Add and subtract integers

Add and subtract integers

Add and subtract integers

Adding and subtracting negative numbers is really the same idea — you just need to remember two sign rules.

Rule 1 — subtraction turned into addition

`a − b = a + (−b)`

Subtracting `b` means adding its opposite. That converts everything into addition.

Likewise:

`a − (−b) = a + b`

Two minus signs in a row "cancel" — the result is plus.

Rule 2 — adding with same or different signs

Same signs (both positive or both negative):
  • add the absolute values;
  • keep the sign.

`(−3) + (−4) = −(3 + 4) = −7`

Different signs (one positive, one negative):
  • subtract the absolute values (larger − smaller);
  • the sign is the same as the number with the larger absolute value.

`(−7) + 3 = −(7 − 3) = −4` (|−7| > |3|, so the result is negative)

`7 + (−3) = +(7 − 3) = 4` (|7| > |−3|, so the result is positive)

Picture on the number line

You can think of adding and subtracting integers as steps on the number line:

  • `+5` means 5 steps to the right.
  • `−5` means 5 steps to the left.
  • `a − b` is the same as `a + (−b)`, so subtracting is "steps in the opposite direction".

Common mistakes

  • `−3 − 5 ≠ 2`. Correct: `−3 − 5 = −3 + (−5) = −8` (both pull left).
  • `7 − (−3) ≠ 4`. Correct: `7 − (−3) = 7 + 3 = 10`.
  • `(−2) + (−3) ≠ −1`. Correct: both are negative → `−(2 + 3) = −5`.

Try it yourself