Решебник по математике 6 класс Виленкин Часть 1, 2 Часть 1. Параграф 3. Отношения и пропорции Задание 84

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Пояснение.

Решение.

\[\textbf{а)}\ 7\ :28 = 5,5\ :4x\]

\[4x = \frac{28 \cdot 5,5}{7}\]

\[x = \frac{4 \cdot 5,5}{4}\]

\[x = 5,5.\]

\[\textbf{б)}\ 3x\ :11 = 1\frac{1}{2}\ :2\frac{3}{4}\]

\[3x \cdot 2\frac{3}{4} = 11 \cdot 1\frac{1}{2}\]

\[3x = 11 \cdot \frac{3}{2}\ :\frac{11}{4}\]

\[3x = 11 \cdot \frac{3}{2} \cdot \frac{4}{11}\]

\[3x = 6\]

\[x = 6\ :3\]

\[x = 2.\]

\[\textbf{в)}\ 1,35\ :0,6 = 1,08\ :0,4x\]

\[1,35 \cdot 0,4x = 1,08 \cdot 0,6\]

\[x = \frac{108 \cdot 6}{135 \cdot 4} = \frac{27 \cdot 2}{45} = \frac{3 \cdot 2}{5}\]

\[x = 1,2.\]

\[\textbf{г)}\ 2\frac{1}{4}\ :1 = 3x\ :\frac{2}{3}\]

\[3x = 2\frac{1}{4} \cdot \frac{2}{3}\]

\[3x = \frac{9}{4} \cdot \frac{2}{3} = \frac{3}{2}\]

\[3x = 1,5\]

\[x = 1,5\ :3\]

\[x = 0,5.\]