Negative Plus Negative Calculator

Adding negative numbers can be confusing, but it follows simple mathematical rules. This guide explains how to calculate negative plus negative numbers, provides examples, and includes an interactive calculator to help you practice.

What is Negative Plus Negative?

When you add two negative numbers together, the result is always negative. This might seem counterintuitive at first, but it follows the fundamental rules of arithmetic. Negative numbers represent values that are less than zero, and adding them together combines their "negativity."

The key concept here is that negative numbers are subtracted from zero. For example, -3 means 3 units below zero. When you add -3 and -2, you're moving 3 units below zero and then another 2 units below zero, resulting in a total of 5 units below zero, or -5.

How to Calculate Negative Numbers

Calculating negative numbers follows these basic rules:

Negative plus negative equals negative
Negative plus positive equals subtraction
Positive plus negative equals subtraction

For negative plus negative calculations, you can use the following steps:

Ignore the negative signs
Add the absolute values of the numbers
Apply the negative sign to the result

Important Note

The negative sign is part of the number itself. You can't separate it and add the numbers first. Always keep the negative signs until the final step.

Negative Plus Negative Examples

Here are some examples of negative plus negative calculations:

-2 + (-3) = -5
-7 + (-4) = -11
-1 + (-9) = -10
-5 + (-5) = -10

In each case, we're combining two negative numbers, which always results in a negative number. The absolute values are added together, and the negative sign is applied to the final result.

Negative Plus Negative Formula

Formula

a + b = -(|a| + |b|)

Where a and b are negative numbers

This formula shows that when you add two negative numbers, you're essentially adding their absolute values and then applying the negative sign to the result.

For example:

-3 + (-2) = -(3 + 2) = -5
-8 + (-5) = -(8 + 5) = -13

Negative Plus Negative Chart

This chart visually demonstrates how negative plus negative calculations work:

The chart shows that adding two negative numbers always results in a more negative number, moving further away from zero on the number line.

FAQ

Why does negative plus negative equal negative?: Negative numbers represent values below zero. Adding them together combines their "negativity," resulting in a number that's further below zero.
Can I add negative numbers by ignoring the signs first?: No, you must keep the negative signs until the final step. Adding the absolute values first would give you a positive result, which is incorrect.
What happens when you add a negative and a positive number?: When you add a negative and a positive number, you subtract the smaller absolute value from the larger one and take the sign of the number with the larger absolute value.
Is there a difference between -3 + -2 and -2 + -3?: No, addition is commutative, so the order doesn't matter. Both expressions equal -5.
How do I calculate negative plus negative with decimals?: Follow the same rules as with whole numbers. Add the absolute values of the decimals and apply the negative sign to the result.