EPS

for a bonus issue of, say, 2 for 5 – where you used to have 5 shares, now you have 7. So for every 5, there are now 7. So you need to multiply the number of shares in issue during periods BEFORE the bonus issue by the bonus fraction because, instead of having your original 5 shares, now …..

Rights fraction is similar in that it adjusts for the “free” element of a rights issue. I really don’t think that you need to know the “logic of the fraction” Just be prepared to calculate the fraction and appreciate that, by applying the fraction to all the shares held in periods BEFORE the rights issue, that will automatically increase the weighted average number of shares in issue thus adjusting for the free element