Fractions, Decimals, Percentages and Money: Year 6 Study Guide
Three different ways of writing the same part-whole relationship, used constantly in daily life.
Year 6 students add and subtract fractions with unlike denominators (using the LCM) and multiply a fraction by a whole number. They connect fractions, decimals and percentages: 3/5 = 0.6 = 60%. To change a fraction to a percentage, divide the numerator by the denominator and multiply by 100.
In money contexts they calculate discounts and use the 10% GST (goods and services tax) that applies to most goods and services in Australia. These skills help with shopping and planning.
Equivalent forms
| Fraction | Decimal | Percentage |
|---|---|---|
| 1/2 | 0.5 | 50% |
| 1/4 | 0.25 | 25% |
| 1/5 | 0.2 | 20% |
| 3/8 | 0.375 | 37.5% |
| 2/3 | 0.666… | 66.7% |
Operations with fractions
Add: 2/3 + 1/4 = 8/12 + 3/12 = 11/12. Subtract: 5/6 − 1/4 = 10/12 − 3/12 = 7/12. Multiply a fraction by a whole number: 3 × 2/5 = 6/5 = 1 1/5. Find a fraction of a quantity: 3/4 of 80 = 80 ÷ 4 × 3 = 60.
LCM of 3 and 4 is 12.
8/12 and 3/12.
11/12.
Divide by the HCF if possible.
Discounts and GST
A 20% discount on $85: 10% is $8.50, 20% is $17, sale price $68. GST is 10% of the price before GST, so a $60 item becomes $66 with GST included. To find the price without GST from a total with GST, divide by 1.1: $66 ÷ 1.1 = $60. Unit pricing helps compare products: price ÷ quantity.
Worked examples and common mistakes
Example: A game is $40 with 15% off: 10% is $4, 5% is $2, so the discount is $6 and the price is $34. Common mistakes: adding denominators, subtracting 10% when the GST is already included and mixing up 'off' with 'of'. Estimate with benchmarks (10%, 25%, 50%) first.
Check your understanding: model answers
1. 9/12 − 2/12 = 7/12. 2. 35%. 3. $90.
✨ Key Takeaways
- Use the LCM to add unlike fractions.
- Fraction ÷ is also a decimal.
- 10% = divide by 10.
- GST is 10% in Australia.
💬 Questions for Discussion & Reflection
- Work out 3/4 − 1/6.
- Write 7/20 as a percentage.
- A $120 jacket is 25% off. What is the price?
Print a fractions equivalence chart →