The rules for multiplying integers determine the sign of the product based on the signs of the numbers being multiplied. These rules are essential for performing arithmetic operations with signed numbers.
Integer Multiplication Rules
The sign of the product when multiplying integers depends on whether the integers have the same sign or different signs. Here's a summary:
- Positive x Positive = Positive: A positive number multiplied by a positive number results in a positive number.
- Example: 3 x 4 = 12
- Positive x Negative = Negative: A positive number multiplied by a negative number results in a negative number.
- Example: 3 x (-4) = -12
- Negative x Positive = Negative: A negative number multiplied by a positive number results in a negative number.
- Example: (-3) x 4 = -12
- Negative x Negative = Positive: A negative number multiplied by a negative number results in a positive number.
- Example: (-3) x (-4) = 12
Summary Table
| Integer 1 Sign | Integer 2 Sign | Product Sign | Example |
|---|---|---|---|
| Positive | Positive | Positive | 2 x 3 = 6 |
| Positive | Negative | Negative | 2 x (-3) = -6 |
| Negative | Positive | Negative | (-2) x 3 = -6 |
| Negative | Negative | Positive | (-2) x (-3) = 6 |
These rules are fundamental to understanding how integers interact under multiplication and are consistently applied in various mathematical contexts.
