Definition of a Negative Number
A negative number is any real number that is less than zero. On a number line, negative numbers are located to the left of zero, extending infinitely in that direction. They are typically denoted by a minus sign (-) placed before the numeral, for example, -5 or -0.75.
Key Properties and Rules
Negative numbers have distinct properties: adding two negative numbers results in a larger negative number (e.g., -3 + -2 = -5); subtracting a negative number is equivalent to adding a positive number (e.g., 5 - (-3) = 5 + 3 = 8); and multiplying or dividing two negative numbers yields a positive result, while multiplying or dividing a negative and a positive number yields a negative result.
Real-World Examples of Negative Numbers
Negative numbers are used to represent concepts such as debt (e.g., owing $10 is -$10), temperatures below freezing (e.g., -5°C), elevations below sea level (e.g., -100 feet), and deficits in budgeting or sports scores. They provide a standardized way to describe values that fall below a zero reference point.
Importance in Mathematics and Science
In mathematics, negative numbers are crucial for solving equations, understanding number theory, and forming the basis of number systems like integers and rational numbers. In science, they are indispensable for expressing measurements such as electrical charge, temperature deviations, and direction in vector quantities, allowing for a comprehensive description of physical phenomena.