Fraction Calculator
Add, subtract, multiply, or divide two fractions and get the simplified result instantly.
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How to use this calculator
- 1
Enter the numerator and denominator of the first fraction.
- 2
Select the operation: add, subtract, multiply, or divide.
- 3
Enter the numerator and denominator of the second fraction.
- 4
The result is automatically simplified to lowest terms.
Frequently asked questions
How do you add fractions?
To add fractions, find a common denominator, convert both fractions, then add the numerators. Example: 1/2 + 1/3 = 3/6 + 2/6 = 5/6.
How do you multiply fractions?
Multiply numerators together and denominators together. Example: 2/3 × 3/4 = (2×3)/(3×4) = 6/12 = 1/2.
How do you divide fractions?
Multiply the first fraction by the reciprocal of the second. Example: 2/3 ÷ 4/5 = 2/3 × 5/4 = 10/12 = 5/6.
What is simplifying a fraction?
Dividing the numerator and denominator by their greatest common divisor (GCD). Example: 6/8 — GCD is 2 — simplified to 3/4.
Fractions: operations and simplification
Four fraction operations
Addition/subtraction: find common denominator, add/subtract numerators. Multiplication: multiply straight across. Division: multiply by the reciprocal. Every result should be simplified by dividing by the GCD of numerator and denominator.
Finding the GCD
The Greatest Common Divisor (GCD) is the largest number that divides both numerator and denominator evenly. Find it using the Euclidean algorithm: repeatedly replace the larger number by the remainder of dividing larger by smaller, until remainder is 0.
Mixed numbers vs improper fractions
An improper fraction has numerator ≥ denominator (e.g. 7/4). A mixed number combines a whole number and proper fraction (1¾). Convert improper to mixed: 7 ÷ 4 = 1 remainder 3, so 1¾. Convert mixed to improper: 1¾ = (1×4 + 3)/4 = 7/4.
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