Упр.1029 ГДЗ Никольский Потапов 5 класс (Математика)

Задача

Вычислите:

а) $$\frac{20 : 2\frac{2}{15} + 25\frac{5}{7} : 1\frac{1}{35}}{21\frac{7}{9} : 4\frac{2}{3} — 1}$$;

б) $$\frac{6\frac{3}{4} : 9 + 24 : \frac{6}{7} — \frac{1}{9} : \frac{4}{21}}{53\frac{2}{3} — 22\frac{14}{15} : 2\frac{2}{3}}$$;

в) $$\frac{20\frac{3}{10} — \left(2\frac{1}{10} \cdot 4 + \frac{19}{20} \cdot 10\right)}{1 : 5}$$;

г) $$\frac{4\frac{2}{5} — 2\frac{3}{4} + 7\frac{7}{15} — 8\frac{7}{60}}{7\frac{1}{4} — 5\frac{3}{4}}$$;

д) $$\frac{\left(\frac{1}{6} + \frac{1}{10} + \frac{1}{15}\right) : \left(\frac{1}{6} + \frac{1}{30}\right)}{\left(\frac{1}{6} + \frac{1}{4} — \frac{1}{5}\right) : \left(\frac{1}{4} — \frac{1}{6}\right)}$$;

е) $$\frac{5\frac{1}{5} : \frac{39}{40}}{2\frac{4}{5} : \frac{7}{10} \cdot \frac{3}{4}} + \frac{\left(2 — 1\frac{3}{20}\right) \cdot 48}{\frac{1}{4} \cdot 20 + 1 : 10}$$.

Подробный ответ

а) $$\frac{20:2\frac{2}{15}+25\frac{5}{7}:1\frac{1}{35}}{21\frac{7}{9}:4\frac{2}{3}-1}$$

$$20:2\frac{2}{15}=20:\frac{32}{15}=20\cdot\frac{15}{32}=\frac{75}{8}=9\frac{3}{8}$$
$$25\frac{5}{7}:1\frac{1}{35}=\frac{180}{7}:\frac{36}{35}=\frac{180}{7}\cdot\frac{35}{36}=25$$
$$9\frac{3}{8}+25=34\frac{3}{8}$$
$$21\frac{7}{9}:4\frac{2}{3}=\frac{196}{9}:\frac{14}{3}=\frac{196}{9}\cdot\frac{3}{14}=\frac{14}{3}=4\frac{2}{3}$$
$$4\frac{2}{3}-1=3\frac{2}{3}$$
$$34\frac{3}{8}:3\frac{2}{3}=\frac{275}{8}:\frac{11}{3}=\frac{275}{8}\cdot\frac{3}{11}=\frac{75}{8}=9\frac{3}{8}$$

б) $$\frac{6\frac{3}{4}:9+24: \frac{6}{7}-\frac{1}{9}:\frac{4}{21}}{53\frac{2}{3}-22\frac{14}{15}:2\frac{2}{3}}$$

$$6\frac{3}{4}:9=\frac{27}{4}:9=\frac{27}{4}\cdot\frac{1}{9}=\frac{3}{4}$$
$$24:\frac{6}{7}=24\cdot\frac{7}{6}=28$$
$$\frac{1}{9}:\frac{4}{21}=\frac{1}{9}\cdot\frac{21}{4}=\frac{7}{12}$$
$$\frac{3}{4}+28-\frac{7}{12}=28\frac{1}{6}$$
$$22\frac{14}{15}:2\frac{2}{3}=\frac{344}{15}:\frac{8}{3}=\frac{344}{15}\cdot\frac{3}{8}=\frac{43}{5}=8\frac{3}{5}$$
$$53\frac{2}{3}-8\frac{3}{5}=45\frac{1}{15}$$
$$28\frac{1}{6}:45\frac{1}{15}=\frac{169}{6}:\frac{676}{15}=\frac{169}{6}\cdot\frac{15}{676}=\frac{5}{8}$$

в) $$\frac{20\frac{3}{10}-\left(2\frac{1}{10}\cdot 4+\frac{19}{20}\cdot 10\right)}{1:5}$$

$$2\frac{1}{10}\cdot 4=\frac{21}{10}\cdot 4=\frac{42}{5}=8\frac{2}{5}$$
$$\frac{19}{20}\cdot 10=\frac{19}{2}=9\frac{1}{2}$$
$$8\frac{2}{5}+9\frac{1}{2}=17\frac{9}{10}$$
$$20\frac{3}{10}-17\frac{9}{10}=2\frac{2}{5}$$
$$1:5=\frac{1}{5}$$
$$2\frac{2}{5}:\frac{1}{5}=12$$

г) $$\frac{4\frac{2}{5}-2\frac{3}{4}+7\frac{7}{15}-8\frac{7}{60}}{7\frac{1}{4}-5\frac{3}{4}}$$

$$4\frac{2}{5}-2\frac{3}{4}+7\frac{7}{15}-8\frac{7}{60}$$
$$=\frac{264}{60}-\frac{165}{60}+\frac{308}{60}-\frac{487}{60}=\frac{1}{2}$$
$$7\frac{1}{4}-5\frac{3}{4}=1\frac{1}{2}$$
$$\frac{1}{2}:1\frac{1}{2}=\frac{1}{2}:\frac{3}{2}=\frac{1}{3}$$

д) $$\frac{\left(\frac{1}{6}+\frac{1}{10}+\frac{1}{15}\right):\left(\frac{1}{6}+\frac{1}{30}\right)}{\left(\frac{1}{6}+\frac{1}{4}-\frac{1}{5}\right):\left(\frac{1}{4}-\frac{1}{6}\right)}$$

$$\frac{1}{6}+\frac{1}{10}+\frac{1}{15}=\frac{5}{30}+\frac{3}{30}+\frac{2}{30}=\frac{1}{3}$$
$$\frac{1}{6}+\frac{1}{30}=\frac{5}{30}+\frac{1}{30}=\frac{1}{5}$$
$$\left(\frac{1}{3}:\frac{1}{5}\right)=\frac{5}{3}$$
$$\frac{1}{6}+\frac{1}{4}-\frac{1}{5}=\frac{10}{60}+\frac{15}{60}-\frac{12}{60}=\frac{13}{60}$$
$$\frac{1}{4}-\frac{1}{6}=\frac{3}{12}-\frac{2}{12}=\frac{1}{12}$$
$$\left(\frac{13}{60}:\frac{1}{12}\right)=\frac{13}{5}$$
$$\frac{5}{3}:\frac{13}{5}=\frac{25}{39}$$

е) $$\frac{5\frac{1}{5}:\frac{39}{40}}{2\frac{4}{5}:\frac{7}{10}\cdot\frac{3}{4}}+\frac{\left(2-1\frac{3}{20}\right)\cdot 48}{\frac{1}{4}\cdot 20+1:10}$$

$$5\frac{1}{5}:\frac{39}{40}=\frac{26}{5}\cdot\frac{40}{39}=\frac{64}{3}$$
$$2\frac{4}{5}:\frac{7}{10}\cdot\frac{3}{4}=\frac{14}{5}\cdot\frac{10}{7}\cdot\frac{3}{4}=3$$
$$\frac{64}{3}:3=\frac{64}{9}$$
$$2-1\frac{3}{20}=2-\frac{23}{20}=\frac{17}{20}$$
$$\left(2-1\frac{3}{20}\right)\cdot 48=\frac{17}{20}\cdot 48=\frac{204}{5}$$
$$\frac{1}{4}\cdot 20+1:10=5+\frac{1}{10}=\frac{51}{10}$$
$$\frac{204}{5}:\frac{51}{10}=8$$
$$\frac{64}{9}+8=9\frac{7}{9}$$