Fraction Calculator
Add, subtract, multiply and divide fractions with full step-by-step workings
// History
How to Do Fraction Arithmetic
Fractions represent parts of a whole. The top number (numerator) tells how many parts you have; the bottom number (denominator) tells how many parts make up a whole. All fraction operations follow a consistent set of rules.
The Four Operations
Mixed Numbers
A mixed number has a whole part and a fraction (e.g. 2¾). To convert to an improper fraction: multiply the whole by the denominator and add the numerator. 2¾ = (2×4 + 3)/4 = 11/4. This calculator handles mixed numbers automatically.
Finding the GCD
The Greatest Common Divisor (GCD) — also called the Highest Common Factor (HCF) — is the largest number that divides both the numerator and denominator exactly. It is used to simplify fractions to their lowest terms. This calculator uses the Euclidean algorithm to find the GCD.
From the Blog
// Reciprocal Trick
To divide by a fraction, flip it (find its reciprocal) and multiply. ½ ÷ ¼ = ½ × 4/1 = 2.
// Simplify First
When multiplying fractions, simplify diagonally before multiplying — it keeps numbers small. 4/9 × 3/8 → 1/3 × 1/2 = 1/6.
// LCD not just CD
Use the Least Common Denominator (not just any common denominator) to keep numbers manageable when adding or subtracting.
// Mixed Numbers
Always convert mixed numbers to improper fractions before doing arithmetic, then convert back at the end.