During an enrichment lesson, each pupil in a class was given either 2 or 3 dice. The ratio of the number of pupils to the number of dice given was 9 : 23. What fraction of the pupils were given 2 dice each?

1. Express the number of pupils and dice in terms of units based on the given ratio.

Let the number of pupils be $9$ units and the total number of dice be $23$ units.

2. Use the assumption method to find the number of pupils who received 2 dice.

Assume all $9$ units of pupils were given $3$ dice each.
Total dice would be $9 \times 3 = 27$ units.
Difference in total dice = $27 - 23 = 4$ units.
Difference in dice per pupil = $3 - 2 = 1$.
Number of pupils with $2$ dice = $4 \div 1 = 4$ units.

3. Calculate the fraction of pupils given 2 dice.

Fraction of pupils with $2$ dice = $\frac{4}{9}$