Math: 6÷2(1+2) = ?

6/2(1+2)

Brackets first: 1+2 = 3
Then multiplication and division from left to right
Division comes first because it's farthest to the left
6/2=3
So now it's 3(3)
3x3= 9

(1+2) first(brakets)=3
so now we have x+6/2x3=9
next part is 6/2=3(MD rule Work left to right)
so now we have x+3times3=9
next part is 3x3 which equals 9 which gives us
x+9=9
to solve for x you will do x=9-9
so x=0

1 is the only correct answer

[link to en.wikipedia.org]

"Today, parentheses or brackets are used to explicitly denote precedence by grouping parts of an expression that should be evaluated first. Thus, to force addition to precede multiplication, we write (2 + 3) × 4 = 20, and to force addition to precede exponentiation, we write (3 + 5)2 = 64."

"The order of operations used throughout mathematics, science, technology and many computer programming languages is expressed here:[2]
exponents and roots
multiplication and division
addition and subtraction"



"Mnemonics are often used to help students remember the rules, but the rules taught by the use of acronyms can be misleading. In the United States the acronym PEMDAS is common. It stands for Parentheses, Exponents, Multiplication, Division, Addition, Subtraction. PEMDAS is often expanded to "Please Excuse My Dear Aunt Sally" with the first letter of each word creating the acronym PEMDAS. Canada uses BEDMAS and the UK uses BIDMAS or BODMAS. In Canada and other English speaking countries, Parentheses may be called Brackets, or symbols of inclusion and Exponentiation may be called either Indices, Powers or Orders, which have the same precedence as Roots or Radicals. Since multiplication and division are of equal precedence, M and D are often interchanged, leading to such acronyms as BOMDAS.
These mnemonics may be misleading when written this way, especially if the user is not aware that multiplication and division are of equal precedence, as are addition and subtraction. Using any of the above rules in the order "addition first, subtraction afterward" would also give the wrong answer to the problem"

Sorry BUT I use the slash --> / so NOT the ÷ for the division.

SO I mean:

x+__6__ = 9
..2(1+2)

--->> then:...8......

Last Edited by IWASTHERE on 01/15/2013 02:12 PM

6/2(1+2)
=6/(1+1)(1+2)
=(6/1+6/1)(1+2)
=(6+6)(1+2)
=6*1+6*1+6*2+6*2
=6+6+12+12
=12+12+12
=24+12
=36

I am not a mathematician but I cannot find any error in this. Like multiplying into a bracket, we likewise can divide into a bracket (I think )

I am not going to sit here and argue all day. So it depends how you define, giving it a rest.

I will not concede that there are multiple answers, there are not. The answer is 9.

x=0

I did engineering in 4 years, along with learning french as a second language to attain a functional profile, among other things...
The answer is 1. Always.



That is the ONLY way to get 9. Otherwise, they would have written it 6(2+1)/2.

Lol, thank you. If you search the thread I have said just that for over a year, lol.

Last Edited by Patrick Bateman on 01/15/2013 04:00 PM

Lol wrong, twice. I did not ssay there were multiple answers, I said the problem is poorly written which could lead the the confusion. I have also stated, at least 100 times now, the answer is 1. You want to keep arguing, whatever, I said my piece.

First,
if you want to say 0.5x, then you HAVE to write (1/2)x with parentheses or, x "all over 2" with a horiztonal fraction bar, or write x/2. I have never seen (1/2)x before I researched this equation, but since searching online, I HAVE seen fractional coefficients written this way, only because computers are limited to the horizontal typing space.
Therefore:
x/2 = (1/2)x = 0.5x
1/2n = 1/(2n) This sort of notation is used especially with pi, ln, or e. We have never had to say 1/(2pi). It was simply 1/2pi, or 1/2e^2.
I have always used ab/cd to mean (ab)/(cd) and I topped almost all of my calculus classes since high school through university.(moot point, I know)
Just to re-iterate, to use 6/2 as a fraction, parentheses are REQUIRED. Every book will tell you this.

Now consider the Identity Law:
a = 1a = 1(a)
We know there is ALWAYS an 'invisible' 1 as a ceofficient of a variable if no other number is there. Therefore:
a/a = 1, and if a is also 1a, then a/1a = 1. Blindly using 'pemdas', some folks would do this:
a/1a = a/1*a = a*a = a^2. I hope this drives home the silliness of this calculation.

Now, on to my second point:
consider: factoring, simplifying equations, and the distributive property.
Lets start with the number 6.
6 = (4+2). There is a common factor here: 2. So let's factor it out of both terms.
(4+2) = 2(2+1). The outside 2 remains a part of of the 2 inner terms at all times. It cannot be used in an operation by itself without the rest of (4+2). The reverse of factoring is distribution, so, 2(2+1) = 6. This has to be true always. The argument I have seen to this is that (6/2) can be distributed. This is true ONLY is 6/2 is in parentheses, otherwise, the 6 and 2 are separated by a division slash, and the 2 is a factor of 2+1.

So, let's prove the initial equation:
6/6 = 1
6/(4+2) = 1
6/2(2+1) = 1

the same can be done for other factors:
6/6 = 1
6/(3+3) = 1
6/3(1+1) = 1
Distribution is actually a part of "Simplifying Equations" and is not bound to the order of operations as "multiplication", since it is in fact "removing parentheses by distributing". This can be googled and several references found.
Simplifying 2(2+1) + 3(2+1) = 5(2+1). We "combined like terms" here, by adding, and did not perform the "parntheses" part of order of operations, nor did we multiply, which is also higher priority than adding, because we only simplified.

Lastly, I hear the argument that "This is strictly numbers and you don't use algebra rules since there are no variables". That is the most asinine arguement I have heard yet. All axioms, laws, and properties use variables, meaning that they hold true for "any number", hence the proofs with variables.
I welcome thoughts on this, in an intellectually formed response. I am tired of the 'flaming' that goes on by imbciles on some other forums with rebuttals like "it is 9. go back to grade 3 you moron", or "google says it is 9", when google changes the equation to (6/2)*(2+1), and wolfram contradicts itself with 2n/2n = 1, and 6/2n = 3/n, but then says 6/2(2+1) is 9. wolframs "terms" state that any answer should be verified with common sense and accuracy should also be verified.

I am not arguing. The answer is 9. There is no debate to be had.

My God the stupidity is absolutely fucking mind boggling.

You guys seriously need to tell me where you got your degrees. I need to make sure my kids never set foot in that fucking institution:

"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."

[link to www.purplemath.com]


It is so fucking simple it is unreal... absolutely fucking unreal. I just cannot even comprehend how your minds are this fucked up.

Reverse engineer the equation using 9 then, dumas.

You sir, are the fucked up one. Continue reading your URL:
"When simplifying expressions with parentheses, you will be applying the Distributive Property." -purplemath

"Parentheses" in the order of operations to require Distributive Property.
Ref: Purplemath
[link to www.purplemath.com]

I have a bachelors degree in horticulture, and I can tell you the answer is 9. I used tomato plants to represent the numbers, and the answer is definitely 9.

OMG. OMG. OMG. OMG. PLEASE JUST FUCKING OPEN YOUR BRAIN, AND LEARN SOMETHING!



There is no separate term, YOU DO NOT DO THE DISTRIBUTIVE PROPERTY! THIS IS NOT A FUCKING FRACTION! Fucking learn something dude. JESUS FUCKING CHRIST.

Let this man explain to your STUPID fucking mind even more clearly because I don't have the patience to deal with MENTALLY FUCKING RETARDED morons.

More explanation:

6÷2(x+2)

Use the distributive property... how would you do that? Guess what? You would DIVIDE FIRST YOU FUCKING FRUIT. GO BACK TO SCHOOL YOU ARE FUCKING RETARDED.

were the tomato plants inside or outside???

:0078::ohlol:

stupid question. The tomato plants have been inside since 2010.

.
10/10! Distribution is the key word here.

is this not just a simple BEDMAS type situation?

they wouldn't get in. Full scholarship only with rigorous academic requirements, and since they are YOUR kids...

That fucking moron thinks a/1a = a^2. He also fails to use distribution to eliminate parentheses.