In a school, \( \frac{2}{3} \) of the students study a language - OCR - GCSE Maths - Question 4 - 2017 - Paper 1

The number of students who study Spanish is given by:

[ \text{Students studying Spanish} = \frac{2}{5} \times \left( \frac{2}{3} n \right) = \frac{4}{15} n ]

To find the number of students who do not study Spanish, subtract those who study Spanish from the total number of language students:

[ \text{Students not studying Spanish} = \frac{2}{3} n - \frac{4}{15} n ] To perform this operation, find a common denominator:

[ \frac{2}{3} n = \frac{10}{15} n ] Thus, [ \text{Students not studying Spanish} = \frac{10}{15} n - \frac{4}{15} n = \frac{6}{15} n = \frac{2}{5} n ]

The ratio of students who study Spanish to those who do not is:

[ \text{Ratio} = \frac{\text{Students studying Spanish}}{\text{Students not studying Spanish}} = \frac{\frac{4}{15} n}{\frac{2}{5} n} = \frac{4}{15} \times \frac{5}{2} = \frac{4 \times 5}{15 \times 2} = \frac{20}{30} = \frac{2}{3} ] Thus, simplifying gives us: [ 4:6 \text{ or } 4:11 \text{ or } exact equivalent} ]