Solve 108-(-46-(3-24)): Complex Order of Operations with Nested Parentheses

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

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

$108-(-46-(3-24)) =$

In this exercise, there are only subtraction 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.

Reminder - Addition and Subtraction of Directed Numbers

When we have two numbers with different signs, it's important to determine which number is larger in absolute value (absolute - distance from zero). The larger number will determine the sign of the result, and we'll actually perform a subtraction exercise.

$108-(-46-(3-24)) = 108-(-46-(-21)) =$

Pay Attention

When an exercise contains a sequence of two signs (which are usually separated by parentheses) we'll distinguish between several cases:

When there's a sequence of two plus signs, the result will also be plus.

When there's a sequence of two minus signs, the result will also be plus.

When there's a sequence of minus and plus or plus and minus, the result will be minus. 

$108-(-46-(-21)) =108-(-46+21) =$

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

$108-(-46+21) = 108-(-25) =$
$108-(-25) = 108+25 = 133$

Therefore the answer is option d - (133)