Задание 4. Вычислите, используя свойства арифметики: 1) (14/20 + 2 15/27) · 27; 2) (2 1/2 − 12/15) · 1/34; 3) (2 4/10 + 1 13/20) · 4/9; 4) (8/16 − 3 3/18) · 12; 5) (1 3/20 + 2 7/10) · 3/11; 6) 1 8/16 : (4 13/14 + 3/7); 7) 1 17/34 : (8 1/6 + 2 6/24); 8) 2 11/36 : (1 3/27 + 3 10/20); 9) 2 3/5 : (1 12/30 − 1 10/27); 10) 18 1/5 · (2 12/30 − 2 5/6).

1. \((\frac{14}{20}+2\frac{15}{27})\cdot27=(\frac7{10}+2\frac59)\cdot27=\frac{149}{10}\cdot27=402\frac3{10}\).
2. \((2\frac12-\frac{12}{15})\cdot\frac1{34}=(\frac52-\frac45)\cdot\frac1{34}=\frac{17}{10}\cdot\frac1{34}=\frac1{20}\).
3. \((2\frac4{10}+1\frac{13}{20})\cdot\frac49=(2\frac25+1\frac{13}{20})\cdot\frac49=\frac{81}{20}\cdot\frac49=\frac95\).
4. \((\frac8{16}-3\frac3{18})\cdot12=(\frac12-3\frac16)\cdot12=-\frac83\cdot12=-32\).
5. \((1\frac3{20}+2\frac7{10})\cdot\frac3{11}=(1\frac3{20}+2\frac{14}{20})\cdot\frac3{11}=\frac{77}{20}\cdot\frac3{11}=\frac{21}{20}=1\frac1{20}\).
6. \(1\frac8{16}:(4\frac{13}{14}+\frac37)=\frac32:(4\frac{19}{14})=\frac32:\frac{75}{14}=\frac7{25}\).
7. \(1\frac{17}{34}:(8\frac16+2\frac6{24})=\frac32:(8\frac16+2\frac14)=\frac32:\frac{125}{12}=\frac{18}{125}\).
8. \(2\frac{11}{36}:(1\frac3{27}+3\frac{10}{20})=\frac{83}{36}:(1\frac19+3\frac12)=\frac{83}{36}:\frac{83}{18}=\frac12\).
9. \(2\frac35:(1\frac{12}{30}-1\frac{10}{27})=\frac{13}{5}:(1\frac25-1\frac{10}{27})=\frac{13}{5}:\frac{8}{135}=\frac{351}{8}=43\frac78\).
10. \(18\frac15\cdot(2\frac{12}{30}-2\frac56)=\frac{91}{5}\cdot(2\frac25-2\frac56)=\frac{91}{5}\cdot(-\frac{13}{30})=-\frac{1183}{150}=-7\frac{133}{150}\).

Ответ: 1) 402 3/10; 2) 1/20; 3) 9/5; 4) −32; 5) 1 1/20; 6) 7/25; 7) 18/125; 8) 1/2; 9) 43 7/8; 10) −7 133/150.