Mixed Fraction Calculator
Convert between improper fractions and mixed numbers in both directions.
About Mixed Fraction Calculator
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
Worked example
With the default values below, Mixed Fraction Calculator returns Conversion Result of 3 2/5. Change any input above and every figure here is recalculated in your browser.
Inputs used
- Conversion Directionone of Improper → Mixed, Mixed → Improper
- Improper → Mixed
- Numerator
- 17
- Denominatorminimum 1
- 5
- Whole Number
- 0
Results
- Conversion Result
- 3 2/5
- Whole Part
- 3
- Fraction Numerator
- 2
- Fraction Denominator
- 5
Step by step
- 1Divide numerator by denominator
- 2Simplify remainder fractionAlready in lowest terms
- 3Result= 3 2/5
Assumptions and limits
- The result is derived only from the 4 inputs listed above. Anything not among them is not part of the calculation.
- In particular, this calculator does not take inflation, tax, fees or charges or compounding frequency into account.
- Figures are rounded for display to whole numbers, so totals built from several rounded parts can differ slightly from the unrounded arithmetic.
How these calculators are built and tested is described on the Methodology page. If a figure looks wrong, please report it.
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.