Math
Fraction calculator
Enter two fractions and pick an operation (+, −, ×, ÷). The result is reduced to lowest terms automatically, with the decimal value shown for reference.
Formula
Fractions are exact — unlike decimals, 1/3 stays exactly 1/3 rather than 0.33333… The calculator works entirely with integers, computes the answer using the standard four-operation rules, then reduces using the greatest common divisor (Euclid's algorithm).
Addition and subtraction use a common denominator (the product of the two denominators, then simplified). Multiplication multiplies numerators and denominators directly. Division flips the second fraction and multiplies. All results are reduced to lowest terms — so 6/8 becomes 3/4, and 4/2 becomes 2.
Mixed-number form is shown alongside when the result is improper (numerator > denominator).
Examples
- 011/2 + 1/3→ (1·3 + 1·2)/(2·3) = 5/6 ≈ 0.8333
- 023/4 × 2/5→ (3·2)/(4·5) = 6/20 = 3/10 = 0.3
- 035/6 − 1/4→ (5·4 − 1·6)/(6·4) = 14/24 = 7/12 ≈ 0.5833
- 047/8 ÷ 1/2→ (7·2)/(8·1) = 14/8 = 7/4 = 1 3/4 = 1.75
FAQ
- We reduce using Euclid's algorithm — find the greatest common divisor of numerator and denominator, then divide both by it. Standard math practice is to always express fractions in lowest terms unless instructed otherwise.
References
Note: Results are accurate to floating-point precision (~15 significant digits) for the standard formula shown above. See our terms of use for general usage information.