Fraction Calculator
Add, subtract, multiply and divide two fractions, with automatic simplification and mixed-number view.
What is it
A fraction is a numerator over a denominator. To add or subtract, you first put both fractions on the same denominator, then add the tops. To multiply, just multiply top by top and bottom by bottom; to divide, flip the second fraction and multiply. The result is then simplified by dividing top and bottom by their greatest common divisor, and you can view it as an improper fraction or a mixed number.
Notes & fun facts
Why do we flip the fraction when dividing? Because dividing by a half is the same as doubling: 3 ÷ 1/2 = 6. The "flip and multiply" rule is just the short way of saying "count how many pieces of this size fit into that".
Origin & history
Fraction arithmetic was already developed by Indian mathematicians: Brahmagupta in 628 AD wrote rules for adding, subtracting, multiplying and dividing fractions with a numerator-over-denominator notation. The methods travelled through the Islamic world — al-Hassar in the 12th century drew the horizontal fraction bar we still use today. Fibonacci brought them to Europe in his Liber Abaci of 1202.