How to Subtract Negative Numbers- Rules and Examples

What Subtracting Negative Numbers Actually Means

Most people freeze up when they see two minus signs next to each other. 5 - -3. What do you even do with that?

The rule is stupidly simple once you strip away the confusion. Subtracting a negative number is the same as adding a positive number.

That's it. That's the whole concept.

So 5 - -3 becomes 5 + 3, which equals 8.

The Double Negative Rule Explained

When you subtract a negative, the two minus signs combine into a plus. This isn't math magic—it's just how the operation works.

Think of it this way: a negative number represents debt. Subtracting that debt means you're removing something you owe. Removing debt is the same as gaining money.

If you owe someone $5, and that debt gets canceled, you're $5 richer. That's subtraction of a negative in real-world terms.

Why People Get Confused

The confusion comes from mixing up the signs. You have:

• A minus sign (the operation)
• A negative sign (the type of number)

When both appear, your brain reads them as "subtraction" twice. But mathematically, minus negative equals plus. The operation flips the sign of the number.

The Rules You Need to Memorize

These two rules cover every case you'll encounter:

1. Positive - Negative = Positive + Positive (add the numbers)
2. Negative - Negative = Add the absolute values, keep the sign

Write these on a flashcard. Test yourself until they're automatic.

Step-by-Step: How to Subtract Negative Numbers

Step 1: Identify the Operation

Look for the minus sign between the two numbers. That tells you subtraction is happening.

Step 2: Check the Second Number

Is the number after the minus sign negative? Look for the negative sign in front of it.

Step 3: Convert Two Minuses to a Plus

Whenever you see number - -number, rewrite it as number + positive number.

Step 4: Solve the Addition Problem

Now just add the two positive numbers. That's your answer.

Examples That Make It Clear

Example 1: Positive Minus Negative

7 - -4 = ?

Convert: 7 - -4 becomes 7 + 4

Answer: 11

Example 2: Negative Minus Negative

-6 - -2 = ?

Convert: -6 - -2 becomes -6 + 2

Answer: -4

When the first number is larger in absolute value, the result stays negative.

Example 3: Larger Negative Minus Smaller Negative

-3 - -9 = ?

Convert: -3 - -9 becomes -3 + 9

Answer: 6

The positive number wins because 9 is bigger than 3.

Number Line Visualization

Picture a number line if the concept still feels abstract.

When you subtract a positive, you move left. When you subtract a negative, you move right. That's the counterintuitive part.

Subtracting -3 means jumping 3 spaces to the right, which adds 3 to your value.

Try it: start at 2 on a number line. Subtract -4 means you move 4 spaces right, landing on 6.

Quick Reference Table

Common Mistakes to Avoid

• Treating it as simple subtraction. 5 - -3 is not 5 - 3. The double negative changes everything.
• Forgetting to flip the sign. The negative number becomes positive after you convert.
• Dropping the negative sign entirely. Keep track of which negative sign is the operation and which is the number's sign.
• Adding instead of subtracting when you shouldn't. This rule only applies when there's a minus sign directly before a negative number.

Practice Problems

Test yourself. Answers at the bottom.

1. -5 - -12 = ?
2. 3 - -8 = ?
3. -9 - -4 = ?
4. 20 - -15 = ?
5. -1 - -1 = ?

Answers

1. 7
2. 11
3. -5
4. 35
5. 0

When You'll Actually Use This

Physics problems with vectors. Financial calculations where debt gets forgiven. Temperature changes below zero. Any situation involving gains and losses where the losses themselves get removed.

It's not some abstract concept you'll never encounter. It comes up constantly in real math and science.

The skill transfers directly to algebra, where you'll see expressions like x - (-y) constantly. If you can't handle the arithmetic now, variables will destroy you later.