5.560 Вычислите: 1) \(\frac{1}{4}:\frac{1}{4}⋅\frac{2}{7}\); 2) \(\frac{1}{3}:\frac{7}{8}⋅\frac{9}{14}\); 3) \(\frac{1}{3}:\frac{7}{8}⋅\frac{9}{14}\); 4) \(\frac{6}{7}:\frac{5}{7}⋅\frac{4}{9}\)

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Вопрос:

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Accepted Answer

Краткое пояснение: Сначала выполняем деление, затем умножение.

1) \(\frac{1}{4}:\frac{1}{4}⋅\frac{2}{7} = 1 \cdot \frac{2}{7} = \frac{2}{7}\)
2) \(\frac{1}{3}:\frac{7}{8}⋅\frac{9}{14} = \frac{1}{3} \cdot \frac{8}{7} \cdot \frac{9}{14} = \frac{1 \cdot 8 \cdot 9}{3 \cdot 7 \cdot 14} = \frac{72}{294} = \frac{12}{49}\)
3) \(\frac{1}{3}:\frac{7}{8}⋅\frac{9}{14} = \frac{1}{3} \cdot \frac{8}{7} \cdot \frac{9}{14} = \frac{1 \cdot 8 \cdot 9}{3 \cdot 7 \cdot 14} = \frac{72}{294} = \frac{12}{49}\)
4) \(\frac{6}{7}:\frac{5}{7}⋅\frac{4}{9} = \frac{6}{7} \cdot \frac{7}{5} \cdot \frac{4}{9} = \frac{6 \cdot 7 \cdot 4}{7 \cdot 5 \cdot 9} = \frac{168}{315} = \frac{8}{15}\)

Ответ: 1) \(\frac{2}{7}\); 2) \(\frac{12}{49}\); 3) \(\frac{12}{49}\); 4) \(\frac{8}{15}\)