Arithmetic Operations
Mixed Number Subtraction
Subtracting mixed numbers can be done in two ways. Choose whichever suits the numbers involved.
Method 1 – Subtract Parts Separately
- Subtract the fraction parts (find LCD if needed).
- If the fraction part of the subtrahend is larger, borrow 1 whole from the minuend's whole part and add it to the fraction as an improper fraction.
- Subtract the whole parts.
- Combine.
Example: 5¾ − 2½
- Fractions: 3/4 − 1/2 = 3/4 − 2/4 = 1/4.
- Whole: 5 − 2 = 3.
- Answer: 3¼
Example – Borrowing: 4¼ − 1¾
- Fractions: 1/4 − 3/4 impossible. Borrow 1 from whole: 4¼ = 3 + 5/4.
- 5/4 − 3/4 = 2/4 = 1/2.
- Whole: 3 − 1 = 2.
- Answer: 2½
Method 2 – Convert to Improper Fractions
Example: 3½ − 1⅔
3½ = 7/2. 1⅔ = 5/3. LCD=6: 21/6 − 10/6 = 11/6 = 1⅙
Key Takeaways
- Subtract fraction parts first; borrow a whole unit if needed.
- Converting to improper fractions avoids borrowing issues.
- Always simplify and verify: answer + subtrahend = minuend.
Practice: Subtract Mixed Numbers
Two mixed numbers are shown below. Give your answer as a mixed number (e.g. 3 1/4). If you get it wrong (or leave it blank), we'll convert to improper fractions together.
Calculate the difference.