The additive inverse of a fraction is the number that, when added to the original fraction, results in zero.
In simpler terms, the additive inverse of a fraction a/b is -a/b. This is because a/b + (-a/b) = 0.
Here's a breakdown:
- Definition: The additive inverse is also known as the opposite. It's the number that "undoes" the original number when added together.
- Positive Fractions: The additive inverse of a positive fraction is the same fraction with a negative sign in front of it. For example, the additive inverse of
2/3is-2/3. - Negative Fractions: The additive inverse of a negative fraction is the same fraction without the negative sign. For example, the additive inverse of
-5/7is5/7.
Examples:
| Fraction | Additive Inverse | Verification |
|---|---|---|
| 1/4 | -1/4 | 1/4 + (-1/4) = 0 |
| -3/5 | 3/5 | -3/5 + 3/5 = 0 |
| 7/2 | -7/2 | 7/2 + (-7/2) = 0 |
In essence, the additive inverse changes the sign of the fraction to its opposite, ensuring that their sum equals zero.
