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Percentages

Percentages. A percentage is a number out of one hundred (Klerk, 2007, p. 96). Can be written as a fraction, a percentage or as a decimal fraction. e.g 15 out of 100 can be written as: Fraction Percentage 15% Decimal Fraction 0.15. Taxes are expressed as percentages.

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Percentages

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  1. Percentages • A percentage is a number out of one hundred (Klerk, 2007, p. 96) • Can be written as a fraction, a percentage or as a decimal fraction. • e.g 15 out of 100 can be written as: • Fraction Percentage 15% Decimal Fraction 0.15 • Taxes are expressed as percentages. • e.g Goods & Services Tax (GST) = 10% (Klerk, 2007, p.96)

  2. Let’s work through an example: • Alex is purchasing a new car. The base model price is $32,000 excluding GST. He also wants to add the following options/accessories: • Automatic transmission $2 500 ex gst • Airconditioning $1 500 ex gst • Window Tinting $370 ex gst • Tow bar $550 ex gst • Calculate the cost of each of the following vehicles after GST of 10% has been added. The basic model of the car Or, we could add the 10% to 100%, which represents the cost of the item and our calculation would be Automatic car with airconditioning Cost incl gst = (

  3. A car with window tinting and a tow bar. A car with all of the above added extras. The above example shows us that the final price represents 110%. Therefore, the GST represents of the final price. This can be applied to everyday situations and we can calculate the value of the GST by dividing the final price of an item by 11.

  4. Let’s look at an example: Michael has just purchased a vehicle for $46 500 incl GST. He is applying for a loan and wants to pay a deposit that is equivalent to the GST on the vehicle. How much deposit will Michael have to pay? Working backwards to find the original amount following a percentage increase or decrease is called a reverse percentage. Let’s take a look at a couple of examples.

  5. Calculating the original amount following a % increase: Example: Price of fuel has increased by 5% to 145.9 cents/L in the past year. What was the price of fuel a year ago? = 1.389 = 138.9 cents/L Let’s now have a look at calculating the original amount following a % decrease?

  6. Example: Price of fuel has decreased by 7% to 134.9 cents/L in the past year. What was the price of fuel a year ago? = 1.451 = 145.1 cents/L Now try the Percentages Worksheet. Use the Percentages calculator and the solutions page to check your answers. This completes our lesson on Percentages. There are more exercises on percentages on the Test Yourself page.

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