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

Задача

a) (3/8 + 0,25 + 1/6) : 1 7/12;
б) 8 : 0,16 — 3 3/4 * 6,4;
в) 6,25 * 8 — 3 2/3 : 5,5 + 2,4 * 4 7/12;
г) ((1 2/5)2 — 1,6) : 0,12.

Подробный ответ

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)

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