# Adding Two Negatives: Rules and Consequences

_{January 21, 2024 by JoyAnswer.org, Category : Mathematics}

Do two negatives added together make a positive? Explore the rules and consequences of adding two negatives in mathematics. This article provides insights into the mathematical principles governing the addition of negative numbers.

## Do two negatives added together make a positive?

No, adding two negatives together does not result in a positive value. When you add two negative numbers, the sum is negative. This is a fundamental rule in arithmetic and algebra.

For example:$(-3) + (-2) = -5$

Here, both numbers are negative, and their sum is also negative.

To understand this concept, you can think of adding negative numbers as a process of moving to the left on the number line. Adding a negative number is equivalent to moving in the negative direction. When you add two negative numbers, you're essentially moving farther to the left, resulting in a negative sum.

In summary, the rule for adding two negatives is that the sum is negative. It is only when you multiply two negatives that the result is positive.

**Here's a breakdown of adding negative numbers:**

**1. Do Two Negatives Add to a Positive?**

No, adding two negative numbers together results in a negative number, not a positive one.

**2. How Addition of Negative Numbers Works:**

**Number Line:**Imagine a number line, where positive numbers lie to the right of zero and negative numbers to the left. Adding a negative means moving further left, resulting in a more negative sum.**Example:**-5 + (-3) = -8. You move 5 steps left (-5), then 3 more steps left (-3), ending up at -8, which is more negative than either starting number.

**3. Practical Scenarios:**

**Debt:**If you owe $5 (-5) and then borrow another $3 (-3), your total debt increases to $8 (-8).**Temperature:**If it's -5 degrees Celsius and the temperature drops 3 more degrees (-3), it becomes -8 degrees, a colder temperature.

**4. Relationship with Subtraction:**

**Subtracting a positive equals adding a negative:**5 - 3 is the same as 5 + (-3), both resulting in 2.**Subtracting a negative equals adding a positive:**5 - (-3) is the same as 5 + 3, both resulting in 8.

**5. Application in Mathematical Operations:**

**Solving equations:**Understanding negative addition is crucial for solving algebraic equations involving negative numbers.**Vector addition:**In physics, negative numbers represent opposite directions. Adding vectors with negative components requires applying negative addition rules.**Financial calculations:**Dealing with debts, losses, or expenses involves negative numbers and their addition.

**Key Points:**

- Adding two negatives moves you further away from zero on the number line, resulting in a more negative number.
- Consider practical scenarios to visualize the concept.
- Negative addition and subtraction are closely related.
- It's essential for various mathematical operations across different fields.