13. A group of students attend a math club. Half of the students are boys and \( \frac{4}{9} \) of the boys have brown eyes. What fraction of the group are boys with brown eyes?

Let's break it down! If half of the students are boys, then the number of boys is \( \frac{1}{2} \) of the total group. If we denote the total number of students as \( S \), the number of boys would be \( \frac{S}{2} \). Now, \( \frac{4}{9} \) of the boys have brown eyes. To find the number of boys with brown eyes, we multiply the total number of boys by \( \frac{4}{9} \). This gives us: \[ \text{Boys with brown eyes} = \frac{4}{9} \times \frac{S}{2} = \frac{4S}{18} = \frac{2S}{9} \] To find the fraction of the entire group that these boys represent, we divide the number of boys with brown eyes by the total number of students: \[ \text{Fraction of the group that are boys with brown eyes} = \frac{\frac{2S}{9}}{S} = \frac{2}{9} \] So, the final answer is \( \frac{2}{9} \).