The rules for adding integers can be summarized into four key principles that determine the sign and value of the result.
Understanding the Rules
These rules ensure you can add any combination of positive and negative numbers, including zero. Let's break them down:
- Adding Two Positive Integers: The sum of two positive integers is always a positive number. This is the most basic form of addition.
- Example: 5 + 3 = 8
- Adding Two Negative Integers: The sum of two negative integers is always a negative number. Think of it as accumulating debt.
- Example: -4 + (-2) = -6
- Adding Integers with Zero: Adding zero to any integer results in the same integer. Zero is the additive identity.
- Example: 7 + 0 = 7 and -3 + 0 = -3
- Additive Inverse: The sum of an integer and its additive inverse (the same number with the opposite sign) always equals zero.
- Example: 6 + (-6) = 0 and -9 + 9 = 0
Summary Table of Integer Addition Rules
| Scenario | Result Sign | Example |
|---|---|---|
| Positive + Positive | Positive | 2 + 7 = 9 |
| Negative + Negative | Negative | -3 + (-5) = -8 |
| Integer + 0 | Same Sign | 8 + 0 = 8, -4 + 0 = -4 |
| Integer + Its Additive Inverse | Zero | 10 + (-10) = 0 |
These simple rules form the foundation for all integer additions, enabling accurate calculations in various situations. Understanding these rules makes addition of integers straightforward and helps build a solid base for more advanced mathematical operations.
