Free fraction calculator
Simplify fractions to lowest terms and perform fraction arithmetic — enter a numerator and denominator to see the simplified result, updated live, as you type.
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Simplified by dividing numerator and denominator by their GCF. Denominator of 0 is undefined.
Results are estimates. Consult a professional.
How the fraction calculator works
A fraction represents a part of a whole, written as numerator/denominator. This calculator simplifies fractions and performs addition, subtraction, multiplication, and division. Every result is automatically reduced to its lowest terms by dividing both numerator and denominator by their greatest common divisor (GCD).
Worked example: simplify 18/24 and add 1/3 + 1/4
Two fundamental operations. Simplification uses the GCD; addition uses a common denominator before combining numerators.
Common fraction, decimal, and percentage equivalents
Recognising these benchmark fractions on sight speeds up mental arithmetic and helps sanity-check calculator results.
| Fraction | Decimal | Percentage |
|---|---|---|
| 1/2 | 0.5 | 50% |
| 1/3 | 0.333… | 33.33% |
| 2/3 | 0.667… | 66.67% |
| 1/4 | 0.25 | 25% |
| 3/4 | 0.75 | 75% |
| 1/5 | 0.2 | 20% |
| 1/8 | 0.125 | 12.5% |
| 3/8 | 0.375 | 37.5% |
| 5/8 | 0.625 | 62.5% |
| 7/8 | 0.875 | 87.5% |
Source: standard fraction–decimal–percent conversions
Tips for working with fractions
Fractions appear in cooking, construction measurements, probability, and algebra. These habits reduce errors and speed up calculations.
- Find GCD before multiplying — for multiplication or division, cross-cancel common factors in the numerators and denominators before multiplying; this keeps numbers smaller and avoids reducing a very large fraction at the end.
- Never add denominators directly — 1/3 + 1/4 ≠ 2/7. Always find a common denominator first (or use the cross-multiply formula) before adding or subtracting.
- Dividing = multiplying by the reciprocal — to divide by a fraction, flip it and multiply: (a/b) ÷ (c/d) = (a/b) × (d/c). This is the most reliable method.
- Always simplify your final answer — leave no fraction with a GCD > 1 between numerator and denominator; most teachers and graders require answers in lowest terms.
- Convert mixed numbers first — if working with 2½, convert to an improper fraction (5/2) before applying any operation. Mixed numbers cannot be multiplied or divided directly.
Accuracy and limitations
Fraction arithmetic on integers is exact — there is no floating-point rounding involved when the numerator and denominator are whole numbers. The GCD is computed using the Euclidean algorithm, which is always precise. Results may have very large numerators or denominators if the inputs are large primes with no common factors (e.g., adding 1/9,999,991 + 1/9,999,973 produces a 17-digit denominator). The display will show the exact reduced fraction in all cases supported by JavaScript's number range (up to 2⁵³ − 1 ≈ 9 × 10¹⁵).
Key terms
About this calculator
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