Multiplying Integers – Rules for Signs
When multiplying integers, the size of the answer is found by multiplying the magnitudes. The sign of the answer follows a simple rule.
The Sign Rules
| Calculation | Rule | Result Sign |
|---|---|---|
| (+) × (+) | Positive × Positive | Positive (+) |
| (+) × (−) | Positive × Negative | Negative (−) |
| (−) × (+) | Negative × Positive | Negative (−) |
| (−) × (−) | Negative × Negative | Positive (+) |
Memory aid: Same signs → positive. Different signs → negative.
Why Does Negative × Negative = Positive?
Look at the pattern for 3 × ...:
3 × 3 = 9 3 × 2 = 6 3 × 1 = 3 3 × 0 = 0 3 × (−1) = −3 3 × (−2) = −6
Now apply the same logic to (−3) × ...:
(−3) × 2 = −6 (−3) × 1 = −3 (−3) × 0 = 0 (−3) × (−1) = +3 (−3) × (−2) = +6
Worked Examples
Examples
(+5) × (+4) = +20
(+5) × (−4) = −20
(−5) × (+4) = −20
(−5) × (−4) = +20
Key Takeaways
- Same signs → positive product.
- Different signs → negative product.
- The magnitude is always positive (just the usual multiplication).
- This pattern extends to division as well.
Practice Questions
- Calculate (+7) × (+8).
- Calculate (+6) × (−5).
- Calculate (−9) × (−4).
- Calculate (−3) × (+12).
- The temperature drops 4°C every hour for 6 hours. Express the total change as an integer.