**The Difference Between Two Negative Numbers is Always Negative**

When two negative numbers are subtracted, the result will always be another negative number. This concept is an important part of understanding the fundamentals of arithmetic. To understand why the difference between two negative numbers is always negative, it is important to understand the concept of number lines and the rules of subtraction.

### Number Lines

A number line is a visual representation of a line with a series of numbers along it. It is used to show the order of numbers in relation to each other. A number line is typically used to illustrate the concept of adding and subtracting. The number line starts at zero and then runs infinitely in both directions. Positive numbers are located to the right of zero and negative numbers are located to the left of zero.

### Rules of Subtraction

When subtracting two numbers, the larger number is subtracted from the smaller number. For example, if we subtract 5 from 10, we would get 5 (10 – 5 = 5). If we subtract 10 from 5, the result would be -5 (5 – 10 = -5).

When a negative number is subtracted from another negative number, the result is still a negative number. This is because the “larger” negative number is still being subtracted from the “smaller” negative number, even though the order is reversed.

### The Difference Between Two Negative Numbers is Always Negative

The difference between two negative numbers is always negative because the larger negative number is always subtracted from the smaller negative number, regardless of the order. Let’s look at an example:

If we subtract -5 from -10, the result is -5 (-10 – (-5) = -5).

If we subtract -10 from -5, the result is also -5 (-5 – (-10) = -5).

In both cases, the larger negative number is subtracted from the smaller negative number and the result is a negative number.

### Conclusion

The difference between two negative numbers is always negative because the larger negative number is always subtracted from the smaller negative number, regardless of the order. Understanding the concept of number lines and the rules of subtraction can help make this concept easier to understand. Knowing this concept is important for a good understanding of arithmetic.

## Understanding the Mathematical Principle

The idea of subtracting two negative numbers and the result being a negative number can be a confusing concept for some. However, it is simply a mathematical principle that is based on the concept of **opposites**. When two negative numbers are subtracted, the result is negative because it is the opposite of the result from subtracting two positive numbers.

For example, let’s take two negative numbers such as -5 and -2. To calculate the result, the negative numbers must be subtracted. This can be written in an equation as -5 – (-2). Since both numbers are negative, the result is **negative**. In this example, the result would be -3.

To further illustrate this principle, let’s take the same example but switch one of the negative numbers to a positive number. If the equation is written as -5 – (2), both of the numbers are not negative. The result would be **positive**. In this example, the result would be -7.

## Applying the Principle to Real-Life Situations

The principle of subtracting two negative numbers and the result being negative can be applied to real-life situations. An example of this would be a person’s bank account balance. Let’s say that a person has a balance of -$100 and then spends -$50. The new balance would be calculated by taking the original balance of -$100 and subtracting -$50, which would result in a new balance of -$150.

This type of situation can also be seen in the stock market. For example, let’s say that an investor has a portfolio with a value of -$100 and then they invest an additional -$50. The new portfolio value would be calculated by taking the original value of -$100 and subtracting -$50, which would result in a new portfolio value of -$150.

It is important to note that the principle of subtracting two negative numbers and the result being negative applies to any situation where the numbers are both negative.

## Conclusion

The concept of subtracting two negative numbers and the result being negative can be difficult to understand at first. However, it is a mathematical principle that is based on the concept of opposites. When two negative numbers are subtracted, the result is negative because it is the opposite of the result from subtracting two positive numbers.

This principle can be applied to real-life situations such as a person’s bank account balance or a portfolio in the stock market. It is important to note that the principle applies to any situation where the numbers are both negative.