




Joined: Oct 2010
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BellaOnline Editor Renaissance Human

BellaOnline Editor Renaissance Human
Joined: Oct 2010
Posts: 11,813 
Re: 6ï¿½2(1+2)=? I believe that using the order of operations, the answer would be 9. PEMDAS (some say GEMDASG standing for grouping symbols) says that the order of operations = parenthesis, exponents, multiplications OR divisionsleft to rightwhichever comes first, finally additions OR subtractions left to rightwhichever comes first.
Beetlemess is right. The other ways of working it out, like the one on Facebook have mathematical flaws. They do not really follow the order of operations. There's a bit of math sleight of hand going on. Beetlemess elegantly listed all of the steps and reasons why it should be worked so that the answer is 9.
Tina, the Facebook thing is just not correct math. "If it were written 6 / 2 x 3 the answer would be 9 but if the 3 were an x and it were written 6/2x, the answer would be 1."
6/2 = 3 and 3*x = 3x it does not equal 1 As a variable, x could equal any number. if you had 3x/3x that would equal 1.
Some people think that PEMDAS means you do the multiplication first. Those folks would think that they would do the 2 * 3 first and then divide by 6. That would give them 1, but it would be incorrect.
The distributive property does need to be taken into account. However, first do what is in the parenthesis. Then, the division is completed. After that, you distribute the 3 times the 3 for an answer of 9.
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Joined: Apr 2011
Posts: 4
Newbie

Newbie
Joined: Apr 2011
Posts: 4 
Try This
go to [url=http://www.freemathhelp.com/distributiveproperty.html]free math help / distributive property[/url]
and type in 6/2(1+2)=x and hit solve
it will show you how they got their answer













Joined: Jun 2009
Posts: 4,108
BellaOnline Editor Elephant

BellaOnline Editor Elephant
Joined: Jun 2009
Posts: 4,108 
I visited the above site and it worked. Go to the bottom of the page and type in the math problem, hit answer and the problem will be solved for you. Free Math Help













Joined: Apr 2011
Posts: 4
Newbie

Newbie
Joined: Apr 2011
Posts: 4 
I stand corrected....
If you type in 6/2(2+1)=x and hit solve, the answer is x=1
If you type in 6/2(2+1) and hit solve, the answer is 9
...I give up!













Joined: Apr 2011
Posts: 4
Newbie

Newbie
Joined: Apr 2011
Posts: 4 
I stand corrected....
If you type in 6/2(2+1)=x and hit solve, the answer is x=1
If you type in 6/2(2+1) and hit solve, the answer is 9
...I give up!













Joined: May 2010
Posts: 11,656 Likes: 29
BellaOnline Editor Renaissance Human

BellaOnline Editor Renaissance Human
Joined: May 2010
Posts: 11,656 Likes: 29 
Yes, if it were written 6 / 2 x 3, the answer would be 9.
But it isn't written that way. And when you write 2(1+2), the whole thing is an expression that needs to be treated as a unit in terms of any other operations.
The expression 2(2+1) equals to 6 and needs to be treated as if it were the number 6.
If you were using letters a and b instead of the 2 and 1 in the parentheses, it would be 2(a+b). This is a tidy way of writing (2a + 2b) because it's treated as a unit. Plugging the numbers back in, it would be the sum of 2x2 (4) and 2x1 (2), i.e., 6.
6 divided by 6 is 1.













Joined: Jan 2009
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Highest Posting Power Known to Humanity

Highest Posting Power Known to Humanity
Joined: Jan 2009
Posts: 60,166 
I'm not moved from my "9" stance.
6 divided by 2 times the quantity 1+2 is calcualted in that order...
Had the equation been 6/(2(1+2)) => then it would be 6 divided by the quantity of 2 time the quantity of 1+2.
But since there are no parens to define a calculated quantity for the denominator, only the numerical value can be used.
B "We do not inherit the Earth from our ancestors, we borrow it from our children."













Joined: May 2010
Posts: 11,656 Likes: 29
BellaOnline Editor Renaissance Human

BellaOnline Editor Renaissance Human
Joined: May 2010
Posts: 11,656 Likes: 29 
You don't have to put the 2(1+2) into further brackets, because without an operator between the 2 and the (1+2), it is always read as one expression which, in this case, equals 6.













Joined: Jun 2009
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BellaOnline Editor Elephant

BellaOnline Editor Elephant
Joined: Jun 2009
Posts: 4,108 
Mona, I have to say that I do agree with you. I remember teaching my own kids algebra. According to the way they were taught and what the answer keys said, the correct answer would be 1.













Joined: Nov 2007
Posts: 17,644
Highest Posting Power Known to Humanity

Highest Posting Power Known to Humanity
Joined: Nov 2007
Posts: 17,644 
I really do not see what all the confusion is about. Beetlemess mentioned the "Order of Operations" which is very clear. The Order of Operations states that if there is a problem that has all of the following operations: Parentheses, Exponents, Multiplication, Division, Addition and Subtraction, then the Operations must be performed in the order in which they are stated. Therefore, 6ï¿½2(1+2)= 9. "It seems as though the answer depends on which way you look at the problem. But we can't have this kind of flexibility in mathematics; math won't work if you can't be sure of the answer, or if the exact same problem can calculate to two or more different answers. To eliminate this confusion, we have some rules of precedence, established at least as far back as the 1500s, called the "order of operations". The "operations" are addition, subtraction, multiplication, division, exponentiation, and grouping; the "order" of these operations states which operations take precedence (are taken care of) before which other operations. A common technique for remembering the order of operations is the abbreviation "PEMDAS", which is turned into the phrase "Please Excuse My Dear Aunt Sally". It stands for "Parentheses, Exponents, Multiplication and Division, and Addition and Subtraction"." See: Order of Operations
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