Perform exact arithmetic on two fractions and convert the reduced answer into mixed-number, decimal and percentage forms.
Math calculator
Add, subtract, multiply or divide proper, improper or mixed fractions and see every common equivalent form.
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Simplified fraction
The exact reduced fraction and useful equivalent forms will appear here.
Methodology
For addition and subtraction, cross-products create a common denominator. Multiplication multiplies numerators and denominators directly. Division multiplies the first fraction by the reciprocal of the second. The final numerator and denominator are divided by their greatest common divisor, and the sign is kept on the numerator.
Worked example
For 1/6 + 1/4, the cross-products give (1×4 + 1×6) / (6×4) = 10/24. Dividing both terms by their greatest common divisor, 2, gives 5/12, approximately 0.4167 or 41.6667%.
Exact and approximate forms
Fractions preserve an exact rational value. Mixed numbers can be easier to read for quantities above one, while decimal and percentage forms are useful for measurement and comparison. Repeating decimals are displayed with limited digits.
Reference
The operation and simplification rules follow the fraction chapters in OpenStax Prealgebra.
OpenStax fraction and decimal key conceptsRelated math tools
Common questions
The numerator and denominator are divided by their greatest common divisor. The denominator is always normalized to a positive number.
Cross-multiply each numerator by the other denominator, add the products, multiply the denominators, then reduce the result.
No. Division by zero is undefined, so either input fraction with a zero denominator is rejected.
A mixed number combines a whole-number part and a proper fraction, such as 2 1/3. The exact improper fraction is also shown.
The reduced fraction is exact. Decimal and percentage displays may be rounded because some rational numbers repeat forever in decimal form.
Inputs must be whole-number numerators and non-zero whole-number denominators, with each part limited to an absolute value of one billion. Results that exceed safe integer precision are rejected. Use the reduced fraction when an exact answer matters; decimal forms can repeat and require rounding.