1. The problem is to find the sum of two fractions. 2. The formula to add fractions is $$\frac{a}{b} + \frac{c}{d} = \frac{ad + bc}{bd}$$ where $a$, $b$, $c$, and $d$ are integers and $b, d \neq 0$. 3. Important rule: To add fractions, they must have a common denominator. If they don't, find the least common denominator (LCD) and convert each fraction. 4. Example 1: $$\frac{1}{2} + \frac{1}{3}$$ - LCD of 2 and 3 is 6. - Convert: $$\frac{1}{2} = \frac{3}{6}$$ and $$\frac{1}{3} = \frac{2}{6}$$ - Add: $$\frac{3}{6} + \frac{2}{6} = \frac{5}{6}$$ 5. Example 2: $$\frac{3}{4} + \frac{2}{5}$$ - LCD of 4 and 5 is 20. - Convert: $$\frac{3}{4} = \frac{15}{20}$$ and $$\frac{2}{5} = \frac{8}{20}$$ - Add: $$\frac{15}{20} + \frac{8}{20} = \frac{23}{20} = 1 \frac{3}{20}$$ 6. Example 3: $$\frac{5}{6} + \frac{1}{2}$$ - LCD of 6 and 2 is 6. - Convert: $$\frac{1}{2} = \frac{3}{6}$$ - Add: $$\frac{5}{6} + \frac{3}{6} = \frac{8}{6} = 1 \frac{2}{6} = 1 \frac{1}{3}$$ 7. Example 4: $$\frac{7}{8} + \frac{1}{4}$$ - LCD of 8 and 4 is 8. - Convert: $$\frac{1}{4} = \frac{2}{8}$$ - Add: $$\frac{7}{8} + \frac{2}{8} = \frac{9}{8} = 1 \frac{1}{8}$$ 8. Example 5: $$\frac{2}{3} + \frac{3}{9}$$ - LCD of 3 and 9 is 9. - Convert: $$\frac{2}{3} = \frac{6}{9}$$ - Add: $$\frac{6}{9} + \frac{3}{9} = \frac{9}{9} = 1$$ 9. Example 6: $$\frac{4}{5} + \frac{1}{10}$$ - LCD of 5 and 10 is 10. - Convert: $$\frac{4}{5} = \frac{8}{10}$$ - Add: $$\frac{8}{10} + \frac{1}{10} = \frac{9}{10}$$ 10. Example 7: $$\frac{3}{7} + \frac{2}{14}$$ - LCD of 7 and 14 is 14. - Convert: $$\frac{3}{7} = \frac{6}{14}$$ - Add: $$\frac{6}{14} + \frac{2}{14} = \frac{8}{14} = \frac{4}{7}$$ 11. Example 8: $$\frac{1}{6} + \frac{1}{3}$$ - LCD of 6 and 3 is 6. - Convert: $$\frac{1}{3} = \frac{2}{6}$$ - Add: $$\frac{1}{6} + \frac{2}{6} = \frac{3}{6} = \frac{1}{2}$$ 12. Example 9: $$\frac{5}{12} + \frac{1}{4}$$ - LCD of 12 and 4 is 12. - Convert: $$\frac{1}{4} = \frac{3}{12}$$ - Add: $$\frac{5}{12} + \frac{3}{12} = \frac{8}{12} = \frac{2}{3}$$ 13. Example 10: $$\frac{7}{9} + \frac{2}{3}$$ - LCD of 9 and 3 is 9. - Convert: $$\frac{2}{3} = \frac{6}{9}$$ - Add: $$\frac{7}{9} + \frac{6}{9} = \frac{13}{9} = 1 \frac{4}{9}$$ 14. Example 11: $$\frac{1}{5} + \frac{3}{10}$$ - LCD of 5 and 10 is 10. - Convert: $$\frac{1}{5} = \frac{2}{10}$$ - Add: $$\frac{2}{10} + \frac{3}{10} = \frac{5}{10} = \frac{1}{2}$$ 15. Example 12: $$\frac{2}{7} + \frac{3}{14}$$ - LCD of 7 and 14 is 14. - Convert: $$\frac{2}{7} = \frac{4}{14}$$ - Add: $$\frac{4}{14} + \frac{3}{14} = \frac{7}{14} = \frac{1}{2}$$ 16. Example 13: $$\frac{3}{8} + \frac{1}{2}$$ - LCD of 8 and 2 is 8. - Convert: $$\frac{1}{2} = \frac{4}{8}$$ - Add: $$\frac{3}{8} + \frac{4}{8} = \frac{7}{8}$$ 17. Example 14: $$\frac{5}{6} + \frac{1}{3}$$ - LCD of 6 and 3 is 6. - Convert: $$\frac{1}{3} = \frac{2}{6}$$ - Add: $$\frac{5}{6} + \frac{2}{6} = \frac{7}{6} = 1 \frac{1}{6}$$ 18. Example 15: $$\frac{4}{9} + \frac{5}{18}$$ - LCD of 9 and 18 is 18. - Convert: $$\frac{4}{9} = \frac{8}{18}$$ - Add: $$\frac{8}{18} + \frac{5}{18} = \frac{13}{18}$$ 19. Example 16: $$\frac{1}{3} + \frac{1}{6}$$ - LCD of 3 and 6 is 6. - Convert: $$\frac{1}{3} = \frac{2}{6}$$ - Add: $$\frac{2}{6} + \frac{1}{6} = \frac{3}{6} = \frac{1}{2}$$ 20. Example 17: $$\frac{7}{10} + \frac{1}{5}$$ - LCD of 10 and 5 is 10. - Convert: $$\frac{1}{5} = \frac{2}{10}$$ - Add: $$\frac{7}{10} + \frac{2}{10} = \frac{9}{10}$$ 21. Example 18: $$\frac{3}{4} + \frac{1}{8}$$ - LCD of 4 and 8 is 8. - Convert: $$\frac{3}{4} = \frac{6}{8}$$ - Add: $$\frac{6}{8} + \frac{1}{8} = \frac{7}{8}$$ 22. Example 19: $$\frac{2}{5} + \frac{3}{10}$$ - LCD of 5 and 10 is 10. - Convert: $$\frac{2}{5} = \frac{4}{10}$$ - Add: $$\frac{4}{10} + \frac{3}{10} = \frac{7}{10}$$ 23. Example 20: $$\frac{1}{2} + \frac{1}{4}$$ - LCD of 2 and 4 is 4. - Convert: $$\frac{1}{2} = \frac{2}{4}$$ - Add: $$\frac{2}{4} + \frac{1}{4} = \frac{3}{4}$$ 24. Example 21: $$\frac{5}{8} + \frac{1}{16}$$ - LCD of 8 and 16 is 16. - Convert: $$\frac{5}{8} = \frac{10}{16}$$ - Add: $$\frac{10}{16} + \frac{1}{16} = \frac{11}{16}$$ 25. Example 22: $$\frac{3}{10} + \frac{2}{5}$$ - LCD of 10 and 5 is 10. - Convert: $$\frac{2}{5} = \frac{4}{10}$$ - Add: $$\frac{3}{10} + \frac{4}{10} = \frac{7}{10}$$ 26. Example 23: $$\frac{1}{7} + \frac{2}{14}$$ - LCD of 7 and 14 is 14. - Convert: $$\frac{1}{7} = \frac{2}{14}$$ - Add: $$\frac{2}{14} + \frac{2}{14} = \frac{4}{14} = \frac{2}{7}$$ 27. Example 24: $$\frac{4}{5} + \frac{3}{10}$$ - LCD of 5 and 10 is 10. - Convert: $$\frac{4}{5} = \frac{8}{10}$$ - Add: $$\frac{8}{10} + \frac{3}{10} = \frac{11}{10} = 1 \frac{1}{10}$$ 28. Example 25: $$\frac{2}{3} + \frac{1}{6}$$ - LCD of 3 and 6 is 6. - Convert: $$\frac{2}{3} = \frac{4}{6}$$ - Add: $$\frac{4}{6} + \frac{1}{6} = \frac{5}{6}$$ 29. Example 26: $$\frac{3}{5} + \frac{1}{10}$$ - LCD of 5 and 10 is 10. - Convert: $$\frac{3}{5} = \frac{6}{10}$$ - Add: $$\frac{6}{10} + \frac{1}{10} = \frac{7}{10}$$ 30. Example 27: $$\frac{1}{4} + \frac{1}{8}$$ - LCD of 4 and 8 is 8. - Convert: $$\frac{1}{4} = \frac{2}{8}$$ - Add: $$\frac{2}{8} + \frac{1}{8} = \frac{3}{8}$$ This completes 30 fraction sums with detailed steps and explanations.