Subtracting a Proper Fraction from a Mixed Number: Step-by-Step Example
22 October 2026
Subtracting a proper fraction from a mixed number can feel tricky at first, but it becomes much easier when you break it into clear steps. Here is a worked example to show exactly how it's done.
Worked example
4 1/3 - 3/5
Step 1: Change the mixed number to an improper fraction.
4 1/3 = (4 × 3 + 1)/3 = 13/3
Step 2: Find a common denominator for 13/3 and 3/5.
The denominators are 3 and 5. The common denominator is 15.
Step 3: Convert both fractions to have denominator 15.
13/3 = (13 × 5)/(3 × 5) = 65/15
3/5 = (3 × 3)/(5 × 3) = 9/15
Step 4: Subtract the fractions. 65/15 - 9/15 = (65 - 9)/15 = 56/15
Step 5: Change the improper fraction back to a mixed number.
56 ÷ 15 = 3 remainder 11. So, 56/15 = 3 11/15
The answer is 3 11/15.
| Step | Working |
|---|---|
| Mixed number to improper fraction | 4 1/3 = 13/3 |
| Find common denominator | 3 and 5 → 15 |
| Convert to denominator 15 | 13/3 = 65/15, 3/5 = 9/15 |
| Subtract | 65/15 - 9/15 = 56/15 |
| Back to mixed number | 56/15 = 3 11/15 |
Now your child can see each part of the process, from changing the mixed number to an improper fraction right through to finding the answer. With this method, similar questions on subtracting proper fractions from mixed numbers will be much easier to tackle.
