Decision tools built for clarity
Fraction Calculator
Work with common fraction operations and reduced values.
Choose simplify to enter one fraction, or choose add, subtract, multiply, or divide and enter two fractions; every denominator must be non-zero.
Methodology
Formula or transformation
Performs the selected operation with exact rational arithmetic and reduces the result to lowest terms.
Variables
- First rational number
- Second rational number
- Exact rational result
- Mixed-number representation
- Decimal approximation
Units
- Dimensionless value
Rounding policy
The fraction stays exact; only the decimal approximation is rounded using half away from zero.
Simplify reduces one fraction by its greatest common divisor. Add, subtract, multiply, and divide apply the selected operation to two fractions and reduce the result.
Work with common fraction operations and reduced values.
Reviewed sources
- OpenStax — Add and subtract fractions Reviewed on 2026-09-04
- OpenStax — Multiply and divide fractions Reviewed on 2026-09-04
Formula review history
-
Initial formula and source review.
Reviewed 2026-09-04 for formula version exact-rational-arithmetic-v1
Assumptions
- Each denominator is a non-zero integer.
- The submitted values represent exact rational numbers.
Limitations
- Division by a zero-valued second fraction is undefined.
- The decimal display may be rounded even though the reduced fraction remains exact.
Worked example
For 1/2 + 1/3, the common denominator is 6: 3/6 + 2/6 = 5/6, or about 0.833333.
Frequently asked questions
Why is the fraction reduced?
Dividing numerator and denominator by their greatest common divisor gives an equivalent simplest form.
Can a denominator be zero?
No. A fraction with zero denominator is undefined.