1
Addition and subtraction need a shared denominator
The implementation cross-multiplies each numerator by the other denominator. Multiplication combines numerators and denominators directly; division multiplies by the reciprocal.
Fraction Calculator
Add, subtract, multiply, and divide fractions with step-by-step simplification and mixed number support.
Tested tool guide
Math and conversion tools
Checked July 30, 2026
What Fraction Calculator does, with a checked example
This calculator applies the selected arithmetic operation to two numerator-denominator pairs, normalizes the sign, and divides the result by its greatest common divisor. It displays the simplified fraction, mixed-number form, decimal value, unsimplified intermediate result, and the divisor used for reduction.
Worked example
A concrete input and expected output from the current implementation.
Input
2/3 + 1/6
Expected output
5/6; decimal 0.83333333
Cross multiplication gives 2 x 6 + 1 x 3 over 3 x 6, or 15/18. Dividing numerator and denominator by 3 produces 5/6.
How the result is produced
2
The sign is kept in the numerator
If an operation produces a negative denominator, both terms are multiplied by -1 before simplification. This produces a conventional positive denominator.
Good uses
- Check hand calculations for recipes or measurements.
- Convert an improper result into a mixed number.
- See the unsimplified fraction and reduction factor.
Limits and checks
- A denominator cannot be zero.
- Dividing by a fraction with numerator zero is undefined.
- Decimal display is rounded and may repeat indefinitely.
Common questions
Why is 15/18 reduced to 5/6?
Three is the greatest integer that divides both 15 and 18. Dividing both by 3 preserves the fraction value.
What is an improper fraction?
Its numerator has magnitude at least as large as its denominator. The mixed-number display separates complete wholes from the remaining proper fraction.
References and verification
The example and behavioral notes were checked against the browser implementation. Standards and primary references below define the relevant format, formula, or platform behavior.
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