Упр.1136 ГДЗ Никольский Потапов 5 класс (Математика)

Задача

а) (3 1/2 : 4 2/3 + 4 2/3 : 3 1/2) · 4 4/5;
б) 3 1/8 : ((4 5/12 — 3 13/24) · 4/7 + (3 1/18 — 2 7/12) · 1 10/17);
в) 2 3/4 : ((4 5/7 — 1 11/14) · 4 2/3 + (3 2/9 — 1 5/6) · 18/25);
г) (15 : 3 3/4 — (10 1/2 : 1 1/2) · 3/14 : (1 23/52 — 1 1/4);
д) ((7/15 + 14/45 + 2/9) · 10 1/3 — 1 1/11 · (2 2/3 — 1 3/4))/((3/7 — 1/4) : 3/28 — 1);
е) (15 : 5/18 : 3 3/8 · (1/16 + 11/36 + 5/48 + 5/18))/((11 5/11 — 8 21/22) : 1 2/3).

Подробный ответ

а)

$$ \left(3\frac{1}{2}:4\frac{2}{3}+4\frac{2}{3}:3\frac{1}{2}\right)\cdot 4\frac{4}{5} = \left(\frac{7}{2}:\frac{14}{3}+\frac{14}{3}:\frac{7}{2}\right)\cdot \frac{24}{5} $$
$$ = \left(\frac{7}{2}\cdot\frac{3}{14}+\frac{14}{3}\cdot\frac{2}{7}\right)\cdot \frac{24}{5} = \left(\frac{3}{4}+\frac{4}{3}\right)\cdot \frac{24}{5} $$
$$ = \frac{25}{12}\cdot \frac{24}{5} = 10 $$

б)

$$ 3\frac{1}{8}:\left(\left(4\frac{5}{12}-3\frac{13}{24}\right)\cdot \frac{4}{7} +\left(3\frac{1}{18}-2\frac{7}{12}\right)\cdot 1\frac{10}{17}\right) $$
$$ = \frac{25}{8}:\left(\left(\frac{29}{6}-\frac{85}{24}\right)\cdot \frac{4}{7} +\left(\frac{55}{18}-\frac{31}{12}\right)\cdot \frac{27}{17}\right) $$
$$ = \frac{25}{8}:\left(\frac{31}{24}\cdot \frac{4}{7}+\frac{23}{36}\cdot \frac{27}{17}\right) = \frac{25}{8}:\left(\frac{31}{42}+\frac{23}{68}\right) $$
$$ = \frac{25}{8}:\left(\frac{2}{4}+\frac{3}{4}\right) = \frac{25}{8}:\frac{5}{4} = \frac{25}{8}\cdot \frac{4}{5} = \frac{5}{2} $$

в)

$$ 2\frac{3}{4}:\left(\left(4\frac{5}{7}-1\frac{11}{14}\right)\cdot 4\frac{2}{3} +\left(3\frac{2}{9}-1\frac{5}{6}\right)\cdot \frac{18}{25}\right) $$
$$ = \frac{11}{4}:\left(\left(\frac{33}{7}-\frac{25}{14}\right)\cdot \frac{14}{3} +\left(\frac{29}{9}-\frac{11}{6}\right)\cdot \frac{18}{25}\right) $$
$$ = \frac{11}{4}:\left(\frac{41}{14}\cdot \frac{14}{3}+\frac{25}{18}\cdot \frac{18}{25}\right) = \frac{11}{4}:\left(\frac{41}{3}+1\right) $$
$$ = \frac{11}{4}:\frac{44}{3} = \frac{11}{4}\cdot \frac{3}{44} = \frac{3}{16} $$

г)

$$ \left(15:3\frac{3}{4}-\left(10\frac{1}{2}:1\frac{1}{2}\right)\cdot \frac{3}{14}\right):\left(1\frac{23}{52}-1\frac{1}{4}\right) $$
$$ = \left(15:\frac{15}{4}-\left(\frac{21}{2}:\frac{3}{2}\right)\cdot \frac{3}{14}\right):\left(\frac{75}{52}-\frac{5}{4}\right) $$
$$ = \left(4-7\cdot \frac{3}{14}\right):\frac{5}{26} = \left(4-\frac{3}{2}\right):\frac{5}{26} = \frac{5}{2}:\frac{5}{26} = 13 $$

д)

$$ \frac{\left(\frac{7}{15}+\frac{14}{45}+\frac{2}{9}\right)\cdot 10\frac{1}{3}-1\frac{1}{11}\cdot \left(2\frac{2}{3}-1\frac{3}{4}\right)} {\left(\frac{3}{7}-\frac{1}{4}\right):\frac{3}{28}-1} $$
$$ = \frac{\left(\frac{21}{45}+\frac{14}{45}+\frac{10}{45}\right)\cdot \frac{31}{3}-\frac{12}{11}\cdot \left(\frac{8}{3}-\frac{7}{4}\right)} {\left(\frac{12}{28}-\frac{7}{28}\right):\frac{3}{28}-1} $$
$$ = \frac{1\cdot \frac{31}{3}-\frac{12}{11}\cdot \frac{11}{12}} {\frac{5}{28}:\frac{3}{28}-1} = \frac{\frac{31}{3}-1}{\frac{5}{3}-1} = \frac{\frac{28}{3}}{\frac{2}{3}} = 14 $$

е)

$$ \frac{15:\frac{5}{18}:3\frac{3}{8}\cdot \left(\frac{1}{16}+\frac{11}{36}+\frac{5}{48}+\frac{5}{18}\right)} {\left(11\frac{5}{11}-8\frac{21}{22}\right):1\frac{2}{3}} $$
$$ = \frac{15\cdot \frac{18}{5}:\frac{27}{8}\cdot \left(\left(\frac{1}{16}+\frac{5}{48}\right)+\left(\frac{11}{36}+\frac{5}{18}\right)\right)} {\left(10\frac{32}{22}-8\frac{21}{22}\right):\frac{5}{3}} $$
$$ = \frac{15\cdot \frac{18}{5}:\frac{27}{8}\cdot \left(\frac{8}{48}+\frac{21}{36}\right)} {\left(2\frac{11}{22}\right):\frac{5}{3}} = \frac{15\cdot \frac{18}{5}:\frac{27}{8}\cdot \frac{3}{2}} {\frac{5}{3}:\frac{5}{3}} $$
$$ = \frac{4\cdot 3}{2} = 6 $$