Вариант 2 1. Найдите значение выражения: a)7$$\frac{11}{12}$$:3$$\frac{1}{6}$$; 2 3 б)4-215 3,4 1,71 в) 20.4 г)45

Решим пример a) 7$$\frac{11}{12}$$:3$$\frac{1}{6}$$:

Преобразуем смешанные дроби в неправильные:

7$$\frac{11}{12}$$ = $$\frac{7 \cdot 12 + 11}{12}$$ = $$\frac{84 + 11}{12}$$ = $$\frac{95}{12}$$

3$$\frac{1}{6}$$ = $$\frac{3 \cdot 6 + 1}{6}$$ = $$\frac{18 + 1}{6}$$ = $$\frac{19}{6}$$

Теперь разделим две дроби:

$$\frac{95}{12}$$ : $$\frac{19}{6}$$ = $$\frac{95}{12}$$ × $$\frac{6}{19}$$ = $$\frac{95 \cdot 6}{12 \cdot 19}$$ = $$\frac{5 \cdot 19 \cdot 6}{6 \cdot 2 \cdot 19}$$ = $$\frac{5}{2}$$ = 2$$\frac{1}{2}$$ = 2,5

Решим пример б) 4$$\frac{2}{5}$$-$$\frac{3}{215}$$:

4$$\frac{2}{5}$$ = $$\frac{4 \cdot 5 + 2}{5}$$ = $$\frac{20 + 2}{5}$$ = $$\frac{22}{5}$$

$$\frac{22}{5}$$-$$\frac{3}{215}$$ =$$\frac{22 \cdot 43}{5 \cdot 43}$$-$$\frac{3}{215}$$ = $$\frac{946}{215}$$-$$\frac{3}{215}$$ = $$\frac{946-3}{215}$$ = $$\frac{943}{215}$$ = 4$$\frac{83}{215}$$

Решим пример в) $$\frac{3,4}{20,4}$$:

$$\frac{3,4}{20,4}$$ = $$\frac{34}{204}$$ = $$\frac{17 \cdot 2}{17 \cdot 12}$$ = $$\frac{2}{12}$$ = $$\frac{1}{6}$$

Решим пример г) $$\frac{1,71}{45}$$:

$$\frac{1,71}{45}$$ = $$\frac{171}{4500}$$ = $$\frac{9 \cdot 19}{9 \cdot 500}$$ = $$\frac{19}{500}$$

Ответ: a) 2,5; б) 4$$\frac{83}{215}$$; в) $$\frac{1}{6}$$; г) $$\frac{19}{500}$$