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

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.

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

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, so 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 we'll remove the parentheses

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

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

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

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

Let's show the solution we got as a fraction and try 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 -

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