Задание №4. Вычислите обыкновенные дроби, а потом сократите: а) (9/14 − 2/7) + 9/35; б) (3/4 − 1/6) + 7/12; в) 7/15 + (8/9 − 5/6); г) (7/18 − 1/6) + 7/9; д) 12/170 + 13/17 − 2/34; е) 15/17 − (1/5 + 1/6).

1. \(\left(\frac{9}{14}-\frac{2}{7}\right)+\frac{9}{35}=\left(\frac{9}{14}-\frac{4}{14}\right)+\frac{9}{35}=\frac{5}{14}+\frac{9}{35}=\frac{25}{70}+\frac{18}{70}=\frac{43}{70}\).
2. \(\left(\frac{3}{4}-\frac{1}{6}\right)+\frac{7}{12}=\left(\frac{9}{12}-\frac{2}{12}\right)+\frac{7}{12}=\frac{7}{12}+\frac{7}{12}=\frac{7}{6}\).
3. \(\frac{7}{15}+\left(\frac{8}{9}-\frac{5}{6}\right)=\frac{7}{15}+\left(\frac{16}{18}-\frac{15}{18}\right)=\frac{7}{15}+\frac{1}{18}=\frac{42}{90}+\frac{5}{90}=\frac{47}{90}\).
4. \(\left(\frac{7}{18}-\frac{1}{6}\right)+\frac{7}{9}=\left(\frac{7}{18}-\frac{3}{18}\right)+\frac{14}{18}=\frac{18}{18}=1\).
5. \(\frac{12}{170}+\frac{13}{17}-\frac{2}{34}=\frac{6}{85}+\frac{65}{85}-\frac{5}{85}=\frac{66}{85}\).
6. \(\frac{15}{17}-\left(\frac{1}{5}+\frac{1}{6}\right)=\frac{15}{17}-\frac{11}{30}=\frac{450}{510}-\frac{187}{510}=\frac{263}{510}\).

Ответ: а) \(\frac{43}{70}\); б) \(\frac{7}{6}\); в) \(\frac{47}{90}\); г) \(1\); д) \(\frac{66}{85}\); е) \(\frac{263}{510}\).