# Negative Numbers Arithmetic: Adding Negatives Explained

January 19, 2024 by JoyAnswer.org, Category : Mathematics

What does a negative plus a negative number equal? Understand the addition of negative numbers. This article explains the concept of adding negatives, providing clarity on the rules and outcomes in mathematical operations.

## What does a negative plus a negative number equal?

When you add two negative numbers together, the result is another negative number. In arithmetic, the addition of negatives follows a specific rule:

If you have two negative numbers, when you add them, you sum their magnitudes (absolute values) and give the result the negative sign.

Mathematically, if you have `-a + (-b)`, the result is `- (a + b)`.

Here's an example:

• If you add `-3` and `-5`, you first add their magnitudes (ignoring the signs): `3 + 5 = 8`.
• Then, you assign the negative sign to the result: `-8`.

So, `-3 + (-5) = -8`.

In summary, adding two negative numbers results in a negative number, and you simply add their magnitudes to find the magnitude of the result. The negative sign is then applied to the sum of magnitudes.

## Navigating Arithmetic: The Outcome of Adding Negative Numbers

When adding negative numbers, it's crucial to remember that they represent values less than zero. Here's what happens when you combine them:

## What happens when you add two negative numbers together?

• The result is always a negative number.
• The sum's absolute value (its distance from zero) is the combined absolute values of the original numbers.

For example:

• (-5) + (-3) = -8
• (-10) + (-2) = -12

## Rules and Conventions in Adding Negative Numerals

- Adding a negative number is like moving to the left on the number line.- Adding two negative numbers means moving even further to the left, resulting in a larger negative number.

Key Rules:

1. Adding Two Negative Numbers: Results in a negative number greater in magnitude than either original number.
2. Adding a Negative Number to a Positive Number:
• Sum is smaller than the positive number.
• Sign of the sum depends on the magnitudes of the numbers.
3. Triangle Inequality: The absolute value of the sum is always less than or equal to the sum of the absolute values of the original numbers.

Example:

• 5 + (-3) = 2 (positive sum, as 5 is larger than 3)
• 2 + (-5) = -3 (negative sum, as 5 is larger than 2)

Visualizing on a Number Line:

• Imagine a number line with 0 in the center, positive numbers to the right, and negative numbers to the left.
• Adding a negative number is like moving to the left.
• Adding two negative numbers means taking two leftward steps, resulting in a position further to the left (a larger negative number).

Tags Negative Numbers , Arithmetic

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