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Negative numbers are numbers less than zero. They are represented with a minus sign (-) in front of them. Negative numbers often appear in real-life scenarios such as temperature readings below zero, bank overdrafts, and depths below sea level.

For instance, -7 indicates seven units below zero. When dealing with negative numbers, it can be helpful to visualize them on a number line. Numbers to the left of zero are negative, and the further left you go, the smaller the values get.

In arithmetic operations, combining negative numbers follows specific rules:

• Adding a negative number is equivalent to subtracting its absolute value.
• Subtracting a negative number is equivalent to adding its absolute value.
• The product of two negative numbers is positive.
• The product of a positive and a negative number is negative.

Understanding these fundamental rules helps in simplifying expressions like -7 - 2.

When adding and subtracting integers, it's crucial to understand how signs affect the operations. Practicing these concepts helps in solving expressions effortlessly.

Here's a quick guide to integer addition and subtraction:

• Adding integers with the same sign: Add their absolute values and apply the common sign. For example, -7 - 2. Both numbers are negative, so we add their absolute values: 7 + 2 = 9, and the result carries a negative sign, yielding -9.
• Adding integers with different signs: Find the difference of their absolute values and apply the sign of the number with the larger absolute value. For instance, 7 + (-2). The absolute values are 7 and 2, and the difference is 5. Since 7 has a larger absolute value and is positive, our result is 5.
• Subtracting an integer: Convert the subtraction into an addition operation by changing the sign of the number being subtracted. For example, 10 - (-3) becomes 10 + 3.

Understanding these rules simplifies expressions and avoids errors, especially with exercises like -7 - 2.

The absolute value of a number refers to its distance from zero on the number line, regardless of its direction. It is always a non-negative value. The absolute value is denoted using vertical bars, such as \(|-7|\) and \(|2|\).

To find the absolute value of a number:

• If the number is positive or zero, its absolute value is the number itself. For example, \(|5| = 5\).
• If the number is negative, its absolute value is the number without the minus sign. For instance, \(|-7| = 7\).

Absolute values are particularly useful when dealing with negative numbers in arithmetic.

In the original exercise, -7 and -2 both have absolute values of 7 and 2, respectively. When adding these absolute values, we get 9. The negative sign is then applied because both numbers were originally negative. Thus, -7 - 2 simplifies to -9.
Absolute value helps in understanding distances and magnitudes without considering the direction, making it a handy tool in many mathematical contexts.