Integer rules in math define how integers behave under basic arithmetic operations such as addition and multiplication. These rules ensure the result of these operations remains an integer.
Basic Integer Rules
Here are the fundamental integer rules as they relate to addition and multiplication:
- Addition Rules:
- Sum of two positive integers is an integer. For example, 3 + 5 = 8.
- Sum of two negative integers is an integer. For example, -3 + (-5) = -8.
- Multiplication Rules:
- Product of two positive integers is an integer. For example, 3 * 5 = 15.
- Product of two negative integers is an integer. For example, -3 * -5 = 15.
Further Insights into Integer Operations
While the reference focused on the basic rules, it's important to understand more about how integers behave:
- Addition of a positive and negative integer: The result depends on the magnitudes of the numbers.
- If the positive integer has a larger absolute value, the result is positive. For instance, 7 + (-3) = 4.
- If the negative integer has a larger absolute value, the result is negative. For instance, 3 + (-7) = -4.
- Multiplication of a positive and negative integer: The result is always negative. For example, 3 (-5) = -15 and -3 5 = -15.
Summary Table of Integer Rules
| Operation | Rule | Example | Result |
|---|---|---|---|
| Positive + Positive | Sum is a positive integer | 5 + 7 | 12 |
| Negative + Negative | Sum is a negative integer | -5 + (-7) | -12 |
| Positive * Positive | Product is a positive integer | 5 * 7 | 35 |
| Negative * Negative | Product is a positive integer | -5 * (-7) | 35 |
| Positive + Negative | Sum may be positive or negative | 5 + (-7) | -2 |
| Negative + Positive | Sum may be positive or negative | -5 + 7 | 2 |
| Positive * Negative | Product is a negative integer | 5 * (-7) | -35 |
| Negative * Positive | Product is a negative integer | -5 * 7 | -35 |
These rules are fundamental to performing arithmetic operations with integers. Understanding them is key to success in more complex mathematical calculations.
