Step by step

1. Write as improper fractions

1 1/2 = (1 × 2 + 1)/2 = 3/2

2. Least common denominator

LCM(2, 3) = 6

3. Rewrite over the common denominator

3/2 = 9/6; 2/3 = 4/6

4. Add the numerators

9 + 4 = 13, so 13/6

5. Simplify

13/6 is already in lowest terms

6. Convert to a mixed number

13 ÷ 6 = 2 remainder 1, so 2 1/6

Answer

13/6 = 2 1/6

The decimal repeats forever: the digits in parentheses keep repeating, so 2.1(6) = 2.166666666…