IMC 2009 Q6
6. Which of the following is half way between \(\dfrac{4}{5}\) and \(-\dfrac{2}{3}\)?
- A \(\dfrac{1}{15}\)
- B \(\dfrac{7}{30}\)
- C \(\dfrac{7}{15}\)
- D \(\dfrac{17}{30}\)
- E \(\dfrac{3}{4}\)
Intermediate Mathematical Challenge 2009, Question 6. © UK Mathematics Trust. Original paper on ukmt.org.uk
Answer: A \(\dfrac{1}{15}\)
\(\dfrac{4}{5} = \dfrac{12}{15}\) and \(-\dfrac{2}{3} = -\dfrac{10}{15}\), so the number half way between these is \(\dfrac{1}{2}\left(\dfrac{-10}{15} + \dfrac{12}{15}\right)\), that is \(\dfrac{1}{15}\).
Solution © UK Mathematics Trust, from the IMC 2009 solutions.