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Absolute values are a crucial concept when dealing with negative numbers and addition.
The absolute value of a number is its distance from zero on the number line, regardless of direction.
It's always a positive number or zero. For example, the absolute value of both -24 and 24 is 24.
You can denote absolute values with vertical bars, like this: \( \left| -24 \right| = 24 \).
Understanding absolute values helps simplify problems involving negative numbers.
When adding negative numbers, you'll often need to work with absolute values first to make the problem easier to solve.
For instance, in our example, we calculate the absolute values of -24 and -17 to get 24 and 17 respectively.

When working with integers, it’s essential to understand how to handle different operations.
This includes addition, subtraction, multiplication, and division of both positive and negative numbers.
Let’s focus on addition in the context of negative numbers.
When adding integers, keeping track of their signs is very important.
If you add two positive numbers, the result is positive.
If you add two negative numbers, the result is negative, and you add the absolute values of those numbers to get the final result.
For example, adding -24 and -17 means computing \( \left| -24 \right| + \left| -17 \right| = 24 + 17 = 41 \), then applying the negative sign to get -41.

Adding negative numbers might seem tricky at first, but it's straightforward once you get the hang of it.
Remember the following steps:

• Identify the numbers involved.
• Understand that you are combining two losses or debts, which makes the total loss larger.
• Calculate the sum of the absolute values.
• Apply the negative sign to the result.

In our specific case of -24 + (-17), we:

• Identify that -24 and -17 are the numbers to combine.
• Realize they are both negative.
• Find their absolute values: 24 and 17.
• Add these absolute values to get 41.
• Since we are adding two negatives, the result must be negative. Thus, the final answer is -41.

This method ensures accuracy and helps simplify problems involving negative number addition.