Fraction Calculator
Add, subtract, multiply, and divide fractions with step-by-step working.
Returns a simplified fraction, mixed number, and decimal with LCM denominator.
A fraction represents a part of a whole. It consists of a numerator (top number) and a denominator (bottom number), separated by a fraction bar. The denominator tells you how many equal parts the whole is divided into; the numerator tells you how many of those parts you have.
Key fraction operations:
Addition/Subtraction — requires a common denominator: 1/3 + 1/4 = 4/12 + 3/12 = 7/12
Multiplication — multiply numerators and denominators straight across: 2/3 × 3/5 = 6/15 = 2/5 (simplified)
Division — multiply by the reciprocal of the divisor: 3/4 ÷ 2/3 = 3/4 × 3/2 = 9/8 = 1 and 1/8
Simplification (reducing): Divide numerator and denominator by their Greatest Common Divisor (GCD). 24/36 → GCD is 12 → 24/12 = 2, 36/12 = 3 → simplified to 2/3
Converting:
- Fraction to decimal: divide numerator by denominator (3/4 = 0.75)
- Decimal to fraction: write as X/1000 then simplify (0.375 = 375/1000 = 3/8)
- Mixed number to improper fraction: (2 and 3/4) = (2×4 + 3)/4 = 11/4
Worked examples:
Baking recipe — halving: Recipe needs 3/4 cup flour. Halving gives 3/4 × 1/2 = 3/8 cup.
Sharing pizza: 5 friends share 3 pizzas equally: 3/5 pizza each.
Why fractions matter: Fractions are exact — unlike decimals, which sometimes round. 1/3 as a decimal is 0.33333… (repeating), never exactly right. Using 1/3 in calculations keeps precision that decimal rounding would lose.