Lesson 8 ~25 min Unit 1 · Financial Maths +85 XP

GST, Calculating and Reverse

Australia's $10\%$ Goods and Services Tax, adding it, subtracting it, and finding out what's on your receipt.

Today's hook: A receipt shows a total of $\$66$. It says 'GST included'. How much GST did you actually pay?

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Think First

warm-up

A receipt shows a total of $\$66$. It says 'GST included'. How much GST did you actually pay? Jot down your first reaction, then we'll see who's right.

Record your answer in your workbook.

The Big Idea

+5 XP

GST in Australia is $10\%$. To add GST: multiply by $1.10$. To back out GST from an inc-GST price: divide by $1.10$. GST is NOT $\tfrac{1}{10}$ of the total, it is $\tfrac{1}{11}$.

GST $= 10\%$. An exc-GST price of $\$60$ becomes $60 \times 1.10 = \$66$ inc-GST. To go backwards from a $\$66$ total: $66 \div 1.10 = \$60$. The GST itself is $\$66 - \$60 = \$6$, which is $\tfrac{1}{11}$ of the total. $\tfrac{1}{11}$, not $\tfrac{1}{10}$.

Inc-GST $= $ Exc-GST $\times 1.10$ $\Leftrightarrow$ Exc-GST $= $ Inc-GST $\div 1.10$

Add GST: $\times 1.10$

$10\%$ on top of an exc-GST price.

Strip GST: $\div 1.10$

Back out the tax from an inc-GST total.

GST is $\tfrac{1}{11}$ of total

Of the inc-GST price. Quick shortcut.

What You'll Master

objectives

Know

GST in Australia is $10\%$
Inc-GST = Exc-GST $\times 1.10$
Exc-GST = Inc-GST $\div 1.10$
GST is $\tfrac{1}{11}$ of the inc-GST total
Most food groceries are GST-free

Understand

Why dividing by $1.10$ reverses the GST increase
Why GST is $\tfrac{1}{11}$ of total, not $\tfrac{1}{10}$
How to spot GST-free vs taxable items

Can Do

Add GST to any exc-GST price
Strip GST from any inc-GST price
Find the GST component of a total receipt

Words You Need

vocabulary

GSTGoods and Services Tax, Australia's $10\%$ value-added tax.

Exc-GSTThe price BEFORE GST is added (excluding GST).

Inc-GSTThe price AFTER GST is added (including GST).

GST-freeItems not subject to GST (most basic groceries, some health, education).

ABNAustralian Business Number, needed to charge GST.

Input tax creditA business can claim back GST paid on purchases (Year 10 topic).

Spot the Trap

heads-up

Wrong: "$\$66$ inc-GST means GST = $\$6.60$ ($10\%$ of $66$)", NO. $10\%$ is on the EXC-GST price, not the inc-GST price.

Right: GST on $\$66$ inc-GST: $66 \div 11 = \$6$. Pre-GST was $\$60$.

Wrong: "To strip GST from $\$110$, subtract $10\%$: $110 - 11 = \$99$", NO. Strip means $\div 1.10$, gives $\$100$.

Right: $\$110 \div 1.10 = \$100$ (exc-GST). GST was $\$10$.

Adding GST

+5 XP

Forward direction. Given an exc-GST price, multiply by $1.10$ to find the inc-GST price.

A laptop has an exc-GST price of $\$1200$. GST adds $10\%$. Multiplier: $1.10$. So inc-GST price is $1200 \times 1.10 = \$1320$. The GST itself is the $\$120$ added on, which is $10\%$ of $\$1200$.

Inc-GST $= $ Exc-GST $\times 1.10$

$\times 1.10$

One step on any calculator.

GST = $10\%$ of exc

Not of inc, that's the trap.

Result $>$ original

Inc-GST is always $10\%$ more.

Stripping GST (Reverse)

+5 XP

Backward direction. Given an inc-GST price, divide by $1.10$ to get back to exc-GST. Alternatively: GST is $\tfrac{1}{11}$ of the total.

A receipt shows a $\$66$ total with GST included. To find the exc-GST price: $66 \div 1.10 = \$60$. The GST itself is $66 - 60 = \$6$, which is also $\tfrac{66}{11} = \$6$. The $\tfrac{1}{11}$ shortcut works because the inc-GST price represents $\tfrac{11}{10}$ of the exc-GST price.

Exc-GST $= $ Inc-GST $\div 1.10$, GST $= $ Inc-GST $\div 11$

$\div 1.10$

To strip GST cleanly.

Or $\div 11$ for the GST

Quick shortcut for the tax amount.

Check by adding back

$\$60 \times 1.10 = \$66$ ✓.

Watch Me Solve It · 3 examples

Watch Me Solve It · The receipt

+15 XP per step

PROBLEM

A receipt total is $\$66$, GST included. Find the GST amount.

1

Use the $\tfrac{1}{11}$ shortcut

GST $= 66 \div 11$

GST is one-eleventh of inc-GST total.
2

Compute

$66 \div 11 = \$6$

That's the GST.
3

Verify

Pre-GST $= 66 - 6 = \$60$; $\$60 \times 1.10 = \$66$ ✓

Sanity check passed.

Answer$\$6$ GST

Watch Me Solve It · Add GST

+15 XP per step

PROBLEM

A bookshop sells an exc-GST book for $\$24$. What is the inc-GST price?

1

Multiply by 1.10

$24 \times 1.10$

GST is $10\%$.
2

Compute

$24 \times 1.10 = \$26.40$

Inc-GST.
3

Check the GST

$\$26.40 - \$24 = \$2.40$; $10\%$ of $24$ = $\$2.40$ ✓

Matches.

Answer$\$26.40$

Watch Me Solve It · Strip GST

+15 XP per step

PROBLEM

A jacket's inc-GST price is $\$132$. What was the exc-GST price?

1

Divide by 1.10

$132 \div 1.10$

Reverse the GST.
2

Compute

$132 \div 1.10 = \$120$

Exc-GST price.
3

GST amount

$132 - 120 = \$12$; or $132 \div 11 = \$12$ ✓

Confirmed.

AnswerExc-GST $= \$120$, GST $= \$12$

Common Pitfalls

heads-up

Taking $10\%$ of the inc-GST total as the GST

Treating $10\%$ of $\$66$ as the GST, wrong by $\$0.60$.

Fix: GST is $10\%$ of EXC-GST, or $\tfrac{1}{11}$ of inc-GST.

Subtracting $10\%$ to strip GST

$\$110 - 10\% = \$99$, but actual exc-GST is $\$100$.

Fix: To strip, DIVIDE by $1.10$, don't subtract $10\%$.

Forgetting about GST-free items

Assuming all items on a receipt have GST.

Fix: Most fresh food (bread, milk, fruit) is GST-free. Only taxable items add GST.

Copy Into Your Books

Adding GST

Inc-GST = Exc-GST $\times 1.10$
GST = $10\%$ of exc-GST
$\$100 \to \$110$

Stripping GST

Exc-GST = Inc-GST $\div 1.10$
GST = Inc-GST $\div 11$
$\$110 \to \$100$, GST $\$10$

Quick Rules

$\tfrac{1}{11}$ of total = GST
$\tfrac{10}{11}$ of total = exc-GST
$\$66$ total $\to \$6$ GST

GST-Free Items

Most fresh food (bread, milk, fruit, veg)
Most health services
Education courses

How are you completing this lesson?

Brain Trainer · 4 problems

Brain Trainer · GST, Calculating and Reverse

4 problems

Four drill problems to sharpen your skills. Work each, then reveal the answer.

1 Add GST to an exc-GST price of $\$80$.

$80 \times 1.10 = \$88$.$\$88$
2 A receipt shows $\$33$ inc-GST. What is the GST?

$33 \div 11 = \$3$.$\$3$
3 Find the exc-GST price for an inc-GST of $\$220$.

$220 \div 1.10 = \$200$.$\$200$
4 An item costs $\$45$ exc-GST. What is the GST?

$0.10 \times 45 = \$4.50$.$\$4.50$

Complete in your workbook.

Quick Check · 5 questions

A laptop is $\$900$ exc-GST. The inc-GST price is:

+10 XP

A receipt shows $\$77$ total inc-GST. The GST is:

+10 XP

The exc-GST price corresponding to $\$165$ inc-GST is:

+10 XP

A coffee at $\$5.50$ inc-GST has GST of:

+10 XP

Which item is most likely GST-free?

+10 XP

Show Your Working · 3 questions

Show Your Working

9 marks total

Apply Medium 3 MARKS

Q6. Calculate, showing working: (a) The inc-GST price of an item that is $\$240$ exc-GST. (b) The GST on a $\$132$ inc-GST receipt. (c) The exc-GST price of an item shown at $\$77$ inc-GST.

Answer in your workbook.

Understand Easy 2 MARKS

Q7. Lucia's receipt shows: bread $\$4$ (no GST), shampoo $\$5.50$ (inc-GST), drink $\$3.30$ (inc-GST). (a) What is her total bill? (b) How much GST did she pay in total?

Answer in your workbook.

Reason Hard 4 MARKS

Q8. A restaurant lists prices on the menu as “inc-GST”. A meal is $\$33$. (a) Find the exc-GST price and the GST amount. (b) A diner pays a $10\%$ tip on the inc-GST price. How much is the tip in dollars? (c) Some diners argue tips should be on the EXC-GST price, what difference would this make on this meal? Comment briefly.

Answer in your workbook.

Comprehensive Answers

Quick Check

1. C$\$990$.

2. A$\$7$.

3. B$\$150$.

4. B$\$0.50$.

5. B bread.

Show Your Working Model Answers

Q6 (3 marks): (a) $240 \times 1.10 = \$264$ [1]. (b) $132 \div 11 = \$12$ [1]. (c) $77 \div 1.10 = \$70$ [1].

Q7 (2 marks): (a) Total $= 4 + 5.50 + 3.30 = \$12.80$ [1]. (b) GST $= (5.50 \div 11) + (3.30 \div 11) = \$0.50 + \$0.30 = \$0.80$ [1].

Q8 (4 marks): (a) Exc-GST $= 33 \div 1.10 = \$30$. GST $= \$3$ [2]. (b) Tip on inc-GST: $0.10 \times 33 = \$3.30$ [1]. (c) Tip on exc-GST would be $0.10 \times 30 = \$3.00$, $\$0.30$ less. Tipping on inc-GST means the diner pays a little “tip on the GST”, which is arguably unfair to the customer [1].

Stretch Challenge · +25 XP, +10 coins

The Catering Quote

A caterer quotes $\$1320$ inc-GST for an event. Their cost of food (GST-free) was $\$400$. (a) What was the labour (exc-GST) component of the quote? (b) The caterer wants $\$50$ MORE profit. By how much should they raise the inc-GST quote, given that the food is still GST-free?

Reveal solution

(a) Total exc-GST $= 1320 \div 1.10 = \$1200$. Food was $\$400$ (GST-free, so still $\$400$). Labour $= 1200 - 400 = \$800$ exc-GST. (b) To add $\$50$ profit to the labour: new labour $= \$850$. Inc-GST labour $= 850 \times 1.10 = \$935$. New total $= 935 + 400 = \$1335$. Raise the quote by $\$15$ ($1335 - 1320$).

Quick Review

GST = $10\%$

In Australia

Add: $\times 1.10$

Exc-GST to inc-GST

Strip: $\div 1.10$

Inc-GST to exc-GST

GST = $\tfrac{1}{11}$

Of the inc-GST total

Not $\tfrac{1}{10}$

Of the total, common error

Some items GST-free

Bread, milk, fruit

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