# 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.

- 1. What does a negative plus a negative number equal?
- 2. Navigating Arithmetic: The Outcome of Adding Negative Numbers
- 3. What happens when you add two negative numbers together?
- 4. Rules and Conventions in Adding Negative Numerals

## 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:

**Rule for Adding Negative Numbers:**

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:**

**Adding Two Negative Numbers:**Results in a negative number greater in magnitude than either original number.**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.

**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).