№6. Вычислите: а) \((\frac{3}{5} + \frac{1}{2}) \cdot \frac{20}{23}\); б) \(\frac{4}{7} \cdot \frac{21}{16} - \frac{15}{16} : 3\)

а) Решение:

\[(\frac{3}{5} + \frac{1}{2}) \cdot \frac{20}{23} = (\frac{3 \cdot 2}{5 \cdot 2} + \frac{1 \cdot 5}{2 \cdot 5}) \cdot \frac{20}{23} = (\frac{6}{10} + \frac{5}{10}) \cdot \frac{20}{23} = \frac{11}{10} \cdot \frac{20}{23} = \frac{11 \cdot 20}{10 \cdot 23} = \frac{11 \cdot 10 \cdot 2}{10 \cdot 23} = \frac{11 \cdot 2}{23} = \frac{22}{23}\]

б) Решение:

\[\frac{4}{7} \cdot \frac{21}{16} - \frac{15}{16} : 3 = \frac{4 \cdot 21}{7 \cdot 16} - \frac{15}{16} \cdot \frac{1}{3} = \frac{4 \cdot 7 \cdot 3}{7 \cdot 4 \cdot 4} - \frac{15 \cdot 1}{16 \cdot 3} = \frac{3}{4} - \frac{15}{48} = \frac{3}{4} - \frac{15}{16 \cdot 3} = \frac{3}{4} - \frac{5}{16} = \frac{3 \cdot 4}{4 \cdot 4} - \frac{5}{16} = \frac{12}{16} - \frac{5}{16} = \frac{12 - 5}{16} = \frac{7}{16}\]