Solve 24÷(2×(16×(2+1))): Complex Order of Operations Problem

Solve the following problem:

$24:(2\times(16\times(2+1)))=$

Recall the order of operations: Parentheses precede all other operations, followed by multiplication and division (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.

$24:(2\times(16\times(2+1)))=$

In this exercise, there are addition operations in the inner parentheses, and the rest of the exercise includes multiplication and division operations and parentheses within parentheses.

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

At each step in solving operations within parentheses, we'll make sure to follow the order of operations

$24:(2\times(16\times(2+1)))= 24:(2\times(16\times(3)))=$

$24:(2\times(16\times(3)))= 24:(2\times(16\times3))=$

Note - In the inner parentheses there was only addition operation, hence we followed the order of operations when we solved this operation first and not the multiplication and division operations

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

$24:(2\times(16\times3))=24:(2\times(48)) =$
$24:(2\times(48)) =24:(2\times48) =$

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

$24:(2\times48) = 24:(96) =$

$24:(96) = 24:96 =$

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

$24:96=\frac{24}{96}=$

The largest number by which we can reduce the fraction is 24

$\frac{24}{96}=\frac{24:24}{96:24}=$

Let's solve

$\frac{24:24}{96:24}= \frac{1}{4}$

Therefore the answer is section a -

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