CALCULATOR

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## Percentage Increase and Percentage Decrease Calculator

We have some questions for you! Help us out through this

INTRO

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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’s the worst. Now, imagine how great it would be if you could just increase your max battery by $50%$? 🤩

$1$

Increasing by $50%$ is like adding in $0.5$ of the old battery to get a much better new battery.

So now we have $1+0.5=1.5$ blocks of battery. And since a full block is worth $4$ hours, the new amount of battery time we have is $1.5×4=6$ hours.

This calculation actually uses the following percentage change formula:

$final value66 =(1+%change as decimal)×initial value=(1+.5)×4=(1.5)×4 $

And if, instead, we wanted to represent a percentage decrease, we would subtract the percentage change (in decimal format) from $1$ instead of adding it.

Try it out yourself!

### Smaller

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### Bigger

$1$

$final value =(1+%change as decimal)×initial value=(1+0)×initial value=(1)×initial value $

### So there are two different percentage change equations? 🤯

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

$percent change=initial valuefinal value−initial value ×100$

Calculator

Lesson

Practice

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KEY STEPS

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## 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 $2$ places to the left.

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

- If we’re decreasing, we
**subtract**. - If we’re increasing, we
**add**.

### Step 3. Set up the equation.

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

$final value=(1−%change as decimal)×initial value$

or

$final value=(1+%change as decimal)×initial value$

### Step 4. Solve for the unknown.

LESSON

— Calculating Final Value of Percentage Increase and Decrease

PRACTICE

— Calculating Final Value of Percentage Increase and Decrease

LESSON

— Calculating Initial Value of Percentage Increase and Decrease

PRACTICE

— Calculating Initial Value of Percentage Increase and Decrease

CONCLUSION

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