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Operations with Integers

The additive inverse

You owe ₹8 and you hold ₹8. Together that is ₹0.

Start at 8 on the line.
Step 1 of 4
  1. Start at 8 on the line.
  2. Its mirror mark is −8: same distance from 0, other side.
  3. Add them: 8 + (−8) = 0.
  4. Mirror −8 back. You reach 8.

Rule: Adding a number to its additive inverse 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 additive inverse. So 12 − 5 and 12 + (−5) are the same.

Four numbers and their additive inverses
Number aAdditive inverse −aa + (−a)(−1) × a
8−80−8
−8808
0000
−1515015

Slide x until (−1) × x matches the target.

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This track

  1. 0 Start here
  2. 1 Two moves the same way
  3. 2 A move each way
  4. 3 Taking away, another way round
  5. 4 Two dashes on one line
  6. 5 Without the line
  7. 6 Checkpoint: adding and taking away
  8. 7 The same move, counted again
  9. 8 Past the end of the times table
  10. 9 Sharing it out
  11. 10 What zero does
  12. 11 Where we use them
  13. 12 Checkpoint: multiplying, sharing and zero
  14. 13 Zero pairs
  15. 14 The additive inverse
  16. 15 Many numbers, one sign
  17. 16 A number times a bracket
  18. 17 The big picture
  19. 18 Track quiz

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