Упр.620 Часть 2 ГДЗ Виленкин Жохов 6 класс (Математика)

Задача

a) 1 1/3 * (8 2/3 : 1 4/9 — 3 3/8 + 1 5/8) — 1 5/6;
Р±) (3 1/15 — 1 1/15 : 1 3/5 + 2/5) * 2 1/7 — 1 1/7;
РІ) 19,6 * 2 1/2 — (2,0625 — 1 5/12) : 1/8;
Рі) 5/16 * 0,125 + 1,456 : 7/25 + 4,5 * 4/5.

Подробный ответ

а)

$$ 1\frac{1}{3}\cdot\left(8\frac{2}{3}:1\frac{4}{9}-3\frac{3}{8}+1\frac{5}{8}\right)-1\frac{5}{6} $$
$$ =\frac{4}{3}\cdot\left(\frac{26}{3}:\frac{13}{9}-2\frac{1}{8}+1\frac{5}{8}\right)-1\frac{5}{6} $$
$$ =\frac{4}{3}\cdot\left(\frac{26}{3}\cdot\frac{9}{13}-1\frac{6}{8}\right)-1\frac{5}{6} =\frac{4}{3}\cdot\left(2\cdot 3-1\frac{3}{4}\right)-1\frac{5}{6} $$
$$ =\frac{4}{3}\cdot\left(6-1\frac{3}{4}\right)-1\frac{5}{6} =\frac{4}{3}\cdot 4\frac{1}{4}-1\frac{5}{6} $$
$$ =\frac{4}{3}\cdot\frac{17}{4}-1\frac{5}{6} =\frac{17}{3}-1\frac{5}{6} =5\frac{2}{3}-1\frac{5}{6} =5\frac{4}{6}-1\frac{5}{6} =4\frac{10}{6}-1\frac{5}{6} =3\frac{5}{6}. $$

б)

$$ \left(3\frac{1}{15}-1\frac{1}{15}:1\frac{3}{5}+ \frac{2}{5}\right)\cdot 2\frac{1}{7}-1\frac{1}{7} $$
$$ =\left(3\frac{1}{15}-\frac{16}{15}:\frac{8}{5}+\frac{2}{5}\right)\cdot\frac{15}{7}-1\frac{1}{7} $$
$$ =\left(3\frac{1}{15}-\frac{16}{15}\cdot\frac{5}{8}+\frac{2}{5}\right)\cdot\frac{15}{7}-1\frac{1}{7} $$
$$ =\left(3\frac{1}{15}-\frac{2}{3}+\frac{2}{5}\right)\cdot\frac{15}{7}-1\frac{1}{7} $$
$$ =\left(2\frac{16}{15}-\frac{10}{15}+\frac{6}{15}\right)\cdot\frac{15}{7}-1\frac{1}{7} $$
$$ =\left(2\frac{12}{15}\right)\cdot\frac{15}{7}-1\frac{1}{7} =2\frac{4}{5}\cdot\frac{15}{7}-1\frac{1}{7} $$
$$ =\frac{14}{5}\cdot\frac{15}{7}-1\frac{1}{7} =6-1\frac{1}{7} =4\frac{6}{7}. $$

в)

$$ 19{,}6\cdot 2\frac{1}{2}-(2{,}0625-1\frac{5}{12}):\frac{1}{8} $$
$$ =\frac{196}{10}\cdot\frac{5}{2}-\left(2\frac{1}{16}-1\frac{5}{12}\right)\cdot 8 $$
$$ =49-\left(2\frac{3}{48}-1\frac{20}{48}\right)\cdot 8 =49-\left(1\frac{31}{48}\right)\cdot 8 $$
$$ =49-\frac{31}{48}\cdot 8 =49-\frac{31}{6} =49-5\frac{1}{6} =43\frac{5}{6}. $$

г)

$$ \frac{5}{16}\cdot 0{,}125+1{,}456:\frac{7}{25}+4{,}5\cdot\frac{4}{5} $$
$$ =\frac{5}{16}\cdot\frac{1}{8}+\frac{1456}{1000}:\frac{7}{25}+\frac{45}{10}\cdot\frac{4}{5} $$
$$ =\frac{5}{16}\cdot\frac{1}{8}+\frac{182}{125}\cdot\frac{25}{7}+\frac{9}{2}\cdot\frac{4}{5} $$
$$ =\frac{5}{128}+ \frac{26}{5}+\frac{18}{5} =\frac{5}{128}+ \frac{44}{5}. $$
$$ \frac{44}{5}=8\frac{4}{5}, \quad \frac{5}{128}\approx 0{,}04, $$
поэтому
$$ 8\frac{4}{5}+\frac{5}{128}=11{,}3. $$