Самостоятельная работа: Сложение и вычитание дробей с разными знаменателями. Вариант 1 № 1. Вычислите: a) $$ \frac{2}{3} + \frac{5}{8} $$; б) $$ \frac{7}{12} - \frac{3}{8} $$; в) $$ \frac{11}{16} - \frac{5}{8} $$; г) $$ \frac{6}{35} + \frac{3}{10} $$; д) $$ \frac{7}{8} + \frac{11}{12} - \frac{5}{6} $$. №2. Вычислите: a) $$ 12 \frac{3}{8} + 8 \frac{1}{6} $$; б) $$ 9 \frac{8}{21} + 4 \frac{11}{14} $$; в) $$ 4 \frac{2}{7} - 1 \frac{4}{9} $$; г) $$ 8 \frac{5}{36} - 1 \frac{43}{108} $$; д) $$ 3 \frac{1}{16} - \frac{1}{8} $$. №3. Решите уравнения a) $$ 10 \frac{5}{8} - x = 7 \frac{3}{5} $$; б) $$ (x - 2 \frac{7}{8}) + 3 \frac{5}{6} = 4 \frac{2}{3} $$.

№ 1. Вычислите:

a) $$ \frac{2}{3} + \frac{5}{8} = \frac{2\cdot8 + 5\cdot3}{3\cdot8} = \frac{16+15}{24} = \frac{31}{24} = 1 \frac{7}{24} $$.

б) $$ \frac{7}{12} - \frac{3}{8} = \frac{7\cdot2 - 3\cdot3}{24} = \frac{14-9}{24} = \frac{5}{24} $$.

в) $$ \frac{11}{16} - \frac{5}{8} = \frac{11 - 5\cdot2}{16} = \frac{11-10}{16} = \frac{1}{16} $$.

г) $$ \frac{6}{35} + \frac{3}{10} = \frac{6\cdot2 + 3\cdot7}{70} = \frac{12+21}{70} = \frac{33}{70} $$.

д) $$ \frac{7}{8} + \frac{11}{12} - \frac{5}{6} = \frac{7\cdot3 + 11\cdot2 - 5\cdot4}{24} = \frac{21+22-20}{24} = \frac{23}{24} $$.

№2. Вычислите:

a) $$ 12 \frac{3}{8} + 8 \frac{1}{6} = 12 + 8 + \frac{3}{8} + \frac{1}{6} = 20 + \frac{3\cdot3 + 1\cdot4}{24} = 20 + \frac{9+4}{24} = 20 + \frac{13}{24} = 20 \frac{13}{24} $$.

б) $$ 9 \frac{8}{21} + 4 \frac{11}{14} = 9 + 4 + \frac{8}{21} + \frac{11}{14} = 13 + \frac{8\cdot2 + 11\cdot3}{42} = 13 + \frac{16+33}{42} = 13 + \frac{49}{42} = 13 + 1 \frac{7}{42} = 14 \frac{1}{6} $$.

в) $$ 4 \frac{2}{7} - 1 \frac{4}{9} = 4 - 1 + \frac{2}{7} - \frac{4}{9} = 3 + \frac{2\cdot9 - 4\cdot7}{63} = 3 + \frac{18 - 28}{63} = 3 - \frac{10}{63} = 2 + \frac{63-10}{63} = 2 \frac{53}{63} $$.

г) $$ 8 \frac{5}{36} - 1 \frac{43}{108} = 8 - 1 + \frac{5}{36} - \frac{43}{108} = 7 + \frac{5\cdot3 - 43}{108} = 7 + \frac{15 - 43}{108} = 7 - \frac{28}{108} = 7 - \frac{7}{27} = 6 + \frac{27-7}{27} = 6 \frac{20}{27} $$.

д) $$ 3 \frac{1}{16} - \frac{1}{8} = 3 + \frac{1}{16} - \frac{1}{8} = 3 + \frac{1 - 2}{16} = 3 - \frac{1}{16} = 2 + \frac{16 - 1}{16} = 2 \frac{15}{16} $$.

№3. Решите уравнения

a) $$ 10 \frac{5}{8} - x = 7 \frac{3}{5} $$. $$ x = 10 \frac{5}{8} - 7 \frac{3}{5} = 10 - 7 + \frac{5}{8} - \frac{3}{5} = 3 + \frac{5\cdot5 - 3\cdot8}{40} = 3 + \frac{25 - 24}{40} = 3 + \frac{1}{40} = 3 \frac{1}{40} $$.

б) $$ (x - 2 \frac{7}{8}) + 3 \frac{5}{6} = 4 \frac{2}{3} $$. $$ x - 2 \frac{7}{8} = 4 \frac{2}{3} - 3 \frac{5}{6} = 4 - 3 + \frac{2}{3} - \frac{5}{6} = 1 + \frac{4-5}{6} = 1 - \frac{1}{6} = \frac{5}{6} $$. $$ x = \frac{5}{6} + 2 \frac{7}{8} = \frac{5}{6} + \frac{23}{8} = \frac{5\cdot4 + 23\cdot3}{24} = \frac{20 + 69}{24} = \frac{89}{24} = 3 \frac{17}{24} $$.