Упр.3.38 ГДЗ Виленкин Жохов 6 класс Часть 1, Просвещение (Математика)
- Выполните действия:
а) $$\frac{3\frac{1}{12}+2\frac{1}{6}-\frac{1}{8}}{1{,}4+0{,}6\cdot4{,}5}$$;
б) $$\frac{10\frac{10}{11}:12}{2\frac{21}{22}}\cdot6\frac{1}{2}$$;
в) $$\frac{8:2\frac{2}{5}}{5\frac{1}{4}:7}:\frac{2\frac{1}{7}:\frac{5}{7}}{4:\frac{8}{9}}$$.
а) Преобразуем смешанные числа и десятичные дроби:
$$\frac{3\frac{1}{12}+2\frac{1}{6}-\frac{1}{8}}{1{,}4+0{,}6\cdot 4{,}5} = \frac{\frac{37}{12}+\frac{13}{6}-\frac{1}{8}}{1{,}4+2{,}7}$$
$$\frac{37}{12}+\frac{13}{6}-\frac{1}{8} = \frac{74}{24}+\frac{52}{24}-\frac{3}{24} = \frac{123}{24} = \frac{41}{8}$$
$$1{,}4+2{,}7=4{,}1=\frac{41}{10}$$
$$\frac{41}{8}:\frac{41}{10} = \frac{41}{8}\cdot\frac{10}{41} = \frac{10}{8} = \frac{5}{4} = 1\frac{1}{4}$$
б)
$$\left(\frac{10\frac{10}{11}:12}{2\frac{21}{22}}\right)\cdot 6\frac{1}{2} = \left(\frac{\frac{120}{11}:12}{\frac{65}{22}}\right)\cdot \frac{13}{2}$$
$$\frac{120}{11}:12 = \frac{120}{11}\cdot\frac{1}{12} = \frac{10}{11}$$
$$\frac{10}{11}:\frac{65}{22} = \frac{10}{11}\cdot\frac{22}{65} = \frac{4}{13}$$
$$\frac{4}{13}\cdot\frac{13}{2} = 2$$
в)
$$\left(\frac{8:2\frac{2}{5}}{5\frac{1}{4}:7}\right):\left(\frac{2\frac{1}{7}: \frac{5}{7}}{4:\frac{8}{9}}\right)$$
$$8:2\frac{2}{5}=8:\frac{12}{5}=\frac{10}{3}, \qquad 5\frac{1}{4}:7=\frac{21}{4}:7=\frac{3}{4}$$
$$2\frac{1}{7}:\frac{5}{7}=\frac{15}{7}:\frac{5}{7}=3, \qquad 4:\frac{8}{9}=4\cdot\frac{9}{8}=\frac{9}{2}$$
Тогда
$$\left(\frac{10}{3}:\frac{3}{4}\right):\left(3:\frac{9}{2}\right) = \left(\frac{10}{3}\cdot\frac{4}{3}\right):\left(3\cdot\frac{2}{9}\right) = \frac{40}{9}:\frac{2}{3}$$
$$\frac{40}{9}:\frac{2}{3} = \frac{40}{9}\cdot\frac{3}{2} = \frac{20}{3} = 6\frac{2}{3}$$
Ответ
а) $$1\frac{1}{4}$$; б) $$2$$; в) $$6\frac{2}{3}$$.
