2,379 Найдите значение выражения: a) (2+\frac{1}{4}+\frac{5}{6})\cdot (4-\frac{3}{49}); б) (2+3\frac{3}{18})\cdot (20-17\frac{9}{16}); в) (2+1\frac{8}{9})\cdot (3\frac{4}{5}-\frac{38}{55}); г) \frac{13}{15}\cdot \frac{5}{11}-7\frac{1}{5}\cdot \frac{1}{6}.

a) $$(2+\frac{1}{4}+\frac{5}{6})\cdot (4-\frac{3}{49}) = (2+\frac{1 \cdot 3}{4 \cdot 3}+\frac{5 \cdot 2}{6 \cdot 2})\cdot (4-\frac{3}{49}) = (2+\frac{3}{12}+\frac{10}{12})\cdot (4-\frac{3}{49}) = (2+\frac{13}{12})\cdot (4-\frac{3}{49}) = (2+1\frac{1}{12})\cdot (4-\frac{3}{49}) = 3\frac{1}{12} \cdot (4-\frac{3}{49}) = \frac{3 \cdot 12+1}{12} \cdot (\frac{4 \cdot 49}{49}-\frac{3}{49}) = \frac{37}{12} \cdot \frac{196-3}{49} = \frac{37}{12} \cdot \frac{193}{49} = \frac{37 \cdot 193}{12 \cdot 49} = \frac{7141}{588} = 12\frac{125}{588}$$ б) $$(2+3\frac{3}{18})\cdot (20-17\frac{9}{16}) = (5\frac{3}{18})\cdot (20-17\frac{9}{16}) = (5\frac{1}{6})\cdot (20-17\frac{9}{16}) = \frac{5 \cdot 6+1}{6} \cdot (\frac{20 \cdot 16}{16}-\frac{17 \cdot 16+9}{16}) = \frac{31}{6} \cdot (\frac{320}{16}-\frac{272+9}{16}) = \frac{31}{6} \cdot (\frac{320}{16}-\frac{281}{16}) = \frac{31}{6} \cdot \frac{320-281}{16} = \frac{31}{6} \cdot \frac{39}{16} = \frac{31 \cdot 39}{6 \cdot 16} = \frac{1209}{96} = 12\frac{57}{96} = 12\frac{19}{32}$$ в) $$(2+1\frac{8}{9})\cdot (3\frac{4}{5}-\frac{38}{55}) = (3\frac{8}{9})\cdot (3\frac{4}{5}-\frac{38}{55}) = (\frac{3 \cdot 9 + 8}{9})\cdot (\frac{3 \cdot 5+4}{5}-\frac{38}{55}) = (\frac{27+8}{9})\cdot (\frac{19}{5}-\frac{38}{55}) = \frac{35}{9} \cdot (\frac{19 \cdot 11}{5 \cdot 11}-\frac{38}{55}) = \frac{35}{9} \cdot (\frac{209}{55}-\frac{38}{55}) = \frac{35}{9} \cdot \frac{209-38}{55} = \frac{35}{9} \cdot \frac{171}{55} = \frac{35 \cdot 171}{9 \cdot 55} = \frac{5985}{495} = 12\frac{45}{495} = 12\frac{1}{11}$$ г) $$\frac{13}{15}\cdot \frac{5}{11}-7\frac{1}{5}\cdot \frac{1}{6} = \frac{13 \cdot 5}{15 \cdot 11}-\frac{7 \cdot 5+1}{5}\cdot \frac{1}{6} = \frac{65}{165}-\frac{36}{5}\cdot \frac{1}{6} = \frac{65}{165}-\frac{36}{30} = \frac{65}{165}-\frac{6}{5} = \frac{65}{165}-\frac{6 \cdot 33}{5 \cdot 33} = \frac{65}{165}-\frac{198}{165} = \frac{65-198}{165} = \frac{-133}{165} = -\frac{133}{165}$$ Ответ: а) $$12\frac{125}{588}$$; б) $$12\frac{19}{32}$$; в) $$12\frac{1}{11}$$; г) $$- \frac{133}{165}$$