Improper Fraction to Mixed Number Calculator
Type an improper fraction like 17/5 to get a mixed number, or a mixed number like 3 2/5 to get the improper fraction.
17/5 as a mixed number
3 2/5
17/5 = 3 2/5: 3 wholes and 2/5 left over.
- Improper fraction
- 17/5
- As a decimal
- 3.4
How to convert between improper fractions and mixed numbers
An improper fraction has a numerator at least as big as its denominator, such as 17/5. To write it as a mixed number, divide: 17 ÷ 5 = 3 remainder 2. The quotient is the whole number and the remainder sits over the same denominator, so 17/5 = 3 2/5. Three full wholes use 15 fifths and 2 fifths are left over.
To go back, multiply the whole number by the denominator and add the numerator: 3 2/5 = (3 × 5 + 2)/5 = 17/5. This is the first step before multiplying or dividing mixed numbers.
For a negative mixed number the minus sign belongs to the whole thing: −3 2/5 means −(3 + 2/5) = −17/5, not −3 + 2/5. Simplify the fraction part if you can: 22/6 = 3 4/6 = 3 2/3.
n/d = q r/d, where n = q × d + r and 0 ≤ r < d
- Mixed numbers appear in grade 4 standards, where students add and subtract them by replacing each with an equivalent fraction (4.NF.B.3c). Source: Common Core State Standards, Grade 4 Number and Operations: Fractions.
- A fraction whose numerator is at least its denominator is called improper; a whole number plus a proper fraction is a mixed number. Source: Wikipedia, Fraction.
Improper fractions as mixed numbers
Each improper fraction divided out, with its decimal value.
| Improper fraction | Mixed number | Decimal |
|---|---|---|
| 3/2 | 1 1/2 | 1.5 |
| 5/2 | 2 1/2 | 2.5 |
| 7/3 | 2 1/3 | 2.3333 |
| 9/4 | 2 1/4 | 2.25 |
| 11/4 | 2 3/4 | 2.75 |
| 13/5 | 2 3/5 | 2.6 |
| 17/5 | 3 2/5 | 3.4 |
| 22/7 | 3 1/7 | 3.1429 |
| 25/8 | 3 1/8 | 3.125 |
| 31/6 | 5 1/6 | 5.1667 |
Show all 15 rowsShow fewer
| 47/10 | 4 7/10 | 4.7 |
| 50/9 | 5 5/9 | 5.5556 |
| 100/7 | 14 2/7 | 14.2857 |
| 125/12 | 10 5/12 | 10.4167 |
| 355/113 | 3 16/113 | 3.1416 |
Frequently Asked Questions
Is 22/7 equal to π?
No, it is an approximation: 22/7 = 3 1/7 ≈ 3.142857, while π ≈ 3.141593. 355/113 = 3 16/113 is much closer, matching π to six decimal places.
Which is better, an improper fraction or a mixed number?
Mixed numbers are easier to picture (3 2/5 pizzas); improper fractions are easier to calculate with. Most algebra leaves answers improper; recipes and measurements use mixed numbers.
What if the remainder is zero?
Then the fraction is a whole number: 20/5 = 4 exactly, with no fraction part.