Вычислить. Сложение и вычитание: 1) (9/14 − 2/7) + 9/35; 2) (3/4 − 1/6) + 7/12; 3) 7/15 + (8/9 − 5/6); 4) (1/3 − 1/13) + 7/26; 5) (1/45 + 1/6) − 1/15.

Question

Вопрос:

Accepted Answer

Приводим к общему знаменателю: \(\left(\frac{9}{14}-\frac{2}{7}\right)+\frac{9}{35}=\frac{9}{14}-\frac{4}{14}+\frac{9}{35}=\frac{5}{14}+\frac{9}{35}=\frac{25}{70}+\frac{18}{70}=\frac{43}{70}\).
\(\left(\frac{3}{4}-\frac{1}{6}\right)+\frac{7}{12}=\frac{9}{12}-\frac{2}{12}+\frac{7}{12}=\frac{14}{12}=\frac{7}{6}\).
\(\frac{7}{15}+\left(\frac{8}{9}-\frac{5}{6}\right)=\frac{7}{15}+\left(\frac{16}{18}-\frac{15}{18}\right)=\frac{7}{15}+\frac{1}{18}=\frac{42}{90}+\frac{5}{90}=\frac{47}{90}\).
\(\left(\frac{1}{3}-\frac{1}{13}\right)+\frac{7}{26}=\frac{10}{39}+\frac{7}{26}=\frac{20}{78}+\frac{21}{78}=\frac{41}{78}\).
\(\left(\frac{1}{45}+\frac{1}{6}\right)-\frac{1}{15}=\frac{2}{90}+\frac{15}{90}-\frac{6}{90}=\frac{11}{90}\).

Ответ: 1) 43/70; 2) 7/6; 3) 47/90; 4) 41/78; 5) 11/90.