\displaystyle 10\% \text{ of } 60	\displaystyle =	\displaystyle \dfrac{1}{10} \times 60	Replace 10\% with \dfrac{1}{10} and "of" with \times
	\displaystyle =	\displaystyle 6	Cancel out the 0s

Idea summary

We can find a percentage of a quantity by converting the percentage to a fraction and multiplying by the quantity.

Percentage discounts

How can we work out percentage discounts? In this video, we see how to do that, as well as work out the discounted price we need to pay.

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Examples

Example 2

William is going to buy a jumper that is marked as 50\% off. The original price is \$96.

What is the value of the discount?

Worked Solution

Create a strategy

50\% of the price is the same as half the price.

Apply the idea

\displaystyle \text{Discount}	\displaystyle =	\displaystyle 96\times 50\%	Multiply by 50\%
	\displaystyle =	\displaystyle 96\times \dfrac{1}{2}	Multiply by \dfrac{1}{2}
	\displaystyle =	\displaystyle \$48	Halve 96

What is the price that William will pay for the jumper?

Worked Solution

Create a strategy

Subtract the discount from the original price.

Apply the idea

\displaystyle \text{Price}	\displaystyle =	\displaystyle 96 - 48	Subtract 48 from 96
	\displaystyle =	\displaystyle \$48

Idea summary

To find the discount, multiply the original price by the percentage of the discount.

To find the discounted price, subtract the discount from the original price.

Goods and sales tax

In Australia, Goods and Services Tax, or GST for short, is a 10\% tax that is charged on top of most things you buy. Let's learn more about calculating GST.

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Examples

Example 3

Joanne's bike cost \$90, excluding the 10\% goods and services tax (GST).

How much GST will Joanne get charged?

Worked Solution

Create a strategy

Find the 10\% of \$90.

Apply the idea

\displaystyle \text{GST}	\displaystyle =	\displaystyle 90 \times 10\%	Multiply 90 by 10\%
	\displaystyle =	\displaystyle 90 \times \dfrac{1}{10}	Convert the percentage to a fraction
	\displaystyle =	\displaystyle \$9	Cancel out the 0s

What is the total amount Joanne pays for her bike?

Worked Solution

Create a strategy

We can use the formula: \text{Cost of items} + \text{GST} = \text{Total amount paid}

Apply the idea

\displaystyle \text{Total amount paid}	\displaystyle =	\displaystyle 90 + 9	Add the GST and cost
	\displaystyle =	\displaystyle \$99

Idea summary

In Australia, Goods and Services Tax (GST) is a 10\% tax on most things you buy. That means you pay an extra 10\% of the cost.

\text{Cost of items} + \text{GST} = \text{Total amount paid}

Outcomes

AC9M6N08

approximate numerical solutions to problems involving rational numbers and percentages, including financial contexts, using appropriate estimation strategies

AC9M6N09

use mathematical modelling to solve practical problems, involving rational numbers and percentages, including in financial contexts; formulate the problems, choosing operations and efficient calculation strategies, and using digital tools where appropriate; interpret and communicate solutions in terms of the situation, justifying the choices made

8.06 Personal finance and percentages

Ideas

Are you ready?

Examples

Example 1

Percentage discounts

Examples

Example 2

Goods and sales tax

Examples

Example 3

Outcomes

AC9M6N08

AC9M6N09

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