Вопрос:

Вычислите: 1) \(\frac47 a : \frac{16}{23}\), \(a=7\); 2) \(\frac35 a : \frac67\), \(a=5\); 3) \(\frac49 a : \frac1{11}\), \(a=11\); 4) \(\frac{11}{15}a : \frac{10}{11}\), \(a=2\); 5) \(\frac{15}{17}a : \frac7{17}\), \(a=1\); 6) \(\frac3{13}a : \frac5{13}\), \(a=4\); 7) \(\frac59\cdot\frac7{10}a\), \(a=3\); 8) \(\frac13a : \frac49\), \(a=5\); 9) \(\frac8{17}a\cdot\frac{51}{16}\), \(a=2\); 10) \(\frac{51}{50}a : \frac{17}{100}\), \(a=10\); 11) \(\frac7{11}\cdot\frac{121}{126}a\), \(a=5\); 12) \(\frac5{12}a\cdot\frac35\), \(a=4\).

Ответ:

  1. \(\frac47\cdot7:\frac{16}{23}=4\cdot\frac{23}{16}=\frac{23}{4}\).
  2. \(\frac35\cdot5:\frac67=3\cdot\frac76=\frac72\).
  3. \(\frac49\cdot11:\frac1{11}=\frac{44}{9}\cdot11=\frac{484}{9}\).
  4. \(\frac{11}{15}\cdot2:\frac{10}{11}=\frac{22}{15}\cdot\frac{11}{10}=\frac{121}{75}\).
  5. \(\frac{15}{17}:\frac7{17}=\frac{15}{7}\).
  6. \(\frac3{13}\cdot4:\frac5{13}=\frac{12}{13}\cdot\frac{13}{5}=\frac{12}{5}\).
  7. \(\frac59\cdot\frac7{10}\cdot3=\frac{7}{6}\).
  8. \(\frac13\cdot5:\frac49=\frac53\cdot\frac94=\frac{15}{4}\).
  9. \(\frac8{17}\cdot2\cdot\frac{51}{16}=3\).
  10. \(\frac{51}{50}\cdot10:\frac{17}{100}=\frac{51}{5}\cdot\frac{100}{17}=60\).
  11. \(\frac7{11}\cdot\frac{121}{126}\cdot5=\frac{11}{18}\cdot5=\frac{55}{18}\).
  12. \(\frac5{12}\cdot4\cdot\frac35=1\).