When adding two integers, we will have to consider two cases. The first case is when the two integers have the same sign. The second case is when the two integers have different signs. Let's go over the rules and then demonstrate them with some examples.

## Adding Integers with the SAME Sign

RULE: To add integers with the same sign, add their absolute values then copy the common sign.

**Example 1:** \(\left( { + 5} \right) + \left( { + 3} \right) \)

Since the signs of the two integers are the same (both positive), we will add their absolute values.

The absolute value of \(+5\) is \(5\).

The absolute value of \(+3\) is \(3\).

Let's add them together, \(5+3=8\)

Because both are positive numbers, we copy the common sign which is positive.

Therefore, \(\left( { + 5} \right) + \left( { + 3} \right) = + 8\)

**Example 2:** \(\left( { - 13} \right) + \left( { - 7} \right)\)

Just like in example 1, the signs are the same because they are both negative. That means we are going to add their absolute value.

The absolute of \({ - 13}\) is \(13\).

The absolute of \({ - 9}\) is \(9\).

Let's add their absolute values, \(13 + 9 = 22\).

Because both are negative numbers, we copy the common sign which is negative.

Therefore, \(\left( { - 13} \right) + \left( { - 9} \right) = - 22\).

## Adding Integers with DIFFERENT Signs

RULE: To add integers with different signs, subtract their absolute values then copy the sign of the number which has the greater absolute value.

**Example 3:** \(\left( { - 11} \right) + \left( +5 \right)\)

The two numbers have different signs that means we are going to subtract their absolute values.

The absolute value of \(-11\) is \(11\).

The absolute value of \(+5\) is \(5\).

Subtracting their absolute values, we get \(11 - 5 = 6\).

Since \(-11\) has the greater absolute value and its sign is negative, our final answer will have a negative sign.

Therefore, \(\left( { - 11} \right) + \left( { + 5} \right) = - 6\)

**Example 4:** \(\left( { + 14} \right) + \left( { - 5} \right)\)

They have difference signs so we should subtract their absolute values.

The absolute value of \(+14\) is \(14\).

The absolute value of \(-5\) is \(5\).

Subtracting their absolute values, we have \(14 - 5 = 9\).

And since \(+14\) has the greater absolute and it's positive, our final answer must be a positive number.

Therefore, \(\left( { + 14} \right) + \left( { - 5} \right) = 9\).