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Negative numbers represent values less than zero. They are commonly used to express loss, debt, or temperature below freezing, among other concepts.

Negative numbers are represented with a minus sign (-) in front of them. For example, -3 means three units less than zero. They are crucial in mathematics to perform various operations and solve real-world problems.

Understanding negative numbers helps in many areas, such as balancing equations and comprehending concepts like elevation below sea level or financial deficits.

Multiplying numbers involves combining equal groups. The rules for multiplication, especially with negative numbers, are essential for getting the correct results:

The absolute value of a number is its distance from zero on the number line, regardless of direction. It is denoted by vertical bars around the number, like this: \( | x | \).

For instance, \( | -8 | = 8 \) and \( | 8 | = 8 \). The absolute value function strips the sign, focusing solely on magnitude.

Understanding absolute value is crucial when performing operations like multiplication, especially with negative numbers. For example, when multiplying -8 by 5, we first find the absolute values and multiply them: \ | -8 | = 8 \ and \ | 5 | = 5 \.

By multiplying these absolute values, we get 40. Then, we apply the correct sign according to multiplication rules, yielding -40 in the given exercise.

• It helps simplify problems.
• Allows easier handling of operations with negative values.
• Provides clarity on the magnitude and size of numbers.