Вопрос:

Вычислить: 1) −3 2/15 + 4 1/5; 2) −2 2/3 − 5/12; 3) −8 2/9 + 4; 4) 3 5/12 − 7; 5) 4 5/6 − 2 7/8; 6) 15/17 · (−34/45); 7) −3 1/9 · (−2 1/7); 8) 6 3/5 · (−10); 9) 4/7 : (−4/9); 10) −11 2/5 : 3 4/5; 11) −16/17 : (−8); 12) −12 : 1 3/7.

Ответ:

  1. \( -3\frac{2}{15}+4\frac{1}{5}=-\frac{47}{15}+\frac{63}{15}=\frac{16}{15} \).
  2. \( -2\frac{2}{3}-\frac{5}{12}=-\frac{32}{12}-\frac{5}{12}=-\frac{37}{12} \).
  3. \( -8\frac{2}{9}+4=-\frac{74}{9}+\frac{36}{9}=-\frac{38}{9} \).
  4. \( 3\frac{5}{12}-7=\frac{41}{12}-\frac{84}{12}=-\frac{43}{12} \).
  5. \( 4\frac{5}{6}-2\frac{7}{8}=\frac{29}{6}-\frac{23}{8}=\frac{116-69}{24}=\frac{47}{24} \).
  6. \( \frac{15}{17}\cdot\left(-\frac{34}{45}\right)=-\frac{2}{3} \).
  7. \( -3\frac{1}{9}\cdot\left(-2\frac{1}{7}\right)=-\frac{28}{9}\cdot\left(-\frac{15}{7}\right)=\frac{20}{3} \).
  8. \( 6\frac{3}{5}\cdot(-10)=\frac{33}{5}\cdot(-10)=-66 \).
  9. \( \frac{4}{7}:\left(-\frac{4}{9}\right)=\frac{4}{7}\cdot\left(-\frac{9}{4}\right)=-\frac{9}{7} \).
  10. \( -11\frac{2}{5}:3\frac{4}{5}=-\frac{57}{5}:\frac{19}{5}=-3 \).
  11. \( -\frac{16}{17}:(-8)=\frac{16}{17}\cdot\frac{1}{8}=\frac{2}{17} \).
  12. \( -12:1\frac{3}{7}=-12:\frac{10}{7}=-12\cdot\frac{7}{10}=-\frac{42}{5} \).

Ответ: 1) \(\frac{16}{15}\); 2) \(-\frac{37}{12}\); 3) \(-\frac{38}{9}\); 4) \(-\frac{43}{12}\); 5) \(\frac{47}{24}\); 6) \(-\frac{2}{3}\); 7) \(\frac{20}{3}\); 8) \(-66\); 9) \(-\frac{9}{7}\); 10) \(-3\); 11) \(\frac{2}{17}\); 12) \(-\frac{42}{5}\).