The sum of the reciprocals of two consecutive natural numbers is $\frac{11}{30}$. What is the larger number?

Explanation

1. 01

   $\frac{1}{x} + \frac{1}{x + 1} = \frac{2x + 1}{x(x + 1)} = \frac{11}{30}$.

2. 02

   Match: $x(x + 1) = 30$ and $2x + 1 = 11$ both give $x = 5$.

3. 03

   The numbers are 5 and 6, so the larger is 6. Check: $\frac{1}{5} + \frac{1}{6} = \frac{11}{30}$.