To help you analyze multiplication patterns based on the signs of the factors and products, here's a chart filled with possible combinations of factors and their corresponding products:
| Factor 1 | Factor 2 | Product | Sign of Factor 1 | Sign of Factor 2 | Sign of Product | |----------|----------|----------|------------------|------------------|------------------| | Positive | Positive | Positive | + | + | + | | Positive | Negative | Negative | + | - | - | | Negative | Positive | Negative | - | + | - | | Negative | Negative | Positive | - | - | + | | Zero | Positive | Zero | 0 | + | 0 | | Zero | Negative | Zero | 0 | - | 0 | | Zero | Zero | Zero | 0 | 0 | 0 |
Patterns Observed:
- Positive × Positive = Positive: The product is positive if both factors are positive.
- Positive × Negative = Negative: The product is negative if one factor is positive and the other is negative.
- Negative × Positive = Negative: Similar to the previous, the product remains negative.
- Negative × Negative = Positive: The product is positive when both factors are negative.
- Multiplication by Zero: Any number multiplied by zero results in zero.
Conclusion:
- The product is positive if both factors are the same sign (both positive or both negative).
- The product is negative if the factors have different signs.
- The presence of zero in multiplication always results in zero, regardless of the other factor.
Feel free to use these insights to test various numbers using a calculator or other tools you have available!