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Negative numbers are those that are less than zero. A negative number is represented with a minus sign (-) in front of it. They appear on the left side of zero on a number line.

For example, numbers like

• -1, -2, and -5

are all negative. Negative numbers indicate a decrease or loss, very much like a debt.

When working with negative numbers, it's crucial to understand that the further you go to the left on the number line, the smaller the value of the number becomes. For example,

• -5 is less than -2.

Understanding this concept is the first step to mastering operations involving negative numbers.

The absolute value of a number refers to its distance from zero on the number line, without considering its direction. It is represented by two vertical bars around the number, like this: \( |x| \) for \( x \).

For instance, the absolute value of -2 is 2, since it is two units away from zero. Similarly, the absolute value of -5 is 5.

One of the key properties of absolute value is that it is always non-negative, reflecting only the magnitude of the number. When dealing with negative numbers, finding the absolute value assists in simplifying operations like addition or subtraction. This is especially useful when adding negative numbers, as it allows you to add their magnitudes first before reapplying the negative sign.

Adding numbers, whether negative or positive, follows some basic principles. When you add two positive numbers, the result is straightforward – you simply find their sum.

However, adding negative numbers involves incorporating their absolute values into the process. Here's how it works:

• Step 1: Identify the absolute values of the negative numbers.
• Step 2: Add these absolute values together. This turns the operation into a simpler arithmetic addition, like adding 2 and 5 to get 7.
• Step 3: Since the original numbers are negative, apply a negative sign to the outcome of your addition.

For example, when adding -2 and -5:

• First, find the absolute values, which are 2 and 5.
• Add them together to get 7.
• Apply the negative sign back to the result, resulting in -7.

This process helps make sense of how combining negative numbers works and ensures accuracy in mathematical calculations.