Вопрос:

Вычислите: 1) (9/10 − 7/15) · 3; 2) (3/4 − 1/6) · 3; 3) (2 1/4 − 1 3/19) · 19; 4) (1/13 − 2 3/4) · 26; 5) (1/5 + 8/15) · 6; 6) (5/22 − 8/11) · 11/5; 7) (9/17 − 11/34) · 17/2; 8) (17/15 − 1/12) · 20/3; 9) (10/13 + 15/4) · 26/5; 10) (5/26 − 3/25) · 13/2.

Ответ:

  1. \((\frac{9}{10}-\frac{7}{15})\cdot3=(\frac{27}{30}-\frac{14}{30})\cdot3=\frac{13}{30}\cdot3=\frac{13}{10}\).
  2. \((\frac{3}{4}-\frac{1}{6})\cdot3=(\frac{9}{12}-\frac{2}{12})\cdot3=\frac{7}{12}\cdot3=\frac{7}{4}\).
  3. \((2\frac{1}{4}-1\frac{3}{19})\cdot19=(\frac{9}{4}-\frac{22}{19})\cdot19=\frac{83}{4}\).
  4. \((\frac{1}{13}-2\frac{3}{4})\cdot26=(\frac{1}{13}-\frac{11}{4})\cdot26=-\frac{139}{2}\).
  5. \((\frac{1}{5}+\frac{8}{15})\cdot6=(\frac{3}{15}+\frac{8}{15})\cdot6=\frac{11}{15}\cdot6=\frac{22}{5}\).
  6. \((\frac{5}{22}-\frac{8}{11})\cdot\frac{11}{5}=(\frac{5}{22}-\frac{16}{22})\cdot\frac{11}{5}=-\frac{1}{2}\cdot\frac{11}{5}=-\frac{11}{10}\).
  7. \((\frac{9}{17}-\frac{11}{34})\cdot\frac{17}{2}=(\frac{18}{34}-\frac{11}{34})\cdot\frac{17}{2}=\frac{7}{34}\cdot\frac{17}{2}=\frac{7}{4}\).
  8. \((\frac{17}{15}-\frac{1}{12})\cdot\frac{20}{3}=(\frac{68}{60}-\frac{5}{60})\cdot\frac{20}{3}=\frac{21}{20}\cdot\frac{20}{3}=7\).
  9. \((\frac{10}{13}+\frac{15}{4})\cdot\frac{26}{5}=(\frac{40}{52}+\frac{195}{52})\cdot\frac{26}{5}=\frac{235}{52}\cdot\frac{26}{5}=\frac{47}{2}\).
  10. \((\frac{5}{26}-\frac{3}{25})\cdot\frac{13}{2}=(\frac{125}{650}-\frac{78}{650})\cdot\frac{13}{2}=\frac{47}{650}\cdot\frac{13}{2}=\frac{47}{100}\).

Ответ: 1) \(\frac{13}{10}\); 2) \(\frac{7}{4}\); 3) \(\frac{83}{4}\); 4) \(-\frac{139}{2}\); 5) \(\frac{22}{5}\); 6) \(-\frac{11}{10}\); 7) \(\frac{7}{4}\); 8) \(7\); 9) \(\frac{47}{2}\); 10) \(\frac{47}{100}\).