4.187. Вычислите: A) (+3+(-4 E) + (+) 3) 15-4(1) Б) E) *(2-1)(3 и) (++)(-)(-) Й) (40-29-28-84 K) K40+3 П) C) Ф) (2)(1) (8-7)-1-(3-23) )8(+)+15-(53) x)(4-2)(7-5) 4) (1+2-14-(3-1)5 10 щ) 1234 b) 3.5 0) (+)(23-15 P) T) 105+(3-2)(1) (1)-(2-2) (19 3)5+42210) 21음+4·1

A) $$(\frac{3}{4} + \frac{5}{6}) \cdot 3 + (\frac{5}{6} - \frac{3}{4}) \cdot 4 = (\frac{9}{12} + \frac{10}{12}) \cdot 3 + (\frac{10}{12} - \frac{9}{12}) \cdot 4 = \frac{19}{12} \cdot 3 + \frac{1}{12} \cdot 4 = \frac{19}{4} + \frac{1}{3} = \frac{57}{12} + \frac{4}{12} = \frac{61}{12} = 5\frac{1}{12}$$

Ответ: $$5\frac{1}{12}$$

Б) $$\frac{1}{6} + \frac{1}{18} + \frac{3}{4} = \frac{6}{36} + \frac{2}{36} + \frac{27}{36} = \frac{35}{36}$$

Ответ: $$\frac{35}{36}$$

В) $$(2\frac{3}{5} + 1\frac{1}{7}) \cdot 14 - (2\frac{1}{2} - 1\frac{3}{8}) \cdot 4 = (\frac{13}{5} + \frac{8}{7}) \cdot 14 - (\frac{5}{2} - \frac{11}{8}) \cdot 4 = (\frac{91 + 40}{35}) \cdot 14 - (\frac{20 - 11}{8}) \cdot 4 = \frac{131}{35} \cdot 14 - \frac{9}{8} \cdot 4 = \frac{131 \cdot 2}{5} - \frac{9}{2} = \frac{262}{5} - \frac{9}{2} = \frac{524}{10} - \frac{45}{10} = \frac{479}{10} = 47\frac{9}{10}$$

Ответ: $$47\frac{9}{10}$$

Г) $$4\frac{11}{48} \cdot 7 - 1\frac{4}{9} = \frac{203}{48} \cdot 7 - \frac{13}{9} = \frac{1421}{48} - \frac{13}{9} = \frac{4263}{144} - \frac{208}{144} = \frac{4055}{144} = 28\frac{23}{144}$$

Ответ: $$28\frac{23}{144}$$

Д) $$(2\frac{2}{3} + \frac{5}{11}) \cdot \frac{1}{8} - \frac{5}{12} \cdot \frac{1}{3} = (\frac{8}{3} + \frac{5}{11}) \cdot \frac{1}{8} - \frac{5}{36} = (\frac{88 + 15}{33}) \cdot \frac{1}{8} - \frac{5}{36} = \frac{103}{33} \cdot \frac{1}{8} - \frac{5}{36} = \frac{103}{264} - \frac{5}{36} = \frac{309}{792} - \frac{110}{792} = \frac{199}{792}$$

Ответ: $$\frac{199}{792}$$

E) $$(1\frac{1}{9} + 2\frac{4}{6} - 2\frac{5}{6}) \cdot (3\frac{2}{2} - 1\frac{11}{14}) = (\frac{10}{9} + \frac{16}{6} - \frac{17}{6}) \cdot (\frac{8}{2} - \frac{25}{14}) = (\frac{10}{9} - \frac{1}{6}) \cdot (4 - \frac{25}{14}) = (\frac{20}{18} - \frac{3}{18}) \cdot (\frac{56}{14} - \frac{25}{14}) = \frac{17}{18} \cdot \frac{31}{14} = \frac{527}{252} = 2\frac{23}{252}$$

Ответ: $$2\frac{23}{252}$$

Ж) $$(2\frac{1}{2} - 1\frac{3}{8}) \cdot (3\frac{1}{2} - 2\frac{1}{6}) \cdot 1\frac{1}{3} = (\frac{5}{2} - \frac{11}{8}) \cdot (\frac{7}{2} - \frac{13}{6}) \cdot \frac{4}{3} = (\frac{20}{8} - \frac{11}{8}) \cdot (\frac{21}{6} - \frac{13}{6}) \cdot \frac{4}{3} = \frac{9}{8} \cdot \frac{8}{6} \cdot \frac{4}{3} = \frac{3}{2} \cdot \frac{4}{3} = 2$$

Ответ: $$2$$

З) $$15\frac{4}{7} - 4\frac{3}{8} \cdot (1\frac{3}{7} + \frac{34}{35}) = \frac{109}{7} - \frac{35}{8} \cdot (\frac{10}{7} + \frac{34}{35}) = \frac{109}{7} - \frac{35}{8} \cdot (\frac{50}{35} + \frac{34}{35}) = \frac{109}{7} - \frac{35}{8} \cdot \frac{84}{35} = \frac{109}{7} - \frac{84}{8} = \frac{109}{7} - \frac{21}{2} = \frac{218}{14} - \frac{147}{14} = \frac{71}{14} = 5\frac{1}{14}$$

Ответ: $$5\frac{1}{14}$$

И) $$(40\frac{7}{15} - 29\frac{8}{35}) \cdot 28 - 8\frac{4}{7} \cdot \frac{1}{5} = (\frac{607}{15} - \frac{1023}{35}) \cdot 28 - \frac{60}{7} \cdot \frac{1}{5} = (\frac{4249 - 3069}{105}) \cdot 28 - \frac{12}{7} = (\frac{1180}{105}) \cdot 28 - \frac{12}{7} = (\frac{236}{21}) \cdot 28 - \frac{12}{7} = \frac{236 \cdot 4}{3} - \frac{12}{7} = \frac{944}{3} - \frac{12}{7} = \frac{6608 - 36}{21} = \frac{6572}{21} = 312\frac{20}{21}$$

Ответ: $$312\frac{20}{21}$$

Й) $$\left(4\frac{1}{5} + 1\frac{10}{2} \cdot \frac{3}{17} - \frac{2}{5} \cdot \frac{2}{3}\right) \cdot \frac{9}{17} - 7\frac{3}{4} = (\frac{21}{5} + \frac{27}{17} - \frac{2}{5} \cdot \frac{2}{3}) \cdot \frac{9}{17} - \frac{31}{4} = (\frac{21}{5} + \frac{27}{17} - \frac{4}{15}) \cdot \frac{9}{17} - \frac{31}{4} = (\frac{63 \cdot 3}{15} + \frac{27 \cdot 15}{17 \cdot 15} - \frac{4}{15}) \cdot \frac{9}{17} - \frac{31}{4} = \frac{185}{15} \cdot \frac{9}{17} - \frac{31}{4} = \frac{37}{3} \cdot \frac{9}{17} - \frac{31}{4} = \frac{111}{17} - \frac{31}{4} = \frac{444}{68} - \frac{527}{68} = -\frac{83}{68} = -1\frac{15}{68}$$

Ответ: $$-1\frac{15}{68}$$

К) $$4\frac{1}{10} + 3\frac{35}{36} + 1\frac{65}{69} = \frac{41}{10} + \frac{143}{36} + \frac{134}{69} = \frac{8493}{2070} + \frac{8135}{2070} + \frac{4020}{2070} = \frac{20648}{2070} = 9\frac{2058}{2070} = 9\frac{343}{345}$$

Ответ: $$9\frac{343}{345}$$

Л) $$(2\frac{5}{6} - \frac{3}{4} - 1\frac{1}{10} + \frac{8}{15}) \cdot 4\frac{1}{2} \cdot (1-\frac{5}{12} - \frac{1}{2}) = (\frac{17}{6} - \frac{3}{4} - \frac{11}{10} + \frac{8}{15}) \cdot \frac{9}{2} \cdot (\frac{12}{12} - \frac{5}{12} - \frac{6}{12}) = (\frac{170}{60} - \frac{45}{60} - \frac{66}{60} + \frac{32}{60}) \cdot \frac{9}{2} \cdot \frac{1}{12} = \frac{91}{60} \cdot \frac{9}{2} \cdot \frac{1}{12} = \frac{91}{60} \cdot \frac{3}{8} = \frac{91}{20} \cdot \frac{1}{8} = \frac{91}{160}$$

Ответ: $$\frac{91}{160}$$

M) $$(1\frac{3}{4} \cdot 4\frac{3}{5} + 1\frac{3}{16}) \cdot (4\frac{1}{4} + 1\frac{3}{71}) \cdot \frac{16}{2} + \frac{2}{27} \cdot 4\frac{1}{2} = (\frac{7}{4} \cdot \frac{23}{5} + \frac{19}{16}) \cdot (\frac{17}{4} + \frac{72}{71}) \cdot 8 + \frac{2}{27} \cdot \frac{9}{2} = (\frac{161}{20} + \frac{19}{16}) \cdot (\frac{1207}{284} + \frac{288}{284}) \cdot 8 + \frac{1}{3} = (\frac{644}{80} + \frac{95}{80}) \cdot (\frac{1495}{284}) \cdot 8 + \frac{1}{3} = (\frac{739}{80}) \cdot (\frac{1495}{284}) \cdot 8 + \frac{1}{3} = \frac{739}{10} \cdot \frac{1495}{284} + \frac{1}{3} = \frac{1104805}{2840} + \frac{1}{3} = \frac{220961}{568} + \frac{1}{3} = \frac{662883 + 568}{1704} = \frac{663451}{1704} = 389\frac{1135}{1704}$$

Ответ: $$389\frac{1135}{1704}$$

Н) $$(2\frac{8}{2} - 7\frac{3}{8}) \cdot 5\frac{2}{5} - 1\frac{4}{3} \cdot (3-\frac{2}{3} - 2\frac{2}{9}) = (4 - \frac{59}{8}) \cdot \frac{27}{5} - \frac{7}{3} \cdot (3 - \frac{2}{3} - \frac{20}{9}) = (\frac{32}{8} - \frac{59}{8}) \cdot \frac{27}{5} - \frac{7}{3} \cdot (\frac{27}{9} - \frac{6}{9} - \frac{20}{9}) = (\frac{-27}{8}) \cdot \frac{27}{5} - \frac{7}{3} \cdot (\frac{1}{9}) = -\frac{729}{40} - \frac{7}{27} = \frac{-19683 - 280}{1080} = \frac{-19963}{1080} = -18\frac{403}{1080}$$

Ответ: $$-18\frac{403}{1080}$$

О) $$\left(4\frac{5}{6} + \frac{1}{7}\right) \cdot \left(23\frac{2}{3} - 15\frac{5}{9}\right) \cdot \frac{45}{58} = \left(\frac{29}{6} + \frac{1}{7}\right) \cdot \left(\frac{71}{3} - \frac{140}{9}\right) \cdot \frac{45}{58} = \left(\frac{203}{42} + \frac{6}{42}\right) \cdot \left(\frac{213 - 140}{9}\right) \cdot \frac{45}{58} = \frac{209}{42} \cdot \frac{73}{9} \cdot \frac{45}{58} = \frac{209}{42} \cdot \frac{73}{1} \cdot \frac{5}{58} = \frac{209}{42} \cdot \frac{73 \cdot 5}{58} = \frac{76285}{2436} = 31\frac{829}{2436}$$

Ответ: $$31\frac{829}{2436}$$

П) $$\left(\frac{5}{12} - 3\frac{7}{36}\right) \div 2\frac{1}{2} + 4\frac{1}{3} \div 2\frac{26}{2} = (\frac{5}{12} - \frac{115}{36}) \div \frac{5}{2} + \frac{13}{3} \div \frac{52}{2} = (\frac{15 - 115}{36}) \cdot \frac{2}{5} + \frac{13}{3} \cdot \frac{2}{52} = \frac{-100}{36} \cdot \frac{2}{5} + \frac{1}{3} \cdot \frac{2}{4} = \frac{-20}{9} \cdot \frac{1}{1} + \frac{1}{3} \cdot \frac{1}{2} = -\frac{20}{9} + \frac{1}{6} = \frac{-40 + 3}{18} = \frac{-37}{18} = -2\frac{1}{18}$$

Ответ: $$-2\frac{1}{18}$$

С) $$\left(\frac{3}{5} + 2\frac{1}{10} + \frac{7}{17}\right) \cdot \frac{3}{17} - \left(2\frac{7}{23} - 1\frac{45}{46}\right) \cdot \frac{69}{80} \cdot 1\frac{1}{3} = (\frac{3}{5} + \frac{21}{10} + \frac{7}{17}) \cdot \frac{3}{17} - (\frac{53}{23} - \frac{91}{46}) \cdot \frac{69}{80} \cdot \frac{4}{3} = (\frac{102 + 357 + 70}{170}) \cdot \frac{3}{17} - (\frac{106 - 91}{46}) \cdot \frac{69}{80} \cdot \frac{4}{3} = \frac{529}{170} \cdot \frac{3}{17} - (\frac{15}{46}) \cdot \frac{69}{80} \cdot \frac{4}{3} = \frac{529}{170} \cdot \frac{3}{17} - (\frac{1}{2}) \cdot \frac{3}{80} \cdot \frac{4}{1} = \frac{1587}{2890} - (\frac{15}{40}) \cdot (\frac{3}{1}) = \frac{1587}{2890} - \frac{45}{40} = \frac{1587}{2890} - \frac{9}{8} = \frac{6348 - 26010}{11560} = \frac{-19662}{11560} = -1\frac{4051}{5780}$$

Ответ: $$-1\frac{4051}{5780}$$

T) $$\left(\frac{5}{12} + \frac{17}{30} + \frac{17}{20}\right) \cdot 60 - 55\frac{3}{4} \div 4\frac{3}{7} - 31 = (\frac{25 + 34 + 51}{60}) \cdot 60 - \frac{223}{4} \div \frac{31}{7} - 31 = (\frac{110}{60}) \cdot 60 - \frac{223}{4} \cdot \frac{7}{31} - 31 = \frac{110}{1} - \frac{1561}{124} - 31 = \frac{13640 - 1561 - 3844}{124} = \frac{8235}{124} = 66\frac{51}{124}$$

Ответ: $$66\frac{51}{124}$$

Ф) $$8\frac{2}{11} \cdot \left(4\frac{3}{4} + \frac{4}{57} + 2\frac{7}{3} + \frac{2}{46}\right) + 15 \div \left(5\frac{7}{8} + \frac{3}{47} - 3\frac{3}{2} - 2\frac{31}{55}\right) = \frac{90}{11} \cdot \left(\frac{19}{4} + \frac{4}{57} + \frac{13}{3} + \frac{1}{23}\right) + 15 \div \left(\frac{47}{8} + \frac{3}{47} - \frac{9}{2} - \frac{141}{55}\right)$$

Х) $$\left(4 - 2\frac{5}{6}\right) \cdot \frac{5}{12} \div \left(7\frac{1}{12} - 5\frac{5}{4}\right) = (4 - \frac{17}{6}) \cdot \frac{5}{12} \div (\frac{85}{12} - \frac{25}{4}) = (\frac{24 - 17}{6}) \cdot \frac{5}{12} \div (\frac{85 - 75}{12}) = \frac{7}{6} \cdot \frac{5}{12} \div \frac{10}{12} = \frac{35}{72} \div \frac{5}{6} = \frac{35}{72} \cdot \frac{6}{5} = \frac{7}{12}$$

Ответ: $$\frac{7}{12}$$

Ч) $$\left(1\frac{5}{6} + 2\frac{4}{9} - 1\frac{3}{4}\right) \div 4 - \left(3\frac{1}{2} - 1\frac{7}{10}\right) \cdot 5 = (\frac{11}{6} + \frac{22}{9} - \frac{7}{4}) \div 4 - (\frac{7}{2} - \frac{17}{10}) \cdot 5 = (\frac{66 + 44}{36} - \frac{7}{4}) \div 4 - (\frac{35 - 17}{10}) \cdot 5 = (\frac{110}{36} - \frac{63}{36}) \div 4 - \frac{18}{10} \cdot 5 = \frac{47}{36} \div 4 - \frac{9}{5} \cdot 5 = \frac{47}{36} \div 4 - 9 = \frac{47}{36} \cdot \frac{1}{4} - 9 = \frac{47}{144} - 9 = \frac{47 - 1296}{144} = -\frac{1249}{144} = -8\frac{97}{144}$$

Ответ: $$-8\frac{97}{144}$$

Ш) $$12 \div 1\frac{1}{6} - 1\frac{3}{2} \div 4\frac{1}{5} = 12 \div \frac{7}{6} - \frac{5}{2} \div \frac{21}{5} = \frac{72}{7} - \frac{25}{42} = \frac{432 - 25}{42} = \frac{407}{42} = 9\frac{29}{42}$$

Ответ: $$9\frac{29}{42}$$

Ы) $$3 \cdot 5 - 1\frac{1}{4} \div 5\frac{4}{7} - 2\frac{1}{11} = 15 - \frac{5}{4} \div \frac{39}{7} - \frac{23}{11} = 15 - \frac{5}{4} \cdot \frac{7}{39} - \frac{23}{11} = 15 - \frac{35}{156} - \frac{23}{11} = \frac{25740 - 385 - 3588}{1716} = \frac{21767}{1716} = 12\frac{1295}{1716}$$

Ответ: $$12\frac{1295}{1716}$$

b) $$(\frac{5}{8} + \frac{11}{36}) \cdot \frac{6}{67} = (\frac{45 + 22}{72}) \cdot \frac{6}{67} = \frac{67}{72} \cdot \frac{6}{67} = \frac{1}{12}$$

Ответ: $$\frac{1}{12}$$

Э) $$3\frac{3}{8} \div 5 + 4\frac{1}{6} - 2\frac{2}{10} + \frac{9}{20} \cdot 6 = \frac{27}{8} \div 5 + \frac{25}{6} - \frac{22}{10} + \frac{54}{20} = \frac{27}{40} + \frac{25}{6} - \frac{11}{5} + \frac{27}{10} = \frac{27 \cdot 3}{120} + \frac{25 \cdot 20}{120} - \frac{11 \cdot 24}{120} + \frac{27 \cdot 12}{120} = \frac{81 + 500 - 264 + 324}{120} = \frac{641}{120} = 5\frac{41}{120}$$

Ответ: $$5\frac{41}{120}$$

Ю) $$2\div 1\frac{5}{12} + 4 \div 1\frac{1}{8} + 1\div 1\frac{1}{4} - 1\div \frac{9}{4} = 2 \div \frac{17}{12} + 4 \div \frac{9}{8} + 1 \div \frac{5}{4} - 1 \div \frac{13}{4} = \frac{24}{17} + \frac{32}{9} + \frac{4}{5} - \frac{4}{9} = \frac{24 \cdot 45}{765} + \frac{32 \cdot 85}{765} + \frac{4 \cdot 153}{765} - \frac{4 \cdot 85}{765} = \frac{1080 + 2720 + 612 - 340}{765} = \frac{4072}{765} = 5\frac{247}{765}$$

Ответ: $$5\frac{247}{765}$$