Adding fractions
Online calculator — enter the values and get the result instantly, with the formula and a worked example.
a, c, e = numerator
b, d, f = denominator
-- = fraction line
Adding fractions means combining two or more fractions into a single fraction that represents their total. Each fraction has a numerator, the top number showing how many parts you have, and a denominator, the bottom number showing how many equal parts make up one whole. The key rule is that fractions can only be added directly when they share the same denominator, because you can only count parts that are the same size. When the denominators differ, you first rewrite the fractions over a common denominator, usually the least common multiple, so the pieces match before you combine them. Once the denominators agree, you simply add the numerators and keep the denominator unchanged, then simplify the result to its lowest terms if possible.
This operation appears constantly in everyday life and in more advanced study, from splitting a recipe or measuring lengths to working with money, probabilities, and algebraic expressions. Mastering it builds the foundation for ratios, rational numbers, and later calculus, which is why it is one of the most important early skills in arithmetic.
Worked example
Add 1/2 + 1/3:
1. Find a common denominator (the least common multiple of 2 and 3 is 6).
2. Convert the fractions: 1/2 = 3/6 and 1/3 = 2/6.
3. Add the numerators and keep the denominator: 3/6 + 2/6 = 5/6.
Result: 1/2 + 1/3 = 5/6.
