Out of the fractions $$\frac{4}{5},\frac{8}{9},\frac{6}{7},\frac{1}{3},\frac{3}{8}$$ what is the sum of the largest and smallest fractions ?

In order to find the sum of the largest and smallest numbers, let us first arrange the number in ascending order.

The LCM of the denominators of the fractions $$\frac{4}{5},\frac{8}{9},\frac{6}{7},\frac{1}{3},\frac{3}{8}$$ is the LCM of $$5,9,7,3,8 = 2520$$

Hence, the fractions with the denominator $$2520$$ look as below

$$\frac{4}{5} = \frac{2016}{2520}$$
$$\frac{8}{9} = \frac{2240}{2520}$$
$$\frac{6}{7} = \frac{2160}{2520}$$
$$\frac{1}{3} = \frac{840}{2520}$$
$$\frac{3}{8} = \frac{945}{2520}$$

Hence, the smallest of the fractions is $$\frac{1}{3}$$ and the largest is $$\frac{8}{9}$$ and their sum equals $$\frac{11}{9}$$

As this is not given in the options, the correct answer is option (e)