Improper Fraction to Mixed Number Calculator
Convert improper fractions to mixed numbers and mixed numbers back to improper fractions, simplified, with the decimal value and working.
An improper fraction has a numerator at least as large as its denominator, like 17/5. This calculator converts improper fractions to mixed numbers (17/5 = 3 2/5) and mixed numbers back to improper fractions, simplifies the result and gives the decimal value. It shows the division or multiplication step, and negative fractions work too.
How to use this tool
- Type an improper fraction such as 17/5, or a mixed number such as 3 2/5 (whole part, a space, then the fraction).
- Read the mixed number, the simplified improper fraction and the decimal.
- Check the working under the results to see the step that produced the answer.
Formula
Improper → mixed: a/b = q r/b, with q = whole part of a ÷ b and r = remainder Mixed → improper: w n/d = (w × d + n) / d
Both forms are simplified by dividing the numerator and denominator by their greatest common divisor. A minus sign applies to the whole mixed number: −2 1/3 means −(2 + 1/3), which is −7/3.
Example
17/5: 17 ÷ 5 = 3 remainder 2, so 17/5 = 3 2/5, or 3.4 as a decimal. 22/8: 22 ÷ 8 = 2 remainder 6, and 6/8 simplifies to 3/4, giving 2 3/4 (11/4 as a simplified improper fraction). Going the other way, 3 2/5 = (3 × 5 + 2) / 5 = 17/5.
Frequently asked questions
How do you turn an improper fraction into a mixed number?
Divide the numerator by the denominator. The whole-number answer is the whole part, the remainder becomes the new numerator, and the denominator stays the same. Simplify the fraction part if you can.
How do you turn a mixed number into an improper fraction?
Multiply the whole number by the denominator, add the numerator, and put the total over the original denominator: 4 1/3 = (4 × 3 + 1)/3 = 13/3.
Is 5/5 an improper fraction?
Yes. Any fraction whose numerator is equal to or greater than its denominator is improper; 5/5 equals the whole number 1.
Why use improper fractions at all?
They are easier to multiply and divide. Convert mixed numbers to improper fractions first, do the arithmetic, then convert back to a mixed number for the final answer.
Last updated: 2026-10-30