# How to Work Out Percentage Increases and Decreases

Welcome to our How to work out percentage increases and decreases page.

One this page we have clear step-by-step instructions for finding percentage change as well as worked examples and an easy to use percentage increase calculator to check your work.

## How to Work out Percentage Increases and Decreases

### How to find the Percentage increase

Take a look at the 3 easy steps below for finding how to find the percentage change between 2 numbers.

Step 1) Subtract the original number from the new number.

Step 2) Divide this number by the original number.

Step 3) Multiply this number by 100 to convert it to a percentage.

If the number is negative, then it is a percentage decrease, if it is positive then it is an increase.

#### Examples

Example 1) A toy normally costs \$450. It is sold for \$360 in a sale. Work out the percentage it has been reduced by.

Step 1)

We subtract the original number from the new number.

360 - 450 = -90

Step 2)

We need to divide this number by the original number.

-90 ÷ 450 = -0.2

Step 3)

Multiply by 100 to convert to a percentage.

-0.2 x 100 = -20%

Answer: It has been reduced by 20%

We can also say that the new price is 100 - 20 = 80% of the old price.

Example 2) Tyger buys a car for \$3200. He renovates it and eventually sell it for \$3800. Work out the percentage increase he sold the car for.

Step 1)

We subtract the original number from the new number.

3800 - 3200 = 600

Step 2)

We need to divide this number by the original number.

600 ÷ 3200 = 0.1875

Step 3)

Multiply by 100 to convert to a percentage.

0.1875 x 100 = 18.75%

Answer: he sold the car for 18.75% more than he paid for it.

We can also say that the price he sold it for was 100 + 18.75 = 118.75% of the price he paid for it.

Example 3) Sally fills her car with 12 gallons of gas. She goes on a journey and ends up with just 7.5 gallons left in the tank. What is the percentage change?

Step 1)

We subtract the original number from the new number.

7.5 - 12 = -4.5

Step 2)

We need to divide this number by the original number.

-4.5 ÷ 12 = -0.375

Step 3)

Multiply by 100 to convert to a percentage.

-0.375 x 100 = -37.5%

Answer: she has 37.5% less gas than when she started.

We can also say that she has 100 - 37.5 = 62.5% of the gas she started with.

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