Упр.1028 ГДЗ Никольский Потапов 5 класс (Математика)

1. Вычислите: а) $$\left(\frac{2}{15}+1\frac{7}{12}\right)\cdot\frac{30}{103}-2:2\frac{1}{4}\cdot\frac{9}{32}+2\frac{1}{3}$$; б) $$\left(7\frac{1}{2}\cdot2\frac{2}{3}-12\frac{1}{4}: \frac{7}{9}\right):6+3\frac{1}{8}+5\frac{2}{7}$$; в) $$5\frac{1}{3}:6\frac{2}{5}+\left(12:3\frac{3}{5}-\frac{2}{3}\right)\cdot\frac{2}{3}+7\frac{2}{5}$$; г) $$21\frac{2}{59}-\frac{2}{5}\cdot\left(3\frac{15}{28}:\frac{9}{28}-1:1\frac{10}{49}\right):2$$.

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)

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

Ответ

а) $$\frac{11}{12}$$; б) $$9$$; в) $$10\frac{1}{90}$$; г) $$19$$.