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$\frac{1}{2} + \frac{1}{3} = \frac{3+5}{6} = \frac{5}{6} \\ \frac{2}{3}+ \frac{1}{4}= \frac{4*2+3}{12} = \frac{11}{12} \\ \frac{5}{7}- \frac{1}{6} = \frac{6*5-7}{42} = \frac{23}{42} \\ \frac{1}{8}+ \frac{1}{4}= \frac{2+4}{16} = \frac{6}{16} \\ \frac{1}{4}+ \frac{2}{5}= \frac{5+2*4}{20} = \frac{13}{20} \\ \frac{3}{4}+ \frac{2}{5}= \frac{3*5+2*4}{20} = \frac{23}{20} \\ \frac{3}{4} - \frac{1}{3} = \frac{3*3-4}{12} = \frac{5}{12} \\ \frac{2}{3}- \frac{5}{9}= \frac{2*3-5}{9} = \frac{1}{9}$