Fraction calculator

How it works

To add or subtract fractions, first give them a common denominator. The smallest one is the least common multiple of the denominators: for $\frac{5}{12} + \frac{7}{18}$ it is $\operatorname{lcm}(12, 18) = 36$, so the sum is $\frac{15}{36} + \frac{14}{36} = \frac{29}{36}$. To multiply, multiply the numerators and the denominators (cancelling common factors across first keeps the numbers small); to divide, multiply by the reciprocal. Every result is brought to lowest terms by dividing numerator and denominator by their gcd.

A mixed number like $2\tfrac{1}{3}$ means $2 + \frac{1}{3} = \frac{7}{3}$. In the expression, type it with a space: 2 1/3. A decimal with $k$ digits after the point is a fraction over $10^k$, so $0.125 = \frac{125}{1000} = \frac{1}{8}$.

The decimal expansion comes from long division. Each step multiplies the remainder by 10 and divides by the denominator; since there are only finitely many possible remainders, one comes back and from then on the digits repeat: $\frac{1}{7} = 0.\overline{142857}$. The expansion stops exactly when the denominator, in lowest terms, has no prime factors other than 2 and 5.