Упр.80 Вариант 4 Дидактические материалы ГДЗ Мерзляк Полонский 6 класс (Математика)

Найдите значение выражения:

1. $$5\frac{1}{3} : \frac{8}{9} : \frac{1}{3}$$;
2. $$5\frac{1}{3} : \left(\frac{8}{9} : \frac{1}{3}\right)$$;
3. $$\left(8\frac{5}{7} — 6\frac{5}{6} : 1\frac{5}{36}\right) : 4\frac{3}{4}$$;
4. $$\left(2\frac{5}{6} + 2\frac{2}{9}\right) : 3\frac{1}{4} — \frac{2}{7} : 1\frac{2}{7}$$.

1) $$5\frac{1}{3}:\frac{8}{9}:\frac{1}{3}=\frac{16}{3}\cdot\frac{9}{8}\cdot\frac{3}{1}=\frac{16\cdot 9\cdot 3}{3\cdot 8\cdot 1}=18.$$

2) $$5\frac{1}{3}:\left(\frac{8}{9}:\frac{1}{3}\right)=\frac{16}{3}:\frac{8}{3}=\frac{16}{3}\cdot\frac{3}{8}=2.$$

3) $$\left(8\frac{5}{7}-6\frac{5}{6}:\,1\frac{5}{36}\right):4\frac{3}{4}$$

$$6\frac{5}{6}:\,1\frac{5}{36}=\frac{41}{6}:\frac{41}{36}=\frac{41}{6}\cdot\frac{36}{41}=6,$$

тогда

$$\left(8\frac{5}{7}-6\right):4\frac{3}{4}=2\frac{5}{7}:4\frac{3}{4}=\frac{19}{7}:\frac{19}{4}=\frac{19}{7}\cdot\frac{4}{19}=\frac{4}{7}.$$

4) $$\left(2\frac{5}{6}+2\frac{2}{9}\right):3\frac{1}{4}-\frac{2}{7}:1\frac{2}{7}$$

$$2\frac{5}{6}+2\frac{2}{9}=2\frac{15}{18}+2\frac{4}{18}=4\frac{19}{18}=\frac{91}{18},$$

$$3\frac{1}{4}=\frac{13}{4},\qquad 1\frac{2}{7}=\frac{9}{7},$$

тогда

$$\frac{91}{18}:\frac{13}{4}-\frac{2}{7}:\frac{9}{7}=\frac{91}{18}\cdot\frac{4}{13}-\frac{2}{7}\cdot\frac{7}{9}=\frac{7\cdot 2}{9}-\frac{2}{9}=\frac{14}{9}-\frac{2}{9}=\frac{12}{9}=1\frac{1}{3}.$$

Ответ: 1) $$18$$; 2) $$2$$; 3) $$\frac{4}{7}$$; 4) $$1\frac{1}{3}$$.