When adding and subtracting integers, the key lies in understanding how the signs of the numbers interact. Here's a breakdown of the rules:
Rules for Adding Integers
The rules for adding integers are based on whether the integers have the same or different signs:
-
Same Signs: When adding two integers with the same sign (both positive or both negative), you add their absolute values and keep the common sign.
- Example: 3 + 2 = 5 (both positive, so add 3 and 2, keep positive sign)
- Example: -3 + -2 = -5 (both negative, so add 3 and 2, keep negative sign)
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Different Signs: When adding two integers with different signs (one positive and one negative), you subtract the smaller absolute value from the larger absolute value. The result takes the sign of the integer with the larger absolute value.
- Example: -3 + 2 = -1 (subtract 2 from 3, 3 has larger absolute value and is negative, so result is -1)
- Example: 3 + -2 = 1 (subtract 2 from 3, 3 has larger absolute value and is positive, so result is 1)
Rules for Subtracting Integers
Subtracting integers can be simplified by converting the subtraction to addition:
- Subtracting a positive number: Subtracting a positive number is equivalent to adding a negative number. For example, 5 - 3 is the same as 5 + (-3). You then follow the rules for addition (different signs subtract the numbers, and keep the sign of the bigger number).
- Subtracting a negative number: Subtracting a negative number is equivalent to adding its positive counterpart. For example, 5 - (-3) is the same as 5 + 3. Then add the integers based on the rule for the same signs (add the numbers, and keep the same sign).
In summary, here’s a table:
| Operation | Scenario | Action | Example |
|---|---|---|---|
| Addition | Same Signs (Both +) | Add numbers, keep positive sign | 3 + 2 = 5 |
| Addition | Same Signs (Both -) | Add numbers, keep negative sign | -3 + -2 = -5 |
| Addition | Different Signs | Subtract smaller absolute value from larger, keep sign of bigger number | -3 + 2 = -1 |
| Addition | Different Signs | Subtract smaller absolute value from larger, keep sign of bigger number | 3 + -2 = 1 |
| Subtraction | Subtracting a positive number | Same as adding a negative. Follow addition rules. | 5 - 3 = 5 + (-3) = 2 |
| Subtraction | Subtracting a negative number | Same as adding a positive. Follow addition rules. | 5 - (-3) = 5 + 3 = 8 |
By converting subtraction to addition of the opposite, you can apply the addition rules to all integer operations.
