Упр.1028 ГДЗ Никольский Потапов 5 класс (Математика)

Задача

а) (2/15 + 1 7/12) · 30/103 — 2 : 2 1/4 · 9/32 + 2 1/3;
б) (7 1/2 · 2 2/3 — 12 1/4 : 7/9) : 6 + 3 1/8 + 5 2/7;
в) 5 1/3 : 6 2/5 + (12 : 3 3/5 — 2/3) · 2/3 + 7 2/5;
г) 21 2/59 — 2/5 · (3 15/28 : 9/28 — 1 : 1 10/49) : 2.

Подробный ответ

а) Преобразуем смешанные числа в неправильные дроби и выполняем действия по порядку:

$$ \left(\frac{2}{15}+1\frac{7}{12}\right)\cdot \frac{30}{103}-2:2\frac{1}{4}\cdot \frac{9}{32}+2\frac{1}{3} $$
$$ \frac{2}{15}+1\frac{7}{12}=\frac{2}{15}+\frac{19}{12}=\frac{8}{60}+\frac{95}{60}=\frac{103}{60} $$
$$ \frac{103}{60}\cdot \frac{30}{103}=\frac{1}{2} $$
$$ 2:2\frac{1}{4}\cdot \frac{9}{32}=2:\frac{9}{4}\cdot \frac{9}{32}=2\cdot \frac{4}{9}\cdot \frac{9}{32}=\frac{1}{4} $$
$$ \frac{1}{2}-\frac{1}{4}+\frac{2}{3}=\frac{1}{4}+\frac{2}{3}=\frac{3}{12}+\frac{8}{12}=\frac{11}{12} $$

б)

$$ \left(7\frac{1}{2}\cdot 2\frac{2}{3}-12\frac{1}{4}:\frac{7}{9}\right):6+3\frac{1}{8}+5\frac{2}{7} $$
$$ 7\frac{1}{2}\cdot 2\frac{2}{3}=\frac{15}{2}\cdot \frac{8}{3}=20 $$
$$ 12\frac{1}{4}:\frac{7}{9}=\frac{49}{4}:\frac{7}{9}=\frac{49}{4}\cdot \frac{9}{7}=15\frac{3}{4} $$
$$ 20-15\frac{3}{4}=4\frac{1}{4} $$
$$ 4\frac{1}{4}:6=\frac{17}{4}:6=\frac{17}{24} $$
$$ \frac{17}{24}+3\frac{1}{8}+5\frac{2}{7} =\frac{17}{24}+\frac{25}{8}+\frac{37}{7} =\frac{17}{24}+\frac{75}{24}+\frac{124}{24} =\frac{216}{24}=9 $$

в)

$$ 5\frac{1}{3}:6\frac{2}{5}+\left(12:3\frac{3}{5}-\frac{2}{3}\right)\cdot \frac{2}{3}+7\frac{2}{5} $$
$$ 5\frac{1}{3}:6\frac{2}{5}=\frac{16}{3}:\frac{32}{5}=\frac{16}{3}\cdot \frac{5}{32}=\frac{5}{6} $$
$$ 12:3\frac{3}{5}=12:\frac{18}{5}=12\cdot \frac{5}{18}=\frac{10}{3} $$
$$ \frac{10}{3}-\frac{2}{3}=\frac{8}{3} $$
$$ \frac{8}{3}\cdot \frac{2}{3}=\frac{16}{9}=1\frac{7}{9} $$
$$ \frac{5}{6}+1\frac{7}{9}+7\frac{2}{5} =\frac{75}{90}+\frac{160}{90}+\frac{666}{90} =\frac{901}{90}=10\frac{1}{90} $$

г)

$$ 21\frac{2}{59}-\frac{2}{5}\cdot \left(3\frac{15}{28}:\frac{9}{28}-1:\,1\frac{10}{49}\right):2 $$
$$ 3\frac{15}{28}:\frac{9}{28}=\frac{99}{28}:\frac{9}{28}=11 $$
$$ 1:1\frac{10}{49}=1:\frac{59}{49}=\frac{49}{59} $$
$$ 11-\frac{49}{59}=10\frac{10}{59} $$
$$ \frac{2}{5}\cdot 10\frac{10}{59}:2=\frac{2}{5}\cdot \frac{600}{59}:2=\frac{240}{59}:2=\frac{120}{59}=2\frac{2}{59} $$
$$ 21\frac{2}{59}-2\frac{2}{59}=19 $$