Let's assume the number to be x.
According to the problem statement, the sum of a number and its reciprocal is 2 1/6 or 13/6.
So we can set up the equation:
x + 1/x = 13/6
Multiplying both sides by 6x, we get:
6x^2 + 6 = 13x
Bringing all the terms to one side, we get:
6x^2 - 13x + 6 = 0
We can solve for x using the quadratic formula:
x = [13 ± sqrt(13^2 - 4(6)(6))] / (2*6)
x = [13 ± sqrt(169)] / 12
x = [13 ± 13] / 12
So, x can be either 2/3 or 3/2. Therefore, the number is either 2/3 or 3/2.