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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