1. Найдите значение выражения: 1) 9 1/4 · 8 − 3 2/3 · 4 1/2 − 10 4/5 · 4 7/12; 2) 1 1/22 · 3 2/3 − (2 5/6 + 3 5/6 · 7/23) · 3/5; 3) (3 1/4 + 2 1/6) : 2 3/5 − 2/3 : 4/9; 4) (5,07 : 1/20 − 23,4 : 13/50) · 1/4 + 0,074 · 1/2; 5) (−31,7 : 63,4 − 23,4 : (−11,7)) · (−2,4); 6) (−1,2 + 4,32 : (−1,8)) : (−0,001) · (−0,3); 7) (7/16 − (−5/24)) : (−1 15/16); 8) (10/21 − 25/28) : (−11/14 + 24/35); 9) −2 2/3 + 2 1/3 · (−15 3/7 − (−4,8) : 4/15).

1. Преобразуем смешанные числа: \(9\frac14=\frac{37}{4}\), \(3\frac23=\frac{11}{3}\), \(4\frac12=\frac92\), \(10\frac45=\frac{54}{5}\), \(4\frac7{12}=\frac{55}{12}\).

   \(\frac{37}{4}\cdot8-\frac{11}{3}\cdot\frac92-\frac{54}{5}\cdot\frac{55}{12}=74-\frac{33}{2}-\frac{99}{2}=74-66=8\).

2. \(1\frac1{22}=\frac{23}{22}\), \(3\frac23=\frac{11}{3}\), \(2\frac56=\frac{17}{6}\), \(3\frac56=\frac{23}{6}\).

   \(\frac{23}{22}\cdot\frac{11}{3}-\left(\frac{17}{6}+\frac{23}{6}\cdot\frac7{23}\right)\cdot\frac35=\frac{23}{6}-\left(\frac{17}{6}+\frac76\right)\cdot\frac35=\frac{23}{6}-4\cdot\frac35=\frac{23}{6}-\frac{18}{15}=\frac{97}{30}=3\frac7{30}\).

3. \(3\frac14+2\frac16=\frac{13}{4}+\frac{13}{6}=\frac{65}{12}\).

   \(\frac{65}{12}:\frac{13}{5}-\frac23:\frac49=\frac{65}{12}\cdot\frac5{13}-\frac23\cdot\frac94=\frac{25}{12}-\frac32=\frac7{12}\).

4. \(5{,}07:\frac1{20}=101{,}4\), \(23{,}4:\frac{13}{50}=90\).

   \((101{,}4-90)\cdot\frac14+0{,}074\cdot\frac12=11{,}4\cdot\frac14+0{,}037=2{,}85+0{,}037=2{,}887\).

5. \(-31{,}7:63{,}4=-0{,}5\), а \(23{,}4:(-11{,}7)=-2\).

   \((-0{,}5-(-2))\cdot(-2{,}4)=1{,}5\cdot(-2{,}4)=-3{,}6\).

6. \(4{,}32:(-1{,}8)=-2{,}4\), поэтому \((-1{,}2-2{,}4):(-0{,}001)\cdot(-0{,}3)=(-3{,}6):(-0{,}001)\cdot(-0{,}3)=3600\cdot(-0{,}3)=-1080\).

7. \(\frac7{16}+\frac5{24}=\frac{21}{48}+\frac{10}{48}=\frac{31}{48}\), \(-1\frac{15}{16}=-\frac{31}{16}\).

   \(\frac{31}{48}:\left(-\frac{31}{16}\right)=-\frac{1}{3}\).

8. \(\frac{10}{21}-\frac{25}{28}=\frac{40}{84}-\frac{75}{84}=-\frac{35}{84}=-\frac5{12}\).

   \(-\frac{11}{14}+\frac{24}{35}=-\frac{55}{70}+\frac{48}{70}=-\frac7{70}=-\frac1{10}\).

   \((-\frac5{12}):(-\frac1{10})=\frac{25}{6}=4\frac16\).

9. \((-4{,}8):\frac4{15}=-18\), поэтому скобки равны \(-15\frac37-(-18)=\frac{45}{7}\).

   \(-2\frac23+2\frac13\cdot\frac{45}{7}=-\frac83+\frac73\cdot\frac{45}{7}=-\frac83+15=\frac{37}{3}=12\frac13\).

Ответ: 1) 8; 2) \(3\frac7{30}\); 3) \(\frac7{12}\); 4) 2,887; 5) −3,6; 6) −1080; 7) −\(\frac13\); 8) \(4\frac16\); 9) \(12\frac13\).