Fraction Calculator
Add, subtract, multiply or divide two fractions, with the result automatically simplified to lowest terms.
What this calculator does
Enter two fractions and an operation, and this calculator performs the arithmetic and reduces the result to its simplest form — the same fraction, but with the smallest possible whole-number numerator and denominator.
The formulas
- Addition: a/b + c/d = (a×d + c×b) / (b×d)
- Subtraction: a/b − c/d = (a×d − c×b) / (b×d)
- Multiplication: a/b × c/d = (a×c) / (b×d)
- Division: a/b ÷ c/d = (a×d) / (b×c)
After the raw calculation, the result is divided by its GCF (see the LCM & GCF Calculator) to reduce it to lowest terms.
Worked example
1/2 + 3/4: using the addition formula, (1×4 + 3×2) / (2×4) = (4 + 6) / 8 = 10/8. The GCF of 10 and 8 is 2, so dividing both by 2 gives the simplified result: 5/4 (equal to 1.25 as a decimal).
Common mistakes
- Adding numerators and denominators straight across (1/2 + 1/2 is not 2/4 — it's 1) — fractions need a common denominator before adding or subtracting.
- Forgetting to simplify the final answer — 10/8 and 5/4 represent the same value, but 5/4 is the standard form.
- Mixing up the flip step in division — dividing by a fraction means multiplying by its reciprocal (flip numerator and denominator), a step people often skip.
Limitations
This calculator works with simple (numerator/denominator) fractions, not mixed numbers — convert a mixed number like 2¾ to an improper fraction (11/4) before entering it. A zero denominator on either fraction, or a zero numerator on the second fraction during division, isn't a valid input and is flagged rather than computed.
Frequently asked questions
Yes — the result is always reduced to lowest terms using the greatest common factor of the resulting numerator and denominator, and the unsimplified version is also shown for reference.
Yes — enter a negative numerator or denominator and the sign is handled correctly, including keeping the sign consistently on the numerator in the result.
Convert the mixed number to an improper fraction first: multiply the whole number by the denominator, add the numerator, and keep the same denominator. For example, 2¾ becomes 11/4.
It's the same result expressed as a decimal, which is useful for double-checking your answer or using it in a context that expects a decimal rather than a fraction.