Вопрос:

Найдите значение выражения: а) 9 − 3 1/5 · 1 2/3 + 1 1/3; б) 3 2/3 − 7/15 + 4 2/5 · 1/4; в) (3 5/6 − 2 3/4) : 7/12 + 5 1/2; г) 2 2/3 · (2 1/3 + 2 5/12) − 4 4/5; д) 1 4/21 : 5/7 − 2/5 · 5/7; е) 55/48 : (11/16 + 3/32) − 14/15 · 5/7; ж) 3 1/7 · 3/11 + 3/8 : 7/12; з) 2 2/3 : 1 7/9 + 55/84 : (43/63 − 23/36).

Ответ:

  1. а) \(9-\frac{16}{5}\cdot\frac53+\frac43=9-\frac{16}{3}+\frac43=\frac{11}{3}\).
  2. б) \(\frac{11}{3}-\frac7{15}+\frac{22}{5}\cdot\frac14=\frac{55-7}{15}+\frac{11}{10}=\frac{16}{5}+\frac{11}{10}=\frac{43}{10}=4\frac3{10}\).
  3. в) \(\left(\frac{23}{6}-\frac{11}{4}\right):\frac7{12}+\frac{11}{2}=\frac{13}{12}\cdot\frac{12}{7}+\frac{11}{2}=\frac{13}{7}+\frac{11}{2}=\frac{103}{14}=7\frac5{14}\).
  4. г) \(\frac83\left(\frac73+\frac{29}{12}\right)-\frac{24}{5}=\frac83\cdot\frac{19}{4}-\frac{24}{5}=\frac{38}{3}-\frac{24}{5}=\frac{118}{15}=7\frac{13}{15}\).
  5. д) \(\frac{25}{21}:\frac57-\frac25\cdot\frac57=\frac53-\frac27=\frac{29}{21}\).
  6. е) \(\frac{55}{48}:\left(\frac{22}{32}+\frac3{32}\right)-\frac{14}{15}\cdot\frac57=\frac{55}{48}\cdot\frac{32}{25}-\frac23=\frac{11}{15}-\frac23=\frac15\).
  7. ж) \(\frac{22}{7}\cdot\frac3{11}+\frac38:\frac7{12}=\frac67+\frac38\cdot\frac{12}{7}=\frac67+\frac9{14}=\frac{21}{14}=1\frac12\).
  8. з) \(\frac83:\frac{16}{9}+\frac{55}{84}:\left(\frac{43}{63}-\frac{23}{36}\right)=\frac32+\frac{55}{84}:\frac1{252}=\frac32+165=166\frac12\).

Ответ: а) \(\frac{11}{3}\); б) \(4\frac3{10}\); в) \(7\frac5{14}\); г) \(7\frac{13}{15}\); д) \(\frac{29}{21}\); е) \(\frac15\); ж) \(1\frac12\); з) \(166\frac12\).