Free Fraction Calculator
Add, subtract, multiply, and divide any two fractions instantly. Results are automatically simplified to lowest terms. Supports proper fractions, improper fractions, and shows the decimal equivalent. Free, private — all calculations run in your browser.
Understanding Your Result
- Simplified form — 13/12 is already in lowest terms (GCD of numerator and denominator = 1).
- Mixed number — 13/12 as a mixed number is 1 1/12 (whole part + proper fraction).
- LCD — The Least Common Denominator of 4 and 3 is 12. This is used to find equivalent fractions for addition and subtraction.
- Decimal — 1.08333333 — the fraction as a decimal. This may be a repeating decimal (rounded to 8 decimal places).
About This Fraction Calculator
The Fraction Calculator performs all four arithmetic operations — addition, subtraction, multiplication, and division — on any pair of fractions and returns an exact result simplified to its lowest terms. Unlike decimal calculators, it never rounds: the answer to 1/3 + 1/6 is exactly 1/2, not 0.4999999. This makes it ideal for mathematics, cooking, carpentry, engineering ratios, and any situation where an exact rational answer is required rather than an approximation.
The Formulas — How Each Operation Works
For two fractions a/b and c/d, the four operations are defined as follows:
Subtraction: a/b − c/d = (ad − bc) / bd
Multiplication: a/b × c/d = ac / bd
Division: a/b ÷ c/d = ad / bc
After computing the raw result, the calculator divides both numerator and denominator by their Greatest Common Divisor (GCD), computed via the Euclidean algorithm, to produce the fully simplified fraction. The GCD of two integers a and b is the largest integer that divides both without remainder: for example, GCD(12, 18) = 6, so 12/18 simplifies to 2/3.
Addition and Subtraction — The LCD Method
To add or subtract fractions, both must share a common denominator. The formula above (using bd as denominator) always works but can produce unnecessarily large numbers. A more efficient approach is to use the Least Common Denominator (LCD), which is the Least Common Multiple (LCM) of the two denominators. For example, to compute 5/6 + 7/8: the LCD is LCM(6, 8) = 24. Convert: 20/24 + 21/24 = 41/24. Using the formula directly would give 40/48 + 42/48 = 82/48, which simplifies to the same 41/24 but requires an extra simplification step.
Multiplication and Division — Cross-Cancellation
Multiplication is the simplest operation: multiply numerators, multiply denominators, then simplify. Division uses the reciprocal rule: dividing by c/d is the same as multiplying by d/c. A powerful shortcut is cross-cancellation: before multiplying, cancel any common factors between a numerator of one fraction and a denominator of the other. For 4/9 × 3/8: cancel 4 and 8 by 4 (→ 1/9 × 3/2), and cancel 3 and 9 by 3 (→ 1/3 × 1/2 = 1/6). This avoids computing 12/72 and then simplifying.
Mixed Numbers vs. Improper Fractions
A mixed number like 2 3/4 combines a whole number and a proper fraction. An improper fraction like 11/4 has a numerator larger than its denominator. They represent the same value. For computation, convert mixed numbers to improper fractions first: multiply the whole number by the denominator and add the numerator: 2 3/4 → (2 × 4 + 3)/4 = 11/4. Apply the arithmetic operation, then convert back if needed: 11 ÷ 4 = 2 remainder 3 → 2 3/4.
Privacy Notice
All calculations in this fraction calculator are performed entirely in your browser. No input data is transmitted to any server, stored in any database, or shared with third parties. Your data stays completely private on your device. See our Privacy Policy for full details.
When to Use This Calculator
Scale recipe quantities up or down accurately. Halving 3/4 cup becomes 3/8 cup — the fraction calculator gives the exact measurement instantly.
Imperial measurements are full of fractions: 3/8 inch, 5/16 inch. Add or subtract lumber measurements precisely without converting to decimals.
Check your child's fraction homework or work through problems step by step. Covers all four operations with automatic simplification shown.
Probability results are naturally expressed as fractions. Calculate combined probabilities like 1/4 × 2/3 = 1/6 with exact fractional results.
Gear ratios, mixture ratios, and scale factors in engineering are often expressed as fractions. Get exact rational answers for technical specifications.
💡 Pro Tips
Cross-cancel before multiplying fractions to keep numbers small. For example, 4/9 × 3/8 — notice that 4 and 8 share a factor of 4 (4÷4=1, 8÷4=2), and 3 and 9 share a factor of 3 (3÷3=1, 9÷3=3). So the product simplifies immediately to 1/3 × 1/2 = 1/6, avoiding the need to simplify 12/72 at the end.
For addition and subtraction, always find the LCD rather than just multiplying the two denominators. Multiplying denominators works but creates large numbers that then need heavy simplification. For 5/6 + 7/8, the LCD is 24 (not 48), giving 20/24 + 21/24 = 41/24 — smaller and easier to work with.
Convert mixed numbers to improper fractions before performing arithmetic, then convert back at the end. Mixed numbers like 2 3/4 are harder to add directly because the whole-number parts and fractional parts must be handled separately. As an improper fraction (11/4), standard fraction rules apply cleanly.
Estimate the answer before calculating as a sanity check. For 3/7 + 4/9, both fractions are close to 1/2, so the answer should be close to 1. The actual answer is 55/63 ≈ 0.873 — close to 1, which confirms the calculation is reasonable. This habit catches errors instantly.
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