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Negative numbers are numbers less than zero. They are often used to represent losses or decreases in various contexts. When visualizing numbers on a number line, negative numbers are to the left of zero.
Negative numbers carry a negative sign, "-" which is an indicator that they are less than zero. This is different from positive numbers, which either have a "+" sign or no sign at all.
A crucial aspect of working with negative numbers is remembering the rules of addition and subtraction, especially when dealing with two negative numbers. When adding two negative numbers, as seen in the problem \(-640 + (-200)\), you are essentially combining their sizes, but keeping the negative sign.

The absolute value of a number is its distance from zero on a number line, disregarding any sign. Hence, it is always a non-negative number.
For example, the absolute value of both -640 and +640 is 640. The notation for absolute value is two vertical bars around the number, so for -640, it's written as \(|-640| = 640\).
When adding or comparing negative numbers, it's often useful to think about the absolute values. By adding the absolute values of negative numbers, you determine how far the sum will move in the negative direction on the number line. This helps you confirm what the sign of the result will be.

Working with integer addition, especially involving negative numbers, requires understanding some key addition properties.
- **Commutative Property:** This property states that changing the order of the numbers in the addition does not change the result. For example, \(-640 + (-200) = -200 + (-640)\).
- **Associative Property:** This indicates that when addings three or more numbers, the grouping of numbers does not affect the sum. For instance, \((a + b) + c = a + (b + c)\).
- **Additive Identity:** This property tells us that any number plus zero remains unchanged. For example, \(-640 + 0 = -640\).
Applying these properties can make calculations easier and more intuitive, especially when breaking down problems into smaller, manageable parts.