The simple answer: 9
This is a simple "order of operations" problem.
Let's use the american acronym "PEMDAS" or (P)(E)(MD)(AS)
So we have.
6÷2(1+2)
add what is inside the parentheses
6÷2(3)
now since all that is left is multiplication and division you go left to right.
So. 6÷2
3(3)
now multiply
9.
Now that I have given the steps for this particular problem I'll give an outrageous example with an array of variables mixed with multiplication and division. I'll then assign those variables numbers and solve for many different arrangements of those same variables.
Also if you were to just take "A/B*C" from my example you have an identicle problem to the one that you asked here, you could simply assign A=6, B=2, C=(1+2) and you would have the same problem.
which would look like
A/B*C
((A/B)C)
(A)(1/B)(C)
(AC)/(B)
(AC)(1/B)
all of these will give you 9 if you simply plug the numbers back in
So now for a rediculous example with 12 variables.
A/B*C*D*E*F/G/H/I/J*K*L
this is the same as
A/BCDEF/G/H/I/JKL
It’s also the same as
(((((((((((A/B)C)D)E)F)/G)/H)/I)/J)K)L)
It is also the same as
(A)(1/B)(C)(D)(E)(F)(1/G)(1/H)(1/I)(1/J)(K)(L)
which is also the same as
(ACDEFKL)/(BGHIJ)
Which is also the same as
(A*C*D*E*F*K*L)/(B*G*H*I*J)
You can even plug numbers into any of these expressions and you will get the same answer for all of them.
lets assign them values and do it!
A=2, B=3, C=4, D=5, E=6, F=7, G=8, H=9, I=10, J=11, K=12, L=13
2/3*4*5*6*7/8/9/10/11*12*13 = 11.0303…
(((((((((((2/3)4)5)6)7)/8)/9)/10)/11)12)13) =11.0303…
(2)(1/3)(4)(5)(6)(7)(1/8)(1/9)(1/10)(1/11)(12)(13) = 11.0303…
(2*4*5*6*7*12*13)/(3*8*9*10*11) = 11.0303…
Also if you were to just take "A/B*C" from my example you have an identicle problem to the one that you asked here, you could simply assign A=6, B=2, C=(1+2) and you would have the same problem.