Упр.381 Часть 2 ГДЗ Дорофеев Петерсон 5 класс (Математика)

1) 2 1/6 — 1 2/9 : 3 2/3; 4) (5/6 + 2 3/4) : 4 7/9 · 2 2/3 — 1 2/3;
2) 4 2/5 : (7/10 + 2 3/5); 5) (1 1/8 + 1 1/2) : 3 : (5 1/2 — 9/20 : 1 4/5);
3) 5 · (2/3)^3 : (4/9)^2; 6) 9/10 · 1 1/14 : 2 4/7 · 24 — 2 4/15 : (1 1/5 — 2/3).

1) $$2\frac{1}{6}-1\frac{2}{9}:3\frac{2}{3}=2\frac{1}{6}-\frac{11}{9}:\frac{11}{3}=2\frac{1}{6}-\frac{11}{9}\cdot\frac{3}{11}=2\frac{1}{6}-\frac{1}{3}=1\frac{5}{6}.$$

2) $$4\frac{2}{5}:\left(\frac{7}{10}+2\frac{3}{5}\right)=\frac{22}{5}:\left(\frac{7}{10}+\frac{26}{10}\right)=\frac{22}{5}:\frac{33}{10}=\frac{22}{5}\cdot\frac{10}{33}=\frac{4}{3}=1\frac{1}{3}.$$

3) $$5\cdot\left(\frac{2}{3}\right)^3:\left(\frac{4}{9}\right)^2=5\cdot\frac{8}{27}:\frac{16}{81}=5\cdot\frac{8}{27}\cdot\frac{81}{16}=\frac{15}{2}=7\frac{1}{2}.$$

4) $$\left(\frac{5}{6}+2\frac{3}{4}\right):4\frac{7}{9}\cdot2\frac{2}{3}-1\frac{2}{3}=\left(\frac{5}{6}+\frac{11}{4}\right):\frac{43}{9}\cdot\frac{8}{3}-1\frac{2}{3}$$

$$=\left(\frac{10}{12}+\frac{33}{12}\right):\frac{43}{9}\cdot\frac{8}{3}-1\frac{2}{3}=\frac{43}{12}:\frac{43}{9}\cdot\frac{8}{3}-1\frac{2}{3}$$

$$=\frac{43}{12}\cdot\frac{9}{43}\cdot\frac{8}{3}-1\frac{2}{3}=2-1\frac{2}{3}=\frac{1}{3}.$$

5) $$\left(1\frac{1}{8}+1\frac{1}{2}\right):3:\left(5\frac{1}{2}-\frac{9}{20}:1\frac{4}{5}\right)$$

$$=\left(1\frac{1}{8}+1\frac{4}{8}\right):3:\left(5\frac{1}{2}-\frac{9}{20}:\frac{9}{5}\right)$$

$$=\left(2\frac{5}{8}\right):3:\left(5\frac{1}{2}-\frac{9}{20}\cdot\frac{5}{9}\right)=\frac{21}{8}:3:\left(5\frac{1}{2}-\frac{1}{4}\right)$$

$$=\frac{21}{8}:3:5\frac{1}{4}=\frac{21}{8}:\frac{21}{4}=\frac{21}{8}\cdot\frac{4}{21}=\frac{1}{6}.$$

6) $$\frac{9}{10}\cdot1\frac{1}{14}:2\frac{4}{7}\cdot24-2\frac{4}{15}:\left(1\frac{1}{5}-\frac{2}{3}\right)$$

$$=\frac{9}{10}\cdot\frac{15}{14}:\frac{18}{7}\cdot24-\frac{34}{15}:\left(\frac{6}{5}-\frac{2}{3}\right)$$

$$=\frac{9}{10}\cdot\frac{15}{14}\cdot\frac{7}{18}\cdot24-\frac{34}{15}:\left(\frac{18}{15}-\frac{10}{15}\right)$$

$$=9-\frac{34}{15}:\frac{8}{15}=9-\frac{34}{15}\cdot\frac{15}{8}=9-\frac{17}{4}=4\frac{3}{4}.$$

Ответ

1) $$1\frac{5}{6}$$; 2) $$1\frac{1}{3}$$; 3) $$7\frac{1}{2}$$; 4) $$\frac{1}{3}$$; 5) $$\frac{1}{6}$$; 6) $$4\frac{3}{4}$$.