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# Finding a Percentage Change

(KS3, Year 7)

## The Lesson

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.This is 20% (said as "20 percent"). It means 20 parts out of 100.

## 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.## Question

What is the percentage change from 20 to 25?## Step-by-Step:

# 1

Find the difference between the old and new number.
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

# 2

Divide the answer (5) by the old number (20).

5 ÷ 20 = 0.25

# 3

Multiply the answer (0.25) by 100%.

0.25 × 100% = 25%

## Answer:

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.

## Question

What is the percentage change from 20 to 25?## Step-by-Step:

# 1

Start with the formula:

(ignore the − sign if n

Percentage change =

^{(nnew − nold)}⁄_{|nold| × 100%}**Don't forget:**/ means ÷**and**|n_{old}| means the absolute value of n_{old}(ignore the − sign if n

_{old}is negative).# 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%## Answer:

The percentage change from 20 to 25 is 25%.## 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.

## Beware

## 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.

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