Вопрос:

Найдите значение выражения: 1) 18·(1/9)^2 − 20·1/9; 2) 2/25 + 1/4; 3) 3/4 − 9/8; 4) 1/(1/30 + 1/42); 5) (1 11/16 − 3 7/8)·4; 6) (5/6 + 7/15)·3; 7) 1,5/(1 + 1/5); 8) 1/4 + 37/20; 9) 1/10 − 35/50; 10) 9/5 : 2/3; 11) 6/5 : 4/11; 12) 6/(5·4).

Ответ:

  1. \(18\cdot\left(\frac{1}{9}\right)^2-20\cdot\frac{1}{9}=18\cdot\frac{1}{81}-\frac{20}{9}=\frac{2}{9}-\frac{20}{9}=-2\).
  2. \(\frac{2}{25}+\frac{1}{4}=\frac{8}{100}+\frac{25}{100}=\frac{33}{100}\).
  3. \(\frac{3}{4}-\frac{9}{8}=\frac{6}{8}-\frac{9}{8}=-\frac{3}{8}\).
  4. \(\frac{1}{\frac{1}{30}+\frac{1}{42}}=\frac{1}{\frac{7}{210}+\frac{5}{210}}=\frac{1}{\frac{12}{210}}=\frac{35}{2}\).
  5. \(\left(1\frac{11}{16}-3\frac{7}{8}\right)\cdot4=\left(\frac{27}{16}-\frac{62}{16}\right)\cdot4=-\frac{35}{16}\cdot4=-\frac{35}{4}\).
  6. \(\left(\frac{5}{6}+\frac{7}{15}\right)\cdot3=\left(\frac{25}{30}+\frac{14}{30}\right)\cdot3=\frac{39}{30}\cdot3=\frac{39}{10}\).
  7. \(\frac{1.5}{1+\frac{1}{5}}=\frac{\frac{3}{2}}{\frac{6}{5}}=\frac{3}{2}\cdot\frac{5}{6}=\frac{5}{4}\).
  8. \(\frac{1}{4}+\frac{37}{20}=\frac{5}{20}+\frac{37}{20}=\frac{42}{20}=\frac{21}{10}\).
  9. \(\frac{1}{10}-\frac{35}{50}=\frac{5}{50}-\frac{35}{50}=-\frac{30}{50}=-\frac{3}{5}\).
  10. \(\frac{9}{5}:\frac{2}{3}=\frac{9}{5}\cdot\frac{3}{2}=\frac{27}{10}\).
  11. \(\frac{6}{5}:\frac{4}{11}=\frac{6}{5}\cdot\frac{11}{4}=\frac{33}{10}\).
  12. \(\frac{6}{5\cdot4}=\frac{6}{20}=\frac{3}{10}\).

Ответ: 1) −2; 2) \(\frac{33}{100}\); 3) \(-\frac{3}{8}\); 4) \(\frac{35}{2}\); 5) \(-\frac{35}{4}\); 6) \(\frac{39}{10}\); 7) \(\frac{5}{4}\); 8) \(\frac{21}{10}\); 9) \(-\frac{3}{5}\); 10) \(\frac{27}{10}\); 11) \(\frac{33}{10}\); 12) \(\frac{3}{10}\).