Fraction Calculator
Add, subtract, multiply and divide fractions. Result is simplified automatically.
Fraction arithmetic: step-by-step
A fraction represents a part of a whole. The number on top is the numerator (how many parts you have); the number on the bottom is the denominator (how many equal parts the whole is divided into). All four arithmetic operations follow specific algorithms, and every result should be simplified by dividing both numerator and denominator by their greatest common divisor (GCD).
The four operations
| Operation | Formula | Example | Result |
|---|---|---|---|
| Addition | a/b + c/d = (a×d + c×b) / (b×d) | 1/2 + 1/3 = (3+2)/6 | 5/6 |
| Subtraction | a/b − c/d = (a×d − c×b) / (b×d) | 3/4 − 1/3 = (9−4)/12 | 5/12 |
| Multiplication | a/b × c/d = (a×c) / (b×d) | 2/3 × 3/4 | 6/12 = 1/2 |
| Division | a/b ÷ c/d = (a×d) / (b×c) | 2/3 ÷ 4/5 = (2×5)/(3×4) | 10/12 = 5/6 |
Finding the GCD to simplify fractions
The greatest common divisor (GCD) is the largest number that divides evenly into both numerator and denominator. Dividing both by the GCD reduces the fraction to its simplest form. The Euclidean algorithm finds the GCD efficiently: repeatedly replace the larger number with the remainder when divided by the smaller.
Simplify 12/18:
GCD(12, 18): 18 = 12×1 + 6 → GCD(12,6): 12 = 6×2 + 0 → GCD = 6
12/18 ÷ 6/6 = 2/3 ✓
Simplify 36/48:
GCD(36,48) = 12
36/48 ÷ 12/12 = 3/4 ✓Mixed numbers and improper fractions
An improper fraction has a numerator larger than its denominator (e.g. 7/3). A mixed number combines a whole number and a proper fraction (2 and 1/3). Converting between them is often needed before arithmetic.
Mixed to improper: 2¹/₃ = (2×3 + 1)/3 = 7/3
Improper to mixed: 7/3 → 7 ÷ 3 = 2 remainder 1 → 2¹/₃
Adding mixed numbers:
1²/₃ + 2¹/₄ → convert → 5/3 + 9/4 = 20/12 + 27/12 = 47/12 = 3¹¹/₁₂Common fraction–decimal–percentage equivalents
Frequently asked questions
How do I add two fractions?
Give them a common denominator, add the numerators, then simplify. For example, 1/3 + 1/6 = 2/6 + 1/6 = 3/6 = 1/2.
How do I simplify a fraction?
Divide the numerator and denominator by their greatest common divisor. For example, 8/12 ÷ 4/4 = 2/3.
How do I convert a fraction to a decimal?
Divide the numerator by the denominator. For example, 3/4 = 3 ÷ 4 = 0.75.
What is an improper fraction?
An improper fraction has a numerator larger than its denominator, like 7/4. It can be written as the mixed number 1 3/4.
Add/Subtract: (a×d ± c×b)/(b×d) | Multiply: (a×c)/(b×d) | Divide: (a×d)/(b×c). Result auto-simplified using GCD.