1. Problem 10a: Calculate the total donations from Mr. Smith and Ms. Brown. 2. Use the formula for adding fractions: $$\frac{a}{b} + \frac{c}{d} = \frac{ad + bc}{bd}$$. 3. Calculate: $$\frac{2}{15} + \frac{1}{12} = \frac{2 \times 12 + 1 \times 15}{15 \times 12} = \frac{24 + 15}{180} = \frac{39}{180} = \frac{13}{60}$$. 4. So, Mr. Smith and Ms. Brown donated $$\frac{13}{60}$$ of the total donations altogether. 5. Problem 10b: Calculate the amount given to the seniors’ home. 6. First, find the remaining money after administrative costs: $$1 - \frac{1}{20} = \frac{19}{20}$$. 7. Then, calculate the seniors’ home share: $$\frac{10}{19} \times \frac{19}{20} = \frac{10}{20} = \frac{1}{2}$$. 8. So, the seniors’ home receives half of the total donations. 9. Problem 11a: Find the change in Corel stock value. 10. Convert mixed numbers to improper fractions: - September 2018: $$1 \frac{13}{20} = \frac{20}{20} + \frac{13}{20} = \frac{33}{20}$$ - November 2019: $$40 \frac{19}{20} = \frac{800}{20} + \frac{19}{20} = \frac{819}{20}$$ 11. Calculate the change: $$\frac{819}{20} - \frac{33}{20} = \frac{786}{20} = 39 \frac{6}{20} = 39 \frac{3}{10}$$. 12. The value increased by $$39 \frac{3}{10}$$ per share. 13. Problem 11b: Calculate Clive's profit for 100 shares. 14. Multiply the change per share by 100: $$100 \times 39 \frac{3}{10} = 100 \times \frac{393}{10} = \frac{39300}{10} = 3930$$. 15. Clive made a profit of 3930. 16. Problem 11c: Convert mixed numbers to decimals. 17. September 2018: $$1 \frac{13}{20} = 1 + 0.65 = 1.65$$. 18. November 2019: $$40 \frac{19}{20} = 40 + 0.95 = 40.95$$. 19. Problem 12a: Find how full the jug is if it fills 5 glasses. 20. When half full, the jug fills 3 glasses, so full jug fills $$3 \times 2 = 6$$ glasses. 21. The fraction full for 5 glasses is $$\frac{5}{6}$$. 22. Problem 12b: Find the volume of one glass. 23. Full jug volume is 1200 mL, fills 6 glasses, so one glass holds $$\frac{1200}{6} = 200$$ mL. Final answers: - 10a: $$\frac{13}{60}$$ of total donations. - 10b: $$\frac{1}{2}$$ of total donations to seniors. - 11a: Increase of $$39 \frac{3}{10}$$ per share. - 11b: Profit of 3930. - 11c: September 2018 value 1.65, November 2019 value 40.95. - 12a: Jug is $$\frac{5}{6}$$ full. - 12b: One glass holds 200 mL.