Упр.1132 ГДЗ Никольский Потапов 5 класс (Математика)

Выполните действия: $$\frac{\left(53\frac{3}{4}+9\frac{1}{6}\right)\cdot1\frac{1}{5}}{\left(10\frac{3}{10}-8\frac{1}{2}\right)\cdot\frac{5}{9}}-\frac{\left(6\frac{4}{5}-3\frac{3}{7}\right)\cdot5\frac{5}{6}}{3\frac{2}{3}-3\frac{1}{6}}-29\frac{5}{6}.$$

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

$$\frac{\left(53\frac{3}{4}+9\frac{1}{6}\right)\cdot 1\frac{1}{5}}{\left(10\frac{3}{10}-8\frac{1}{2}\right)\cdot \frac{5}{9}} — \frac{\left(6\frac{4}{5}-3\frac{3}{7}\right)\cdot 5\frac{5}{6}}{3\frac{2}{3}-3\frac{1}{6}} -29\frac{5}{6}$$

$$53\frac{3}{4}=53\frac{9}{12},\quad 9\frac{1}{6}=9\frac{2}{12},\quad 1\frac{1}{5}=\frac{6}{5}$$
$$10\frac{3}{10}=10\frac{5}{10},\quad 8\frac{1}{2}=8\frac{5}{10}$$
$$6\frac{4}{5}=6\frac{28}{35},\quad 3\frac{3}{7}=3\frac{15}{35},\quad 5\frac{5}{6}=\frac{35}{6}$$
$$3\frac{2}{3}=3\frac{4}{6},\quad 3\frac{1}{6}=3\frac{1}{6}$$

Тогда

$$\frac{\left(53\frac{9}{12}+9\frac{2}{12}\right)\cdot \frac{6}{5}}{\left(10\frac{5}{10}-8\frac{5}{10}\right)\cdot \frac{5}{9}} — \frac{\left(6\frac{28}{35}-3\frac{15}{35}\right)\cdot \frac{35}{6}}{3\frac{4}{6}-3\frac{1}{6}} -29\frac{5}{6}$$

$$=\frac{62\frac{11}{12}\cdot \frac{6}{5}}{2\cdot \frac{5}{9}} — \frac{3\frac{13}{35}\cdot \frac{35}{6}}{\frac{3}{6}} -29\frac{5}{6}$$

$$= \frac{\frac{755}{12}\cdot \frac{6}{5}}{\frac{1}{1}\cdot \frac{5}{9}} — \frac{\frac{118}{35}\cdot \frac{35}{6}}{\frac{1}{2}} -29\frac{5}{6}$$

$$= \frac{151}{2}\div \frac{5}{9} — \frac{59}{3}\div \frac{1}{2} -29\frac{5}{6}$$

$$= \frac{151}{2}\cdot \frac{9}{5} — \frac{59}{3}\cdot 2 -29\frac{5}{6}$$

$$=75\frac{3}{6}-39\frac{1}{3}-29\frac{5}{6}$$

$$=75\frac{6}{6}-39\frac{2}{6}-29\frac{5}{6} =75-39\frac{1}{3}-29\frac{5}{6}$$

$$=36\frac{1}{6}-29\frac{5}{6} =35\frac{7}{6}-29\frac{5}{6} =6\frac{2}{6} =6\frac{1}{3}$$

Ответ

$$6\frac{1}{3}$$