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

Recall the order of operations: parentheses precede all other operations, multiplication and division follow (from left to right) and finally addition and subtraction (from left to right)

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 entirely:

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

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

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

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

Shown below is the solution that we obtained expressed as a fraction. Proceed to reduce it.

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

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

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

Proceed to solve it:

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

Therefore the answer is option c -

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