**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**

## 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**

Before we get into calculating how much you can save at a sale, let’s briefly review how to easily calculate 10% of any amount of money.
To find 10% of any number or amount, all you have to do is divide that number by 10. TIP: Heres a tip to help you easily calculate 10% of any amount of money. First, write the amount out with the decimal point and the digits representing the number of cents—like you’d see on a cash register. For example: $2.50 or $85.00. |

Now, to find 10% of that amount, just move the decimal point one position to the left.

So, what’s 10% of $2.50? Just move the decimal place one position to the left. The result is $0.25, which is the same as 25 cents.

What’s 10% of $85.00? Again, move the decimal point one position to the left—the result is $8.50

So, what’s 10% of $2.50? Just move the decimal place one position to the left. The result is $0.25, which is the same as 25 cents.

What’s 10% of $85.00? Again, move the decimal point one position to the left—the result is $8.50

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

**To find 10% off input - Full price ÷ 10 = 10% off full price**

**To find 20% off, input - Full price ÷ 10 x 2 = 20% off full price**

**How could you find 30% and 5% off?**

**I am building on concepts **

## Finding a Percentage off by multiplying its decimal

An easy way to calculate percentages off is to multiply the price by the decimal equivalent of a percentage.

Firstly you need to convert your percentage into a decimal e.g 36% becomes 0.36, 25% becomes 0.25 etc.

Once you have converted the percentage, just follow these steps:

Firstly you need to convert your percentage into a decimal e.g 36% becomes 0.36, 25% becomes 0.25 etc.

Once you have converted the percentage, just follow these steps:

- Multiply normally, ignoring the decimal points.
- Then put the decimal point in the answer - it will have as many decimal places as the two original numbers combined.

**I am consolidating concepts and investigating**

## 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. |