🔑 The Golden Rule
Same signs → Positive result. Different signs → Negative result.
This applies to BOTH multiplication AND division. Once you master this one rule, all four operations become easy!
When both numbers are on the same team (both + or both −), the result is always positive. When they're on different teams, the result is always negative.
The sign rule is identical for multiplication and division. Only the arithmetic operation differs — the sign of the result follows the exact same pattern!
When two integers have the same sign, their product is always positive. Multiply the absolute values and keep the + sign.
(+3) × (+4): multiply 3 × 4 = 12, same signs → +12
(−5) × (−2): multiply 5 × 2 = 10, same signs → +10
What is (−9) × (−4)? (Same signs — multiply 9×4, result is positive)
When two integers have different signs, their product is always negative. Multiply the absolute values and make the result negative.
(+6) × (−3): multiply 6 × 3 = 18, different signs → −18
(−7) × (+4): multiply 7 × 4 = 28, different signs → −28
What is (+8) × (−7)? (Different signs — multiply 8×7, make it negative)
When two integers have the same sign, their quotient is always positive. Divide the absolute values and keep the + sign.
(+12) ÷ (+4): divide 12 ÷ 4 = 3, same signs → +3
(−20) ÷ (−5): divide 20 ÷ 5 = 4, same signs → +4
What is (−36) ÷ (−9)? (Same signs — divide 36÷9, result is positive)
When two integers have different signs, their quotient is always negative. Divide the absolute values and make the result negative.
(+15) ÷ (−3): divide 15 ÷ 3 = 5, different signs → −5
(−18) ÷ (+6): divide 18 ÷ 6 = 3, different signs → −3
What is (−42) ÷ (+7)? (Different signs — divide 42÷7, make it negative)
| First | Operation | Second | Result Sign | Example |
|---|---|---|---|---|
| + | × or ÷ | + | + (Positive) | (+3)×(+4) = +12 |
| − | × or ÷ | − | + (Positive) | (−5)×(−2) = +10 |
| + | × or ÷ | − | − (Negative) | (+6)×(−3) = −18 |
| − | × or ÷ | + | − (Negative) | (−7)×(+4) = −28 |
🔑 One Rule to Remember Them All
Same signs = Positive | Different signs = Negative
Count the number of negative signs: even number of negatives → positive, odd number → negative!