Fractions — Grade 5 Mathematics

In Grade 5, we add and subtract fractions with different denominators using the Lowest Common Multiple (LCM), multiply fractions by fractions and whole numbers, and convert fluently between mixed numbers and improper fractions.

Adding & Subtracting: Different Denominators

Find the Lowest Common Multiple (LCM) of the denominators to create a common denominator.

Example: ²⁄₃ + ³⁄₄
LCM(3, 4) = 12
²⁄₃ = ⁸⁄₁₂ (×4) ³⁄₄ = ⁹⁄₁₂ (×3)
⁸⁄₁₂ + ⁹⁄₁₂ = ¹⁷⁄₁₂ = 1⁵⁄₁₂

Multiplying Fractions

Multiply numerators together and denominators together. Simplify if possible.

23 × 35 = 615 = 25

34 × 25 = 620 = 3/10

💡 Shortcut: Cross-cancel before multiplying — cancel common factors diagonally to keep numbers small.

Worked Examples

Example 1 — Add with Different Denominators

Calculate ⁵⁄₆ + ²⁄₉.

LCM(6, 9) = 18
⁵⁄₆ = ¹⁵⁄₁₈; ²⁄₉ = ⁴⁄₁₈
¹⁵⁄₁₈ + ⁴⁄₁₈ = ¹⁹⁄₁₈ = 1¹⁄₁₈

Example 2 — Multiply Fractions

Calculate ⁴⁄₅ × ⁵⁄₈.

Cross-cancel: ⁴ and ⁸ share factor 4 → ¹ and ²; ⁵ and ⁵ share factor 5 → ¹ and ¹
= ¹⁄₂
Answer: ½

Example 3 — Mixed Number Subtraction 🍕

Calculate 3½ − 1⅔.

Convert: 3½ = 7/2; 1⅔ = 5/3
LCM(2,3) = 6: 7/2 = 21/6; 5/3 = 10/6
21/6 − 10/6 = 11/6 = 1⁵⁄₆

Practice Questions

1. Calculate ³⁄₄ + ²⁄₅.

✅ LCM(4,5)=20; ¹⁵⁄₂₀ + ⁸⁄₂₀ = ²³⁄₂₀ = 1³⁄₂₀

2. Calculate ⁷⁄₈ − ¹⁄₃.

✅ LCM(8,3)=24; ²¹⁄₂₄ − ⁸⁄₂₄ = ¹³⁄₂₄

3. Calculate ²⁄₃ × ⁹⁄₁₀.

✅ Cross-cancel: 2 and 10→5; 9 and 3→3; = ³⁄₅ = 3/5

4. Convert 2¾ to an improper fraction.

✅ 2 × 4 + 3 = 11 → ¹¹⁄₄

5. Calculate ³⁄₅ × 20.

✅ 20 ÷ 5 = 4; 4 × 3 = 12

Key Points to Remember

Different denominators? Find the LCM, convert both fractions, then add/subtract.
Multiplying fractions: multiply tops, multiply bottoms. Simplify at the end.
Cross-cancel before multiplying to avoid large numbers.
Mixed number → improper: (whole × denominator) + numerator, over the denominator.
Fraction × whole number: multiply the numerator; or divide the whole by the denominator first.

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