Вычислите значение выражения: 1) \(2+\frac{1}{4}\)\(\cdot\)3\(\frac{1}{2}\):\(8\frac{1}{2}-1\frac{2}{5}\)\(\cdot\)1,2

Решение:

Задание состоит из двух примеров. Решим первый пример:

1. \(2+\frac{1}{4} = \frac{8}{4} + \frac{1}{4} = \frac{9}{4}\)
2. \(3\frac{1}{2} = \frac{7}{2}\)
3. \(8\frac{1}{2} = \frac{17}{2}\)
4. \(1\frac{2}{5} = \frac{7}{5}\)
5. \(\frac{17}{2} - \frac{7}{5} = \frac{17 \cdot 5 - 7 \cdot 2}{10} = \frac{85 - 14}{10} = \frac{71}{10}\)
6. \(\frac{9}{4} \cdot \frac{7}{2} = \frac{63}{8}\)
7. \(\frac{63}{8} : \frac{71}{10} = \frac{63}{8} \cdot \frac{10}{71} = \frac{63 \cdot 5}{4 \cdot 71} = \frac{315}{284}\)
8. \(1,2 = \frac{12}{10} = \frac{6}{5}\)
9. \(\frac{315}{284} \cdot \frac{6}{5} = \frac{63 \cdot 6}{284} = \frac{378}{284} = \frac{189}{142}\)

Теперь решим второй пример:

2) \((\frac{1}{16} \cdot \frac{9}{5} + 1\frac{1}{3}) : (\frac{17}{12} - 9\frac{2}{5})\)

1. \(\frac{1}{16} \cdot \frac{9}{5} = \frac{9}{80}\)
2. \(\frac{9}{80} + 1\frac{1}{3} = \frac{9}{80} + \frac{4}{3} = \frac{9 \cdot 3 + 4 \cdot 80}{240} = \frac{27 + 320}{240} = \frac{347}{240}\)
3. \(9\frac{2}{5} = \frac{47}{5}\)
4. \(\frac{17}{12} - \frac{47}{5} = \frac{17 \cdot 5 - 47 \cdot 12}{60} = \frac{85 - 564}{60} = \frac{-479}{60}\)
5. \(\frac{347}{240} : \frac{-479}{60} = \frac{347}{240} \cdot \frac{60}{-479} = \frac{347}{4 \cdot (-479)} = \frac{347}{-1916}\)

Ответ: 1) \(\frac{189}{142}\), 2) \(\frac{-347}{1916}\).