Упр.573 Часть 1 ГДЗ Виленкин Жохов 6 класс (Математика)

Задача

а) (3 3/5 — 2 1/15) * 5;
б) (1 14/17 — 1 1/34) * 34;
в) 8 3/17 * 5 1/4 + 3 14/17 * 5 1/4;
г) 3 4/13 * 15 3/41 — 3 4/13 * 2 3/41;
д) (2 3/4 + 4 1/8) * 1 5/11;
е) 1 2/5 * (1 1/14 — 5/7).

Подробный ответ

а) $$\left(3\frac{3}{5}-2\frac{1}{15}\right)\cdot 5=\left(3\frac{9}{15}-2\frac{1}{15}\right)\cdot 5=1\frac{8}{15}\cdot 5.$$

$$1\frac{8}{15}\cdot 5=5+\frac{8}{15}\cdot 5=5+\frac{8}{3}=5+2\frac{2}{3}=7\frac{2}{3}.$$

б) $$\left(1\frac{14}{17}-1\frac{1}{34}\right)\cdot 34=\left(\frac{31}{17}-\frac{35}{34}\right)\cdot 34.$$

$$\frac{31}{17}\cdot 34-\frac{35}{34}\cdot 34=31\cdot 2-35=62-35=27.$$

в) $$8\frac{3}{17}\cdot 5\frac{1}{4}+3\frac{14}{17}\cdot 5\frac{1}{4}=5\frac{1}{4}\left(8\frac{3}{17}+3\frac{14}{17}\right).$$

$$5\frac{1}{4}\left(8\frac{3}{17}+3\frac{14}{17}\right)=5\frac{1}{4}\cdot 11\frac{17}{17}=5\frac{1}{4}\cdot 12.$$

$$5\frac{1}{4}\cdot 12=5\cdot 12+\frac{1}{4}\cdot 12=60+3=63.$$

г) $$3\frac{4}{13}\cdot 15\frac{3}{41}-3\frac{4}{13}\cdot 2\frac{3}{41}=3\frac{4}{13}\left(15\frac{3}{41}-2\frac{3}{41}\right).$$

$$3\frac{4}{13}\left(15\frac{3}{41}-2\frac{3}{41}\right)=3\frac{4}{13}\cdot 13.$$

$$3\frac{4}{13}\cdot 13=3\cdot 13+\frac{4}{13}\cdot 13=39+4=43.$$

д) $$\left(2\frac{3}{4}+4\frac{1}{8}\right)\cdot 1\frac{5}{11}=\left(2\frac{6}{8}+4\frac{1}{8}\right)\cdot 1\frac{5}{11}=6\frac{7}{8}\cdot 1\frac{5}{11}.$$

$$6\frac{7}{8}\cdot 1\frac{5}{11}=\frac{55}{8}\cdot \frac{16}{11}=\frac{5\cdot 16}{8\cdot 11}=5\cdot 2=10.$$

е) $$1\frac{2}{5}\cdot \left(1\frac{1}{14}-\frac{5}{7}\right)=1\frac{2}{5}\cdot \left(\frac{15}{14}-\frac{10}{14}\right).$$

$$1\frac{2}{5}\cdot \frac{5}{14}=\frac{7}{5}\cdot \frac{5}{14}=\frac{1}{2}.$$