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
Simplifying Fractions in Student Assessment Data
❓ Question: In a diagnostic spelling assessment, 12 out of 16 students achieved a passing mark. Express the fraction of students who passed in simplest form.
📝 Step-by-Step Method:
1
Identify the raw fraction of passing students.
2
Find the highest common factor (HCF) of 12 and 16.
3
Divide both numerator and denominator by 4.
🎯 Final Answer: 3/4 of the class passed
💡 Why It Is Correct: Dividing both numerator and denominator by their greatest common factor (4) simplifies 12/16 to 3/4.
2. Decimals and Precision Operations
Example 2
Multiplying Decimals in Material Resource Planning
❓ Question: A teacher requires 0.5 metres of ribbon for each craft project. If students complete 0.2 of the total projects today, how many metres of ribbon were consumed?
📝 Step-by-Step Method:
1
Multiply the numbers ignoring decimal points.
2
Count total decimal places in factors (0.5 has 1, 0.2 has 1 → 2 total decimal places).
3
Place decimal point 2 positions from the right in the product.
🎯 Final Answer: 0.10 metres (10 cm)
💡 Why It Is Correct: Multiplying 0.5 by 0.2 yields 0.10 metres because 5 × 2 = 10 with two decimal places.
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
Classroom Equipment Educational Discount
❓ Question: An interactive whiteboard costs $200 and qualifies for a 15% educational discount. Calculate the final price.
📝 Step-by-Step Method:
1
Calculate discount amount: 15% of $200.
2
Subtract discount from original price.
🎯 Final Answer: $170
💡 Why It Is Correct: A 15% discount on $200 reduces the cost by $30, leaving a final price of $170.
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%.