3. Вычислите: 1) $$(0,018+0,982):(8\cdot0,5-0,8)$$; 2) $$27,3\cdot5,1\cdot(-2,2):(-0,00019)$$; 3) $$\left(6\frac{8}{15}-4\frac{21}{45}\right)\cdot4,5-2\frac{1}{6}:0,52$$; 4) $$\left(\frac{9}{22}+1\frac{12}{33}\right)\cdot1,32-\frac{8}{13}\cdot0,1625$$.

Пошаговое решение:

• 1) $$(0,018+0,982):(8\cdot0,5-0,8)$$
  • $$0,018+0,982 = 1$$
  • $$8\cdot0,5 = 4$$
  • $$4-0,8 = 3,2$$
  • $$1:3,2 = 10:32 = 5:16 = 0,3125$$
• 2) $$27,3\cdot5,1\cdot(-2,2):(-0,00019)$$
  • $$27,3\cdot5,1 = 139,23$$
  • $$139,23\cdot(-2,2) = -306,306$$
  • $$-306,306 : (-0,00019) = 1612136,8421$$ (приблизительно)
• 3) $$\left(6\frac{8}{15}-4\frac{21}{45}\right)\cdot4,5-2\frac{1}{6}:0,52$$
  • $$6\frac{8}{15} = \frac{98}{15}$$
  • $$4\frac{21}{45} = \frac{201}{45} = \frac{67}{15}$$
  • $$\frac{98}{15}-\frac{67}{15} = \frac{31}{15}$$
  • $$4,5 = \frac{9}{2}$$
  • $$2\frac{1}{6} = \frac{13}{6}$$
  • $$0,52 = \frac{52}{100} = \frac{13}{25}$$
  • $$\frac{31}{15} \cdot \frac{9}{2} = \frac{31\cdot3}{5\cdot2} = \frac{93}{10} = 9,3$$
  • $$\frac{13}{6} : \frac{13}{25} = \frac{13}{6} \cdot \frac{25}{13} = \frac{25}{6}$$
  • $$9,3 - \frac{25}{6} = \frac{93}{10} - \frac{25}{6} = \frac{279}{30} - \frac{125}{30} = \frac{154}{30} = \frac{77}{15} \approx 5,1333$$
• 4) $$\left(\frac{9}{22}+1\frac{12}{33}\right)\cdot1,32-\frac{8}{13}\cdot0,1625$$
  • $$1\frac{12}{33} = \frac{45}{33} = \frac{15}{11}$$
  • $$\frac{9}{22} + \frac{15}{11} = \frac{9}{22} + \frac{30}{22} = \frac{39}{22}$$
  • $$1,32 = \frac{132}{100} = \frac{33}{25}$$
  • $$0,1625 = \frac{1625}{10000} = \frac{13}{80}$$
  • $$\frac{39}{22} \cdot \frac{33}{25} = \frac{39\cdot3}{2\cdot25} = \frac{117}{50}$$
  • $$\frac{8}{13} \cdot \frac{13}{80} = \frac{1}{10}$$
  • $$\frac{117}{50} - \frac{1}{10} = \frac{117}{50} - \frac{5}{50} = \frac{112}{50} = \frac{56}{25} = 2,24$$

Ответ: 1) 0,3125; 2) 1612136,8421; 3) 77/15; 4) 2,24.