## Math: 6÷2(1+2) = ? | |

Anonymous Coward User ID: 32110288 United States 01/13/2013 11:36 AM Report Abusive Post Report Copyright Violation | Mensa posted this on their FB page about a week ago. I can only assume someone has answered it already but I'll give it a go. Quoting: 6÷2(1+2) = ? 3(1+2) = ? 3(3) = 9 Order of operations are a grade 9 level understanding of math. Person445 Sorry but you divided 6 by 2 before getting rid of the () thus violating the order of operations. Anonymous Coward 28938484 The parenthesis only applies to what is inside of them. |

Patrick BatemanUser ID: 32018985 United States 01/13/2013 11:37 AM Report Abusive Post Report Copyright Violation | If you think the equation should = 9 then it should look like this: Quoting: (6/2)(1+2)= 3*3 =9 but we have: 6/2(1+2)= 6/6 =1 because you do the sum in the bracket first. So the answer is 1. Anonymous Coward 26789708 Correct. Anonymous Coward 29086850 INCORRECT. Anonymous Coward 32110288 It is a poorly written problem in the least needs an extra set of parentheses to get the desired answer. |

Anonymous Coward User ID: 32057798 Canada 01/13/2013 11:37 AM Report Abusive Post Report Copyright Violation | |

Anonymous Coward User ID: 27301486 Germany 01/13/2013 11:39 AM Report Abusive Post Report Copyright Violation | |

Anonymous Coward User ID: 32057798 Canada 01/13/2013 11:39 AM Report Abusive Post Report Copyright Violation | If you think it is NOT 1, PROVE OTHERWISE. Prove that property of distribution is WRONG. Prove that fractions as coefficients do not require ( ). Quoting: Anonymous Coward 32057798 The answer is 9. 6 : 2 x (1+2) = 6 : 2 x 3 = 9 Anonymous Coward 27301486 Why are you inserting a TIMES symbol so you can ignore Distribution? |

Coma Patient #7User ID: 29804770 United States 01/13/2013 11:41 AM Report Abusive Post Report Copyright Violation | A similar debate popped up not that long ago and had people arguing non-stop. Check the reference at the bottom. The real answer is that the equation itself is ambiguous and should have been written better. This equation should have been written as... ( 6 / 2 ) * ( 1 + 2 ) = or 6 / [ 2 ( 1 + 2 ) ] = Using the standardized order of operations... 6 / 2 ( 1 + 2 ) 6 / 2 ( 3 ) or 6 / 2 * 3 Answer = 9 Using parenthetical implications via multiplication by juxtaposition and the distributive property... 6 / 2 ( 1 + 2 ) 6 / [ ( 2 * 1 ) + ( 2 * 2 ) ] 6 / 6 Answer = 1 Both of you are correct. Considering the ambiguity and poor nomenclature of the equation, you should ask whomever posed the problem to define his/her notation preferences. No self-respecting mathematician would write the equation in this manner. Anytime you see ab/cd you will see this disagreement. [link to answers.yahoo.com] Through will of thought we control our emotions and thoughts are often no more difficult to control then we make them to be. |

Patrick BatemanUser ID: 32018985 United States 01/13/2013 11:41 AM Report Abusive Post Report Copyright Violation | If you think it is NOT 1, PROVE OTHERWISE. Prove that property of distribution is WRONG. Prove that fractions as coefficients do not require ( ). Quoting: Anonymous Coward 32057798 I agree, but also still believe it is a flawed problem, and could be argued each way. But from what I have been taught, the answer would be 1. Lol, I debated many people about this about 100 pages and a year or so ago in this thread, lol. Last Edited by Patrick Bateman on 01/13/2013 11:41 AM |

Patrick BatemanUser ID: 32018985 United States 01/13/2013 11:41 AM Report Abusive Post Report Copyright Violation | The answer has been stated, it can be either because it's poorly stated. Here's one of the better explanations I've read, copy/paste. Quoting: A similar debate popped up not that long ago and had people arguing non-stop. Check the reference at the bottom. The real answer is that the equation itself is ambiguous and should have been written better. This equation should have been written as... ( 6 / 2 ) * ( 1 + 2 ) = or 6 / [ 2 ( 1 + 2 ) ] = Using the standardized order of operations... 6 / 2 ( 1 + 2 ) 6 / 2 ( 3 ) or 6 / 2 * 3 Answer = 9 Using parenthetical implications via multiplication by juxtaposition and the distributive property... 6 / 2 ( 1 + 2 ) 6 / [ ( 2 * 1 ) + ( 2 * 2 ) ] 6 / 6 Answer = 1 Both of you are correct. Considering the ambiguity and poor nomenclature of the equation, you should ask whomever posed the problem to define his/her notation preferences. No self-respecting mathematician would write the equation in this manner. Anytime you see ab/cd you will see this disagreement. [link to answers.yahoo.com] Coma Patient #7 Exactly! |

Anonymous Coward User ID: 27301486 Germany 01/13/2013 11:42 AM Report Abusive Post Report Copyright Violation | If you think it is NOT 1, PROVE OTHERWISE. Prove that property of distribution is WRONG. Prove that fractions as coefficients do not require ( ). Quoting: Anonymous Coward 32057798 The answer is 9. 6 : 2 x (1+2) = 6 : 2 x 3 = 9 Anonymous Coward 27301486 Why are you inserting a TIMES symbol so you can ignore Distribution? Anonymous Coward 32057798 Because that is what it means. 2(1+2) = 2 x (1+2) |

Anonymous Coward User ID: 32057798 Canada 01/13/2013 11:53 AM Report Abusive Post Report Copyright Violation | That does NOT exempt you from applying distribution OR removing parentheses first. Has NO ONE seen ANY of these references??!?!?!? Distribute BEFORE "pedmas" used to REMOVE parentheses too: [link to www.algebra.com] Get Rid of parentheses with Distribution: [link to www.helpalgebra.com] If there is some factor multiplying the parentheses, then the only way to get rid of the parentheses is to multiply using the distributive law. [link to www.jamesbrennan.org] "When simplifying expressions with parentheses, you will be applying the Distributive Property." -purplemath |

Anonymous Coward User ID: 32057798 Canada 01/13/2013 11:56 AM Report Abusive Post Report Copyright Violation | |

Anonymous Coward User ID: 27301486 Germany 01/13/2013 11:58 AM Report Abusive Post Report Copyright Violation | That does NOT exempt you from applying distribution OR removing parentheses first. Has NO ONE seen ANY of these references??!?!?!? Distribute BEFORE "pedmas" used to REMOVE parentheses too: [link to www.algebra.com] Get Rid of parentheses with Distribution: [link to www.helpalgebra.com] If there is some factor multiplying the parentheses, then the only way to get rid of the parentheses is to multiply using the distributive law. [link to www.jamesbrennan.org] "When simplifying expressions with parentheses, you will be applying the Distributive Property." -purplemath Anonymous Coward 32057798 The factor multiplaying the paranthesis is 3. 6 ÷ 2 x (1+2) = 3 x (1+2) = 3 x (1) + 3 x (2) = 9 |

Anonymous Coward User ID: 1428208 United States 01/13/2013 12:04 PM Report Abusive Post Report Copyright Violation | |

Anonymous Coward User ID: 32057798 Canada 01/13/2013 12:04 PM Report Abusive Post Report Copyright Violation | The factor multiplaying the paranthesis is 3. Quoting: 6 ÷ 2 x (1+2) = 3 x (1+2) = 3 x (1) + 3 x (2) = 9 Anonymous Coward 27301486 Do you SEE any parentheses around 6/2 ?? NO ! Parentheses are FIRST in the order of operations, not DIVISION, so if you want to distribute, you do that first! Since when is 6÷2 ever factored from a set of terms?? Distribution is factoring in reverse. You to get a handle on other concepts to solve this equation properly. (4+2) = 2(2+1) If you want to say this: (6 + 3) = 3(2+1) = (6/2)*(2+1) you REQUIRE parentheses. Open any book on online PDF math books... they ALL say this. |

Anonymous Coward User ID: 32057798 Canada 01/13/2013 12:07 PM Report Abusive Post Report Copyright Violation | Yes, but you didn't do step 1. So before anyone else says "Wrong" you may want to actually read something and educate yourself, and then prove ALL of the following references incorrect. See below: --------------------------- [link to en.wikibooks.org] "We use the distributive property to help us find a way around the order of operations while still being sure that we keep the value of the expression." Distribute to REMOVE parentheses [link to www.algebra.com] Get Rid of parentheses with Distribution: [link to www.helpalgebra.com] If there is some factor multiplying the parentheses, then the only way to get rid of the parentheses is to multiply using the distributive law. [link to www.jamesbrennan.org] "When simplifying expressions with parentheses, you will be applying the Distributive Property." -purplemath These guys got it right, they use "Parentheses" in the order of operations to require Distributive Property. Ref: Purplemath The Distributive Property in ALgebra: The Distributive Property is handy to help you get rid of parentheses. a(b + c) = ab + ac [link to math.about.com] |

Anonymous Coward User ID: 27301486 Germany 01/13/2013 12:09 PM Report Abusive Post Report Copyright Violation | |

Anonymous Coward User ID: 32057798 Canada 01/13/2013 12:10 PM Report Abusive Post Report Copyright Violation | |

Anonymous Coward User ID: 27301486 Germany 01/13/2013 12:11 PM Report Abusive Post Report Copyright Violation | Parentheses are FIRST in the order of operations, not DIVISION, so if you want to distribute, you do that first! Quoting: Anonymous Coward 32057798 Then you have: 6 ÷ 2 x (1+2) = 6 ÷ 2 x 3 = 3 x 3 = 9 Anonymous Coward 27301486 WRONG. I proved that already. Anyone else? Anonymous Coward 32057798 It's correct. Where is it wrong? |

Anonymous Coward User ID: 27301486 Germany 01/13/2013 12:11 PM Report Abusive Post Report Copyright Violation | Parentheses are FIRST in the order of operations, not DIVISION, so if you want to distribute, you do that first! Quoting: Anonymous Coward 32057798 Then you have: 6 ÷ 2 x (1+2) = 6 ÷ 2 x 3 = 3 x 3 = 9 Anonymous Coward 27301486 WRONG. I proved that already. Anyone else? Anonymous Coward 32057798 I just applied your own rule, can you not see that? |

Anonymous Coward User ID: 13045367 Netherlands 01/13/2013 12:12 PM Report Abusive Post Report Copyright Violation | Casio says 1, en Texas Instruments says 9. It is nine. That's just 3 because 1 +2 1 +2 brackets. So we have: 6 ÷ 2 x 3 Multiplication and division is on a par in terms of priority calculations, because a division does not actually exist: a division by two is a multiplication by 1/2. A multiplication therefore has no priority for a division, as this is the case at a summation. 2 + 3 X 5 = 17. Given multiplication and division rank equally, they are just left to right. So first 6/2 gives 3 times 3 is 9 and that In order to get to 1 you should depart from that rule and that can only by EXTRA parentheses to insert: 6 ÷ (2 x 3) as one would give. |

Anonymous Coward User ID: 32057798 Canada 01/13/2013 12:13 PM Report Abusive Post Report Copyright Violation | |

Anonymous Coward User ID: 32057798 Canada 01/13/2013 12:14 PM Report Abusive Post Report Copyright Violation | Casio says 1, en Texas Instruments says 9. Quoting: It is nine. That's just 3 because 1 +2 1 +2 brackets. So we have: 6 ÷ 2 x 3 Multiplication and division is on a par in terms of priority calculations, because a division does not actually exist: a division by two is a multiplication by 1/2. A multiplication therefore has no priority for a division, as this is the case at a summation. 2 + 3 X 5 = 17. Given multiplication and division rank equally, they are just left to right. So first 6/2 gives 3 times 3 is 9 and that In order to get to 1 you should depart from that rule and that can only by EXTRA parentheses to insert: 6 ÷ (2 x 3) as one would give. Anonymous Coward 13045367 You didn't eliminate parentheses properly, Read the above post with 5 or so references to the proper way of doing math. |

Anonymous Coward User ID: 9645738 United States 01/13/2013 12:14 PM Report Abusive Post Report Copyright Violation | |

Anonymous Coward User ID: 27301486 Germany 01/13/2013 12:15 PM Report Abusive Post Report Copyright Violation | Casio says 1, en Texas Instruments says 9. Quoting: It is nine. That's just 3 because 1 +2 1 +2 brackets. So we have: 6 ÷ 2 x 3 Multiplication and division is on a par in terms of priority calculations, because a division does not actually exist: a division by two is a multiplication by 1/2. A multiplication therefore has no priority for a division, as this is the case at a summation. 2 + 3 X 5 = 17. Given multiplication and division rank equally, they are just left to right. So first 6/2 gives 3 times 3 is 9 and that In order to get to 1 you should depart from that rule and that can only by EXTRA parentheses to insert: 6 ÷ (2 x 3) as one would give. Anonymous Coward 13045367 You didn't eliminate parentheses properly, Read the above post with 5 or so references to the proper way of doing math. Anonymous Coward 32057798 You do not apply your own rules properly, that is where your confusion comes from. |

Anonymous Coward User ID: 13045367 Netherlands 01/13/2013 12:15 PM Report Abusive Post Report Copyright Violation | It is nine. That's just 3 because 1 +2 1 +2 brackets. So we have: 6 ÷ 2 x 3 Multiplication and division is on a par in terms of priority calculations, because a division does not actually exist: a division by two is a multiplication by 1/2. A multiplication therefore has no priority for a division, as this is the case at a summation. 2 + 3 X 5 = 17. Given multiplication and division rank equally, they are just left to right. So first 6/2 gives 3 times 3 is 9 and that In order to get to 1 you should depart from that rule and that can only by EXTRA parentheses to insert: 6 ÷ (2 x 3) as one would give. Anonymous Coward 13045367 You didn't eliminate parentheses properly, Read the above post with 5 or so references to the proper way of doing math. Anonymous Coward 32057798 It's the answer from an einstein proffessor in math so dont act you are right. |

Anonymous Coward User ID: 32057798 Canada 01/13/2013 12:16 PM Report Abusive Post Report Copyright Violation | |

Anonymous Coward User ID: 32057798 Canada 01/13/2013 12:16 PM Report Abusive Post Report Copyright Violation | Here you go...in BLUE. Yes, but you didn't do step 1. So before anyone else says "Wrong" you may want to actually read something and educate yourself, and then prove ALL of the following references incorrect. See below: --------------------------- [link to en.wikibooks.org] "We use the distributive property to help us find a way around the order of operations while still being sure that we keep the value of the expression." Distribute to REMOVE parentheses [link to www.algebra.com] Get Rid of parentheses with Distribution: [link to www.helpalgebra.com] If there is some factor multiplying the parentheses, then the only way to get rid of the parentheses is to multiply using the distributive law. [link to www.jamesbrennan.org] "When simplifying expressions with parentheses, you will be applying the Distributive Property." -purplemath These guys got it right, they use "Parentheses" in the order of operations to require Distributive Property. Ref: Purplemath The Distributive Property in ALgebra: The Distributive Property is handy to help you get rid of parentheses. a(b + c) = ab + ac [link to math.about.com] Anonymous Coward 32057798 |

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Anonymous Coward User ID: 32057798 Canada 01/13/2013 12:17 PM Report Abusive Post Report Copyright Violation | |

Anonymous Coward User ID: 32057798 Canada 01/13/2013 12:18 PM Report Abusive Post Report Copyright Violation | |