Two Negatives Subtracting Calculator

Subtracting two negative numbers might seem confusing at first, but it follows simple mathematical rules. This guide explains the process clearly and provides a calculator to help you practice.

How to Subtract Two Negative Numbers

The basic rule for subtracting negative numbers is:

Subtraction Rule for Negatives

a - b = a + (-b)

When subtracting a negative number, you're actually adding its positive counterpart.

For example, if you have -5 - (-3), you can rewrite it as -5 + 3. The two negatives cancel out, leaving you with a simple addition problem.

Step-by-Step Process

Identify the two negative numbers you're working with.
Remove the negative sign from the second number (the one being subtracted).
Change the subtraction sign to an addition sign.
Perform the addition of the two numbers.

This process works because subtracting a negative is the same as adding a positive. The calculator on this page can help you practice this with different numbers.

The Math Rules for Negative Subtraction

Understanding the underlying rules helps you work with negative numbers more confidently. Here are the key principles:

Negative Subtraction Rules

1. a - (-b) = a + b

2. -a - (-b) = -a + b

3. -a - b = -(a + b)

The first rule shows how subtracting a negative becomes addition. The second rule demonstrates that subtracting a negative from another negative still results in addition. The third rule shows what happens when you subtract a positive from a negative.

Key Insight

When subtracting two negatives, the result is always positive. This is because you're effectively adding the absolute values of the numbers.

Real-World Examples of Negative Subtraction

Negative numbers appear in many real-world scenarios. Here are some practical examples:

Financial Context

Imagine you have a bank balance of -$50 (you're $50 in debt). If you receive a $30 payment that reduces your debt, your new balance would be -$50 - (-$30) = -$20.

Temperature Changes

If the temperature drops from -5°C to -10°C, the change is -5°C - (-10°C) = -5°C. The temperature decreased by 5 degrees.

Elevation Changes

If you're at an elevation of -200 meters below sea level and climb to -100 meters, your elevation change is -200 - (-100) = -100 meters.

Common Mistakes When Subtracting Negatives

Many people struggle with negative subtraction because they forget the basic rules. Here are common errors to avoid:

Adding the numbers instead of subtracting: -5 - (-3) should be -5 + 3, not -5 - 3.
Forgetting to change the operation: -5 - (-3) should be -5 + 3, not -5 - 3.
Confusing subtraction with addition when both numbers are negative.

Pro Tip

Remember that two negatives make a positive. This mental shortcut can help you avoid mistakes when working with negative numbers.

FAQ

What is the rule for subtracting two negative numbers?

When subtracting two negative numbers, you add the absolute values of the numbers. For example, -5 - (-3) = -5 + 3 = -2.

Why do two negatives make a positive?

Two negatives make a positive because subtracting a negative is the same as adding a positive. The negatives cancel out, leaving you with a positive result.

Can you subtract a negative number from a positive number?

Yes, you can subtract a negative number from a positive number. This is equivalent to adding the absolute value of the negative number to the positive number. For example, 5 - (-3) = 5 + 3 = 8.

What happens when you subtract a positive number from a negative number?

When you subtract a positive number from a negative number, you get a more negative result. For example, -5 - 3 = -8.

How do you subtract negative numbers in algebra?

In algebra, subtracting negative numbers follows the same rules as arithmetic. You remove the negative sign from the second number and change the subtraction to addition. For example, x - (-y) = x + y.