The additive inverse of 100 is -100.
Understanding the Additive Inverse
The additive inverse of any number is the number that, when added to the original number, results in a sum of zero. It is also often referred to as the "opposite number." For any real number 'a', its additive inverse is '-a', such that the sum a + (-a) = 0.
This concept is fundamental in arithmetic and algebra, helping to define operations like subtraction and understand number properties on the number line.
How to Find the Additive Inverse
To find the additive inverse of a number:
- If the number is positive, its additive inverse is the same number with a negative sign.
- If the number is negative, its additive inverse is the same number with a positive sign (removing the negative sign).
- The additive inverse of zero is zero itself.
Examples of Additive Inverses
Let's look at some examples to illustrate this concept, including the specific case of 100:
| Number | Additive Inverse | Result (Number + Additive Inverse) |
|---|---|---|
| 10 | -10 | 10 + (-10) = 0 |
| 20 | -20 | 20 + (-20) = 0 |
| 50 | -50 | 50 + (-50) = 0 |
| 100 | -100 | 100 + (-100) = 0 |
| -5 | 5 | -5 + 5 = 0 |
| 0 | 0 | 0 + 0 = 0 |
As shown, for the number 100, its additive inverse is -100 because when you add them together (100 + (-100)), the sum is 0.
Practical Insights
Understanding additive inverses is crucial for:
- Solving Equations: When isolating a variable, you often use the additive inverse to move terms across the equality sign.
- Number Line Operations: Moving in opposite directions by the same magnitude on a number line brings you back to the starting point (zero if starting from zero).
- Conceptualizing Subtraction: Subtraction can be viewed as adding the additive inverse of a number (e.g.,
a - bis equivalent toa + (-b)).
