ratio Venn diagrams

the idea for this task is from one of John Mason's presentations e.g. in Vancouver 2014
(see the workshop powerpoint resources on his website)

it involves an appreciation of set intersections and equivalent fractions

the powerpoint is here

prove that 1 : 5 is impossible

prove that there is only one way for 4 : 5

prove that 1 : 6 is impossible

John Mason's extension task