Решите уравнение:
а) $\frac{2}{7}х = 2\frac{2}{7}$;
б) $\frac{3}{5}y = 2\frac{9}{10} - \frac{1}{5}$;
в) $\frac{3}{7}a + \frac{2}{5} = 1$;
г) $3\frac{1}{3} : k = 1\frac{1}{3} : 2$;
д) $y : 1\frac{1}{2} = 2\frac{1}{3} * \frac{1}{3}$;
е) $\frac{2}{7}х + \frac{3}{7}х = 2\frac{7}{14}$;
ж) $m + \frac{3}{8}m = \frac{1}{4}$;
з) $y - \frac{2}{9}y = 4\frac{2}{3}$;
и) $\frac{2}{5}z + \frac{2}{3}z - \frac{7}{15}z = 2\frac{1}{2}$;
к) $3\frac{1}{2} * (\frac{2}{3}х + \frac{4}{7}) = 2\frac{1}{3}$;
л) $(\frac{5}{8}х - \frac{1}{5}) * \frac{3}{4} = \frac{3}{4}$;
м) $\frac{3}{5}z + \frac{2}{3}z - 3 = \frac{4}{5}$.

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Решение

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Математика 6 класс Виленкин. Номер №609

Решение а

$\frac{2}{7}х = 2\frac{2}{7}$
$х = \frac{16}{7} : \frac{2}{7}$
$х = \frac{16}{7} * \frac{7}{2}$
$х = \frac{8}{1} * \frac{1}{1} = 8$

Решение б

$\frac{3}{5}y = 2\frac{9}{10} - \frac{1}{5}$
$\frac{3}{5}y = 2\frac{9}{10} - \frac{2}{10}$
$\frac{3}{5}y = 2\frac{7}{10}$
$y = \frac{27}{10} : \frac{3}{5} = \frac{27}{10} * \frac{5}{3} = \frac{9}{2} * \frac{1}{1} = 4\frac{1}{2}$

Решение в

$\frac{3}{7}a + \frac{2}{5} = 1$
$\frac{3}{7}a = 1 - \frac{2}{5}$
$a = \frac{3}{5} : \frac{3}{7} = \frac{3}{5} * \frac{7}{3} = \frac{7}{5} = 1\frac{2}{5}$

Решение г

$3\frac{1}{3} : k = 1\frac{1}{3} : 2$
$3\frac{1}{3} : k = \frac{4}{3} * \frac{1}{2}$
$k = 3\frac{1}{3} : \frac{2}{3} = \frac{10}{3} * \frac{3}{2} = 5$

Решение д

$y : 1\frac{1}{2} = 2\frac{1}{3} * \frac{1}{3}$
$y : 1\frac{1}{2} = \frac{7}{3} * \frac{1}{3}$
$y = \frac{7}{9} * \frac{3}{2} = \frac{7}{3} * \frac{1}{2} = \frac{7}{6} = 1\frac{1}{6}$

Решение е

$\frac{2}{7}х + \frac{3}{7}х = 2\frac{7}{14}$
$\frac{5}{7}х = 2\frac{1}{2}$
$х = \frac{5}{2} : \frac{5}{7} = \frac{5}{2} * \frac{7}{5} = \frac{7}{2} = 3\frac{1}{2}$

Решение ж

$m + \frac{3}{8}m = \frac{1}{4}$
$1\frac{3}{8}m = \frac{1}{4}$
$m = \frac{1}{4} : 1\frac{3}{8} = \frac{1}{4} * \frac{8}{11} = \frac{2}{11}$

Решение з

$y - \frac{2}{9}y = 4\frac{2}{3}$
$\frac{7}{9}y = 4\frac{2}{3}$
$\frac{7}{9}y = \frac{14}{3} : \frac{7}{9} = \frac{14}{3} * \frac{9}{3} = 14$

Решение и

$\frac{2}{5}z + \frac{2}{3}z - \frac{7}{15}z = 2\frac{1}{2}$
$\frac{6}{15}z + \frac{10}{15}z - \frac{7}{15}z = 2\frac{1}{2}$
$\frac{9}{15}z = 2\frac{1}{2}$
$\frac{3}{5}z = \frac{5}{2}$
$z = \frac{5}{2} : \frac{3}{5} = \frac{5}{2} * \frac{5}{3} = \frac{25}{6} = 4\frac{1}{6}$

Решение к

$3\frac{1}{2} * (\frac{2}{3}х + \frac{4}{7}) = 2\frac{1}{3}$
$\frac{2}{3}х + \frac{4}{7} = 2\frac{1}{3} : 3\frac{1}{2}$
$\frac{2}{3}х + \frac{4}{7} = \frac{7}{3} * \frac{2}{7}$
$\frac{2}{3}х = \frac{2}{3} - \frac{4}{7}$
$\frac{2}{3}х = \frac{14}{21} - \frac{12}{21}$
$\frac{2}{3}х = \frac{2}{21}$
$х = \frac{2}{21} : \frac{2}{3} = \frac{2}{21} * \frac{3}{2} = \frac{1}{7}$

Решение л

$(\frac{5}{8}х - \frac{1}{5}) * \frac{3}{4} = \frac{3}{4}$
$\frac{5}{8}х - \frac{1}{5} = \frac{3}{4} : \frac{3}{4}$
$\frac{5}{8}х - \frac{1}{5} = \frac{3}{4} * \frac{4}{3}$
$\frac{5}{8}х = 1 + \frac{1}{5}$
$х = \frac{6}{5} : \frac{5}{8} = \frac{6}{5} * \frac{8}{5} = \frac{48}{25} = 1\frac{23}{25}$

Решение м

$\frac{3}{5}z + \frac{2}{3}z - 3 = \frac{4}{5}$
$\frac{9}{15}z + \frac{10}{15}z - 3 = \frac{4}{5}$
$\frac{19}{15}z - 3 = \frac{4}{5}$
$\frac{19}{15}z = 3\frac{4}{5}$
$\frac{19}{15}z = \frac{19}{5}$
$z = \frac{19}{5} : \frac{19}{15} = \frac{19}{5} * \frac{15}{19} = 3$