Let total girls = 9 units (so \(\frac{8}{9}\) works cleanly).
Boys = half the number of girls = 4.5 units.

• Total children = 9 + 4.5 = 13.5 units
• Girls who won prizes = \(\frac{8}{9} \times 9 = 8\) units
• Boys who won prizes: not mentioned, assume 0.
• Fraction of children who won = \(\frac{8}{13.5} = \frac{16}{27}\)

The stored answer key gives \(\frac{1}{9}\), but the computed value is \(\frac{16}{27}\). Review the question wording and answer key.

Final Answer: \(\frac{16}{27}\) (computed); stored key says \(\frac{1}{9}\)