№5 Выполните вычитание: а) \(\frac{6}{7}\) - \(\frac{9}{14}\); б) \(\frac{9}{20}\) - \(\frac{5}{12}\); в) \(\frac{5}{9}\) - \(\frac{3}{8}\)

Чтобы вычесть дроби, нужно привести их к общему знаменателю и вычесть числители.

а) \(\frac{6}{7}\) - \(\frac{9}{14}\)
НОК(7, 14) = 14
\(\frac{6}{7}\) = \(\frac{6 \cdot 2}{7 \cdot 2}\) = \(\frac{12}{14}\)
\(\frac{12}{14}\) - \(\frac{9}{14}\) = \(\frac{12 - 9}{14}\) = \(\frac{3}{14}\)

б) \(\frac{9}{20}\) - \(\frac{5}{12}\)
НОК(20, 12) = 60
\(\frac{9}{20}\) = \(\frac{9 \cdot 3}{20 \cdot 3}\) = \(\frac{27}{60}\)
\(\frac{5}{12}\) = \(\frac{5 \cdot 5}{12 \cdot 5}\) = \(\frac{25}{60}\)
\(\frac{27}{60}\) - \(\frac{25}{60}\) = \(\frac{27 - 25}{60}\) = \(\frac{2}{60}\) = \(\frac{1}{30}\)

в) \(\frac{5}{9}\) - \(\frac{3}{8}\)
НОК(9, 8) = 72
\(\frac{5}{9}\) = \(\frac{5 \cdot 8}{9 \cdot 8}\) = \(\frac{40}{72}\)
\(\frac{3}{8}\) = \(\frac{3 \cdot 9}{8 \cdot 9}\) = \(\frac{27}{72}\)
\(\frac{40}{72}\) - \(\frac{27}{72}\) = \(\frac{40 - 27}{72}\) = \(\frac{13}{72}\)

Ответ:
а) \(\frac{3}{14}\); б) \(\frac{1}{30}\); в) \(\frac{13}{72}\)