18. Примените распределительный закон и сократите дробь: а) \(\frac{5 \cdot 16 - 5 \cdot 7}{15}\); б) \(\frac{4 \cdot 15 - 4 \cdot 7}{12}\); в) \(\frac{9 \cdot 13 + 9 \cdot 4}{15 \cdot 17}\); г) \(\frac{12 \cdot 13}{8 \cdot 11 + 8 \cdot 2}\); д) \(\frac{14 \cdot 7 - 5 \cdot 14}{21 \cdot 8 + 21 \cdot 4}\); е) \(\frac{24 \cdot 2 + 4 \cdot 24}{36 \cdot 9 - 7 \cdot 36}\)

а) \(\frac{5 \cdot 16 - 5 \cdot 7}{15}\) = \(\frac{5 \cdot (16 - 7)}{15}\) = \(\frac{5 \cdot 9}{15}\) = \(\frac{45}{15}\) = 3
б) \(\frac{4 \cdot 15 - 4 \cdot 7}{12}\) = \(\frac{4 \cdot (15 - 7)}{12}\) = \(\frac{4 \cdot 8}{12}\) = \(\frac{32}{12}\) = \(\frac{8}{3}\)
в) \(\frac{9 \cdot 13 + 9 \cdot 4}{15 \cdot 17}\) = \(\frac{9 \cdot (13 + 4)}{15 \cdot 17}\) = \(\frac{9 \cdot 17}{15 \cdot 17}\) = \(\frac{9}{15}\) = \(\frac{3}{5}\)
г) \(\frac{12 \cdot 13}{8 \cdot 11 + 8 \cdot 2}\) = \(\frac{12 \cdot 13}{8 \cdot (11 + 2)}\) = \(\frac{12 \cdot 13}{8 \cdot 13}\) = \(\frac{12}{8}\) = \(\frac{3}{2}\)
д) \(\frac{14 \cdot 7 - 5 \cdot 14}{21 \cdot 8 + 21 \cdot 4}\) = \(\frac{14 \cdot (7 - 5)}{21 \cdot (8 + 4)}\) = \(\frac{14 \cdot 2}{21 \cdot 12}\) = \(\frac{28}{252}\) = \(\frac{2 \cdot 14}{18 \cdot 14}\) = \(\frac{2}{18}\) = \(\frac{1}{9}\)
е) \(\frac{24 \cdot 2 + 4 \cdot 24}{36 \cdot 9 - 7 \cdot 36}\) = \(\frac{24 \cdot (2 + 4)}{36 \cdot (9 - 7)}\) = \(\frac{24 \cdot 6}{36 \cdot 2}\) = \(\frac{144}{72}\) = 2