Keep the First Integer
Do not change the first number in the subtraction expression.
Free Math Guide
Subtracting Integers Explained
Learn how to subtract positive and negative integers by changing subtraction into addition and adding the opposite.
Subtracting integers becomes much easier when you rewrite the problem as addition. The key idea is simple: keep the first number, change subtraction to addition, and change the second integer to its opposite.
How to Subtract Integers
To subtract an integer, change the subtraction problem into an addition problem by adding the opposite of the second integer.
Change Subtraction to Addition
Replace the subtraction symbol with an addition symbol.
Change the Second Integer
Replace the second integer with its opposite.
Add Using Integer Rules
Once the expression is rewritten, solve it as an integer addition problem.
Keep, Change, Change
Keep the first integer, change subtraction to addition, and change the second integer to its opposite.
What Does “Add the Opposite” Mean?
Opposite integers are the same distance from zero but have different signs. The opposite of 7 is −7, and the opposite of −7 is 7.
Opposite of a Positive Integer
The opposite of 6 is −6
Subtracting 6 is equivalent to adding −6.
Opposite of a Negative Integer
The opposite of −6 is 6
Subtracting −6 is equivalent to adding 6.
Subtracting a number means adding its opposite.
Changing Subtraction Into Addition
Rewrite the expression before trying to calculate. This helps prevent sign errors.
Original:
8 − 3
Rewrite:
8 + (−3)
Answer:
5
Original:
8 − (−3)
Rewrite:
8 + 3
Answer:
11
Subtracting a Positive Integer
When you subtract a positive integer, change the positive integer to a negative integer and add.
Positive Minus Positive
10 − 4 = 10 + (−4) = 6
- Keep 10.
- Change subtraction to addition.
- Change 4 to −4.
- Add 10 + (−4).
Negative Minus Positive
−5 − 3 = −5 + (−3) = −8
- Keep −5.
- Change subtraction to addition.
- Change 3 to −3.
- Add two negative integers.
Subtracting a positive number moves the value toward the left on a number line.
Subtracting a Negative Integer
When you subtract a negative integer, the negative integer changes to its positive opposite. The rewritten expression becomes addition.
Positive Minus Negative
7 − (−4) = 7 + 4 = 11
- Keep 7.
- Change subtraction to addition.
- Change −4 to 4.
- Add 7 + 4.
Negative Minus Negative
−9 − (−5) = −9 + 5 = −4
- Keep −9.
- Change subtraction to addition.
- Change −5 to 5.
- Add integers with different signs.
Why Two Signs Appear
In an expression such as 7 − (−4), the first symbol is the subtraction operation. The second symbol is part of the negative integer −4.
Subtracting Integers on a Number Line
A number line helps show why subtracting a positive moves left and subtracting a negative moves right.
−5
−4
−3
−2
−1
0
1
2
3
4
5
Subtract a Positive
Move left on the number line.
Subtract a Negative
Move right on the number line.
Move Left
3 − 5 = −2
Start at 3 and move 5 spaces to the left. You land on −2.
Move Right
−2 − (−5) = 3
Start at −2 and move 5 spaces to the right. You land on 3.
How to Check an Integer Subtraction Answer
After rewriting the problem, make sure you changed only the second integer and then applied the correct addition rule.
Check the First Integer
The first integer should remain unchanged.
Check the Operation
The subtraction symbol should become an addition symbol.
Check the Second Integer
The second integer should change to its opposite.
Check the Final Addition
Use the correct same-sign or different-sign addition rule.
Common Integer Subtraction Mistakes
Changing the First Integer
Keep the first integer exactly as it appears. Only the subtraction symbol and second integer should change.
Changing Both Integers
The opposite is applied only to the integer being subtracted.
Forgetting to Change Subtraction to Addition
Once the second integer changes to its opposite, the operation must also become addition.
Treating Two Negative Signs as Multiplication
In 8 − (−3), one sign is the subtraction operation and the other belongs to the negative integer.
Forgetting the Integer Addition Rules
Rewriting the problem is only the first step. You must still add integers using the correct sign rule.
Ready to Practice?
Try the Interactive Integer Subtraction Tool
Practice subtracting positive and negative integers with immediate feedback, unlimited questions, and focused practice rounds.
Start Integer Subtraction PracticeRelated Math Resources
Need Help With Integers?
Personalized online tutoring can help students understand negative numbers, integer operations, pre-algebra, and more.
Ask About Math Tutoring