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

1. \(\left(\frac{14}{20}+2\frac{15}{27}\right)\cdot27=\left(\frac7{10}+2\frac59\right)\cdot27=\frac{293}{90}\cdot27=87\frac9{10}\).
2. \(\left(2\frac12-\frac{12}{15}\right)\cdot\frac1{34}=\left(\frac52-\frac45\right)\cdot\frac1{34}=\frac{17}{10}\cdot\frac1{34}=\frac1{20}\).
3. \(1\frac8{16}:\left(4\frac{13}{14}+\frac37\right)=\frac32:\left(4\frac{13}{14}+\frac6{14}\right)=\frac32:\frac{75}{14}=\frac7{25}\).
4. \(1\frac{17}{34}:\left(8\frac16+2\frac6{24}\right)=\frac32:\left(8\frac16+\frac12\right)=\frac32:\frac{26}{3}=\frac9{52}\).

Ответ: 1) \(87\frac9{10}\); 2) \(\frac1{20}\); 6) \(\frac7{25}\); 7) \(\frac9{52}\).