1. Stating the problem: We will add or simplify each set of fractions provided. 2. For $\frac{9}{4} + \frac{10}{4} + \frac{8}{6}$: - First, combine $\frac{9}{4} + \frac{10}{4} = \frac{19}{4}$ since they have the same denominator. - Find common denominator for $\frac{19}{4}$ and $\frac{8}{6}$. The least common denominator (LCD) is 12. - Convert: $\frac{19}{4} = \frac{57}{12}$ and $\frac{8}{6} = \frac{16}{12}$. - Add: $\frac{57}{12} + \frac{16}{12} = \frac{73}{12}$. 3. For $\frac{5}{4} + \frac{5}{12} + \frac{7}{3}$: - The LCD for 4, 12, and 3 is 12. - Convert each fraction: $\frac{5}{4} = \frac{15}{12}$, $\frac{5}{12}$ stays, $\frac{7}{3} = \frac{28}{12}$. - Add: $15/12 + 5/12 + 28/12 = 48/12 = 4$. 4. For $\frac{6}{4} + \frac{5}{5} + \frac{7}{2}$: - Simplify $\frac{5}{5} = 1$. - LCD for 4 and 2 is 4. - Convert $\frac{7}{2} = \frac{14}{4}$. - Sum: $\frac{6}{4} + 1 + \frac{14}{4} = \frac{6}{4} + \frac{14}{4} + 1 = \frac{20}{4} + 1 = 5 + 1 = 6$. 5. For $\frac{1}{4} = \frac{14}{3} + \frac{13}{20} + \frac{9}{12}$: - This appears to be an equation rather than addition. - Sum right side with LCD 60 (3,20,12): - $\frac{14}{3} = \frac{280}{60}$, $\frac{13}{20} = \frac{39}{60}$, $\frac{9}{12} = \frac{45}{60}$. - Sum: $280/60 + 39/60 + 45/60 = 364/60 = \frac{91}{15}$. - Compare left side $\frac{1}{4} = \frac{15}{60}$ to $\frac{364}{60}$. Not equal. 6. For $-\frac{4}{3} + \frac{20}{12}$: - Convert $\frac{20}{12} = \frac{5}{3}$. - Sum: $-\frac{4}{3} + \frac{5}{3} = \frac{1}{3}$. 7. For $-1 - \frac{5}{2}$: - Convert $-1 = -\frac{2}{2}$. - Sum: $-\frac{2}{2} - \frac{5}{2} = -\frac{7}{2}$. 8. For $\frac{9}{8}$ (single fraction), answer is $\frac{9}{8}$. 9. For $\frac{2}{6} + \frac{1}{3}$: - Simplify $\frac{2}{6} = \frac{1}{3}$. - Sum: $\frac{1}{3} + \frac{1}{3} = \frac{2}{3}$. 10. For $\frac{1}{20}$ single fraction, answer is $\frac{1}{20}$. [Second set] 11. For $\frac{6}{4} + \frac{10}{4} + \frac{8}{6}$: - Sum $\frac{6}{4} + \frac{10}{4} = \frac{16}{4} = 4$. - Convert $\frac{8}{6} = \frac{4}{3}$. - Convert to common denominator 12: $4 = \frac{48}{12}$, $\frac{4}{3} = \frac{16}{12}$. - Sum $\frac{48}{12} + \frac{16}{12} = \frac{64}{12} = \frac{16}{3}$. 12. For $\frac{5}{5} + \frac{5}{6} + \frac{8}{8}$: - Simplify $\frac{5}{5} = 1$ and $\frac{8}{8} = 1$. - Sum $1 + \frac{5}{6} + 1 = 2 + \frac{5}{6} = \frac{12}{6} + \frac{5}{6} = \frac{17}{6}$. 13. For $\frac{6}{1} + \frac{5}{5} + \frac{7}{7}$: - Simplify $\frac{5}{5} = 1$, $\frac{7}{7} =1$. - Sum: $6 + 1 + 1 = 8$. 14. For $\frac{4}{3} + \frac{3}{2} + \frac{3}{3}$: - Simplify $\frac{3}{3} = 1$. - LCD of 3 and 2 is 6. - Convert: $\frac{4}{3} = \frac{8}{6}$, $\frac{3}{2} = \frac{9}{6}$. - Sum: $\frac{8}{6} + \frac{9}{6} + 1 = \frac{17}{6} + \frac{6}{6} = \frac{23}{6}$. 15. For $\frac{13}{20} + \frac{9}{12}$: - LCD 60. - Convert: $\frac{13}{20} = \frac{39}{60}$, $\frac{9}{12} = \frac{45}{60}$. - Sum: $\frac{84}{60} = \frac{7}{5}$. 16. For $7 + \frac{5}{2}$: - Convert $7 = \frac{14}{2}$. - Sum: $\frac{14}{2} + \frac{5}{2} = \frac{19}{2}$. 17. For $\frac{5}{2} + \frac{7}{5}$: - LCD 10. - Convert: $\frac{5}{2} = \frac{25}{10}$, $\frac{7}{5} = \frac{14}{10}$. - Sum: $\frac{39}{10}$. 18. For $2 + \frac{1}{5}$: - Convert $2 = \frac{10}{5}$. - Sum: $\frac{10}{5} + \frac{1}{5} = \frac{11}{5}$. 19. For $\frac{2}{0}$ (undefined), $\frac{1}{4}$, $\frac{1}{10}$: - $\frac{2}{0}$ is undefined. - Remaining fractions stay as is. Final answers summarized: 1) $\frac{73}{12}$ 2) $4$ 3) $6$ 4) No equality (left $\neq$ right) 5) $\frac{1}{3}$ 6) $-\frac{7}{2}$ 7) $\frac{9}{8}$ 8) $\frac{2}{3}$ 9) $\frac{1}{20}$ 10) $\frac{16}{3}$ 11) $\frac{17}{6}$ 12) $8$ 13) $\frac{23}{6}$ 14) $\frac{7}{5}$ 15) $\frac{19}{2}$ 16) $\frac{39}{10}$ 17) $\frac{11}{5}$ 18) $\frac{1}{4}$ and $\frac{1}{10}$ (ignoring undefined $\frac{2}{0}$).