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) $$\frac{2}{3} + \frac{5}{8} = \frac{2 \cdot 8}{3 \cdot 8} + \frac{5 \cdot 3}{8 \cdot 3} = \frac{16}{24} + \frac{15}{24} = \frac{16+15}{24} = \frac{31}{24} = 1\frac{7}{24}$$

б) $$\frac{7}{12} - \frac{3}{8} = \frac{7 \cdot 2}{12 \cdot 2} - \frac{3 \cdot 3}{8 \cdot 3} = \frac{14}{24} - \frac{9}{24} = \frac{14-9}{24} = \frac{5}{24}$$

в) $$\frac{11}{16} - \frac{5}{8} = \frac{11}{16} - \frac{5 \cdot 2}{8 \cdot 2} = \frac{11}{16} - \frac{10}{16} = \frac{11-10}{16} = \frac{1}{16}$$

г) $$\frac{6}{35} + \frac{3}{10} = \frac{6 \cdot 2}{35 \cdot 2} + \frac{3 \cdot 7}{10 \cdot 7} = \frac{12}{70} + \frac{21}{70} = \frac{12+21}{70} = \frac{33}{70}$$

д) $$\frac{7}{8} + \frac{11}{12} - \frac{5}{6} = \frac{7 \cdot 3}{8 \cdot 3} + \frac{11 \cdot 2}{12 \cdot 2} - \frac{5 \cdot 4}{6 \cdot 4} = \frac{21}{24} + \frac{22}{24} - \frac{20}{24} = \frac{21+22-20}{24} = \frac{23}{24}$$

№2. Вычислите:

a) $$12\frac{3}{8} + 8\frac{1}{6} = 12 + \frac{3}{8} + 8 + \frac{1}{6} = (12+8) + (\frac{3}{8} + \frac{1}{6}) = 20 + (\frac{3 \cdot 3}{8 \cdot 3} + \frac{1 \cdot 4}{6 \cdot 4}) = 20 + (\frac{9}{24} + \frac{4}{24}) = 20 + \frac{13}{24} = 20\frac{13}{24}$$

б) $$9\frac{8}{21} + 4\frac{11}{14} = 9 + \frac{8}{21} + 4 + \frac{11}{14} = (9+4) + (\frac{8}{21} + \frac{11}{14}) = 13 + (\frac{8 \cdot 2}{21 \cdot 2} + \frac{11 \cdot 3}{14 \cdot 3}) = 13 + (\frac{16}{42} + \frac{33}{42}) = 13 + \frac{49}{42} = 13 + 1\frac{7}{42} = 14\frac{7}{42} = 14\frac{1}{6}$$

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

г) $$8\frac{5}{36} - 1\frac{43}{108} = 8 + \frac{5}{36} - (1 + \frac{43}{108}) = (8 - 1) + (\frac{5}{36} - \frac{43}{108}) = 7 + (\frac{5 \cdot 3}{36 \cdot 3} - \frac{43}{108}) = 7 + (\frac{15}{108} - \frac{43}{108}) = 7 - \frac{28}{108} = 7 - \frac{7}{27} = 6\frac{27}{27} - \frac{7}{27} = 6\frac{20}{27}$$

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

№3. Решите уравнения:

a) $$10\frac{5}{8} - x = 7\frac{3}{5}$$

$$x = 10\frac{5}{8} - 7\frac{3}{5} = 10 + \frac{5}{8} - (7 + \frac{3}{5}) = (10 - 7) + (\frac{5}{8} - \frac{3}{5}) = 3 + (\frac{5 \cdot 5}{8 \cdot 5} - \frac{3 \cdot 8}{5 \cdot 8}) = 3 + (\frac{25}{40} - \frac{24}{40}) = 3 + \frac{1}{40} = 3\frac{1}{40}$$

$$x = 3\frac{1}{40}$$

б) $$(x - 2\frac{7}{8}) + 3\frac{5}{6} = 4\frac{2}{3}$$

$$x - 2\frac{7}{8} = 4\frac{2}{3} - 3\frac{5}{6} = 4 + \frac{2}{3} - (3 + \frac{5}{6}) = (4 - 3) + (\frac{2}{3} - \frac{5}{6}) = 1 + (\frac{2 \cdot 2}{3 \cdot 2} - \frac{5}{6}) = 1 + (\frac{4}{6} - \frac{5}{6}) = 1 - \frac{1}{6} = \frac{6}{6} - \frac{1}{6} = \frac{5}{6}$$

$$x = \frac{5}{6} + 2\frac{7}{8} = \frac{5}{6} + 2 + \frac{7}{8} = 2 + (\frac{5}{6} + \frac{7}{8}) = 2 + (\frac{5 \cdot 4}{6 \cdot 4} + \frac{7 \cdot 3}{8 \cdot 3}) = 2 + (\frac{20}{24} + \frac{21}{24}) = 2 + \frac{41}{24} = 2 + 1\frac{17}{24} = 3\frac{17}{24}$$

$$x = 3\frac{17}{24}$$