Subtracting Negative Integers- Rules and Examples

What Subtracting Negative Integers Actually Means

Most people freeze up when they see two minus signs in a row. Subtracting negative integers trips up students and adults alike, but the rule is dead simple once you strip away the confusion.

Here's the core concept: subtracting a negative number is the same as adding its positive counterpart.

That sentence alone solves 90% of the confusion. Keep reading for the why, the how, and plenty of examples.

The Basic Rule: Keep, Change, Change

Teachers love this mnemonic because it works. When you subtract a negative integer, follow three steps:

• Keep the first number
• Change the subtraction sign to addition
• Change the negative sign to positive

So 5 - (-3) becomes 5 + 3 = 8.

That's it. That's the whole rule.

Why This Works: The Number Line Explanation

Picture a number line. Positive numbers go right. Negative numbers go left.

When you subtract, you move left. But subtracting a negative means you're removing a leftward movement. The only way to "remove" a leftward step is to go right instead.

Think of it like double negatives in speech. "I didn't skip class" means you went to class. In math, not subtracting a negative means adding a positive.

Subtracting Negative Integers: Examples Walkthrough

Example 1: Positive minus negative

7 - (-2) = ?

Keep the 7. Change the minus to plus. Change -2 to +2.

7 + 2 = 9

Example 2: Negative minus negative

-4 - (-6) = ?

Keep the -4. Change the minus to plus. Change -6 to +6.

-4 + 6 = 2

Example 3: Negative minus positive (different operation, same confusion)

-5 - 3 = ?

This is NOT subtracting a negative. You're subtracting a positive from a negative. Stay left on the number line.

-5 - 3 = -8

Notice the difference. Two negatives in a row (with the minus between them) is where the rule applies.

Example 4: Chain operations

-2 - (-5) - (-1) = ?

Work left to right.

Step 1: -2 - (-5) → -2 + 5 = 3

Step 2: 3 - (-1) → 3 + 1 = 4

Common Mistakes to Avoid

• Confusing the signs: Only apply "keep change change" when you see a minus followed by a negative number. A minus followed by a positive is just regular subtraction.
• Forgetting to change both: Students often change the minus to plus but forget to flip the negative to positive. Both changes are required.
• Dropping parentheses: When rewriting -4 - (-3), write it as -4 + 3, not -4 + -3. That extra negative creates a third sign to track.

Quick Reference Table

How to Subtract Negative Integers: Step-by-Step

Here's a practical method for any subtraction problem involving negatives:

1. Scan for two signs in a row. Look for a minus sign immediately followed by a negative number.
2. Apply keep change change. Replace the minus with plus, and flip the negative to positive.
3. Simplify from left to right if you have multiple operations.
4. Double-check your sign changes. If you didn't flip the negative to positive, you've made an error.

Real-World Analogy

Imagine you owe someone $10. That's -10 in your account.

If that debt gets canceled (subtracted), you didn't gain $10 literally—but your balance goes up by $10.

-10 - (-10) = 0. The debt is gone. You're back to zero.

Now imagine they cancel a $20 debt instead.

-10 - (-20) = 10. You end up $10 ahead because a larger debt was erased.

This is why subtracting a negative can actually increase your value more than adding a positive in some cases.

The Bottom Line

Subtracting negative integers follows one rule: two negatives in a row become addition. Keep, change, change.

If you remember nothing else, remember this—every time you see a minus sign followed by a number in parentheses with a negative sign, flip both and add.

Practice ten problems and you'll have it locked in. There's no trick here, just a pattern that becomes automatic with repetition.