After watching this video lesson, you will be able to calculate the percentage increase and decrease of changes that happen over time.

You will also learn what you need in order to make your calculations.

## Percentage Changes

Changes happen every day. Like, one day the temperature outside can be nice and warm, and you wear a shirt and shorts to go play outside. But, then the next day can be cold, and you end up wearing your grandma’s sweater with pants. In business, important changes, such as less sales one year compared to the previous year, need to be analyzed.

To help businesses analyze these changes, we calculate the **percentage increase or decrease**, the amount of increase or decrease expressed as a percentage.

## How to Calculate

How do we calculate this percentage increase or decrease? We begin by first calculating the first total and then comparing it to the second total. For example, if we are analyzing the change in sales from one year to the next, our first total will be the sales of the one year, and our second total will be the sales of the next year. We then determine if there is an increase or decrease happening. For example, we have an increase if the second total is greater than the first and we have a decrease if the second total is lower than the first.Once we have determined whether the change is an increase or decrease, we then calculate how much the change is by subtracting the lesser from the greater.

We then divide it by the first total. To find the percentage, we then multiply by 100.We can write a simple formula for the percentage increase or decrease.

We can say that the percentage increase or decrease is (the increase or decrease) / (first total) * 100.No matter what problem we are given, as long as we are able to find the first total and the amount of increase or decrease, then we can calculate the percentage increase or decrease. Let’s take a look at a couple of examples.

## Example 1

A pet store owner is analyzing his sales for this month. He wants to compare it to his sales last month. He doesn’t know if his sales increased or decreased. He also wants to find out by how much his sales increased or decreased.

The numbers he has available to work with are the following:

Month 1 Sales | Month 2 Sales |
---|---|

Puppies: $400 | Puppies: $300 |

Kittens: $700 | Kittens: $900 |

Fish: $100 | Fish: $50 |

Small Animals: $200 | Small Animals: $250 |

Looking at his numbers, we see that we first have to find the total for each month. So, for each month, we add up all the sales.

- For month one, we have 400 + 700 + 100 + 200 = 1400. So, month one gave the owner a total of $1,400.
- For month two, we have 300 + 900 + 50 + 250 = 1500.
So, month two has a total sales of $1,500.

Comparing these two totals with each other, we see that month two has a total greater than month one. So, we have an increase going on. How much is our increase? $1,500 is $100 greater than $1,400. So, our increase is $100.To find our percentage increase then, we divide our 100 by our month one total.

We get 100/1400 = 0.0714. Multiply this by 100, we get a percentage of 7.1%. So our sales increased by 7.1%.

And we are done!

## Example 2

This time, we have a teacher looking at her attendance charts. She wants to know if the attendance this week is better than the attendance last week. She wants to know because this week, she changed her teaching approach to a more humorous one. The previous week, she was very serious and didn’t allow any fooling around.

Looking at her records, she sees that the previous week, she had an attendance record of 95%. This week, her attendance record is 90%. Do we have an increase or decrease?We have a decrease since the second total is lower.

How much is our decrease? We have 95 – 90 = 5. We decreased by five percent. How much of a percentage decrease is this? We divide our 5 / 95 * 100. We get approximately 5.3%. So, we have a percentage decrease of 5.3%.

And we are done.Notice here that in this problem we are already dealing with percentages. But our process is still the same. So, as long as we have the same format of our totals, then we use the same process regardless if the numbers are already percentages or not.

## Lesson Summary

Let’s review what we’ve learned. A **percentage increase or decrease** is the amount of increase or decrease expressed as a percentage.

To calculate it, we first calculate the first total and then the second total. If we are comparing two consecutive years, the first year gives us the first total, and the second year gives us the second total. Then we determine if there is an increase or decrease happening. Then we calculate the amount of this increase or decrease. To find the percentage, we divide the amount of increase or decrease by the first total and multiply by 100.

## Learning Outcomes

By the end of this lesson you should be able to:

- State the formula for determining percent increase or decrease
- Calculate the percentage of increase of decrease