Adding and subtracting
Fractions can only be added when they describe the same sized pieces, which means finding a common denominator first. Multiplying the two denominators always works: 3/4 + 5/6 becomes 18/24 + 20/24 = 38/24, which simplifies to 19/12. Using the lowest common denominator (12 here) keeps the numbers smaller, but the answer is identical once simplified.
Multiplying and dividing
Multiplication needs no common denominator — multiply across the top and across the bottom. Division means multiplying by the reciprocal: 3/4 ÷ 5/6 is the same as 3/4 × 6/5 = 18/20 = 9/10. Flip the second fraction, then multiply.
Simplifying
To reduce a fraction to lowest terms, divide the numerator and the denominator by their greatest common divisor. The calculator uses the Euclidean algorithm: repeatedly replace the larger number with the remainder of dividing it by the smaller, until nothing is left over.
Mixed numbers and decimals
An improper fraction such as 19/12 can be written as the mixed number 1 7/12. Recipes and measurements prefer mixed numbers; further calculation is easier with improper fractions. The decimal form is exact when the denominator's only prime factors are 2 and 5; otherwise it repeats, and the figure shown here is rounded. To turn a fraction straight into a percentage, the percentage calculator is quicker.