3.38 Выполните действия: а) $$\frac{3}{12}+2\frac{1}{6}- \frac{1}{8}$$\n$$\frac{1,4+0,6}{4,5}$$; б) $$\frac{10}{21}: \frac{10}{22}: \frac{12}{63}$$\nв) $$8:\frac{1}{5}:2\frac{2}{7}$$; $$\frac{5}{4}:7 \frac{1}{4}: \frac{8}{9}$$

Решение:

а) $$\frac{3}{12}+2\frac{1}{6}- \frac{1}{8}$$
$$\frac{1,4+0,6}{4,5}$$

1. $$ \frac{3}{12}+2\frac{1}{6}- \frac{1}{8} = \frac{1}{4} + \frac{13}{6} - \frac{1}{8} = \frac{6}{24} + \frac{52}{24} - \frac{3}{24} = \frac{6 + 52 - 3}{24} = \frac{55}{24} = 2\frac{7}{24}$$.
2. $$\frac{1,4+0,6}{4,5} = \frac{2}{4,5} = \frac{20}{45} = \frac{4}{9}$$.

б) $$\frac{10}{21}: \frac{10}{22}: \frac{12}{63}$$

1. $$\frac{10}{21}: \frac{10}{22}: \frac{12}{63} = \frac{10}{21} \cdot \frac{22}{10} \cdot \frac{63}{12} = \frac{22}{21} \cdot \frac{63}{12} = \frac{11}{1} \cdot \frac{3}{6} = \frac{11}{1} \cdot \frac{1}{2} = \frac{11}{2} = 5\frac{1}{2}$$.

в) $$8:\frac{1}{5}:2\frac{2}{7}$$; $$\frac{5}{4}:7 \frac{1}{4}: \frac{8}{9}$$

1. $$8:\frac{1}{5}:2\frac{2}{7} = 8 \cdot 5 : \frac{16}{7} = 40 \cdot \frac{7}{16} = 5 \cdot \frac{7}{2} = \frac{35}{2} = 17 \frac{1}{2}$$.
2. $$\frac{5}{4}:7 \frac{1}{4}: \frac{8}{9} = \frac{5}{4}: \frac{29}{4}: \frac{8}{9} = \frac{5}{4} \cdot \frac{4}{29} \cdot \frac{9}{8} = \frac{5}{1} \cdot \frac{1}{29} \cdot \frac{9}{8} = \frac{45}{232}$$.

Ответ: а) $$2\frac{7}{24}$$, $$\frac{4}{9}$$; б) $$5\frac{1}{2}$$; в) $$17 \frac{1}{2}$$, $$\frac{45}{232}$$.