Addition and Subtraction of Integers
Addition and subtraction of integers are two operations that we perform on integers to increase or decrease their values. You already know about the addition and subtraction of whole numbers. Do you know that whole numbers are a part of integers? Integers include whole numbers and their negatives. Every number shown on a number line that does not have a fractional part is an integer. But, like whole numbers, can we add or subtract integers also? For example, If the temperature in your city was 2^{º} C and it falls by 7^{º} C. What is the current temperature in your city? Let's go ahead and learn more about these two basic operations on integers.
What is Meant by Addition and Subtraction of Integers?
Integers are the natural numbers, the negatives of these numbers, or zero. An integer is a complete entity. Integers are the numbers that can be positive, negative, or zero, numbers with no fractional part (no decimals). Like whole numbers, we can add or subtract integers also.
Addition and subtraction of integers mean to carry out the operations of addition and subtraction on two or more integers by putting addition and subtraction operator in between. Before going deeper into the concept, it is very important to learn what is an absolute value of an integer. On a number line, the distance of a number from 0 is called the absolute value of an integer. And distance indicates no direction as it is a scalar quantity. It's always positive.
Addition of Integers
Addition generally means to increase the value. But, in the case of integers, the addition operation might lead to an increase or decrease in the value of the given number. If we add a negative integer, the value of the given number will decrease and if we add a positive integer the value will increase. Consider the following examples.
Sally has 3 marbles. She gets 4 more from her brother. So she has (3 + 4= 7) marbles now.
The temperature increases from 4 to 5^{º} Fahrenheit. So the increase in temperature is (4 + 5 = 1).
In the above examples, we used the concept of the addition of integers. While showing the addition of integers on a number line, we have to move towards the right side or the positive side when we add a positive integer to a given number. On the other hand, when we add a negative number, we move towards the left side of the number line, as we are taking out some value from the given number, so the resultant number will be smaller than the original number.
The addition and subtraction of integers can be best demonstrated on a number line. But it is very timeconsuming to work on the number line as soon as we get an addition problem. So, let's learn all the rules of the addition of integers.
Rules for Adding Integers
When we learn about the addition of integers, three cases come up as the addition rule of integers, and they are:
 Addition of two positive numbers
 Addition of a positive number and a negative number
 Addition of two negative numbers
Let's learn these rules one by one.
Rule  Explanation  Examples  
Addition of two positive numbers  (+a)+(+b) = (a+b)  While adding two positive numbers we simply add both the numbers and get an answer which is a positive value, just like the addition of whole numbers. 
3+4=7 2+11=13 
Addition of a positive number and a negative number  (a+(b)) = (ab)  While adding a positive and a negative number, we take the difference of the absolute values of both the numbers and attach the sign of the greater number with the answer. 
4+(5)=(1) (5)+7=2 
Addition of two negative numbers  (a)+(b) = (a+b)  While adding two negative numbers, we take the sum of both the numbers and attach a negative sign with the answer. 
(2)+(4)=(6) (5)+(8)=(13) 
In the image below, observe all three addition rules for integers on the number line.
Subtraction of Integers
Subtraction generally means to decrease the value. But, in the case of integers, a subtraction operation might lead to an increase or decrease in the value of the given number. If we subtract a negative integer from a number, the value of the given number will increase and if we subtract a positive integer the value will decrease. Consider a few examples given below and observe the operation we are using on integers.
A worker steps down the ladder by 2 steps from the 5th step he is working on: (5  2 = 3)
The temperature drips down by 4^{º} from 1^{º} Fahrenheit: (14=5)
In the above examples, we use the concept of subtraction of integers. While showing subtraction of integers on a number line, we have to move towards the left side or negative side when we are subtracting a positive number from a given number. On the other hand, we move towards the right side or positive side when we subtract a negative number from a given number.
Rules for Subtracting Integers
You must have studied that addition and subtraction are inverse operations. So, every subtraction problem can be written as an addition problem. Let's learn how by a few examples.
24=2+(4)
63=6+(3)
43=4+(3)
While writing any subtraction problem also, we have to take the sign of subtrahend inside the bracket and add the addition operator between both the terms. This is one way of solving subtraction questions.
Let's learn the rules of subtraction also to ease out our calculations while dealing with operations on integers.
Rule  Explanation  Examples  
Subtraction of two positive numbers  (+a)(+b)=ab  While subtracting two positive numbers we simply take the difference of absolute values of both the numbers and attach a sign of the greater number with the answer. 
34=1 112=9 
Subtraction of a positive number and a negative number 
a(b)=(a+b) (a)b=(a+b) 
While subtracting a positive and a negative number, we take the sum of the absolute values of both the numbers and attach the sign of the minuend with the answer. 
4(5)=9 (5)7=12 
Subtraction of two negative numbers  (a)(b)=±(ab)  While subtracting two negative numbers, we just have to remember one rule that whenever there is a negative sign outside the bracket, the sign of the term inside the bracket will be changed. Then, we have to take the difference of the absolute values of both the numbers and attach the revised sign of the greater number with the answer. 
(2)(4)=2 (8)(5)=(3) 
Points to Remember:
 If there is no sign with a number, we consider it as a positive number. For example, 2 can be rewritten as +2.
 Every subtraction fact can be rewritten as an addition fact. For example, 910 can be rewritten as 9+(10).
 Always write negative numbers in a bracket in an expression.
 If there is an expression in which there are both addition and subtraction operations, we can solve any operator first. For example, 910+4. In this expression, we can either solve (910) first or (10+4) first. It won't affect our answer.
Important Topics
Solved Examples

Example 1: A plane is flying at the height of 3000 feet above sea level. At some point, it is exactly above the submarine floating 700 feet below sea level. Use the concept of subtraction of integers and calculate the vertical distance between them?
Solution:
The height at which the plane is flying = 3000 feet. The depth of the submarine = 700 feet (Negative, as it is below the sea level) To calculate the vertical distance between them, we will use the subtraction of two integers operation:
3000 (700) = 3000 + 700 = 3700 feet
Therefore, the vertical distance between them is 3700 feet.

Example 2: Calculate (23) using a number line.
Solution:
On a number line, we will start from +2 as it is our minuend. Then we have to take 3 steps towards the left, as we are decreasing the value of 2 by 3. This is how we reach (1), which is our answer.
FAQs on Addition and Subtraction of Integers
What is the Rule for Adding a Positive and Negative Integer?
The rule for the addition of a positive and negative integer states that the difference between the two integers needs to be calculated in order to find their addition. The sign of the result will be the same as that of the larger integer of the two.
What is an Integer in Math?
An integer is a number with no decimal or fractional part from the set of negative and positive numbers, including zero. Examples of integers are: 5, 0, 1, 5, 8, 97, 34, etc.
What are the Rules for Subtraction of Integers?
Every subtraction fact can be rewritten as an addition fact. So, we can apply addition rules on subtraction problems also.
What is the Rule for Addition and Subtraction of Negative Numbers?
 To add two negative numbers, we take the sum of both the numbers and attach a negative sign with the answer.
 While subtracting two negative numbers, we just have to remember one rule that whenever there is a negative sign outside the bracket, the sign of the term inside the bracket will be changed. Then, we have to take the difference of the absolute values of both the numbers and attach the revised sign of the greater number with the answer.
How do you Add or Subtract Integers?
Addition and subtraction of integers can be done with the help of a number line and by following certain rules of addition and subtraction.
What are the Properties of Integers?
Various arithmetic operations can be performed on integers, like addition, subtraction, multiplication, and division. The major Properties of Integers are:
 Closure Property
 Associative Property
 Commutative Property
 Distributive Property
 Additive Inverse Property
 Multiplicative Inverse Property
 Identity Property
What are the Applications of Integers?
The application of positive and negative numbers in the real world is different. They are generally used to represent two contradicting situations.
 One common reallife application of integers is temperature measurement. The negative and positive numbers and zero in the scale denote different temperature readings.
 Bank credit and debit statements also use integers to represent the negative or positive values of the amount.
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