287. Выполните действия: а) 3 + 8; б) 10 - 3; в) 4 + 5; г) 8 - 4; д) 4 + 5; е) 7 - 2; ж) 7 -; з) 10 - 3.

a) $$3 + 8\frac{5}{12} = 3 + \frac{8 \cdot 12 + 5}{12} = 3 + \frac{96 + 5}{12} = 3 + \frac{101}{12} = 3 + 8\frac{5}{12} = 11\frac{5}{12}$$

б)

$$10\frac{6}{7} - 3 = \frac{10 \cdot 7 + 6}{7} - 3 = \frac{70 + 6}{7} - 3 = \frac{76}{7} - 3 = 10\frac{6}{7} - 3 = 7\frac{6}{7}$$

в)

$$4\frac{2}{13} + 5\frac{7}{13} = 4 + 5 + \frac{2}{13} + \frac{7}{13} = 9 + \frac{2 + 7}{13} = 9 + \frac{9}{13} = 9\frac{9}{13}$$

г)

$$8\frac{7}{12} - 4\frac{2}{12} = 8 - 4 + \frac{7}{12} - \frac{2}{12} = 4 + \frac{7 - 2}{12} = 4 + \frac{5}{12} = 4\frac{5}{12}$$

д)

$$4\frac{8}{11} + 5\frac{7}{11} = 4 + 5 + \frac{8}{11} + \frac{7}{11} = 9 + \frac{8 + 7}{11} = 9 + \frac{15}{11} = 9 + 1\frac{4}{11} = 10\frac{4}{11}$$

e)

$$7\frac{5}{9} - 2\frac{8}{9} = 7 - 2 + \frac{5}{9} - \frac{8}{9} = 5 + \frac{5 - 8}{9} = 5 - \frac{3}{9} = 5 - \frac{1}{3} = 4\frac{3}{3} - \frac{1}{3} = 4\frac{2}{3}$$

ж)

$$7 - \frac{3}{8} = \frac{7 \cdot 8 - 3}{8} = \frac{56 - 3}{8} = \frac{53}{8} = 6\frac{5}{8}$$

з)

$$10 - 3\frac{7}{15} = \frac{10 \cdot 15 - (3 \cdot 15 + 7)}{15} = \frac{150 - (45 + 7)}{15} = \frac{150 - 52}{15} = \frac{98}{15} = 6\frac{8}{15}$$

Ответ: а) $$11\frac{5}{12}$$; б) $$7\frac{6}{7}$$; в) $$9\frac{9}{13}$$; г) $$4\frac{5}{12}$$; д) $$10\frac{4}{11}$$; е) $$4\frac{2}{3}$$; ж) $$6\frac{5}{8}$$; з) $$6\frac{8}{15}$$