Addition of Integers Rules

Integers are whole numbers that can be positive, negative, and zero. Adding an integer needs a specific set of rules. The addition of integers rules is important to understand as they have to be used while adding and subtracting integers rules. We have one set of common rules which hold good for the addition and subtraction of integers.

To understand adding integers rules, let’s jump right in!

Introduction to Addition of Integers

Integers are defined as numbers including negative numbers (numbers with a ‘-’ sign), positive numbers, and zero. Only whole numbers (0,1,2,3,....) come under  integers. Fractions, decimals, and mixed fractions do not fall under integers as they do not fall under whole numbers.

Number Line

Integer Rules

We can perform various mathematical operations using integers but adding and subtracting integers rules will be discussed in this article. Firstly adding integers rules will be discussed and by using those rules the concept of adding integers will get easy for you.

Rules for the Addition of Integers

Rules for Adding Integers

There are special rules for adding integers (adding integers rules). As integers have symbols along with the value of the number, it is important to follow these rules while adding.

For simplicity purposes and to understand the core concepts better, we are going to consider the addition of 2 digits having ‘+’ or ‘-’ signs.

How to Add Integers

Case 1- When Both the Digits are Positive 

When the 2 numbers to be added are both positive, we add both the digits and assign their symbol as positive. 

For example, 3 + 4 = 7

Remember that we usually use positive digits and thus it is not always necessary to mention ‘+’ before a positive number.

We add positive digits 3 and 4 to obtain a positive sum 7

Addition of 2 Positive Integers

Case 2- When Both the Digits are Negative 

When the 2 numbers to be added are both negative, we add both the digits and assign their symbol as negative. 

For example, (-3) + (-4) = (-7)

Remember that it is important to mention ‘-’ before a negative number.

We add negative digits 3 and 4 to obtain a negative sum which is (-7)

Remember the following phrase

“While adding the same signs, keep the signs!”

Case 3- When the Bigger Number has a Positive Sign

When the bigger number of the 2 digits added is positive, we subtract the smaller number from the bigger number and assign the symbol to be positive

For example, (-3) + 4 = 1

We are subtracting 4-3 which is 1 and assigning it the symbol of the bigger number which is positive, our answer as +1

Addition and Subtraction of Integers 

Case 4- When the Bigger Number has a Negative Sign

When the bigger number of the 2 digits added is negative, we subtract the smaller number from the bigger number and assign its symbol to be negative

For example, 3 + (-4) = (-1) 

We are simply subtracting 4-3 which is 1 and assigning it the symbol of the bigger number which is negative, our answer as (-1)

Remember the following phrase

“While adding opposite signs, subtract and keep the sign of the bigger number!”

Adding Negative Integer to Positive Integer

Solved Examples

Q1. Find the sum of (+14) + (-19)

Ans: Here both the numbers have different signs and a more significant number has a negative sign

So we subtract 19 - 14 = 5

We assign a ‘-’ sign as the bigger number is negative.

The answer is -5

Q2. Find the sum of (-18) + (-13)

Ans: Here both the numbers have the same negative sign

So we add 18 + 13 = 31

We assign a ‘-’ sign as both numbers are negative.

The answer is -31

Q3. Find the sum of (-10) + (+16)

Ans: Here both the numbers have different signs and the more significant number has a positive sign

So we subtract 16 - 10 = 6

We assign a ‘+’ sign as the bigger number is positive.

The answer is +6

Q4. Find the sum of (+13) + (+7)

Ans: Here both the numbers have the same positive sign

So we add 13 + 7 = 20

We assign a ‘+’ sign as both numbers are positive.

The answer is 20

Q5. Find the sum of (-5) + (-8)

Ans: Here both the numbers have the same negative sign

So we add 5 + 8 = 13

We assign a ‘-’ sign as both numbers are negative.

The answer is -13

Practice Questions

Q1. Find the sum of 72 + 34. 

Ans: 106

Q2. Find the sum of (-56) + 28. 

Ans: (-28)

Q3. Find the sum of 89 + (-37). 

Ans: 52

Q4. Find the sum of (-91) + (-15).

Ans: -106

Q5. Find the sum of 43 + 23. 

Ans: 66

Summary

The addition of integers has certain rules based on the signs and values of the integers. To summarize how to add integers, we have 4 cases. When both the numbers to be added are positive or negative, the numbers are added and their signs are kept the same as the number added. When a bigger number added is positive, we subtract the given numbers and keep the positive signs to the sum obtained. When a bigger number added is negative, we subtract the given numbers and keep the negative sign to the sum obtained.