The additive inverse of 256 is -256. The additive inverse of any number is the number that, when added to the original, gives zero (the additive identity). So 256 + (-256) = 0. This concept is taught in Class 6–8 Mathematics under Integers.
Additive inverse of 256 = -256.
Verification: 256 + (-256) = 0.
Additive inverse of any number n = -n.
The sum of a number and its additive inverse = 0 (additive identity).
Additive inverse of 0 = 0.
Multiplicative inverse of 256 = 1/256 (different from additive inverse).
Definition: • Additive Inverse of a number n = -n • Property: n + (-n) = 0 • The sum of a number and its additive inverse is always 0
Additive Inverse of 256: • Additive inverse of 256 = -256 • Check: 256 + (-256) = 0 ✓
Rule: • Additive inverse of a positive number = the negative of that number • Additive inverse of a negative number = the positive of that number
Examples:
| Number | Additive Inverse | Verification |
|---|---|---|
| 256 | -256 | 256 + (-256) = 0 |
| -256 | 256 | -256 + 256 = 0 |
| 100 | -100 | 100 + (-100) = 0 |
| -75 | 75 | -75 + 75 = 0 |
| 0 | 0 | 0 + 0 = 0 |
| ½ | -½ | ½ + (-½) = 0 |
| -3.5 | 3.5 | -3.5 + 3.5 = 0 |
Additive Identity: • 0 is the Additive Identity: n + 0 = n • The additive inverse of 0 is 0 itself
Additive Inverse vs Multiplicative Inverse:
| Property | Additive Inverse | Multiplicative Inverse |
|---|---|---|
| Also called | Negative of a number | Reciprocal |
| Formula | -n | 1/n |
| Result when combined | n + (-n) = 0 | n × (1/n) = 1 |
| Identity element | 0 | 1 |
| Example (for 256) | -256 | 1/256 |
Key Point: The additive inverse of 256 is -256 (not 1/256, which is the multiplicative inverse).
The additive inverse of 256 is -256. This is because 256 + (-256) = 0. The additive inverse of any number n is -n, since their sum equals 0 (the additive identity). For negative numbers, the additive inverse is positive: additive inverse of -256 = +256.
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