Fraction Calculator
Add, subtract, multiply, and divide fractions — automatically simplified with mixed numbers and decimals
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Quick summary
Enter two fractions and pick an operation. Addition and subtraction use the common denominator (a/b ± c/d = (ad ± cb)/bd); multiplication multiplies straight across; division multiplies by the reciprocal. Results are simplified by the greatest common divisor and shown as improper fractions, mixed numbers, and decimals.
Reviewed by Simple Calculators TeamLast reviewed
How to use this calculator
- Enter the inputs requested by the calculator.
- Choose the units or options that match your situation and review the assumptions.
- Run or update the calculation to see the result.
- Review the result, breakdown, and formulas shown on the page.
- Check the inputs, units, dates, and limitations before saving or sharing the result.
Frequently asked questions
How do I add fractions with different denominators?
Cross-multiply to a common denominator: 1/2 + 1/3 = (1×3 + 1×2)/(2×3) = 5/6. Using the least common denominator keeps numbers smaller, but any common denominator works — simplification fixes the rest.
How do I divide fractions?
Multiply by the reciprocal — flip the second fraction: 1/2 ÷ 1/4 = 1/2 × 4/1 = 4/2 = 2. “Keep, change, flip” is the classroom mnemonic.
How do I simplify a fraction?
Divide numerator and denominator by their greatest common divisor (GCD). For 6/12, the GCD is 6, giving 1/2. A fraction is fully simplified when the GCD is 1.
What is a mixed number?
A whole number plus a proper fraction: 7/6 = 1 1/6. Improper fractions (numerator ≥ denominator) and mixed numbers are the same value written differently — recipes use mixed, algebra prefers improper.
Key terms
- GCD
- Greatest common divisor — the largest integer dividing both numerator and denominator; the key to simplification.
- Reciprocal
- A fraction flipped: the reciprocal of 3/4 is 4/3. Dividing by a fraction multiplies by its reciprocal.
- Improper Fraction
- Numerator at least as large as the denominator (7/6) — convertible to a mixed number (1 1/6).
Methodology, sources & limitations
This page shows the formula, assumptions, and limitations used for this estimate. Rates, thresholds, and other time-sensitive inputs can change, so verify them against the relevant official source before relying on a result.
For our review approach and the primary sources we consult, see the methodology and source policy. If you spot an outdated figure or formula, please contact us with a correction.