Упр.83 Вариант 1 Дидактические материалы ГДЗ Мерзляк Полонский 6 класс (Математика)

Вычислите значение выражения:

1. $$\left(2\frac{1}{4}+3\frac{2}{3}\right):\left(8\frac{1}{2}-1\frac{2}{5}\right)\cdot 1{,}2$$;
2. $$\left(1\frac{9}{16}\cdot 3\frac{1}{5}+1\frac{2}{3}-9:2\frac{2}{5}\right):\left(17\frac{7}{12}-6\frac{1}{3}\right)$$.

1) $$\left(2\frac14+3\frac23\right):\left(8\frac12-1\frac25\right)\cdot1{,}2$$

$$2\frac14+3\frac23=2\frac3{12}+3\frac8{12}=5\frac{11}{12}$$
$$8\frac12-1\frac25=8\frac5{10}-1\frac4{10}=7\frac1{10}$$
$$5\frac{11}{12}:7\frac1{10}=\frac{71}{12}:\frac{71}{10}=\frac{71}{12}\cdot\frac{10}{71}=\frac56$$
$$\frac56\cdot1{,}2=\frac56\cdot\frac{12}{10}=1$$

2) $$\left(1\frac{9}{16}\cdot3\frac15+1\frac23-9:2\frac25\right):\left(17\frac7{12}-6\frac13\right)$$

$$1\frac{9}{16}\cdot3\frac15=\frac{25}{16}\cdot\frac{16}{5}=5$$
$$9:2\frac25=9:\frac{12}{5}=9\cdot\frac{5}{12}=\frac{15}{4}=3\frac34$$
$$5+1\frac23-3\frac34=6\frac23-3\frac34=6\frac8{12}-3\frac9{12}=2\frac{11}{12}$$
$$17\frac7{12}-6\frac13=17\frac7{12}-6\frac4{12}=11\frac3{12}=11\frac14$$
$$2\frac{11}{12}:11\frac14=\frac{35}{12}:\frac{45}{4}=\frac{35}{12}\cdot\frac{4}{45}=\frac{7}{27}$$

Ответ: 1) $$1$$; 2) $$\frac{7}{27}$$.