Fraction Calculator (Add, Subtract, Multiply, Divide, Simplify)
Add, subtract, multiply, or divide two fractions and see the result as both a reduced fraction and a decimal. View the step-by-step process for finding a common denominator and simplifying.
Tips
- Finding a common denominator means rewriting fractions with different denominators so they share the same one (their least common multiple). Addition and subtraction require this step before combining numerators.
- Simplifying (reducing) a fraction means dividing both the numerator and denominator by their greatest common divisor until no further division is possible. This tool automatically reduces every result.
- Multiplication just multiplies the numerators together and the denominators together — no common denominator needed. Example: 1/2 x 2/3 = 2/6 = 1/3 after reducing.
- An easy way to remember division: "multiply by the reciprocal of the divisor." Example: 1/2 / (2/3) = 1/2 x 3/2 = 3/4.
- Entering 0 as a denominator, or dividing by a fraction whose numerator is 0, will produce an error — a fraction's denominator must always be a nonzero integer.
Frequently Asked Questions
Side Note — Ancient Egypt's curious 'unit fractions'
The numerator-over-denominator notation we use today wasn't how fractions were originally written. Ancient Egyptians worked almost exclusively with 'unit fractions' — fractions with a numerator of 1, like 1/2, 1/3, 1/4 — and expressed every other fraction as a sum of distinct unit fractions. For example, 2/5 was written as 1/3 + 1/15 (as recorded in sources such as the Rhind Mathematical Papyrus).
This "Egyptian fraction" approach may look inefficient, but it connects to a genuine theorem in modern mathematics: any positive rational number can be written as a sum of finitely many distinct unit fractions (famously constructed via a greedy algorithm attributed to Fibonacci). It remains an interesting topic in pure mathematics today.
The numerator/denominator notation with a horizontal fraction bar that we learn in school is generally credited to Arabic mathematicians around the 12th century, later spreading to Europe and evolving into its modern form. Operations like simplifying and finding common denominators only became naturally definable once this notation took hold.