Last updated on July 4th, 2025
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.
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.
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:
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.
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.
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 |
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.
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.
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.
The subtraction of integers has numerous real-life applications across various fields. Let us explore how the subtracting integers is used in different areas:
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:
What is 8 – 3?
5
Both numbers are positive.
Subtract 3 from 8: 8 – 3 = 5.
What is 5 – 12?
–7
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.
What is −4 − 2?
−6
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.
What is 6 −(−3)?
9
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.
What is −7 −(−2)?
−5
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.
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.
: She loves to read number jokes and games.