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When approaching a problem that involves subtracting negative numbers, such as \( -30.75 - 159.27 \), a helpful strategy is to convert the subtraction into addition. This is because the addition of negative numbers is often more straightforward to understand and calculate.

To change a subtraction into addition, use the rule \( a - b = a + (-b) \). This rule simply means that when you subtract a number, you're actually adding its opposite (also called its additive inverse). If we apply this change to our example, we would rewrite the expression as \( -30.75 + (-159.27) \).

Once we've converted our subtraction problem into addition, we face the challenge of adding negative numbers. It's crucial here to remember that adding two negative numbers results in a sum that is more negative.

You might find it useful to visualize this with examples from the real world, such as owing money. If you owe \(30.75 and then borrow another \)159.27, you increase your debt. The principle remains the same with negative numbers; you're essentially 'adding' more negativity, so to speak. In our exercise, \( -30.75 + (-159.27) \), by adding the absolute values \( 30.75 + 159.27 = 190.02 \), and then applying the negative sign, we efficiently find the sum, \( -190.02 \).

The concept of absolute value is tremendously useful when dealing with the addition of negative numbers. Absolute value refers to the distance a number is from zero on the number line, regardless of its direction. In mathematical terms, it's always a positive number or zero.

To illustrate, the absolute value of both \( -30.75 \) and \( 30.75 \) is \( 30.75 \), because both are 30.75 units away from zero. In the context of our exercise, taking the absolute values of the negative numbers and adding them together \( | -30.75 | + | -159.27 | = 30.75 + 159.27 \) gives a clear pathway to solve the addition problem without the confusion that might come from working directly with negative numbers.