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Subtracting Two Negative Numbers Calculator

Reviewed by Calculator Editorial Team

Subtracting two negative numbers might seem counterintuitive at first, but there are clear rules to follow. This guide explains how to perform negative number subtraction correctly, provides examples, and includes a calculator to help you practice.

How to Subtract Negative Numbers

The process of subtracting negative numbers follows specific mathematical rules. Here's a step-by-step guide:

Negative Subtraction Formula

When subtracting two negative numbers, the result is the absolute value of the second number minus the absolute value of the first number, with the sign of the number that has the larger absolute value.

Formula: a - b = |b| - |a| (if |b| > |a|)

Step-by-Step Process

  1. Identify the two negative numbers you want to subtract.
  2. Remove the negative signs to work with their absolute values.
  3. Subtract the second number's absolute value from the first number's absolute value.
  4. Apply the sign of the number with the larger absolute value to the result.

Key Point

Subtracting two negative numbers is equivalent to adding their absolute values and keeping the negative sign.

Negative Subtraction Rules

Understanding the rules of negative number subtraction is essential for accurate calculations. Here are the fundamental rules:

Rule 1: Subtracting a Negative Number

When you subtract a negative number, it's the same as adding its positive counterpart.

Example: 5 - (-3) = 5 + 3 = 8

Rule 2: Subtracting from a Negative Number

When you subtract a positive number from a negative number, you're moving further in the negative direction.

Example: -5 - 3 = -8

Rule 3: Subtracting Two Negative Numbers

When subtracting two negative numbers, subtract the smaller absolute value from the larger absolute value and keep the sign of the number with the larger absolute value.

Example: -7 - (-3) = -7 + 3 = -4

Visualization Tip

Imagine the number line. Subtracting a negative number moves you to the right, while subtracting a positive number moves you to the left.

Worked Examples

Let's look at several examples to solidify your understanding of negative number subtraction.

Example 1: Simple Negative Subtraction

Problem: -4 - (-2)

Solution:

  1. Remove the negative signs: 4 and 2
  2. Subtract: 4 - 2 = 2
  3. Apply the sign of the number with the larger absolute value: -4 has a larger absolute value, so the result is negative
  4. Final answer: -2

Example 2: Subtracting Larger Numbers

Problem: -15 - (-7)

Solution:

  1. Remove the negative signs: 15 and 7
  2. Subtract: 15 - 7 = 8
  3. Apply the sign of the number with the larger absolute value: -15 has a larger absolute value, so the result is negative
  4. Final answer: -8

Example 3: Equal Absolute Values

Problem: -6 - (-6)

Solution:

  1. Remove the negative signs: 6 and 6
  2. Subtract: 6 - 6 = 0
  3. The result is zero regardless of the original signs
  4. Final answer: 0

Common Mistakes

Even experienced mathematicians can make mistakes when dealing with negative numbers. Here are some common errors to avoid:

Mistake 1: Forgetting to Remove Negative Signs

Some people mistakenly think you should add the negative signs together. Remember, subtracting a negative is the same as adding a positive.

Mistake 2: Incorrect Sign Application

When subtracting two negative numbers, it's easy to forget to apply the sign of the number with the larger absolute value to the result.

Mistake 3: Misapplying the Rules

Confusing the rules for subtracting from a negative number with subtracting two negative numbers can lead to incorrect results.

Double-Checking Tip

Always verify your calculations by working through the problem step-by-step and using the calculator to confirm your answer.

FAQ

What is the rule for subtracting two negative numbers?

The rule is to subtract the smaller absolute value from the larger absolute value and keep the sign of the number with the larger absolute value. This is equivalent to adding the two numbers' absolute values and keeping the negative sign.

Is subtracting a negative number the same as adding a positive number?

Yes, subtracting a negative number is equivalent to adding its positive counterpart. This is one of the fundamental rules of negative number arithmetic.

What happens when you subtract two identical negative numbers?

The result will always be zero because the absolute values are equal, and the signs cancel each other out.

How do you subtract a negative number from a positive number?

When subtracting a negative number from a positive number, you're effectively adding the absolute value of the negative number to the positive number. The result will be positive.

Why is subtracting negative numbers sometimes called "adding"?

The term "adding" comes from the mathematical equivalence of subtracting a negative number to adding its positive counterpart. Both operations have the same effect on the result.