Part A: Numeracy
2
Fractions, Decimals & Percentages
Master equivalence, conversions, operations, and percentage calculations
Learning Objectives
- Convert flexibly between fractions, decimals, and percentages
- Simplify fractions to lowest terms and perform basic operations
- Align decimal points for addition, subtraction, and multiplication
- Calculate percentage changes, discounts, and test score conversions
- Apply financial and numerical reasoning in school budgeting contexts
Chapter Progress: 0%
1. Fractions and Equivalents
Understanding Fractions
A fraction represents a part of a whole quantity. The numerator (top number) counts the parts being considered, while the denominator (bottom number) defines the total equal parts making up the whole.
Example 1
ACER Authentic Problem: Converting Decimal Study Load to Fraction (Sept 2023 Q18)
❓ Question: What fraction of a year of full-time study is a subject which has an EFTSL of 0.125?
📄 Source Passage / Reference Data:
STUDY LOAD
The Equivalent Full-Time Student Load (EFTSL) is a measure of the study load, expressed as a fraction of a year, of a subject when taken by a full-time student. For example, a subject with an EFTSL of 0.5 is half of a normal full-time year.
📝 Step-by-Step Method:
1
Express the decimal as a fraction over its place value (thousandths).
2
Divide numerator and denominator by the common factor 25.
3
Simplify further by dividing numerator and denominator by 5.
🔍 Evidence Extracted: "0.125 = 125/1000 = 1/8"
🎯 Final Answer: 1/8 of a year
💡 Why It Is Correct: 0.125 is equivalent to 125 thousandths. Dividing both numerator and denominator by 125 simplifies the fraction directly to 1/8.
⚡ LANTITE Exam Strategy: Official ACER Tip: Common benchmark decimals like 0.125 (1/8), 0.25 (1/4), 0.375 (3/8), 0.5 (1/2), 0.625 (5/8), 0.75 (3/4), 0.875 (7/8) should be memorised for rapid mental conversion.
2. Decimals and Precision Operations
Example 2
ACER Authentic Problem: Part-Time Teaching Load Decimal (July 2017 Q10)
❓ Question: Sue has a part-time teaching load. In a 5-day week she teaches only three days. What is Sue’s teaching load expressed as a decimal?
📄 Source Passage / Reference Data:
PART-TIME
Sue has a part-time teaching load. In a 5-day week she teaches only three days.
📝 Step-by-Step Method:
1
Form the fraction of days taught over total working week days.
2
Convert the fraction to an equivalent tenths fraction.
3
Write as a decimal.
🔍 Evidence Extracted: "3 out of 5 days = 3/5 = 0.6"
🎯 Final Answer: 0.6
💡 Why It Is Correct: Dividing 3 by 5 yields 0.6. Expressing fifths as tenths makes decimal conversion straightforward.
⚡ LANTITE Exam Strategy: LANTITE Fraction to Decimal: To convert fifths to decimals, simply double the numerator and place the decimal point (e.g., 3/5 → 6/10 = 0.6).
3. Percentage Conversions & Key Benchmarks
Common Equivalent Benchmarks
| Fraction | Decimal | Percentage |
|---|---|---|
| 1/2 | 0.5 | 50% |
| 1/4 | 0.25 | 25% |
| 3/4 | 0.75 | 75% |
| 1/5 | 0.2 | 20% |
| 1/10 | 0.1 | 10% |
| 1/3 | 0.333... | 33.33% |
4. Percentage Change & School Resource Discounts
Calculating Discount Price
Discounted Price = Original Price × (100% - Discount %)
Original Price = Retail item cost ($)
Discount % = Percentage reduction
Example
$200 × (100% - 15%) = $200 × 0.85 = $170
Example 3
ACER Authentic Problem: Backpack Mass Percentage (Sept 2023 Q16)
❓ Question: On a 2-day walk, Tony wants to keep the mass of his full backpack to no more than 15% of his body mass. Tony’s body mass is 80 kilograms. What is the maximum mass that Tony’s full backpack should be?
📄 Source Passage / Reference Data:
BACKPACK MASS
Tony weighs 80 kg and needs his backpack mass to be at most 15% of his body mass.
📝 Step-by-Step Method:
1
Calculate 10% of 80 kg.
2
Calculate 5% by halving 10%.
3
Add 10% and 5% to find 15%.
🔍 Evidence Extracted: "15% of 80 kg = 12 kg"
🎯 Final Answer: 12 kilograms
💡 Why It Is Correct: 15% can be broken into 10% (8 kg) plus 5% (4 kg), totaling 12 kg. Alternatively, 80 × 0.15 = 12 kg.
⚡ LANTITE Exam Strategy: Official ACER Mental Math Strategy: Calculate 10% by shifting decimal one place left, then halve it to find 5%.
Chapter 2 Practice Quiz
Chapter Summary: Chapter 2: Fractions, Decimals & Percentages Summary
Key Concepts
Important Formulas
Top Tips
Chapter 2 Flashcards
1 / 4Benchmarks
What is 1/8 as a decimal and percentage?
0.125 and 12.5%.