Improper fraction to mixed number converter
Switch between improper fractions like 17/5 and mixed numbers like 3 2/5 in either direction. To calculate with mixed numbers, use the fraction calculator.
Improper → mixed
- Divide 17 by 5.
17 ÷ 5 = 3 remainder 2 - The whole number is 3; the remainder 2 goes over 5.
3 2/5
Mixed → improper
- Multiply the whole number by the denominator: 3 × 7 = 21. That's how many 7ths are in 3 wholes.
- Add the numerator: 21 + 2 = 23.
- Keep the same denominator.
23/7
Mixed numbers vs improper fractions
A mixed number is a whole number and a proper fraction side by side: 2 3/4 means 2 + 3/4. An improper fraction writes the same amount as a single fraction: 11/4. The bars above show both at once — full bars are the wholes, the last partly shaded bar is the fraction part.
Why convert?
For multiplying and dividing, always convert mixed numbers to improper fractions first; multiplying the parts separately gives wrong answers. For adding and subtracting, either works (see borrowing when subtracting). Convert back at the end so the answer is easy to read.
Quick reference
| Improper | Mixed | Decimal |
|---|---|---|
| 3/2 | 1 1/2 | 1.5 |
| 5/2 | 2 1/2 | 2.5 |
| 4/3 | 1 1/3 | 1.3333 |
| 5/3 | 1 2/3 | 1.6667 |
| 5/4 | 1 1/4 | 1.25 |
| 7/4 | 1 3/4 | 1.75 |
| 9/4 | 2 1/4 | 2.25 |
| 11/8 | 1 3/8 | 1.375 |
| 13/8 | 1 5/8 | 1.625 |
| 8/5 | 1 3/5 | 1.6 |
| 17/6 | 2 5/6 | 2.8333 |
Questions people ask
How do you turn an improper fraction into a mixed number?
Divide the numerator by the denominator. The quotient is the whole number, the remainder is the new numerator, and the denominator stays the same. 17/5 = 17 ÷ 5 = 3 remainder 2 = 3 2/5.
How do you turn a mixed number into an improper fraction?
Multiply the whole number by the denominator, add the numerator, and put the result over the same denominator. 3 2/7 = (3 × 7 + 2)/7 = 23/7.
What is an improper fraction?
A fraction whose numerator is equal to or larger than its denominator, like 7/4 or 5/5. Its value is 1 or more.
Is 7/4 or 1 3/4 the correct answer?
Both are the same number. Mixed numbers are easier to picture and are usually expected as final answers in school; improper fractions are easier to calculate with.