Mixed Numbers
Convert a mixed number to an improper fraction and back — both directions, with every step shown.
Already in lowest terms.
- Multiply the whole number by the denominator: 2 × 4 = 8.
- Add the numerator: 8 + 3 = 11.
- Keep the denominator to get 11/4.
To turn a mixed number into an improper fraction, multiply the whole number by the denominator, add the numerator, and keep the denominator. So 2¾ = (2 × 4 + 3) ÷ 4 = 11/4. To go back, divide: 11 ÷ 4 = 2 remainder 3, giving 2¾.
Mixed numbers and improper fractions
A mixed number pairs a whole number with a proper fraction, like 2¾ (two and three-quarters). An improper fraction writes the same value with a numerator larger than its denominator, like 11⁄4. They describe exactly the same quantity — improper fractions are easier to multiply and divide, while mixed numbers are easier to read at a glance.
reverse it by dividing: numerator ÷ denominator gives the whole part and the remainder
Worked example — both directions
Mixed → improper: 2¾ becomes (2 × 4 + 3) ÷ 4 = 11⁄4. Improper → mixed: 11⁄4 divides as 11 ÷ 4 = 2 remainder 3, so the whole part is 2 and the leftover is 3⁄4, giving 2¾.
- 1 Multiply the whole number by the denominator. For 2¾: 2 × 4 = 8.
- 2 Add the numerator. 8 + 3 = 11 — this becomes the new numerator.
- 3 Keep the same denominator. The denominator stays 4, giving the improper fraction 11⁄4.
- 4 Reduce if possible. Divide numerator and denominator by their gcd. gcd(11, 4) = 1, so 11⁄4 is already in lowest terms.
Common conversions
Each row shows the same value written both ways. Reduce the fraction part by the greatest common divisor.
| Mixed number | Improper fraction |
|---|---|
| 1½ | 3/2 |
| 2¼ | 9/4 |
| 3⅓ | 10/3 |
| 2½ | 5/2 |
| 2⅓ | 7/3 |
| 3¾ | 15/4 |
Reducing and negative mixed numbers
Always reduce the fraction part. When you convert back to a mixed number, divide the remainder and the denominator by their greatest common divisor — 6⁄8 reduces to 3⁄4, so 2 6⁄8 is really 2¾.
Remainder zero means a whole number. 8⁄4 divides as 8 ÷ 4 = 2 remainder 0, so it is simply 2 — there is no fraction part.
Negatives apply to the whole quantity. −2¾ means −(2 + ¾) = −11⁄4, not −2 + ¾. Convert the size first, then attach the minus sign to the result.