1. **Problem Q6:** Write the ratio of full-time staff to part-time staff in simplest form. Given: Full-time staff = 12, Part-time staff = 18. 2. **Formula and rule:** Ratio is written as $\text{full-time} : \text{part-time} = 12 : 18$. To simplify, divide both numbers by their greatest common divisor (GCD). 3. **Find GCD:** GCD of 12 and 18 is 6. 4. **Simplify ratio:** $$\frac{12}{18} = \frac{\cancel{6} \times 2}{\cancel{6} \times 3} = \frac{2}{3}$$ So, the simplest ratio is $2 : 3$. --- 1. **Problem Q7:** Express the ratio of marketing expenditure to operations expenditure. Given: Marketing = 30000, Operations = 90000. 2. **Write ratio:** $30000 : 90000$. 3. **Find GCD:** GCD of 30000 and 90000 is 30000. 4. **Simplify ratio:** $$\frac{30000}{90000} = \frac{\cancel{30000} \times 1}{\cancel{30000} \times 3} = \frac{1}{3}$$ So, the simplest ratio is $1 : 3$. --- 1. **Problem Q8:** Write the ratio of Product A to Product B. Given: Product A = 45, Product B = 75. 2. **Write ratio:** $45 : 75$. 3. **Find GCD:** GCD of 45 and 75 is 15. 4. **Simplify ratio:** $$\frac{45}{75} = \frac{\cancel{15} \times 3}{\cancel{15} \times 5} = \frac{3}{5}$$ So, the simplest ratio is $3 : 5$. --- **Final answers:** - Q6: $2 : 3$ - Q7: $1 : 3$ - Q8: $3 : 5$