- Operations with Integers
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- Integer addition: Problem type 1
- Integer addition: Problem type 2
- Integer subtraction: Problem type 1
- Integer subtraction: Problem type 2
- Operations with absolute value: Problem type 1
- Computing the distance between two integers on a number line
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# Integer addition: Problem type 1

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.

**Add**

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

**Add**

−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