason I am doing it differently than I solved the algebra problems, is because I am solving this correctly. Quoting: you cannot treat everything that comes after a ÷ as a denominator of a fraction....Luckily for me, in my schooling, my teachers never used a ÷ but just wrote out the fractions. I didn't become aware that teachers were writing out a ÷ expecting their students to treat it as a fraction... The answer is 9, always will be. I am sorry you cannot learn new things and are so deadset in your ways. Anonymous Coward 31557420 Well, let me refresh your memory on that one: [link to cstl.syr.edu] This is how you do algebra without calculators. Anonymous Coward 32057798 You have a point, that is how it is always... now I think it has been erroneously so... obviously that seems very unlikely now doesn't it? I need to speak with someone with a PhD in mathematics... I am calling my friend. |

Anonymous Coward User ID: 31557420 United States 01/17/2013 10:30 PM Report Abusive Post Report Copyright Violation | No. You need n to = 1/3 to make your equation work. But you cant show a valid proof. Anyone can type horseshit, but horsepucky is still an F-, yeah that's right, not just an F, but an F- Anonymous Coward 32057798 You know what I am doing. I already wrote it out. You think I am wrong but you know how I got there... |

fnord User ID: 32102656 United States 01/17/2013 10:33 PM Report Abusive Post Report Copyright Violation | Look at any book. All fractions used as coefficients use Quoting: 6n2 or (6/2)n therefore, to distribute 6/2, you would NEED parentheses around it. Otherwise, you distribute the 2 into the parentheses, which is called "Eliminating parentheses by distribution". It is not performing multiplication operator, since it is a "property" of math, ie, equality, and you are REPLACING, not multiplying. This is where other people are confused. They think "distributive property" is bound to the order of operations as part of multiplication. It is not. So, What do we have? 2(2+1) is 2 quantities, or groups, of 2+1. In English, "I have 2 bags, with 2 apples and 1 orange in each bag." ie, 6 pieces of fruit. Therefore 2(2+1) = [(2+1) + (2+1)] 6 ÷ [(2+1) + (2+1)] = 1 Ans: 1 Back to 6 ÷ 2n = 3/n. n = 2+1. Ans: 1 again. Distribute: 6 ÷ 2(2+1) = 6 ÷ [2(2) + 2(1)] 6 ÷ 6 = 1 If I add the 2+1 first, i STILL have to distribute, using the Identity Law of a+0 = a 6 ÷ 2(2+1) = 6 ÷ 2(3) = Here, I still have parentheses with a coefficient, so I can still distribute like this: 6 ÷ 2(3 + 0) Here I used the identity law to make it clear 6 ÷ [2(3) + 2(0)] 6 ÷ 6 = 1 No matter what math laws, rules, axioms, or properties are used, you always get ONE if you apply the rules correctly, which is the great thing about math, there is only ONE correct answer for simple equations like this one.Anonymous Coward 32057798 The answer depends not only upon the relative precedence of multiplication/division, parenthesation, and addition/subtraction, but also on whether a left to right rule is in force in the evaluation of operations of the same precedence. For instance, if one assumes that operations of the same precedence are evaluated left to right, and parenthesized expressions are evaluated first, the evaluation proceeds as: 6/2(2+1)=3*(2+1)=3*3=9 If operations of the same precedence are evaluated right to left, and parenthesized expressions are evaluated first, the evaluation proceeds as: 6/2*(2+1) = 6/2*3 = 6/6 = 1 |

Anonymous Astrophysicist User ID: 1492235 United States 01/17/2013 10:34 PM Report Abusive Post Report Copyright Violation | Number 3 is very easy. I am just dumb and over thought it. I will redo #2 completely instead of just correcting my old work. Quoting: x=1/4y^2-5y Anonymous Coward 31557420 yeah, that's it. Now solve: 6 ÷ 2n = ? Anonymous Coward 32057798 6/2n=? 6=?(2n) [Multiply both sides of equation by 2n] 1=?(2n)/6 [divide both sides of equation by 6] 1=?(2X3)/6 [here is where the raw logic comes it] 1=?(6/6) 1=? n=3 Now, verifying we re enter the numbers into the original equation 6/2n =? 6/(2X3)=1 6/6=1 Have a nice day and suck my balls, asshole. There is NO other correct answer to this question and the fact that it has unknowns on both sides of the equation DOES NOT preclude it's being solved using simple logic. Anonymous Astrophysicist 1492235 Actually one could get two separate and correct answers for this equation entering two values for n and getting a different integer value for ? To explain instance, if n was =1 ,? would be =3 (integer, correct solution) and if n=2 , ? =1.5 (incorrect solution)and if n=3 ,? =1(correct solution), if n=4 then ?= 6/8 (incorrect solution) , if n=5 then ? =6/10 (incorrect solution and simply results in a smaller fraction for the value of ? (or decimal) the larger the value if n gets. For instance, if n=6 ,? =1/2, and if n=7 ?= 3/7 and if n=8 ? = 3/8 , so there are actually two solutions which result in integers as results for both ? and m[/b[, if n=1, ?= 3 and if n=3, ?=1. There are two solutions but it IS NOT a linear equation nor is able to be plotted since no answer besides 1 or 3 for ? results in an integer for n |

Anonymous Astrophysicist User ID: 1492235 United States 01/17/2013 10:35 PM Report Abusive Post Report Copyright Violation | 6/2n=? Quoting: 6=?(2n) [Multiply both sides of equation by 2n] 1=?(2n)/6 [divide both sides of equation by 6] 1=?(2X3)/6 [here is where the raw logic comes it] 1=?(6/6) 1=? n=3 Now, verifying we re enter the numbers into the original equation 6/2n =? 6/(2X3)=1 6/6=1 Have a nice day and suck my balls, asshole. There is NO other correct answer to this question and the fact that it has unknowns on both sides of the equation DOES NOT preclude it's being solved using simple logic. Anonymous Astrophysicist 1492235 I am confused. You proved me correct. n = 3 = 2 + 1 Answer = 1, also correct Why did you tell me to suck your nutsac ? Anonymous Coward 32057798 I wasn't talking to you, I hate math. There are actually two answers , see my last post |

Anonymous Coward User ID: 32057798 Canada 01/17/2013 10:37 PM Report Abusive Post Report Copyright Violation | Also folks nowadays think they must convert into operators, such as 2n = 2*n Well, 2n is a single unit, and yes, it is evaluated as 2 * n, however, it is STILL a single unit, and must be treated like the following: 2n = (2n) = (2*n) 2 is a quantity here. I have 2 n's. Like 2 cars. I don't say " I have 2 times cars" A carton of eggs, or a dozen eggs: 12 eggs. A mole of carbon: 6.022x10^23 atoms 24g ÷ 1mole of carbon 24g ÷ 6.022x10^23 and NOT (24 ÷ 6.022) x 10^23 |

Anonymous Astrophysicist User ID: 1492235 United States 01/17/2013 10:38 PM Report Abusive Post Report Copyright Violation | Number 3 is very easy. I am just dumb and over thought it. I will redo #2 completely instead of just correcting my old work. Quoting: x=1/4y^2-5y Anonymous Coward 31557420 yeah, that's it. Now solve: 6 ÷ 2n = ? Anonymous Coward 32057798 6/2n=? 6=?(2n) [Multiply both sides of equation by 2n] 1=?(2n)/6 [divide both sides of equation by 6] 1=?(2X3)/6 [here is where the raw logic comes it] 1=?(6/6) 1=? n=3 Now, verifying we re enter the numbers into the original equation 6/2n =? 6/(2X3)=1 6/6=1 Have a nice day and suck my balls, asshole. There is NO other correct answer to this question and the fact that it has unknowns on both sides of the equation DOES NOT preclude it's being solved using simple logic. Anonymous Astrophysicist 1492235 n= 1/3 Is the correct way to solve for n... Anonymous Coward 31557420 HORSE PATTIES |

Anonymous Coward User ID: 32057798 Canada 01/17/2013 10:38 PM Report Abusive Post Report Copyright Violation | |

Anonymous Coward User ID: 31557420 United States 01/17/2013 10:39 PM Report Abusive Post Report Copyright Violation | 6/2n=? Quoting: 6=?(2n) [Multiply both sides of equation by 2n] 1=?(2n)/6 [divide both sides of equation by 6] 1=?(2X3)/6 [here is where the raw logic comes it] 1=?(6/6) 1=? n=3 Now, verifying we re enter the numbers into the original equation 6/2n =? 6/(2X3)=1 6/6=1 Have a nice day and suck my balls, asshole. There is NO other correct answer to this question and the fact that it has unknowns on both sides of the equation DOES NOT preclude it's being solved using simple logic. Anonymous Astrophysicist 1492235 I am confused. You proved me correct. n = 3 = 2 + 1 Answer = 1, also correct Why did you tell me to suck your nutsac ? Anonymous Coward 32057798 I wasn't talking to you, I hate math. There are actually two answers , see my last post Anonymous Astrophysicist 1492235 No there are not. I am either right, or he is. And considering Occam's razor that means he probably is... There would have had to have been too many math professors writing problems on worksheets wrong. Unless it is only because you treat variables wrong, treat them with implied parentheses... which we actually do, you can't separate the coefficient of an x variable and multiply it with the coefficient of a y variable even when they are in the same factor... |

Anonymous Coward User ID: 31557420 United States 01/17/2013 10:42 PM Report Abusive Post Report Copyright Violation | |

Anonymous Coward User ID: 32057798 Canada 01/17/2013 10:42 PM Report Abusive Post Report Copyright Violation | 6÷2(1+n) When you want to eliminate the parentheses by distribution, are you first going to distribute the 2 or divide 6 by 2? obviously divide 6 by 2. Quoting: Now why would you put the (1+n) in the denominator? If it is supposed to be there it should be written there in a fraction or be power to ^-1 Anonymous Coward 31557420 Can you read? I explained why you cannot divide first. It is on the right side of the obelus, hence it ALREADY IS ^-1 Do I have to show you the math basics too?? 6 ÷ 2n = 6 * (2n)^-1 If I wanted (2+1) to be in the numerator, I would write: 6(2+1)÷2 How basic is that? |

Anonymous Coward User ID: 31557420 United States 01/17/2013 10:43 PM Report Abusive Post Report Copyright Violation | Also folks nowadays think they must convert into operators, such as 2n = 2*n Quoting: Well, 2n is a single unit, and yes, it is evaluated as 2 * n, however, it is STILL a single unit, and must be treated like the following: 2n = (2n) = (2*n) 2 is a quantity here. I have 2 n's. Like 2 cars. I don't say " I have 2 times cars" A carton of eggs, or a dozen eggs: 12 eggs. A mole of carbon: 6.022x10^23 atoms 24g ÷ 1mole of carbon 24g ÷ 6.022x10^23 and NOT (24 ÷ 6.022) x 10^23 Anonymous Coward 32057798 Yes, agreed 100% with you here. As I said variables have implied parentheses. |

Anonymous Coward User ID: 32057798 Canada 01/17/2013 10:44 PM Report Abusive Post Report Copyright Violation | |

Anonymous Coward User ID: 31557420 United States 01/17/2013 10:47 PM Report Abusive Post Report Copyright Violation | 6÷2(1+n) When you want to eliminate the parentheses by distribution, are you first going to distribute the 2 or divide 6 by 2? obviously divide 6 by 2. Quoting: Now why would you put the (1+n) in the denominator? If it is supposed to be there it should be written there in a fraction or be power to ^-1 Anonymous Coward 31557420 Can you read? I explained why you cannot divide first. It is on the right side of the obelus, hence it ALREADY IS ^-1 Do I have to show you the math basics too?? 6 ÷ 2n = 6 * (2n)^-1 If I wanted (2+1) to be in the numerator, I would write: 6(2+1)÷2 How basic is that? Anonymous Coward 32057798 This is exactly what we are arguing over here: [link to www.matthewcompher.com] |

Anonymous Coward User ID: 32424557 Australia 01/17/2013 10:50 PM Report Abusive Post Report Copyright Violation | I bet none of you half wits can do any of these 3 simple algebra equations: Quoting: [link to i50.tinypic.com] Anonymous Coward 32057798 Here is what I got: 1. 9y^2 z^6/x^2 (that's meant to be fraction, as in it's over x^2) 2. 17a^2 b^2 x 3. x = 1/4y2 + y |

Anonymous Coward User ID: 31557420 United States 01/17/2013 10:51 PM Report Abusive Post Report Copyright Violation | 6÷2(1+n) When you want to eliminate the parentheses by distribution, are you first going to distribute the 2 or divide 6 by 2? obviously divide 6 by 2. Quoting: Now why would you put the (1+n) in the denominator? If it is supposed to be there it should be written there in a fraction or be power to ^-1 Anonymous Coward 31557420 Can you read? I explained why you cannot divide first. It is on the right side of the obelus, hence it ALREADY IS ^-1 Do I have to show you the math basics too?? 6 ÷ 2n = 6 * (2n)^-1 If I wanted (2+1) to be in the numerator, I would write: 6(2+1)÷2 How basic is that? Anonymous Coward 32057798 This is exactly what we are arguing over here: [link to www.matthewcompher.com] Anonymous Coward 31557420 You read it yet? |

Anonymous Coward User ID: 32057798 Canada 01/17/2013 10:53 PM Report Abusive Post Report Copyright Violation | You have a point, that is how it is always... now I think it has been erroneously so... obviously that seems very unlikely now doesn't it? Quoting: I need to speak with someone with a PhD in mathematics... I am calling my friend. Anonymous Coward 31557420 The best fighter pilots in the world make mistakes. The smartest people in the world make errors. Don't let one PhD convince you his answer is the "right" one. There are several Doctorates still debating this very thing. Trust me. Again, don't think of it how you should enter it into a calculator. That said, even wolfram knows 2n/2n = 1 and 6/2n = 3/n, but then it doesn't know how to properly substitute 2+1 for n. That is because you can't teach logic to computers. Once they are programmed, they will parse a certain way. That said, I see you are now second guessing yourself. That, my friend, takes balls. You have the biggest balls here, for 2 reasons: 1 - admitting you could be wrong 2 - researching more to educate yourself The rest of these guys that refuse to read any further than their own nose, could learn something from you. |

Anonymous Coward User ID: 18119934 Canada 01/17/2013 10:54 PM Report Abusive Post Report Copyright Violation | [link to www.basic-mathematics.com] Copy and paste it into this math solver webpage. See what the computer tells you the answer is. 6÷2(1+2)=y You could sub all of these for variables: 6÷2*(1+2)=y You always do bracket first (that IS the rules). Thus it becomes: 6÷2*(3)=y 6÷2*3=y I think we can all agree on that. OK............. Now let's sub these with some variables: 6÷2*3=y n will now mean 3: 6÷2*n=y Which becomes: 6÷2n=y Let's rearrange to put all variable on one side. 6=2ny Now let's solve for ny 6÷2=ny 3=ny Now let's swap n back with a 3. 3=3y Now let's solve for y. 3=3y 3÷3=y 1=y I still get my same answer (because I followed the proper math-rules). |

Anonymous Coward User ID: 32057798 Canada 01/17/2013 10:56 PM Report Abusive Post Report Copyright Violation | I will read it in a sec. I have researched the exact meaning of the obelus, depicted here: [link to www.freeimagehosting.net] It was used as a grouping symbol. Not that is applies anymore, it was first used like this: 6 ÷ 2 + 1 really meant 6 ÷ (2+1). neither here nor there, but I thought you would find that interesting, i guess. |

Anonymous Coward User ID: 18119934 Canada 01/17/2013 10:56 PM Report Abusive Post Report Copyright Violation | |

fnord User ID: 32102656 United States 01/17/2013 10:58 PM Report Abusive Post Report Copyright Violation | If simple arithmetic is a subject of such controversy, how can we hope to have any rational basis for agreement on any other thought processes? Logical reasoning is useful for a lot of things, but not for deciding what is right or wrong, or true or false. Those decisions must be made by the whole being, in context with the whole Universe. |

Anonymous Coward User ID: 31557420 United States 01/17/2013 11:01 PM Report Abusive Post Report Copyright Violation | I will read it in a sec. I have researched the exact meaning of the obelus, depicted here: [link to www.freeimagehosting.net] It was used as a grouping symbol. Not that is applies anymore, it was first used like this: 6 ÷ 2 + 1 really meant 6 ÷ (2+1). neither here nor there, but I thought you would find that interesting, i guess. Anonymous Coward 32057798 I do, and you are right. But it is here and there lol... You are right. I was wrong. My TI83 is wrong, wolfram alpha is wrong... Do you have a source for that image? |

Anonymous Coward User ID: 32057798 Canada 01/17/2013 11:03 PM Report Abusive Post Report Copyright Violation | That is hilarious. He referenced the exact page of the book I found earlier this week. But again, if you go back to that algebra page I gave you, we group variables together, and even YOU did those math equations using those very same rules, yet you are using a different 'rule' to get your 9, therefore, contradicting yourself. Anyway, I gotta run for now. Sorry for a few snappy remarks at you earlier, I thought you were one of the other guys trolling, then I realized it was you after I replied :D |

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