In year 11, 3/7 of pupils go on holiday abroad in the summer break. Out of these, 1/3 go to France. Determine the ratio of pupils who go to France in summer to pupils who do not go to France in summer.

We can approach this question by breaking it into two steps; first use the information given to work out what proportion of pupils in year 11 went to France. Once we have this, we can go on to find the ratio.We are told that 1/3 of the students who go abroad go to France. This means that (1/3)x(the proportion of students going abroad) = the proportion of students going to France. We are also told that the proportion of students going abroad is 3/7, so we can pop that into the expression above to get:(1/3)x(3/7)=the proportion of students going to France.This gives us 3/21. Now we can use this to find the ratio. We now know that 3/21 students go to France. This means that 1-(3/21)=18/21 students do not go to France. So we have 3/21 : 18/21 which can be simplified to 3:18.