Mixed Number Addition
A mixed number has a whole number part and a fraction part, like 3¾ or 2⅓. Adding them requires handling each part separately, then combining the results.
Method 1 – Add Parts Separately
- Add the whole number parts.
- Add the fraction parts (using LCD if needed).
- If the fraction part is improper (≥1), convert it and add to the whole number total.
Example: 2¾ + 3½
- Whole numbers: 2 + 3 = 5
- Fractions: 3/4 + 1/2 = 3/4 + 2/4 = 5/4 = 1¼
- Combine: 5 + 1¼ = 6¼
Method 2 – Convert to Improper Fractions
- Convert each mixed number to an improper fraction.
- Find the LCD and add.
- Convert the result back to a mixed number.
Example: 1⅔ + 2⅓
- 1⅔ = 5/3. 2⅓ = 7/3.
- Same denominator: 5/3 + 7/3 = 12/3 = 4.
1⅔ + 2⅓ = 4
Example – Different Denominators: 3½ + 1⅔
- 3½ = 7/2. 1⅔ = 5/3.
- LCD = 6: 21/6 + 10/6 = 31/6 = 5⅙.
3½ + 1⅔ = 5⅙
Which Method to Use?
| Situation | Recommended method |
|---|---|
| Simple fractions, small numbers | Method 1 (add parts) |
| Multiple mixed numbers | Method 2 (convert to improper) |
| Fractions sum to ≥1 | Method 2 is cleaner |
Key Takeaways
- Add whole parts and fraction parts separately, or convert all to improper fractions.
- If the fraction part exceeds 1 after adding, carry the excess into the whole number.
- Always simplify your final answer.
Practice Questions
- Calculate 1½ + 2¼.
- Add 3⅓ + 1⅔.
- Calculate 2¾ + 4¾.
- Add 1⅙ + 2⅗.
- A plank is 2½ metres long. Another is 1¾ metres. What is the total length?