# Adding Integers

When adding two integers, we need to consider two scenarios. The first scenario occurs when both integers have the same sign. The second scenario arises when the integers have different signs. Let’s review the rules for each case and then illustrate them with examples.

## Adding Integers with the SAME Sign

RULE: To add integers with the same sign, add their absolute values and apply 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 and then use the sign of the number with the larger 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 larger absolute value and its sign is negative, our final answer must 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 larger absolute and it’s positive, our final answer must be a positive number.

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