# How to Find a Percentage Change (Mathematics Lesson)

# Finding a Percentage Change

A percentage change tells you how a number has changed from one value to another value, expressed as a percentage.Imagine you wanted to find the percentage change from 20 to 25.

# How to Find a Percentage Change

Finding a percentage change is easy. Find the difference between the numbers and express this a percentage of the original number.#### An Example Question

What is the percentage change from 20 to 25?Step 1

Subtract the old number from the new number. In our example, the old number is 20 and the new number is 25.

25 - 20 = 5

Step 2

5 ÷ 20 = 0.25

Step 3

0.25 × 100% = 25%

The percentage change from 20 to 25 is 25%.
# How to Find a Percentage Change Using a Formula

A percentage change can be found using the formula below:In this formula, n

_{old}is the old value and n

_{new}is the new value.

Let's use the formula to find the percentage change from 20 to 25.

#### An Example Question

What is the percentage change from 20 to 25?Step 1

Start with the formula:
Percentage change = (n

_{new}- n_{old}) / |n_{old}| × 100%**Don't forget:**/ means ÷

**and**|n

_{old}| means the absolute value of n

_{old}(ignore the - sign if n

_{old}is negative).

Step 2

Substitute the numbers into the formula. In our example, n_{old}= 20 and n

_{new}= 25.

Percentage change = (25 - 20) / |20| × 100%

Percentage change = (5) / 20 × 100%

Percentage change = 5 ÷ 20 × 100%

Percentage change = 0.25 × 100%

Percentage change = 25%

Percentage change = (5) / 20 × 100%

Percentage change = 5 ÷ 20 × 100%

Percentage change = 0.25 × 100%

Percentage change = 25%

# Percentage Increase, Percentage Decrease

In the example above, the number**increased**from 20 to 25. The percentage change was positive. This is a

**percentage increase**.

A

**percentage decrease**happens when the number gets smaller. The percentage change will be negative.

The slider below gives another example of how to find a percentage change. This time, it is a percentage decrease.

##### Interactive Test

**show**

Here's a second test on finding a percentage change.

Here's a third test on finding a percentage change.

##### Note

# What Is a Percentage Change?

A percentage change is the change from one value to another value, expressed as a percentage.# What Does |n_{old}| Mean in the Formula?

The vertical lines mean the absolute value of n_{old}needs to be found.

This means that the value is always taken as positive, even if it is negative.

If the old number n

_{old}equals 5, |n

_{old}| also equals 5.

But if the old number n

_{old}equals -5, |n

_{old}| equals 5. You ignore the - sign.

# Be Careful How You Talk About Percentage Changes

A percentage change expresses a change in values as a percentage.You might say, "the share price has risen 5% today". This means the share price started the day at one value, $1, and ended it at a value that is 5% of $1 higher ($1.05).

It expresses the change between two numbers, values or quantities; not a change between percentages.

Sometimes people do refer to changes in percentages. For example, "the interest rate on my savings account has risen from 3% to 4%. The interest rate has risen by 1%".

This is not a percentage change in the sense we are using it. It is a difference in percentages (found by subtracting percentages).

Rather than saying "the interest rate has risen by 1%", you should say "the interest rate has risen by 1 percentage point".

# Getting Back to Where You Started

An advert in a shop once boasted:This is wrong. But why?

Imagine the shop did take 50% off. It reduced a price tag from $10 to $5. This would be a 50% decrease. (You can check this!)

Did it put 50% on the $5 item to sell it at $100? No. $5 to $10 is a 100% increase, not a 50% increase, (Again, you can check this).

An equal and opposite percentage change will not reverse a percentage change.