Adding and subtracting fractions depends on finding a common denominator. The least common denominator is the least common multiple of the denominators that occur in the computation. Find least common denominators and compute the following additions and subtractions. \( \begin{array}{ll}\text { (a) } \frac{3}{4}+\frac{1}{6} & \text { (b) } \frac{7}{9}+\frac{2}{21} \\ \text { (c) } \frac{8}{9}-\frac{4}{11} & \text { (d) } \frac{9}{20}-\frac{1}{4} \\ \text { (a) } \frac{3}{4}+\frac{1}{6}=\square \\ \text { (Simplify your answer. Type a whole number or fraction.) }\end{array} \)

To find the least common denominator (LCD) for each pair of fractions, we first identify their denominators and then calculate the least common multiple. For part (a) \(\frac{3}{4} + \frac{1}{6}\), the denominators are 4 and 6. The least common multiple of 4 and 6 is 12, making the LCD. Now, we can rewrite the fractions: \(\frac{3}{4} = \frac{9}{12}\) and \(\frac{1}{6} = \frac{2}{12}\). So, \(\frac{3}{4} + \frac{1}{6} = \frac{9}{12} + \frac{2}{12} = \frac{11}{12}\). Moving on to part (b) \(\frac{7}{9} + \frac{2}{21}\), the denominators are 9 and 21. The least common multiple is 63. Rewriting the fractions gives us: \(\frac{7}{9} = \frac{49}{63}\) and \(\frac{2}{21} = \frac{6}{63}\). Thus, \(\frac{7}{9} + \frac{2}{21} = \frac{49}{63} + \frac{6}{63} = \frac{55}{63}\). For part (c) \(\frac{8}{9} - \frac{4}{11}\), 9 and 11 have an LCD of 99. Rewriting yields: \(\frac{8}{9} = \frac{88}{99}\) and \(\frac{4}{11} = \frac{36}{99}\). So, \(\frac{8}{9} - \frac{4}{11} = \frac{88}{99} - \frac{36}{99} = \frac{52}{99}\). Lastly, in part (d) \(\frac{9}{20} - \frac{1}{4}\), the denominators are 20 and 4. The LCD here is 20. Rewriting gives us: \(\frac{9}{20} = \frac{9}{20}\) and \(\frac{1}{4} = \frac{5}{20}\). Therefore, \(\frac{9}{20} - \frac{1}{4} = \frac{9}{20} - \frac{5}{20} = \frac{4}{20} = \frac{1}{5}\) after simplification. So here are your results: (a) \(\frac{3}{4} + \frac{1}{6} = \frac{11}{12}\) (b) \(\frac{7}{9} + \frac{2}{21} = \frac{55}{63}\) (c) \(\frac{8}{9} - \frac{4}{11} = \frac{52}{99}\) (d) \(\frac{9}{20} - \frac{1}{4} = \frac{1}{5}\)