Solve Complex Expression: 3÷(6×(12÷(2×3))) Order of Operations

Let's recall the order of operations: calculate what's in parentheses, multiplication and division (from left to right), addition and subtraction (from left to right)

We emphasize that when there are parentheses within parentheses, we start with the innermost ones first.

$3:(6\times(12:(2\operatorname{\times}3)))=$

In this exercise, there are only multiplication and division operations and parentheses within parentheses.

Therefore, we will first perform the operation in the innermost parentheses, and after calculating we can remove the inner parentheses. We'll continue doing this until there are no more parentheses in the exercise.

$3:(6\times(12:(2\times3)))=3:(6\times(12:(6))) =$

$3:(6\times(12:(6))) =3:(6\times(12:6)) =$

Now we'll perform the operation in the remaining parentheses and after calculating we'll remove the parentheses

$3:(6\times(12:6)) =3:(6\times(2)) =$
$3:(6\times(2))=3:(6\times2)=$

And again we'll perform the operation in the remaining parentheses and after calculating we'll remove the parentheses

$3:(6\times2)= 3:(12)=$

$3:(12)= 3:12 =$

We'll show the solution we got with the fraction and try to reduce it

$3:12=\frac{3}{12}=$

The largest number by which we can reduce the fraction is 3

$\frac{3}{12}=\frac{3:3}{12:3}=$

Let's solve

$\frac{3:3}{12:3}=\frac{1}{4}$

Therefore the answer is option c -

$(\frac{1}{4})$