Your friend bought you a birthday present in the sale.....cheapskate.....

You want to know how much the item was worth before the sale.

Or they may have missed the sale and had to pay more, because the original price had been increased.

Finding the original amount of something before a percentage change took place is also known as reverse percentages.

This key word reverse is going to help us throughout this activity.

A radio sells for £63,__ after__ a 40% increase in the cost price. Find the cost price.

We know that the radio x 1.40 = £63 just reverse the process (work backwards) 63÷1.40 = £45

A packet of washing powder is advertised as having extra '20% extra powder'.

If it contains 1.32kg, what would the amount in the original pack be?

Powder x 1.20 = 1.32kg Let us reverse 1.32 ÷ 1.20 = 1.1kg

A television has been reduced by 8% in a sale. It now costs £586.

What was the cost of the television before the reduction in price?

This time as it is a reduction we need to take 8% away from 100% = 92% this is our multiplier.

We now do the inverse(opposite)

£586 ÷ 0.92 = £636.96

__ Let us extend this a little bit__

You many get questions that don't appear that straight forward and may need a different approach.

At a hockey game there are 60 children. This is 20% of everyone at the game. How many people are at the game?

Think about what you know. 20% = 60 so 20% x 5 = 100%

60 x 5 = 300 people altogether

__One more method you may need to adopt__

In a shoe factory 33% of the shoes are leather and the remaining 4355 are suede. How many shoes are leather?

As we cannot easily turn 33% into 100% we have to adopt a different approach. Think about what you know.

If 33% of the shoes are leather the suede shoes make up the remaining 67%. To make life easy we want to find 1%.

The only numbers we have to work with are for the suede shoes.

4355 ÷ 67 = 65

1% = 65. Therefore 33% = 65 x 33 = 2145

I wonder if they are blue suede shoes? Ask someone older if you need to.....