Many numbers, one sign
A long product has many minus signs. Can you tell its sign before you multiply?
- The factors: (−2) × 3 × (−1) × (−4).
- Start with (−2). It is below zero.
- Times 3: the sign stays.
- Times (−1): the sign flips.
- Times (−4): it flips again. The product is −24.
- Three negative factors. An odd count.
Yes, if no number in the product is 0. Count the minus signs. An odd count gives a negative product.
Each number in a product is a factor. A negative factor flips the sign once. A plus becomes a minus, and a minus becomes a plus. A positive factor leaves the sign alone. Start from plus. Two flips end at plus again. So an even count gives a positive product.
Rule: No zero among the factors? Count the negative ones. An even count gives a product more than zero. An odd count gives a product less than zero. A zero factor makes the product 0.
The product stays the same in any order. So you can count the negative factors in any place.
| Factors | Negative factors | Product |
|---|---|---|
| 2 × 3 × 4 | 0 | 24 |
| (−2) × 3 × 4 | 1 | −24 |
| (−2) × (−3) × 4 | 2 | 24 |
| (−2) × (−3) × (−4) | 3 | −24 |
| (−2) × (−3) × (−4) × (−1) | 4 | 24 |
| (−2) × 0 × (−4) | 2 | 0 |
Name the sign first. Then tap a factor to flip its sign.
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