Fraction Calculator — Add, Subtract, Multiply, Divide
Enter two fractions and choose an operation. Get the result as a simplified fraction, decimal, and mixed number — with every step shown so you can follow along or check homework.
How Fractions Work
A fraction represents a part of a whole. The top number (numerator) tells you how many parts you have, and the bottom number (denominator) tells you how many equal parts the whole is divided into. Fractions are fundamental to cooking, construction, music, and virtually every area of mathematics.
Fraction Operation Formulas
a/b + c/d = (a×d + c×b) / (b×d)
a/b − c/d = (a×d − c×b) / (b×d)
a/b × c/d = (a×c) / (b×d)
a/b ÷ c/d = (a×d) / (b×c)
Simplifying and Converting Fractions
To simplify a fraction, find the Greatest Common Divisor (GCD) of the numerator and denominator using the Euclidean algorithm, then divide both by it. For example, 18/24: GCD(18, 24) = 6, so 18/24 simplifies to 3/4. A fraction is in its simplest form when the GCD of its numerator and denominator is 1.
Converting Between Formats
Fraction to decimal: Divide the numerator by the denominator. 3/8 = 0.375.
Fraction to mixed number: Divide the numerator by the denominator. The quotient is the whole number, the remainder is the new numerator. 11/4 = 2 remainder 3, so 11/4 = 2 3/4.
Mixed number to improper fraction: Multiply the whole number by the denominator, add the numerator. 2 3/4 = (2×4 + 3)/4 = 11/4.
Fractions in Everyday Life
Fractions appear in countless real-world situations. Recipes call for half a cup of flour or a quarter teaspoon of salt, requiring fraction arithmetic when scaling portions. Construction workers use fractions for measurements in inches, while musicians rely on fractional note values like quarter notes and eighth notes to keep time. Understanding how to add, subtract, multiply, and divide fractions quickly makes these everyday tasks far more manageable.
Finding the Least Common Denominator
When adding or subtracting fractions, you need a common denominator. The Least Common Denominator (LCD) is the smallest number that both denominators divide into evenly. For 1/6 + 1/4: LCD of 6 and 4 is 12. Convert: 2/12 + 3/12 = 5/12.