## How to Calculate Percentage Increase with Negative Number

Calculating percentage increase is a useful skill in many areas of life, whether you’re looking at the growth of your investments or the increase in prices at the grocery store. But what do you do when you’re faced with negative numbers? In this article, we’ll show you how to calculate percentage increase with negative numbers using simple steps.

### Understanding the Concept of Percentage Increase

Percentage increase is a measure of how much a value has grown compared to its original value. It is expressed as a percentage and is calculated by dividing the difference between the new value and the original value by the original value, then multiplying the result by 100. For example, if a stock was worth $100 last year and is now worth $120, the percentage increase is:

```
($120 - $100) / $100 x 100 = 20%
```

### Knowing the Formula for Percentage Increase

The formula for calculating percentage increase is:

```
(new value - original value) / original value x 100
```

### Determining the Original Value and the New Value

To calculate percentage increase, you need to know the original value and the new value. The original value is the starting point, while the new value is the value after some change has occurred. For example, if the price of a product was $10 yesterday and is now $12, the original value is $10 and the new value is $12.

### Subtracting the Original Value from the New Value to Get the Difference

The next step is to subtract the original value from the new value to get the difference. This tells you how much the value has changed. If the result is positive, it means the value has increased. If the result is negative, it means the value has decreased. For example, if the original value is $10 and the new value is $12, the difference is:

```
$12 - $10 = $2
```

### Dividing the Difference by the Original Value

Once you have the difference, you need to divide it by the original value. This tells you what percentage the value has changed. If the result is positive, it means the value has increased. If the result is negative, it means the value has decreased. For example, if the original value is $10 and the new value is $12, the difference is $2. To find the percentage increase, you divide $2 by $10:

```
$2 / $10 = 0.2
```

### Multiplying the Result by 100 to Get the Percentage Increase

Finally, you need to multiply the result by 100 to get the percentage increase. This gives you the percentage change from the original value to the new value. For example, if the original value is $10 and the new value is $12, the difference is $2 and the percentage increase is:

```
0.2 x 100 = 20%
```

### Example: If the Original Value is -5 and the New Value is -3, What is the Percentage Increase?

Now let’s look at an example with negative numbers. If the original value is -5 and the new value is -3, what is the percentage increase?

First, we need to subtract the original value from the new value to get the difference:

```
-3 - (-5) = 2
```

Next, we need to divide the difference by the original value:

```
2 / (-5) = -0.4
```

Finally, we need to multiply the result by 100 to get the percentage increase:

```
-0.4 x 100 = -40%
```

So the percentage increase is -40%, which means the value has decreased.

### Remembering that a Negative Percentage Increase Means a Decrease in Value

It’s important to remember that a negative percentage increase means a decrease in value. For example, if the original value is $10 and the new value is $8, the percentage increase is:

```
($8 - $10) / $10 x 100 = -20%
```

In this case, the value has decreased by 20%.

### Example: If the Original Value is -10 and the New Value is -20, What is the Percentage Increase?

Let’s look at another example with negative numbers. If the original value is -10 and the new value is -20, what is the percentage increase?

First, we need to subtract the original value from the new value to get the difference:

```
-20 - (-10) = -10
```

Next, we need to divide the difference by the original value:

```
-10 / (-10) = 1
```

Finally, we need to multiply the result by 100 to get the percentage increase:

```
1 x 100 = 100%
```

So the percentage increase is 100%, which means the value has increased from -10 to -20.

### Remembering that a Positive Percentage Increase Means an Increase in Value

On the other hand, a positive percentage increase means an increase in value. For example, if the original value is $10 and the new value is $12, the percentage increase is:

```
($12 - $10) / $10 x 100 = 20%
```

In this case, the value has increased by 20%.

### Example: If the Original Value is -8 and the New Value is -4, What is the Percentage Increase?

Let’s look at one more example with negative numbers. If the original value is -8 and the new value is -4, what is the percentage increase?

First, we need to subtract the original value from the new value to get the difference:

```
-4 - (-8) = 4
```

Next, we need to divide the difference by the original value:

```
4 / (-8) = -0.5
```

Finally, we need to multiply the result by 100 to get the percentage increase:

```
-0.5 x 100 = -50%
```

So the percentage increase is -50%, which means the value has decreased.

### Remembering that the Absolute Value of a Negative Percentage Increase is the Same as the Percentage Decrease

It’s worth noting that the absolute value of a negative percentage increase is the same as the percentage decrease. For example, if the original value is $10 and the new value is $8, the percentage decrease is:

```
($8 - $10) / $10 x 100 = -20%
```

In this case, the value has decreased by 20%, which is the absolute value of the negative percentage increase we saw earlier.

In conclusion, calculating percentage increase with negative numbers is a straightforward process that can be done using simple steps. By understanding the concept and formula of percentage increase, and following the steps outlined above, you can accurately calculate percentage increase with negative numbers. With this skill, you’ll be able to analyze data more effectively and make informed decisions in a wide range of situations.