When you multiply or divide two numbers, positive or negative, follow one simple rule:
| If Signs are the Same, the answer is poSitive but if Not, the answer is Negative. |
7 × 8 = 56 and (−7) × (−8) = 56 (−7) × 8 = −56 and 7 × (−8) = −56 56 ÷ 7 = 8 and −56 ÷ (−8) = 7 56 ÷ (−7) = −8 and −56 ÷ 8 = −7 |
That is, positive × positive or negative × negative will result in a positive. In contrast, positive × negative will result in a negative.
This principle can be extended to multiplication and division by more than two numbers. For example, if three numbers are multiplied together, the result will be positive if there are NO negative numbers, or two negative numbers. The result will be negative if there is one or three negative numbers.
This pattern can be summarized as follows. When you multiply or divide a group of nonzero numbers, the result will be positive if you have an EVEN number of negative numbers. The result will be negative if you have an ODD number of negative numbers.
Is the product −12 × −15 × 3 × 4 × 5 × −2 positive or negative?
If xy ≠ 0, is −x × −y definitely positive?