Negative Plus Negative- Math Rules Explained

What Does Negative Plus Negative Equal?

Negative plus negative always equals a more negative number. That's the whole rule. There's no trick, no exception, no special case for beginners to worry about.

If you owe $20 and you borrow another $20, you now owe $40. That's negative plus negative in real life. The math works exactly the same way.

The Basic Rule

When you add two negative numbers together, you add their absolute values and keep the negative sign.

Here's what that looks like:

• (-5) + (-3) = -8
• (-12) + (-7) = -19
• (-100) + (-50) = -150

The numbers get bigger in the negative direction. That's it.

Why This Makes Sense on a Number Line

Picture a number line. Zero is in the middle. Positive numbers go right. Negative numbers go left.

When you start at -5 and add -3, you move 3 more spaces to the left. You end up at -8.

You can never accidentally land on a positive number when adding two negatives. You're always going left on the number line. The only way to get back to positive territory is to add a positive number or subtract a negative.

Common Mistakes

Confusing Addition with Subtraction

Students often mix up these rules:

• Negative plus negative = more negative
• Negative minus negative = can go either way

The minus sign is where people get tripped up. When you see (-5) - (-3), you're subtracting a negative, which is the same as adding: (-5) + 3 = -2.

Dropping the Parentheses

Writing "-5 + -3" without clear parentheses confuses people. Always keep operations clear. Write it as (-5) + (-3) until you're comfortable with the logic.

Practical Examples

See the pattern? Add the positive versions, slap a minus sign in front.

How to Solve Negative Plus Negative Problems

Step 1: Ignore the negative signs temporarily. Pretend they're positive.

Step 2: Add those positive numbers together using normal addition.

Step 3: Put a negative sign in front of your answer.

Let's work through an example: Solve (-23) + (-41)

Step 1: 23 + 41

Step 2: 23 + 41 = 64

Step 3: Answer is -64

That's the entire process. No memorization tricks needed.

When You'll Use This

• Finance: Stacking up debts. Overdraft fees stacking on an already negative balance.
• Temperature: Cold nights getting colder. -5°C dropping another 3 degrees.
• Altitude: Diving below sea level. -100 feet going down another 50 feet.
• Sports: Scoring below par in golf. -3 plus another -2 gives you -5.

Quick Reference

• (-) + (-) = always negative
• Never equals positive or zero
• The sum is always more negative than either number

Negative plus negative is straightforward. Add the numbers, keep the sign. That's the rule and that's all there is to it.