What is a Fraction?
A fraction represents part of a whole or part of a collection.
Written as: Numerator / Denominator
- Numerator: number of parts taken (top)
- Denominator: total equal parts the whole is divided into (bottom)
Example: If a pizza is cut into 8 equal slices and you take 3, you have 3/8 of the pizza.
Types of Fractions
By Comparing Numerator and Denominator
| Type | Condition | Example |
|---|---|---|
| Proper fraction | Numerator < Denominator | 3/5, 1/4, 7/10 |
| Improper fraction | Numerator ≥ Denominator | 7/4, 5/3, 9/9 |
| Mixed fraction | Whole number + proper fraction | 1¾, 2½, 3⅓ |
Converting improper to mixed: 7/4 = 4/4 + 3/4 = 1 + 3/4 = 1¾ (Divide: 7 ÷ 4 = 1 remainder 3 → 1 and 3/4)
Converting mixed to improper: 2¾ = (2 × 4 + 3)/4 = 11/4
By Denominator
| Type | Condition | Example |
|---|---|---|
| Like fractions | Same denominator | 2/5, 3/5, 4/5 |
| Unlike fractions | Different denominators | 2/3, 3/4, 5/7 |
Fractions on a Number Line
Fractions are placed between whole numbers on the number line.
The denominator tells you how many equal parts to divide each unit into.
Equivalent Fractions
Fractions that represent the same value — same point on the number line.
To find equivalent fractions: multiply or divide both numerator and denominator by the same non-zero number.
Example:
- 1/2 = 2/4 = 3/6 = 4/8 (multiply numerator and denominator by 2, 3, 4, …)
- 6/9 = 2/3 (divide both by 3)
To check if two fractions are equivalent: cross-multiply.
- Is 2/3 equivalent to 8/12? → 2 × 12 = 24; 3 × 8 = 24 → Yes ✅
Simplest Form (Lowest Terms)
A fraction is in simplest form when HCF of numerator and denominator is 1.
To simplify: divide both numerator and denominator by their HCF.
Example: Simplify 18/24.
- HCF(18, 24) = 6
- 18/24 = (18÷6)/(24÷6) = 3/4
Comparing Fractions
Like Fractions (Same Denominator)
Compare numerators directly: 3/7 < 5/7 (3 < 5)
Unlike Fractions (Different Denominators)
Convert to like fractions using LCM, then compare.
Example: Compare 2/3 and 3/4.
- LCM(3, 4) = 12
- 2/3 = 8/12; 3/4 = 9/12
- 8/12 < 9/12 → 2/3 < 3/4
Unit Fractions (Numerator = 1)
Larger denominator = smaller fraction: 1/8 < 1/3 (8 > 3)
Addition and Subtraction of Fractions
Like Fractions
Add/subtract numerators, keep denominator:
- 2/7 + 3/7 = 5/7
- 5/9 − 2/9 = 3/9 = 1/3
Unlike Fractions
1. Find LCM of denominators. 2. Convert to like fractions. 3. Add/subtract numerators.
Example: 1/3 + 1/4
- LCM(3, 4) = 12
- 1/3 = 4/12; 1/4 = 3/12
- 4/12 + 3/12 = 7/12
Example: 3/4 − 1/6
- LCM(4, 6) = 12
- 3/4 = 9/12; 1/6 = 2/12
- 9/12 − 2/12 = 7/12
Mixed Fractions
Add whole numbers and fractions separately.
Example: 2½ + 1¼ = (2 + 1) + (½ + ¼) = 3 + (2/4 + 1/4) = 3 + 3/4 = 3¾
Key Vocabulary
| Term | Meaning |
|---|---|
| Fraction | Part of a whole (numerator/denominator) |
| Numerator | Top number — parts taken |
| Denominator | Bottom number — total equal parts |
| Proper fraction | Numerator < denominator |
| Improper fraction | Numerator ≥ denominator |
| Mixed fraction | Whole number + proper fraction |
| Equivalent fraction | Same value, different numerator/denominator |
| Simplest form | HCF of numerator and denominator = 1 |
| Like fractions | Same denominator |
| Unit fraction | Numerator = 1 (e.g., 1/5) |
Exam Tips
- To add/subtract unlike fractions: always find LCM first.
- Simplest form: divide by HCF — show work step by step.
- Mixed to improper: multiply whole number by denominator, add numerator: 3¼ = (3×4+1)/4 = 13/4.
- Unit fractions: 1/3 > 1/7 (larger denominator = smaller fraction).
- A fraction equal to 1: numerator = denominator (e.g., 5/5 = 1).
- Equivalent fractions: cross-multiplication method to verify.