17. Выполните действие: а) $$5\frac{1}{6} + 4\frac{3}{4}$$; б) $$7\frac{5}{8} - 5\frac{2}{7}$$; в) $$3\frac{4}{10} - 1\frac{5}{15}$$; г) $$5\frac{2}{6} - 3\frac{2}{7}$$;

Решение:

a) $$5\frac{1}{6} + 4\frac{3}{4} = \frac{31}{6} + \frac{19}{4} = \frac{31*2}{6*2} + \frac{19*3}{4*3} = \frac{62}{12} + \frac{57}{12} = \frac{119}{12} = 9\frac{11}{12}$$

б) $$7\frac{5}{8} - 5\frac{2}{7} = \frac{61}{8} - \frac{37}{7} = \frac{61*7}{8*7} - \frac{37*8}{7*8} = \frac{427}{56} - \frac{296}{56} = \frac{131}{56} = 2\frac{19}{56}$$

в) $$3\frac{4}{10} - 1\frac{5}{15} = 3\frac{2}{5} - 1\frac{1}{3} = \frac{17}{5} - \frac{4}{3} = \frac{17*3}{5*3} - \frac{4*5}{3*5} = \frac{51}{15} - \frac{20}{15} = \frac{31}{15} = 2\frac{1}{15}$$

г) $$5\frac{2}{6} - 3\frac{2}{7} = 5\frac{1}{3} - 3\frac{2}{7} = \frac{16}{3} - \frac{23}{7} = \frac{16*7}{3*7} - \frac{23*3}{7*3} = \frac{112}{21} - \frac{69}{21} = \frac{43}{21} = 2\frac{1}{21}$$

Ответ:

• a) $$9\frac{11}{12}$$
• б) $$2\frac{19}{56}$$
• в) $$2\frac{1}{15}$$
• г) $$2\frac{1}{21}$$