Question - Calculating Fractions

a) \frac{2}{3} + \frac{7}{3} - \frac{1}{4} = \frac{2 + 7 \cdot 1 - \frac{3}{4}}{3} = \frac{9 - 0.75}{3} = \frac{8.25}{3} = \frac{33}{12} = \frac{11}{4}

b) 2 \frac{1}{3} + \frac{1}{2} - \frac{1}{5} - \frac{1}{15} = \frac{7}{3} + \frac{1}{2} - \frac{1}{5} - \frac{1}{15} = \frac{70 + 15 - 6 - 2}{30} = \frac{77}{30}

c) \frac{13}{36} - \frac{5}{4} - \frac{2}{9} = \frac{13}{36} - \frac{45}{36} - \frac{8}{36} = \frac{13 - 45 - 8}{36} = \frac{-40}{36} = -\frac{10}{9}

d) 3 + \left( -\frac{5}{4} \right) + 2 \frac{3}{4} = 3 - \frac{5}{4} + \frac{11}{4} = 3 + \frac{6}{4} = 3 + \frac{3}{2} = \frac{6 + 3}{2} = \frac{9}{2}

e) \frac{5}{6} - \frac{2}{9} = \frac{15}{18} - \frac{4}{18} = \frac{11}{18}

f) 7 \frac{1}{4} - \left( 4 - \frac{1}{2} \right) = \frac{29}{4} - \left( \frac{8}{2} - \frac{1}{2} \right) = \frac{29}{4} - \frac{7}{2} = \frac{29 - 14}{4} = \frac{15}{4}