Решебник по алгебре 8 класс Мерзляк ФГОС Задание 66

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\[1)\ \frac{7}{18} + \frac{5}{18} = \frac{12}{18} = \frac{2}{3}\]

\[2)\ \frac{9}{16} + \frac{7}{16} = \frac{16}{16} = 1\]

\[3)\ \frac{23}{32} - \frac{15}{32} = \frac{8}{32} = \frac{1}{4}\ \]

\[4)\ 4 - 1\frac{3}{11} = 4 - \frac{14}{11} =\]

\[= \frac{4 \cdot 11 - 14}{11} = \frac{44 - 14}{11} =\]

\[= \frac{30}{11} = 2\frac{8}{11}\]

\[\boxed{\text{66.\ }\text{Еуроки\ -\ ДЗ\ без\ мороки}}\]

Пояснение.

Решение.

\[1)\ \frac{x}{6} + \frac{y}{6} = \frac{x + y}{6}\]

\[2)\ \frac{a}{3} - \frac{b}{3} = \frac{a - b}{3}\]

\[3)\ \frac{m}{n} + \frac{4m}{n} = \frac{m + 4m}{n} = \frac{5m}{n}\]

\[4)\ \frac{6c}{d} - \frac{2c}{d} = \frac{6c - 2c}{d} = \frac{4c}{d}\ \]

\[5)\ \frac{m + n}{6} - \frac{m - 2n}{6} =\]

\[= \frac{m + n - m + 2n}{6} = \frac{3n}{6} = \frac{n}{2}\]

\[6)\ \frac{2a - 3b}{6ab} + \frac{9b - 2a}{6ab} =\]

\[= \frac{2a - 3b + 9b - 2a}{6ab} = \frac{6b}{6ab} = \frac{1}{a}\]

\[7)\ - \frac{5c + 4d}{\text{cd}} + \frac{4d + 9c}{\text{cd}} =\]

\[= \frac{4d + 9c - 5c - 4d}{\text{cd}} = \frac{4c}{\text{cd}} = \frac{4}{d}\]

\[8)\ \frac{8m + 3}{10m^{2}} - \frac{2m + 3}{10m^{2}} =\]

\[= \frac{8m + 3 - 2m - 3}{10m^{2}} =\]

\[= \frac{6m}{10m^{2}} = \frac{3}{5m}\]