1. The problem is to add pairs of fractions and simplify the results. 2. The formula for adding fractions with the same denominator is: $$\frac{a}{d} + \frac{b}{d} = \frac{a+b}{d}$$ 3. For each pair, add the numerators and keep the denominator the same. 4. Simplify the resulting fraction if possible by dividing numerator and denominator by their greatest common divisor (GCD). 5. Let's solve the first pair as an example: $$\frac{6}{15} + \frac{8}{15} = \frac{6+8}{15} = \frac{14}{15}$$ No simplification needed since 14 and 15 have no common factors other than 1. 6. Next pair: $$\frac{9}{16} + \frac{4}{16} = \frac{9+4}{16} = \frac{13}{16}$$ 7. Next: $$\frac{3}{10} + \frac{4}{10} = \frac{3+4}{10} = \frac{7}{10}$$ 8. Next: $$\frac{7}{12} + \frac{3}{12} = \frac{7+3}{12} = \frac{10}{12}$$ Simplify: $$\frac{\cancel{10}}{\cancel{12}} = \frac{5}{6}$$ 9. Next: $$\frac{6}{15} + \frac{4}{15} = \frac{6+4}{15} = \frac{10}{15}$$ Simplify: $$\frac{\cancel{10}}{\cancel{15}} = \frac{2}{3}$$ 10. Next: $$\frac{9}{20} + \frac{3}{20} = \frac{9+3}{20} = \frac{12}{20}$$ Simplify: $$\frac{\cancel{12}}{\cancel{20}} = \frac{3}{5}$$ 11. Next: $$\frac{8}{10} + \frac{1}{10} = \frac{8+1}{10} = \frac{9}{10}$$ 12. Next: $$\frac{2}{13} + \frac{3}{13} = \frac{2+3}{13} = \frac{5}{13}$$ 13. Next: $$\frac{6}{10} + \frac{3}{10} = \frac{6+3}{10} = \frac{9}{10}$$ 14. Next: $$\frac{9}{18} + \frac{16}{18} = \frac{9+16}{18} = \frac{25}{18}$$ 15. Next: $$\frac{9}{12} + \frac{2}{12} = \frac{9+2}{12} = \frac{11}{12}$$ 16. Next: $$\frac{7}{13} + \frac{2}{13} = \frac{7+2}{13} = \frac{9}{13}$$ 17. Next: $$\frac{8}{5} + \frac{5}{12}$$ Different denominators, find common denominator: $$\text{LCM}(5,12) = 60$$ Convert: $$\frac{8}{5} = \frac{8 \times 12}{60} = \frac{96}{60}$$ $$\frac{5}{12} = \frac{5 \times 5}{60} = \frac{25}{60}$$ Add: $$\frac{96}{60} + \frac{25}{60} = \frac{121}{60}$$ 18. Next: $$\frac{4}{10} + \frac{6}{10} = \frac{4+6}{10} = \frac{10}{10} = 1$$ 19. Next: $$\frac{7}{26} + \frac{6}{26} = \frac{7+6}{26} = \frac{13}{26} = \frac{1}{2}$$ 20. Next: $$\frac{8}{10} + \frac{5}{10} = \frac{8+5}{10} = \frac{13}{10}$$ 21. Next: $$\frac{14}{10} + \frac{6}{10} = \frac{14+6}{10} = \frac{20}{10} = 2$$ 22. Next: $$\frac{9}{25} + \frac{6}{25} = \frac{9+6}{25} = \frac{15}{25} = \frac{3}{5}$$ 23. Next: $$\frac{2}{8} + \frac{5}{8} = \frac{2+5}{8} = \frac{7}{8}$$ 24. Next: $$\frac{7}{18} + \frac{5}{18} = \frac{7+5}{18} = \frac{12}{18} = \frac{2}{3}$$ 25. Next: $$\frac{5}{10} + \frac{3}{10} = \frac{5+3}{10} = \frac{8}{10} = \frac{4}{5}$$ 26. Next: $$\frac{6}{18} + \frac{4}{18} = \frac{6+4}{18} = \frac{10}{18} = \frac{5}{9}$$ 27. Next: $$\frac{7}{8} + \frac{3}{8} = \frac{7+3}{8} = \frac{10}{8} = \frac{5}{4}$$ 28. Next: $$\frac{3}{4} + \frac{3}{4} = \frac{3+3}{4} = \frac{6}{4} = \frac{3}{2}$$ 29. Next: $$\frac{9}{16} + \frac{1}{16} = \frac{9+1}{16} = \frac{10}{16} = \frac{5}{8}$$ 30. Next: $$\frac{3}{14} + \frac{6}{14} = \frac{3+6}{14} = \frac{9}{14}$$ 31. Next: $$\frac{6}{8} + \frac{7}{8} = \frac{6+7}{8} = \frac{13}{8}$$ 32. Next: $$\frac{5}{15} + \frac{5}{15} = \frac{5+5}{15} = \frac{10}{15} = \frac{2}{3}$$ 33. Next: $$\frac{7}{28} + \frac{8}{28} = \frac{7+8}{28} = \frac{15}{28}$$ 34. Next: $$\frac{3}{13} + \frac{8}{13} = \frac{3+8}{13} = \frac{11}{13}$$ 35. Next: $$\frac{14}{30} + \frac{12}{30} = \frac{14+12}{30} = \frac{26}{30} = \frac{13}{15}$$ 36. Next: $$\frac{8}{9} + \frac{7}{9} = \frac{8+7}{9} = \frac{15}{9} = \frac{5}{3}$$ 37. Next: $$\frac{11}{19} + \frac{13}{19} = \frac{11+13}{19} = \frac{24}{19}$$ 38. Next: $$\frac{5}{14} + \frac{7}{14} = \frac{5+7}{14} = \frac{12}{14} = \frac{6}{7}$$ 39. Next: $$\frac{3}{17} + \frac{8}{17} = \frac{3+8}{17} = \frac{11}{17}$$ 40. Next: $$\frac{6}{32} + \frac{8}{32} = \frac{6+8}{32} = \frac{14}{32} = \frac{7}{16}$$ 41. Next: $$\frac{5}{8} + \frac{4}{8} = \frac{5+4}{8} = \frac{9}{8}$$ 42. Next: $$\frac{7}{12} + \frac{6}{12} = \frac{7+6}{12} = \frac{13}{12}$$ 43. Next: $$\frac{13}{23} + \frac{12}{23} = \frac{13+12}{23} = \frac{25}{23}$$ 44. Next: $$\frac{5}{22} + \frac{6}{22} = \frac{5+6}{22} = \frac{11}{22} = \frac{1}{2}$$ 45. Next: $$\frac{6}{15} + \frac{8}{15} = \frac{6+8}{15} = \frac{14}{15}$$ 46. Next: $$\frac{6}{7} + \frac{8}{7} = \frac{6+8}{7} = \frac{14}{7} = 2$$ 47. Next: $$\frac{10}{16} + \frac{4}{16} = \frac{10+4}{16} = \frac{14}{16} = \frac{7}{8}$$ 48. Next: $$\frac{2}{24} + \frac{10}{24} = \frac{2+10}{24} = \frac{12}{24} = \frac{1}{2}$$ 49. Next: $$\frac{9}{26} + \frac{4}{26} = \frac{9+4}{26} = \frac{13}{26} = \frac{1}{2}$$ 50. Next: $$\frac{6}{9} + \frac{2}{9} = \frac{6+2}{9} = \frac{8}{9}$$ 51. Next: $$\frac{4}{11} + \frac{9}{11} = \frac{4+9}{11} = \frac{13}{11}$$ 52. Next: $$\frac{7}{21} + \frac{5}{21} = \frac{7+5}{21} = \frac{12}{21} = \frac{4}{7}$$ 53. Next: $$\frac{3}{9} + \frac{8}{9} = \frac{3+8}{9} = \frac{11}{9}$$ 54. Last: $$\frac{9}{28} + \frac{9}{28} = \frac{9+9}{28} = \frac{18}{28} = \frac{9}{14}$$ Final answers for each pair in order: 14/15, 13/16, 7/10, 5/6, 2/3, 3/5, 9/10, 5/13, 9/10, 25/18, 11/12, 9/13, 121/60, 1, 1/2, 13/10, 2, 3/5, 7/8, 2/3, 4/5, 5/9, 5/4, 3/2, 5/8, 9/14, 13/8, 2/3, 15/28, 11/13, 13/15, 5/3, 24/19, 6/7, 11/17, 7/16, 9/8, 13/12, 25/23, 1/2, 14/15, 2, 7/8, 1/2, 1/2, 8/9, 13/11, 4/7, 11/9, 9/14