Fraction Calculator: Add, Subtract, Simplify & Convert
Free fraction calculator: add, subtract, multiply, divide fractions and mixed numbers. How to add fractions with different denominators; simplify fractions online, reduce to lowest terms, convert decimal to fraction. Mixed numbers calculator with steps; LCM and GCD shown. Trusted by students and educators. No sign-upโall calculations run locally.
What This Calculator Does & Who It's For
Calculator Purpose & Ideal Users
- What You'll Get:Operations: Result for two fractions with step-by-step common denominator (LCM) for addition and subtraction. Mixed numbers: Whole + numerator/denominator for both inputs; result as mixed or improper. Simplifier: Reduce any fraction or mixed number to lowest terms; GCD shown; optional whole number. Decimal โ Fraction: Decimal to fraction (e.g. 0.375 โ 3/8) or fraction to decimal. Big Number: Arbitrary-precision arithmetic via BigInt. Pie charts: Part-to-whole SVG (denominator = slices, numerator = shaded).
- Ideal Users:Students & teachers: How to add fractions with different denominators, mixed numbers calculator with steps, reduce fraction to lowest terms, convert decimal to fraction, fraction to decimal converter. Homework & exams: Step-by-step LCM and GCD; pie charts for part-to-whole. Anyone: Quick fraction arithmetic and conversions, no sign-up.
- Scope & Limits:Integers for numerators and denominators; zero denominator is invalid. DecimalโFraction accepts finite decimals. Big Number mode uses string input and BigInt for full precision. All calculations run in your browser; no data is sent to servers.
This fraction calculator gives you five tools in one: add, subtract, multiply, and divide fractions; work with mixed numbers; simplify fractions online (including mixed); convert decimal to fraction or fraction to decimal; and handle big-number fractions with full precision.
What Is a Fraction? Part-to-Whole and This Fraction Calculator
A fraction is a part of a whole, written as a/b (numerator over denominator). The denominator is how many equal parts the whole is split into; the numerator is how many of those parts you have (e.g. 3/4 = three out of four parts). Definitions of numerator, denominator, and why the denominator cannot be zero are in the FAQ above. This fraction calculator supports proper and improper fractions, mixed numbers, and very large integers (BigInt) so you can add, subtract, multiply, divide, simplify, and convert without losing precision.
How to Add Fractions with Different Denominators: Common Denominator and LCM
To add or subtract fractions you need a common denominator. Formulas:
and
In practice we use the Least Common Multiple (LCM) of the denominators so numbers stay smaller, then scale the numerators. The Operations tab shows the LCM, scaled numerators, and simplified result. Multiplication and division do not need a common denominator:
and
Simplify Fraction to Lowest Terms: GCD and Reduce Fractions
A fraction is in lowest terms when numerator and denominator have no common factor except 1. To reduce a fraction, divide both by their GCD (Greatest Common Divisor):
The Simplifier tab accepts a fraction or mixed number (optional whole), shows the GCD used, and displays the result in lowest terms. For step-by-step examples (e.g. 8/12 โ 2/3), see the FAQ above
Fraction Calculator FAQ
? What is a numerator?
The numerator is the top number in a fraction. It tells you how many parts of the whole you have. In the fraction 3/4, 3 is the numeratorโyou have 3 out of 4 equal parts. The numerator can be zero (meaning no parts) or any integer; it is always written above the fraction bar.
? Why can the denominator not be zero?
The denominator (the bottom number) cannot be zero because division by zero is undefined. A fraction represents numerator รท denominator; dividing by zero has no meaningful value in standard arithmetic. So fractions like 5/0 or 1/0 are invalid. This calculator will treat zero denominators as an error and prompt you to enter a non-zero denominator.
? How do you simplify a fraction?
To simplify a fraction, divide both the numerator and the denominator by their Greatest Common Divisor (GCD). For example, 8/12 has GCD(8,12) = 4, so 8รท4/12รท4 = 2/3. The result is in lowest terms. Use the Simplifier tab in this calculator to reduce any fraction to its simplest form and see the GCD used.
? How do I add fractions with different denominators?
To add fractions with different denominators, first find a common denominatorโusually the Least Common Multiple (LCM) of the denominators. Convert each fraction to that denominator by scaling numerator and denominator, then add the numerators. Example: 1/2 + 1/3 โ LCM(2,3)=6 โ 3/6 + 2/6 = 5/6. The Operations tab shows this step-by-step with LCM and scaled numerators.
? How do I convert a decimal to a fraction?
To convert a decimal to a fraction, write the decimal as a fraction with a power of 10 in the denominator (e.g. 0.375 = 375/1000), then simplify. This calculator does it automatically: enter the decimal in the Decimal โ Fraction converter and get the reduced fraction (e.g. 0.375 โ 3/8).