🧱 See It
3 × (−2) means "3 groups of negative-2." Build three groups, two negative tiles each:
3 groups × 2 negative tiles each = 6 negative tiles total = −6.
But what about (−3) × 2? You can't build "negative-3 groups" — that doesn't mean anything physically. Instead, read it as "the opposite of 3 groups of 2." Three groups of 2 is 6, so the opposite is −6. Multiplying by a negative flips the sign of the normal, both-positive answer.
✏️ Draw It
Once the signs are sorted, multiplying and dividing follow the exact same sign pattern. Use this as a lookup chart, not something to memorize by heart:
| Signs | × Result | ÷ Result |
|---|---|---|
| Same (+, + or −, −) | positive | positive |
| Different (+, − or −, +) | negative | negative |
Same signs going in → positive comes out. Different signs going in → negative comes out. Multiplication and division match.
🔢 Write It
The rule in words: multiply or divide the numbers as if they were both positive, then figure out the sign separately.
- Same sign (both positive, or both negative) → answer is positive.
- Different signs (one positive, one negative) → answer is negative.
For example: (−4) × (−3) = +12 — same signs, so positive. But (−4) × 3 = −12 — different signs, so negative. Same two numbers, different sign pairing, opposite results.
💡 Worked Examples
Example 1: (−6) × (−2)
- Check the signs: negative and negative — that's the same sign.
- Same sign → the answer will be positive.
- Multiply the numbers, ignoring signs:
6 × 2 = 12 - Answer:
(−6) × (−2) = 12
Example 2: (−20) ÷ 4
- Check the signs: negative and positive — that's a different sign pairing.
- Different signs → the answer will be negative.
- Divide the numbers, ignoring signs:
20 ÷ 4 = 5 - Answer:
(−20) ÷ 4 = −5
🧠 Quick Reference
| Signs | Answer's Sign |
|---|---|
| +, + | + |
| −, − | + |
| +, − | − |
| −, + | − |