Algebra!

It's actually not hard to just list all the numbers out. 

We have

$\frac{1}{3}, \frac{2}{3}, \frac{4}{3},\frac{5}{3}, \frac{7}{3}, \frac{8}{3}, \frac{10}{3}, \frac{11}{3}, \frac{13}{3}, \frac{14}{3}$

The ones we excluded from this list, like 3/3 and 6/3 are not in simplest form, therefore eliminated. 

Now, adding all these values up, we get $75/3=25$

That means 25 is our answer!

Thanks! :)