Mixed Fraction Calculator
Convert between improper fractions and mixed numbers in both directions.
Inputs
For Mixed→Improper, enter the fractional part numerator.
Used only for Mixed→Improper conversion.
Conversion Result
3 2/5
Whole Part
3
Fraction Numerator
2
Fraction Denominator
5
Step by step
Divide numerator by denominator
17 ÷ 5 = 3 remainder 2
Simplify remainder fraction
2/5 = 2/5
Already in lowest terms
Result
= 3 2/5
How it works
A mixed number combines a whole part with a proper fraction (e.g. 3 2/5). An improper fraction has a numerator larger than its denominator (e.g. 17/5). To convert improper→mixed, divide; to convert mixed→improper, multiply the whole by the denominator and add the numerator.
Formulas
Improper to Mixed
whole = numerator ÷ denominator (integer part); remainder = numerator mod denominator
- numerator
- The top of the improper fraction
- denominator
- The bottom of the fraction
Mixed to Improper
Improper numerator = whole × denominator + numerator
- w
- Whole number part
- n
- Fractional numerator
- d
- Denominator
Frequently Asked Questions
When is a fraction 'improper'?
When the absolute value of the numerator is greater than or equal to the denominator. For example, 7/4, 13/5, and 9/9 are all improper.
Do mixed numbers and improper fractions represent the same value?
Yes — 3 2/5 and 17/5 are the same quantity, just written differently. Mixed form is more intuitive for everyday use; improper form is easier for arithmetic.