1. **State the problem:** We know that three-fifths of the Grade 8 class are in the band. (a) On Tuesday, only half of these band students went to band practice. We want to find what fraction of the whole class went to band practice on Tuesday. 2. **Formula and explanation:** If $\frac{3}{5}$ of the class are in the band, and half of those went to practice, then the fraction of the class that went to practice is: $$\text{Fraction who went} = \frac{1}{2} \times \frac{3}{5}$$ 3. **Calculate the fraction:** $$\frac{1}{2} \times \frac{3}{5} = \frac{1 \times 3}{2 \times 5} = \frac{3}{10}$$ So, $\frac{3}{10}$ of the class went to band practice on Tuesday. 4. **Answer to part (a):** The fraction of the class that went to band practice on Tuesday is $\frac{3}{10}$. 5. **Part (b) question:** How many students might be in the class? How do you know? 6. **Explanation for part (b):** Since $\frac{3}{5}$ of the class are in the band, the total number of students must be divisible by 5 to have a whole number of band members. Also, since half of the band members went to practice, the number of band members must be even to split exactly in half. 7. **Find possible class sizes:** - Let the total number of students be $N$. - Band members = $\frac{3}{5}N$ must be an integer. - Half of band members = $\frac{1}{2} \times \frac{3}{5}N = \frac{3}{10}N$ must be an integer. Therefore, $N$ must be divisible by 10. 8. **Examples:** - If $N=10$, band members = $\frac{3}{5} \times 10 = 6$, half of band members = 3. - If $N=20$, band members = 12, half = 6. So the class size could be 10, 20, 30, etc., any multiple of 10. **Final answers:** (a) $\frac{3}{10}$ of the class went to band practice on Tuesday. (b) The class size must be a multiple of 10 to have whole numbers of band members and half of them attending practice.