Fractions Worksheet Find the sum. \( \begin{array}{ll}\text { 1. } \frac{1}{2}+\frac{1}{4}= & \text { 2. } \frac{1}{3}+\frac{5}{7}= \\ \text { 3. } \frac{8}{9}+\frac{1}{3}= & \text { 4. } \frac{5}{12}+\frac{1}{5}= \\ \text { 5. } \frac{1}{6}+\frac{10}{12}= & \text { 6. } \frac{4}{10}+\frac{4}{9}= \\ \text { 7. } \frac{2}{5}+\frac{2}{7}= & \text { 8. } \frac{5}{9}+\frac{4}{6}=\end{array} \)

1. To add \(\frac{1}{2}\) and \(\frac{1}{4}\), we need a common denominator. The least common denominator (LCD) of 2 and 4 is 4. \[ \frac{1}{2} = \frac{2}{4} \] Now, add the fractions: \[ \frac{2}{4} + \frac{1}{4} = \frac{3}{4} \] 2. For \(\frac{1}{3} + \frac{5}{7}\), the LCD of 3 and 7 is 21. \[ \frac{1}{3} = \frac{7}{21}, \quad \frac{5}{7} = \frac{15}{21} \] Add them: \[ \frac{7}{21} + \frac{15}{21} = \frac{22}{21} \] 3. When adding \(\frac{8}{9} + \frac{1}{3}\), the LCD of 9 and 3 is 9. \[ \frac{1}{3} = \frac{3}{9} \] Thus, \[ \frac{8}{9} + \frac{3}{9} = \frac{11}{9} \] 4. For \(\frac{5}{12} + \frac{1}{5}\), the LCD of 12 and 5 is 60. \[ \frac{5}{12} = \frac{25}{60}, \quad \frac{1}{5} = \frac{12}{60} \] Then, \[ \frac{25}{60} + \frac{12}{60} = \frac{37}{60} \] 5. Adding \(\frac{1}{6} + \frac{10}{12}\), first simplify \(\frac{10}{12}\): \[ \frac{10}{12} = \frac{5}{6} \] Now, add the fractions: \[ \frac{1}{6} + \frac{5}{6} = \frac{6}{6} = 1 \] 6. For \(\frac{4}{10} + \frac{4}{9}\), simplify \(\frac{4}{10}\) to \(\frac{2}{5}\) first or use a common denominator. Using a common denominator of 90: \[ \frac{4}{10} = \frac{4 \times 9}{10 \times 9} = \frac{36}{90}, \quad \frac{4}{9} = \frac{4 \times 10}{9 \times 10} = \frac{40}{90} \] Thus, \[ \frac{36}{90} + \frac{40}{90} = \frac{76}{90} \] Simplify by dividing numerator and denominator by 2: \[ \frac{76}{90} = \frac{38}{45} \] 7. To add \(\frac{2}{5} + \frac{2}{7}\), find the LCD of 5 and 7, which is 35. \[ \frac{2}{5} = \frac{14}{35}, \quad \frac{2}{7} = \frac{10}{35} \] Add them: \[ \frac{14}{35} + \frac{10}{35} = \frac{24}{35} \] 8. Finally, for \(\frac{5}{9} + \frac{4}{6}\), first simplify \(\frac{4}{6}\): \[ \frac{4}{6} = \frac{2}{3} \] The LCD of 9 and 3 is 9: \[ \frac{2}{3} = \frac{6}{9} \] Thus, \[ \frac{5}{9} + \frac{6}{9} = \frac{11}{9} \]