Adding and Subtracting Negative and Positive Numbers Calculator

This guide explains the fundamental rules for adding and subtracting negative and positive numbers. We'll cover the basic principles, provide examples, and show you how to use our calculator to verify your results.

Basic Rules for Adding and Subtracting Numbers

When working with negative and positive numbers, there are specific rules to follow:

Positive numbers are numbers greater than zero.
Negative numbers are numbers less than zero.
Adding a positive number is the same as counting up.
Adding a negative number is the same as counting down.
Subtracting a positive number is the same as adding a negative number.

Key Rule: The sign of the result depends on the larger absolute value.

Adding Two Positive Numbers

When adding two positive numbers, you simply add their absolute values and keep the positive sign.

Example: 5 + 3 = 8

Both numbers are positive, so you add them directly: 5 + 3 = 8.

Adding a Positive and Negative Number

When adding a positive and negative number, subtract the smaller absolute value from the larger one and take the sign of the number with the larger absolute value.

Example 1: 5 + (-3) = 2

5 is larger than 3, so you subtract: 5 - 3 = 2.

Example 2: 3 + (-5) = -2

5 is larger than 3, so you subtract: 5 - 3 = 2 and take the negative sign: -2.

Adding Two Negative Numbers

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

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

Both numbers are negative, so you add their absolute values: 5 + 3 = 8 and keep the negative sign: -8.

Subtraction Rules

Subtraction can be thought of as adding a negative number. Here are the key rules:

Subtracting a positive number is the same as adding a negative number.
Subtracting a negative number is the same as adding a positive number.

Example 1: 5 - 3 = 5 + (-3) = 2

Example 2: 5 - (-3) = 5 + 3 = 8

Worked Examples

Expression	Calculation	Result
5 + 3	5 + 3 = 8	8
5 + (-3)	5 - 3 = 2	2
-5 + (-3)	-5 - 3 = -8	-8
5 - 3	5 + (-3) = 2	2
5 - (-3)	5 + 3 = 8	8

FAQ

What is the rule for adding two negative numbers?: When adding two negative numbers, add their absolute values and keep the negative sign. For example, -5 + (-3) = -8.
How do you subtract a negative number?: Subtracting a negative number is the same as adding a positive number. For example, 5 - (-3) = 8.
What happens when you add a positive and negative number with the same absolute value?: The result will be zero. For example, 5 + (-5) = 0.
Can you add more than two numbers at once?: Yes, you can add as many numbers as you need by following the same rules for each pair.
What's the difference between adding and subtracting numbers?: Adding combines numbers, while subtracting removes one number from another. Subtraction can be thought of as adding a negative number.