Упр.8.121 ГДЗ Дорофеев Шарыгин 5 класс (Математика)

а) 17 : (3/5 + 1/4) + (7/8 — 1/4) · (4/5)^2;
б) 70 : (5/8 + 5/6) + (3 1/9 — 1/3) · (3/10)^2.

а) Преобразуем дроби в скобках:

$$ 17 : \left(\frac{3}{5}+\frac{1}{4}\right)+\left(\frac{7}{8}-\frac{1}{4}\right)\cdot\left(\frac{4}{5}\right)^2 $$
$$ \frac{3}{5}+\frac{1}{4}=\frac{12}{20}+\frac{5}{20}=\frac{17}{20} $$
$$ \frac{7}{8}-\frac{1}{4}=\frac{7}{8}-\frac{2}{8}=\frac{5}{8} $$
$$ \left(\frac{4}{5}\right)^2=\frac{16}{25} $$
Тогда
$$ 17:\frac{17}{20}+\frac{5}{8}\cdot\frac{16}{25} $$
$$ 17:\frac{17}{20}=17\cdot\frac{20}{17}=20 $$
$$ \frac{5}{8}\cdot\frac{16}{25}=\frac{2}{5} $$
$$ 20+\frac{2}{5}=20\frac{2}{5} $$

б)

$$ 70 : \left(\frac{5}{8}+\frac{5}{6}\right)+\left(3\frac{1}{9}-\frac{1}{3}\right)\cdot\left(\frac{3}{10}\right)^2 $$
$$ \frac{5}{8}+\frac{5}{6}=\frac{15}{24}+\frac{20}{24}=\frac{35}{24} $$
$$ 3\frac{1}{9}=\frac{28}{9}, \qquad \frac{28}{9}-\frac{1}{3}=\frac{28}{9}-\frac{3}{9}=\frac{25}{9} $$
$$ \left(\frac{3}{10}\right)^2=\frac{9}{100} $$
Тогда
$$ 70:\frac{35}{24}+\frac{25}{9}\cdot\frac{9}{100} $$
$$ 70:\frac{35}{24}=70\cdot\frac{24}{35}=2\cdot 24=48 $$
$$ \frac{25}{9}\cdot\frac{9}{100}=\frac{1}{4} $$
$$ 48+\frac{1}{4}=48\frac{1}{4} $$

Ответ

а) $$20\frac{2}{5}$$;
б) $$48\frac{1}{4}$$.