Упр.613 Часть 1 ГДЗ Виленкин Жохов 6 класс (Математика)

Найдите значение выражения:

а) $$\left(\frac{3}{8}+0{,}25+\frac{1}{6}\right):1\frac{7}{12}$$;

б) $$8:0{,}16-3\frac{3}{4}\cdot 6{,}4$$;

в) $$6{,}25\cdot 8-3\frac{2}{3}:5{,}5+2{,}4\cdot 4\frac{7}{12}$$;

г) $$\left(\left(1\frac{2}{5}\right)^2-1{,}6\right):0{,}12$$.

а) Преобразуем десятичную дробь и смешанное число:

$$\left(\frac{3}{8}+0{,}25+\frac{1}{6}\right):1\frac{7}{12} = \left(\frac{3}{8}+\frac{1}{4}+\frac{1}{6}\right):\frac{19}{12}$$
$$\frac{3}{8}+\frac{1}{4}+\frac{1}{6} = \frac{9}{24}+\frac{6}{24}+\frac{4}{24} = \frac{19}{24}$$
$$\frac{19}{24}:\frac{19}{12} = \frac{19}{24}\cdot\frac{12}{19} = \frac{1}{2}$$

б)

$$8:0{,}16-3\frac{3}{4}\cdot 6{,}4 = 8:\frac{16}{100}-3\frac{3}{4}\cdot\frac{64}{10}$$
$$8:\frac{16}{100}=8:\frac{4}{25}=8\cdot\frac{25}{4}=50$$
$$3\frac{3}{4}\cdot 6{,}4=\frac{15}{4}\cdot\frac{64}{10}=24$$
$$50-24=26$$

в)

$$6{,}25\cdot 8-3\frac{2}{3}:5{,}5+2{,}4\cdot 4\frac{7}{12} = \frac{625}{100}\cdot 8-\frac{11}{3}:\frac{11}{2}+\frac{24}{10}\cdot\frac{55}{12}$$
$$\frac{625}{100}\cdot 8=25\cdot 2=50$$
$$\frac{11}{3}:\frac{11}{2}=\frac{11}{3}\cdot\frac{2}{11}=\frac{2}{3}$$
$$\frac{24}{10}\cdot\frac{55}{12}=\frac{2}{5}\cdot\frac{55}{1}=11$$
$$50-\frac{2}{3}+11=61-\frac{2}{3}=60\frac{1}{3}$$

г)

$$\left(\left(1\frac{2}{5}\right)^2-1{,}6\right):0{,}12 = \left(\left(\frac{7}{5}\right)^2-\frac{16}{10}\right):\frac{12}{100}$$
$$\left(\frac{7}{5}\right)^2=\frac{49}{25}, \qquad \frac{16}{10}=\frac{8}{5}=\frac{40}{25}$$
$$\left(\frac{49}{25}-\frac{40}{25}\right):\frac{12}{100} = \frac{9}{25}:\frac{3}{25} = \frac{9}{25}\cdot\frac{25}{3} = 3$$

Ответ

а) $$\frac{1}{2}$$; б) $$26$$; в) $$60\frac{1}{3}$$; г) $$3$$.