Adding and Subtracting Negative Number Calculator

How to Add and Subtract Negative Numbers

Working with negative numbers requires understanding a few key rules:

1. Adding a negative number is the same as subtracting its positive counterpart.
2. Subtracting a negative number is the same as adding its positive counterpart.
3. Two negative numbers added together give a negative result.

These rules form the foundation for all operations with negative numbers. Let's explore each one in more detail.

Rules for Adding and Subtracting Negatives

Rule 1: Adding a Negative Number

When you add a negative number, it's equivalent to subtracting its positive value. For example:

• 5 + (-3) = 5 - 3 = 2
• 10 + (-7) = 10 - 7 = 3

Rule 2: Subtracting a Negative Number

Subtracting a negative number is the same as adding its positive value. For example:

• 5 - (-3) = 5 + 3 = 8
• 10 - (-7) = 10 + 7 = 17

Rule 3: Adding Two Negative Numbers

When you add two negative numbers, the result is negative. For example:

• (-3) + (-5) = -8
• (-10) + (-7) = -17

Worked Examples

Let's look at some practical examples to reinforce these rules.

Example 1: Adding a Negative Number

Calculate 8 + (-5):

1. According to Rule 1: 8 + (-5) = 8 - 5
2. 8 - 5 = 3

The result is 3.

Example 2: Subtracting a Negative Number

Calculate 12 - (-4):

1. According to Rule 2: 12 - (-4) = 12 + 4
2. 12 + 4 = 16

The result is 16.

Example 3: Adding Two Negative Numbers

Calculate (-6) + (-9):

1. According to Rule 3: (-6) + (-9) = -(6 + 9)
2. 6 + 9 = 15
3. -15

The result is -15.

Practical Applications

Understanding how to add and subtract negative numbers has many real-world applications:

• Temperature changes: A temperature drop of 5°C followed by a rise of 3°C can be calculated as -5 + 3 = -2°C
• Bank transactions: A deposit of $100 followed by a withdrawal of $150 can be calculated as 100 - 150 = -50
• Elevation changes: Climbing 200 meters then descending 300 meters can be calculated as 200 - 300 = -100 meters