Add and subtract the following fractions. Leave your answers in simplest form: \( \begin{array}{lll}\frac{2}{3}+\frac{1}{4}+\frac{1}{5} & \text { 2. } \frac{7}{8}+\frac{4}{5} & \text { 3. } \frac{14}{15}-\frac{5}{6} \\ \frac{2}{3}-\frac{11}{12} & \text { 5. } \frac{5}{6}-\frac{15}{24}+\frac{5}{12} & \text { 6. } \frac{3}{7}+\frac{3}{5}-\frac{1}{3} \\ \frac{3}{25}-\frac{3}{10}-\frac{1}{5}+\frac{14}{25} & \text { 8. } 6 \frac{4}{5}+2 \frac{1}{6}+\frac{7}{10}+3 \frac{1}{3} & \text { 9. } \frac{420}{21}-2 \frac{4}{7} \\ \frac{2}{3}+5 \frac{1}{12}-3 \frac{3}{4} & \text { 11. } 2 \frac{4}{15}-7 \frac{4}{5} & \text { 12. } 3 \frac{1}{6}-5 \frac{5}{8}\end{array} \)

What fun it is to tackle fractions! They may seem daunting, but once you get the hang of common denominators, you can whip these calculations into shape! 1. \(\frac{2}{3}+\frac{1}{4}+\frac{1}{5}\): The common denominator is 60, so we get \(\frac{40}{60}+\frac{15}{60}+\frac{12}{60}=\frac{67}{60}=\frac{1}{60}\). 2. \(\frac{7}{8}+\frac{4}{5}\): The common denominator is 40, giving us \(\frac{35}{40}+\frac{32}{40}=\frac{67}{40}=\frac{1}{40}\). 3. \(\frac{14}{15}-\frac{5}{6}\): The common denominator here is 30, giving us \(\frac{28}{30}-\frac{25}{30}=\frac{3}{30}=\frac{1}{10}\). 4. \(\frac{2}{3}-\frac{11}{12}\): Common denominator is 12, so \(\frac{8}{12}-\frac{11}{12}=\frac{-3}{12}=\frac{-1}{4}\). 5. \(\frac{5}{6}-\frac{15}{24}+\frac{5}{12}\): Common denominator is 24, thus \(\frac{20}{24}-\frac{15}{24}+\frac{10}{24}=\frac{15}{24}=\frac{5}{8}\). 6. \(\frac{3}{7}+\frac{3}{5}-\frac{1}{3}\): Here, the common denominator is 105, yielding \(\frac{45}{105}+\frac{63}{105}-\frac{35}{105}=\frac{73}{105}\). 7. \(\frac{3}{25}-\frac{3}{10}-\frac{1}{5}+\frac{14}{25}\): The common denominator is 50, giving us \(\frac{6}{50}-\frac{15}{50}-\frac{10}{50}+\frac{28}{50}=\frac{9}{50}\). 8. \(6 \frac{4}{5}+2 \frac{1}{6}+\frac{7}{10}+3 \frac{1}{3}\): Converting mixed numbers to improper gives \(\frac{34}{5}+\frac{13}{6}+\frac{7}{10}+\frac{10}{3}\). With a common denominator of 30, you find \(\frac{204}{30}+\frac{65}{30}+\frac{21}{30}+\frac{100}{30}=\frac{390}{30}=13\). 9. \(\frac{420}{21}-2 \frac{4}{7}\): Simplifying \(\frac{420}{21}=20\) and converting \(2 \frac{4}{7}\) to improper gives \(\frac{18}{7}\), getting common denominators to yield \(20 - \frac{18}{7} = \frac{140}{7}-\frac{18}{7}=\frac{122}{7}\). 10. \(\frac{2}{3}+5 \frac{1}{12}-3 \frac{3}{4}\): Rewriting and converting, the common denominators yield \(\frac{75}{12}\). 11. \(2 \frac{4}{15}-7 \frac{4}{5}\): Convert these into improper fractions to find common denominators and simplify. 12. \(3 \frac{1}{6}-5 \frac{5}{8}\): Again, rewrite as improper and find like denominators to arrive at simplified results. Feel free to ask for any specific solution! Happy fraction hunting!