Simplify -30-((-41)-((-4)-(-8))): Order of Operations with Nested Parentheses

Let's begin by remembering the order of arithmetic operations: calculation of the operation within parentheses, multiplication and division (from left to right), addition and subtraction (from left to right)

We must also underline that when there are parentheses within parentheses, we should start with the innermost first.

$-30-((-41)-((-4)-(-8))) =$In this exercise, there are only subtraction operations and parentheses within parentheses.

Therefore, we will first perform the operation of the inner parentheses. After which we will be able to remove the inner parentheses and will be left with only one pair of parentheses.

Keep in mind

What happens when there is a sequence of two signs present in the exercise (these are usually separated by parentheses) Let's highlight several different cases:

When a sequence with two plus signs appears, the result will also be a plus.

When a sequence with two minus signs appears, the result will also be a plus.

When a sequence with minus and plus signs or plus and minus signs appears, the result will be minus.

$-30-((-41)-((-4)-(-8))) = -30-((-41)-((-4)+8))$

Reminder: addition and subtraction of directed numbers

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

$-30-((-41)-((-4)+8)) = -30-((-41)-(4))$
$-30-((-41)-(4)) = -30-(-41-4)$

Now we will perform the operation of the remaining parentheses and after the calculation, we will remove the parentheses.

$-30-(-41-4) = -30-(-45)$

$-30-(-45) = -30+45 = 15$

Therefore, the correct answer is option b: (15)