583 a) 1\frac{1}{2} - \frac{2}{3}; б) 1\frac{1}{4} - \frac{1}{3}; в) 1\frac{1}{8} - \frac{1}{4}; г) 1\frac{2}{3} - \frac{5}{6}; д) 2\frac{3}{10} - \frac{4}{15}.

а) $$1\frac{1}{2} - \frac{2}{3} = \frac{3}{2} - \frac{2}{3} = \frac{3 \cdot 3}{2 \cdot 3} - \frac{2 \cdot 2}{3 \cdot 2} = \frac{9}{6} - \frac{4}{6} = \frac{9 - 4}{6} = \frac{5}{6}$$

б) $$1\frac{1}{4} - \frac{1}{3} = \frac{5}{4} - \frac{1}{3} = \frac{5 \cdot 3}{4 \cdot 3} - \frac{1 \cdot 4}{3 \cdot 4} = \frac{15}{12} - \frac{4}{12} = \frac{15 - 4}{12} = \frac{11}{12}$$

в) $$1\frac{1}{8} - \frac{1}{4} = \frac{9}{8} - \frac{1}{4} = \frac{9}{8} - \frac{1 \cdot 2}{4 \cdot 2} = \frac{9}{8} - \frac{2}{8} = \frac{9 - 2}{8} = \frac{7}{8}$$

г) $$1\frac{2}{3} - \frac{5}{6} = \frac{5}{3} - \frac{5}{6} = \frac{5 \cdot 2}{3 \cdot 2} - \frac{5}{6} = \frac{10}{6} - \frac{5}{6} = \frac{10 - 5}{6} = \frac{5}{6}$$

д) $$2\frac{3}{10} - \frac{4}{15} = \frac{23}{10} - \frac{4}{15} = \frac{23 \cdot 3}{10 \cdot 3} - \frac{4 \cdot 2}{15 \cdot 2} = \frac{69}{30} - \frac{8}{30} = \frac{69 - 8}{30} = \frac{61}{30} = 2\frac{1}{30}$$

Ответ: а) $$\frac{5}{6}$$; б) $$\frac{11}{12}$$; в) $$\frac{7}{8}$$; г) $$\frac{5}{6}$$; д) $$2\frac{1}{30}$$