GK 2019 Q4
4. A large square is divided into smaller squares, as shown. What fraction of the large square is shaded grey?
- A \(\tfrac{2}{3}\)
- B \(\tfrac{2}{5}\)
- C \(\tfrac{4}{7}\)
- D \(\tfrac{4}{9}\)
- E \(\tfrac{5}{12}\)
Grey Kangaroo 2019, Question 4. © UK Mathematics Trust. Original paper on ukmt.org.uk
Answer: D \(\tfrac{4}{9}\)
The largest grey square is a quarter of the large square. The smaller grey squares are each one ninth of the size of the largest grey square. Hence the fraction of the large square which is shaded is \(\tfrac{1}{4} + \tfrac{7}{9} \times \tfrac{1}{4} = \tfrac{1}{4} \times \left(1 + \tfrac{7}{9}\right) = \tfrac{1}{4} \times \tfrac{16}{9} = \tfrac{4}{9}\)
Solution © UK Mathematics Trust, from the GK 2019 solutions.