The additive inverse of a number is the value that, when added to the original number, results in a sum of zero. In simpler terms, it's the number with the opposite sign.
Understanding Additive Inverse
The core concept of the additive inverse is based on the negation of a number. The reference states that if 'x' is the original number, its additive inverse is '-x'. This ensures that:
x + (-x) = 0
This property is fundamental in mathematics and is used extensively in solving equations and simplifying expressions.
Examples of Additive Inverses
Here's a table illustrating some examples:
| Original Number (x) | Additive Inverse (-x) | Sum (x + (-x)) |
|---|---|---|
| 5 | -5 | 0 |
| -3 | 3 | 0 |
| 100 | -100 | 0 |
| -25 | 25 | 0 |
| 0 | 0 | 0 |
Practical Applications
- Solving Equations: Additive inverses are crucial for isolating variables in algebraic equations. For example, to solve x + 5 = 10, we add the additive inverse of 5 (which is -5) to both sides: x + 5 + (-5) = 10 + (-5), simplifying to x = 5.
- Simplifying Expressions: Additive inverses help in combining like terms.
- Computer Science: In computer programming, additive inverses are used in various algorithms and data structures, such as representing negative numbers.
Key Properties
- Negation: The additive inverse is simply the negation of the original number.
- Zero Sum: The sum of a number and its additive inverse is always zero.
- Uniqueness: Every number has a unique additive inverse.
