**Australian Curriculum **

Investigate and calculate percentage discounts of 10%, 25% and 50% on sale items, with and without digital technologies (ACMNA132)

Make connections between equivalent fractions, decimals and percentages(ACMNA131)

Multiply decimals by whole numbers and perform divisions by non-zero whole numbers where the results are terminating decimals, with and without digital technologies (ACMNA129)

**Maths Rotations**

## Mr Rayners rotations

## We are learning to calculate percentage discounts to find sale prices

Have a go at completing the game activities, this is consolidating what you already know and building on your long term memory.

Click on the image to be directed to the game

Click on the image to be directed to the game

**I need some more practice**

If you find a number is too large to calculate, or you have an odd number try the method below.

**You can check your answers on a calculator -**

**To find 50% off, input - Full price ÷ 2 = 50% off full price**

**To find 25% off, input - Full price ÷ 4 = 25% off full price**

**I am building on concepts **

**I am consolidating concepts and investigating**

To calculate percentage decrease: First: work out the difference (decrease) between the two numbers you are comparing. Then: divide the decrease by the original number and multiply the answer by 100. If your answer is a negative number then this is a percentage increase.

## Reverse Percentages - Finding the original sale price

Sometimes a question will ask you to work backwards and find the original price of something after the price has increased. If you are given a quantity after a percentage increase or decrease, and you need to find the original amount, use this method:

We are told the selling price is a 40% in the cost price. So the selling price is 100% + 40% = 140% of the cost price.

We know that the selling price is $63, so 140% = $63.

Now calculate 1%: 140% = $63 £63 ÷ 140 = $0.45 (1%)

The cost price is 100%, so multiply £0.45 by 100.

Cost price = 0.45 × 100 = £45.

We know that the selling price is $63, so 140% = $63.

Now calculate 1%: 140% = $63 £63 ÷ 140 = $0.45 (1%)

The cost price is 100%, so multiply £0.45 by 100.

Cost price = 0.45 × 100 = £45.

EXAMPLE TWO PRICE DECREASEA new car falls in value by 30% in a year. After a year, it is worth £8,400. Find the price of the car when it was new. SolutionRemember that the original price of the car is 100%. Original price = 100%. Second-hand price = 100% - 30% = 70%. So $8,400 = 70% of the original price. So 1% of original price = $8,400 ÷ 70 1% = $120 Original price (1% x 100 = 100% ) = (8400 ÷ 70) x 100 = $12,000. |