Упр.570 Часть 1 ГДЗ Виленкин Жохов 6 класс (Математика)

Задача

а) 21/25 * 5/7 — 3/16 * 4/15;
б) 5 5/12 * 4/13 — 2 5/8 * 3/14;
в) 15 2/5 * 1 5/7 + 6 10/27 * 3 3/8;
г) 15 4/7 — 4 3/8 * (1 3/7 — 34/35);
д) (3/4)3;
е) (5/6)2.

Подробный ответ

а) $$\frac{21}{25}\cdot\frac{5}{7}-\frac{3}{16}\cdot\frac{4}{15}$$

$$\frac{21\cdot 5}{25\cdot 7}-\frac{3\cdot 4}{16\cdot 15} =\frac{3}{5}-\frac{1}{20} =\frac{12}{20}-\frac{1}{20} =\frac{11}{20}$$

б) $$5\frac{5}{12}\cdot\frac{4}{13}-2\frac{5}{8}\cdot\frac{3}{14}$$

$$5\frac{5}{12}=\frac{65}{12},\qquad 2\frac{5}{8}=\frac{21}{8}$$
$$\frac{65}{12}\cdot\frac{4}{13}-\frac{21}{8}\cdot\frac{3}{14} =\frac{5}{3}-\frac{9}{16}$$
$$\frac{5}{3}-\frac{9}{16} =\frac{80}{48}-\frac{27}{48} =\frac{53}{48} =1\frac{5}{48}$$

в) $$15\frac{2}{5}\cdot1\frac{5}{7}+6\frac{10}{27}\cdot3\frac{3}{8}$$

$$15\frac{2}{5}=\frac{77}{5},\qquad 1\frac{5}{7}=\frac{12}{7},\qquad 6\frac{10}{27}=\frac{172}{27},\qquad 3\frac{3}{8}=\frac{27}{8}$$
$$\frac{77}{5}\cdot\frac{12}{7}+\frac{172}{27}\cdot\frac{27}{8} =\frac{132}{5}+\frac{43}{2}$$
$$\frac{132}{5}+\frac{43}{2} =\frac{264}{10}+\frac{215}{10} =\frac{479}{10} =47\frac{9}{10}$$

г) $$15\frac{4}{7}-4\frac{3}{8}\cdot\left(1\frac{3}{7}-\frac{34}{35}\right)$$

$$1\frac{3}{7}=\frac{10}{7}=\frac{50}{35}$$
$$15\frac{4}{7}-4\frac{3}{8}\cdot\left(\frac{50}{35}-\frac{34}{35}\right)$$
$$15\frac{4}{7}-4\frac{3}{8}\cdot\frac{16}{35}$$
$$15\frac{4}{7}-\frac{35}{8}\cdot\frac{16}{35} =15\frac{4}{7}-2 =13\frac{4}{7}$$

д) $$\left(\frac{3}{4}\right)^3=\frac{3^3}{4^3}=\frac{27}{64}$$

е) $$\left(\frac{5}{6}\right)^2=\frac{5^2}{6^2}=\frac{25}{36}$$