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VCE VCE VM Numeracy (Year 12) · Unit 3 — Number, Shape, Measures and Relationships · 11m read

Number — Percentages, Ratios, Rates and Estimation in Real Life

VM Numeracy is maths for real life and work. Number skills — percentages, ratios and rates — come up in shopping, pay, trades and budgeting every day.

Learning objective: Use percentages, ratios, rates and estimation to solve everyday and workplace problems such as discounts, GST, pay rates and mixing ratios.

By the end of this lesson you can:

  • I can calculate percentage increases, decreases and GST.
  • I can use ratios and rates to compare options.
  • I can estimate to check whether an answer is reasonable.

Number sense is a shopping superpower. Spot the real deal, check your pay and avoid being ripped off — all with quick mental maths.

Key skills

PERCENTAGES
• Find a percentage: 15% of $80 = 0.15 × 80 = $12.
• Increase: multiply by (1 + rate). Decrease: multiply by (1 − rate).
• GST in Australia is 10%: price excluding GST × 1.1 = price including GST; GST included in a price = price ÷ 11.

RATIOS — compare quantities: concrete mix 1 : 2 : 3 (cement : sand : gravel); scale up by multiplying every part.

RATES — one quantity per another: $/hour, km/h, $/kg, L/100 km. Use unit rates to compare value.

ESTIMATION — round numbers to check answers quickly ("about $30 × 5 = $150").

Worked example (Easy)

A jacket costs $120 and is 25% off. A second store sells it for $95. Which is cheaper?

  1. Discount. 25% of 120 = 30.
  2. Sale price. 120 − 30 = $90.
  3. Compare. $90 < $95.

Answer: The first store is cheaper at $90.

Worked example (Medium)

A 2 kg bag of rice costs $5.40 and a 5 kg bag costs $12.50. Which is better value?

  1. Unit rate 1. 5.40 ÷ 2 = $2.70 per kg.
  2. Unit rate 2. 12.50 ÷ 5 = $2.50 per kg.

Answer: The 5 kg bag is better value at $2.50/kg (if you will use it before it expires).

Common mistakes

  • Finding GST in a GST-inclusive price by taking 10% 10% of the inclusive price overstates GST. Fix: GST included = price ÷ 11.
  • Adding percentage changes A 10% rise then a 10% fall does not return to the start. Fix: Multiply by each factor in turn.

Practice questions

  1. How much GST is included in a $55 price?

    1. $5.50
    2. $5.00
    3. $0.55
    4. $11.00

    (1 marks)

  2. A painter mixes paint and tint in the ratio 8 : 1. How much tint is needed for 4 L of paint?

    (2 marks)

Summary

  • Percentages: multiply by (1 ± rate).
  • GST is 10%; GST included = price ÷ 11.
  • Use ratios to scale and unit rates to compare value.
  • Estimate to check answers.

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