Fraction Calculator — Add, Subtract, Multiply, Divide & Simplify FractionsProper · Improper · Mixed Numbers · LCD · GCF · Decimal Conversion
Use this free Fraction Calculator to instantly add fractions, subtract fractions, multiply fractions, and divide fractions — including proper fractions, improper fractions, and mixed numbers — with full step-by-step working shown at each stage. This online fraction calculator automatically applies the Lowest Common Denominator (LCD) for addition and subtraction, uses the Greatest Common Factor (GCF) to deliver fully simplified fractions in their lowest terms, and converts every result into three equivalent forms: simplified fraction (a/b) · mixed number (e.g. 2¾) · decimal equivalent — giving you a complete picture of every fraction calculation result in under a second.
This fraction simplifier and calculator is used across a wide range of everyday, academic, and professional applications: school maths — fractions homework & exam problem solving · adding and subtracting fractions with different denominators · multiplying and dividing fractions & mixed numbers · recipe scaling & cooking measurement fraction conversion · construction & carpentry fractional measurement calculations · financial ratio, interest rate & percentage fraction analysis. Trusted by primary and secondary school students, maths teachers, parents helping with homework, engineers, architects, and finance professionals for fast, accurate fraction arithmetic with full simplification, LCD finding, and GCF reduction — supporting everything from basic fraction operations to complex mixed number calculations across GCSE, A-Level, SAT, GRE, and competitive exam maths.
⚠ Accuracy Disclaimer: This fraction calculator is intended for educational, academic, and everyday estimation purposes only. While results are mathematically precise for standard fraction arithmetic, always independently verify calculations when used in safety-critical engineering measurements, legal or financial documentation, pharmaceutical dosage calculations, or any context where absolute precision and rounding accuracy are essential. For high-precision decimal fraction calculations, consider using a scientific calculator or CAS (Computer Algebra System).
Fractions are a fundamental representation of parts of a whole — expressed as a numerator divided by a denominator (a/b) — and are among the most important and widely applied concepts in both pure mathematics and everyday real-world calculations. From adding fractions with unlike denominators using the Lowest Common Denominator (LCD), to simplifying improper fractions using the Greatest Common Factor (GCF), to converting between proper fractions, improper fractions, mixed numbers, and decimal equivalents — mastering fraction arithmetic is essential for school and competitive exam maths (GCSE, SAT, GRE, GMAT), recipe scaling and cooking measurements, construction and carpentry fractional dimensions, financial ratio and percentage calculations, pharmaceutical dosage measurement, and engineering tolerances and technical drawing. This fraction calculator instantly converts every result into three equivalent formats — a fully simplified fraction in lowest terms, a mixed number, and a decimal equivalent — making fraction simplification, comparison, and interpretation fast, accurate, and accessible for students, teachers, engineers, and professionals alike.
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Fraction Calculator — Add, Subtract, Multiply, Divide, and Simplify With Full Steps
Fraction arithmetic requires finding common denominators for addition and subtraction, which is where most errors occur. Adding 1/3 + 1/4 requires converting both to twelfths: 4/12 + 3/12 = 7/12. Multiplying fractions is simpler: multiply numerators, multiply denominators, then simplify. Dividing by a fraction means multiplying by its reciprocal: 2/3 ÷ 4/5 = 2/3 × 5/4 = 10/12 = 5/6. The fraction calculator performs all four operations showing every step, which is more valuable than just getting the answer — seeing each step prevents systematic errors from recurring.
Mixed numbers (3½, 2¾) must be converted to improper fractions before arithmetic operations. 3½ becomes 7/2; 2¾ becomes 11/4. After the operation, the result is converted back to a mixed number if it is greater than 1. The calculator handles mixed number input directly — you enter 3½ and it converts internally — and presents results in both improper fraction and mixed number form so you can use whichever is more natural for your context.
Simplification by greatest common divisor (GCD) reduces fractions to lowest terms. 24/36 simplifies to 2/3 because GCD(24,36) = 12. The Euclidean algorithm efficiently finds the GCD of large numbers without trial division. A fraction that cannot be simplified (GCD = 1) is already in its lowest terms and is called irreducible. The calculator always presents the simplified result and shows the GCD used, so you understand why a fraction reduces the way it does rather than just accepting the output.