6 / 2 x (1 + 2) =?       // Original - complete parentheses 1+2 to get 3 in equasion
6 / 2 x 3 = ?   // Simplified - simpler equasion. pemdas definition tells to go from left to right
     3 x 3 = 9

www.mathsisfun.com/operation-order-pemdas.html
www.purplemath.com/modules/orderops.htm
en.wikipedia.org/wiki/Order_of_operations
etc

honestly i cant be asked to argue anymore cos we've obviously been taught different things
its just the fact that nobody can standardize it over different countries
plus you usually dont get division signs in algebra anyways
you just get fractions
theres never really any confirmation

>>#186, its 6:2x3

multiplication and division are equal, so we have to do it from left to right
6:2x3=?
3x3=9

>>#190
its a coefficient its part of the parentheses
6/2x =/= x( 6/2 )

ya sorry mathway says other wise

show me

honestly i wanna say thats wrong but im still just surprised a massive website like that wouldnt program their calculator correctly
even google does it wrong

it looks like the online calculators just dont do terms correctly
6 is one term and 2(1+2) is another
heres an actual calculator with the same thing
excuse the ****** quality

Can confirm the answer is 1, also excuse my **** quality pic.

**** Casio

well mines more recent so they probs changed it between the two
thats weird though
like someone just changed how maths works

because it knows what terms are

its because you have to type the x symbol in
and the programming has it go left to right with multiplication and division so it you divide by 2 first
it treats it like a seperate term **** doesnt work

First problem: no multiplikation symbol

a(b+c) = a*(b+c)

=> a : b(c+d) = a : b * (c+d) != a : (b * (c+d)

second problem: division

a : b * c = (a:b)*c != a : (b*c) = a : b : c
a - b + c = (a-b)+c != a - (b+c) = a - b - c

this makes

6 : 2(1+2) = 6 : 2 * 3 = (6:2) * 3 = 3 * 3 = 9

Unfortunately I'm too lazy to show the higher math behind it (easy in german, hard in non native language) but if someone is interested just search for "Multiplicative Inverse Axiom"

if theres no multiplication symbol it's a coefficient and you treat it as one term
so you have to multiply before you divide

One term. So a : b * (c+d) = a : b *d for d = c+d. From there it's nothing but left to right as division is multiplikation with the inverse. There is no division before multiplikation rule as it is the same function.

Sorry. It's a : b * (c+d) = a : b *e for e = c+d

heres my reasoning
you treat the parentheses as a variable before you know the result of them
because coefficients work the same way for both
6/2x =/= 3x
its 3x^-1
so you wouldnt get 9
if you put x back in with 3x^-1 then that's 3/3 = 1
the order of operations means you work out parentheses first and coefficients are the same term as the parentheses
so again
you multiply first

Well 6 : 2 * x = 6 : 2x but not 6 : (2 * x).

8 : 2 * 2 is 8 not 2.

what
2x is the same thing as 2*x but in the same term
which also applies for coefficients
and i didnt write 8 anywhere

parentheses* not coefficients

Please don't ignore that a : b(c+d) = a : b * (c+d) != a : (b * (c+d).

I took another example with 8 : 2 * 2 = 8 to show this. Using your argumentation we would have 8 / (2 * 2) = 2 which is wrong. There is something called left associative operation which is the standard way of interpretation if not stated otherwise. The problem here is that the way you used might not be wrong in terms of mathematical theorems but it is in mathematical associative axioms.

b(c+d) =/= b * (c+d)
b(c+d) == (b* (c+d))

And again, this isn't stated in the original term. It states:

6 : 2(1+2)=?
a : b(c+d) = a : b * (c+d) = ?
a : b * e = ?

This is what you have to do using the left associative operation - which you have to do unless stated otherwise (using brakets).

Yours would have been stated as
6 : (2(1+2))=?

yes and thats what's implied
it doesnt say 2*(1+2) it says 2(1+2)
and likewise its not b*e its be

So there is another operator for you besides +,-,* and : which gives a different meaning than *? Because I only know these four. Don't misinterpret this as beeing cocky or anything. I'm really enjoying this conversation as your arguments are strong and clearly understandable while beeing based on math.

The thing is, that your operator states that a*(b+c) != a(b+c)

Andra: As I can't reply to #190 :

The definition of a coefficient alway has the word multiplication in it and doesn't differ from the form a*x = ax.

its not really its own operator
more like algebraic notation
a coefficient is different to just multiplying because of the order
coefficients always come first

And the mathematical conclusion:

The Multiplicative Inverse Axiom states that the product of a real number and its multiplicative inverse is 1. Every real number has a unique multiplicative inverse. The reciprocal of a nonzero number is the multiplicative inverse of that number. Reciprocal of x is 1/x. x * 1/x = 1. x * x´ = 1 for x´ = 1/x

Typical notations for x´ are x^-1 or 1/x. The division is defined as multiplication with the inverse of the divisor. So a : b * c = a * b^-1 * c != a * b^-1 * c^-1 = a : b : c = a : (b:c).
And for us 6 : 2 * (1 + 2) = 6 : 2 * 3 = 6 * 2^-1 * 3= 6 * 1/2 * 3 = 9