In this post we will learn about addition of integers.

First we will understand the rules of addition different integers.

After that we will move on to solve worksheets related to this concept.

**Sum of Integers**

Understand that there are three types of integers

(a) Positive Integer

(b) Negative Integer

(c) Zero

Different rules are applied for addition of different set of integers.

There are mainly three possibilities of adding integers-

- Addition of two positive integers.
- Addition of two negative integers.
- Addition of one positive and one negative integers.

The rule summary off addition of integer is given below:

Read below for full description of rules along with example explanation.

**Sum of two positive integer**

When we add a two positive integers, the result will also be a positive integer.

Let us learn addition of two integers with the help of examples:

a. **Sum of two integer****s**

⟹ (3) + (2) = 5

⟹ (4) + (6) = 10

Positive integers can be written with plus(+) sign in solving the problem. There is no need to show plus sign in answer

**b. Sum of more the two integers**

⟹ **(4) + (5) + (8)** ⟹ (4 + 5) + (8) ⟹ (9) + (8) ⟹ 17

**⟹** **(1) + (2) + (3) + (4) **⟹ (1+2) + (3 + 4) ⟹ 3 + 7 => 10

**c.** **Sum of two and three digit integers **

⟹ **(12) + (20)** = 32

⟹** (600) + (150) + (200)** ⟹ (750) + (200) ⟹ 950

**d. Addition of zero**

Addition of zero does not affect any changes in integers.

Lets we add 0 and +4

⟹ **(0) + (4)** ⟹ 4

⟹ **(16) + (0) + (20)** ⟹ 36

**Sum of Two Negative Integers**

Addition of negative integer results in negative integer.

Follow the below steps for adding negative integers

(a) Add the numbers

(b) Get the final sum and put minus sign in front of the answer

**a.** **Addition of two negative integers-**

⟹ **(-4) + (-5)** = -9

⟹ **(-2) + (-7)** = -9

Here we simply added the numbers and put minus (-) sign in front of the answer

Explanation of addition using number line

**b.** **Addition of more them two negative integers**–

**Example 01**

⟹ **(-1) + (-2) + (-3) **

⟹ (-1-2) + (-3)

⟹ (-3) + (-3)

⟹ – 6

**Example 02**

⟹ **(-2) + (-5) + (-4) + (-1)**

⟹ (- 2 – 5) + ( – 4 – 1)

⟹ (-7) + (-5) = -12

**c**. **Addition of two and three digit negative integer**

**(-11) + (-15) + (-10)**

⟹ (-11 – 15) + (-10)

⟹ (-26) + (-10)

⟹ -36

**d**. **Addition of zero in negative integers**

There is no affect of addition of zero in negative integer, we get the same value of integer

(-3) + (0) => -3

**Sum of Positive and Negative Integer**

On adding positive and negative integers, we get following results

(a) If positive digit is greater than negative digit, the final answer will be positive integer

If Positive digit > Negative digit

Final Sum = Positive Integer

(b) If Positive digit is less than negative digit, the final answer will be negative integer

If Positive Digit < Negative Digit

Then Final Sum = Negative Integer

Let us understand the above concepts with the help of example:

**a. Positive Digit > Negative Digit**

⟹ **(-7) + (8)**

Positive Digit = 8

Negative Digit = 7

Solving the equation

⟹ **(-7) + (8)**

⟹ **1**

Hence addition is positive integer

**b. Positive Digit < Negative Digit**

⟹ **(-7) + (5)**

Positive Digit = 5

Negative Digit = 7

Solving the equation

⟹ **(-7) + (5)**

⟹** 5 – 7**

⟹ **-2**

Hence after addition we get negative integer

**c**. **Adding more than two integers**

Here we solve in pairs of positive and negative integers

**Example 01**

⟹ **(-2) + (4) + (-9) + (3)**

⟹ (-2) + (-9) + (4) + (3)

⟹ (- 2 – 9) + (4 + 3)

⟹ -11 + 7

⟹ -4

**Example 02****(-1) + (-2) + (-3) + (4) **

⟹ (-1-2-3) + 4

⟹ (- 6) + 4

⟹ -2

**d**. **Addition of zero**

Addition of zero does not affect any change

**(-5) + (6) + 0** ⟹ 1

**(-5) + (+5) + 0** ⟹ (-5 + 5 ) + 0 ⟹ 0

**e. Addition of two and three digit negative number-**

(-20) + (150) + (-40)

⟹ (-20 – 40) + 150

⟹ (-60) + 150

⟹ 90