# Integer addition: Problem type 1

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Integers are whole numbers and their opposites taken together. They don’t have decimal or fractional parts.

For example, the following set of numbers are integers

Z = {…−3, −2, −1, 0, 1, 2, 3…}

In this lesson, we solve problems involving addition of integers

In this addition of two integers, there are two cases.

• When the integers have a common or same sign.

• When the integers have different signs, i.e., one integer is positive while the other is negative.

### Rules of Integer Addition

In case, the signs of the integers are common or same (either both positive or both negative)

• We add the absolute values of the integers, i.e., add the integers after ignoring their signs.

• Then we attach the common sign to the sum from above step.

In case, the signs of the integers are different (one positive and another negative)

• We first take the absolute values of the integers by ignoring their signs.

• We subtract the smaller number from the larger.

• Then we attach the sign of the integer with larger absolute value to the difference obtained in above step.

### Formula

If the signs of integers are same, we add and keep the sign.

If the signs of integers are different, we subtract and keep the sign of larger number.

3 + (−7)

### Solution

Step 1:

The signs of the numbers are different. So, we subtract the absolute values of the integers.

|−7| –|3| = 7 – 3 = 4

Step 2:

The sign of the number with larger absolute value (−7) is −.

We keep this sign with the difference obtained in above step

So, 3 + (−7) = − 4

−5 + (−8)

### Solution

Step 1:

The signs of the numbers are same. So, we add the absolute values of the integers.

|−5| +| − 8| = 5 + 8 = 13

Step 2:

The common sign of both numbers is −.

We keep this sign with the sum obtained in above step

So, −5 + (−8) = − 13