Упр.343 Часть 2 ГДЗ Дорофеев Петерсон 5 класс (Математика)

2) 5 17/20 + (3 1/2 — 2 3/8) · 1 1/3 · (4 1/3 — 1 5/6); 4) [(1 2/3)^2 — 1 1/2] · 4 2/23 + 21/23 · (2 5/6 — 2 5/6).

1) $$\left(4-2\frac{5}{6}-\frac{5}{12}\right)\cdot\left(7\frac{1}{12}-5\frac{3}{4}\right)$$

$$4-2\frac{5}{6}-\frac{5}{12}=4-2\frac{10}{12}-\frac{5}{12}=3\frac{12}{12}-2\frac{10}{12}-\frac{5}{12}=1\frac{2}{12}-\frac{5}{12}=\frac{14}{12}-\frac{5}{12}=\frac{9}{12}=\frac{3}{4}$$
$$7\frac{1}{12}-5\frac{3}{4}=7\frac{1}{12}-5\frac{9}{12}=2\frac{13}{12}-\frac{9}{12}=1\frac{1}{3}$$
$$\frac{3}{4}\cdot 1\frac{1}{3}=\frac{3}{4}\cdot\frac{4}{3}=1$$

2) $$5\frac{17}{20}+\left(3\frac{1}{2}-2\frac{3}{8}\right)\cdot 1\frac{1}{3}\cdot\left(4\frac{1}{3}-1\frac{5}{6}\right)$$

$$3\frac{1}{2}-2\frac{3}{8}=3\frac{4}{8}-2\frac{3}{8}=1\frac{1}{8}$$
$$4\frac{1}{3}-1\frac{5}{6}=4\frac{2}{6}-1\frac{5}{6}=2\frac{3}{6}=2\frac{1}{2}$$
$$1\frac{1}{8}\cdot 1\frac{1}{3}\cdot 2\frac{1}{2}=\frac{9}{8}\cdot\frac{4}{3}\cdot\frac{5}{2}=\frac{9\cdot 4\cdot 5}{8\cdot 3\cdot 2}=\frac{15}{4}=3\frac{3}{4}$$
$$5\frac{17}{20}+3\frac{3}{4}=5\frac{17}{20}+3\frac{15}{20}=8\frac{32}{20}=8\frac{8}{5}=9\frac{3}{5}$$

3) $$\left(1\frac{5}{6}+2\frac{4}{9}-1\frac{3}{4}\right)\cdot 4-\left(3\frac{1}{2}-1\frac{7}{10}\right)\cdot 5$$

$$1\frac{5}{6}+2\frac{4}{9}-1\frac{3}{4}=1\frac{30}{36}+2\frac{16}{36}-1\frac{27}{36}=2\frac{19}{36}$$
$$2\frac{19}{36}\cdot 4=8\frac{19}{9}$$
$$3\frac{1}{2}-1\frac{7}{10}=3\frac{5}{10}-1\frac{7}{10}=1\frac{8}{10}=1\frac{4}{5}$$
$$1\frac{4}{5}\cdot 5=9$$
$$8\frac{19}{9}-9=10\frac{1}{9}-9=1\frac{1}{9}$$

4) $$\left[\left(1\frac{2}{3}\right)^2-1\frac{1}{2}\right]\cdot 4\frac{2}{23}+\frac{21}{23}\cdot\left(2\frac{5}{6}-2\frac{5}{6}\right)$$

$$2\frac{5}{6}-2\frac{5}{6}=0,$$
поэтому второе слагаемое равно нулю.
$$\left(1\frac{2}{3}\right)^2=\left(\frac{5}{3}\right)^2=\frac{25}{9}$$
$$\frac{25}{9}-1\frac{1}{2}=\frac{25}{9}-\frac{3}{2}=\frac{50-27}{18}=\frac{23}{18}$$
$$\frac{23}{18}\cdot 4\frac{2}{23}=\frac{23}{18}\cdot\frac{94}{23}=\frac{94}{18}=\frac{47}{9}=5\frac{2}{9}$$

Ответ

1) $$1$$; 2) $$9\frac{3}{5}$$; 3) $$1\frac{1}{9}$$; 4) $$5\frac{2}{9}$$.