Fraction Calculator
Add, subtract, multiply, and divide fractions — simplified results and mixed number conversion included.
Enter fractions as: 3/4, mixed numbers as: 2 1/4, or whole numbers as: 5
Input Examples:
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What Is a Fraction?
A fraction represents a part of a whole. It is written as two numbers separated by a slash: the numerator (top number) tells you how many parts you have, and the denominator (bottom number) tells you how many equal parts the whole is divided into. For example, 3/4 means three out of four equal parts. Fractions come in three forms: proper fractions (numerator < denominator, e.g., 2/5), improper fractions (numerator ≥ denominator, e.g., 7/4), and mixed numbers (a whole number plus a proper fraction, e.g., 1¾).
Fraction arithmetic is a foundational skill that shows up in everyday life far more than most people realize. A recipe calling for 2/3 cup of flour halved becomes 1/3 cup — that's fraction division. A carpenter cutting a 3/8-inch board and a 5/16-inch board needs to add fractions to find the total thickness. A chemistry student calculating molar ratios works with fractions constantly. Understanding how to add, subtract, multiply, and divide fractions — and how to simplify results — is essential for cooking, construction, finance, science, and mathematics at every level.
How to Use This Calculator
- 1Enter the numerator and denominator for the first fraction in the top fields.
- 2Select the operation you want to perform: addition (+), subtraction (−), multiplication (×), or division (÷).
- 3Enter the numerator and denominator for the second fraction in the bottom fields.
- 4Click Calculate — the result appears as a simplified fraction, a decimal, and (when applicable) a mixed number.
Fraction Arithmetic Formulas
Addition: a/b + c/d = (a×d + c×b) / (b×d) → then simplify
Subtraction: a/b − c/d = (a×d − c×b) / (b×d) → then simplify
Multiplication: a/b × c/d = (a×c) / (b×d) → then simplify
Division: a/b ÷ c/d = (a×d) / (b×c) → multiply by reciprocal
Simplification: Divide numerator and denominator by GCD
GCD(12, 8) = 4 → 12/8 = 3/2 = 1½
Mixed number: when |numerator| > denominator
1¾ = (1×4 + 3)/4 = 7/4Always simplify results by dividing both the numerator and denominator by their greatest common divisor (GCD). When the numerator is larger than the denominator, the fraction can also be expressed as a mixed number for easier reading.
Worked Examples
Addition: 2/3 + 3/4
Cross-multiply the numerators with the opposite denominators, then add: (2×4 + 3×3) / (3×4) = (8 + 9) / 12 = 17/12. Since 17 > 12, convert to a mixed number: 17 ÷ 12 = 1 remainder 5, so the result is 1 5/12.
Subtraction: 5/6 − 1/4
Cross-multiply and subtract: (5×4 − 1×6) / (6×4) = (20 − 6) / 24 = 14/24. Simplify by finding GCD(14, 24) = 2: 14 ÷ 2 = 7, 24 ÷ 2 = 12, giving the simplified result 7/12.
Multiplication: 3/8 × 4/9
Multiply numerators together and denominators together: (3×4) / (8×9) = 12/72. Find GCD(12, 72) = 12, then simplify: 12 ÷ 12 = 1, 72 ÷ 12 = 6, giving the final answer 1/6.