Fraction Calculator with Mixed Numbers and Steps
Work with ordinary fractions, mixed numbers or decimal-to-fraction conversion using exact integer arithmetic. The result is reduced to lowest terms and displayed as an improper fraction, mixed number, decimal and percentage with an auditable operation trail.
Choose a fraction task
Exact fraction result
Complete fraction calculation guide
This fraction calculator provides a dedicated calculation workflow rather than a generic converter. The engine uses integer arithmetic for fraction operations so values are not rounded before simplification. Decimal conversion uses a bounded continued-fraction approximation when the decimal is not a finite rational within the chosen denominator limit.
Fractions and mixed numbers
A mixed number combines a whole number with a proper fraction. The calculator first converts each mixed number to an improper fraction while preserving its sign, then performs the selected operation.
Automatic simplification
The numerator and denominator are divided by their greatest common divisor. A negative result keeps the sign on the numerator, and the denominator is always returned as a positive integer.
Addition and subtraction steps
For unlike denominators, the calculator forms an exact common denominator and shows the cross-products used in the numerator. The final result is simplified after the operation rather than by decimal rounding.
Multiplication and division safeguards
Multiplication uses numerator-by-numerator and denominator-by-denominator products. Division multiplies by the reciprocal of the second fraction and rejects division by a zero-valued fraction.
Decimal conversion
Finite decimals can be represented exactly as an integer over a power of ten. Repeating or long decimals are approximated with continued fractions up to the user-selected maximum denominator, and the approximation error is displayed.
Can the denominator be zero?
No. A zero denominator is undefined and the calculator blocks it before performing an operation.
Does the calculator support negative mixed numbers?
Yes. The sign is applied to the entire mixed number and preserved through exact simplification.
Why can decimal conversion be approximate?
Some decimals are rounded representations of repeating values, so a maximum denominator is needed to choose a practical rational approximation.