Mathematics • Year 8 • Unit 1 • Lesson 8
GST, Calculating and Reverse
Build fluency with Australia's 10% Goods and Services Tax. Add GST (× 1.10), strip GST (÷ 1.10), and use the 1/11 shortcut to find the GST inside any inc-GST total.
1. I do, fully worked example
Read every line. This is the classic "strip GST from a receipt" problem, the one shop owners do daily.
Problem. A receipt total is $66, GST included. Find (a) the GST amount, and (b) the exc-GST price.
Step 1, Use the 1/11 shortcut for the GST itself.
GST = 66 ÷ 11 = $6
Reason: when the inc-GST total represents 11/10 of the exc-GST price, the GST is exactly 1/11 of the total. Memorise this trick.
Step 2, Subtract to get the exc-GST price.
Exc-GST = 66 − 6 = $60
Reason: total minus tax = pre-tax price. (Or: divide by 1.10 directly.)
Step 3, Verify with the alternative method.
Exc-GST = 66 ÷ 1.10 = $60 ✓
Reason: dividing the inc-GST total by 1.10 reverses the × 1.10 that originally added the GST.
Step 4, Final check: add the GST back.
60 × 1.10 = $66 ✓
Reason: pre-tax × 1.10 must return the original total.
Answer: GST = $6, exc-GST price = $60.
2. We do, fill in the missing steps
Same shape as Section 1, but with the working faded. Fill in each blank. 4 marks
Problem. A jacket's inc-GST price is $132. Find the GST amount and the exc-GST price.
Step 1, GST using the 1/11 shortcut:
GST = 132 ÷ ______ = $______
Step 2, Subtract to get the exc-GST price:
Exc-GST = 132 − ______ = $______
Step 3, Verify by dividing by 1.10:
Exc-GST = 132 ÷ ______ = $______ ✓
Step 4, Add GST back as a final check:
______ × 1.10 = $______ ✓
3. You do, independent practice
Show your working under each problem. The first four are foundation (add GST or strip GST with clean numbers). The middle two are standard (real-receipt amounts). The last two are extension (mixed GST-free + taxable items).
Foundation, clean numbers
3.1 Add GST to an exc-GST price of $80. 1 mark
3.2 A receipt shows $33 inc-GST. What is the GST? 1 mark
3.3 Find the exc-GST price for an inc-GST of $220. 1 mark
3.4 An item costs $45 exc-GST. What is the GST in dollars? 1 mark
Standard, real-receipt amounts
3.5 A coffee at $5.50 inc-GST. What is the GST amount (use the 1/11 shortcut)? 2 marks
3.6 A bookshop sells an exc-GST book for $24. Find both the inc-GST price and the GST in dollars. 2 marks
Extension, mixed receipts
3.7 Lucia's receipt shows: bread $4 (GST-free), 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? 2 marks
3.8 A receipt totals $132 inc-GST. Of that, $44 was for GST-free fresh fruit. (a) What was the inc-GST total for the taxable items? (b) How much GST is included in the taxable subtotal? 2 marks
How did this worksheet feel?
What I'll revisit before next class:
Section 2, We do ($132 inc-GST jacket)
Step 1: GST = 132 ÷ 11 = $12.
Step 2: Exc-GST = 132 − 12 = $120.
Step 3: Exc-GST = 132 ÷ 1.10 = $120 ✓.
Step 4: 120 × 1.10 = $132 ✓.
3.1, Add GST to $80
Inc-GST = 80 × 1.10 = $88.
3.2, Receipt $33 inc-GST
GST = 33 ÷ 11 = $3.
3.3, Exc-GST for $220 inc-GST
Exc-GST = 220 ÷ 1.10 = $200. (Or: GST = 220 ÷ 11 = $20, so exc-GST = 220 − 20 = $200.)
3.4, Item $45 exc-GST
GST = 0.10 × 45 = $4.50.
3.5, Coffee $5.50 inc-GST
GST = 5.50 ÷ 11 = $0.50 (50 cents).
3.6, Bookshop $24 exc-GST
Inc-GST = 24 × 1.10 = $26.40. GST = 26.40 − 24 = $2.40 (or 0.10 × 24 = $2.40).
3.7, Lucia's mixed receipt
(a) Total bill = 4 + 5.50 + 3.30 = $12.80.
(b) GST: bread is GST-free (no GST). Shampoo GST = 5.50 ÷ 11 = $0.50. Drink GST = 3.30 ÷ 11 = $0.30. Total GST = $0.80.
3.8, $132 total with $44 GST-free fruit
(a) Taxable inc-GST subtotal = 132 − 44 = $88.
(b) GST on the taxable subtotal = 88 ÷ 11 = $8.