Question

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Answer 1

Вычислить:

$\boxed{\tt1.}\;\;\dfrac{14}{15} - \dfrac{7}{10} = \dfrac{14\cdot2 - 7\cdot3}{30} = \dfrac{28 - 21}{30} = \dfrac{7}{30}.$

$\boxed{\tt2.}\;\;\dfrac{9}{25} - \dfrac{7}{20} = \dfrac{9\cdot4 - 7\cdot5}{100} = \dfrac{36 - 35}{100} = \dfrac{1}{100} = 0,01.$

$\boxed{\tt3.}\;\;\dfrac{20}{45} + \dfrac{26}{54} = \dfrac{20\cdot6 + 26\cdot5}{270} = \dfrac{120 + 130}{270} = \dfrac{250}{270} = \dfrac{25}{27}.$

$\boxed{\tt4.}\;\;\dfrac{11}{24} + \dfrac{3}{16} = \dfrac{11\cdot2 + 3\cdot3}{48} = \dfrac{22 + 9}{48} = \dfrac{31}{48}.$

$\boxed{\tt5.}\;\;\dfrac{9}{16} + \dfrac{7}{24} - \dfrac{3}{8} = \dfrac{9\cdot3 + 7\cdot2 - 3\cdot6}{48} = \dfrac{27 + 14 - 18}{48} = \dfrac{23}{48}.$

$\boxed{\tt6.}\;\;\dfrac{2}{5} + \dfrac{4}{15} - \dfrac{5}{9} = \dfrac{2\cdot9 + 4\cdot3 - 5\cdot5}{45} = \dfrac{18 + 12 -25}{45} = \dfrac{5}{45} = \dfrac{1}{9}.$

Решить уравнения:

$\boxed{\tt7.}\;\;x + 7\dfrac{4}{15} = 9\dfrac{7}{10},\\\\x = 9\dfrac{7}{10} - 7\dfrac{4}{15},\\\\x = 9\dfrac{7\cdot3}{30} - 7\dfrac{4\cdot2}{30},\\\\x = 9\dfrac{21}{30} - 7\dfrac{8}{30},\\\\x = (9 - 7) + \left(\dfrac{21}{30} - \dfrac{8}{30}\right),\\\\x = 2 + \dfrac{21 - 8}{30},\\\\x = 2\dfrac{13}{30}.$

$\boxed{\tt8.}\;\;x - 3\dfrac{8}{9} = 5\dfrac{1}{12},\\\\x = 5\dfrac{1}{12} + 3\dfrac{8}{9},\\\\x = 5\dfrac{3}{36} + 3\dfrac{8\cdot4}{36},\\\\x = 5\dfrac{3}{36} + 3\dfrac{32}{36},\\\\x = (5 + 3) + \left(\dfrac{3}{36} + \dfrac{32}{36}\right),\\\\x = 8 + \dfrac{3 + 32}{36},\\\\x = 8\dfrac{35}{36}.$

$\boxed{\tt9.}\;\;6\dfrac{3}{11} + x = 10\dfrac{6}{7},\\\\x = 10\dfrac{6}{7} - 6\dfrac{3}{11},\\\\x = 10\dfrac{6\cdot11}{77} - 6\dfrac{3\cdot7}{77},\\\\x = 10\dfrac{66}{77} - 6\dfrac{21}{77},\\\\x = (10 - 6) + \left(\dfrac{66}{77} - \dfrac{21}{77}\right),\\\\x = 4 + \dfrac{66 - 21}{77},\\\\x = 4\dfrac{45}{77}.$

$\boxed{\tt10.}\;\;2\dfrac{4}{9} + x = 9\dfrac{5}{36},\\\\x = 9\dfrac{5}{36} - 2\dfrac{4}{9},\\\\x = 9\dfrac{5}{36} - 2\dfrac{4\cdot4}{36},\\\\x = 9\dfrac{5}{36} - 2\dfrac{16}{36},\\\\x = 8\dfrac{41}{36} - 2\dfrac{16}{36},\\\\x = (8 - 2) + \left(\dfrac{41}{36} - \dfrac{16}{36}\right),\\\\x = 6 + \dfrac{41 - 16}{36},\\\\x = 6\dfrac{25}{36}.$