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In mathematics, numbers can be positive or negative. Positive numbers are those that are greater than zero, indicating a value or quantity that is being added. Conversely, negative numbers are less than zero, signifying a value or quantity that is being taken away or below a starting point. For example, a temperature of (-8) degrees is eight degrees below zero.

Negative numbers are represented on the number line to the left of zero, moving increasingly lower as you move further left. They are typically denoted with a minus sign (-). When working with negative numbers, it's important to understand that adding a negative number is equivalent to subtracting its absolute value, which is the number without the negative sign, from the starting quantity.

The number line is a powerful tool for visualizing and performing operations with both positive and negative numbers. It can be thought of as a horizontal line where every point represents a unique number, with zero at the center, positive numbers to the right, and negative numbers to the left.

To better understand how to add negative and positive numbers using a number line, picture yourself standing on the number that represents the first number in the equation. If the second number is positive, you would take steps to the right. If it's negative, you would move to the left. The final position where you stand after moving the number of steps equal to the second number is the answer to the addition problem. For example, starting on (-8) and moving three steps to the right lands you on (-5), showing (-8) + 3 = -5.

Subtracting integers might seem a bit more complex than adding positive numbers, but the number line simplifies this process. When you subtract integers, you're finding the difference between two numbers. If you are subtracting a positive integer, move to the left on the number line. If you are subtracting a negative integer, move to the right, since subtracting a negative is the same as adding a positive.

Looking at our initial problem, adding (-8) + 3, you can reframe it as subtracting a negative: -8 - (-3). This makes it clearer why you move to the right, as subtracting (-3) means adding 3. So, subtracting an integer can sometimes involve adding, and this is particularly evident when dealing with negative numbers.