Integer Subtraction – Positive and Negative Numbers
Subtracting integers extends the basic subtraction you know to include negative numbers. The key rule makes it surprisingly simple.
The Golden Rule
Subtracting a positive is the same as moving left on the number line. Subtracting a negative is the same as adding a positive.
5 − 3 = 2 (subtract positive: move left)
5 − (−3) = 5 + 3 = 8 (subtract negative = add positive)
Summary Table
| Calculation | Rule applied | Result |
|---|---|---|
| (+8) − (+5) | Positive − Positive | +3 |
| (+8) − (−5) | Subtract negative = add positive | +13 |
| (−4) − (+3) | Negative − Positive (more negative) | −7 |
| (−4) − (−3) | Subtract negative = add positive | −1 |
Number Line Examples
Start at +6, subtract +9: move left 9 → land on −3
Start at −2, subtract −5: same as −2 + 5 = +3 (move right 5)
Common Mistakes
- Forgetting that −(−n) = +n.
- Treating (−3) − (−3) as −6 instead of 0.
Key Takeaways
- Subtracting a positive: move left (result is smaller).
- Subtracting a negative: change to addition (result is larger).
- The number line provides a reliable visual check.
Practice: Subtract Integers
Two signed numbers are shown below. If you get it wrong (or leave it blank), we'll apply the golden rule together.
Calculate the difference.