QUICK LINKS


Introduction

QUICK LINKS


Introduction

Percentage Increase and Decrease

INTRO
‚ÄĒ

To help us understand percentage increase and decrease, think about the last time you watched your phone's last 1% of battery drain away…

We know, it‚Äôs the worst. Now, imagine how great it would be if you could just increase your max battery by ? ūü§©
Increasing by is like adding in of the old battery to get a much better new battery.
So now we have blocks of battery. And since a full block is worth hours, the new amount of battery time we have is hours.

This calculation actually uses the following percentage change formula:

And if, instead, we wanted to represent a percentage decrease, we would subtract the percentage change (in decimal format) from instead of adding it.

Try it out yourself!

Smaller

‚ú® Drag ‚ú®

Bigger

So there are two different percentage change equations? ūü§Į

Ehh, sort of. The percentage change formula above comes from a formula we may be more familiar with:

Divide both sides by to convert the percentage change into a decimal:
Multiply both sides by the initial value:
Add the initial value to both sides:
Factor out the initial value:
Rearrange a little, and voila! We have a new simplified percentage increase and percentage decrease formula:
Check out our
Calculator
or explore our
Lesson
and
Practice
sections to learn more about how to calculate initial and final values with percentage increase and decrease.

You can also use the Quick Links menu on the left to jump to a section of your choice.

You can also use the Quick Links dropdown above to jump to a section of your choice.

CALCULATOR
‚ÄĒ

Percentage Increase and Percentage Decrease Calculator

What are you solving for?
What isby?

Step 1. Convert the percentage change to a decimal.

The percentage change as decimal represents the change relative to the initial value.
Remove the percentage sign and move the decimal places to the left.
‚§Ľ‚§Ľ

Step 2. Determine whether to add or subtract the change to/from 1.

Since we’re increasing, we add.

Step 3. Set up the equation.

The final value equals the change from multiplied by the initial value:

Step 4. Solve for the unknown.

So, our answer is
.
KEY STEPS
‚ÄĒ

How to Find the Initial and Final Value of a Percentage Increase or Decrease

Step 1. Convert the percentage change to a decimal.

The percentage change as decimal represents the change relative to the initial value.
Remove the percentage sign and move the decimal places to the left.

Step 2. Determine whether to add or subtract the change to/from 1.

  • If we‚Äôre decreasing, we subtract.
  • If we‚Äôre increasing, we add.

Step 3. Set up the equation.

The final value equals the result from Step 2 multiplied by the initial value:

or

Step 4. Solve for the unknown.

LESSON
‚ÄĒ Calculating Final Value of Percentage Increase and Decrease

Calculating Final Value of Percentage Increase and Decrease

Calculating the final value of a percentage change means we want to find the amount after a percentage increase or decrease.

If the percentage change is , we use the following equation:
Which means that our final value will be greater than our initial value.

Let’s take a look at a few examples to make this make sense!

EXAMPLE 1

Let’s start a percentage increase problem. What is increased by ?

EXAMPLE 2

Nice work! Now, let’s try a percentage decrease problem. What is decreased by ?
Awesome! Expand the
Practice
below to try some more problems or expand the next
Lesson
to see how we handle a percent decrease in our numbers.
PRACTICE
‚ÄĒ Calculating Final Value of Percentage Increase and Decrease

Practice: Calculating Final Value of Percentage Increase and Decrease

Question 1 of 10: What is increased by ?

Step 1. Convert the percentage change to a decimal.

The percentage change as decimal represents the change relative to the initial value.
Remove the percentage sign and move the decimal places to the left.
‚§Ľ‚§Ľ

Step 2. Determine whether to add or subtract the change from 1.

Original Question: What is increased by ?
Since we’re increasing, we add.

Step 3. Set up the equation.

Original Question: What is increased by ?
The final value equals the result from Step 2 multiplied by the initial value:
Use for the value we're solving for.

Step 4. Solve for the unknown.

Awesome job! The final value is  .

LESSON
‚ÄĒ Calculating Initial Value of Percentage Increase and Decrease

Calculating Initial Value of Percentage Increase and Decrease

Calculating the initial value of a percentage change means we want to find the amount before a percentage increase or decrease.

If the percentage change is , we use the following equation:
Which means that our initial value will be less than our final value.

Let’s take a look at a few examples to make this make sense!

EXAMPLE 1

Let's start with a percentage increase problem. is what number increased by ?

EXAMPLE 2

Nice work! Now, let’s try a percentage decrease problem. is what number decreased by ?
Awesome! If you’d like to practice additional problems finding the initial value, expand the
Practice
below before closing out this lesson! ‚ö°
PRACTICE
‚ÄĒ Calculating Initial Value of Percentage Increase and Decrease

Practice: Calculating Initial Value of Percentage Increase and Percentage Decrease

Question 1 of 10: is what number increased by ?

Step 1. Convert the percentage change to a decimal.

The percentage change as decimal represents the change relative to the initial value.
Remove the percentage sign and move the decimal places to the left.
‚§Ľ‚§Ľ

Step 2. Determine whether to add or subtract the change from 1.

Original Question: is what number increased by ?
Since we’re increasing, we add.

Step 3. Set up the equation.

Original Question: is what number increased by ?
The final value equals the result from Step 2 multiplied by the initial value:
Use for the value we're solving for.

Step 4. Solve for the unknown.

Awesome job! The initial value is  .

CONCLUSION
‚ÄĒ
Nice work, look at you go! Thanks for checking out this lesson ‚ėļÔłŹūüôŹ. Where to next?
Leave Feedback