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Negative numbers are numbers less than zero. They are represented with a minus sign (-) in front of them. For example, -5, -3.2, and -8.35 are all negative numbers. Negative numbers often represent a deficit or something that is below a baseline. They are used in various real-world situations, such as temperatures below freezing, bank overdrafts, or elevations below sea level.
When adding negative numbers, you essentially move further down the number line. The more negative the number, the further left it is from zero on the number line.

Positive numbers are greater than zero and are represented without any sign or with a plus sign (+) in front of them. Examples include 5, 3.2, and 8.35. Positive numbers denote an accumulation or something that is above a baseline. You will often find positive numbers in situations like counting money, measuring distances, or recording temperatures above freezing.
When adding positive numbers, you are moving to the right on the number line, further away from zero. The more significant the number, the higher the value.

The result of addition depends on the nature of the numbers involved. When you add a positive number to another positive number, the result is an even larger positive number. Conversely, when adding two negative numbers, the result is a more significant negative number.

Now, let's talk about the addition of opposites. Opposite numbers are pairs like 8.35 and -8.35. They are the same distance from zero but in opposite directions. When you add a number to its opposite, the positive and negative parts cancel each other out. This means \(-8.35 + 8.35 = 0\). The sum of a number and its opposite is always zero, reflecting that they fully neutralize each other.
Understanding this concept of adding opposites is crucial, especially in algebra and solving equations, as it simplifies complex problems and helps in balancing equations easily.