The rules of multiplication of integers govern how to determine the sign of the product based on the signs of the integers being multiplied. Here's a breakdown:
Rules for Multiplying Integers
The key lies in understanding how positive and negative signs interact during multiplication. We can summarize the rules as follows:
| Integer 1 Sign | Integer 2 Sign | Product Sign | Example |
|---|---|---|---|
| Positive | Positive | Positive | 2 * 3 = 6 |
| Positive | Negative | Negative | 2 * -3 = -6 |
| Negative | Positive | Negative | -2 * 3 = -6 |
| Negative | Negative | Positive | -2 * -3 = 6 |
Detailed Explanation of the Rules
- RULE 1: The product of a positive integer and a negative integer is negative.
- Example: 5 * -4 = -20. This can be thought of as adding -4 to itself five times: -4 + -4 + -4 + -4 + -4 = -20.
- RULE 2: The product of two positive integers is positive.
- Example: 3 * 7 = 21. This is basic multiplication as you learned in elementary school.
- RULE 3: The product of two negative integers is positive.
- Example: -6 * -2 = 12. This rule often requires more explanation. A negative times a negative can be understood in terms of repeated subtraction.
Practical Insights
- An even number of negative signs yields a positive product. For example, -1 -1 -1 * -1 = 1.
- An odd number of negative signs yields a negative product. For example, -1 -1 -1 = -1.
These multiplication rules extend when multiplying more than two integers. Simply multiply the absolute values of the integers, and then determine the sign of the product based on the number of negative integers.
