Lesson 14 of 19
The additive inverse
Show on a big screenYou owe ₹8 and you hold ₹8. Together that is ₹0.
Step 1 of 4
- Start at 8 on the line.
- Its mirror mark is −8: same distance from 0, other side.
- Add them: 8 + (−8) = 0.
- Mirror −8 back. You reach 8.
Rule: Adding a number to its gives 0. For a, that partner is written −a. Multiplying by −1 finds the partner. Additive inverse — the partner that adds back to 0. It is the opposite you already know.
Here a stands for any number, such as 8 or −8.
The partner of 8 is −8. The partner of −8 is 8, so −(−8) = 8. Zero is its own partner, since 0 + 0 = 0.
Taking away a number is adding its . So 12 − 5 and 12 + (−5) are the same.
| Number a | Additive inverse −a | a + (−a) | (−1) × a |
|---|---|---|---|
| 8 | −8 | 0 | −8 |
| −8 | 8 | 0 | 8 |
| 0 | 0 | 0 | 0 |
| −15 | 15 | 0 | 15 |
Slide x until (−1) × x matches the target.
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Try the lab to finish this lesson.