Fractions — Grade 3 Mathematics
In Grade 3, we go beyond simple fractions to understand improper fractions (where the numerator is larger than the denominator), mixed numbers, and how to find and use equivalent fractions.
Types of Fractions
Proper fraction: numerator < denominator (e.g., 34)
Improper fraction: numerator ≥ denominator (e.g., 74)
Mixed number: a whole number + a proper fraction (e.g., 134)
Converting: 74 = 4 ÷ 4 = 1 whole + 3 left over = 134
Improper fraction: numerator ≥ denominator (e.g., 74)
Mixed number: a whole number + a proper fraction (e.g., 134)
Converting: 74 = 4 ÷ 4 = 1 whole + 3 left over = 134
Fraction Wall — Equivalent Fractions
1 whole
1/2
1/2
1/3
1/3
1/3
1/4
1/4
1/4
1/4
1/6
1/6
1/6
1/6
1/6
1/6
1/8
1/8
1/8
1/8
1/8
1/8
1/8
1/8
Reading the wall: 12 = 24 = 36 = 48 — these are all equivalent fractions.
💡 Finding equivalents: Multiply (or divide) both numerator AND denominator by the same number: 34 = 68 (×2) = 912 (×3)
Worked Examples
Example 1 — Improper → Mixed Number
Convert 113 to a mixed number.
- 11 ÷ 3 = 3 remainder 2
- = 3 wholes + 23
- = 323
Example 2 — Mixed Number → Improper
Convert 235 to an improper fraction.
- Multiply whole number by denominator: 2 × 5 = 10
- Add numerator: 10 + 3 = 13
- Keep denominator: 135
Example 3 — Real World: Pizza Slices 🍕
Omar eats 9 slices of pizza. Each pizza has 4 slices. How many whole pizzas is that? Write as a mixed number.
- 9 slices ÷ 4 per pizza = 2 remainder 1
- = 214 pizzas
- As improper fraction: 94
Practice Questions
1. Convert 17/5 to a mixed number.
✅ 17 ÷ 5 = 3 r2 → 3²⁄₅
2. Convert 4⅓ to an improper fraction.
✅ (4 × 3) + 1 = 13 → ¹³⁄₃
3. Find an equivalent fraction for ²⁄₃ with denominator 12.
✅ 3 × 4 = 12; 2 × 4 = 8 → ⁸⁄₁₂
4. Which is larger: ³⁄₄ or ⁵⁄₈?
✅ ³⁄₄ = ⁶⁄₈ and ⁵⁄₈; 6 > 5, so ³⁄₄ > ⁵⁄₈
5. A cake is cut into 6 equal pieces. Omar eats 2 pieces. What fraction remains?
✅ 6 − 2 = 4 pieces left → ⁴⁄₆ = ²⁄₃
Key Points to Remember
- Proper: numerator < denominator. Improper: numerator ≥ denominator.
- Improper → mixed: divide numerator by denominator; remainder goes over denominator.
- Mixed → improper: (whole × denominator) + numerator, keep same denominator.
- Equivalent fractions: multiply or divide top and bottom by the same number.
- To compare fractions with different denominators, find a common denominator.