Adding numbers with integers involves understanding the concept of positive and negative numbers and applying specific rules based on their signs. Here's a breakdown:
1. Understanding Integers
Integers are whole numbers (not fractions or decimals) that can be positive, negative, or zero. Examples include: -3, -2, -1, 0, 1, 2, 3.
2. Rules for Adding Integers
There are two primary scenarios when adding integers:
-
Same Signs: If both integers have the same sign (both positive or both negative), add their absolute values and keep the common sign.
- Example: 3 + 5 = 8 (Both positive, so add 3 and 5, and the answer is positive 8)
- Example: (-2) + (-4) = -6 (Both negative, so add 2 and 4, and the answer is negative 6)
-
Different Signs: If the integers have different signs (one positive and one negative), subtract the smaller absolute value from the larger absolute value. The result will have the sign of the integer with the larger absolute value.
- Example: 7 + (-3) = 4 (Absolute value of 7 is 7, absolute value of -3 is 3. 7-3=4. Since 7 has a larger absolute value and is positive, the answer is positive 4).
- Example: (-9) + 2 = -7 (Absolute value of -9 is 9, absolute value of 2 is 2. 9-2=7. Since -9 has a larger absolute value and is negative, the answer is negative 7).
3. Absolute Value
The absolute value of a number is its distance from zero, regardless of its sign. It is denoted by vertical bars: | |.
- |5| = 5
- |-5| = 5
- |0| = 0
4. Examples
Here are some more examples to illustrate the rules:
- (-10) + 5 = -5
- 12 + (-4) = 8
- (-6) + (-3) = -9
- 8 + 2 = 10
5. Number Line Visualization
You can also visualize adding integers on a number line.
- Adding a positive integer moves you to the right on the number line.
- Adding a negative integer moves you to the left on the number line.
6. Key Takeaways
- When adding integers with the same sign, add their absolute values and keep the common sign.
- When adding integers with different signs, subtract their absolute values (larger minus smaller) and take the sign of the number with the larger absolute value.
In summary, adding integers depends on whether they have the same or different signs. Applying the rules of absolute values and signs consistently leads to the correct result.
