# Adding Integers

1. If the addends have the same sign, add the absolute values and the result will also have the same sign.

3 + 5 = 8

(−3) + (5) = −8

2. If the addends have different signs, subtract the absolute values (subtract the lowest from the largest) and the result is in the same sign as the number of the largest absolute value.

− 3 + 5 = 2

3 + (−5) = −2

### Properties of the Addition of Integers

1. **Closure**:

The result of adding two integers is another integer.

**a + b **

**3 + (−5) **

2. **Associative**:

The way in which the addends are grouped does not change the result.

(**a + b) + c = a + (b + c)**

(2 + 3) + (−5) = 2 + [3 + (−5)]

5 − 5 = 2 + (−2)

0 = 0

3. **Commutative**:

The order of the addends does not change the sum.

**a + b = b + a **

2 + (−5) = (−5) + 2

−3 = −3

4. **Additive identity**:

The** 0** is the neutral element in the addition because every number added with it gives the same number.

**a + 0 = a **

(−5) + 0 = −5

5. **Additive Inverse**

The sum of a number and its inverse is always 0.

**a + (−a) = 0**

5 + (−5) = 0

**The opposite of the opposite of a integer is equal to the absolute value of the same number. **

−(−5) = 5