Fraction Calculator

How to Use This Calculator

Enter the numerators and denominators for two fractions, then click "Calculate" to add, subtract, multiply, or divide them. Results are automatically simplified to lowest terms using the greatest common divisor (GCD).

Fraction Operation Formulas

Step-by-Step: Adding Fractions with Different Denominators

Example: 1/2 + 1/3

1. Find a common denominator: 2 × 3 = 6
2. Convert both fractions: 1/2 = 3/6, and 1/3 = 2/6
3. Add the numerators: 3/6 + 2/6 = 5/6
4. Check if 5/6 simplifies: GCD(5,6) = 1, so 5/6 is already in lowest terms

Using the least common multiple (LCM) instead of just multiplying denominators often gives smaller numbers. For 1/4 + 1/6, LCM(4,6) = 12, so 3/12 + 2/12 = 5/12 — smaller than using 4×6=24 as denominator (6/24 + 4/24 = 10/24 = 5/12 after simplification).

Step-by-Step: Multiplying and Dividing Fractions

Multiplication: Multiply numerators together and denominators together. 2/3 × 3/5 = (2×3)/(3×5) = 6/15 = 2/5 (after simplifying by GCD 3).

Division: Multiply by the reciprocal of the second fraction. 3/4 ÷ 2/5 = 3/4 × 5/2 = 15/8 = 1 7/8 as a mixed number.

Simplifying Fractions

A fraction is in its simplest (lowest) form when the numerator and denominator share no common factors other than 1. To simplify, find the GCD of numerator and denominator, then divide both by it. Example: 12/18 → GCD(12,18) = 6 → 2/3. You can also simplify step-by-step by dividing by small prime factors: 12/18 ÷ 2/2 = 6/9 ÷ 3/3 = 2/3.

Mixed Numbers and Improper Fractions

An improper fraction has a numerator larger than its denominator (e.g., 7/4). A mixed number combines a whole number and a proper fraction (1 3/4). To convert: 7/4 → divide 7÷4 = 1 remainder 3 → 1 3/4. To convert back: 1 3/4 → (1×4 + 3)/4 = 7/4. This calculator uses improper fractions internally; results above 1 can be expressed as mixed numbers by dividing the numerator by the denominator.