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VCE VCE VM Numeracy (Year 11) · Unit 1 — Number, Shape, Quantity and Measures, Relationships · 11m read

Number Sense — Percentages, GST, Discounts and Estimation

Number skills are used every day — at the shops, at work and when managing money. Unit 1 starts by making these skills quick and reliable.

Learning objective: Calculate percentages, discounts and GST, and use estimation to check answers in everyday purchases.

By the end of this lesson you can:

  • I can find a percentage of an amount.
  • I can calculate discounts and GST.
  • I can estimate to check if an answer is reasonable.

A built-in price checker. Quick percentage skills are like carrying a price checker in your head — you can spot a real bargain or a pricing mistake instantly.

Key skills

PERCENTAGE OF AN AMOUNT — convert the percentage to a decimal and multiply.
15% of $240 = 0.15 × 240 = $36.

DISCOUNT — sale price = original × (1 − discount rate).
20% off $85 = 85 × 0.8 = $68.

GST (10% in Australia)
• Add GST: price × 1.1.
• GST inside a GST-inclusive price: price ÷ 11.
A $55 item (including GST) contains $5 GST.

ESTIMATION — round first: 19.8 × 4.9 ≈ 20 × 5 = 100.

Worked example (Easy)

A jacket is $120 with 25% off. Another store sells it for $95. Which is cheaper?

  1. Discount. 25% of 120 = 0.25 × 120 = $30.
  2. Sale price. 120 − 30 = $90.
  3. Compare. $90 is less than $95.

Answer: The discounted jacket at $90 is $5 cheaper.

Common mistakes

  • Finding GST in a GST-inclusive price by taking 10% 10% of $55 is $5.50, but the GST is only $5. Fix: Divide a GST-inclusive price by 11.
  • Adding successive discounts 20% then 10% off is not 30% off. Fix: Apply each discount in turn: × 0.8 × 0.9 = × 0.72 (28% off).

Practice questions

  1. What is 15% of $240?

    1. $24
    2. $36
    3. $15
    4. $204

    (1 marks)

  2. How much GST is included in a $132 price (GST included)?

    1. $13.20
    2. $12
    3. $11
    4. $10

    (1 marks)

  3. A $60 game is reduced by 20%, then a further 10% at the checkout. Find the final price.

    (2 marks)

Summary

  • Percentage → decimal → multiply.
  • Sale price = price × (1 − rate).
  • Add GST: × 1.1; GST inside a price: ÷ 11.
  • Estimate to check answers.

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