Упр.341 ГДЗ Мерзляк Полонский 6 класс (Математика)
Найдите значение выражения:
1) $$\left(\frac{11}{18}\colon\frac{4}{9}\right)\cdot\frac{3}{16}$$;
2) $$\frac{11}{18}\colon\frac{4}{9}\cdot\frac{3}{16}$$;
3) $$1\frac{3}{5}\cdot\left(\frac{3}{4}+1\frac{3}{8}\right)$$;
4) $$1\frac{3}{5}\cdot\frac{3}{4}+1\frac{3}{8}$$;
5) $$13\frac{4}{5}\colon3\frac{1}{5}\cdot3\frac{3}{4}$$;
6) $$1\frac{3}{25}\cdot2\frac{1}{7}\colon2\frac{1}{9}\cdot\frac{27}{190}$$;
7) $$4\frac{7}{12}\cdot1\frac{3}{11}+1\frac{1}{15}\cdot\frac{45}{64}$$;
8) $$\left(8\colon2\frac{1}{7}\cdot3\frac{1}{9}\right)\cdot\frac{27}{44}$$;
9) $$\left(\frac{4}{5}+\frac{4}{7}\right)\cdot\left(7\frac{11}{12}\colon5\frac{7}{9}\right)$$;
10) $$\frac{4}{5}+\frac{4}{7}\cdot\left(7\frac{11}{12}\colon5\frac{7}{9}\right)$$.
1) $$\left(\frac{11}{18}-\frac{4}{9}\right)\cdot\frac{3}{16}=\left(\frac{11}{18}-\frac{8}{18}\right)\cdot\frac{3}{16}=\frac{3}{18}\cdot\frac{3}{16}=\frac{1}{6}\cdot\frac{3}{16}=\frac{1}{32}.$$
2) $$\frac{11}{18}-\frac{4}{9}\cdot\frac{3}{16}=\frac{11}{18}-\frac{4}{3\cdot 4\cdot 16}=\frac{11}{18}-\frac{1}{12}=\frac{22}{36}-\frac{3}{36}=\frac{19}{36}.$$
3) $$1\frac{3}{5}\cdot\left(\frac{3}{4}+1\frac{3}{8}\right)=\frac{8}{5}\cdot\left(\frac{6}{8}+1\frac{3}{8}\right)=\frac{8}{5}\cdot1\frac{9}{8}=\frac{8}{5}\cdot\frac{17}{8}=\frac{17}{5}=3\frac{2}{5}.$$
4) $$1\frac{3}{5}\cdot\frac{3}{4}+1\frac{3}{8}=\frac{8}{5}\cdot\frac{3}{4}+1\frac{3}{8}=\frac{6}{5}+1\frac{3}{8}=1\frac{1}{5}+1\frac{3}{8}.$$
$$1\frac{1}{5}+1\frac{3}{8}=1\frac{8}{40}+1\frac{15}{40}=2\frac{23}{40}.$$
5) $$13\frac{4}{5}-3\frac{1}{5}\cdot3\frac{3}{4}=13\frac{4}{5}-\frac{16}{5}\cdot\frac{15}{4}=13\frac{4}{5}-\frac{16\cdot15}{5\cdot4}=13\frac{4}{5}-12=1\frac{4}{5}.$$
6) $$1\frac{3}{25}\cdot2\frac{1}{7}-2\frac{1}{9}\cdot\frac{27}{190}=\frac{28}{25}\cdot\frac{15}{7}-\frac{19}{9}\cdot\frac{27}{190}.$$
$$\frac{28}{25}\cdot\frac{15}{7}=\frac{4\cdot3}{5\cdot1}=\frac{12}{5},\qquad \frac{19}{9}\cdot\frac{27}{190}=\frac{3}{10}.$$
$$\frac{12}{5}-\frac{3}{10}=\frac{24}{10}-\frac{3}{10}=\frac{21}{10}=2\frac{1}{10}.$$
7) $$4\frac{7}{12}\cdot1\frac{3}{11}+1\frac{1}{15}\cdot\frac{45}{64}=\frac{55}{12}\cdot\frac{14}{11}+\frac{16}{15}\cdot\frac{45}{64}.$$
$$\frac{55}{12}\cdot\frac{14}{11}=\frac{5\cdot7}{6\cdot1}=\frac{35}{6},\qquad \frac{16}{15}\cdot\frac{45}{64}=\frac{3}{4}.$$
$$\frac{35}{6}+\frac{3}{4}=\frac{70}{12}+\frac{9}{12}=\frac{79}{12}=6\frac{7}{12}.$$
8) $$\left(8-2\frac{1}{7}\cdot3\frac{1}{9}\right)\cdot\frac{27}{44}=\left(8-\frac{15}{7}\cdot\frac{28}{9}\right)\cdot\frac{27}{44}.$$
$$\frac{15}{7}\cdot\frac{28}{9}=\frac{20}{3},\qquad 8-\frac{20}{3}=7\frac{3}{3}-6\frac{2}{3}=1\frac{1}{3}=\frac{4}{3}.$$
$$\frac{4}{3}\cdot\frac{27}{44}=\frac{9}{11}.$$
9) $$\left(\frac{4}{5}+\frac{4}{7}\right)\cdot\left(7\frac{11}{12}-5\frac{7}{9}\right)=\frac{48}{35}\cdot\left(\frac{95}{12}-\frac{52}{9}\right).$$
$$\frac{95}{12}-\frac{52}{9}=\frac{285}{36}-\frac{208}{36}=\frac{77}{36},$$
$$\frac{48}{35}\cdot\frac{77}{36}=\frac{4\cdot11}{5\cdot3}=\frac{44}{15}=2\frac{14}{15}.$$
10) $$\frac{4}{5}+\frac{4}{7}\cdot\left(7\frac{11}{12}-5\frac{7}{9}\right)=\frac{4}{5}+\frac{4}{7}\cdot\frac{77}{36}=\frac{4}{5}+\frac{11}{9}.$$
$$\frac{4}{5}+\frac{11}{9}=\frac{36}{45}+\frac{55}{45}=\frac{91}{45}=2\frac{1}{45}.$$
Ответ
1) $$\frac{1}{32}$$; 2) $$\frac{19}{36}$$; 3) $$3\frac{2}{5}$$; 4) $$2\frac{23}{40}$$; 5) $$1\frac{4}{5}$$; 6) $$2\frac{1}{10}$$; 7) $$6\frac{7}{12}$$; 8) $$\frac{9}{11}$$; 9) $$2\frac{14}{15}$$; 10) $$2\frac{1}{45}$$.
