A mixed number combines a whole number and a proper fraction, like 3 2/5. An improper fraction has a numerator at least as large as its denominator, like 17/5. Both name the same amount, but improper fractions are far easier to multiply, divide and plug into formulas. This calculator converts any mixed number and shows the arithmetic.
How to use the converter
- Type the whole number in the left box and the fraction part in the stacked boxes.
- For a negative mixed number, put the minus sign on the whole number.
- The tape shows the improper fraction exactly as the method produces it, the same fraction in lowest terms, and its decimal and percent values.
The formula
- Multiply the whole number by the denominator.
- Add the numerator.
- Keep the denominator.
- Simplify if the numerator and denominator share a factor.
Worked example: 3 2/5
- 3 × 5 = 15 — that is how many fifths are in 3 wholes.
- 15 + 2 = 17 fifths in total.
- Write 17 over 5: 3 2/5 = 17/5 (3.4).
A second example where simplifying matters: 2 4/6 → 2 × 6 + 4 = 16 → 16/6, and dividing by the common factor 2 gives 8/3. You could also simplify the fraction part first (2 4/6 = 2 2/3) and get 8/3 directly.
Picture it
Think of pizzas cut into 5 slices each. Three whole pizzas are 15 slices, and 2 more slices make 17 slices — 17 pieces of size one-fifth, or 17/5. The denominator never changes because the size of the slices never changes.
Common conversions
| Mixed number | Work | Improper fraction |
|---|---|---|
| 1 1/2 | 1 × 2 + 1 | 3/2 |
| 2 3/4 | 2 × 4 + 3 | 11/4 |
| 3 1/3 | 3 × 3 + 1 | 10/3 |
| 4 5/8 | 4 × 8 + 5 | 37/8 |
| 5 7/16 | 5 × 16 + 7 | 87/16 |
| 10 1/10 | 10 × 10 + 1 | 101/10 |
Mistakes to avoid
- Multiplying by the numerator instead of the denominator. 3 2/5 is not (3 × 2 + 5)/5.
- Changing the denominator. The answer keeps the original denominator, 5, not 15 or 17.
- Splitting the sign. −3 2/5 is −17/5, not −13/5.
To go the other way, use the improper fraction to mixed number calculator. For arithmetic with mixed numbers, the mixed numbers calculator converts automatically, and the mixed number to decimal calculator gives the decimal form.
Frequently asked questions
How do you change a mixed number to an improper fraction?
Multiply the whole number by the denominator, add the numerator, and write the result over the same denominator. For 3 2/5: 3 × 5 = 15, 15 + 2 = 17, so 3 2/5 = 17/5.
Why does this method work?
The whole number 3 equals 15/5, because each whole is five fifths. Adding the 2/5 gives 17/5. Multiplying the whole by the denominator simply counts how many fraction-sized pieces the whole part contains.
How do I convert a negative mixed number?
Convert the positive version and then attach the minus sign. −3 2/5 becomes −17/5. Do not subtract the numerator: −3 2/5 means −(3 + 2/5), not −3 + 2/5.
When should I use improper fractions instead of mixed numbers?
Use improper fractions while calculating, especially for multiplication and division, because they follow the simple fraction rules. Convert back to a mixed number for the final answer if it is easier to read.