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Last updated on July 4th, 2025

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Subtracting Integers

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Subtracting integers is the difference between two integers, which may be positive, negative, or zero. Subtracting a negative number is the same as adding its positive counterpart. This means a - (-b) is the same as a + b. In this article, we will learn more about subtracting integers.

Subtracting Integers for Indian Students
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What are Integers?

Integers are the set of whole numbers including positive, negative, and zero. Fractions and decimals do not belong to integers. It is represented as {..., -3, -2, -1, 0, 1, 2, 3,...} and extend in both directions on the number line. Integers are used for counting, measuring temperatures, handling financial transactions, and determining elevations above or below sea level.

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What are the Properties of Subtraction of Integers?

Subtraction of integers involves the minuend and the subtrahend. The subtrahend is the number that is being subtracted, while the minuend is the number from which another number is being subtracted. There are several important properties related to the subtraction of integers, and they are as follows:

 

 

  • Closure Property: Difference between any two integers always results in an integer.

     
  • Associative Property: Subtraction is not associative because the grouping of integers being subtracted affects the result.

     
  • Identity Property: Subtracting zero from any integer leaves the integer unchanged.

     
  • Inverse Property: An integer plus its additive inverse always results in zero.
     
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How to Subtract Integers?

Subtraction is one of the most basic mathematical operation. To subtract integers, we follow these steps:

 


Step 1: Identify the minuend and the subtrahend

 


Step 2: If both integers have the same sign, subtract their absolute values and assign the same sign to the result.

 


Step 3: If the integers have different signs, subtract their absolute values. The result takes the sign of the greater integer with absolute value.
 

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What are the Rules for Subtracting Integers?

Like all mathematical operations, even subtraction has a set of rules to be followed. In fact,
there are various rules for subtracting integers, and some of them are mentioned below.

 

 

  • Subtracting integers with the same sign

 

  • Subtracting integers with different signs

 

  • Subtracting a positive integer from another positive integer results in a positive integer if the minuend is larger.

 

  • When subtracting a negative integer from another negative integer, the results can be positive or negative depending on their absolute values.

 

  • Subtracting a negative integer from another positive integer results in adding the two numbers.


    The given chart below shows all the rules of subtracting integers:

     
Signs of Integers

Operation

Sign After Operation

Example
+ - + 

subtract

+

8 - 2 = 6

+ - -

add

+

8 - (-2) = 10

+ - -

add

+

3 -(-7) = 10
+ - +

subtract

-

2 – 8 = -6

- - -

subtract

-

-8 -(-2) = -6

- - -

subtract

+

-2 - (-8) = 6

- - +

add

-

-2 - 8 = -10

- - +

add

-

-8 - 2 = -10

 

Professor Greenline from BrightChamps

Subtracting Integers with the Same Sign:

While subtracting integers with same sign, following steps are - 

 


Step 1: Before subtraction, identify the sign of the integers. If they have the same sign, proceed to the next step.

 


Step 2: Subtract the absolute values of the integers without considering the signs.

 


Step 3: If the absolute value of minuend is larger, then the result will have the same sign as the minuend, otherwise, it takes the opposite sign.
 

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Subtracting Integers with Different Signs:

The following steps are to be followed for subtracting integers with different signs - 

 

Step 1: Before subtraction, identify the signs of the integers. If they have different signs, proceed to the next step

 


Step 2: We should subtract the smaller absolute value from the larger absolute value. Signs should be ignored in this step.

 


Step 3: Assign the sign of the number with the greater absolute value to the result.
 

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Subtracting Integers on Number Line:

We must follow the following steps to subtract integers on the number line:

 


Step 1: First locate the first integer on the number line.

 


Step 2: When subtracting a positive integer, move left; when subtracting a negative integer, move right.

 


Step 3: Move the number of steps equal to the absolute value of the integer being subtracted.

 


Step 4: The final position is where you end up on the number line after subtraction.
 

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Real-life Applications of Subtracting Integers

The subtraction of integers has numerous real-life applications across various fields. Let us explore how the subtracting integers is used in different areas:

 

 

  • Banking and Finances - For easy calculation in bank transactions or maintaining balance, basic subtraction operation is used. For example, if you have $500 in your account and withdraw $700, then 500 – 700 = -200. This shows that you now have a negative balance of $200 in your account.

     
  • Elevation and Depth - While trekking or walking, trekkers or hikers use the distance mentioned in the milestones to understand how much distance is left or how much height have they climbed up or down. For example, if a hiker is at 500 m above sea level and the elevation change is 500 – 800 = −300 meters, indicating the hiker is now 300 meters below sea level.

     
  • Sports Scoring and Penalties - For sports like football, golf, basketball, points are added or subtracted on scoring or penalty respectively. For example, if a team has 14 points but loses 7 due to a penalty, their new score is 14 – 7 = 7. 
     
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Common Mistakes and How to Avoid Them in Subtracting Integers

Students tend to make mistakes when solving problems that involve subtracting integers. Let us see some common mistakes and how to avoid them in integer subtraction:

Mistake 1

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Confusing Subtraction with Addition

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Students should remember that subtracting a negative number is the same as adding a positive number. Whenever you see “-(-number)” change it to “+number” and then solve. For example, 2- (-5) = 7

Mistake 2

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Incorrectly Placing the Negative Sign
 

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For visualizing all integers on a number line, it is easier to solve the problem. In many cases with similar signs, students often make error in calculation. 
 

Mistake 3

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Ignoring Zero in Subtracting 
 

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Subtracting a negative number from zero has the same rule as subtracting a negative from any other number, which becomes addition.
 

Mistake 4

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Mixing Up Positive and Negative Differences
 

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Subtracting a negative number, with a greater value, is the same as adding. With mixing up the positive and negative numbers, students may make mistakes.

Mistake 5

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Rushing Through Calculations Without Checking Work

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 Without making any mental calculation, it is advisable to work on integers on number line and apply basic operations like addition, subtraction on number line only.

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Solved Examples on Subtracting Integers

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Problem 1

What is 8 – 3?

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5
 

Explanation

Both numbers are positive.


Subtract 3 from 8: 8 – 3 = 5.
 

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Problem 2

What is 5 – 12?

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–7
 

Explanation

Both numbers are positive, but 12 is larger than 5.


5 − 12 = −7 (Since 12 − 5 = 7). The result is negative because we subtract the larger number from the smaller one.


Subtracting a larger number from a smaller one results in a negative answer.
 

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Problem 3

What is −4 − 2?

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 −6
 

Explanation

Start with −4


Subtracting 2 moves you further left on the number line: −4−2=−6.


When you subtract a positive number from a negative number, the result becomes more negative.
 

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Problem 4

What is 6 −(−3)?

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 9

Explanation

Recognize that subtracting a negative number is the same as adding its positive: 6 −(−3) = 6 + 3.


Add: 6 + 3 = 9.


Changing subtraction of a negative into addition simplifies the operation.
 

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Problem 5

What is −7 −(−2)?

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−5

Explanation

Convert the subtraction of a negative to addition: 


−7 − (−2) = −7 + 2.


Calculate: −7 + 2 = −5.


Subtracting a negative number makes the value less negative.
 

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FAQs on Subtracting Integers

1.What does it mean to subtract integers?

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2.What is the basic rule for subtracting integers?

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3.How do I subtract a negative integer from a positive integer?

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4.Why is subtracting a negative integer considered addition?

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5.Are there any shortcuts or tips for subtracting integers?

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6.How can children in India use numbers in everyday life to understand Subtracting Integers?

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7.What are some fun ways kids in India can practice Subtracting Integers with numbers?

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8.What role do numbers and Subtracting Integers play in helping children in India develop problem-solving skills?

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9.How can families in India create number-rich environments to improve Subtracting Integers skills?

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Hiralee Lalitkumar Makwana

About the Author

Hiralee Lalitkumar Makwana has almost two years of teaching experience. She is a number ninja as she loves numbers. Her interest in numbers can be seen in the way she cracks math puzzles and hidden patterns.

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Fun Fact

: She loves to read number jokes and games.

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