Fraction Calculator
Add, subtract, multiply, and divide fractions — including mixed numbers — and get the exact result as a simplified fraction, a mixed number, and a decimal. Every step of the calculation (common denominator, multiplication, simplification) is shown.
Enter your fractions
Result
Step-by-step calculation
How to use the Fraction Calculator
- Pick an operation: +, −, ×, or ÷.
- Enter the numerator and denominator of each fraction. Denominators must be non-zero.
- Check Mixed number if the fraction has a whole part, then enter the whole number too.
- Press Calculate. You'll get the simplified result as an improper fraction, a mixed number, and a decimal, with the full step-by-step solution.
Method and formulas
Adding and subtracting
Find a common denominator (usually the LCM of the two denominators), convert both fractions, then add or subtract the numerators:
a/b + c/d = (a·d + c·b) ÷ (b·d)
a/b − c/d = (a·d − c·b) ÷ (b·d)
Multiplying
Multiply numerators together and denominators together:
(a/b) × (c/d) = (a·c) ÷ (b·d)
Dividing
Multiply the first fraction by the reciprocal of the second:
(a/b) ÷ (c/d) = (a·d) ÷ (b·c)
The result is then simplified by dividing both numerator and denominator by their greatest common divisor (GCD).
Mixed numbers
Convert to improper fractions first: W n/d = (W·d + n) ÷ d.
After computing, the result is converted back to a mixed number if desired.
Worked example: 1/2 + 1/3
- Identify: 1/2 + 1/3.
- Common denominator: LCM(2, 3) = 6.
- Convert: 1/2 = 3/6, 1/3 = 2/6.
- Add numerators: 3 + 2 = 5, so the sum is 5/6.
- Simplify: gcd(5, 6) = 1, so 5/6 is already simplest.
So 1/2 + 1/3 = 5/6 ≈ 0.8333.
How to interpret the result
- Simplified fraction — numerator and denominator share no common factor.
- Mixed number — the whole part plus a proper fraction, when the result exceeds 1.
- Decimal — often the easiest form to compare, but may be repeating or rounded.
- Negative results — the negative sign sits on the numerator (e.g. −3/4).
- Result = 0 — the numerator is zero, so the fraction is exactly zero regardless of the denominator.
Assumptions and limitations
- Both numerators and denominators must be integers (no decimals). Use the decimal-to-fraction feature of the number entry field to convert if needed.
- Denominators cannot be zero; the calculator rejects this case explicitly.
- Division by a fraction whose numerator is zero is rejected (cannot divide by zero).
- Mixed numbers are converted to improper fractions internally — the result is re-expressed as a mixed number when the magnitude exceeds 1.
- Very large numerators/denominators are handled as JavaScript Numbers (up to 2⁵³). Beyond that, precision may be lost.