Вопрос:

Вычислите: 1) 8/9 − 7/8; 2) 3/28 + 5/14; 3) 9/28 − 2/20; 4) 11/24 − 3/16; 5) 3/14 : 2/21; 6) 1 7/8 : 2 11/32; 7) 3/4 · 5/6; 8) 8/9 · 27/32; 9) 42 · 4/7; 10) 6/35 · 14/15; 11) 3/4 : 2; 12) 3/4 · 2; 13) 2 10/13 : 3 3/26.

Ответ:

  1. \(\frac{8}{9}-\frac{7}{8}=\frac{64-63}{72}=\frac{1}{72}\).
  2. \(\frac{3}{28}+\frac{5}{14}=\frac{3}{28}+\frac{10}{28}=\frac{13}{28}\).
  3. \(\frac{9}{28}-\frac{2}{20}=\frac{9}{28}-\frac{1}{10}=\frac{90-28}{280}=\frac{31}{140}\).
  4. \(\frac{11}{24}-\frac{3}{16}=\frac{22}{48}-\frac{9}{48}=\frac{13}{48}\).
  5. \(\frac{3}{14}:\frac{2}{21}=\frac{3}{14}\cdot\frac{21}{2}=\frac{9}{4}=2\frac{1}{4}\).
  6. \(1\frac{7}{8}:2\frac{11}{32}=\frac{15}{8}:\frac{75}{32}=\frac{15}{8}\cdot\frac{32}{75}=\frac{4}{5}\).
  7. \(\frac{3}{4}\cdot\frac{5}{6}=\frac{15}{24}=\frac{5}{8}\).
  8. \(\frac{8}{9}\cdot\frac{27}{32}=\frac{3}{4}\).
  9. \(42\cdot\frac{4}{7}=6\cdot4=24\).
  10. \(\frac{6}{35}\cdot\frac{14}{15}=\frac{4}{25}\).
  11. \(\frac{3}{4}:2=\frac{3}{4}\cdot\frac{1}{2}=\frac{3}{8}\).
  12. \(\frac{3}{4}\cdot2=\frac{3}{2}=1\frac{1}{2}\).
  13. \(2\frac{10}{13}:3\frac{3}{26}=\frac{36}{13}:\frac{81}{26}=\frac{36}{13}\cdot\frac{26}{81}=\frac{8}{9}\).

Ответ: 1) \(\frac{1}{72}\); 2) \(\frac{13}{28}\); 3) \(\frac{31}{140}\); 4) \(\frac{13}{48}\); 5) \(2\frac{1}{4}\); 6) \(\frac{4}{5}\); 7) \(\frac{5}{8}\); 8) \(\frac{3}{4}\); 9) 24; 10) \(\frac{4}{25}\); 11) \(\frac{3}{8}\); 12) \(1\frac{1}{2}\); 13) \(\frac{8}{9}\).