# Percentage Increase and Decrease

## The Significance of Percentage Increases and Decreases

In our everyday lives, we experience various changes in quantities and values. These changes can be accurately measured using percentages. This informative piece will delve into the concept of percentage increases and decreases and how they can assist in comparing different quantities and values.

### What Exactly is a Percentage?

A percentage is a fraction of a number, usually referred to as "parts per 100". It is symbolized by %, which is equivalent to 1/100. To obtain a percentage of a number, we divide the number by 100.

### Understanding Percentage Increase and Decrease

A percentage increase represents the rise in a number, amount, or quantity, expressed in percentage. Conversely, a percentage decrease indicates the reduction of a number, amount, or quantity, also conveyed as a percentage. The key difference between these two is that one involves an increase, while the other depicts a decrease. However, in both cases, there is a change in the value.

### Formulas for Calculating Percentage Increase and Decrease

To determine the percentage increase, we first need to find the difference between the two numbers being compared. We then convert this difference to a percentage by dividing it by the original number and multiplying by 100. The formula is as follows:

Percentage Increase = (New Number - Original Number) / Original Number * 100

Similarly, to calculate the percentage decrease, we follow the same steps, but with a different formula:

Percentage Decrease = (Original Number - New Number) / Original Number * 100

### Adjusting Numbers by a Certain Percentage

When we want to increase or decrease a number by a particular percentage, we first find the percentage of that number and then add or subtract it from the original number. Here are a few examples:

• Increasing a number by 20%: identify 20% of the number and add it to the original number
• Decreasing a number by 20%: determine 20% of the number and subtract it from the original number

### Calculating Percentage Change Over Time

There may be instances where we need to determine the percentage change over time, such as analyzing growth or reduction over a specific period. In such situations, we use the following formula:

Percentage Change = (New Number / Original Number - 1) * 100 / Time

The outcome may be a negative number, but we simply ignore the sign and state that the quantities decreased by that percentage. The unit used to express percentage change over time is "% per time".

### Examples of Percentage Increases and Decreases

Let's apply the formulas we've learned to some examples:

• Example 1: The price of a bag of rice increased from £20 to £35. What is the percentage increase?

Solution: The percentage increase formula is:

Percentage Increase = (New Number - Original Number) / Original Number * 100

First, we find the increase:

Increase = £35 - £20 = £15

Next, we find the percentage increase:

Percentage Increase = (15 / 20) * 100 = 75%.

This means the price increased by 75%.

• Example 2: A bag contains 15 balls. After some time, the number of balls increased to 35. What is the percentage increase?

Solution: The percentage increase formula is:

Percentage Increase = (New Number - Original Number) / Original Number * 100

First, we find the increase:

Increase = 35 - 15 = 20

Next, we find the percentage increase:

Percentage Increase = (20 / 15) * 100 = 133.33%.

This means the number of balls increased by 133.33%.

## Calculating Percentage Increase and Decrease Made Easy

When dealing with numbers, it's common to want to know the percentage increase or decrease. This can be especially helpful when comparing numbers over time. In this article, we will dive into the formulas and steps for finding both percentage increase and decrease, as well as how to handle calculations over a period of time.

## Percentage Decrease

If you're wondering how much something decreased by, the decrease amount can seem daunting. But with a simple formula, it becomes much more manageable. For example, Jenna's savings account has decreased by £200. We can find the percentage decrease by using the formula (Decrease/Original number x 100), which in this case gives us a decrease of 20%.

For a different scenario, let's say a company produced 500 units of their product last month, but only produced 450 units this month. The decrease is 50 units, making the percentage decrease 10%.

## Percentage Increase

In some cases, we may want to know the percentage increase of a number. For example, Sarah's business made a profit of £5000 last month, and £6000 this month. Using the formula (New number - Original number), the increase is £1000, making the percentage increase 20%. Similarly, an organization had 100 volunteers last year, but now has 120. The increase is 20 volunteers, making the percentage increase also 20%.

## Percentage Change Over Time

When looking at numbers over a period of time, we use a slightly different method. Let's say two years ago, a company's stock was worth £20 per share, and today it is worth £25 per share. We divide the new value by the original value and subtract 1. This gives us 0.25, which we then multiply by 100 to get 25%. This means that the company's stock has increased by 25% over the 2-year span.

Similarly, if a restaurant had 200 customers on a Saturday night, but only had 180 this Saturday, we can calculate the 10% decrease over time using the formula (Decrease/Original number x 100).

## Key Points to Remember

• Percentage increase and decrease can be found using simple formulas.
• If a negative value is obtained, simply remove the negative sign to indicate a decrease.
• The percentage symbol (%) is used to denote percentage.
• Calculating over a period of time requires a different approach.

## How to Calculate Percentage Increase and Decrease

To find the percentage increase or decrease, we follow a simple process. First, we find the difference between the two numbers being compared. Then, we divide this difference by the original number and multiply by 100 to convert it to a percentage. For example, to find the percentage increase from 500 to 750, we divide the increase of 250 by the original number 500, giving us a 50% increase.

## Keep in Mind the Formulas

The formulas for finding percentage increase and decrease are simply (Increase/Original number x 100) and (Decrease/Original number x 100), respectively. These formulas can be used for any scenario, making calculations quick and easy to do.

## Increasing and Decreasing Percentages

To increase a number by a certain percentage, we find the percentage of the number and then add this value to the original number. For example, to increase £100 by 10%, we first find 10% of £100, which is £10. Then, we add this to the original £100, giving us a total of £110.

Similarly, to decrease a number by a certain percentage, we follow the same process but subtract the percentage value instead of adding it. Now, you know how to confidently and quickly calculate percentage increase and decrease for any given situation.

## Mastering Percentage Increase and Decrease: A Comprehensive Guide with Examples

Understanding how to calculate percentage increases and decreases is essential for various tasks, from analyzing financial data to making budget decisions. In this article, we'll explore the steps to finding the percentage change of a value, as well as how to average multiple percentages for a more accurate representation of overall changes.

Let's start with the basics. When looking to increase a number by a certain percentage, the first step is to calculate the actual value of that percentage. This can be done by multiplying the original number by the percentage, then dividing by 100. For example, if we want to increase 50 by 25%, we would do the following calculation: (50 * 25) / 100 = 12.5. This means that we need to add 12.5 to 50, resulting in a final value of 62.5.

When it comes to decreasing a number by a percentage, the process is similar. However, instead of adding the calculated amount, we need to subtract it from the original number. For instance, if we want to decrease 150 by 20%, we would do (150 * 20) / 100 = 30. This means that we need to subtract 30 from 150, resulting in a final value of 120.

Now, let's look at some real-life examples. Let's say you bought a stock for £100, but its value increased by 50%. This means that the new value is 100 + (100 * 50) / 100 = 150. On the other hand, if you bought a car for £20,000, but its value decreased by 10%, the new value would be 20,000 - (20,000 * 10) / 100 = 18,000.

## Calculating the Average of Multiple Percentage Changes

But what if we have multiple percentage changes and we want to find the overall average? This can be done by summing up all the individual percentages and dividing by the total number of percentages. For example, if we have two percentages - 20% increase and 10% decrease - the average would be (20 + (-10)) / 2 = 5%. However, if we have more than two percentages, we need to consider additional factors such as sample size to get a more accurate average.

In conclusion, being able to calculate percentage increases and decreases is a valuable skill in various situations. By following these straightforward steps, you can easily determine the impact of changes in numerical values. Just remember that calculating the average of multiple percentages may require some additional considerations, but can still be done using a similar approach. Now that you have the tools, go forth and make accurate calculations with confidence!