Упр.1132 ГДЗ Никольский Потапов 5 класс (Математика)

((53 3/4 + 9 1/6) · 1 1/5)/((10 3/10 — 8 1/2) · 5/9) — ((6 4/5 — 3 3/7) · 5 5/6)/(3 2/3 — 3 1/6) — 29 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

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