Fraction Calculator

Step-by-step solution

1. 1

   The expression

   Addition of two fractions.

   $$\frac{1}{2} + \frac{1}{3}$$
2. 2

   Find a common denominator

   2 and 3 share no common factor, so the least common denominator is their product, 6.

   $$\operatorname{lcm}(2,\, 3) = 6$$
3. 3

   Rewrite both fractions

   Extend each fraction so that both have the common denominator 6.

   $$\frac{1}{2} = \frac{1 \cdot 3}{2 \cdot 3} = \frac{3}{6} \\ \frac{1}{3} = \frac{1 \cdot 2}{3 \cdot 2} = \frac{2}{6}$$
4. 4

   Add the numerators

   Keep the common denominator and add the numerators: 3 + 2 = 5.

   $$\frac{3}{6} + \frac{2}{6} = \frac{5}{6}$$
5. 5

   Reduce to lowest terms

   Numerator and denominator share no common factor, so the fraction is already in lowest terms.

   $$\gcd(5, 6) = 1$$
6. 6

   Result

   1/2 + 1/3 = 5/6

   $$\frac{1}{2} + \frac{1}{3} = \frac{5}{6}$$