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

Solve the following expression:

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

Adhering to the order of operations: First calculate what's inside of the parentheses, proceed to the multiplication and division operations (left to right) and finally perform the addition and subtraction operations. (left to right)

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, after which 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 in fact 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 after which we'll remove the parentheses

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

Therefore the answer is option d - (133)