Adam, ben, Cathy and dana share some lollies. First Adam takes 2/3 of the lollies, then Ben takes 1/4 of the remainder, and the Cathy takes 1/3of what was left. Dana gets all the rest. What fraction of the original number of lollies does Dana get?

A = 2/3 ... remainder 1/3

B = 1/4 (1/3) = 1/12

2/3 + 1/12 = 8/12 + 1/12 = 9/12 reduces to 3/4 remainder 1/4

C = 1/3 (1/4) = 1/12

3/4 + 1/12 = 9/12 + 1/12 = 10/12 reduces to 5/6 remainder 1/6

so Gana gets 1/6

check ...

adam gets 2/3 or 8/12

ben gets 1/12

cathy gets 1/12

Gana gets 1/6 or 2/12

added = 12/12 or 1 ... correct

Dana gets 1/6 <==