[
  "Let the number of girls be 9 units so that 8/9 of them (8 units) won prizes. Boys = half of girls = 4.5 units.",
  "Total children = 9 + 4.5 = 13.5 units. Girls who won = 8 units.",
  "Fraction who won = 8 / 13.5 = 16/27. (Note: the stored answer key gives 1/9; the computed answer is 16/27.)"
]