Adding integers with absolute values involves considering their signs. The process differs depending on whether the integers have the same sign or different signs.
Adding Integers with the Same Sign
When adding two integers with the same sign (both positive or both negative):
- Find the absolute value of each integer. The absolute value of a number is its distance from zero, and it's always non-negative. For example, |-3| = 3 and |5| = 5.
- Add the absolute values together.
- Give the result the same sign as the original integers.
Example 1: Adding two positive integers
3 + 5 = ?
- |3| = 3
- |5| = 5
- 3 + 5 = 8
- Therefore, 3 + 5 = 8 (positive)
Example 2: Adding two negative integers
-4 + -2 = ?
- |-4| = 4
- |-2| = 2
- 4 + 2 = 6
- Therefore, -4 + -2 = -6 (negative)
Adding Integers with Different Signs
When adding two integers with different signs (one positive and one negative):
- Find the absolute value of each integer.
- Subtract the smaller absolute value from the larger absolute value.
- Give the result the same sign as the integer with the larger absolute value.
Example 1: Adding a positive and a negative integer
-7 + 4 = ?
- |-7| = 7
- |4| = 4
- 7 - 4 = 3
- Therefore, -7 + 4 = -3 (negative because |-7| > |4|)
Example 2: Adding a positive and a negative integer
5 + -2 = ?
- |5| = 5
- |-2| = 2
- 5 - 2 = 3
- Therefore, 5 + -2 = 3 (positive because |5| > |-2|)
In summary, adding integers with absolute value requires you to consider the signs of the numbers and perform addition or subtraction based on whether the signs are the same or different. Remember to always apply the appropriate sign to the final answer based on the original integers.
