Perform fraction arithmetic with exact rational answers and automatic simplification.
Fractions represent exact parts of a whole, which is why recipes, music theory, probability, and construction still rely on them. Adding or subtracting fractions requires a common denominator, while multiplication and division follow different rules that are easy to mix up under time pressure.
This fraction calculator keeps arithmetic exact by working with numerators and denominators rather than premature decimals. That matters when a measurement must stay rational, such as cutting lumber in half-inch increments or scaling a recipe that originally serves five people.
After each operation, the tool reduces results to lowest terms and can express improper fractions as mixed numbers when that is clearer. If you are checking homework, compare both the simplified fraction and the decimal approximation only after confirming the fraction form is correct.
For real projects, write intermediate steps: find common denominators for addition, multiply straight across for products, and invert the divisor for division. The calculator mirrors those steps so you can spot where a manual solution diverged.
Type numerator and denominator (or mixed number if supported).
Select add, subtract, multiply, or divide.
Provide the second rational value.
Run the operation using exact fraction arithmetic.
Confirm the reduced fraction or mixed-number output.
Optional decimal check for measurement tasks.
a/b + c/d = (ad + bc) / bd; a/b x c/d = ac / bd; a/b ÷ c/d = a/b x d/c
Addition and subtraction use a common denominator. Multiplication multiplies numerators and denominators. Division multiplies by the reciprocal of the divisor.
(3x6 + 5x4)/(4x6) = 38/24 = 19/12
Sum = 19/12 (1 7/12).
(2x9)/(3x10) = 18/30 = 3/5
Product = 3/5.
7/8 x 4/1 = 28/8 = 7/2
Quotient = 7/2 (3 1/2).